%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM926+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 : n012.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 10:35:46 AM UTC 2026
% Result : Theorem 6.08s 1.15s
% Output : CNFRefutation 6.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 135
% Syntax : Number of formulae : 1233 ( 753 unt; 0 typ; 0 def)
% Number of atoms : 6022 (2367 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 17508 (1576 ~;1342 |; 21 &;14287 @)
% ( 105 <=>; 177 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 33 usr; 13 con; 0-3 aty)
% Number of variables : 2704 ( 0 ^;2682 !; 22 ?;2704 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_bit0,type,
bit0: $i > $i ).
thf(tp_bit1,type,
bit1: $i > $i ).
thf(tp_comm_semiring_1,type,
comm_semiring_1: $i > $o ).
thf(tp_int,type,
int: $i ).
thf(tp_linorder,type,
linorder: $i > $o ).
thf(tp_linordered_idom,type,
linordered_idom: $i > $o ).
thf(tp_m,type,
m: $i ).
thf(tp_monoid_mult,type,
monoid_mult: $i > $o ).
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_char_0,type,
ring_char_0: $i > $o ).
thf(tp_s,type,
s: $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY410,type,
sK4_SY410: $i ).
thf(tp_sK5_SY438,type,
sK5_SY438: $i ).
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_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_1 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(4,axiom,
monoid_mult @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
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,
comm_semiring_1 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(8,axiom,
number @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
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,
monoid_mult @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
thf(13,axiom,
linorder @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
thf(14,axiom,
number_semiring @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(15,axiom,
comm_semiring_1 @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(16,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(17,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_97_rel__simps_I32_J) ).
thf(18,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_96_less__eq__int__code_I14_J) ).
thf(19,axiom,
! [K: $i] :
( ( ord_less_eq @ int @ pls @ ( bit1 @ K ) )
<=> ( ord_less_eq @ int @ pls @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_rel__simps_I22_J) ).
thf(20,axiom,
! [K: $i] :
( ( ord_less @ int @ pls @ ( bit0 @ K ) )
<=> ( ord_less @ int @ pls @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_rel__simps_I4_J) ).
thf(21,axiom,
! [K: $i] :
( ( ord_less @ int @ ( bit0 @ K ) @ pls )
<=> ( ord_less @ int @ K @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_rel__simps_I10_J) ).
thf(22,axiom,
! [K: $i,L: $i] :
( ( ord_less @ int @ ( bit1 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less @ int @ K @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_rel__simps_I16_J) ).
thf(23,axiom,
! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_less__int__code_I15_J) ).
thf(24,axiom,
! [K: $i] :
( ( ord_less @ int @ ( bit1 @ K ) @ pls )
<=> ( ord_less @ int @ K @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_rel__simps_I12_J) ).
thf(25,axiom,
! [Z: $i,W: $i] :
( ( plus_plus @ int @ Z @ W )
= ( plus_plus @ int @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_zadd__commute) ).
thf(26,axiom,
! [X_1: $i,Y_1: $i,Z: $i] :
( ( plus_plus @ int @ X_1 @ ( plus_plus @ int @ Y_1 @ Z ) )
= ( plus_plus @ int @ Y_1 @ ( plus_plus @ int @ X_1 @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_zadd__left__commute) ).
thf(27,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_87_zadd__assoc) ).
thf(28,axiom,
! [K_1: $i] :
( ( number_number_of @ int @ K_1 )
= K_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_number__of__is__id) ).
thf(29,axiom,
! [Z: $i,W: $i] :
( ( times_times @ int @ Z @ W )
= ( times_times @ int @ W @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_zmult__commute) ).
thf(30,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_84_zmult__assoc) ).
thf(31,axiom,
! [K: $i,L: $i] :
( ( ( bit0 @ K )
= ( bit0 @ L ) )
<=> ( K = L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_rel__simps_I48_J) ).
thf(32,axiom,
! [K: $i,L: $i] :
( ( ( bit1 @ K )
= ( bit1 @ L ) )
<=> ( K = L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_rel__simps_I51_J) ).
thf(33,axiom,
! [X_a: $i] :
( ( number @ X_a )
=> ! [W_1: $i,X_2: $i] :
( ( ( number_number_of @ X_a @ W_1 )
= ( ti @ X_a @ X_2 ) )
<=> ( ( ti @ X_a @ X_2 )
= ( number_number_of @ X_a @ W_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_number__of__reorient) ).
thf(34,axiom,
! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( ring_char_0 @ X_a ) )
=> ! [X_2: $i,Y_2: $i] :
( ( ( number_number_of @ X_a @ X_2 )
= ( number_number_of @ X_a @ Y_2 ) )
<=> ( X_2 = Y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_eq__number__of) ).
thf(35,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,C: $i] :
( ( plus_plus @ X_a @ A_1 @ C )
= ( plus_plus @ X_a @ C @ A_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(36,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,C: $i,D: $i] :
( ( plus_plus @ X_a @ A_1 @ ( plus_plus @ X_a @ C @ D ) )
= ( plus_plus @ X_a @ C @ ( plus_plus @ X_a @ A_1 @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(37,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,C: $i,D: $i] :
( ( plus_plus @ X_a @ A_1 @ ( plus_plus @ X_a @ C @ D ) )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(38,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ C )
= ( plus_plus @ X_a @ A_1 @ ( plus_plus @ X_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(39,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ C )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(40,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i,D: $i] :
( ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ ( plus_plus @ X_a @ C @ D ) )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ C ) @ ( plus_plus @ X_a @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(41,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i] :
( ( times_times @ X_a @ A_1 @ B )
= ( times_times @ X_a @ B @ A_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(42,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ Rx @ ( times_times @ X_a @ Lx @ Ry ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(43,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Rx ) @ Ry ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(44,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ Rx )
= ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Ly @ Rx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(45,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ Rx )
= ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Rx ) @ Ly ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(46,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Ly @ ( times_times @ X_a @ Rx @ Ry ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(47,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ Rx @ ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ Ry ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(48,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Rx ) @ ( times_times @ X_a @ Ly @ Ry ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(49,axiom,
! [Y_1: $i,X_1: $i] :
( ( twoSqu33214720sum2sq @ X_1 )
=> ( ( twoSqu33214720sum2sq @ Y_1 )
=> ( twoSqu33214720sum2sq @ ( times_times @ int @ X_1 @ Y_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_is__mult__sum2sq) ).
thf(50,axiom,
zprime @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_zprime__2) ).
thf(51,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_63_zle__add1__eq__le) ).
thf(52,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_62_add1__zle__eq) ).
thf(53,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_61_zless__imp__add1__zle) ).
thf(54,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_60_rel__simps_I15_J) ).
thf(55,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_59_less__int__code_I14_J) ).
thf(56,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_58_rel__simps_I33_J) ).
thf(57,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_57_less__eq__int__code_I15_J) ).
thf(58,axiom,
! [K: $i] :
( ( ord_less @ int @ pls @ ( bit1 @ K ) )
<=> ( ord_less_eq @ int @ pls @ K ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_rel__simps_I5_J) ).
thf(59,axiom,
! [K: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K ) @ pls )
<=> ( ord_less @ int @ K @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_rel__simps_I29_J) ).
thf(60,axiom,
( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_Numeral1__eq1__nat) ).
thf(61,axiom,
( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_nat__numeral__1__eq__1) ).
thf(62,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_52_add__nat__number__of) ).
thf(63,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_51_zadd__left__mono) ).
thf(64,axiom,
! [K_1: $i,I: $i,J: $i] :
( ( ord_less @ int @ I @ J )
=> ( ord_less @ int @ ( plus_plus @ int @ I @ K_1 ) @ ( plus_plus @ int @ J @ K_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_zadd__strict__right__mono) ).
thf(65,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_49_less__eq__number__of__int__code) ).
thf(66,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_48_less__number__of__int__code) ).
thf(67,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_47_rel__simps_I31_J) ).
thf(68,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_46_less__eq__int__code_I13_J) ).
thf(69,axiom,
ord_less_eq @ int @ pls @ pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_rel__simps_I19_J) ).
thf(70,axiom,
! [K: $i,L: $i] :
( ( ord_less @ int @ ( bit0 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less @ int @ K @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_rel__simps_I14_J) ).
thf(71,axiom,
! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_less__int__code_I13_J) ).
thf(72,axiom,
~ ( ord_less @ int @ pls @ pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_rel__simps_I2_J) ).
thf(73,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_41_rel__simps_I34_J) ).
thf(74,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_40_less__eq__int__code_I16_J) ).
thf(75,axiom,
! [K: $i,L: $i] :
( ( ord_less @ int @ ( bit1 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less @ int @ K @ L ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_rel__simps_I17_J) ).
thf(76,axiom,
! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_less__int__code_I16_J) ).
thf(77,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_37_nat__1__add__1) ).
thf(78,axiom,
! [Z: $i] :
( ( times_times @ nat @ Z @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ nat @ Z @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_nat__mult__2__right) ).
thf(79,axiom,
! [Z: $i] :
( ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z )
= ( plus_plus @ nat @ Z @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_nat__mult__2) ).
thf(80,axiom,
! [X_1: $i,Y_1: $i,Z: $i] :
( ( power_power @ int @ X_1 @ ( plus_plus @ nat @ Y_1 @ Z ) )
= ( times_times @ int @ ( power_power @ int @ X_1 @ Y_1 ) @ ( power_power @ int @ X_1 @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_zpower__zadd__distrib) ).
thf(81,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,P: $i,Q: $i] :
( ( times_times @ X_a @ ( power_power @ X_a @ X_1 @ P ) @ ( power_power @ X_a @ X_1 @ Q ) )
= ( power_power @ X_a @ X_1 @ ( plus_plus @ nat @ P @ Q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(82,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_32_zadd__zless__mono) ).
thf(83,axiom,
! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_2: $i,Y_2: $i] :
( ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_2 ) @ ( number_number_of @ X_a @ Y_2 ) )
<=> ( ord_less_eq @ int @ X_2 @ Y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_le__number__of) ).
thf(84,axiom,
! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_2: $i,Y_2: $i] :
( ( ord_less @ X_a @ ( number_number_of @ X_a @ X_2 ) @ ( number_number_of @ X_a @ Y_2 ) )
<=> ( ord_less @ int @ X_2 @ Y_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_less__number__of) ).
thf(86,axiom,
! [X_1: $i,Y_1: $i,Z: $i] :
( ( power_power @ int @ ( power_power @ int @ X_1 @ Y_1 ) @ Z )
= ( power_power @ int @ X_1 @ ( times_times @ nat @ Y_1 @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_zpower__zpower) ).
thf(87,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i] :
( ( power_power @ X_a @ X_1 @ ( one_one @ nat ) )
= ( ti @ X_a @ X_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(88,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,P: $i,Q: $i] :
( ( power_power @ X_a @ ( power_power @ X_a @ X_1 @ P ) @ Q )
= ( power_power @ X_a @ X_1 @ ( times_times @ nat @ P @ Q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(89,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_25_zle__antisym) ).
thf(90,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_24_zle__trans) ).
thf(91,axiom,
! [X_1: $i,Y_1: $i] :
( ( ord_less @ int @ X_1 @ Y_1 )
| ( X_1 = Y_1 )
| ( ord_less @ int @ Y_1 @ X_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_zless__linear) ).
thf(92,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_22_zless__le) ).
thf(93,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_21_zle__linear) ).
thf(94,axiom,
! [W: $i] : ( ord_less_eq @ int @ W @ W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_zle__refl) ).
thf(95,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_19__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(96,axiom,
! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( one_one @ X_a ) )
= ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_one__add__one__is__two) ).
thf(97,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_17_add__special_I3_J) ).
thf(98,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_16_add__special_I2_J) ).
thf(99,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,N: $i] :
( ( power_power @ X_a @ X_1 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) )
= ( times_times @ X_a @ ( power_power @ X_a @ X_1 @ N ) @ ( power_power @ X_a @ X_1 @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(100,axiom,
! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i] :
( ( power_power @ X_a @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ X_a @ A_1 @ A_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_power2__eq__square) ).
thf(101,axiom,
! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i] :
( ( times_times @ X_a @ X_1 @ X_1 )
= ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(102,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(103,axiom,
! [A_1: $i] :
( ( times_times @ int @ A_1 @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_cube__square) ).
thf(104,axiom,
! [X_b: $i] :
( ( ( monoid_mult @ X_b )
& ( number @ X_b ) )
=> ! [W: $i] :
( ( power_power @ X_b @ ( number_number_of @ X_b @ W ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ X_b @ ( number_number_of @ X_b @ W ) @ ( number_number_of @ X_b @ W ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_power2__eq__square__number__of) ).
thf(105,axiom,
! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [X_1: $i,Y_1: $i] :
( ( power_power @ X_a @ ( plus_plus @ X_a @ X_1 @ Y_1 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ 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 ) ) ) ) ) @ ( times_times @ X_a @ ( times_times @ X_a @ ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_1 ) @ Y_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_power2__sum) ).
thf(106,axiom,
! [A_1: $i,B: $i] :
( ( power_power @ int @ ( plus_plus @ int @ A_1 @ B ) @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A_1 ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_zadd__power3) ).
thf(107,axiom,
! [A_1: $i,B: $i] :
( ( power_power @ int @ ( plus_plus @ int @ A_1 @ B ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A_1 ) @ B ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_zadd__power2) ).
thf(108,axiom,
twoSqu33214720sum2sq @ ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_qf1pt) ).
thf(109,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_5_t) ).
thf(110,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_4_p) ).
thf(111,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_3_t__l__p) ).
thf(112,axiom,
( ( ord_less @ int @ ( one_one @ int ) @ t )
=> ? [X: $i,Y: $i] :
( ( plus_plus @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( 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_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
thf(113,axiom,
( ( t
= ( one_one @ int ) )
=> ? [X: $i,Y: $i] :
( ( plus_plus @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( 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_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
thf(114,axiom,
ord_less_eq @ int @ ( one_one @ int ) @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tpos) ).
thf(115,axiom,
( ( ti @ int @ t )
= t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_t_____res) ).
thf(116,axiom,
( ( ti @ int @ s )
= s ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_s_____res) ).
thf(117,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(118,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( monoid_mult @ 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(119,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( monoid_mult @ 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(120,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( monoid_mult @ 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(125,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(126,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(127,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(129,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( monoid_mult @ X_a )
=> ( ( ti @ X_a @ ( times_times @ X_a @ B_1 @ B_2 ) )
= ( times_times @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_res) ).
thf(130,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( monoid_mult @ X_a )
=> ( ( times_times @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
= ( times_times @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_arg2) ).
thf(131,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( monoid_mult @ X_a )
=> ( ( times_times @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
= ( times_times @ X_a @ B_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_arg1) ).
thf(132,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( comm_semiring_1 @ 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_res) ).
thf(133,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( comm_semiring_1 @ 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_arg2) ).
thf(134,axiom,
! [B_1: $i,B_2: $i,X_a: $i] :
( ( comm_semiring_1 @ 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_arg1) ).
thf(135,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(136,axiom,
( ( ti @ int @ m )
= m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_m_res) ).
thf(137,axiom,
( ( ti @ int @ pls )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Int_OPls_res) ).
thf(138,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(139,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(140,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(141,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(142,conjecture,
? [X: $i,Y: $i] :
( ( plus_plus @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( 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',conj_0) ).
thf(143,negated_conjecture,
( ( ? [X: $i,Y: $i] :
( ( plus_plus @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[142]) ).
thf(144,plain,
( ( ? [X: $i,Y: $i] :
( ( plus_plus @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[143]) ).
thf(145,plain,
( ( number @ nat )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(146,plain,
( ( semiring_1 @ nat )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(147,plain,
( ( monoid_mult @ nat )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(148,plain,
( ( linorder @ nat )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(149,plain,
( ( number_semiring @ nat )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(150,plain,
( ( comm_semiring_1 @ nat )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(151,plain,
( ( number @ int )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(152,plain,
( ( number_ring @ int )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(153,plain,
( ( ring_char_0 @ int )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(154,plain,
( ( semiring_1 @ int )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(155,plain,
( ( monoid_mult @ int )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(156,plain,
( ( linorder @ int )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(157,plain,
( ( number_semiring @ int )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(158,plain,
( ( comm_semiring_1 @ int )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(159,plain,
( ( linordered_idom @ int )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(160,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)],[17]) ).
thf(161,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)],[18]) ).
thf(162,plain,
( ( ! [K: $i] :
( ( ord_less_eq @ int @ pls @ ( bit1 @ K ) )
<=> ( ord_less_eq @ int @ pls @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(163,plain,
( ( ! [K: $i] :
( ( ord_less @ int @ pls @ ( bit0 @ K ) )
<=> ( ord_less @ int @ pls @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(164,plain,
( ( ! [K: $i] :
( ( ord_less @ int @ ( bit0 @ K ) @ pls )
<=> ( ord_less @ int @ K @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(165,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less @ int @ ( bit1 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less @ int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(166,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(167,plain,
( ( ! [K: $i] :
( ( ord_less @ int @ ( bit1 @ K ) @ pls )
<=> ( ord_less @ int @ K @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(168,plain,
( ( ! [Z: $i,W: $i] :
( ( plus_plus @ int @ Z @ W )
= ( plus_plus @ int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(169,plain,
( ( ! [X_1: $i,Y_1: $i,Z: $i] :
( ( plus_plus @ int @ X_1 @ ( plus_plus @ int @ Y_1 @ Z ) )
= ( plus_plus @ int @ Y_1 @ ( plus_plus @ int @ X_1 @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(170,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)],[27]) ).
thf(171,plain,
( ( ! [K_1: $i] :
( ( number_number_of @ int @ K_1 )
= K_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(172,plain,
( ( ! [Z: $i,W: $i] :
( ( times_times @ int @ Z @ W )
= ( times_times @ int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(173,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)],[30]) ).
thf(174,plain,
( ( ! [K: $i,L: $i] :
( ( ( bit0 @ K )
= ( bit0 @ L ) )
<=> ( K = L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(175,plain,
( ( ! [K: $i,L: $i] :
( ( ( bit1 @ K )
= ( bit1 @ L ) )
<=> ( K = L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(176,plain,
( ( ! [X_a: $i] :
( ( number @ X_a )
=> ! [W_1: $i,X_2: $i] :
( ( ( number_number_of @ X_a @ W_1 )
= ( ti @ X_a @ X_2 ) )
<=> ( ( ti @ X_a @ X_2 )
= ( number_number_of @ X_a @ W_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(177,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( ring_char_0 @ X_a ) )
=> ! [X_2: $i,Y_2: $i] :
( ( ( number_number_of @ X_a @ X_2 )
= ( number_number_of @ X_a @ Y_2 ) )
<=> ( X_2 = Y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(178,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,C: $i] :
( ( plus_plus @ X_a @ A_1 @ C )
= ( plus_plus @ X_a @ C @ A_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(179,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,C: $i,D: $i] :
( ( plus_plus @ X_a @ A_1 @ ( plus_plus @ X_a @ C @ D ) )
= ( plus_plus @ X_a @ C @ ( plus_plus @ X_a @ A_1 @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(180,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,C: $i,D: $i] :
( ( plus_plus @ X_a @ A_1 @ ( plus_plus @ X_a @ C @ D ) )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ C ) @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(181,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ C )
= ( plus_plus @ X_a @ A_1 @ ( plus_plus @ X_a @ B @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(182,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ C )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ C ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(183,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i,D: $i] :
( ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ ( plus_plus @ X_a @ C @ D ) )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ C ) @ ( plus_plus @ X_a @ B @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(184,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i] :
( ( times_times @ X_a @ A_1 @ B )
= ( times_times @ X_a @ B @ A_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(185,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ Rx @ ( times_times @ X_a @ Lx @ Ry ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(186,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Rx ) @ Ry ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(187,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ Rx )
= ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Ly @ Rx ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(188,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ Rx )
= ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Rx ) @ Ly ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(189,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Ly @ ( times_times @ X_a @ Rx @ Ry ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(190,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ Rx @ ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ Ry ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(191,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Rx ) @ ( times_times @ X_a @ Ly @ Ry ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(192,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( twoSqu33214720sum2sq @ X_1 )
=> ( ( twoSqu33214720sum2sq @ Y_1 )
=> ( twoSqu33214720sum2sq @ ( times_times @ int @ X_1 @ Y_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(193,plain,
( ( zprime @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(194,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)],[51]) ).
thf(195,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)],[52]) ).
thf(196,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)],[53]) ).
thf(197,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less @ int @ ( bit0 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq @ int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(198,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(199,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less @ int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(200,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(201,plain,
( ( ! [K: $i] :
( ( ord_less @ int @ pls @ ( bit1 @ K ) )
<=> ( ord_less_eq @ int @ pls @ K ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(202,plain,
( ( ! [K: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K ) @ pls )
<=> ( ord_less @ int @ K @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(203,plain,
( ( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(204,plain,
( ( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(205,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)],[62]) ).
thf(206,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)],[63]) ).
thf(207,plain,
( ( ! [K_1: $i,I: $i,J: $i] :
( ( ord_less @ int @ I @ J )
=> ( ord_less @ int @ ( plus_plus @ int @ I @ K_1 ) @ ( plus_plus @ int @ J @ K_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(208,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)],[65]) ).
thf(209,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)],[66]) ).
thf(210,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)],[67]) ).
thf(211,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)],[68]) ).
thf(212,plain,
( ( ord_less_eq @ int @ pls @ pls )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(213,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less @ int @ ( bit0 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less @ int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(214,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(215,plain,
( ( ~ ( ord_less @ int @ pls @ pls ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(216,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)],[73]) ).
thf(217,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)],[74]) ).
thf(218,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less @ int @ ( bit1 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less @ int @ K @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(219,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(220,plain,
( ( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(221,plain,
( ( ! [Z: $i] :
( ( times_times @ nat @ Z @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ nat @ Z @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(222,plain,
( ( ! [Z: $i] :
( ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z )
= ( plus_plus @ nat @ Z @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(223,plain,
( ( ! [X_1: $i,Y_1: $i,Z: $i] :
( ( power_power @ int @ X_1 @ ( plus_plus @ nat @ Y_1 @ Z ) )
= ( times_times @ int @ ( power_power @ int @ X_1 @ Y_1 ) @ ( power_power @ int @ X_1 @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(224,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,P: $i,Q: $i] :
( ( times_times @ X_a @ ( power_power @ X_a @ X_1 @ P ) @ ( power_power @ X_a @ X_1 @ Q ) )
= ( power_power @ X_a @ X_1 @ ( plus_plus @ nat @ P @ Q ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(225,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)],[82]) ).
thf(226,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_2: $i,Y_2: $i] :
( ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_2 ) @ ( number_number_of @ X_a @ Y_2 ) )
<=> ( ord_less_eq @ int @ X_2 @ Y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(227,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_2: $i,Y_2: $i] :
( ( ord_less @ X_a @ ( number_number_of @ X_a @ X_2 ) @ ( number_number_of @ X_a @ Y_2 ) )
<=> ( ord_less @ int @ X_2 @ Y_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(228,plain,
( ( ! [X_1: $i,Y_1: $i,Z: $i] :
( ( power_power @ int @ ( power_power @ int @ X_1 @ Y_1 ) @ Z )
= ( power_power @ int @ X_1 @ ( times_times @ nat @ Y_1 @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(229,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i] :
( ( power_power @ X_a @ X_1 @ ( one_one @ nat ) )
= ( ti @ X_a @ X_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(230,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,P: $i,Q: $i] :
( ( power_power @ X_a @ ( power_power @ X_a @ X_1 @ P ) @ Q )
= ( power_power @ X_a @ X_1 @ ( times_times @ nat @ P @ Q ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(231,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)],[89]) ).
thf(232,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)],[90]) ).
thf(233,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( ord_less @ int @ X_1 @ Y_1 )
| ( X_1 = Y_1 )
| ( ord_less @ int @ Y_1 @ X_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(234,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)],[92]) ).
thf(235,plain,
( ( ! [Z: $i,W: $i] :
( ( ord_less_eq @ int @ Z @ W )
| ( ord_less_eq @ int @ W @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(236,plain,
( ( ! [W: $i] : ( ord_less_eq @ int @ W @ W ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(237,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)],[95]) ).
thf(238,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( one_one @ X_a ) )
= ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(239,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)],[97]) ).
thf(240,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)],[98]) ).
thf(241,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,N: $i] :
( ( power_power @ X_a @ X_1 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) )
= ( times_times @ X_a @ ( power_power @ X_a @ X_1 @ N ) @ ( power_power @ X_a @ X_1 @ N ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(242,plain,
( ( ! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i] :
( ( power_power @ X_a @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ X_a @ A_1 @ A_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(243,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i] :
( ( times_times @ X_a @ X_1 @ X_1 )
= ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(244,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)],[102]) ).
thf(245,plain,
( ( ! [A_1: $i] :
( ( times_times @ int @ A_1 @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(246,plain,
( ( ! [X_b: $i] :
( ( ( monoid_mult @ X_b )
& ( number @ X_b ) )
=> ! [W: $i] :
( ( power_power @ X_b @ ( number_number_of @ X_b @ W ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ X_b @ ( number_number_of @ X_b @ W ) @ ( number_number_of @ X_b @ W ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(247,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [X_1: $i,Y_1: $i] :
( ( power_power @ X_a @ ( plus_plus @ X_a @ X_1 @ Y_1 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ 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 ) ) ) ) ) @ ( times_times @ X_a @ ( times_times @ X_a @ ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_1 ) @ Y_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(248,plain,
( ( ! [A_1: $i,B: $i] :
( ( power_power @ int @ ( plus_plus @ int @ A_1 @ B ) @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A_1 ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(249,plain,
( ( ! [A_1: $i,B: $i] :
( ( power_power @ int @ ( plus_plus @ int @ A_1 @ B ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A_1 ) @ B ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(250,plain,
( ( twoSqu33214720sum2sq @ ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ t ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(251,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)],[109]) ).
thf(252,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)],[110]) ).
thf(253,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)],[111]) ).
thf(254,plain,
( ( ( ord_less @ int @ ( one_one @ int ) @ t )
=> ? [X: $i,Y: $i] :
( ( plus_plus @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(255,plain,
( ( ( t
= ( one_one @ int ) )
=> ? [X: $i,Y: $i] :
( ( plus_plus @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(256,plain,
( ( ord_less_eq @ int @ ( one_one @ int ) @ t )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(257,plain,
( ( ( ti @ int @ t )
= t )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(258,plain,
( ( ( ti @ int @ s )
= s )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(259,plain,
( ( ! [B_1: $i] :
( ( twoSqu33214720sum2sq @ ( ti @ int @ B_1 ) )
<=> ( twoSqu33214720sum2sq @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(260,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( monoid_mult @ 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)],[118]) ).
thf(261,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( monoid_mult @ 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)],[119]) ).
thf(262,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( monoid_mult @ 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)],[120]) ).
thf(263,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)],[125]) ).
thf(264,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)],[126]) ).
thf(265,plain,
( ( ! [B_1: $i] :
( ( zprime @ ( ti @ int @ B_1 ) )
<=> ( zprime @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(266,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( monoid_mult @ X_a )
=> ( ( ti @ X_a @ ( times_times @ X_a @ B_1 @ B_2 ) )
= ( times_times @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(267,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( monoid_mult @ X_a )
=> ( ( times_times @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
= ( times_times @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(268,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( monoid_mult @ X_a )
=> ( ( times_times @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
= ( times_times @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(269,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( comm_semiring_1 @ 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)],[132]) ).
thf(270,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( comm_semiring_1 @ 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)],[133]) ).
thf(271,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( comm_semiring_1 @ 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)],[134]) ).
thf(272,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)],[135]) ).
thf(273,plain,
( ( ( ti @ int @ m )
= m )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(274,plain,
( ( ( ti @ int @ pls )
= pls )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(275,plain,
( ( ! [B_1: $i] :
( ( ti @ int @ ( bit1 @ B_1 ) )
= ( bit1 @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(276,plain,
( ( ! [B_1: $i] :
( ( bit1 @ ( ti @ int @ B_1 ) )
= ( bit1 @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(277,plain,
( ( ! [B_1: $i] :
( ( ti @ int @ ( bit0 @ B_1 ) )
= ( bit0 @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(278,plain,
( ( ! [B_1: $i] :
( ( bit0 @ ( ti @ int @ B_1 ) )
= ( bit0 @ B_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(279,plain,
( ( ~ ? [X: $i,Y: $i] :
( ( plus_plus @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[144]) ).
thf(280,plain,
( ( ! [B_1: $i] :
( ( bit0 @ ( ti @ int @ B_1 ) )
= ( bit0 @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[278]) ).
thf(281,plain,
( ( ! [B_1: $i] :
( ( ti @ int @ ( bit0 @ B_1 ) )
= ( bit0 @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[277]) ).
thf(282,plain,
( ( ! [B_1: $i] :
( ( bit1 @ ( ti @ int @ B_1 ) )
= ( bit1 @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[276]) ).
thf(283,plain,
( ( ! [B_1: $i] :
( ( ti @ int @ ( bit1 @ B_1 ) )
= ( bit1 @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[275]) ).
thf(284,plain,
( ( ( ti @ int @ pls )
= pls )
= $true ),
inference(copy,[status(thm)],[274]) ).
thf(285,plain,
( ( ( ti @ int @ m )
= m )
= $true ),
inference(copy,[status(thm)],[273]) ).
thf(286,plain,
( ( ! [X_a: $i] :
( ( semiring_1 @ X_a )
=> ( ( ti @ X_a @ ( one_one @ X_a ) )
= ( one_one @ X_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[272]) ).
thf(287,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( comm_semiring_1 @ 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)],[271]) ).
thf(288,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( comm_semiring_1 @ 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)],[270]) ).
thf(289,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( comm_semiring_1 @ 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)],[269]) ).
thf(290,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( monoid_mult @ X_a )
=> ( ( times_times @ X_a @ ( ti @ X_a @ B_1 ) @ B_2 )
= ( times_times @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(291,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( monoid_mult @ X_a )
=> ( ( times_times @ X_a @ B_1 @ ( ti @ X_a @ B_2 ) )
= ( times_times @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[267]) ).
thf(292,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( monoid_mult @ X_a )
=> ( ( ti @ X_a @ ( times_times @ X_a @ B_1 @ B_2 ) )
= ( times_times @ X_a @ B_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(293,plain,
( ( ! [B_1: $i] :
( ( zprime @ ( ti @ int @ B_1 ) )
<=> ( zprime @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(294,plain,
( ( ! [B_1: $i,X_a: $i] :
( ( number @ X_a )
=> ( ( number_number_of @ X_a @ ( ti @ int @ B_1 ) )
= ( number_number_of @ X_a @ B_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(295,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)],[263]) ).
thf(296,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( monoid_mult @ 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)],[262]) ).
thf(297,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( monoid_mult @ 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)],[261]) ).
thf(298,plain,
( ( ! [B_1: $i,B_2: $i,X_a: $i] :
( ( monoid_mult @ 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)],[260]) ).
thf(299,plain,
( ( ! [B_1: $i] :
( ( twoSqu33214720sum2sq @ ( ti @ int @ B_1 ) )
<=> ( twoSqu33214720sum2sq @ B_1 ) ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(300,plain,
( ( ( ti @ int @ s )
= s )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(301,plain,
( ( ( ti @ int @ t )
= t )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(302,plain,
( ( ord_less_eq @ int @ ( one_one @ int ) @ t )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(303,plain,
( ( ( t
= ( one_one @ int ) )
=> ? [X: $i,Y: $i] :
( ( plus_plus @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(304,plain,
( ( ( ord_less @ int @ ( one_one @ int ) @ t )
=> ? [X: $i,Y: $i] :
( ( plus_plus @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(305,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)],[253]) ).
thf(306,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)],[252]) ).
thf(307,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)],[251]) ).
thf(308,plain,
( ( twoSqu33214720sum2sq @ ( times_times @ int @ ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) @ t ) )
= $true ),
inference(copy,[status(thm)],[250]) ).
thf(309,plain,
( ( ! [A_1: $i,B: $i] :
( ( power_power @ int @ ( plus_plus @ int @ A_1 @ B ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A_1 ) @ B ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(310,plain,
( ( ! [A_1: $i,B: $i] :
( ( power_power @ int @ ( plus_plus @ int @ A_1 @ B ) @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A_1 ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(311,plain,
( ( ! [X_a: $i] :
( ( number_semiring @ X_a )
=> ! [X_1: $i,Y_1: $i] :
( ( power_power @ X_a @ ( plus_plus @ X_a @ X_1 @ Y_1 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ 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 ) ) ) ) ) @ ( times_times @ X_a @ ( times_times @ X_a @ ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_1 ) @ Y_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(312,plain,
( ( ! [X_b: $i] :
( ( ( monoid_mult @ X_b )
& ( number @ X_b ) )
=> ! [W: $i] :
( ( power_power @ X_b @ ( number_number_of @ X_b @ W ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ X_b @ ( number_number_of @ X_b @ W ) @ ( number_number_of @ X_b @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(313,plain,
( ( ! [A_1: $i] :
( ( times_times @ int @ A_1 @ ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ int @ A_1 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(314,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)],[244]) ).
thf(315,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i] :
( ( times_times @ X_a @ X_1 @ X_1 )
= ( power_power @ X_a @ X_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(316,plain,
( ( ! [X_a: $i] :
( ( monoid_mult @ X_a )
=> ! [A_1: $i] :
( ( power_power @ X_a @ A_1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ X_a @ A_1 @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(317,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,N: $i] :
( ( power_power @ X_a @ X_1 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) )
= ( times_times @ X_a @ ( power_power @ X_a @ X_1 @ N ) @ ( power_power @ X_a @ X_1 @ N ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(318,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)],[240]) ).
thf(319,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)],[239]) ).
thf(320,plain,
( ( ! [X_a: $i] :
( ( number_ring @ X_a )
=> ( ( plus_plus @ X_a @ ( one_one @ X_a ) @ ( one_one @ X_a ) )
= ( number_number_of @ X_a @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(321,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)],[237]) ).
thf(322,plain,
( ( ! [W: $i] : ( ord_less_eq @ int @ W @ W ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(323,plain,
( ( ! [Z: $i,W: $i] :
( ( ord_less_eq @ int @ Z @ W )
| ( ord_less_eq @ int @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(324,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)],[234]) ).
thf(325,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( ord_less @ int @ X_1 @ Y_1 )
| ( X_1 = Y_1 )
| ( ord_less @ int @ Y_1 @ X_1 ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(326,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)],[232]) ).
thf(327,plain,
( ( ! [Z: $i,W: $i] :
( ( ord_less_eq @ int @ Z @ W )
=> ( ( ord_less_eq @ int @ W @ Z )
=> ( Z = W ) ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(328,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,P: $i,Q: $i] :
( ( power_power @ X_a @ ( power_power @ X_a @ X_1 @ P ) @ Q )
= ( power_power @ X_a @ X_1 @ ( times_times @ nat @ P @ Q ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(329,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i] :
( ( power_power @ X_a @ X_1 @ ( one_one @ nat ) )
= ( ti @ X_a @ X_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(330,plain,
( ( ! [X_1: $i,Y_1: $i,Z: $i] :
( ( power_power @ int @ ( power_power @ int @ X_1 @ Y_1 ) @ Z )
= ( power_power @ int @ X_1 @ ( times_times @ nat @ Y_1 @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(331,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_2: $i,Y_2: $i] :
( ( ord_less @ X_a @ ( number_number_of @ X_a @ X_2 ) @ ( number_number_of @ X_a @ Y_2 ) )
<=> ( ord_less @ int @ X_2 @ Y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(332,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( linordered_idom @ X_a ) )
=> ! [X_2: $i,Y_2: $i] :
( ( ord_less_eq @ X_a @ ( number_number_of @ X_a @ X_2 ) @ ( number_number_of @ X_a @ Y_2 ) )
<=> ( ord_less_eq @ int @ X_2 @ Y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(333,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)],[225]) ).
thf(334,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [X_1: $i,P: $i,Q: $i] :
( ( times_times @ X_a @ ( power_power @ X_a @ X_1 @ P ) @ ( power_power @ X_a @ X_1 @ Q ) )
= ( power_power @ X_a @ X_1 @ ( plus_plus @ nat @ P @ Q ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(335,plain,
( ( ! [X_1: $i,Y_1: $i,Z: $i] :
( ( power_power @ int @ X_1 @ ( plus_plus @ nat @ Y_1 @ Z ) )
= ( times_times @ int @ ( power_power @ int @ X_1 @ Y_1 ) @ ( power_power @ int @ X_1 @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(336,plain,
( ( ! [Z: $i] :
( ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z )
= ( plus_plus @ nat @ Z @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(337,plain,
( ( ! [Z: $i] :
( ( times_times @ nat @ Z @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ nat @ Z @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(338,plain,
( ( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(339,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(340,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less @ int @ ( bit1 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less @ int @ K @ L ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(341,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(342,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq @ int @ K @ L ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(343,plain,
( ( ~ ( ord_less @ int @ pls @ pls ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(344,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(345,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less @ int @ ( bit0 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less @ int @ K @ L ) ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(346,plain,
( ( ord_less_eq @ int @ pls @ pls )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(347,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(348,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less_eq @ int @ K @ L ) ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(349,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)],[209]) ).
thf(350,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)],[208]) ).
thf(351,plain,
( ( ! [K_1: $i,I: $i,J: $i] :
( ( ord_less @ int @ I @ J )
=> ( ord_less @ int @ ( plus_plus @ int @ I @ K_1 ) @ ( plus_plus @ int @ J @ K_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(352,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)],[206]) ).
thf(353,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)],[205]) ).
thf(354,plain,
( ( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(355,plain,
( ( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(356,plain,
( ( ! [K: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K ) @ pls )
<=> ( ord_less @ int @ K @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(357,plain,
( ( ! [K: $i] :
( ( ord_less @ int @ pls @ ( bit1 @ K ) )
<=> ( ord_less_eq @ int @ pls @ K ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(358,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(359,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less_eq @ int @ ( bit1 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less @ int @ K @ L ) ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(360,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(361,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less @ int @ ( bit0 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq @ int @ K @ L ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(362,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)],[196]) ).
thf(363,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)],[195]) ).
thf(364,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)],[194]) ).
thf(365,plain,
( ( zprime @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(366,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( twoSqu33214720sum2sq @ X_1 )
=> ( ( twoSqu33214720sum2sq @ Y_1 )
=> ( twoSqu33214720sum2sq @ ( times_times @ int @ X_1 @ Y_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(367,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Rx ) @ ( times_times @ X_a @ Ly @ Ry ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(368,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ Rx @ ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ Ry ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(369,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Ly @ ( times_times @ X_a @ Rx @ Ry ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(370,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ Rx )
= ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Rx ) @ Ly ) ) ) )
= $true ),
inference(copy,[status(thm)],[188]) ).
thf(371,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Ly: $i,Rx: $i] :
( ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Ly ) @ Rx )
= ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Ly @ Rx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(372,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ ( times_times @ X_a @ Lx @ Rx ) @ Ry ) ) ) )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(373,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [Lx: $i,Rx: $i,Ry: $i] :
( ( times_times @ X_a @ Lx @ ( times_times @ X_a @ Rx @ Ry ) )
= ( times_times @ X_a @ Rx @ ( times_times @ X_a @ Lx @ Ry ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(374,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i] :
( ( times_times @ X_a @ A_1 @ B )
= ( times_times @ X_a @ B @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(375,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i,D: $i] :
( ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ ( plus_plus @ X_a @ C @ D ) )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ C ) @ ( plus_plus @ X_a @ B @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(376,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ C )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ C ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(377,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,B: $i,C: $i] :
( ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ B ) @ C )
= ( plus_plus @ X_a @ A_1 @ ( plus_plus @ X_a @ B @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(378,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,C: $i,D: $i] :
( ( plus_plus @ X_a @ A_1 @ ( plus_plus @ X_a @ C @ D ) )
= ( plus_plus @ X_a @ ( plus_plus @ X_a @ A_1 @ C ) @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(379,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,C: $i,D: $i] :
( ( plus_plus @ X_a @ A_1 @ ( plus_plus @ X_a @ C @ D ) )
= ( plus_plus @ X_a @ C @ ( plus_plus @ X_a @ A_1 @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(380,plain,
( ( ! [X_a: $i] :
( ( comm_semiring_1 @ X_a )
=> ! [A_1: $i,C: $i] :
( ( plus_plus @ X_a @ A_1 @ C )
= ( plus_plus @ X_a @ C @ A_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(381,plain,
( ( ! [X_a: $i] :
( ( ( number_ring @ X_a )
& ( ring_char_0 @ X_a ) )
=> ! [X_2: $i,Y_2: $i] :
( ( ( number_number_of @ X_a @ X_2 )
= ( number_number_of @ X_a @ Y_2 ) )
<=> ( X_2 = Y_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(382,plain,
( ( ! [X_a: $i] :
( ( number @ X_a )
=> ! [W_1: $i,X_2: $i] :
( ( ( number_number_of @ X_a @ W_1 )
= ( ti @ X_a @ X_2 ) )
<=> ( ( ti @ X_a @ X_2 )
= ( number_number_of @ X_a @ W_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(383,plain,
( ( ! [K: $i,L: $i] :
( ( ( bit1 @ K )
= ( bit1 @ L ) )
<=> ( K = L ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(384,plain,
( ( ! [K: $i,L: $i] :
( ( ( bit0 @ K )
= ( bit0 @ L ) )
<=> ( K = L ) ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(385,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)],[173]) ).
thf(386,plain,
( ( ! [Z: $i,W: $i] :
( ( times_times @ int @ Z @ W )
= ( times_times @ int @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(387,plain,
( ( ! [K_1: $i] :
( ( number_number_of @ int @ K_1 )
= K_1 ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(388,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)],[170]) ).
thf(389,plain,
( ( ! [X_1: $i,Y_1: $i,Z: $i] :
( ( plus_plus @ int @ X_1 @ ( plus_plus @ int @ Y_1 @ Z ) )
= ( plus_plus @ int @ Y_1 @ ( plus_plus @ int @ X_1 @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(390,plain,
( ( ! [Z: $i,W: $i] :
( ( plus_plus @ int @ Z @ W )
= ( plus_plus @ int @ W @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(391,plain,
( ( ! [K: $i] :
( ( ord_less @ int @ ( bit1 @ K ) @ pls )
<=> ( ord_less @ int @ K @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[167]) ).
thf(392,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less @ int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
<=> ( ord_less @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(393,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less @ int @ ( bit1 @ K ) @ ( bit0 @ L ) )
<=> ( ord_less @ int @ K @ L ) ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(394,plain,
( ( ! [K: $i] :
( ( ord_less @ int @ ( bit0 @ K ) @ pls )
<=> ( ord_less @ int @ K @ pls ) ) )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(395,plain,
( ( ! [K: $i] :
( ( ord_less @ int @ pls @ ( bit0 @ K ) )
<=> ( ord_less @ int @ pls @ K ) ) )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(396,plain,
( ( ! [K: $i] :
( ( ord_less_eq @ int @ pls @ ( bit1 @ K ) )
<=> ( ord_less_eq @ int @ pls @ K ) ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(397,plain,
( ( ! [K1: $i,K2: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
<=> ( ord_less_eq @ int @ K1 @ K2 ) ) )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(398,plain,
( ( ! [K: $i,L: $i] :
( ( ord_less_eq @ int @ ( bit0 @ K ) @ ( bit1 @ L ) )
<=> ( ord_less_eq @ int @ K @ L ) ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(399,plain,
( ( linordered_idom @ int )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(400,plain,
( ( comm_semiring_1 @ int )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(401,plain,
( ( number_semiring @ int )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(402,plain,
( ( linorder @ int )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(403,plain,
( ( monoid_mult @ int )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(404,plain,
( ( semiring_1 @ int )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(405,plain,
( ( ring_char_0 @ int )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(406,plain,
( ( number_ring @ int )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(407,plain,
( ( number @ int )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(408,plain,
( ( comm_semiring_1 @ nat )
= $true ),
inference(copy,[status(thm)],[150]) ).
thf(409,plain,
( ( number_semiring @ nat )
= $true ),
inference(copy,[status(thm)],[149]) ).
thf(410,plain,
( ( linorder @ nat )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(411,plain,
( ( monoid_mult @ nat )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(412,plain,
( ( semiring_1 @ nat )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(413,plain,
( ( number @ nat )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(414,plain,
( ( ~ ? [X: $i,Y: $i] :
( ( plus_plus @ int @ ( power_power @ int @ X @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ Y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(copy,[status(thm)],[279]) ).
thf(415,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( comm_semiring_1 @ SX2 )
| ( ( plus_plus @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 )
= ( plus_plus @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(416,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( monoid_mult @ SX2 )
| ( ( times_times @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 )
= ( times_times @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(417,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)],[327]) ).
thf(418,plain,
( ( ! [SX0: $i] :
( ~ ( number_semiring @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( power_power @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX2 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ 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 ) ) ) ) ) @ ( times_times @ SX0 @ ( times_times @ SX0 @ ( number_number_of @ SX0 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SX1 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(419,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( bit1 @ SX0 )
!= ( bit1 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ( ( SX0 != SX1 )
| ( ( bit1 @ SX0 )
= ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(420,plain,
( ( ~ ( ord_less @ int @ ( one_one @ int ) @ t )
| ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(421,plain,
( ( ! [SX0: $i] :
( ~ ( monoid_mult @ SX0 )
| ! [SX1: $i] :
( ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SX0 @ SX1 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(422,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)],[347]) ).
thf(423,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( monoid_mult @ SX0 )
| ~ ( number @ SX0 ) )
| ! [SX1: $i] :
( ( power_power @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(424,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( twoSqu33214720sum2sq @ ( ti @ int @ SX0 ) )
| ( twoSqu33214720sum2sq @ SX0 ) )
| ~ ( ~ ( twoSqu33214720sum2sq @ SX0 )
| ( twoSqu33214720sum2sq @ ( ti @ int @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(425,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)],[360]) ).
thf(426,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393]) ).
thf(427,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ord_less @ int @ SX1 @ SX2 )
| ( ord_less @ int @ ( plus_plus @ int @ SX1 @ SX0 ) @ ( plus_plus @ int @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(428,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)],[396]) ).
thf(429,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( comm_semiring_1 @ SX2 )
| ( ( plus_plus @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) )
= ( plus_plus @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(430,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)],[341]) ).
thf(431,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( times_times @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ ( times_times @ SX0 @ SX3 @ SX4 ) )
= ( times_times @ SX0 @ SX1 @ ( times_times @ SX0 @ SX2 @ ( times_times @ SX0 @ SX3 @ SX4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369]) ).
thf(432,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( plus_plus @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX2 ) @ SX3 )
= ( plus_plus @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX3 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(433,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)],[358]) ).
thf(434,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)],[397]) ).
thf(435,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)],[352]) ).
thf(436,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)],[350]) ).
thf(437,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i] :
( ( power_power @ SX0 @ SX1 @ ( one_one @ nat ) )
= ( ti @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(438,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( times_times @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ ( times_times @ SX0 @ SX3 @ SX4 ) )
= ( times_times @ SX0 @ ( times_times @ SX0 @ SX1 @ SX3 ) @ ( times_times @ SX0 @ SX2 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(439,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)],[361]) ).
thf(440,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ pls )
| ( ord_less @ int @ SX0 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ pls )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(441,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( plus_plus @ SX0 @ SX1 @ ( plus_plus @ SX0 @ SX2 @ SX3 ) )
= ( plus_plus @ SX0 @ SX2 @ ( plus_plus @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(442,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( monoid_mult @ SX2 )
| ( ( ti @ SX2 @ ( power_power @ SX2 @ SX0 @ SX1 ) )
= ( power_power @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(443,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)],[319]) ).
thf(444,plain,
( ( ! [SX0: $i] :
( ~ ( number_ring @ SX0 )
| ( ( plus_plus @ SX0 @ ( one_one @ SX0 ) @ ( one_one @ SX0 ) )
= ( number_number_of @ SX0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(445,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( monoid_mult @ SX2 )
| ( ( power_power @ SX2 @ ( ti @ SX2 @ SX0 ) @ SX1 )
= ( power_power @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(446,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)],[382]) ).
thf(447,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)],[332]) ).
thf(448,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( times_times @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ SX3 )
= ( times_times @ SX0 @ ( times_times @ SX0 @ SX1 @ SX3 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(449,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414]) ).
thf(450,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( plus_plus @ SX0 @ SX1 @ ( plus_plus @ SX0 @ SX2 @ SX3 ) )
= ( plus_plus @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX2 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(451,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)],[318]) ).
thf(452,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(453,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)],[363]) ).
thf(454,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)],[324]) ).
thf(455,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( times_times @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ ( times_times @ SX0 @ SX3 @ SX4 ) )
= ( times_times @ SX0 @ SX3 @ ( times_times @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(456,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( times_times @ SX0 @ SX1 @ ( times_times @ SX0 @ SX2 @ SX3 ) )
= ( times_times @ SX0 @ SX2 @ ( times_times @ SX0 @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373]) ).
thf(457,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( plus_plus @ SX0 @ SX1 @ SX2 )
= ( plus_plus @ SX0 @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(458,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( times_times @ SX0 @ SX1 @ ( times_times @ SX0 @ SX2 @ SX3 ) )
= ( times_times @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(459,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( zprime @ ( ti @ int @ SX0 ) )
| ( zprime @ SX0 ) )
| ~ ( ~ ( zprime @ SX0 )
| ( zprime @ ( ti @ int @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(460,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)],[362]) ).
thf(461,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( times_times @ SX0 @ SX1 @ SX2 )
= ( times_times @ SX0 @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(462,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( bit0 @ SX0 )
!= ( bit0 @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ( ( SX0 != SX1 )
| ( ( bit0 @ SX0 )
= ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(463,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)],[348]) ).
thf(464,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)],[342]) ).
thf(465,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)],[314]) ).
thf(466,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)],[321]) ).
thf(467,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(468,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit1 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(469,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( number_ring @ SX0 )
| ~ ( linordered_idom @ SX0 ) )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( ord_less @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX2 ) )
| ( ord_less @ int @ SX1 @ SX2 ) )
| ~ ( ~ ( ord_less @ int @ SX1 @ SX2 )
| ( ord_less @ SX0 @ ( number_number_of @ SX0 @ SX1 ) @ ( number_number_of @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(470,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( plus_plus @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX2 ) @ ( plus_plus @ SX0 @ SX3 @ SX4 ) )
= ( plus_plus @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX3 ) @ ( plus_plus @ SX0 @ SX2 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(471,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit0 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(472,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)],[356]) ).
thf(473,plain,
( ( ( t
!= ( one_one @ int ) )
| ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(474,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( twoSqu33214720sum2sq @ SX1 )
| ~ ( twoSqu33214720sum2sq @ SX0 )
| ( twoSqu33214720sum2sq @ ( times_times @ int @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(475,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( monoid_mult @ SX2 )
| ( ( times_times @ SX2 @ SX0 @ ( ti @ SX2 @ SX1 ) )
= ( times_times @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(476,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)],[333]) ).
thf(477,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( times_times @ SX0 @ ( times_times @ SX0 @ SX1 @ SX2 ) @ SX3 )
= ( times_times @ SX0 @ SX1 @ ( times_times @ SX0 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(478,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)],[294]) ).
thf(479,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i] :
( ( times_times @ SX0 @ SX1 @ SX1 )
= ( power_power @ SX0 @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(480,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)],[398]) ).
thf(481,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( monoid_mult @ SX2 )
| ( ( ti @ SX2 @ ( times_times @ SX2 @ SX0 @ SX1 ) )
= ( times_times @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(482,plain,
( ( ! [SX0: $i] :
( ~ ( semiring_1 @ SX0 )
| ( ( ti @ SX0 @ ( one_one @ SX0 ) )
= ( one_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(483,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i] :
( ( power_power @ SX0 @ SX1 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SX2 ) )
= ( times_times @ SX0 @ ( power_power @ SX0 @ SX1 @ SX2 ) @ ( power_power @ SX0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(484,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)],[359]) ).
thf(485,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)],[364]) ).
thf(486,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less @ int @ pls @ ( bit0 @ SX0 ) )
| ( ord_less @ int @ pls @ SX0 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SX0 )
| ( ord_less @ int @ pls @ ( bit0 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(487,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( times_times @ SX0 @ ( power_power @ SX0 @ SX1 @ SX2 ) @ ( power_power @ SX0 @ SX1 @ SX3 ) )
= ( power_power @ SX0 @ SX1 @ ( plus_plus @ nat @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(488,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( comm_semiring_1 @ SX2 )
| ( ( ti @ SX2 @ ( plus_plus @ SX2 @ SX0 @ SX1 ) )
= ( plus_plus @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(489,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)],[381]) ).
thf(490,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)],[353]) ).
thf(491,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( power_power @ SX0 @ ( power_power @ SX0 @ SX1 @ SX2 ) @ SX3 )
= ( power_power @ SX0 @ SX1 @ ( times_times @ nat @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(492,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)],[295]) ).
thf(493,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)],[349]) ).
thf(494,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ pls )
| ( ord_less @ int @ SX0 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ pls )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ pls ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(495,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) )
| ( ord_less @ int @ SX0 @ SX1 ) )
| ~ ( ~ ( ord_less @ int @ SX0 @ SX1 )
| ( ord_less @ int @ ( bit1 @ SX0 ) @ ( bit0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392]) ).
thf(496,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)],[326]) ).
thf(497,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( monoid_mult @ SX2 )
| ( ( power_power @ SX2 @ SX0 @ ( ti @ nat @ SX1 ) )
= ( power_power @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(498,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)],[357]) ).
thf(499,plain,
( ( ! [SX0: $i] :
( ~ ( comm_semiring_1 @ SX0 )
| ! [SX1: $i,SX2: $i,SX3: $i] :
( ( plus_plus @ SX0 @ ( plus_plus @ SX0 @ SX1 @ SX2 ) @ SX3 )
= ( plus_plus @ SX0 @ SX1 @ ( plus_plus @ SX0 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(500,plain,
! [SV1: $i] :
( ( ( bit0 @ ( ti @ int @ SV1 ) )
= ( bit0 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(501,plain,
! [SV2: $i] :
( ( ( ti @ int @ ( bit0 @ SV2 ) )
= ( bit0 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(502,plain,
! [SV3: $i] :
( ( ( bit1 @ ( ti @ int @ SV3 ) )
= ( bit1 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(503,plain,
! [SV4: $i] :
( ( ( ti @ int @ ( bit1 @ SV4 ) )
= ( bit1 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(504,plain,
! [SV5: $i] :
( ( ! [SY248: $i] :
( ( power_power @ int @ ( plus_plus @ int @ SV5 @ SY248 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ SV5 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV5 ) @ SY248 ) ) @ ( power_power @ int @ SY248 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(505,plain,
! [SV6: $i] :
( ( ! [SY249: $i] :
( ( power_power @ int @ ( plus_plus @ int @ SV6 @ SY249 ) @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ SV6 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power @ int @ SV6 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ SY249 ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ SV6 ) @ ( power_power @ int @ SY249 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power @ int @ SY249 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(506,plain,
! [SV7: $i] :
( ( ( times_times @ int @ SV7 @ ( power_power @ int @ SV7 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ int @ SV7 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(507,plain,
! [SV8: $i] :
( ( ord_less_eq @ int @ SV8 @ SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(508,plain,
! [SV9: $i] :
( ( ! [SY250: $i] :
( ( ord_less_eq @ int @ SV9 @ SY250 )
| ( ord_less_eq @ int @ SY250 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(509,plain,
! [SV10: $i] :
( ( ! [SY251: $i] :
( ( ord_less @ int @ SV10 @ SY251 )
| ( SV10 = SY251 )
| ( ord_less @ int @ SY251 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(510,plain,
! [SV11: $i] :
( ( ! [SY252: $i,SY253: $i] :
( ( power_power @ int @ ( power_power @ int @ SV11 @ SY252 ) @ SY253 )
= ( power_power @ int @ SV11 @ ( times_times @ nat @ SY252 @ SY253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(511,plain,
! [SV12: $i] :
( ( ! [SY254: $i,SY255: $i] :
( ( power_power @ int @ SV12 @ ( plus_plus @ nat @ SY254 @ SY255 ) )
= ( times_times @ int @ ( power_power @ int @ SV12 @ SY254 ) @ ( power_power @ int @ SV12 @ SY255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(512,plain,
! [SV13: $i] :
( ( ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV13 )
= ( plus_plus @ nat @ SV13 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(513,plain,
! [SV14: $i] :
( ( ( times_times @ nat @ SV14 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ nat @ SV14 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(514,plain,
( ( ord_less @ int @ pls @ pls )
= $false ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(515,plain,
! [SV15: $i] :
( ( ! [SY256: $i,SY257: $i] :
( ( times_times @ int @ ( times_times @ int @ SV15 @ SY256 ) @ SY257 )
= ( times_times @ int @ SV15 @ ( times_times @ int @ SY256 @ SY257 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(516,plain,
! [SV16: $i] :
( ( ! [SY258: $i] :
( ( times_times @ int @ SV16 @ SY258 )
= ( times_times @ int @ SY258 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(517,plain,
! [SV17: $i] :
( ( ( number_number_of @ int @ SV17 )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(518,plain,
! [SV18: $i] :
( ( ! [SY259: $i,SY260: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ SV18 @ SY259 ) @ SY260 )
= ( plus_plus @ int @ SV18 @ ( plus_plus @ int @ SY259 @ SY260 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(519,plain,
! [SV19: $i] :
( ( ! [SY261: $i,SY262: $i] :
( ( plus_plus @ int @ SV19 @ ( plus_plus @ int @ SY261 @ SY262 ) )
= ( plus_plus @ int @ SY261 @ ( plus_plus @ int @ SV19 @ SY262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(520,plain,
! [SV20: $i] :
( ( ! [SY263: $i] :
( ( plus_plus @ int @ SV20 @ SY263 )
= ( plus_plus @ int @ SY263 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(521,plain,
! [SV21: $i] :
( ( ! [SY264: $i,SY265: $i] :
( ~ ( comm_semiring_1 @ SY265 )
| ( ( plus_plus @ SY265 @ ( ti @ SY265 @ SV21 ) @ SY264 )
= ( plus_plus @ SY265 @ SV21 @ SY264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(522,plain,
! [SV22: $i] :
( ( ! [SY266: $i,SY267: $i] :
( ~ ( monoid_mult @ SY267 )
| ( ( times_times @ SY267 @ ( ti @ SY267 @ SV22 ) @ SY266 )
= ( times_times @ SY267 @ SV22 @ SY266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(523,plain,
! [SV23: $i] :
( ( ! [SY268: $i] :
( ~ ( ord_less_eq @ int @ SV23 @ SY268 )
| ~ ( ord_less_eq @ int @ SY268 @ SV23 )
| ( SV23 = SY268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(524,plain,
! [SV24: $i] :
( ( ~ ( number_semiring @ SV24 )
| ! [SY269: $i,SY270: $i] :
( ( power_power @ SV24 @ ( plus_plus @ SV24 @ SY269 @ SY270 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ SV24 @ ( plus_plus @ SV24 @ ( power_power @ SV24 @ SY269 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV24 @ SY270 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ SV24 @ ( times_times @ SV24 @ ( number_number_of @ SV24 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY269 ) @ SY270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(525,plain,
! [SV25: $i] :
( ( ! [SY271: $i] :
~ ( ~ ( ( ( bit1 @ SV25 )
!= ( bit1 @ SY271 ) )
| ( SV25 = SY271 ) )
| ~ ( ( SV25 != SY271 )
| ( ( bit1 @ SV25 )
= ( bit1 @ SY271 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(526,plain,
( ( ( ~ ( ord_less @ int @ ( one_one @ int ) @ t ) )
= $true )
| ( ( ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(527,plain,
! [SV26: $i] :
( ( ~ ( monoid_mult @ SV26 )
| ! [SY272: $i] :
( ( power_power @ SV26 @ SY272 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV26 @ SY272 @ SY272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(528,plain,
! [SV27: $i] :
( ( ! [SY273: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV27 ) @ ( bit0 @ SY273 ) )
| ( ord_less_eq @ int @ SV27 @ SY273 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV27 @ SY273 )
| ( ord_less_eq @ int @ ( bit0 @ SV27 ) @ ( bit0 @ SY273 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(529,plain,
! [SV28: $i] :
( ( ~ ~ ( ~ ( monoid_mult @ SV28 )
| ~ ( number @ SV28 ) )
| ! [SY274: $i] :
( ( power_power @ SV28 @ ( number_number_of @ SV28 @ SY274 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV28 @ ( number_number_of @ SV28 @ SY274 ) @ ( number_number_of @ SV28 @ SY274 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(530,plain,
! [SV29: $i] :
( ( ~ ( ~ ( ~ ( twoSqu33214720sum2sq @ ( ti @ int @ SV29 ) )
| ( twoSqu33214720sum2sq @ SV29 ) )
| ~ ( ~ ( twoSqu33214720sum2sq @ SV29 )
| ( twoSqu33214720sum2sq @ ( ti @ int @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(531,plain,
! [SV30: $i] :
( ( ! [SY275: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV30 ) @ ( bit1 @ SY275 ) )
| ( ord_less_eq @ int @ SV30 @ SY275 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV30 @ SY275 )
| ( ord_less @ int @ ( bit0 @ SV30 ) @ ( bit1 @ SY275 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(532,plain,
! [SV31: $i] :
( ( ! [SY276: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV31 ) @ ( bit0 @ SY276 ) )
| ( ord_less @ int @ SV31 @ SY276 ) )
| ~ ( ~ ( ord_less @ int @ SV31 @ SY276 )
| ( ord_less @ int @ ( bit1 @ SV31 ) @ ( bit0 @ SY276 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(533,plain,
! [SV32: $i] :
( ( ! [SY277: $i,SY278: $i] :
( ~ ( ord_less @ int @ SY277 @ SY278 )
| ( ord_less @ int @ ( plus_plus @ int @ SY277 @ SV32 ) @ ( plus_plus @ int @ SY278 @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(534,plain,
! [SV33: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ SV33 ) )
| ( ord_less_eq @ int @ pls @ SV33 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SV33 )
| ( ord_less_eq @ int @ pls @ ( bit1 @ SV33 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(535,plain,
! [SV34: $i] :
( ( ! [SY279: $i,SY280: $i] :
( ~ ( comm_semiring_1 @ SY280 )
| ( ( plus_plus @ SY280 @ SV34 @ ( ti @ SY280 @ SY279 ) )
= ( plus_plus @ SY280 @ SV34 @ SY279 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(536,plain,
! [SV35: $i] :
( ( ! [SY281: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV35 ) @ ( bit1 @ SY281 ) )
| ( ord_less_eq @ int @ SV35 @ SY281 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV35 @ SY281 )
| ( ord_less_eq @ int @ ( bit1 @ SV35 ) @ ( bit1 @ SY281 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(537,plain,
! [SV36: $i] :
( ( ~ ( comm_semiring_1 @ SV36 )
| ! [SY282: $i,SY283: $i,SY284: $i,SY285: $i] :
( ( times_times @ SV36 @ ( times_times @ SV36 @ SY282 @ SY283 ) @ ( times_times @ SV36 @ SY284 @ SY285 ) )
= ( times_times @ SV36 @ SY282 @ ( times_times @ SV36 @ SY283 @ ( times_times @ SV36 @ SY284 @ SY285 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(538,plain,
! [SV37: $i] :
( ( ~ ( comm_semiring_1 @ SV37 )
| ! [SY286: $i,SY287: $i,SY288: $i] :
( ( plus_plus @ SV37 @ ( plus_plus @ SV37 @ SY286 @ SY287 ) @ SY288 )
= ( plus_plus @ SV37 @ ( plus_plus @ SV37 @ SY286 @ SY288 ) @ SY287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(539,plain,
! [SV38: $i] :
( ( ! [SY289: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit0 @ SY289 ) )
| ( ord_less @ int @ SV38 @ SY289 ) )
| ~ ( ~ ( ord_less @ int @ SV38 @ SY289 )
| ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit0 @ SY289 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(540,plain,
! [SV39: $i] :
( ( ! [SY290: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV39 ) @ ( bit1 @ SY290 ) )
| ( ord_less_eq @ int @ SV39 @ SY290 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV39 @ SY290 )
| ( ord_less_eq @ int @ ( bit0 @ SV39 ) @ ( bit1 @ SY290 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(541,plain,
! [SV40: $i] :
( ( ! [SY291: $i,SY292: $i] :
( ~ ( ord_less_eq @ int @ SY291 @ SY292 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV40 @ SY291 ) @ ( plus_plus @ int @ SV40 @ SY292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(542,plain,
! [SV41: $i] :
( ( ! [SY293: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SY293 ) )
| ( ord_less_eq @ int @ SV41 @ SY293 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV41 @ SY293 )
| ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SY293 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(543,plain,
! [SV42: $i] :
( ( ~ ( comm_semiring_1 @ SV42 )
| ! [SY294: $i] :
( ( power_power @ SV42 @ SY294 @ ( one_one @ nat ) )
= ( ti @ SV42 @ SY294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(544,plain,
! [SV43: $i] :
( ( ~ ( comm_semiring_1 @ SV43 )
| ! [SY295: $i,SY296: $i,SY297: $i,SY298: $i] :
( ( times_times @ SV43 @ ( times_times @ SV43 @ SY295 @ SY296 ) @ ( times_times @ SV43 @ SY297 @ SY298 ) )
= ( times_times @ SV43 @ ( times_times @ SV43 @ SY295 @ SY297 ) @ ( times_times @ SV43 @ SY296 @ SY298 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(545,plain,
! [SV44: $i] :
( ( ! [SY299: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV44 ) @ ( bit1 @ SY299 ) )
| ( ord_less_eq @ int @ SV44 @ SY299 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV44 @ SY299 )
| ( ord_less @ int @ ( bit0 @ SV44 ) @ ( bit1 @ SY299 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(546,plain,
! [SV45: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV45 ) @ pls )
| ( ord_less @ int @ SV45 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SV45 @ pls )
| ( ord_less @ int @ ( bit0 @ SV45 ) @ pls ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(547,plain,
! [SV46: $i] :
( ( ~ ( comm_semiring_1 @ SV46 )
| ! [SY300: $i,SY301: $i,SY302: $i] :
( ( plus_plus @ SV46 @ SY300 @ ( plus_plus @ SV46 @ SY301 @ SY302 ) )
= ( plus_plus @ SV46 @ SY301 @ ( plus_plus @ SV46 @ SY300 @ SY302 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(548,plain,
! [SV47: $i] :
( ( ! [SY303: $i,SY304: $i] :
( ~ ( monoid_mult @ SY304 )
| ( ( ti @ SY304 @ ( power_power @ SY304 @ SV47 @ SY303 ) )
= ( power_power @ SY304 @ SV47 @ SY303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(549,plain,
! [SV48: $i] :
( ( ~ ( number_ring @ SV48 )
| ! [SY305: $i] :
( ( plus_plus @ SV48 @ ( number_number_of @ SV48 @ SY305 ) @ ( one_one @ SV48 ) )
= ( number_number_of @ SV48 @ ( plus_plus @ int @ SY305 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(550,plain,
! [SV49: $i] :
( ( ~ ( number_ring @ SV49 )
| ( ( plus_plus @ SV49 @ ( one_one @ SV49 ) @ ( one_one @ SV49 ) )
= ( number_number_of @ SV49 @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(551,plain,
! [SV50: $i] :
( ( ! [SY306: $i,SY307: $i] :
( ~ ( monoid_mult @ SY307 )
| ( ( power_power @ SY307 @ ( ti @ SY307 @ SV50 ) @ SY306 )
= ( power_power @ SY307 @ SV50 @ SY306 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(552,plain,
! [SV51: $i] :
( ( ~ ( number @ SV51 )
| ! [SY308: $i,SY309: $i] :
~ ( ~ ( ( ( number_number_of @ SV51 @ SY308 )
!= ( ti @ SV51 @ SY309 ) )
| ( ( ti @ SV51 @ SY309 )
= ( number_number_of @ SV51 @ SY308 ) ) )
| ~ ( ( ( ti @ SV51 @ SY309 )
!= ( number_number_of @ SV51 @ SY308 ) )
| ( ( number_number_of @ SV51 @ SY308 )
= ( ti @ SV51 @ SY309 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(553,plain,
! [SV52: $i] :
( ( ~ ~ ( ~ ( number_ring @ SV52 )
| ~ ( linordered_idom @ SV52 ) )
| ! [SY310: $i,SY311: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SY310 ) @ ( number_number_of @ SV52 @ SY311 ) )
| ( ord_less_eq @ int @ SY310 @ SY311 ) )
| ~ ( ~ ( ord_less_eq @ int @ SY310 @ SY311 )
| ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SY310 ) @ ( number_number_of @ SV52 @ SY311 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(554,plain,
! [SV53: $i] :
( ( ~ ( comm_semiring_1 @ SV53 )
| ! [SY312: $i,SY313: $i,SY314: $i] :
( ( times_times @ SV53 @ ( times_times @ SV53 @ SY312 @ SY313 ) @ SY314 )
= ( times_times @ SV53 @ ( times_times @ SV53 @ SY312 @ SY314 ) @ SY313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(555,plain,
( ( ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(556,plain,
! [SV54: $i] :
( ( ~ ( comm_semiring_1 @ SV54 )
| ! [SY315: $i,SY316: $i,SY317: $i] :
( ( plus_plus @ SV54 @ SY315 @ ( plus_plus @ SV54 @ SY316 @ SY317 ) )
= ( plus_plus @ SV54 @ ( plus_plus @ SV54 @ SY315 @ SY316 ) @ SY317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(557,plain,
! [SV55: $i] :
( ( ~ ( number_ring @ SV55 )
| ! [SY318: $i] :
( ( plus_plus @ SV55 @ ( one_one @ SV55 ) @ ( number_number_of @ SV55 @ SY318 ) )
= ( number_number_of @ SV55 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SY318 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(558,plain,
! [SV56: $i] :
( ( ! [SY319: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV56 ) @ ( bit1 @ SY319 ) )
| ( ord_less @ int @ SV56 @ SY319 ) )
| ~ ( ~ ( ord_less @ int @ SV56 @ SY319 )
| ( ord_less @ int @ ( bit1 @ SV56 ) @ ( bit1 @ SY319 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(559,plain,
! [SV57: $i] :
( ( ! [SY320: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SV57 @ ( one_one @ int ) ) @ SY320 )
| ( ord_less @ int @ SV57 @ SY320 ) )
| ~ ( ~ ( ord_less @ int @ SV57 @ SY320 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV57 @ ( one_one @ int ) ) @ SY320 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(560,plain,
! [SV58: $i] :
( ( ! [SY321: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SV58 @ SY321 )
| ~ ( ~ ( ord_less_eq @ int @ SV58 @ SY321 )
| ~ ( ( SV58 != SY321 ) ) ) )
| ~ ( ~ ~ ( ~ ( ord_less_eq @ int @ SV58 @ SY321 )
| ~ ( ( SV58 != SY321 ) ) )
| ( ord_less @ int @ SV58 @ SY321 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(561,plain,
! [SV59: $i] :
( ( ~ ( comm_semiring_1 @ SV59 )
| ! [SY322: $i,SY323: $i,SY324: $i,SY325: $i] :
( ( times_times @ SV59 @ ( times_times @ SV59 @ SY322 @ SY323 ) @ ( times_times @ SV59 @ SY324 @ SY325 ) )
= ( times_times @ SV59 @ SY324 @ ( times_times @ SV59 @ ( times_times @ SV59 @ SY322 @ SY323 ) @ SY325 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(562,plain,
! [SV60: $i] :
( ( ~ ( comm_semiring_1 @ SV60 )
| ! [SY326: $i,SY327: $i,SY328: $i] :
( ( times_times @ SV60 @ SY326 @ ( times_times @ SV60 @ SY327 @ SY328 ) )
= ( times_times @ SV60 @ SY327 @ ( times_times @ SV60 @ SY326 @ SY328 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(563,plain,
! [SV61: $i] :
( ( ~ ( comm_semiring_1 @ SV61 )
| ! [SY329: $i,SY330: $i] :
( ( plus_plus @ SV61 @ SY329 @ SY330 )
= ( plus_plus @ SV61 @ SY330 @ SY329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(564,plain,
! [SV62: $i] :
( ( ~ ( comm_semiring_1 @ SV62 )
| ! [SY331: $i,SY332: $i,SY333: $i] :
( ( times_times @ SV62 @ SY331 @ ( times_times @ SV62 @ SY332 @ SY333 ) )
= ( times_times @ SV62 @ ( times_times @ SV62 @ SY331 @ SY332 ) @ SY333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(565,plain,
! [SV63: $i] :
( ( ~ ( ~ ( ~ ( zprime @ ( ti @ int @ SV63 ) )
| ( zprime @ SV63 ) )
| ~ ( ~ ( zprime @ SV63 )
| ( zprime @ ( ti @ int @ SV63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(566,plain,
! [SV64: $i] :
( ( ! [SY334: $i] :
( ~ ( ord_less @ int @ SV64 @ SY334 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV64 @ ( one_one @ int ) ) @ SY334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(567,plain,
! [SV65: $i] :
( ( ~ ( comm_semiring_1 @ SV65 )
| ! [SY335: $i,SY336: $i] :
( ( times_times @ SV65 @ SY335 @ SY336 )
= ( times_times @ SV65 @ SY336 @ SY335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(568,plain,
! [SV66: $i] :
( ( ! [SY337: $i] :
~ ( ~ ( ( ( bit0 @ SV66 )
!= ( bit0 @ SY337 ) )
| ( SV66 = SY337 ) )
| ~ ( ( SV66 != SY337 )
| ( ( bit0 @ SV66 )
= ( bit0 @ SY337 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(569,plain,
! [SV67: $i] :
( ( ! [SY338: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV67 ) @ ( bit0 @ SY338 ) )
| ( ord_less_eq @ int @ SV67 @ SY338 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV67 @ SY338 )
| ( ord_less_eq @ int @ ( bit0 @ SV67 ) @ ( bit0 @ SY338 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(570,plain,
! [SV68: $i] :
( ( ! [SY339: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV68 ) @ ( bit1 @ SY339 ) )
| ( ord_less_eq @ int @ SV68 @ SY339 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV68 @ SY339 )
| ( ord_less_eq @ int @ ( bit1 @ SV68 ) @ ( bit1 @ SY339 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(571,plain,
! [SV69: $i] :
( ( ~ ( semiring_1 @ SV69 )
| ( ( power_power @ SV69 @ ( one_one @ SV69 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(572,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)],[466]) ).
thf(573,plain,
! [SV70: $i] :
( ( ! [SY340: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV70 ) @ ( bit0 @ SY340 ) )
| ( ord_less @ int @ SV70 @ SY340 ) )
| ~ ( ~ ( ord_less @ int @ SV70 @ SY340 )
| ( ord_less @ int @ ( bit0 @ SV70 ) @ ( bit0 @ SY340 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(574,plain,
! [SV71: $i] :
( ( ! [SY341: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV71 ) @ ( bit1 @ SY341 ) )
| ( ord_less @ int @ SV71 @ SY341 ) )
| ~ ( ~ ( ord_less @ int @ SV71 @ SY341 )
| ( ord_less @ int @ ( bit1 @ SV71 ) @ ( bit1 @ SY341 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(575,plain,
! [SV72: $i] :
( ( ~ ~ ( ~ ( number_ring @ SV72 )
| ~ ( linordered_idom @ SV72 ) )
| ! [SY342: $i,SY343: $i] :
~ ( ~ ( ~ ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SY342 ) @ ( number_number_of @ SV72 @ SY343 ) )
| ( ord_less @ int @ SY342 @ SY343 ) )
| ~ ( ~ ( ord_less @ int @ SY342 @ SY343 )
| ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SY342 ) @ ( number_number_of @ SV72 @ SY343 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(576,plain,
! [SV73: $i] :
( ( ~ ( comm_semiring_1 @ SV73 )
| ! [SY344: $i,SY345: $i,SY346: $i,SY347: $i] :
( ( plus_plus @ SV73 @ ( plus_plus @ SV73 @ SY344 @ SY345 ) @ ( plus_plus @ SV73 @ SY346 @ SY347 ) )
= ( plus_plus @ SV73 @ ( plus_plus @ SV73 @ SY344 @ SY346 ) @ ( plus_plus @ SV73 @ SY345 @ SY347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(577,plain,
! [SV74: $i] :
( ( ! [SY348: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV74 ) @ ( bit0 @ SY348 ) )
| ( ord_less @ int @ SV74 @ SY348 ) )
| ~ ( ~ ( ord_less @ int @ SV74 @ SY348 )
| ( ord_less @ int @ ( bit0 @ SV74 ) @ ( bit0 @ SY348 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(578,plain,
! [SV75: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV75 ) @ pls )
| ( ord_less @ int @ SV75 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SV75 @ pls )
| ( ord_less_eq @ int @ ( bit1 @ SV75 ) @ pls ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(579,plain,
( ( ( t
!= ( one_one @ int ) )
= $true )
| ( ( ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(580,plain,
! [SV76: $i] :
( ( ! [SY349: $i] :
( ~ ( twoSqu33214720sum2sq @ SY349 )
| ~ ( twoSqu33214720sum2sq @ SV76 )
| ( twoSqu33214720sum2sq @ ( times_times @ int @ SY349 @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(581,plain,
! [SV77: $i] :
( ( ! [SY350: $i,SY351: $i] :
( ~ ( monoid_mult @ SY351 )
| ( ( times_times @ SY351 @ SV77 @ ( ti @ SY351 @ SY350 ) )
= ( times_times @ SY351 @ SV77 @ SY350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(582,plain,
! [SV78: $i] :
( ( ! [SY352: $i,SY353: $i,SY354: $i] :
( ~ ( ord_less @ int @ SY353 @ SY354 )
| ~ ( ord_less_eq @ int @ SV78 @ SY352 )
| ( ord_less @ int @ ( plus_plus @ int @ SY353 @ SV78 ) @ ( plus_plus @ int @ SY354 @ SY352 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(583,plain,
! [SV79: $i] :
( ( ~ ( comm_semiring_1 @ SV79 )
| ! [SY355: $i,SY356: $i,SY357: $i] :
( ( times_times @ SV79 @ ( times_times @ SV79 @ SY355 @ SY356 ) @ SY357 )
= ( times_times @ SV79 @ SY355 @ ( times_times @ SV79 @ SY356 @ SY357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(584,plain,
! [SV80: $i] :
( ( ! [SY358: $i] :
( ~ ( number @ SY358 )
| ( ( number_number_of @ SY358 @ ( ti @ int @ SV80 ) )
= ( number_number_of @ SY358 @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(585,plain,
! [SV81: $i] :
( ( ~ ( comm_semiring_1 @ SV81 )
| ! [SY359: $i] :
( ( times_times @ SV81 @ SY359 @ SY359 )
= ( power_power @ SV81 @ SY359 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(586,plain,
! [SV82: $i] :
( ( ! [SY360: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV82 ) @ ( bit1 @ SY360 ) )
| ( ord_less_eq @ int @ SV82 @ SY360 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV82 @ SY360 )
| ( ord_less_eq @ int @ ( bit0 @ SV82 ) @ ( bit1 @ SY360 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(587,plain,
! [SV83: $i] :
( ( ! [SY361: $i,SY362: $i] :
( ~ ( monoid_mult @ SY362 )
| ( ( ti @ SY362 @ ( times_times @ SY362 @ SV83 @ SY361 ) )
= ( times_times @ SY362 @ SV83 @ SY361 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(588,plain,
! [SV84: $i] :
( ( ~ ( semiring_1 @ SV84 )
| ( ( ti @ SV84 @ ( one_one @ SV84 ) )
= ( one_one @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(589,plain,
! [SV85: $i] :
( ( ~ ( comm_semiring_1 @ SV85 )
| ! [SY363: $i,SY364: $i] :
( ( power_power @ SV85 @ SY363 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY364 ) )
= ( times_times @ SV85 @ ( power_power @ SV85 @ SY363 @ SY364 ) @ ( power_power @ SV85 @ SY363 @ SY364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(590,plain,
! [SV86: $i] :
( ( ! [SY365: $i] :
~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV86 ) @ ( bit0 @ SY365 ) )
| ( ord_less @ int @ SV86 @ SY365 ) )
| ~ ( ~ ( ord_less @ int @ SV86 @ SY365 )
| ( ord_less_eq @ int @ ( bit1 @ SV86 ) @ ( bit0 @ SY365 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(591,plain,
! [SV87: $i] :
( ( ! [SY366: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SV87 @ ( plus_plus @ int @ SY366 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ SV87 @ SY366 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV87 @ SY366 )
| ( ord_less @ int @ SV87 @ ( plus_plus @ int @ SY366 @ ( one_one @ int ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(592,plain,
! [SV88: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ pls @ ( bit0 @ SV88 ) )
| ( ord_less @ int @ pls @ SV88 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SV88 )
| ( ord_less @ int @ pls @ ( bit0 @ SV88 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(593,plain,
! [SV89: $i] :
( ( ~ ( comm_semiring_1 @ SV89 )
| ! [SY367: $i,SY368: $i,SY369: $i] :
( ( times_times @ SV89 @ ( power_power @ SV89 @ SY367 @ SY368 ) @ ( power_power @ SV89 @ SY367 @ SY369 ) )
= ( power_power @ SV89 @ SY367 @ ( plus_plus @ nat @ SY368 @ SY369 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(594,plain,
! [SV90: $i] :
( ( ! [SY370: $i,SY371: $i] :
( ~ ( comm_semiring_1 @ SY371 )
| ( ( ti @ SY371 @ ( plus_plus @ SY371 @ SV90 @ SY370 ) )
= ( plus_plus @ SY371 @ SV90 @ SY370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(595,plain,
! [SV91: $i] :
( ( ~ ~ ( ~ ( number_ring @ SV91 )
| ~ ( ring_char_0 @ SV91 ) )
| ! [SY372: $i,SY373: $i] :
~ ( ~ ( ( ( number_number_of @ SV91 @ SY372 )
!= ( number_number_of @ SV91 @ SY373 ) )
| ( SY372 = SY373 ) )
| ~ ( ( SY372 != SY373 )
| ( ( number_number_of @ SV91 @ SY372 )
= ( number_number_of @ SV91 @ SY373 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(596,plain,
! [SV92: $i] :
( ( ! [SY374: $i] :
~ ( ~ ( ~ ( ord_less @ int @ SY374 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SY374 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ SV92 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SY374 @ pls )
| ~ ( ~ ( ~ ( ord_less @ int @ SV92 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SY374 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ SY374 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV92 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SY374 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SY374 @ SV92 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(597,plain,
! [SV93: $i] :
( ( ~ ( comm_semiring_1 @ SV93 )
| ! [SY375: $i,SY376: $i,SY377: $i] :
( ( power_power @ SV93 @ ( power_power @ SV93 @ SY375 @ SY376 ) @ SY377 )
= ( power_power @ SV93 @ SY375 @ ( times_times @ nat @ SY376 @ SY377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(598,plain,
! [SV94: $i] :
( ( ! [SY378: $i] :
( ~ ( number @ SY378 )
| ( ( ti @ SY378 @ ( number_number_of @ SY378 @ SV94 ) )
= ( number_number_of @ SY378 @ SV94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(599,plain,
! [SV95: $i] :
( ( ! [SY379: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV95 ) @ ( number_number_of @ int @ SY379 ) )
| ( ord_less @ int @ SV95 @ SY379 ) )
| ~ ( ~ ( ord_less @ int @ SV95 @ SY379 )
| ( ord_less @ int @ ( number_number_of @ int @ SV95 ) @ ( number_number_of @ int @ SY379 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(600,plain,
! [SV96: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV96 ) @ pls )
| ( ord_less @ int @ SV96 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SV96 @ pls )
| ( ord_less @ int @ ( bit1 @ SV96 ) @ pls ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(601,plain,
! [SV97: $i] :
( ( ! [SY380: $i] :
~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV97 ) @ ( bit0 @ SY380 ) )
| ( ord_less @ int @ SV97 @ SY380 ) )
| ~ ( ~ ( ord_less @ int @ SV97 @ SY380 )
| ( ord_less @ int @ ( bit1 @ SV97 ) @ ( bit0 @ SY380 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(602,plain,
! [SV98: $i] :
( ( ! [SY381: $i,SY382: $i] :
( ~ ( ord_less_eq @ int @ SY381 @ SY382 )
| ~ ( ord_less_eq @ int @ SY382 @ SV98 )
| ( ord_less_eq @ int @ SY381 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(603,plain,
! [SV99: $i] :
( ( ! [SY383: $i,SY384: $i] :
( ~ ( monoid_mult @ SY384 )
| ( ( power_power @ SY384 @ SV99 @ ( ti @ nat @ SY383 ) )
= ( power_power @ SY384 @ SV99 @ SY383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(604,plain,
! [SV100: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ pls @ ( bit1 @ SV100 ) )
| ( ord_less_eq @ int @ pls @ SV100 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SV100 )
| ( ord_less @ int @ pls @ ( bit1 @ SV100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(605,plain,
! [SV101: $i] :
( ( ~ ( comm_semiring_1 @ SV101 )
| ! [SY385: $i,SY386: $i,SY387: $i] :
( ( plus_plus @ SV101 @ ( plus_plus @ SV101 @ SY385 @ SY386 ) @ SY387 )
= ( plus_plus @ SV101 @ SY385 @ ( plus_plus @ SV101 @ SY386 @ SY387 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(606,plain,
! [SV102: $i,SV5: $i] :
( ( ( power_power @ int @ ( plus_plus @ int @ SV5 @ SV102 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ SV5 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV5 ) @ SV102 ) ) @ ( power_power @ int @ SV102 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(607,plain,
! [SV103: $i,SV6: $i] :
( ( ( power_power @ int @ ( plus_plus @ int @ SV6 @ SV103 ) @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ SV6 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power @ int @ SV6 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ SV103 ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ SV6 ) @ ( power_power @ int @ SV103 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power @ int @ SV103 @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(608,plain,
! [SV104: $i,SV9: $i] :
( ( ( ord_less_eq @ int @ SV9 @ SV104 )
| ( ord_less_eq @ int @ SV104 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(609,plain,
! [SV105: $i,SV10: $i] :
( ( ( ord_less @ int @ SV10 @ SV105 )
| ( SV10 = SV105 )
| ( ord_less @ int @ SV105 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(610,plain,
! [SV106: $i,SV11: $i] :
( ( ! [SY388: $i] :
( ( power_power @ int @ ( power_power @ int @ SV11 @ SV106 ) @ SY388 )
= ( power_power @ int @ SV11 @ ( times_times @ nat @ SV106 @ SY388 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(611,plain,
! [SV107: $i,SV12: $i] :
( ( ! [SY389: $i] :
( ( power_power @ int @ SV12 @ ( plus_plus @ nat @ SV107 @ SY389 ) )
= ( times_times @ int @ ( power_power @ int @ SV12 @ SV107 ) @ ( power_power @ int @ SV12 @ SY389 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(612,plain,
! [SV108: $i,SV15: $i] :
( ( ! [SY390: $i] :
( ( times_times @ int @ ( times_times @ int @ SV15 @ SV108 ) @ SY390 )
= ( times_times @ int @ SV15 @ ( times_times @ int @ SV108 @ SY390 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(613,plain,
! [SV109: $i,SV16: $i] :
( ( ( times_times @ int @ SV16 @ SV109 )
= ( times_times @ int @ SV109 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(614,plain,
! [SV110: $i,SV18: $i] :
( ( ! [SY391: $i] :
( ( plus_plus @ int @ ( plus_plus @ int @ SV18 @ SV110 ) @ SY391 )
= ( plus_plus @ int @ SV18 @ ( plus_plus @ int @ SV110 @ SY391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(615,plain,
! [SV111: $i,SV19: $i] :
( ( ! [SY392: $i] :
( ( plus_plus @ int @ SV19 @ ( plus_plus @ int @ SV111 @ SY392 ) )
= ( plus_plus @ int @ SV111 @ ( plus_plus @ int @ SV19 @ SY392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(616,plain,
! [SV112: $i,SV20: $i] :
( ( ( plus_plus @ int @ SV20 @ SV112 )
= ( plus_plus @ int @ SV112 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(617,plain,
! [SV113: $i,SV21: $i] :
( ( ! [SY393: $i] :
( ~ ( comm_semiring_1 @ SY393 )
| ( ( plus_plus @ SY393 @ ( ti @ SY393 @ SV21 ) @ SV113 )
= ( plus_plus @ SY393 @ SV21 @ SV113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(618,plain,
! [SV114: $i,SV22: $i] :
( ( ! [SY394: $i] :
( ~ ( monoid_mult @ SY394 )
| ( ( times_times @ SY394 @ ( ti @ SY394 @ SV22 ) @ SV114 )
= ( times_times @ SY394 @ SV22 @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(619,plain,
! [SV115: $i,SV23: $i] :
( ( ~ ( ord_less_eq @ int @ SV23 @ SV115 )
| ~ ( ord_less_eq @ int @ SV115 @ SV23 )
| ( SV23 = SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(620,plain,
! [SV24: $i] :
( ( ( ~ ( number_semiring @ SV24 ) )
= $true )
| ( ( ! [SY269: $i,SY270: $i] :
( ( power_power @ SV24 @ ( plus_plus @ SV24 @ SY269 @ SY270 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ SV24 @ ( plus_plus @ SV24 @ ( power_power @ SV24 @ SY269 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV24 @ SY270 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ SV24 @ ( times_times @ SV24 @ ( number_number_of @ SV24 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY269 ) @ SY270 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[524]) ).
thf(621,plain,
! [SV116: $i,SV25: $i] :
( ( ~ ( ~ ( ( ( bit1 @ SV25 )
!= ( bit1 @ SV116 ) )
| ( SV25 = SV116 ) )
| ~ ( ( SV25 != SV116 )
| ( ( bit1 @ SV25 )
= ( bit1 @ SV116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(622,plain,
( ( ( ord_less @ int @ ( one_one @ int ) @ t )
= $false )
| ( ( ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(623,plain,
! [SV26: $i] :
( ( ( ~ ( monoid_mult @ SV26 ) )
= $true )
| ( ( ! [SY272: $i] :
( ( power_power @ SV26 @ SY272 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV26 @ SY272 @ SY272 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(624,plain,
! [SV117: $i,SV27: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV27 ) @ ( bit0 @ SV117 ) )
| ( ord_less_eq @ int @ SV27 @ SV117 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV27 @ SV117 )
| ( ord_less_eq @ int @ ( bit0 @ SV27 ) @ ( bit0 @ SV117 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(625,plain,
! [SV28: $i] :
( ( ( ~ ~ ( ~ ( monoid_mult @ SV28 )
| ~ ( number @ SV28 ) ) )
= $true )
| ( ( ! [SY274: $i] :
( ( power_power @ SV28 @ ( number_number_of @ SV28 @ SY274 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV28 @ ( number_number_of @ SV28 @ SY274 ) @ ( number_number_of @ SV28 @ SY274 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[529]) ).
thf(626,plain,
! [SV29: $i] :
( ( ~ ( ~ ( twoSqu33214720sum2sq @ ( ti @ int @ SV29 ) )
| ( twoSqu33214720sum2sq @ SV29 ) )
| ~ ( ~ ( twoSqu33214720sum2sq @ SV29 )
| ( twoSqu33214720sum2sq @ ( ti @ int @ SV29 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(627,plain,
! [SV118: $i,SV30: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV30 ) @ ( bit1 @ SV118 ) )
| ( ord_less_eq @ int @ SV30 @ SV118 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV30 @ SV118 )
| ( ord_less @ int @ ( bit0 @ SV30 ) @ ( bit1 @ SV118 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(628,plain,
! [SV119: $i,SV31: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV31 ) @ ( bit0 @ SV119 ) )
| ( ord_less @ int @ SV31 @ SV119 ) )
| ~ ( ~ ( ord_less @ int @ SV31 @ SV119 )
| ( ord_less @ int @ ( bit1 @ SV31 ) @ ( bit0 @ SV119 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(629,plain,
! [SV32: $i,SV120: $i] :
( ( ! [SY395: $i] :
( ~ ( ord_less @ int @ SV120 @ SY395 )
| ( ord_less @ int @ ( plus_plus @ int @ SV120 @ SV32 ) @ ( plus_plus @ int @ SY395 @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(630,plain,
! [SV33: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ SV33 ) )
| ( ord_less_eq @ int @ pls @ SV33 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SV33 )
| ( ord_less_eq @ int @ pls @ ( bit1 @ SV33 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(631,plain,
! [SV121: $i,SV34: $i] :
( ( ! [SY396: $i] :
( ~ ( comm_semiring_1 @ SY396 )
| ( ( plus_plus @ SY396 @ SV34 @ ( ti @ SY396 @ SV121 ) )
= ( plus_plus @ SY396 @ SV34 @ SV121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(632,plain,
! [SV122: $i,SV35: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV35 ) @ ( bit1 @ SV122 ) )
| ( ord_less_eq @ int @ SV35 @ SV122 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV35 @ SV122 )
| ( ord_less_eq @ int @ ( bit1 @ SV35 ) @ ( bit1 @ SV122 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(633,plain,
! [SV36: $i] :
( ( ( ~ ( comm_semiring_1 @ SV36 ) )
= $true )
| ( ( ! [SY282: $i,SY283: $i,SY284: $i,SY285: $i] :
( ( times_times @ SV36 @ ( times_times @ SV36 @ SY282 @ SY283 ) @ ( times_times @ SV36 @ SY284 @ SY285 ) )
= ( times_times @ SV36 @ SY282 @ ( times_times @ SV36 @ SY283 @ ( times_times @ SV36 @ SY284 @ SY285 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[537]) ).
thf(634,plain,
! [SV37: $i] :
( ( ( ~ ( comm_semiring_1 @ SV37 ) )
= $true )
| ( ( ! [SY286: $i,SY287: $i,SY288: $i] :
( ( plus_plus @ SV37 @ ( plus_plus @ SV37 @ SY286 @ SY287 ) @ SY288 )
= ( plus_plus @ SV37 @ ( plus_plus @ SV37 @ SY286 @ SY288 ) @ SY287 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[538]) ).
thf(635,plain,
! [SV123: $i,SV38: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit0 @ SV123 ) )
| ( ord_less @ int @ SV38 @ SV123 ) )
| ~ ( ~ ( ord_less @ int @ SV38 @ SV123 )
| ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit0 @ SV123 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(636,plain,
! [SV124: $i,SV39: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV39 ) @ ( bit1 @ SV124 ) )
| ( ord_less_eq @ int @ SV39 @ SV124 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV39 @ SV124 )
| ( ord_less_eq @ int @ ( bit0 @ SV39 ) @ ( bit1 @ SV124 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(637,plain,
! [SV40: $i,SV125: $i] :
( ( ! [SY397: $i] :
( ~ ( ord_less_eq @ int @ SV125 @ SY397 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV40 @ SV125 ) @ ( plus_plus @ int @ SV40 @ SY397 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(638,plain,
! [SV126: $i,SV41: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV126 ) )
| ( ord_less_eq @ int @ SV41 @ SV126 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV41 @ SV126 )
| ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV126 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(639,plain,
! [SV42: $i] :
( ( ( ~ ( comm_semiring_1 @ SV42 ) )
= $true )
| ( ( ! [SY294: $i] :
( ( power_power @ SV42 @ SY294 @ ( one_one @ nat ) )
= ( ti @ SV42 @ SY294 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(640,plain,
! [SV43: $i] :
( ( ( ~ ( comm_semiring_1 @ SV43 ) )
= $true )
| ( ( ! [SY295: $i,SY296: $i,SY297: $i,SY298: $i] :
( ( times_times @ SV43 @ ( times_times @ SV43 @ SY295 @ SY296 ) @ ( times_times @ SV43 @ SY297 @ SY298 ) )
= ( times_times @ SV43 @ ( times_times @ SV43 @ SY295 @ SY297 ) @ ( times_times @ SV43 @ SY296 @ SY298 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[544]) ).
thf(641,plain,
! [SV127: $i,SV44: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV44 ) @ ( bit1 @ SV127 ) )
| ( ord_less_eq @ int @ SV44 @ SV127 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV44 @ SV127 )
| ( ord_less @ int @ ( bit0 @ SV44 ) @ ( bit1 @ SV127 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(642,plain,
! [SV45: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV45 ) @ pls )
| ( ord_less @ int @ SV45 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SV45 @ pls )
| ( ord_less @ int @ ( bit0 @ SV45 ) @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(643,plain,
! [SV46: $i] :
( ( ( ~ ( comm_semiring_1 @ SV46 ) )
= $true )
| ( ( ! [SY300: $i,SY301: $i,SY302: $i] :
( ( plus_plus @ SV46 @ SY300 @ ( plus_plus @ SV46 @ SY301 @ SY302 ) )
= ( plus_plus @ SV46 @ SY301 @ ( plus_plus @ SV46 @ SY300 @ SY302 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[547]) ).
thf(644,plain,
! [SV128: $i,SV47: $i] :
( ( ! [SY398: $i] :
( ~ ( monoid_mult @ SY398 )
| ( ( ti @ SY398 @ ( power_power @ SY398 @ SV47 @ SV128 ) )
= ( power_power @ SY398 @ SV47 @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(645,plain,
! [SV48: $i] :
( ( ( ~ ( number_ring @ SV48 ) )
= $true )
| ( ( ! [SY305: $i] :
( ( plus_plus @ SV48 @ ( number_number_of @ SV48 @ SY305 ) @ ( one_one @ SV48 ) )
= ( number_number_of @ SV48 @ ( plus_plus @ int @ SY305 @ ( bit1 @ pls ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[549]) ).
thf(646,plain,
! [SV49: $i] :
( ( ( ~ ( number_ring @ SV49 ) )
= $true )
| ( ( ( plus_plus @ SV49 @ ( one_one @ SV49 ) @ ( one_one @ SV49 ) )
= ( number_number_of @ SV49 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[550]) ).
thf(647,plain,
! [SV129: $i,SV50: $i] :
( ( ! [SY399: $i] :
( ~ ( monoid_mult @ SY399 )
| ( ( power_power @ SY399 @ ( ti @ SY399 @ SV50 ) @ SV129 )
= ( power_power @ SY399 @ SV50 @ SV129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(648,plain,
! [SV51: $i] :
( ( ( ~ ( number @ SV51 ) )
= $true )
| ( ( ! [SY308: $i,SY309: $i] :
~ ( ~ ( ( ( number_number_of @ SV51 @ SY308 )
!= ( ti @ SV51 @ SY309 ) )
| ( ( ti @ SV51 @ SY309 )
= ( number_number_of @ SV51 @ SY308 ) ) )
| ~ ( ( ( ti @ SV51 @ SY309 )
!= ( number_number_of @ SV51 @ SY308 ) )
| ( ( number_number_of @ SV51 @ SY308 )
= ( ti @ SV51 @ SY309 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[552]) ).
thf(649,plain,
! [SV52: $i] :
( ( ( ~ ~ ( ~ ( number_ring @ SV52 )
| ~ ( linordered_idom @ SV52 ) ) )
= $true )
| ( ( ! [SY310: $i,SY311: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SY310 ) @ ( number_number_of @ SV52 @ SY311 ) )
| ( ord_less_eq @ int @ SY310 @ SY311 ) )
| ~ ( ~ ( ord_less_eq @ int @ SY310 @ SY311 )
| ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SY310 ) @ ( number_number_of @ SV52 @ SY311 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(650,plain,
! [SV53: $i] :
( ( ( ~ ( comm_semiring_1 @ SV53 ) )
= $true )
| ( ( ! [SY312: $i,SY313: $i,SY314: $i] :
( ( times_times @ SV53 @ ( times_times @ SV53 @ SY312 @ SY313 ) @ SY314 )
= ( times_times @ SV53 @ ( times_times @ SV53 @ SY312 @ SY314 ) @ SY313 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(651,plain,
( ( ! [SX0: $i] :
~ ~ ! [SX1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[555]) ).
thf(652,plain,
! [SV54: $i] :
( ( ( ~ ( comm_semiring_1 @ SV54 ) )
= $true )
| ( ( ! [SY315: $i,SY316: $i,SY317: $i] :
( ( plus_plus @ SV54 @ SY315 @ ( plus_plus @ SV54 @ SY316 @ SY317 ) )
= ( plus_plus @ SV54 @ ( plus_plus @ SV54 @ SY315 @ SY316 ) @ SY317 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(653,plain,
! [SV55: $i] :
( ( ( ~ ( number_ring @ SV55 ) )
= $true )
| ( ( ! [SY318: $i] :
( ( plus_plus @ SV55 @ ( one_one @ SV55 ) @ ( number_number_of @ SV55 @ SY318 ) )
= ( number_number_of @ SV55 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SY318 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(654,plain,
! [SV130: $i,SV56: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV56 ) @ ( bit1 @ SV130 ) )
| ( ord_less @ int @ SV56 @ SV130 ) )
| ~ ( ~ ( ord_less @ int @ SV56 @ SV130 )
| ( ord_less @ int @ ( bit1 @ SV56 ) @ ( bit1 @ SV130 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(655,plain,
! [SV131: $i,SV57: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SV57 @ ( one_one @ int ) ) @ SV131 )
| ( ord_less @ int @ SV57 @ SV131 ) )
| ~ ( ~ ( ord_less @ int @ SV57 @ SV131 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV57 @ ( one_one @ int ) ) @ SV131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(656,plain,
! [SV132: $i,SV58: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ SV58 @ SV132 )
| ~ ( ~ ( ord_less_eq @ int @ SV58 @ SV132 )
| ~ ( ( SV58 != SV132 ) ) ) )
| ~ ( ~ ~ ( ~ ( ord_less_eq @ int @ SV58 @ SV132 )
| ~ ( ( SV58 != SV132 ) ) )
| ( ord_less @ int @ SV58 @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(657,plain,
! [SV59: $i] :
( ( ( ~ ( comm_semiring_1 @ SV59 ) )
= $true )
| ( ( ! [SY322: $i,SY323: $i,SY324: $i,SY325: $i] :
( ( times_times @ SV59 @ ( times_times @ SV59 @ SY322 @ SY323 ) @ ( times_times @ SV59 @ SY324 @ SY325 ) )
= ( times_times @ SV59 @ SY324 @ ( times_times @ SV59 @ ( times_times @ SV59 @ SY322 @ SY323 ) @ SY325 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[561]) ).
thf(658,plain,
! [SV60: $i] :
( ( ( ~ ( comm_semiring_1 @ SV60 ) )
= $true )
| ( ( ! [SY326: $i,SY327: $i,SY328: $i] :
( ( times_times @ SV60 @ SY326 @ ( times_times @ SV60 @ SY327 @ SY328 ) )
= ( times_times @ SV60 @ SY327 @ ( times_times @ SV60 @ SY326 @ SY328 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(659,plain,
! [SV61: $i] :
( ( ( ~ ( comm_semiring_1 @ SV61 ) )
= $true )
| ( ( ! [SY329: $i,SY330: $i] :
( ( plus_plus @ SV61 @ SY329 @ SY330 )
= ( plus_plus @ SV61 @ SY330 @ SY329 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[563]) ).
thf(660,plain,
! [SV62: $i] :
( ( ( ~ ( comm_semiring_1 @ SV62 ) )
= $true )
| ( ( ! [SY331: $i,SY332: $i,SY333: $i] :
( ( times_times @ SV62 @ SY331 @ ( times_times @ SV62 @ SY332 @ SY333 ) )
= ( times_times @ SV62 @ ( times_times @ SV62 @ SY331 @ SY332 ) @ SY333 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[564]) ).
thf(661,plain,
! [SV63: $i] :
( ( ~ ( ~ ( zprime @ ( ti @ int @ SV63 ) )
| ( zprime @ SV63 ) )
| ~ ( ~ ( zprime @ SV63 )
| ( zprime @ ( ti @ int @ SV63 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(662,plain,
! [SV133: $i,SV64: $i] :
( ( ~ ( ord_less @ int @ SV64 @ SV133 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV64 @ ( one_one @ int ) ) @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(663,plain,
! [SV65: $i] :
( ( ( ~ ( comm_semiring_1 @ SV65 ) )
= $true )
| ( ( ! [SY335: $i,SY336: $i] :
( ( times_times @ SV65 @ SY335 @ SY336 )
= ( times_times @ SV65 @ SY336 @ SY335 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[567]) ).
thf(664,plain,
! [SV134: $i,SV66: $i] :
( ( ~ ( ~ ( ( ( bit0 @ SV66 )
!= ( bit0 @ SV134 ) )
| ( SV66 = SV134 ) )
| ~ ( ( SV66 != SV134 )
| ( ( bit0 @ SV66 )
= ( bit0 @ SV134 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(665,plain,
! [SV135: $i,SV67: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV67 ) @ ( bit0 @ SV135 ) )
| ( ord_less_eq @ int @ SV67 @ SV135 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV67 @ SV135 )
| ( ord_less_eq @ int @ ( bit0 @ SV67 ) @ ( bit0 @ SV135 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(666,plain,
! [SV136: $i,SV68: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV68 ) @ ( bit1 @ SV136 ) )
| ( ord_less_eq @ int @ SV68 @ SV136 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV68 @ SV136 )
| ( ord_less_eq @ int @ ( bit1 @ SV68 ) @ ( bit1 @ SV136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(667,plain,
! [SV69: $i] :
( ( ( ~ ( semiring_1 @ SV69 ) )
= $true )
| ( ( ( power_power @ SV69 @ ( one_one @ SV69 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(668,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)],[572]) ).
thf(669,plain,
! [SV137: $i,SV70: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV70 ) @ ( bit0 @ SV137 ) )
| ( ord_less @ int @ SV70 @ SV137 ) )
| ~ ( ~ ( ord_less @ int @ SV70 @ SV137 )
| ( ord_less @ int @ ( bit0 @ SV70 ) @ ( bit0 @ SV137 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(670,plain,
! [SV138: $i,SV71: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV71 ) @ ( bit1 @ SV138 ) )
| ( ord_less @ int @ SV71 @ SV138 ) )
| ~ ( ~ ( ord_less @ int @ SV71 @ SV138 )
| ( ord_less @ int @ ( bit1 @ SV71 ) @ ( bit1 @ SV138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(671,plain,
! [SV72: $i] :
( ( ( ~ ~ ( ~ ( number_ring @ SV72 )
| ~ ( linordered_idom @ SV72 ) ) )
= $true )
| ( ( ! [SY342: $i,SY343: $i] :
~ ( ~ ( ~ ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SY342 ) @ ( number_number_of @ SV72 @ SY343 ) )
| ( ord_less @ int @ SY342 @ SY343 ) )
| ~ ( ~ ( ord_less @ int @ SY342 @ SY343 )
| ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SY342 ) @ ( number_number_of @ SV72 @ SY343 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[575]) ).
thf(672,plain,
! [SV73: $i] :
( ( ( ~ ( comm_semiring_1 @ SV73 ) )
= $true )
| ( ( ! [SY344: $i,SY345: $i,SY346: $i,SY347: $i] :
( ( plus_plus @ SV73 @ ( plus_plus @ SV73 @ SY344 @ SY345 ) @ ( plus_plus @ SV73 @ SY346 @ SY347 ) )
= ( plus_plus @ SV73 @ ( plus_plus @ SV73 @ SY344 @ SY346 ) @ ( plus_plus @ SV73 @ SY345 @ SY347 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[576]) ).
thf(673,plain,
! [SV139: $i,SV74: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV74 ) @ ( bit0 @ SV139 ) )
| ( ord_less @ int @ SV74 @ SV139 ) )
| ~ ( ~ ( ord_less @ int @ SV74 @ SV139 )
| ( ord_less @ int @ ( bit0 @ SV74 ) @ ( bit0 @ SV139 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(674,plain,
! [SV75: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV75 ) @ pls )
| ( ord_less @ int @ SV75 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SV75 @ pls )
| ( ord_less_eq @ int @ ( bit1 @ SV75 ) @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(675,plain,
( ( ( t
= ( one_one @ int ) )
= $false )
| ( ( ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(676,plain,
! [SV76: $i,SV140: $i] :
( ( ~ ( twoSqu33214720sum2sq @ SV140 )
| ~ ( twoSqu33214720sum2sq @ SV76 )
| ( twoSqu33214720sum2sq @ ( times_times @ int @ SV140 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(677,plain,
! [SV141: $i,SV77: $i] :
( ( ! [SY400: $i] :
( ~ ( monoid_mult @ SY400 )
| ( ( times_times @ SY400 @ SV77 @ ( ti @ SY400 @ SV141 ) )
= ( times_times @ SY400 @ SV77 @ SV141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(678,plain,
! [SV142: $i,SV78: $i] :
( ( ! [SY401: $i,SY402: $i] :
( ~ ( ord_less @ int @ SY401 @ SY402 )
| ~ ( ord_less_eq @ int @ SV78 @ SV142 )
| ( ord_less @ int @ ( plus_plus @ int @ SY401 @ SV78 ) @ ( plus_plus @ int @ SY402 @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(679,plain,
! [SV79: $i] :
( ( ( ~ ( comm_semiring_1 @ SV79 ) )
= $true )
| ( ( ! [SY355: $i,SY356: $i,SY357: $i] :
( ( times_times @ SV79 @ ( times_times @ SV79 @ SY355 @ SY356 ) @ SY357 )
= ( times_times @ SV79 @ SY355 @ ( times_times @ SV79 @ SY356 @ SY357 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[583]) ).
thf(680,plain,
! [SV80: $i,SV143: $i] :
( ( ~ ( number @ SV143 )
| ( ( number_number_of @ SV143 @ ( ti @ int @ SV80 ) )
= ( number_number_of @ SV143 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(681,plain,
! [SV81: $i] :
( ( ( ~ ( comm_semiring_1 @ SV81 ) )
= $true )
| ( ( ! [SY359: $i] :
( ( times_times @ SV81 @ SY359 @ SY359 )
= ( power_power @ SV81 @ SY359 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[585]) ).
thf(682,plain,
! [SV144: $i,SV82: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV82 ) @ ( bit1 @ SV144 ) )
| ( ord_less_eq @ int @ SV82 @ SV144 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV82 @ SV144 )
| ( ord_less_eq @ int @ ( bit0 @ SV82 ) @ ( bit1 @ SV144 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(683,plain,
! [SV145: $i,SV83: $i] :
( ( ! [SY403: $i] :
( ~ ( monoid_mult @ SY403 )
| ( ( ti @ SY403 @ ( times_times @ SY403 @ SV83 @ SV145 ) )
= ( times_times @ SY403 @ SV83 @ SV145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(684,plain,
! [SV84: $i] :
( ( ( ~ ( semiring_1 @ SV84 ) )
= $true )
| ( ( ( ti @ SV84 @ ( one_one @ SV84 ) )
= ( one_one @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(685,plain,
! [SV85: $i] :
( ( ( ~ ( comm_semiring_1 @ SV85 ) )
= $true )
| ( ( ! [SY363: $i,SY364: $i] :
( ( power_power @ SV85 @ SY363 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY364 ) )
= ( times_times @ SV85 @ ( power_power @ SV85 @ SY363 @ SY364 ) @ ( power_power @ SV85 @ SY363 @ SY364 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[589]) ).
thf(686,plain,
! [SV146: $i,SV86: $i] :
( ( ~ ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV86 ) @ ( bit0 @ SV146 ) )
| ( ord_less @ int @ SV86 @ SV146 ) )
| ~ ( ~ ( ord_less @ int @ SV86 @ SV146 )
| ( ord_less_eq @ int @ ( bit1 @ SV86 ) @ ( bit0 @ SV146 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(687,plain,
! [SV147: $i,SV87: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ SV87 @ ( plus_plus @ int @ SV147 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ SV87 @ SV147 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV87 @ SV147 )
| ( ord_less @ int @ SV87 @ ( plus_plus @ int @ SV147 @ ( one_one @ int ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(688,plain,
! [SV88: $i] :
( ( ~ ( ~ ( ord_less @ int @ pls @ ( bit0 @ SV88 ) )
| ( ord_less @ int @ pls @ SV88 ) )
| ~ ( ~ ( ord_less @ int @ pls @ SV88 )
| ( ord_less @ int @ pls @ ( bit0 @ SV88 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(689,plain,
! [SV89: $i] :
( ( ( ~ ( comm_semiring_1 @ SV89 ) )
= $true )
| ( ( ! [SY367: $i,SY368: $i,SY369: $i] :
( ( times_times @ SV89 @ ( power_power @ SV89 @ SY367 @ SY368 ) @ ( power_power @ SV89 @ SY367 @ SY369 ) )
= ( power_power @ SV89 @ SY367 @ ( plus_plus @ nat @ SY368 @ SY369 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[593]) ).
thf(690,plain,
! [SV148: $i,SV90: $i] :
( ( ! [SY404: $i] :
( ~ ( comm_semiring_1 @ SY404 )
| ( ( ti @ SY404 @ ( plus_plus @ SY404 @ SV90 @ SV148 ) )
= ( plus_plus @ SY404 @ SV90 @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(691,plain,
! [SV91: $i] :
( ( ( ~ ~ ( ~ ( number_ring @ SV91 )
| ~ ( ring_char_0 @ SV91 ) ) )
= $true )
| ( ( ! [SY372: $i,SY373: $i] :
~ ( ~ ( ( ( number_number_of @ SV91 @ SY372 )
!= ( number_number_of @ SV91 @ SY373 ) )
| ( SY372 = SY373 ) )
| ~ ( ( SY372 != SY373 )
| ( ( number_number_of @ SV91 @ SY372 )
= ( number_number_of @ SV91 @ SY373 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[595]) ).
thf(692,plain,
! [SV92: $i,SV149: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ SV149 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ SV92 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV149 @ pls )
| ~ ( ~ ( ~ ( ord_less @ int @ SV92 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ SV149 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV92 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV149 @ SV92 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(693,plain,
! [SV93: $i] :
( ( ( ~ ( comm_semiring_1 @ SV93 ) )
= $true )
| ( ( ! [SY375: $i,SY376: $i,SY377: $i] :
( ( power_power @ SV93 @ ( power_power @ SV93 @ SY375 @ SY376 ) @ SY377 )
= ( power_power @ SV93 @ SY375 @ ( times_times @ nat @ SY376 @ SY377 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(694,plain,
! [SV94: $i,SV150: $i] :
( ( ~ ( number @ SV150 )
| ( ( ti @ SV150 @ ( number_number_of @ SV150 @ SV94 ) )
= ( number_number_of @ SV150 @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(695,plain,
! [SV151: $i,SV95: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV95 ) @ ( number_number_of @ int @ SV151 ) )
| ( ord_less @ int @ SV95 @ SV151 ) )
| ~ ( ~ ( ord_less @ int @ SV95 @ SV151 )
| ( ord_less @ int @ ( number_number_of @ int @ SV95 ) @ ( number_number_of @ int @ SV151 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(696,plain,
! [SV96: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV96 ) @ pls )
| ( ord_less @ int @ SV96 @ pls ) )
| ~ ( ~ ( ord_less @ int @ SV96 @ pls )
| ( ord_less @ int @ ( bit1 @ SV96 ) @ pls ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(697,plain,
! [SV152: $i,SV97: $i] :
( ( ~ ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV97 ) @ ( bit0 @ SV152 ) )
| ( ord_less @ int @ SV97 @ SV152 ) )
| ~ ( ~ ( ord_less @ int @ SV97 @ SV152 )
| ( ord_less @ int @ ( bit1 @ SV97 ) @ ( bit0 @ SV152 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(698,plain,
! [SV98: $i,SV153: $i] :
( ( ! [SY405: $i] :
( ~ ( ord_less_eq @ int @ SV153 @ SY405 )
| ~ ( ord_less_eq @ int @ SY405 @ SV98 )
| ( ord_less_eq @ int @ SV153 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(699,plain,
! [SV154: $i,SV99: $i] :
( ( ! [SY406: $i] :
( ~ ( monoid_mult @ SY406 )
| ( ( power_power @ SY406 @ SV99 @ ( ti @ nat @ SV154 ) )
= ( power_power @ SY406 @ SV99 @ SV154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(700,plain,
! [SV100: $i] :
( ( ~ ( ~ ( ord_less @ int @ pls @ ( bit1 @ SV100 ) )
| ( ord_less_eq @ int @ pls @ SV100 ) )
| ~ ( ~ ( ord_less_eq @ int @ pls @ SV100 )
| ( ord_less @ int @ pls @ ( bit1 @ SV100 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(701,plain,
! [SV101: $i] :
( ( ( ~ ( comm_semiring_1 @ SV101 ) )
= $true )
| ( ( ! [SY385: $i,SY386: $i,SY387: $i] :
( ( plus_plus @ SV101 @ ( plus_plus @ SV101 @ SY385 @ SY386 ) @ SY387 )
= ( plus_plus @ SV101 @ SY385 @ ( plus_plus @ SV101 @ SY386 @ SY387 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[605]) ).
thf(702,plain,
! [SV104: $i,SV9: $i] :
( ( ( ord_less_eq @ int @ SV9 @ SV104 )
= $true )
| ( ( ord_less_eq @ int @ SV104 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(703,plain,
! [SV105: $i,SV10: $i] :
( ( ( ( ord_less @ int @ SV10 @ SV105 )
| ( SV10 = SV105 ) )
= $true )
| ( ( ord_less @ int @ SV105 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[609]) ).
thf(704,plain,
! [SV155: $i,SV106: $i,SV11: $i] :
( ( ( power_power @ int @ ( power_power @ int @ SV11 @ SV106 ) @ SV155 )
= ( power_power @ int @ SV11 @ ( times_times @ nat @ SV106 @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(705,plain,
! [SV156: $i,SV107: $i,SV12: $i] :
( ( ( power_power @ int @ SV12 @ ( plus_plus @ nat @ SV107 @ SV156 ) )
= ( times_times @ int @ ( power_power @ int @ SV12 @ SV107 ) @ ( power_power @ int @ SV12 @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(706,plain,
! [SV157: $i,SV108: $i,SV15: $i] :
( ( ( times_times @ int @ ( times_times @ int @ SV15 @ SV108 ) @ SV157 )
= ( times_times @ int @ SV15 @ ( times_times @ int @ SV108 @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(707,plain,
! [SV158: $i,SV110: $i,SV18: $i] :
( ( ( plus_plus @ int @ ( plus_plus @ int @ SV18 @ SV110 ) @ SV158 )
= ( plus_plus @ int @ SV18 @ ( plus_plus @ int @ SV110 @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(708,plain,
! [SV159: $i,SV111: $i,SV19: $i] :
( ( ( plus_plus @ int @ SV19 @ ( plus_plus @ int @ SV111 @ SV159 ) )
= ( plus_plus @ int @ SV111 @ ( plus_plus @ int @ SV19 @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(709,plain,
! [SV113: $i,SV21: $i,SV160: $i] :
( ( ~ ( comm_semiring_1 @ SV160 )
| ( ( plus_plus @ SV160 @ ( ti @ SV160 @ SV21 ) @ SV113 )
= ( plus_plus @ SV160 @ SV21 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(710,plain,
! [SV114: $i,SV22: $i,SV161: $i] :
( ( ~ ( monoid_mult @ SV161 )
| ( ( times_times @ SV161 @ ( ti @ SV161 @ SV22 ) @ SV114 )
= ( times_times @ SV161 @ SV22 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(711,plain,
! [SV115: $i,SV23: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV23 @ SV115 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ SV115 @ SV23 )
| ( SV23 = SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(712,plain,
! [SV24: $i] :
( ( ( number_semiring @ SV24 )
= $false )
| ( ( ! [SY269: $i,SY270: $i] :
( ( power_power @ SV24 @ ( plus_plus @ SV24 @ SY269 @ SY270 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ SV24 @ ( plus_plus @ SV24 @ ( power_power @ SV24 @ SY269 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV24 @ SY270 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ SV24 @ ( times_times @ SV24 @ ( number_number_of @ SV24 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY269 ) @ SY270 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[620]) ).
thf(713,plain,
! [SV116: $i,SV25: $i] :
( ( ~ ( ( ( bit1 @ SV25 )
!= ( bit1 @ SV116 ) )
| ( SV25 = SV116 ) )
| ~ ( ( SV25 != SV116 )
| ( ( bit1 @ SV25 )
= ( bit1 @ SV116 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(714,plain,
( ( ( ! [SX0: $i] :
~ ~ ! [SX1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $false )
| ( ( ord_less @ int @ ( one_one @ int ) @ t )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(715,plain,
! [SV26: $i] :
( ( ( monoid_mult @ SV26 )
= $false )
| ( ( ! [SY272: $i] :
( ( power_power @ SV26 @ SY272 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV26 @ SY272 @ SY272 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(716,plain,
! [SV117: $i,SV27: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV27 ) @ ( bit0 @ SV117 ) )
| ( ord_less_eq @ int @ SV27 @ SV117 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV27 @ SV117 )
| ( ord_less_eq @ int @ ( bit0 @ SV27 ) @ ( bit0 @ SV117 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(717,plain,
! [SV28: $i] :
( ( ( ~ ( ~ ( monoid_mult @ SV28 )
| ~ ( number @ SV28 ) ) )
= $false )
| ( ( ! [SY274: $i] :
( ( power_power @ SV28 @ ( number_number_of @ SV28 @ SY274 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV28 @ ( number_number_of @ SV28 @ SY274 ) @ ( number_number_of @ SV28 @ SY274 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(718,plain,
! [SV29: $i] :
( ( ~ ( ~ ( twoSqu33214720sum2sq @ ( ti @ int @ SV29 ) )
| ( twoSqu33214720sum2sq @ SV29 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[626]) ).
thf(719,plain,
! [SV29: $i] :
( ( ~ ( ~ ( twoSqu33214720sum2sq @ SV29 )
| ( twoSqu33214720sum2sq @ ( ti @ int @ SV29 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[626]) ).
thf(720,plain,
! [SV118: $i,SV30: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV30 ) @ ( bit1 @ SV118 ) )
| ( ord_less_eq @ int @ SV30 @ SV118 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV30 @ SV118 )
| ( ord_less @ int @ ( bit0 @ SV30 ) @ ( bit1 @ SV118 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(721,plain,
! [SV119: $i,SV31: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV31 ) @ ( bit0 @ SV119 ) )
| ( ord_less @ int @ SV31 @ SV119 ) )
| ~ ( ~ ( ord_less @ int @ SV31 @ SV119 )
| ( ord_less @ int @ ( bit1 @ SV31 ) @ ( bit0 @ SV119 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(722,plain,
! [SV32: $i,SV162: $i,SV120: $i] :
( ( ~ ( ord_less @ int @ SV120 @ SV162 )
| ( ord_less @ int @ ( plus_plus @ int @ SV120 @ SV32 ) @ ( plus_plus @ int @ SV162 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(723,plain,
! [SV33: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ SV33 ) )
| ( ord_less_eq @ int @ pls @ SV33 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[630]) ).
thf(724,plain,
! [SV33: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ pls @ SV33 )
| ( ord_less_eq @ int @ pls @ ( bit1 @ SV33 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[630]) ).
thf(725,plain,
! [SV121: $i,SV34: $i,SV163: $i] :
( ( ~ ( comm_semiring_1 @ SV163 )
| ( ( plus_plus @ SV163 @ SV34 @ ( ti @ SV163 @ SV121 ) )
= ( plus_plus @ SV163 @ SV34 @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(726,plain,
! [SV122: $i,SV35: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV35 ) @ ( bit1 @ SV122 ) )
| ( ord_less_eq @ int @ SV35 @ SV122 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV35 @ SV122 )
| ( ord_less_eq @ int @ ( bit1 @ SV35 ) @ ( bit1 @ SV122 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[632]) ).
thf(727,plain,
! [SV36: $i] :
( ( ( comm_semiring_1 @ SV36 )
= $false )
| ( ( ! [SY282: $i,SY283: $i,SY284: $i,SY285: $i] :
( ( times_times @ SV36 @ ( times_times @ SV36 @ SY282 @ SY283 ) @ ( times_times @ SV36 @ SY284 @ SY285 ) )
= ( times_times @ SV36 @ SY282 @ ( times_times @ SV36 @ SY283 @ ( times_times @ SV36 @ SY284 @ SY285 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(728,plain,
! [SV37: $i] :
( ( ( comm_semiring_1 @ SV37 )
= $false )
| ( ( ! [SY286: $i,SY287: $i,SY288: $i] :
( ( plus_plus @ SV37 @ ( plus_plus @ SV37 @ SY286 @ SY287 ) @ SY288 )
= ( plus_plus @ SV37 @ ( plus_plus @ SV37 @ SY286 @ SY288 ) @ SY287 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[634]) ).
thf(729,plain,
! [SV123: $i,SV38: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit0 @ SV123 ) )
| ( ord_less @ int @ SV38 @ SV123 ) )
| ~ ( ~ ( ord_less @ int @ SV38 @ SV123 )
| ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit0 @ SV123 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(730,plain,
! [SV124: $i,SV39: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV39 ) @ ( bit1 @ SV124 ) )
| ( ord_less_eq @ int @ SV39 @ SV124 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV39 @ SV124 )
| ( ord_less_eq @ int @ ( bit0 @ SV39 ) @ ( bit1 @ SV124 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(731,plain,
! [SV40: $i,SV164: $i,SV125: $i] :
( ( ~ ( ord_less_eq @ int @ SV125 @ SV164 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV40 @ SV125 ) @ ( plus_plus @ int @ SV40 @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(732,plain,
! [SV126: $i,SV41: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV126 ) )
| ( ord_less_eq @ int @ SV41 @ SV126 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV41 @ SV126 )
| ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV126 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(733,plain,
! [SV42: $i] :
( ( ( comm_semiring_1 @ SV42 )
= $false )
| ( ( ! [SY294: $i] :
( ( power_power @ SV42 @ SY294 @ ( one_one @ nat ) )
= ( ti @ SV42 @ SY294 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(734,plain,
! [SV43: $i] :
( ( ( comm_semiring_1 @ SV43 )
= $false )
| ( ( ! [SY295: $i,SY296: $i,SY297: $i,SY298: $i] :
( ( times_times @ SV43 @ ( times_times @ SV43 @ SY295 @ SY296 ) @ ( times_times @ SV43 @ SY297 @ SY298 ) )
= ( times_times @ SV43 @ ( times_times @ SV43 @ SY295 @ SY297 ) @ ( times_times @ SV43 @ SY296 @ SY298 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(735,plain,
! [SV127: $i,SV44: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV44 ) @ ( bit1 @ SV127 ) )
| ( ord_less_eq @ int @ SV44 @ SV127 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV44 @ SV127 )
| ( ord_less @ int @ ( bit0 @ SV44 ) @ ( bit1 @ SV127 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[641]) ).
thf(736,plain,
! [SV45: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV45 ) @ pls )
| ( ord_less @ int @ SV45 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[642]) ).
thf(737,plain,
! [SV45: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV45 @ pls )
| ( ord_less @ int @ ( bit0 @ SV45 ) @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[642]) ).
thf(738,plain,
! [SV46: $i] :
( ( ( comm_semiring_1 @ SV46 )
= $false )
| ( ( ! [SY300: $i,SY301: $i,SY302: $i] :
( ( plus_plus @ SV46 @ SY300 @ ( plus_plus @ SV46 @ SY301 @ SY302 ) )
= ( plus_plus @ SV46 @ SY301 @ ( plus_plus @ SV46 @ SY300 @ SY302 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[643]) ).
thf(739,plain,
! [SV128: $i,SV47: $i,SV165: $i] :
( ( ~ ( monoid_mult @ SV165 )
| ( ( ti @ SV165 @ ( power_power @ SV165 @ SV47 @ SV128 ) )
= ( power_power @ SV165 @ SV47 @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(740,plain,
! [SV48: $i] :
( ( ( number_ring @ SV48 )
= $false )
| ( ( ! [SY305: $i] :
( ( plus_plus @ SV48 @ ( number_number_of @ SV48 @ SY305 ) @ ( one_one @ SV48 ) )
= ( number_number_of @ SV48 @ ( plus_plus @ int @ SY305 @ ( bit1 @ pls ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(741,plain,
! [SV49: $i] :
( ( ( number_ring @ SV49 )
= $false )
| ( ( ( plus_plus @ SV49 @ ( one_one @ SV49 ) @ ( one_one @ SV49 ) )
= ( number_number_of @ SV49 @ ( bit0 @ ( bit1 @ pls ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(742,plain,
! [SV129: $i,SV50: $i,SV166: $i] :
( ( ~ ( monoid_mult @ SV166 )
| ( ( power_power @ SV166 @ ( ti @ SV166 @ SV50 ) @ SV129 )
= ( power_power @ SV166 @ SV50 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(743,plain,
! [SV51: $i] :
( ( ( number @ SV51 )
= $false )
| ( ( ! [SY308: $i,SY309: $i] :
~ ( ~ ( ( ( number_number_of @ SV51 @ SY308 )
!= ( ti @ SV51 @ SY309 ) )
| ( ( ti @ SV51 @ SY309 )
= ( number_number_of @ SV51 @ SY308 ) ) )
| ~ ( ( ( ti @ SV51 @ SY309 )
!= ( number_number_of @ SV51 @ SY308 ) )
| ( ( number_number_of @ SV51 @ SY308 )
= ( ti @ SV51 @ SY309 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[648]) ).
thf(744,plain,
! [SV52: $i] :
( ( ( ~ ( ~ ( number_ring @ SV52 )
| ~ ( linordered_idom @ SV52 ) ) )
= $false )
| ( ( ! [SY310: $i,SY311: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SY310 ) @ ( number_number_of @ SV52 @ SY311 ) )
| ( ord_less_eq @ int @ SY310 @ SY311 ) )
| ~ ( ~ ( ord_less_eq @ int @ SY310 @ SY311 )
| ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SY310 ) @ ( number_number_of @ SV52 @ SY311 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(745,plain,
! [SV53: $i] :
( ( ( comm_semiring_1 @ SV53 )
= $false )
| ( ( ! [SY312: $i,SY313: $i,SY314: $i] :
( ( times_times @ SV53 @ ( times_times @ SV53 @ SY312 @ SY313 ) @ SY314 )
= ( times_times @ SV53 @ ( times_times @ SV53 @ SY312 @ SY314 ) @ SY313 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(746,plain,
! [SV167: $i] :
( ( ~ ~ ! [SY407: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SV167 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SY407 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(747,plain,
! [SV54: $i] :
( ( ( comm_semiring_1 @ SV54 )
= $false )
| ( ( ! [SY315: $i,SY316: $i,SY317: $i] :
( ( plus_plus @ SV54 @ SY315 @ ( plus_plus @ SV54 @ SY316 @ SY317 ) )
= ( plus_plus @ SV54 @ ( plus_plus @ SV54 @ SY315 @ SY316 ) @ SY317 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(748,plain,
! [SV55: $i] :
( ( ( number_ring @ SV55 )
= $false )
| ( ( ! [SY318: $i] :
( ( plus_plus @ SV55 @ ( one_one @ SV55 ) @ ( number_number_of @ SV55 @ SY318 ) )
= ( number_number_of @ SV55 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SY318 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[653]) ).
thf(749,plain,
! [SV130: $i,SV56: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV56 ) @ ( bit1 @ SV130 ) )
| ( ord_less @ int @ SV56 @ SV130 ) )
| ~ ( ~ ( ord_less @ int @ SV56 @ SV130 )
| ( ord_less @ int @ ( bit1 @ SV56 ) @ ( bit1 @ SV130 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(750,plain,
! [SV131: $i,SV57: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SV57 @ ( one_one @ int ) ) @ SV131 )
| ( ord_less @ int @ SV57 @ SV131 ) )
| ~ ( ~ ( ord_less @ int @ SV57 @ SV131 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV57 @ ( one_one @ int ) ) @ SV131 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(751,plain,
! [SV132: $i,SV58: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV58 @ SV132 )
| ~ ( ~ ( ord_less_eq @ int @ SV58 @ SV132 )
| ~ ( ( SV58 != SV132 ) ) ) )
| ~ ( ~ ~ ( ~ ( ord_less_eq @ int @ SV58 @ SV132 )
| ~ ( ( SV58 != SV132 ) ) )
| ( ord_less @ int @ SV58 @ SV132 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(752,plain,
! [SV59: $i] :
( ( ( comm_semiring_1 @ SV59 )
= $false )
| ( ( ! [SY322: $i,SY323: $i,SY324: $i,SY325: $i] :
( ( times_times @ SV59 @ ( times_times @ SV59 @ SY322 @ SY323 ) @ ( times_times @ SV59 @ SY324 @ SY325 ) )
= ( times_times @ SV59 @ SY324 @ ( times_times @ SV59 @ ( times_times @ SV59 @ SY322 @ SY323 ) @ SY325 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(753,plain,
! [SV60: $i] :
( ( ( comm_semiring_1 @ SV60 )
= $false )
| ( ( ! [SY326: $i,SY327: $i,SY328: $i] :
( ( times_times @ SV60 @ SY326 @ ( times_times @ SV60 @ SY327 @ SY328 ) )
= ( times_times @ SV60 @ SY327 @ ( times_times @ SV60 @ SY326 @ SY328 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(754,plain,
! [SV61: $i] :
( ( ( comm_semiring_1 @ SV61 )
= $false )
| ( ( ! [SY329: $i,SY330: $i] :
( ( plus_plus @ SV61 @ SY329 @ SY330 )
= ( plus_plus @ SV61 @ SY330 @ SY329 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(755,plain,
! [SV62: $i] :
( ( ( comm_semiring_1 @ SV62 )
= $false )
| ( ( ! [SY331: $i,SY332: $i,SY333: $i] :
( ( times_times @ SV62 @ SY331 @ ( times_times @ SV62 @ SY332 @ SY333 ) )
= ( times_times @ SV62 @ ( times_times @ SV62 @ SY331 @ SY332 ) @ SY333 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(756,plain,
! [SV63: $i] :
( ( ~ ( ~ ( zprime @ ( ti @ int @ SV63 ) )
| ( zprime @ SV63 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[661]) ).
thf(757,plain,
! [SV63: $i] :
( ( ~ ( ~ ( zprime @ SV63 )
| ( zprime @ ( ti @ int @ SV63 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[661]) ).
thf(758,plain,
! [SV133: $i,SV64: $i] :
( ( ( ~ ( ord_less @ int @ SV64 @ SV133 ) )
= $true )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV64 @ ( one_one @ int ) ) @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[662]) ).
thf(759,plain,
! [SV65: $i] :
( ( ( comm_semiring_1 @ SV65 )
= $false )
| ( ( ! [SY335: $i,SY336: $i] :
( ( times_times @ SV65 @ SY335 @ SY336 )
= ( times_times @ SV65 @ SY336 @ SY335 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[663]) ).
thf(760,plain,
! [SV134: $i,SV66: $i] :
( ( ~ ( ( ( bit0 @ SV66 )
!= ( bit0 @ SV134 ) )
| ( SV66 = SV134 ) )
| ~ ( ( SV66 != SV134 )
| ( ( bit0 @ SV66 )
= ( bit0 @ SV134 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(761,plain,
! [SV135: $i,SV67: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV67 ) @ ( bit0 @ SV135 ) )
| ( ord_less_eq @ int @ SV67 @ SV135 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV67 @ SV135 )
| ( ord_less_eq @ int @ ( bit0 @ SV67 ) @ ( bit0 @ SV135 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(762,plain,
! [SV136: $i,SV68: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV68 ) @ ( bit1 @ SV136 ) )
| ( ord_less_eq @ int @ SV68 @ SV136 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV68 @ SV136 )
| ( ord_less_eq @ int @ ( bit1 @ SV68 ) @ ( bit1 @ SV136 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[666]) ).
thf(763,plain,
! [SV69: $i] :
( ( ( semiring_1 @ SV69 )
= $false )
| ( ( ( power_power @ SV69 @ ( one_one @ SV69 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(764,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)],[668]) ).
thf(765,plain,
! [SV137: $i,SV70: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV70 ) @ ( bit0 @ SV137 ) )
| ( ord_less @ int @ SV70 @ SV137 ) )
| ~ ( ~ ( ord_less @ int @ SV70 @ SV137 )
| ( ord_less @ int @ ( bit0 @ SV70 ) @ ( bit0 @ SV137 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(766,plain,
! [SV138: $i,SV71: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV71 ) @ ( bit1 @ SV138 ) )
| ( ord_less @ int @ SV71 @ SV138 ) )
| ~ ( ~ ( ord_less @ int @ SV71 @ SV138 )
| ( ord_less @ int @ ( bit1 @ SV71 ) @ ( bit1 @ SV138 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(767,plain,
! [SV72: $i] :
( ( ( ~ ( ~ ( number_ring @ SV72 )
| ~ ( linordered_idom @ SV72 ) ) )
= $false )
| ( ( ! [SY342: $i,SY343: $i] :
~ ( ~ ( ~ ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SY342 ) @ ( number_number_of @ SV72 @ SY343 ) )
| ( ord_less @ int @ SY342 @ SY343 ) )
| ~ ( ~ ( ord_less @ int @ SY342 @ SY343 )
| ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SY342 ) @ ( number_number_of @ SV72 @ SY343 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(768,plain,
! [SV73: $i] :
( ( ( comm_semiring_1 @ SV73 )
= $false )
| ( ( ! [SY344: $i,SY345: $i,SY346: $i,SY347: $i] :
( ( plus_plus @ SV73 @ ( plus_plus @ SV73 @ SY344 @ SY345 ) @ ( plus_plus @ SV73 @ SY346 @ SY347 ) )
= ( plus_plus @ SV73 @ ( plus_plus @ SV73 @ SY344 @ SY346 ) @ ( plus_plus @ SV73 @ SY345 @ SY347 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(769,plain,
! [SV139: $i,SV74: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV74 ) @ ( bit0 @ SV139 ) )
| ( ord_less @ int @ SV74 @ SV139 ) )
| ~ ( ~ ( ord_less @ int @ SV74 @ SV139 )
| ( ord_less @ int @ ( bit0 @ SV74 ) @ ( bit0 @ SV139 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(770,plain,
! [SV75: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV75 ) @ pls )
| ( ord_less @ int @ SV75 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(771,plain,
! [SV75: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV75 @ pls )
| ( ord_less_eq @ int @ ( bit1 @ SV75 ) @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[674]) ).
thf(772,plain,
( ( ( ! [SX0: $i] :
~ ~ ! [SX1: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SX1 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $false )
| ( ( t
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(773,plain,
! [SV76: $i,SV140: $i] :
( ( ( ~ ( twoSqu33214720sum2sq @ SV140 ) )
= $true )
| ( ( ~ ( twoSqu33214720sum2sq @ SV76 )
| ( twoSqu33214720sum2sq @ ( times_times @ int @ SV140 @ SV76 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(774,plain,
! [SV141: $i,SV77: $i,SV168: $i] :
( ( ~ ( monoid_mult @ SV168 )
| ( ( times_times @ SV168 @ SV77 @ ( ti @ SV168 @ SV141 ) )
= ( times_times @ SV168 @ SV77 @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(775,plain,
! [SV142: $i,SV78: $i,SV169: $i] :
( ( ! [SY408: $i] :
( ~ ( ord_less @ int @ SV169 @ SY408 )
| ~ ( ord_less_eq @ int @ SV78 @ SV142 )
| ( ord_less @ int @ ( plus_plus @ int @ SV169 @ SV78 ) @ ( plus_plus @ int @ SY408 @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(776,plain,
! [SV79: $i] :
( ( ( comm_semiring_1 @ SV79 )
= $false )
| ( ( ! [SY355: $i,SY356: $i,SY357: $i] :
( ( times_times @ SV79 @ ( times_times @ SV79 @ SY355 @ SY356 ) @ SY357 )
= ( times_times @ SV79 @ SY355 @ ( times_times @ SV79 @ SY356 @ SY357 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(777,plain,
! [SV80: $i,SV143: $i] :
( ( ( ~ ( number @ SV143 ) )
= $true )
| ( ( ( number_number_of @ SV143 @ ( ti @ int @ SV80 ) )
= ( number_number_of @ SV143 @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[680]) ).
thf(778,plain,
! [SV81: $i] :
( ( ( comm_semiring_1 @ SV81 )
= $false )
| ( ( ! [SY359: $i] :
( ( times_times @ SV81 @ SY359 @ SY359 )
= ( power_power @ SV81 @ SY359 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[681]) ).
thf(779,plain,
! [SV144: $i,SV82: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV82 ) @ ( bit1 @ SV144 ) )
| ( ord_less_eq @ int @ SV82 @ SV144 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV82 @ SV144 )
| ( ord_less_eq @ int @ ( bit0 @ SV82 ) @ ( bit1 @ SV144 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[682]) ).
thf(780,plain,
! [SV145: $i,SV83: $i,SV170: $i] :
( ( ~ ( monoid_mult @ SV170 )
| ( ( ti @ SV170 @ ( times_times @ SV170 @ SV83 @ SV145 ) )
= ( times_times @ SV170 @ SV83 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(781,plain,
! [SV84: $i] :
( ( ( semiring_1 @ SV84 )
= $false )
| ( ( ( ti @ SV84 @ ( one_one @ SV84 ) )
= ( one_one @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(782,plain,
! [SV85: $i] :
( ( ( comm_semiring_1 @ SV85 )
= $false )
| ( ( ! [SY363: $i,SY364: $i] :
( ( power_power @ SV85 @ SY363 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY364 ) )
= ( times_times @ SV85 @ ( power_power @ SV85 @ SY363 @ SY364 ) @ ( power_power @ SV85 @ SY363 @ SY364 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[685]) ).
thf(783,plain,
! [SV146: $i,SV86: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV86 ) @ ( bit0 @ SV146 ) )
| ( ord_less @ int @ SV86 @ SV146 ) )
| ~ ( ~ ( ord_less @ int @ SV86 @ SV146 )
| ( ord_less_eq @ int @ ( bit1 @ SV86 ) @ ( bit0 @ SV146 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(784,plain,
! [SV147: $i,SV87: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV87 @ ( plus_plus @ int @ SV147 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ SV87 @ SV147 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV87 @ SV147 )
| ( ord_less @ int @ SV87 @ ( plus_plus @ int @ SV147 @ ( one_one @ int ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(785,plain,
! [SV88: $i] :
( ( ~ ( ~ ( ord_less @ int @ pls @ ( bit0 @ SV88 ) )
| ( ord_less @ int @ pls @ SV88 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[688]) ).
thf(786,plain,
! [SV88: $i] :
( ( ~ ( ~ ( ord_less @ int @ pls @ SV88 )
| ( ord_less @ int @ pls @ ( bit0 @ SV88 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[688]) ).
thf(787,plain,
! [SV89: $i] :
( ( ( comm_semiring_1 @ SV89 )
= $false )
| ( ( ! [SY367: $i,SY368: $i,SY369: $i] :
( ( times_times @ SV89 @ ( power_power @ SV89 @ SY367 @ SY368 ) @ ( power_power @ SV89 @ SY367 @ SY369 ) )
= ( power_power @ SV89 @ SY367 @ ( plus_plus @ nat @ SY368 @ SY369 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[689]) ).
thf(788,plain,
! [SV148: $i,SV90: $i,SV171: $i] :
( ( ~ ( comm_semiring_1 @ SV171 )
| ( ( ti @ SV171 @ ( plus_plus @ SV171 @ SV90 @ SV148 ) )
= ( plus_plus @ SV171 @ SV90 @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(789,plain,
! [SV91: $i] :
( ( ( ~ ( ~ ( number_ring @ SV91 )
| ~ ( ring_char_0 @ SV91 ) ) )
= $false )
| ( ( ! [SY372: $i,SY373: $i] :
~ ( ~ ( ( ( number_number_of @ SV91 @ SY372 )
!= ( number_number_of @ SV91 @ SY373 ) )
| ( SY372 = SY373 ) )
| ~ ( ( SY372 != SY373 )
| ( ( number_number_of @ SV91 @ SY372 )
= ( number_number_of @ SV91 @ SY373 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[691]) ).
thf(790,plain,
! [SV92: $i,SV149: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV149 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ SV92 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV149 @ pls )
| ~ ( ~ ( ~ ( ord_less @ int @ SV92 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ SV149 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV92 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV149 @ SV92 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[692]) ).
thf(791,plain,
! [SV93: $i] :
( ( ( comm_semiring_1 @ SV93 )
= $false )
| ( ( ! [SY375: $i,SY376: $i,SY377: $i] :
( ( power_power @ SV93 @ ( power_power @ SV93 @ SY375 @ SY376 ) @ SY377 )
= ( power_power @ SV93 @ SY375 @ ( times_times @ nat @ SY376 @ SY377 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(792,plain,
! [SV94: $i,SV150: $i] :
( ( ( ~ ( number @ SV150 ) )
= $true )
| ( ( ( ti @ SV150 @ ( number_number_of @ SV150 @ SV94 ) )
= ( number_number_of @ SV150 @ SV94 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[694]) ).
thf(793,plain,
! [SV151: $i,SV95: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV95 ) @ ( number_number_of @ int @ SV151 ) )
| ( ord_less @ int @ SV95 @ SV151 ) )
| ~ ( ~ ( ord_less @ int @ SV95 @ SV151 )
| ( ord_less @ int @ ( number_number_of @ int @ SV95 ) @ ( number_number_of @ int @ SV151 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[695]) ).
thf(794,plain,
! [SV96: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV96 ) @ pls )
| ( ord_less @ int @ SV96 @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(795,plain,
! [SV96: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV96 @ pls )
| ( ord_less @ int @ ( bit1 @ SV96 ) @ pls ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(796,plain,
! [SV152: $i,SV97: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV97 ) @ ( bit0 @ SV152 ) )
| ( ord_less @ int @ SV97 @ SV152 ) )
| ~ ( ~ ( ord_less @ int @ SV97 @ SV152 )
| ( ord_less @ int @ ( bit1 @ SV97 ) @ ( bit0 @ SV152 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(797,plain,
! [SV98: $i,SV172: $i,SV153: $i] :
( ( ~ ( ord_less_eq @ int @ SV153 @ SV172 )
| ~ ( ord_less_eq @ int @ SV172 @ SV98 )
| ( ord_less_eq @ int @ SV153 @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(798,plain,
! [SV154: $i,SV99: $i,SV173: $i] :
( ( ~ ( monoid_mult @ SV173 )
| ( ( power_power @ SV173 @ SV99 @ ( ti @ nat @ SV154 ) )
= ( power_power @ SV173 @ SV99 @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(799,plain,
! [SV100: $i] :
( ( ~ ( ~ ( ord_less @ int @ pls @ ( bit1 @ SV100 ) )
| ( ord_less_eq @ int @ pls @ SV100 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[700]) ).
thf(800,plain,
! [SV100: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ pls @ SV100 )
| ( ord_less @ int @ pls @ ( bit1 @ SV100 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[700]) ).
thf(801,plain,
! [SV101: $i] :
( ( ( comm_semiring_1 @ SV101 )
= $false )
| ( ( ! [SY385: $i,SY386: $i,SY387: $i] :
( ( plus_plus @ SV101 @ ( plus_plus @ SV101 @ SY385 @ SY386 ) @ SY387 )
= ( plus_plus @ SV101 @ SY385 @ ( plus_plus @ SV101 @ SY386 @ SY387 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[701]) ).
thf(802,plain,
! [SV105: $i,SV10: $i] :
( ( ( ord_less @ int @ SV10 @ SV105 )
= $true )
| ( ( SV10 = SV105 )
= $true )
| ( ( ord_less @ int @ SV105 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[703]) ).
thf(803,plain,
! [SV113: $i,SV21: $i,SV160: $i] :
( ( ( ~ ( comm_semiring_1 @ SV160 ) )
= $true )
| ( ( ( plus_plus @ SV160 @ ( ti @ SV160 @ SV21 ) @ SV113 )
= ( plus_plus @ SV160 @ SV21 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[709]) ).
thf(804,plain,
! [SV114: $i,SV22: $i,SV161: $i] :
( ( ( ~ ( monoid_mult @ SV161 ) )
= $true )
| ( ( ( times_times @ SV161 @ ( ti @ SV161 @ SV22 ) @ SV114 )
= ( times_times @ SV161 @ SV22 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[710]) ).
thf(805,plain,
! [SV115: $i,SV23: $i] :
( ( ( ord_less_eq @ int @ SV23 @ SV115 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ SV115 @ SV23 )
| ( SV23 = SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[711]) ).
thf(806,plain,
! [SV174: $i,SV24: $i] :
( ( ( ! [SY409: $i] :
( ( power_power @ SV24 @ ( plus_plus @ SV24 @ SV174 @ SY409 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ SV24 @ ( plus_plus @ SV24 @ ( power_power @ SV24 @ SV174 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV24 @ SY409 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ SV24 @ ( times_times @ SV24 @ ( number_number_of @ SV24 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV174 ) @ SY409 ) ) ) )
= $true )
| ( ( number_semiring @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(807,plain,
! [SV116: $i,SV25: $i] :
( ( ~ ( ( ( bit1 @ SV25 )
!= ( bit1 @ SV116 ) )
| ( SV25 = SV116 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[713]) ).
thf(808,plain,
! [SV116: $i,SV25: $i] :
( ( ~ ( ( SV25 != SV116 )
| ( ( bit1 @ SV25 )
= ( bit1 @ SV116 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[713]) ).
thf(809,plain,
( ( ( ~ ~ ! [SY410: $i] :
( ( plus_plus @ int @ ( power_power @ int @ sK2_SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SY410 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $false )
| ( ( ord_less @ int @ ( one_one @ int ) @ t )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[714]) ).
thf(810,plain,
! [SV175: $i,SV26: $i] :
( ( ( ( power_power @ SV26 @ SV175 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV26 @ SV175 @ SV175 ) )
= $true )
| ( ( monoid_mult @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(811,plain,
! [SV117: $i,SV27: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV27 ) @ ( bit0 @ SV117 ) )
| ( ord_less_eq @ int @ SV27 @ SV117 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[716]) ).
thf(812,plain,
! [SV117: $i,SV27: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV27 @ SV117 )
| ( ord_less_eq @ int @ ( bit0 @ SV27 ) @ ( bit0 @ SV117 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[716]) ).
thf(813,plain,
! [SV28: $i] :
( ( ( ~ ( monoid_mult @ SV28 )
| ~ ( number @ SV28 ) )
= $true )
| ( ( ! [SY274: $i] :
( ( power_power @ SV28 @ ( number_number_of @ SV28 @ SY274 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV28 @ ( number_number_of @ SV28 @ SY274 ) @ ( number_number_of @ SV28 @ SY274 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[717]) ).
thf(814,plain,
! [SV29: $i] :
( ( ~ ( twoSqu33214720sum2sq @ ( ti @ int @ SV29 ) )
| ( twoSqu33214720sum2sq @ SV29 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[718]) ).
thf(815,plain,
! [SV29: $i] :
( ( ~ ( twoSqu33214720sum2sq @ SV29 )
| ( twoSqu33214720sum2sq @ ( ti @ int @ SV29 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[719]) ).
thf(816,plain,
! [SV118: $i,SV30: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV30 ) @ ( bit1 @ SV118 ) )
| ( ord_less_eq @ int @ SV30 @ SV118 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[720]) ).
thf(817,plain,
! [SV118: $i,SV30: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV30 @ SV118 )
| ( ord_less @ int @ ( bit0 @ SV30 ) @ ( bit1 @ SV118 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[720]) ).
thf(818,plain,
! [SV119: $i,SV31: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV31 ) @ ( bit0 @ SV119 ) )
| ( ord_less @ int @ SV31 @ SV119 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[721]) ).
thf(819,plain,
! [SV119: $i,SV31: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV31 @ SV119 )
| ( ord_less @ int @ ( bit1 @ SV31 ) @ ( bit0 @ SV119 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[721]) ).
thf(820,plain,
! [SV32: $i,SV162: $i,SV120: $i] :
( ( ( ~ ( ord_less @ int @ SV120 @ SV162 ) )
= $true )
| ( ( ord_less @ int @ ( plus_plus @ int @ SV120 @ SV32 ) @ ( plus_plus @ int @ SV162 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[722]) ).
thf(821,plain,
! [SV33: $i] :
( ( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ SV33 ) )
| ( ord_less_eq @ int @ pls @ SV33 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[723]) ).
thf(822,plain,
! [SV33: $i] :
( ( ~ ( ord_less_eq @ int @ pls @ SV33 )
| ( ord_less_eq @ int @ pls @ ( bit1 @ SV33 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[724]) ).
thf(823,plain,
! [SV121: $i,SV34: $i,SV163: $i] :
( ( ( ~ ( comm_semiring_1 @ SV163 ) )
= $true )
| ( ( ( plus_plus @ SV163 @ SV34 @ ( ti @ SV163 @ SV121 ) )
= ( plus_plus @ SV163 @ SV34 @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[725]) ).
thf(824,plain,
! [SV122: $i,SV35: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV35 ) @ ( bit1 @ SV122 ) )
| ( ord_less_eq @ int @ SV35 @ SV122 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[726]) ).
thf(825,plain,
! [SV122: $i,SV35: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV35 @ SV122 )
| ( ord_less_eq @ int @ ( bit1 @ SV35 ) @ ( bit1 @ SV122 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[726]) ).
thf(826,plain,
! [SV176: $i,SV36: $i] :
( ( ( ! [SY411: $i,SY412: $i,SY413: $i] :
( ( times_times @ SV36 @ ( times_times @ SV36 @ SV176 @ SY411 ) @ ( times_times @ SV36 @ SY412 @ SY413 ) )
= ( times_times @ SV36 @ SV176 @ ( times_times @ SV36 @ SY411 @ ( times_times @ SV36 @ SY412 @ SY413 ) ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(827,plain,
! [SV177: $i,SV37: $i] :
( ( ( ! [SY414: $i,SY415: $i] :
( ( plus_plus @ SV37 @ ( plus_plus @ SV37 @ SV177 @ SY414 ) @ SY415 )
= ( plus_plus @ SV37 @ ( plus_plus @ SV37 @ SV177 @ SY415 ) @ SY414 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(828,plain,
! [SV123: $i,SV38: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit0 @ SV123 ) )
| ( ord_less @ int @ SV38 @ SV123 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[729]) ).
thf(829,plain,
! [SV123: $i,SV38: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV38 @ SV123 )
| ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit0 @ SV123 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[729]) ).
thf(830,plain,
! [SV124: $i,SV39: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV39 ) @ ( bit1 @ SV124 ) )
| ( ord_less_eq @ int @ SV39 @ SV124 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[730]) ).
thf(831,plain,
! [SV124: $i,SV39: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV39 @ SV124 )
| ( ord_less_eq @ int @ ( bit0 @ SV39 ) @ ( bit1 @ SV124 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[730]) ).
thf(832,plain,
! [SV40: $i,SV164: $i,SV125: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV125 @ SV164 ) )
= $true )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV40 @ SV125 ) @ ( plus_plus @ int @ SV40 @ SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[731]) ).
thf(833,plain,
! [SV126: $i,SV41: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV126 ) )
| ( ord_less_eq @ int @ SV41 @ SV126 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[732]) ).
thf(834,plain,
! [SV126: $i,SV41: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV41 @ SV126 )
| ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV126 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[732]) ).
thf(835,plain,
! [SV178: $i,SV42: $i] :
( ( ( ( power_power @ SV42 @ SV178 @ ( one_one @ nat ) )
= ( ti @ SV42 @ SV178 ) )
= $true )
| ( ( comm_semiring_1 @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(836,plain,
! [SV179: $i,SV43: $i] :
( ( ( ! [SY416: $i,SY417: $i,SY418: $i] :
( ( times_times @ SV43 @ ( times_times @ SV43 @ SV179 @ SY416 ) @ ( times_times @ SV43 @ SY417 @ SY418 ) )
= ( times_times @ SV43 @ ( times_times @ SV43 @ SV179 @ SY417 ) @ ( times_times @ SV43 @ SY416 @ SY418 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(837,plain,
! [SV127: $i,SV44: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV44 ) @ ( bit1 @ SV127 ) )
| ( ord_less_eq @ int @ SV44 @ SV127 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[735]) ).
thf(838,plain,
! [SV127: $i,SV44: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV44 @ SV127 )
| ( ord_less @ int @ ( bit0 @ SV44 ) @ ( bit1 @ SV127 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[735]) ).
thf(839,plain,
! [SV45: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV45 ) @ pls )
| ( ord_less @ int @ SV45 @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[736]) ).
thf(840,plain,
! [SV45: $i] :
( ( ~ ( ord_less @ int @ SV45 @ pls )
| ( ord_less @ int @ ( bit0 @ SV45 ) @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[737]) ).
thf(841,plain,
! [SV180: $i,SV46: $i] :
( ( ( ! [SY419: $i,SY420: $i] :
( ( plus_plus @ SV46 @ SV180 @ ( plus_plus @ SV46 @ SY419 @ SY420 ) )
= ( plus_plus @ SV46 @ SY419 @ ( plus_plus @ SV46 @ SV180 @ SY420 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(842,plain,
! [SV128: $i,SV47: $i,SV165: $i] :
( ( ( ~ ( monoid_mult @ SV165 ) )
= $true )
| ( ( ( ti @ SV165 @ ( power_power @ SV165 @ SV47 @ SV128 ) )
= ( power_power @ SV165 @ SV47 @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[739]) ).
thf(843,plain,
! [SV181: $i,SV48: $i] :
( ( ( ( plus_plus @ SV48 @ ( number_number_of @ SV48 @ SV181 ) @ ( one_one @ SV48 ) )
= ( number_number_of @ SV48 @ ( plus_plus @ int @ SV181 @ ( bit1 @ pls ) ) ) )
= $true )
| ( ( number_ring @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(844,plain,
! [SV129: $i,SV50: $i,SV166: $i] :
( ( ( ~ ( monoid_mult @ SV166 ) )
= $true )
| ( ( ( power_power @ SV166 @ ( ti @ SV166 @ SV50 ) @ SV129 )
= ( power_power @ SV166 @ SV50 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[742]) ).
thf(845,plain,
! [SV182: $i,SV51: $i] :
( ( ( ! [SY421: $i] :
~ ( ~ ( ( ( number_number_of @ SV51 @ SV182 )
!= ( ti @ SV51 @ SY421 ) )
| ( ( ti @ SV51 @ SY421 )
= ( number_number_of @ SV51 @ SV182 ) ) )
| ~ ( ( ( ti @ SV51 @ SY421 )
!= ( number_number_of @ SV51 @ SV182 ) )
| ( ( number_number_of @ SV51 @ SV182 )
= ( ti @ SV51 @ SY421 ) ) ) ) )
= $true )
| ( ( number @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(846,plain,
! [SV52: $i] :
( ( ( ~ ( number_ring @ SV52 )
| ~ ( linordered_idom @ SV52 ) )
= $true )
| ( ( ! [SY310: $i,SY311: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SY310 ) @ ( number_number_of @ SV52 @ SY311 ) )
| ( ord_less_eq @ int @ SY310 @ SY311 ) )
| ~ ( ~ ( ord_less_eq @ int @ SY310 @ SY311 )
| ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SY310 ) @ ( number_number_of @ SV52 @ SY311 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[744]) ).
thf(847,plain,
! [SV183: $i,SV53: $i] :
( ( ( ! [SY422: $i,SY423: $i] :
( ( times_times @ SV53 @ ( times_times @ SV53 @ SV183 @ SY422 ) @ SY423 )
= ( times_times @ SV53 @ ( times_times @ SV53 @ SV183 @ SY423 ) @ SY422 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(848,plain,
! [SV167: $i] :
( ( ~ ! [SY407: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SV167 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SY407 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[746]) ).
thf(849,plain,
! [SV184: $i,SV54: $i] :
( ( ( ! [SY424: $i,SY425: $i] :
( ( plus_plus @ SV54 @ SV184 @ ( plus_plus @ SV54 @ SY424 @ SY425 ) )
= ( plus_plus @ SV54 @ ( plus_plus @ SV54 @ SV184 @ SY424 ) @ SY425 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(850,plain,
! [SV185: $i,SV55: $i] :
( ( ( ( plus_plus @ SV55 @ ( one_one @ SV55 ) @ ( number_number_of @ SV55 @ SV185 ) )
= ( number_number_of @ SV55 @ ( plus_plus @ int @ ( bit1 @ pls ) @ SV185 ) ) )
= $true )
| ( ( number_ring @ SV55 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(851,plain,
! [SV130: $i,SV56: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV56 ) @ ( bit1 @ SV130 ) )
| ( ord_less @ int @ SV56 @ SV130 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[749]) ).
thf(852,plain,
! [SV130: $i,SV56: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV56 @ SV130 )
| ( ord_less @ int @ ( bit1 @ SV56 ) @ ( bit1 @ SV130 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[749]) ).
thf(853,plain,
! [SV131: $i,SV57: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SV57 @ ( one_one @ int ) ) @ SV131 )
| ( ord_less @ int @ SV57 @ SV131 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[750]) ).
thf(854,plain,
! [SV131: $i,SV57: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV57 @ SV131 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV57 @ ( one_one @ int ) ) @ SV131 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[750]) ).
thf(855,plain,
! [SV132: $i,SV58: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV58 @ SV132 )
| ~ ( ~ ( ord_less_eq @ int @ SV58 @ SV132 )
| ~ ( ( SV58 != SV132 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[751]) ).
thf(856,plain,
! [SV132: $i,SV58: $i] :
( ( ~ ( ~ ~ ( ~ ( ord_less_eq @ int @ SV58 @ SV132 )
| ~ ( ( SV58 != SV132 ) ) )
| ( ord_less @ int @ SV58 @ SV132 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[751]) ).
thf(857,plain,
! [SV186: $i,SV59: $i] :
( ( ( ! [SY426: $i,SY427: $i,SY428: $i] :
( ( times_times @ SV59 @ ( times_times @ SV59 @ SV186 @ SY426 ) @ ( times_times @ SV59 @ SY427 @ SY428 ) )
= ( times_times @ SV59 @ SY427 @ ( times_times @ SV59 @ ( times_times @ SV59 @ SV186 @ SY426 ) @ SY428 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(858,plain,
! [SV187: $i,SV60: $i] :
( ( ( ! [SY429: $i,SY430: $i] :
( ( times_times @ SV60 @ SV187 @ ( times_times @ SV60 @ SY429 @ SY430 ) )
= ( times_times @ SV60 @ SY429 @ ( times_times @ SV60 @ SV187 @ SY430 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(859,plain,
! [SV188: $i,SV61: $i] :
( ( ( ! [SY431: $i] :
( ( plus_plus @ SV61 @ SV188 @ SY431 )
= ( plus_plus @ SV61 @ SY431 @ SV188 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV61 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(860,plain,
! [SV189: $i,SV62: $i] :
( ( ( ! [SY432: $i,SY433: $i] :
( ( times_times @ SV62 @ SV189 @ ( times_times @ SV62 @ SY432 @ SY433 ) )
= ( times_times @ SV62 @ ( times_times @ SV62 @ SV189 @ SY432 ) @ SY433 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(861,plain,
! [SV63: $i] :
( ( ~ ( zprime @ ( ti @ int @ SV63 ) )
| ( zprime @ SV63 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[756]) ).
thf(862,plain,
! [SV63: $i] :
( ( ~ ( zprime @ SV63 )
| ( zprime @ ( ti @ int @ SV63 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[757]) ).
thf(863,plain,
! [SV133: $i,SV64: $i] :
( ( ( ord_less @ int @ SV64 @ SV133 )
= $false )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV64 @ ( one_one @ int ) ) @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(864,plain,
! [SV190: $i,SV65: $i] :
( ( ( ! [SY434: $i] :
( ( times_times @ SV65 @ SV190 @ SY434 )
= ( times_times @ SV65 @ SY434 @ SV190 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(865,plain,
! [SV134: $i,SV66: $i] :
( ( ~ ( ( ( bit0 @ SV66 )
!= ( bit0 @ SV134 ) )
| ( SV66 = SV134 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[760]) ).
thf(866,plain,
! [SV134: $i,SV66: $i] :
( ( ~ ( ( SV66 != SV134 )
| ( ( bit0 @ SV66 )
= ( bit0 @ SV134 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[760]) ).
thf(867,plain,
! [SV135: $i,SV67: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV67 ) @ ( bit0 @ SV135 ) )
| ( ord_less_eq @ int @ SV67 @ SV135 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[761]) ).
thf(868,plain,
! [SV135: $i,SV67: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV67 @ SV135 )
| ( ord_less_eq @ int @ ( bit0 @ SV67 ) @ ( bit0 @ SV135 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[761]) ).
thf(869,plain,
! [SV136: $i,SV68: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV68 ) @ ( bit1 @ SV136 ) )
| ( ord_less_eq @ int @ SV68 @ SV136 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[762]) ).
thf(870,plain,
! [SV136: $i,SV68: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV68 @ SV136 )
| ( ord_less_eq @ int @ ( bit1 @ SV68 ) @ ( bit1 @ SV136 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[762]) ).
thf(871,plain,
! [SV137: $i,SV70: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV70 ) @ ( bit0 @ SV137 ) )
| ( ord_less @ int @ SV70 @ SV137 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[765]) ).
thf(872,plain,
! [SV137: $i,SV70: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV70 @ SV137 )
| ( ord_less @ int @ ( bit0 @ SV70 ) @ ( bit0 @ SV137 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[765]) ).
thf(873,plain,
! [SV138: $i,SV71: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV71 ) @ ( bit1 @ SV138 ) )
| ( ord_less @ int @ SV71 @ SV138 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[766]) ).
thf(874,plain,
! [SV138: $i,SV71: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV71 @ SV138 )
| ( ord_less @ int @ ( bit1 @ SV71 ) @ ( bit1 @ SV138 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[766]) ).
thf(875,plain,
! [SV72: $i] :
( ( ( ~ ( number_ring @ SV72 )
| ~ ( linordered_idom @ SV72 ) )
= $true )
| ( ( ! [SY342: $i,SY343: $i] :
~ ( ~ ( ~ ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SY342 ) @ ( number_number_of @ SV72 @ SY343 ) )
| ( ord_less @ int @ SY342 @ SY343 ) )
| ~ ( ~ ( ord_less @ int @ SY342 @ SY343 )
| ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SY342 ) @ ( number_number_of @ SV72 @ SY343 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[767]) ).
thf(876,plain,
! [SV191: $i,SV73: $i] :
( ( ( ! [SY435: $i,SY436: $i,SY437: $i] :
( ( plus_plus @ SV73 @ ( plus_plus @ SV73 @ SV191 @ SY435 ) @ ( plus_plus @ SV73 @ SY436 @ SY437 ) )
= ( plus_plus @ SV73 @ ( plus_plus @ SV73 @ SV191 @ SY436 ) @ ( plus_plus @ SV73 @ SY435 @ SY437 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(877,plain,
! [SV139: $i,SV74: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit0 @ SV74 ) @ ( bit0 @ SV139 ) )
| ( ord_less @ int @ SV74 @ SV139 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[769]) ).
thf(878,plain,
! [SV139: $i,SV74: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV74 @ SV139 )
| ( ord_less @ int @ ( bit0 @ SV74 ) @ ( bit0 @ SV139 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[769]) ).
thf(879,plain,
! [SV75: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV75 ) @ pls )
| ( ord_less @ int @ SV75 @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[770]) ).
thf(880,plain,
! [SV75: $i] :
( ( ~ ( ord_less @ int @ SV75 @ pls )
| ( ord_less_eq @ int @ ( bit1 @ SV75 ) @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[771]) ).
thf(881,plain,
( ( ( ~ ~ ! [SY438: $i] :
( ( plus_plus @ int @ ( power_power @ int @ sK3_SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SY438 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $false )
| ( ( t
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[772]) ).
thf(882,plain,
! [SV76: $i,SV140: $i] :
( ( ( twoSqu33214720sum2sq @ SV140 )
= $false )
| ( ( ~ ( twoSqu33214720sum2sq @ SV76 )
| ( twoSqu33214720sum2sq @ ( times_times @ int @ SV140 @ SV76 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[773]) ).
thf(883,plain,
! [SV141: $i,SV77: $i,SV168: $i] :
( ( ( ~ ( monoid_mult @ SV168 ) )
= $true )
| ( ( ( times_times @ SV168 @ SV77 @ ( ti @ SV168 @ SV141 ) )
= ( times_times @ SV168 @ SV77 @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[774]) ).
thf(884,plain,
! [SV142: $i,SV78: $i,SV192: $i,SV169: $i] :
( ( ~ ( ord_less @ int @ SV169 @ SV192 )
| ~ ( ord_less_eq @ int @ SV78 @ SV142 )
| ( ord_less @ int @ ( plus_plus @ int @ SV169 @ SV78 ) @ ( plus_plus @ int @ SV192 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(885,plain,
! [SV193: $i,SV79: $i] :
( ( ( ! [SY439: $i,SY440: $i] :
( ( times_times @ SV79 @ ( times_times @ SV79 @ SV193 @ SY439 ) @ SY440 )
= ( times_times @ SV79 @ SV193 @ ( times_times @ SV79 @ SY439 @ SY440 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(886,plain,
! [SV80: $i,SV143: $i] :
( ( ( number @ SV143 )
= $false )
| ( ( ( number_number_of @ SV143 @ ( ti @ int @ SV80 ) )
= ( number_number_of @ SV143 @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[777]) ).
thf(887,plain,
! [SV194: $i,SV81: $i] :
( ( ( ( times_times @ SV81 @ SV194 @ SV194 )
= ( power_power @ SV81 @ SV194 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV81 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(888,plain,
! [SV144: $i,SV82: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit0 @ SV82 ) @ ( bit1 @ SV144 ) )
| ( ord_less_eq @ int @ SV82 @ SV144 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[779]) ).
thf(889,plain,
! [SV144: $i,SV82: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV82 @ SV144 )
| ( ord_less_eq @ int @ ( bit0 @ SV82 ) @ ( bit1 @ SV144 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[779]) ).
thf(890,plain,
! [SV145: $i,SV83: $i,SV170: $i] :
( ( ( ~ ( monoid_mult @ SV170 ) )
= $true )
| ( ( ( ti @ SV170 @ ( times_times @ SV170 @ SV83 @ SV145 ) )
= ( times_times @ SV170 @ SV83 @ SV145 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[780]) ).
thf(891,plain,
! [SV195: $i,SV85: $i] :
( ( ( ! [SY441: $i] :
( ( power_power @ SV85 @ SV195 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SY441 ) )
= ( times_times @ SV85 @ ( power_power @ SV85 @ SV195 @ SY441 ) @ ( power_power @ SV85 @ SV195 @ SY441 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(892,plain,
! [SV146: $i,SV86: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ ( bit1 @ SV86 ) @ ( bit0 @ SV146 ) )
| ( ord_less @ int @ SV86 @ SV146 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[783]) ).
thf(893,plain,
! [SV146: $i,SV86: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV86 @ SV146 )
| ( ord_less_eq @ int @ ( bit1 @ SV86 ) @ ( bit0 @ SV146 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[783]) ).
thf(894,plain,
! [SV147: $i,SV87: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV87 @ ( plus_plus @ int @ SV147 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ SV87 @ SV147 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[784]) ).
thf(895,plain,
! [SV147: $i,SV87: $i] :
( ( ~ ( ~ ( ord_less_eq @ int @ SV87 @ SV147 )
| ( ord_less @ int @ SV87 @ ( plus_plus @ int @ SV147 @ ( one_one @ int ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[784]) ).
thf(896,plain,
! [SV88: $i] :
( ( ~ ( ord_less @ int @ pls @ ( bit0 @ SV88 ) )
| ( ord_less @ int @ pls @ SV88 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[785]) ).
thf(897,plain,
! [SV88: $i] :
( ( ~ ( ord_less @ int @ pls @ SV88 )
| ( ord_less @ int @ pls @ ( bit0 @ SV88 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[786]) ).
thf(898,plain,
! [SV196: $i,SV89: $i] :
( ( ( ! [SY442: $i,SY443: $i] :
( ( times_times @ SV89 @ ( power_power @ SV89 @ SV196 @ SY442 ) @ ( power_power @ SV89 @ SV196 @ SY443 ) )
= ( power_power @ SV89 @ SV196 @ ( plus_plus @ nat @ SY442 @ SY443 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV89 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(899,plain,
! [SV148: $i,SV90: $i,SV171: $i] :
( ( ( ~ ( comm_semiring_1 @ SV171 ) )
= $true )
| ( ( ( ti @ SV171 @ ( plus_plus @ SV171 @ SV90 @ SV148 ) )
= ( plus_plus @ SV171 @ SV90 @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[788]) ).
thf(900,plain,
! [SV91: $i] :
( ( ( ~ ( number_ring @ SV91 )
| ~ ( ring_char_0 @ SV91 ) )
= $true )
| ( ( ! [SY372: $i,SY373: $i] :
~ ( ~ ( ( ( number_number_of @ SV91 @ SY372 )
!= ( number_number_of @ SV91 @ SY373 ) )
| ( SY372 = SY373 ) )
| ~ ( ( SY372 != SY373 )
| ( ( number_number_of @ SV91 @ SY372 )
= ( number_number_of @ SV91 @ SY373 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[789]) ).
thf(901,plain,
! [SV92: $i,SV149: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV149 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ SV92 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[790]) ).
thf(902,plain,
! [SV92: $i,SV149: $i] :
( ( ~ ( ~ ~ ( ord_less @ int @ SV149 @ pls )
| ~ ( ~ ( ~ ( ord_less @ int @ SV92 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ SV149 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV92 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV149 @ SV92 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[790]) ).
thf(903,plain,
! [SV197: $i,SV93: $i] :
( ( ( ! [SY444: $i,SY445: $i] :
( ( power_power @ SV93 @ ( power_power @ SV93 @ SV197 @ SY444 ) @ SY445 )
= ( power_power @ SV93 @ SV197 @ ( times_times @ nat @ SY444 @ SY445 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(904,plain,
! [SV94: $i,SV150: $i] :
( ( ( number @ SV150 )
= $false )
| ( ( ( ti @ SV150 @ ( number_number_of @ SV150 @ SV94 ) )
= ( number_number_of @ SV150 @ SV94 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[792]) ).
thf(905,plain,
! [SV151: $i,SV95: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV95 ) @ ( number_number_of @ int @ SV151 ) )
| ( ord_less @ int @ SV95 @ SV151 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[793]) ).
thf(906,plain,
! [SV151: $i,SV95: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV95 @ SV151 )
| ( ord_less @ int @ ( number_number_of @ int @ SV95 ) @ ( number_number_of @ int @ SV151 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[793]) ).
thf(907,plain,
! [SV96: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV96 ) @ pls )
| ( ord_less @ int @ SV96 @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[794]) ).
thf(908,plain,
! [SV96: $i] :
( ( ~ ( ord_less @ int @ SV96 @ pls )
| ( ord_less @ int @ ( bit1 @ SV96 ) @ pls ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[795]) ).
thf(909,plain,
! [SV152: $i,SV97: $i] :
( ( ~ ( ~ ( ord_less @ int @ ( bit1 @ SV97 ) @ ( bit0 @ SV152 ) )
| ( ord_less @ int @ SV97 @ SV152 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[796]) ).
thf(910,plain,
! [SV152: $i,SV97: $i] :
( ( ~ ( ~ ( ord_less @ int @ SV97 @ SV152 )
| ( ord_less @ int @ ( bit1 @ SV97 ) @ ( bit0 @ SV152 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[796]) ).
thf(911,plain,
! [SV98: $i,SV172: $i,SV153: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV153 @ SV172 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ SV172 @ SV98 )
| ( ord_less_eq @ int @ SV153 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[797]) ).
thf(912,plain,
! [SV154: $i,SV99: $i,SV173: $i] :
( ( ( ~ ( monoid_mult @ SV173 ) )
= $true )
| ( ( ( power_power @ SV173 @ SV99 @ ( ti @ nat @ SV154 ) )
= ( power_power @ SV173 @ SV99 @ SV154 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[798]) ).
thf(913,plain,
! [SV100: $i] :
( ( ~ ( ord_less @ int @ pls @ ( bit1 @ SV100 ) )
| ( ord_less_eq @ int @ pls @ SV100 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[799]) ).
thf(914,plain,
! [SV100: $i] :
( ( ~ ( ord_less_eq @ int @ pls @ SV100 )
| ( ord_less @ int @ pls @ ( bit1 @ SV100 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[800]) ).
thf(915,plain,
! [SV198: $i,SV101: $i] :
( ( ( ! [SY446: $i,SY447: $i] :
( ( plus_plus @ SV101 @ ( plus_plus @ SV101 @ SV198 @ SY446 ) @ SY447 )
= ( plus_plus @ SV101 @ SV198 @ ( plus_plus @ SV101 @ SY446 @ SY447 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(916,plain,
! [SV113: $i,SV21: $i,SV160: $i] :
( ( ( comm_semiring_1 @ SV160 )
= $false )
| ( ( ( plus_plus @ SV160 @ ( ti @ SV160 @ SV21 ) @ SV113 )
= ( plus_plus @ SV160 @ SV21 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[803]) ).
thf(917,plain,
! [SV114: $i,SV22: $i,SV161: $i] :
( ( ( monoid_mult @ SV161 )
= $false )
| ( ( ( times_times @ SV161 @ ( ti @ SV161 @ SV22 ) @ SV114 )
= ( times_times @ SV161 @ SV22 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[804]) ).
thf(918,plain,
! [SV23: $i,SV115: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV115 @ SV23 ) )
= $true )
| ( ( SV23 = SV115 )
= $true )
| ( ( ord_less_eq @ int @ SV23 @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[805]) ).
thf(919,plain,
! [SV199: $i,SV174: $i,SV24: $i] :
( ( ( ( power_power @ SV24 @ ( plus_plus @ SV24 @ SV174 @ SV199 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ SV24 @ ( plus_plus @ SV24 @ ( power_power @ SV24 @ SV174 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ SV24 @ SV199 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ SV24 @ ( times_times @ SV24 @ ( number_number_of @ SV24 @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV174 ) @ SV199 ) ) )
= $true )
| ( ( number_semiring @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(920,plain,
! [SV116: $i,SV25: $i] :
( ( ( ( bit1 @ SV25 )
!= ( bit1 @ SV116 ) )
| ( SV25 = SV116 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[807]) ).
thf(921,plain,
! [SV116: $i,SV25: $i] :
( ( ( SV25 != SV116 )
| ( ( bit1 @ SV25 )
= ( bit1 @ SV116 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[808]) ).
thf(922,plain,
( ( ( ~ ! [SY410: $i] :
( ( plus_plus @ int @ ( power_power @ int @ sK2_SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SY410 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true )
| ( ( ord_less @ int @ ( one_one @ int ) @ t )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[809]) ).
thf(923,plain,
! [SV117: $i,SV27: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV27 ) @ ( bit0 @ SV117 ) )
| ( ord_less_eq @ int @ SV27 @ SV117 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[811]) ).
thf(924,plain,
! [SV117: $i,SV27: $i] :
( ( ~ ( ord_less_eq @ int @ SV27 @ SV117 )
| ( ord_less_eq @ int @ ( bit0 @ SV27 ) @ ( bit0 @ SV117 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[812]) ).
thf(925,plain,
! [SV28: $i] :
( ( ( ~ ( monoid_mult @ SV28 ) )
= $true )
| ( ( ~ ( number @ SV28 ) )
= $true )
| ( ( ! [SY274: $i] :
( ( power_power @ SV28 @ ( number_number_of @ SV28 @ SY274 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV28 @ ( number_number_of @ SV28 @ SY274 ) @ ( number_number_of @ SV28 @ SY274 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[813]) ).
thf(926,plain,
! [SV29: $i] :
( ( ( ~ ( twoSqu33214720sum2sq @ ( ti @ int @ SV29 ) ) )
= $true )
| ( ( twoSqu33214720sum2sq @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[814]) ).
thf(927,plain,
! [SV29: $i] :
( ( ( ~ ( twoSqu33214720sum2sq @ SV29 ) )
= $true )
| ( ( twoSqu33214720sum2sq @ ( ti @ int @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[815]) ).
thf(928,plain,
! [SV118: $i,SV30: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV30 ) @ ( bit1 @ SV118 ) )
| ( ord_less_eq @ int @ SV30 @ SV118 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[816]) ).
thf(929,plain,
! [SV118: $i,SV30: $i] :
( ( ~ ( ord_less_eq @ int @ SV30 @ SV118 )
| ( ord_less @ int @ ( bit0 @ SV30 ) @ ( bit1 @ SV118 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[817]) ).
thf(930,plain,
! [SV119: $i,SV31: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV31 ) @ ( bit0 @ SV119 ) )
| ( ord_less @ int @ SV31 @ SV119 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[818]) ).
thf(931,plain,
! [SV119: $i,SV31: $i] :
( ( ~ ( ord_less @ int @ SV31 @ SV119 )
| ( ord_less @ int @ ( bit1 @ SV31 ) @ ( bit0 @ SV119 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[819]) ).
thf(932,plain,
! [SV32: $i,SV162: $i,SV120: $i] :
( ( ( ord_less @ int @ SV120 @ SV162 )
= $false )
| ( ( ord_less @ int @ ( plus_plus @ int @ SV120 @ SV32 ) @ ( plus_plus @ int @ SV162 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[820]) ).
thf(933,plain,
! [SV33: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ ( bit1 @ SV33 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[821]) ).
thf(934,plain,
! [SV33: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV33 ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ ( bit1 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[822]) ).
thf(935,plain,
! [SV121: $i,SV34: $i,SV163: $i] :
( ( ( comm_semiring_1 @ SV163 )
= $false )
| ( ( ( plus_plus @ SV163 @ SV34 @ ( ti @ SV163 @ SV121 ) )
= ( plus_plus @ SV163 @ SV34 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(936,plain,
! [SV122: $i,SV35: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV35 ) @ ( bit1 @ SV122 ) )
| ( ord_less_eq @ int @ SV35 @ SV122 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[824]) ).
thf(937,plain,
! [SV122: $i,SV35: $i] :
( ( ~ ( ord_less_eq @ int @ SV35 @ SV122 )
| ( ord_less_eq @ int @ ( bit1 @ SV35 ) @ ( bit1 @ SV122 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[825]) ).
thf(938,plain,
! [SV200: $i,SV176: $i,SV36: $i] :
( ( ( ! [SY448: $i,SY449: $i] :
( ( times_times @ SV36 @ ( times_times @ SV36 @ SV176 @ SV200 ) @ ( times_times @ SV36 @ SY448 @ SY449 ) )
= ( times_times @ SV36 @ SV176 @ ( times_times @ SV36 @ SV200 @ ( times_times @ SV36 @ SY448 @ SY449 ) ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(939,plain,
! [SV201: $i,SV177: $i,SV37: $i] :
( ( ( ! [SY450: $i] :
( ( plus_plus @ SV37 @ ( plus_plus @ SV37 @ SV177 @ SV201 ) @ SY450 )
= ( plus_plus @ SV37 @ ( plus_plus @ SV37 @ SV177 @ SY450 ) @ SV201 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(940,plain,
! [SV123: $i,SV38: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit0 @ SV123 ) )
| ( ord_less @ int @ SV38 @ SV123 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[828]) ).
thf(941,plain,
! [SV123: $i,SV38: $i] :
( ( ~ ( ord_less @ int @ SV38 @ SV123 )
| ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit0 @ SV123 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[829]) ).
thf(942,plain,
! [SV124: $i,SV39: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV39 ) @ ( bit1 @ SV124 ) )
| ( ord_less_eq @ int @ SV39 @ SV124 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[830]) ).
thf(943,plain,
! [SV124: $i,SV39: $i] :
( ( ~ ( ord_less_eq @ int @ SV39 @ SV124 )
| ( ord_less_eq @ int @ ( bit0 @ SV39 ) @ ( bit1 @ SV124 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[831]) ).
thf(944,plain,
! [SV40: $i,SV164: $i,SV125: $i] :
( ( ( ord_less_eq @ int @ SV125 @ SV164 )
= $false )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV40 @ SV125 ) @ ( plus_plus @ int @ SV40 @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[832]) ).
thf(945,plain,
! [SV126: $i,SV41: $i] :
( ( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV126 ) )
| ( ord_less_eq @ int @ SV41 @ SV126 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[833]) ).
thf(946,plain,
! [SV126: $i,SV41: $i] :
( ( ~ ( ord_less_eq @ int @ SV41 @ SV126 )
| ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV126 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[834]) ).
thf(947,plain,
! [SV202: $i,SV179: $i,SV43: $i] :
( ( ( ! [SY451: $i,SY452: $i] :
( ( times_times @ SV43 @ ( times_times @ SV43 @ SV179 @ SV202 ) @ ( times_times @ SV43 @ SY451 @ SY452 ) )
= ( times_times @ SV43 @ ( times_times @ SV43 @ SV179 @ SY451 ) @ ( times_times @ SV43 @ SV202 @ SY452 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(948,plain,
! [SV127: $i,SV44: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV44 ) @ ( bit1 @ SV127 ) )
| ( ord_less_eq @ int @ SV44 @ SV127 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[837]) ).
thf(949,plain,
! [SV127: $i,SV44: $i] :
( ( ~ ( ord_less_eq @ int @ SV44 @ SV127 )
| ( ord_less @ int @ ( bit0 @ SV44 ) @ ( bit1 @ SV127 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[838]) ).
thf(950,plain,
! [SV45: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV45 ) @ pls ) )
= $true )
| ( ( ord_less @ int @ SV45 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[839]) ).
thf(951,plain,
! [SV45: $i] :
( ( ( ~ ( ord_less @ int @ SV45 @ pls ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV45 ) @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[840]) ).
thf(952,plain,
! [SV203: $i,SV180: $i,SV46: $i] :
( ( ( ! [SY453: $i] :
( ( plus_plus @ SV46 @ SV180 @ ( plus_plus @ SV46 @ SV203 @ SY453 ) )
= ( plus_plus @ SV46 @ SV203 @ ( plus_plus @ SV46 @ SV180 @ SY453 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(953,plain,
! [SV128: $i,SV47: $i,SV165: $i] :
( ( ( monoid_mult @ SV165 )
= $false )
| ( ( ( ti @ SV165 @ ( power_power @ SV165 @ SV47 @ SV128 ) )
= ( power_power @ SV165 @ SV47 @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[842]) ).
thf(954,plain,
! [SV129: $i,SV50: $i,SV166: $i] :
( ( ( monoid_mult @ SV166 )
= $false )
| ( ( ( power_power @ SV166 @ ( ti @ SV166 @ SV50 ) @ SV129 )
= ( power_power @ SV166 @ SV50 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(955,plain,
! [SV204: $i,SV182: $i,SV51: $i] :
( ( ( ~ ( ~ ( ( ( number_number_of @ SV51 @ SV182 )
!= ( ti @ SV51 @ SV204 ) )
| ( ( ti @ SV51 @ SV204 )
= ( number_number_of @ SV51 @ SV182 ) ) )
| ~ ( ( ( ti @ SV51 @ SV204 )
!= ( number_number_of @ SV51 @ SV182 ) )
| ( ( number_number_of @ SV51 @ SV182 )
= ( ti @ SV51 @ SV204 ) ) ) ) )
= $true )
| ( ( number @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(956,plain,
! [SV52: $i] :
( ( ( ~ ( number_ring @ SV52 ) )
= $true )
| ( ( ~ ( linordered_idom @ SV52 ) )
= $true )
| ( ( ! [SY310: $i,SY311: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SY310 ) @ ( number_number_of @ SV52 @ SY311 ) )
| ( ord_less_eq @ int @ SY310 @ SY311 ) )
| ~ ( ~ ( ord_less_eq @ int @ SY310 @ SY311 )
| ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SY310 ) @ ( number_number_of @ SV52 @ SY311 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[846]) ).
thf(957,plain,
! [SV205: $i,SV183: $i,SV53: $i] :
( ( ( ! [SY454: $i] :
( ( times_times @ SV53 @ ( times_times @ SV53 @ SV183 @ SV205 ) @ SY454 )
= ( times_times @ SV53 @ ( times_times @ SV53 @ SV183 @ SY454 ) @ SV205 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(958,plain,
! [SV167: $i] :
( ( ! [SY407: $i] :
( ( plus_plus @ int @ ( power_power @ int @ SV167 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SY407 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[848]) ).
thf(959,plain,
! [SV206: $i,SV184: $i,SV54: $i] :
( ( ( ! [SY455: $i] :
( ( plus_plus @ SV54 @ SV184 @ ( plus_plus @ SV54 @ SV206 @ SY455 ) )
= ( plus_plus @ SV54 @ ( plus_plus @ SV54 @ SV184 @ SV206 ) @ SY455 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(960,plain,
! [SV130: $i,SV56: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV56 ) @ ( bit1 @ SV130 ) )
| ( ord_less @ int @ SV56 @ SV130 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[851]) ).
thf(961,plain,
! [SV130: $i,SV56: $i] :
( ( ~ ( ord_less @ int @ SV56 @ SV130 )
| ( ord_less @ int @ ( bit1 @ SV56 ) @ ( bit1 @ SV130 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[852]) ).
thf(962,plain,
! [SV131: $i,SV57: $i] :
( ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SV57 @ ( one_one @ int ) ) @ SV131 )
| ( ord_less @ int @ SV57 @ SV131 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[853]) ).
thf(963,plain,
! [SV131: $i,SV57: $i] :
( ( ~ ( ord_less @ int @ SV57 @ SV131 )
| ( ord_less_eq @ int @ ( plus_plus @ int @ SV57 @ ( one_one @ int ) ) @ SV131 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[854]) ).
thf(964,plain,
! [SV132: $i,SV58: $i] :
( ( ~ ( ord_less @ int @ SV58 @ SV132 )
| ~ ( ~ ( ord_less_eq @ int @ SV58 @ SV132 )
| ~ ( ( SV58 != SV132 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[855]) ).
thf(965,plain,
! [SV132: $i,SV58: $i] :
( ( ~ ~ ( ~ ( ord_less_eq @ int @ SV58 @ SV132 )
| ~ ( ( SV58 != SV132 ) ) )
| ( ord_less @ int @ SV58 @ SV132 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[856]) ).
thf(966,plain,
! [SV207: $i,SV186: $i,SV59: $i] :
( ( ( ! [SY456: $i,SY457: $i] :
( ( times_times @ SV59 @ ( times_times @ SV59 @ SV186 @ SV207 ) @ ( times_times @ SV59 @ SY456 @ SY457 ) )
= ( times_times @ SV59 @ SY456 @ ( times_times @ SV59 @ ( times_times @ SV59 @ SV186 @ SV207 ) @ SY457 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(967,plain,
! [SV208: $i,SV187: $i,SV60: $i] :
( ( ( ! [SY458: $i] :
( ( times_times @ SV60 @ SV187 @ ( times_times @ SV60 @ SV208 @ SY458 ) )
= ( times_times @ SV60 @ SV208 @ ( times_times @ SV60 @ SV187 @ SY458 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(968,plain,
! [SV209: $i,SV188: $i,SV61: $i] :
( ( ( ( plus_plus @ SV61 @ SV188 @ SV209 )
= ( plus_plus @ SV61 @ SV209 @ SV188 ) )
= $true )
| ( ( comm_semiring_1 @ SV61 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(969,plain,
! [SV210: $i,SV189: $i,SV62: $i] :
( ( ( ! [SY459: $i] :
( ( times_times @ SV62 @ SV189 @ ( times_times @ SV62 @ SV210 @ SY459 ) )
= ( times_times @ SV62 @ ( times_times @ SV62 @ SV189 @ SV210 ) @ SY459 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(970,plain,
! [SV63: $i] :
( ( ( ~ ( zprime @ ( ti @ int @ SV63 ) ) )
= $true )
| ( ( zprime @ SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[861]) ).
thf(971,plain,
! [SV63: $i] :
( ( ( ~ ( zprime @ SV63 ) )
= $true )
| ( ( zprime @ ( ti @ int @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[862]) ).
thf(972,plain,
! [SV211: $i,SV190: $i,SV65: $i] :
( ( ( ( times_times @ SV65 @ SV190 @ SV211 )
= ( times_times @ SV65 @ SV211 @ SV190 ) )
= $true )
| ( ( comm_semiring_1 @ SV65 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(973,plain,
! [SV134: $i,SV66: $i] :
( ( ( ( bit0 @ SV66 )
!= ( bit0 @ SV134 ) )
| ( SV66 = SV134 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[865]) ).
thf(974,plain,
! [SV134: $i,SV66: $i] :
( ( ( SV66 != SV134 )
| ( ( bit0 @ SV66 )
= ( bit0 @ SV134 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[866]) ).
thf(975,plain,
! [SV135: $i,SV67: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV67 ) @ ( bit0 @ SV135 ) )
| ( ord_less_eq @ int @ SV67 @ SV135 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[867]) ).
thf(976,plain,
! [SV135: $i,SV67: $i] :
( ( ~ ( ord_less_eq @ int @ SV67 @ SV135 )
| ( ord_less_eq @ int @ ( bit0 @ SV67 ) @ ( bit0 @ SV135 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[868]) ).
thf(977,plain,
! [SV136: $i,SV68: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV68 ) @ ( bit1 @ SV136 ) )
| ( ord_less_eq @ int @ SV68 @ SV136 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[869]) ).
thf(978,plain,
! [SV136: $i,SV68: $i] :
( ( ~ ( ord_less_eq @ int @ SV68 @ SV136 )
| ( ord_less_eq @ int @ ( bit1 @ SV68 ) @ ( bit1 @ SV136 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[870]) ).
thf(979,plain,
! [SV137: $i,SV70: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV70 ) @ ( bit0 @ SV137 ) )
| ( ord_less @ int @ SV70 @ SV137 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[871]) ).
thf(980,plain,
! [SV137: $i,SV70: $i] :
( ( ~ ( ord_less @ int @ SV70 @ SV137 )
| ( ord_less @ int @ ( bit0 @ SV70 ) @ ( bit0 @ SV137 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[872]) ).
thf(981,plain,
! [SV138: $i,SV71: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV71 ) @ ( bit1 @ SV138 ) )
| ( ord_less @ int @ SV71 @ SV138 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[873]) ).
thf(982,plain,
! [SV138: $i,SV71: $i] :
( ( ~ ( ord_less @ int @ SV71 @ SV138 )
| ( ord_less @ int @ ( bit1 @ SV71 ) @ ( bit1 @ SV138 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[874]) ).
thf(983,plain,
! [SV72: $i] :
( ( ( ~ ( number_ring @ SV72 ) )
= $true )
| ( ( ~ ( linordered_idom @ SV72 ) )
= $true )
| ( ( ! [SY342: $i,SY343: $i] :
~ ( ~ ( ~ ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SY342 ) @ ( number_number_of @ SV72 @ SY343 ) )
| ( ord_less @ int @ SY342 @ SY343 ) )
| ~ ( ~ ( ord_less @ int @ SY342 @ SY343 )
| ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SY342 ) @ ( number_number_of @ SV72 @ SY343 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[875]) ).
thf(984,plain,
! [SV212: $i,SV191: $i,SV73: $i] :
( ( ( ! [SY460: $i,SY461: $i] :
( ( plus_plus @ SV73 @ ( plus_plus @ SV73 @ SV191 @ SV212 ) @ ( plus_plus @ SV73 @ SY460 @ SY461 ) )
= ( plus_plus @ SV73 @ ( plus_plus @ SV73 @ SV191 @ SY460 ) @ ( plus_plus @ SV73 @ SV212 @ SY461 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(985,plain,
! [SV139: $i,SV74: $i] :
( ( ~ ( ord_less @ int @ ( bit0 @ SV74 ) @ ( bit0 @ SV139 ) )
| ( ord_less @ int @ SV74 @ SV139 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[877]) ).
thf(986,plain,
! [SV139: $i,SV74: $i] :
( ( ~ ( ord_less @ int @ SV74 @ SV139 )
| ( ord_less @ int @ ( bit0 @ SV74 ) @ ( bit0 @ SV139 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[878]) ).
thf(987,plain,
! [SV75: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV75 ) @ pls ) )
= $true )
| ( ( ord_less @ int @ SV75 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(988,plain,
! [SV75: $i] :
( ( ( ~ ( ord_less @ int @ SV75 @ pls ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ SV75 ) @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(989,plain,
( ( ( ~ ! [SY438: $i] :
( ( plus_plus @ int @ ( power_power @ int @ sK3_SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SY438 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $true )
| ( ( t
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[881]) ).
thf(990,plain,
! [SV140: $i,SV76: $i] :
( ( ( ~ ( twoSqu33214720sum2sq @ SV76 ) )
= $true )
| ( ( twoSqu33214720sum2sq @ ( times_times @ int @ SV140 @ SV76 ) )
= $true )
| ( ( twoSqu33214720sum2sq @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[882]) ).
thf(991,plain,
! [SV141: $i,SV77: $i,SV168: $i] :
( ( ( monoid_mult @ SV168 )
= $false )
| ( ( ( times_times @ SV168 @ SV77 @ ( ti @ SV168 @ SV141 ) )
= ( times_times @ SV168 @ SV77 @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[883]) ).
thf(992,plain,
! [SV142: $i,SV78: $i,SV192: $i,SV169: $i] :
( ( ( ~ ( ord_less @ int @ SV169 @ SV192 ) )
= $true )
| ( ( ~ ( ord_less_eq @ int @ SV78 @ SV142 )
| ( ord_less @ int @ ( plus_plus @ int @ SV169 @ SV78 ) @ ( plus_plus @ int @ SV192 @ SV142 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(993,plain,
! [SV213: $i,SV193: $i,SV79: $i] :
( ( ( ! [SY462: $i] :
( ( times_times @ SV79 @ ( times_times @ SV79 @ SV193 @ SV213 ) @ SY462 )
= ( times_times @ SV79 @ SV193 @ ( times_times @ SV79 @ SV213 @ SY462 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(994,plain,
! [SV144: $i,SV82: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV82 ) @ ( bit1 @ SV144 ) )
| ( ord_less_eq @ int @ SV82 @ SV144 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[888]) ).
thf(995,plain,
! [SV144: $i,SV82: $i] :
( ( ~ ( ord_less_eq @ int @ SV82 @ SV144 )
| ( ord_less_eq @ int @ ( bit0 @ SV82 ) @ ( bit1 @ SV144 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[889]) ).
thf(996,plain,
! [SV145: $i,SV83: $i,SV170: $i] :
( ( ( monoid_mult @ SV170 )
= $false )
| ( ( ( ti @ SV170 @ ( times_times @ SV170 @ SV83 @ SV145 ) )
= ( times_times @ SV170 @ SV83 @ SV145 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(997,plain,
! [SV214: $i,SV195: $i,SV85: $i] :
( ( ( ( power_power @ SV85 @ SV195 @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ SV214 ) )
= ( times_times @ SV85 @ ( power_power @ SV85 @ SV195 @ SV214 ) @ ( power_power @ SV85 @ SV195 @ SV214 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(998,plain,
! [SV146: $i,SV86: $i] :
( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV86 ) @ ( bit0 @ SV146 ) )
| ( ord_less @ int @ SV86 @ SV146 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[892]) ).
thf(999,plain,
! [SV146: $i,SV86: $i] :
( ( ~ ( ord_less @ int @ SV86 @ SV146 )
| ( ord_less_eq @ int @ ( bit1 @ SV86 ) @ ( bit0 @ SV146 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[893]) ).
thf(1000,plain,
! [SV147: $i,SV87: $i] :
( ( ~ ( ord_less @ int @ SV87 @ ( plus_plus @ int @ SV147 @ ( one_one @ int ) ) )
| ( ord_less_eq @ int @ SV87 @ SV147 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[894]) ).
thf(1001,plain,
! [SV147: $i,SV87: $i] :
( ( ~ ( ord_less_eq @ int @ SV87 @ SV147 )
| ( ord_less @ int @ SV87 @ ( plus_plus @ int @ SV147 @ ( one_one @ int ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[895]) ).
thf(1002,plain,
! [SV88: $i] :
( ( ( ~ ( ord_less @ int @ pls @ ( bit0 @ SV88 ) ) )
= $true )
| ( ( ord_less @ int @ pls @ SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[896]) ).
thf(1003,plain,
! [SV88: $i] :
( ( ( ~ ( ord_less @ int @ pls @ SV88 ) )
= $true )
| ( ( ord_less @ int @ pls @ ( bit0 @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[897]) ).
thf(1004,plain,
! [SV215: $i,SV196: $i,SV89: $i] :
( ( ( ! [SY463: $i] :
( ( times_times @ SV89 @ ( power_power @ SV89 @ SV196 @ SV215 ) @ ( power_power @ SV89 @ SV196 @ SY463 ) )
= ( power_power @ SV89 @ SV196 @ ( plus_plus @ nat @ SV215 @ SY463 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV89 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1005,plain,
! [SV148: $i,SV90: $i,SV171: $i] :
( ( ( comm_semiring_1 @ SV171 )
= $false )
| ( ( ( ti @ SV171 @ ( plus_plus @ SV171 @ SV90 @ SV148 ) )
= ( plus_plus @ SV171 @ SV90 @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[899]) ).
thf(1006,plain,
! [SV91: $i] :
( ( ( ~ ( number_ring @ SV91 ) )
= $true )
| ( ( ~ ( ring_char_0 @ SV91 ) )
= $true )
| ( ( ! [SY372: $i,SY373: $i] :
~ ( ~ ( ( ( number_number_of @ SV91 @ SY372 )
!= ( number_number_of @ SV91 @ SY373 ) )
| ( SY372 = SY373 ) )
| ~ ( ( SY372 != SY373 )
| ( ( number_number_of @ SV91 @ SY372 )
= ( number_number_of @ SV91 @ SY373 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[900]) ).
thf(1007,plain,
! [SV92: $i,SV149: $i] :
( ( ~ ( ord_less @ int @ SV149 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ SV92 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[901]) ).
thf(1008,plain,
! [SV92: $i,SV149: $i] :
( ( ~ ~ ( ord_less @ int @ SV149 @ pls )
| ~ ( ~ ( ~ ( ord_less @ int @ SV92 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ SV149 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV92 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV149 @ SV92 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[902]) ).
thf(1009,plain,
! [SV216: $i,SV197: $i,SV93: $i] :
( ( ( ! [SY464: $i] :
( ( power_power @ SV93 @ ( power_power @ SV93 @ SV197 @ SV216 ) @ SY464 )
= ( power_power @ SV93 @ SV197 @ ( times_times @ nat @ SV216 @ SY464 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1010,plain,
! [SV151: $i,SV95: $i] :
( ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV95 ) @ ( number_number_of @ int @ SV151 ) )
| ( ord_less @ int @ SV95 @ SV151 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[905]) ).
thf(1011,plain,
! [SV151: $i,SV95: $i] :
( ( ~ ( ord_less @ int @ SV95 @ SV151 )
| ( ord_less @ int @ ( number_number_of @ int @ SV95 ) @ ( number_number_of @ int @ SV151 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[906]) ).
thf(1012,plain,
! [SV96: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV96 ) @ pls ) )
= $true )
| ( ( ord_less @ int @ SV96 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[907]) ).
thf(1013,plain,
! [SV96: $i] :
( ( ( ~ ( ord_less @ int @ SV96 @ pls ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV96 ) @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(1014,plain,
! [SV152: $i,SV97: $i] :
( ( ~ ( ord_less @ int @ ( bit1 @ SV97 ) @ ( bit0 @ SV152 ) )
| ( ord_less @ int @ SV97 @ SV152 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[909]) ).
thf(1015,plain,
! [SV152: $i,SV97: $i] :
( ( ~ ( ord_less @ int @ SV97 @ SV152 )
| ( ord_less @ int @ ( bit1 @ SV97 ) @ ( bit0 @ SV152 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[910]) ).
thf(1016,plain,
! [SV98: $i,SV172: $i,SV153: $i] :
( ( ( ord_less_eq @ int @ SV153 @ SV172 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ SV172 @ SV98 )
| ( ord_less_eq @ int @ SV153 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(1017,plain,
! [SV154: $i,SV99: $i,SV173: $i] :
( ( ( monoid_mult @ SV173 )
= $false )
| ( ( ( power_power @ SV173 @ SV99 @ ( ti @ nat @ SV154 ) )
= ( power_power @ SV173 @ SV99 @ SV154 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(1018,plain,
! [SV100: $i] :
( ( ( ~ ( ord_less @ int @ pls @ ( bit1 @ SV100 ) ) )
= $true )
| ( ( ord_less_eq @ int @ pls @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[913]) ).
thf(1019,plain,
! [SV100: $i] :
( ( ( ~ ( ord_less_eq @ int @ pls @ SV100 ) )
= $true )
| ( ( ord_less @ int @ pls @ ( bit1 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[914]) ).
thf(1020,plain,
! [SV217: $i,SV198: $i,SV101: $i] :
( ( ( ! [SY465: $i] :
( ( plus_plus @ SV101 @ ( plus_plus @ SV101 @ SV198 @ SV217 ) @ SY465 )
= ( plus_plus @ SV101 @ SV198 @ ( plus_plus @ SV101 @ SV217 @ SY465 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1021,plain,
! [SV23: $i,SV115: $i] :
( ( ( ord_less_eq @ int @ SV115 @ SV23 )
= $false )
| ( ( SV23 = SV115 )
= $true )
| ( ( ord_less_eq @ int @ SV23 @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(1022,plain,
! [SV116: $i,SV25: $i] :
( ( ( ( bit1 @ SV25 )
!= ( bit1 @ SV116 ) )
= $true )
| ( ( SV25 = SV116 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[920]) ).
thf(1023,plain,
! [SV116: $i,SV25: $i] :
( ( ( SV25 != SV116 )
= $true )
| ( ( ( bit1 @ SV25 )
= ( bit1 @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[921]) ).
thf(1024,plain,
( ( ( ! [SY410: $i] :
( ( plus_plus @ int @ ( power_power @ int @ sK2_SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SY410 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $false )
| ( ( ord_less @ int @ ( one_one @ int ) @ t )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(1025,plain,
! [SV117: $i,SV27: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV27 ) @ ( bit0 @ SV117 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV27 @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(1026,plain,
! [SV117: $i,SV27: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV27 @ SV117 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit0 @ SV27 ) @ ( bit0 @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[924]) ).
thf(1027,plain,
! [SV28: $i] :
( ( ( monoid_mult @ SV28 )
= $false )
| ( ( ~ ( number @ SV28 ) )
= $true )
| ( ( ! [SY274: $i] :
( ( power_power @ SV28 @ ( number_number_of @ SV28 @ SY274 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV28 @ ( number_number_of @ SV28 @ SY274 ) @ ( number_number_of @ SV28 @ SY274 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[925]) ).
thf(1028,plain,
! [SV29: $i] :
( ( ( twoSqu33214720sum2sq @ ( ti @ int @ SV29 ) )
= $false )
| ( ( twoSqu33214720sum2sq @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(1029,plain,
! [SV29: $i] :
( ( ( twoSqu33214720sum2sq @ SV29 )
= $false )
| ( ( twoSqu33214720sum2sq @ ( ti @ int @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(1030,plain,
! [SV118: $i,SV30: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV30 ) @ ( bit1 @ SV118 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV30 @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[928]) ).
thf(1031,plain,
! [SV118: $i,SV30: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV30 @ SV118 ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV30 ) @ ( bit1 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(1032,plain,
! [SV119: $i,SV31: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV31 ) @ ( bit0 @ SV119 ) ) )
= $true )
| ( ( ord_less @ int @ SV31 @ SV119 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[930]) ).
thf(1033,plain,
! [SV119: $i,SV31: $i] :
( ( ( ~ ( ord_less @ int @ SV31 @ SV119 ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV31 ) @ ( bit0 @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[931]) ).
thf(1034,plain,
! [SV33: $i] :
( ( ( ord_less_eq @ int @ pls @ ( bit1 @ SV33 ) )
= $false )
| ( ( ord_less_eq @ int @ pls @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[933]) ).
thf(1035,plain,
! [SV33: $i] :
( ( ( ord_less_eq @ int @ pls @ SV33 )
= $false )
| ( ( ord_less_eq @ int @ pls @ ( bit1 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(1036,plain,
! [SV122: $i,SV35: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV35 ) @ ( bit1 @ SV122 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV35 @ SV122 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[936]) ).
thf(1037,plain,
! [SV122: $i,SV35: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV35 @ SV122 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ SV35 ) @ ( bit1 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[937]) ).
thf(1038,plain,
! [SV218: $i,SV200: $i,SV176: $i,SV36: $i] :
( ( ( ! [SY466: $i] :
( ( times_times @ SV36 @ ( times_times @ SV36 @ SV176 @ SV200 ) @ ( times_times @ SV36 @ SV218 @ SY466 ) )
= ( times_times @ SV36 @ SV176 @ ( times_times @ SV36 @ SV200 @ ( times_times @ SV36 @ SV218 @ SY466 ) ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1039,plain,
! [SV219: $i,SV201: $i,SV177: $i,SV37: $i] :
( ( ( ( plus_plus @ SV37 @ ( plus_plus @ SV37 @ SV177 @ SV201 ) @ SV219 )
= ( plus_plus @ SV37 @ ( plus_plus @ SV37 @ SV177 @ SV219 ) @ SV201 ) )
= $true )
| ( ( comm_semiring_1 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1040,plain,
! [SV123: $i,SV38: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit0 @ SV123 ) ) )
= $true )
| ( ( ord_less @ int @ SV38 @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[940]) ).
thf(1041,plain,
! [SV123: $i,SV38: $i] :
( ( ( ~ ( ord_less @ int @ SV38 @ SV123 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit0 @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[941]) ).
thf(1042,plain,
! [SV124: $i,SV39: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV39 ) @ ( bit1 @ SV124 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV39 @ SV124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[942]) ).
thf(1043,plain,
! [SV124: $i,SV39: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV39 @ SV124 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit0 @ SV39 ) @ ( bit1 @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[943]) ).
thf(1044,plain,
! [SV126: $i,SV41: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV126 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV41 @ SV126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[945]) ).
thf(1045,plain,
! [SV126: $i,SV41: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV41 @ SV126 ) )
= $true )
| ( ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[946]) ).
thf(1046,plain,
! [SV220: $i,SV202: $i,SV179: $i,SV43: $i] :
( ( ( ! [SY467: $i] :
( ( times_times @ SV43 @ ( times_times @ SV43 @ SV179 @ SV202 ) @ ( times_times @ SV43 @ SV220 @ SY467 ) )
= ( times_times @ SV43 @ ( times_times @ SV43 @ SV179 @ SV220 ) @ ( times_times @ SV43 @ SV202 @ SY467 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1047,plain,
! [SV127: $i,SV44: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV44 ) @ ( bit1 @ SV127 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV44 @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[948]) ).
thf(1048,plain,
! [SV127: $i,SV44: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV44 @ SV127 ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV44 ) @ ( bit1 @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[949]) ).
thf(1049,plain,
! [SV45: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV45 ) @ pls )
= $false )
| ( ( ord_less @ int @ SV45 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[950]) ).
thf(1050,plain,
! [SV45: $i] :
( ( ( ord_less @ int @ SV45 @ pls )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV45 ) @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[951]) ).
thf(1051,plain,
! [SV221: $i,SV203: $i,SV180: $i,SV46: $i] :
( ( ( ( plus_plus @ SV46 @ SV180 @ ( plus_plus @ SV46 @ SV203 @ SV221 ) )
= ( plus_plus @ SV46 @ SV203 @ ( plus_plus @ SV46 @ SV180 @ SV221 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV46 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1052,plain,
! [SV204: $i,SV182: $i,SV51: $i] :
( ( ( ~ ( ( ( number_number_of @ SV51 @ SV182 )
!= ( ti @ SV51 @ SV204 ) )
| ( ( ti @ SV51 @ SV204 )
= ( number_number_of @ SV51 @ SV182 ) ) )
| ~ ( ( ( ti @ SV51 @ SV204 )
!= ( number_number_of @ SV51 @ SV182 ) )
| ( ( number_number_of @ SV51 @ SV182 )
= ( ti @ SV51 @ SV204 ) ) ) )
= $false )
| ( ( number @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(1053,plain,
! [SV52: $i] :
( ( ( number_ring @ SV52 )
= $false )
| ( ( ~ ( linordered_idom @ SV52 ) )
= $true )
| ( ( ! [SY310: $i,SY311: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SY310 ) @ ( number_number_of @ SV52 @ SY311 ) )
| ( ord_less_eq @ int @ SY310 @ SY311 ) )
| ~ ( ~ ( ord_less_eq @ int @ SY310 @ SY311 )
| ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SY310 ) @ ( number_number_of @ SV52 @ SY311 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[956]) ).
thf(1054,plain,
! [SV222: $i,SV205: $i,SV183: $i,SV53: $i] :
( ( ( ( times_times @ SV53 @ ( times_times @ SV53 @ SV183 @ SV205 ) @ SV222 )
= ( times_times @ SV53 @ ( times_times @ SV53 @ SV183 @ SV222 ) @ SV205 ) )
= $true )
| ( ( comm_semiring_1 @ SV53 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1055,plain,
! [SV223: $i,SV167: $i] :
( ( ( plus_plus @ int @ ( power_power @ int @ SV167 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SV223 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1056,plain,
! [SV224: $i,SV206: $i,SV184: $i,SV54: $i] :
( ( ( ( plus_plus @ SV54 @ SV184 @ ( plus_plus @ SV54 @ SV206 @ SV224 ) )
= ( plus_plus @ SV54 @ ( plus_plus @ SV54 @ SV184 @ SV206 ) @ SV224 ) )
= $true )
| ( ( comm_semiring_1 @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1057,plain,
! [SV130: $i,SV56: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV56 ) @ ( bit1 @ SV130 ) ) )
= $true )
| ( ( ord_less @ int @ SV56 @ SV130 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[960]) ).
thf(1058,plain,
! [SV130: $i,SV56: $i] :
( ( ( ~ ( ord_less @ int @ SV56 @ SV130 ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV56 ) @ ( bit1 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[961]) ).
thf(1059,plain,
! [SV131: $i,SV57: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( plus_plus @ int @ SV57 @ ( one_one @ int ) ) @ SV131 ) )
= $true )
| ( ( ord_less @ int @ SV57 @ SV131 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[962]) ).
thf(1060,plain,
! [SV131: $i,SV57: $i] :
( ( ( ~ ( ord_less @ int @ SV57 @ SV131 ) )
= $true )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV57 @ ( one_one @ int ) ) @ SV131 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[963]) ).
thf(1061,plain,
! [SV132: $i,SV58: $i] :
( ( ( ~ ( ord_less @ int @ SV58 @ SV132 ) )
= $true )
| ( ( ~ ( ~ ( ord_less_eq @ int @ SV58 @ SV132 )
| ~ ( ( SV58 != SV132 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(1062,plain,
! [SV132: $i,SV58: $i] :
( ( ( ~ ~ ( ~ ( ord_less_eq @ int @ SV58 @ SV132 )
| ~ ( ( SV58 != SV132 ) ) ) )
= $true )
| ( ( ord_less @ int @ SV58 @ SV132 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[965]) ).
thf(1063,plain,
! [SV225: $i,SV207: $i,SV186: $i,SV59: $i] :
( ( ( ! [SY468: $i] :
( ( times_times @ SV59 @ ( times_times @ SV59 @ SV186 @ SV207 ) @ ( times_times @ SV59 @ SV225 @ SY468 ) )
= ( times_times @ SV59 @ SV225 @ ( times_times @ SV59 @ ( times_times @ SV59 @ SV186 @ SV207 ) @ SY468 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1064,plain,
! [SV226: $i,SV208: $i,SV187: $i,SV60: $i] :
( ( ( ( times_times @ SV60 @ SV187 @ ( times_times @ SV60 @ SV208 @ SV226 ) )
= ( times_times @ SV60 @ SV208 @ ( times_times @ SV60 @ SV187 @ SV226 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1065,plain,
! [SV227: $i,SV210: $i,SV189: $i,SV62: $i] :
( ( ( ( times_times @ SV62 @ SV189 @ ( times_times @ SV62 @ SV210 @ SV227 ) )
= ( times_times @ SV62 @ ( times_times @ SV62 @ SV189 @ SV210 ) @ SV227 ) )
= $true )
| ( ( comm_semiring_1 @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1066,plain,
! [SV63: $i] :
( ( ( zprime @ ( ti @ int @ SV63 ) )
= $false )
| ( ( zprime @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[970]) ).
thf(1067,plain,
! [SV63: $i] :
( ( ( zprime @ SV63 )
= $false )
| ( ( zprime @ ( ti @ int @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(1068,plain,
! [SV134: $i,SV66: $i] :
( ( ( ( bit0 @ SV66 )
!= ( bit0 @ SV134 ) )
= $true )
| ( ( SV66 = SV134 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[973]) ).
thf(1069,plain,
! [SV134: $i,SV66: $i] :
( ( ( SV66 != SV134 )
= $true )
| ( ( ( bit0 @ SV66 )
= ( bit0 @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[974]) ).
thf(1070,plain,
! [SV135: $i,SV67: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV67 ) @ ( bit0 @ SV135 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV67 @ SV135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[975]) ).
thf(1071,plain,
! [SV135: $i,SV67: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV67 @ SV135 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit0 @ SV67 ) @ ( bit0 @ SV135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[976]) ).
thf(1072,plain,
! [SV136: $i,SV68: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV68 ) @ ( bit1 @ SV136 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV68 @ SV136 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[977]) ).
thf(1073,plain,
! [SV136: $i,SV68: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV68 @ SV136 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ SV68 ) @ ( bit1 @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1074,plain,
! [SV137: $i,SV70: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV70 ) @ ( bit0 @ SV137 ) ) )
= $true )
| ( ( ord_less @ int @ SV70 @ SV137 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(1075,plain,
! [SV137: $i,SV70: $i] :
( ( ( ~ ( ord_less @ int @ SV70 @ SV137 ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV70 ) @ ( bit0 @ SV137 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[980]) ).
thf(1076,plain,
! [SV138: $i,SV71: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV71 ) @ ( bit1 @ SV138 ) ) )
= $true )
| ( ( ord_less @ int @ SV71 @ SV138 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[981]) ).
thf(1077,plain,
! [SV138: $i,SV71: $i] :
( ( ( ~ ( ord_less @ int @ SV71 @ SV138 ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV71 ) @ ( bit1 @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[982]) ).
thf(1078,plain,
! [SV72: $i] :
( ( ( number_ring @ SV72 )
= $false )
| ( ( ~ ( linordered_idom @ SV72 ) )
= $true )
| ( ( ! [SY342: $i,SY343: $i] :
~ ( ~ ( ~ ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SY342 ) @ ( number_number_of @ SV72 @ SY343 ) )
| ( ord_less @ int @ SY342 @ SY343 ) )
| ~ ( ~ ( ord_less @ int @ SY342 @ SY343 )
| ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SY342 ) @ ( number_number_of @ SV72 @ SY343 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1079,plain,
! [SV228: $i,SV212: $i,SV191: $i,SV73: $i] :
( ( ( ! [SY469: $i] :
( ( plus_plus @ SV73 @ ( plus_plus @ SV73 @ SV191 @ SV212 ) @ ( plus_plus @ SV73 @ SV228 @ SY469 ) )
= ( plus_plus @ SV73 @ ( plus_plus @ SV73 @ SV191 @ SV228 ) @ ( plus_plus @ SV73 @ SV212 @ SY469 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1080,plain,
! [SV139: $i,SV74: $i] :
( ( ( ~ ( ord_less @ int @ ( bit0 @ SV74 ) @ ( bit0 @ SV139 ) ) )
= $true )
| ( ( ord_less @ int @ SV74 @ SV139 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[985]) ).
thf(1081,plain,
! [SV139: $i,SV74: $i] :
( ( ( ~ ( ord_less @ int @ SV74 @ SV139 ) )
= $true )
| ( ( ord_less @ int @ ( bit0 @ SV74 ) @ ( bit0 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[986]) ).
thf(1082,plain,
! [SV75: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ SV75 ) @ pls )
= $false )
| ( ( ord_less @ int @ SV75 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1083,plain,
! [SV75: $i] :
( ( ( ord_less @ int @ SV75 @ pls )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ SV75 ) @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1084,plain,
( ( ( ! [SY438: $i] :
( ( plus_plus @ int @ ( power_power @ int @ sK3_SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SY438 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) ) )
= $false )
| ( ( t
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1085,plain,
! [SV140: $i,SV76: $i] :
( ( ( twoSqu33214720sum2sq @ SV76 )
= $false )
| ( ( twoSqu33214720sum2sq @ ( times_times @ int @ SV140 @ SV76 ) )
= $true )
| ( ( twoSqu33214720sum2sq @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1086,plain,
! [SV142: $i,SV78: $i,SV192: $i,SV169: $i] :
( ( ( ord_less @ int @ SV169 @ SV192 )
= $false )
| ( ( ~ ( ord_less_eq @ int @ SV78 @ SV142 )
| ( ord_less @ int @ ( plus_plus @ int @ SV169 @ SV78 ) @ ( plus_plus @ int @ SV192 @ SV142 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1087,plain,
! [SV229: $i,SV213: $i,SV193: $i,SV79: $i] :
( ( ( ( times_times @ SV79 @ ( times_times @ SV79 @ SV193 @ SV213 ) @ SV229 )
= ( times_times @ SV79 @ SV193 @ ( times_times @ SV79 @ SV213 @ SV229 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1088,plain,
! [SV144: $i,SV82: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit0 @ SV82 ) @ ( bit1 @ SV144 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV82 @ SV144 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[994]) ).
thf(1089,plain,
! [SV144: $i,SV82: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV82 @ SV144 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit0 @ SV82 ) @ ( bit1 @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[995]) ).
thf(1090,plain,
! [SV146: $i,SV86: $i] :
( ( ( ~ ( ord_less_eq @ int @ ( bit1 @ SV86 ) @ ( bit0 @ SV146 ) ) )
= $true )
| ( ( ord_less @ int @ SV86 @ SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[998]) ).
thf(1091,plain,
! [SV146: $i,SV86: $i] :
( ( ( ~ ( ord_less @ int @ SV86 @ SV146 ) )
= $true )
| ( ( ord_less_eq @ int @ ( bit1 @ SV86 ) @ ( bit0 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[999]) ).
thf(1092,plain,
! [SV147: $i,SV87: $i] :
( ( ( ~ ( ord_less @ int @ SV87 @ ( plus_plus @ int @ SV147 @ ( one_one @ int ) ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV87 @ SV147 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1000]) ).
thf(1093,plain,
! [SV147: $i,SV87: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV87 @ SV147 ) )
= $true )
| ( ( ord_less @ int @ SV87 @ ( plus_plus @ int @ SV147 @ ( one_one @ int ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1001]) ).
thf(1094,plain,
! [SV88: $i] :
( ( ( ord_less @ int @ pls @ ( bit0 @ SV88 ) )
= $false )
| ( ( ord_less @ int @ pls @ SV88 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1095,plain,
! [SV88: $i] :
( ( ( ord_less @ int @ pls @ SV88 )
= $false )
| ( ( ord_less @ int @ pls @ ( bit0 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1096,plain,
! [SV230: $i,SV215: $i,SV196: $i,SV89: $i] :
( ( ( ( times_times @ SV89 @ ( power_power @ SV89 @ SV196 @ SV215 ) @ ( power_power @ SV89 @ SV196 @ SV230 ) )
= ( power_power @ SV89 @ SV196 @ ( plus_plus @ nat @ SV215 @ SV230 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV89 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1097,plain,
! [SV91: $i] :
( ( ( number_ring @ SV91 )
= $false )
| ( ( ~ ( ring_char_0 @ SV91 ) )
= $true )
| ( ( ! [SY372: $i,SY373: $i] :
~ ( ~ ( ( ( number_number_of @ SV91 @ SY372 )
!= ( number_number_of @ SV91 @ SY373 ) )
| ( SY372 = SY373 ) )
| ~ ( ( SY372 != SY373 )
| ( ( number_number_of @ SV91 @ SY372 )
= ( number_number_of @ SV91 @ SY373 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1006]) ).
thf(1098,plain,
! [SV92: $i,SV149: $i] :
( ( ( ~ ( ord_less @ int @ SV149 @ pls ) )
= $true )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1007]) ).
thf(1099,plain,
! [SV92: $i,SV149: $i] :
( ( ( ~ ~ ( ord_less @ int @ SV149 @ pls ) )
= $true )
| ( ( ~ ( ~ ( ~ ( ord_less @ int @ SV92 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ SV149 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV92 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV149 @ SV92 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1008]) ).
thf(1100,plain,
! [SV231: $i,SV216: $i,SV197: $i,SV93: $i] :
( ( ( ( power_power @ SV93 @ ( power_power @ SV93 @ SV197 @ SV216 ) @ SV231 )
= ( power_power @ SV93 @ SV197 @ ( times_times @ nat @ SV216 @ SV231 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1101,plain,
! [SV151: $i,SV95: $i] :
( ( ( ~ ( ord_less @ int @ ( number_number_of @ int @ SV95 ) @ ( number_number_of @ int @ SV151 ) ) )
= $true )
| ( ( ord_less @ int @ SV95 @ SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1010]) ).
thf(1102,plain,
! [SV151: $i,SV95: $i] :
( ( ( ~ ( ord_less @ int @ SV95 @ SV151 ) )
= $true )
| ( ( ord_less @ int @ ( number_number_of @ int @ SV95 ) @ ( number_number_of @ int @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1011]) ).
thf(1103,plain,
! [SV96: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV96 ) @ pls )
= $false )
| ( ( ord_less @ int @ SV96 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1012]) ).
thf(1104,plain,
! [SV96: $i] :
( ( ( ord_less @ int @ SV96 @ pls )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV96 ) @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1105,plain,
! [SV152: $i,SV97: $i] :
( ( ( ~ ( ord_less @ int @ ( bit1 @ SV97 ) @ ( bit0 @ SV152 ) ) )
= $true )
| ( ( ord_less @ int @ SV97 @ SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1014]) ).
thf(1106,plain,
! [SV152: $i,SV97: $i] :
( ( ( ~ ( ord_less @ int @ SV97 @ SV152 ) )
= $true )
| ( ( ord_less @ int @ ( bit1 @ SV97 ) @ ( bit0 @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1015]) ).
thf(1107,plain,
! [SV153: $i,SV98: $i,SV172: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV172 @ SV98 ) )
= $true )
| ( ( ord_less_eq @ int @ SV153 @ SV98 )
= $true )
| ( ( ord_less_eq @ int @ SV153 @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1016]) ).
thf(1108,plain,
! [SV100: $i] :
( ( ( ord_less @ int @ pls @ ( bit1 @ SV100 ) )
= $false )
| ( ( ord_less_eq @ int @ pls @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1109,plain,
! [SV100: $i] :
( ( ( ord_less_eq @ int @ pls @ SV100 )
= $false )
| ( ( ord_less @ int @ pls @ ( bit1 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1110,plain,
! [SV232: $i,SV217: $i,SV198: $i,SV101: $i] :
( ( ( ( plus_plus @ SV101 @ ( plus_plus @ SV101 @ SV198 @ SV217 ) @ SV232 )
= ( plus_plus @ SV101 @ SV198 @ ( plus_plus @ SV101 @ SV217 @ SV232 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1111,plain,
! [SV116: $i,SV25: $i] :
( ( ( ( bit1 @ SV25 )
= ( bit1 @ SV116 ) )
= $false )
| ( ( SV25 = SV116 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1112,plain,
! [SV116: $i,SV25: $i] :
( ( ( SV25 = SV116 )
= $false )
| ( ( ( bit1 @ SV25 )
= ( bit1 @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1113,plain,
( ( ( ( plus_plus @ int @ ( power_power @ int @ sK2_SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ sK4_SY410 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $false )
| ( ( ord_less @ int @ ( one_one @ int ) @ t )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1024]) ).
thf(1114,plain,
! [SV117: $i,SV27: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ SV27 ) @ ( bit0 @ SV117 ) )
= $false )
| ( ( ord_less_eq @ int @ SV27 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1025]) ).
thf(1115,plain,
! [SV117: $i,SV27: $i] :
( ( ( ord_less_eq @ int @ SV27 @ SV117 )
= $false )
| ( ( ord_less_eq @ int @ ( bit0 @ SV27 ) @ ( bit0 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1026]) ).
thf(1116,plain,
! [SV28: $i] :
( ( ( number @ SV28 )
= $false )
| ( ( monoid_mult @ SV28 )
= $false )
| ( ( ! [SY274: $i] :
( ( power_power @ SV28 @ ( number_number_of @ SV28 @ SY274 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV28 @ ( number_number_of @ SV28 @ SY274 ) @ ( number_number_of @ SV28 @ SY274 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1027]) ).
thf(1117,plain,
! [SV118: $i,SV30: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV30 ) @ ( bit1 @ SV118 ) )
= $false )
| ( ( ord_less_eq @ int @ SV30 @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1030]) ).
thf(1118,plain,
! [SV118: $i,SV30: $i] :
( ( ( ord_less_eq @ int @ SV30 @ SV118 )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV30 ) @ ( bit1 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1031]) ).
thf(1119,plain,
! [SV119: $i,SV31: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV31 ) @ ( bit0 @ SV119 ) )
= $false )
| ( ( ord_less @ int @ SV31 @ SV119 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1120,plain,
! [SV119: $i,SV31: $i] :
( ( ( ord_less @ int @ SV31 @ SV119 )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV31 ) @ ( bit0 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1033]) ).
thf(1121,plain,
! [SV122: $i,SV35: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ SV35 ) @ ( bit1 @ SV122 ) )
= $false )
| ( ( ord_less_eq @ int @ SV35 @ SV122 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1122,plain,
! [SV122: $i,SV35: $i] :
( ( ( ord_less_eq @ int @ SV35 @ SV122 )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ SV35 ) @ ( bit1 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1123,plain,
! [SV233: $i,SV218: $i,SV200: $i,SV176: $i,SV36: $i] :
( ( ( ( times_times @ SV36 @ ( times_times @ SV36 @ SV176 @ SV200 ) @ ( times_times @ SV36 @ SV218 @ SV233 ) )
= ( times_times @ SV36 @ SV176 @ ( times_times @ SV36 @ SV200 @ ( times_times @ SV36 @ SV218 @ SV233 ) ) ) )
= $true )
| ( ( comm_semiring_1 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1124,plain,
! [SV123: $i,SV38: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit0 @ SV123 ) )
= $false )
| ( ( ord_less @ int @ SV38 @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1040]) ).
thf(1125,plain,
! [SV123: $i,SV38: $i] :
( ( ( ord_less @ int @ SV38 @ SV123 )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ SV38 ) @ ( bit0 @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1041]) ).
thf(1126,plain,
! [SV124: $i,SV39: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ SV39 ) @ ( bit1 @ SV124 ) )
= $false )
| ( ( ord_less_eq @ int @ SV39 @ SV124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1042]) ).
thf(1127,plain,
! [SV124: $i,SV39: $i] :
( ( ( ord_less_eq @ int @ SV39 @ SV124 )
= $false )
| ( ( ord_less_eq @ int @ ( bit0 @ SV39 ) @ ( bit1 @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1043]) ).
thf(1128,plain,
! [SV126: $i,SV41: $i] :
( ( ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV126 ) )
= $false )
| ( ( ord_less_eq @ int @ SV41 @ SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1044]) ).
thf(1129,plain,
! [SV126: $i,SV41: $i] :
( ( ( ord_less_eq @ int @ SV41 @ SV126 )
= $false )
| ( ( ord_less_eq @ int @ ( number_number_of @ int @ SV41 ) @ ( number_number_of @ int @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1130,plain,
! [SV234: $i,SV220: $i,SV202: $i,SV179: $i,SV43: $i] :
( ( ( ( times_times @ SV43 @ ( times_times @ SV43 @ SV179 @ SV202 ) @ ( times_times @ SV43 @ SV220 @ SV234 ) )
= ( times_times @ SV43 @ ( times_times @ SV43 @ SV179 @ SV220 ) @ ( times_times @ SV43 @ SV202 @ SV234 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1131,plain,
! [SV127: $i,SV44: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV44 ) @ ( bit1 @ SV127 ) )
= $false )
| ( ( ord_less_eq @ int @ SV44 @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1132,plain,
! [SV127: $i,SV44: $i] :
( ( ( ord_less_eq @ int @ SV44 @ SV127 )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV44 ) @ ( bit1 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1133,plain,
! [SV204: $i,SV182: $i,SV51: $i] :
( ( ( ~ ( ( ( number_number_of @ SV51 @ SV182 )
!= ( ti @ SV51 @ SV204 ) )
| ( ( ti @ SV51 @ SV204 )
= ( number_number_of @ SV51 @ SV182 ) ) ) )
= $false )
| ( ( number @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1134,plain,
! [SV182: $i,SV204: $i,SV51: $i] :
( ( ( ~ ( ( ( ti @ SV51 @ SV204 )
!= ( number_number_of @ SV51 @ SV182 ) )
| ( ( number_number_of @ SV51 @ SV182 )
= ( ti @ SV51 @ SV204 ) ) ) )
= $false )
| ( ( number @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1052]) ).
thf(1135,plain,
! [SV52: $i] :
( ( ( linordered_idom @ SV52 )
= $false )
| ( ( number_ring @ SV52 )
= $false )
| ( ( ! [SY310: $i,SY311: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SY310 ) @ ( number_number_of @ SV52 @ SY311 ) )
| ( ord_less_eq @ int @ SY310 @ SY311 ) )
| ~ ( ~ ( ord_less_eq @ int @ SY310 @ SY311 )
| ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SY310 ) @ ( number_number_of @ SV52 @ SY311 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1053]) ).
thf(1136,plain,
! [SV223: $i,SV167: $i] :
( ( ( plus_plus @ int @ ( power_power @ int @ SV167 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ SV223 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1055]) ).
thf(1137,plain,
! [SV130: $i,SV56: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV56 ) @ ( bit1 @ SV130 ) )
= $false )
| ( ( ord_less @ int @ SV56 @ SV130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1138,plain,
! [SV130: $i,SV56: $i] :
( ( ( ord_less @ int @ SV56 @ SV130 )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV56 ) @ ( bit1 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1139,plain,
! [SV131: $i,SV57: $i] :
( ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV57 @ ( one_one @ int ) ) @ SV131 )
= $false )
| ( ( ord_less @ int @ SV57 @ SV131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1059]) ).
thf(1140,plain,
! [SV131: $i,SV57: $i] :
( ( ( ord_less @ int @ SV57 @ SV131 )
= $false )
| ( ( ord_less_eq @ int @ ( plus_plus @ int @ SV57 @ ( one_one @ int ) ) @ SV131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1060]) ).
thf(1141,plain,
! [SV132: $i,SV58: $i] :
( ( ( ord_less @ int @ SV58 @ SV132 )
= $false )
| ( ( ~ ( ~ ( ord_less_eq @ int @ SV58 @ SV132 )
| ~ ( ( SV58 != SV132 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1061]) ).
thf(1142,plain,
! [SV132: $i,SV58: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ int @ SV58 @ SV132 )
| ~ ( ( SV58 != SV132 ) ) ) )
= $false )
| ( ( ord_less @ int @ SV58 @ SV132 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1062]) ).
thf(1143,plain,
! [SV235: $i,SV225: $i,SV207: $i,SV186: $i,SV59: $i] :
( ( ( ( times_times @ SV59 @ ( times_times @ SV59 @ SV186 @ SV207 ) @ ( times_times @ SV59 @ SV225 @ SV235 ) )
= ( times_times @ SV59 @ SV225 @ ( times_times @ SV59 @ ( times_times @ SV59 @ SV186 @ SV207 ) @ SV235 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1144,plain,
! [SV134: $i,SV66: $i] :
( ( ( ( bit0 @ SV66 )
= ( bit0 @ SV134 ) )
= $false )
| ( ( SV66 = SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1068]) ).
thf(1145,plain,
! [SV134: $i,SV66: $i] :
( ( ( SV66 = SV134 )
= $false )
| ( ( ( bit0 @ SV66 )
= ( bit0 @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1069]) ).
thf(1146,plain,
! [SV135: $i,SV67: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ SV67 ) @ ( bit0 @ SV135 ) )
= $false )
| ( ( ord_less_eq @ int @ SV67 @ SV135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1070]) ).
thf(1147,plain,
! [SV135: $i,SV67: $i] :
( ( ( ord_less_eq @ int @ SV67 @ SV135 )
= $false )
| ( ( ord_less_eq @ int @ ( bit0 @ SV67 ) @ ( bit0 @ SV135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1148,plain,
! [SV136: $i,SV68: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ SV68 ) @ ( bit1 @ SV136 ) )
= $false )
| ( ( ord_less_eq @ int @ SV68 @ SV136 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1149,plain,
! [SV136: $i,SV68: $i] :
( ( ( ord_less_eq @ int @ SV68 @ SV136 )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ SV68 ) @ ( bit1 @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1073]) ).
thf(1150,plain,
! [SV137: $i,SV70: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV70 ) @ ( bit0 @ SV137 ) )
= $false )
| ( ( ord_less @ int @ SV70 @ SV137 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1074]) ).
thf(1151,plain,
! [SV137: $i,SV70: $i] :
( ( ( ord_less @ int @ SV70 @ SV137 )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV70 ) @ ( bit0 @ SV137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1152,plain,
! [SV138: $i,SV71: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV71 ) @ ( bit1 @ SV138 ) )
= $false )
| ( ( ord_less @ int @ SV71 @ SV138 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1076]) ).
thf(1153,plain,
! [SV138: $i,SV71: $i] :
( ( ( ord_less @ int @ SV71 @ SV138 )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV71 ) @ ( bit1 @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1077]) ).
thf(1154,plain,
! [SV72: $i] :
( ( ( linordered_idom @ SV72 )
= $false )
| ( ( number_ring @ SV72 )
= $false )
| ( ( ! [SY342: $i,SY343: $i] :
~ ( ~ ( ~ ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SY342 ) @ ( number_number_of @ SV72 @ SY343 ) )
| ( ord_less @ int @ SY342 @ SY343 ) )
| ~ ( ~ ( ord_less @ int @ SY342 @ SY343 )
| ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SY342 ) @ ( number_number_of @ SV72 @ SY343 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1155,plain,
! [SV236: $i,SV228: $i,SV212: $i,SV191: $i,SV73: $i] :
( ( ( ( plus_plus @ SV73 @ ( plus_plus @ SV73 @ SV191 @ SV212 ) @ ( plus_plus @ SV73 @ SV228 @ SV236 ) )
= ( plus_plus @ SV73 @ ( plus_plus @ SV73 @ SV191 @ SV228 ) @ ( plus_plus @ SV73 @ SV212 @ SV236 ) ) )
= $true )
| ( ( comm_semiring_1 @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1156,plain,
! [SV139: $i,SV74: $i] :
( ( ( ord_less @ int @ ( bit0 @ SV74 ) @ ( bit0 @ SV139 ) )
= $false )
| ( ( ord_less @ int @ SV74 @ SV139 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1080]) ).
thf(1157,plain,
! [SV139: $i,SV74: $i] :
( ( ( ord_less @ int @ SV74 @ SV139 )
= $false )
| ( ( ord_less @ int @ ( bit0 @ SV74 ) @ ( bit0 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1158,plain,
( ( ( ( plus_plus @ int @ ( power_power @ int @ sK3_SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ sK5_SY438 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $false )
| ( ( t
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1084]) ).
thf(1159,plain,
! [SV192: $i,SV169: $i,SV142: $i,SV78: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV78 @ SV142 ) )
= $true )
| ( ( ord_less @ int @ ( plus_plus @ int @ SV169 @ SV78 ) @ ( plus_plus @ int @ SV192 @ SV142 ) )
= $true )
| ( ( ord_less @ int @ SV169 @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1086]) ).
thf(1160,plain,
! [SV144: $i,SV82: $i] :
( ( ( ord_less_eq @ int @ ( bit0 @ SV82 ) @ ( bit1 @ SV144 ) )
= $false )
| ( ( ord_less_eq @ int @ SV82 @ SV144 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1161,plain,
! [SV144: $i,SV82: $i] :
( ( ( ord_less_eq @ int @ SV82 @ SV144 )
= $false )
| ( ( ord_less_eq @ int @ ( bit0 @ SV82 ) @ ( bit1 @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1089]) ).
thf(1162,plain,
! [SV146: $i,SV86: $i] :
( ( ( ord_less_eq @ int @ ( bit1 @ SV86 ) @ ( bit0 @ SV146 ) )
= $false )
| ( ( ord_less @ int @ SV86 @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1090]) ).
thf(1163,plain,
! [SV146: $i,SV86: $i] :
( ( ( ord_less @ int @ SV86 @ SV146 )
= $false )
| ( ( ord_less_eq @ int @ ( bit1 @ SV86 ) @ ( bit0 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1164,plain,
! [SV147: $i,SV87: $i] :
( ( ( ord_less @ int @ SV87 @ ( plus_plus @ int @ SV147 @ ( one_one @ int ) ) )
= $false )
| ( ( ord_less_eq @ int @ SV87 @ SV147 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1165,plain,
! [SV147: $i,SV87: $i] :
( ( ( ord_less_eq @ int @ SV87 @ SV147 )
= $false )
| ( ( ord_less @ int @ SV87 @ ( plus_plus @ int @ SV147 @ ( one_one @ int ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1166,plain,
! [SV91: $i] :
( ( ( ring_char_0 @ SV91 )
= $false )
| ( ( number_ring @ SV91 )
= $false )
| ( ( ! [SY372: $i,SY373: $i] :
~ ( ~ ( ( ( number_number_of @ SV91 @ SY372 )
!= ( number_number_of @ SV91 @ SY373 ) )
| ( SY372 = SY373 ) )
| ~ ( ( SY372 != SY373 )
| ( ( number_number_of @ SV91 @ SY372 )
= ( number_number_of @ SV91 @ SY373 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1167,plain,
! [SV92: $i,SV149: $i] :
( ( ( ord_less @ int @ SV149 @ pls )
= $false )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1098]) ).
thf(1168,plain,
! [SV92: $i,SV149: $i] :
( ( ( ~ ( ord_less @ int @ SV149 @ pls ) )
= $false )
| ( ( ~ ( ~ ( ~ ( ord_less @ int @ SV92 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ SV149 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV92 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV149 @ SV92 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1099]) ).
thf(1169,plain,
! [SV151: $i,SV95: $i] :
( ( ( ord_less @ int @ ( number_number_of @ int @ SV95 ) @ ( number_number_of @ int @ SV151 ) )
= $false )
| ( ( ord_less @ int @ SV95 @ SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1170,plain,
! [SV151: $i,SV95: $i] :
( ( ( ord_less @ int @ SV95 @ SV151 )
= $false )
| ( ( ord_less @ int @ ( number_number_of @ int @ SV95 ) @ ( number_number_of @ int @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1171,plain,
! [SV152: $i,SV97: $i] :
( ( ( ord_less @ int @ ( bit1 @ SV97 ) @ ( bit0 @ SV152 ) )
= $false )
| ( ( ord_less @ int @ SV97 @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1105]) ).
thf(1172,plain,
! [SV152: $i,SV97: $i] :
( ( ( ord_less @ int @ SV97 @ SV152 )
= $false )
| ( ( ord_less @ int @ ( bit1 @ SV97 ) @ ( bit0 @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1173,plain,
! [SV153: $i,SV98: $i,SV172: $i] :
( ( ( ord_less_eq @ int @ SV172 @ SV98 )
= $false )
| ( ( ord_less_eq @ int @ SV153 @ SV98 )
= $true )
| ( ( ord_less_eq @ int @ SV153 @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1174,plain,
( ( ( ( plus_plus @ int @ ( power_power @ int @ sK2_SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ sK4_SY410 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true )
| ( ( ord_less @ int @ ( one_one @ int ) @ t )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1113]) ).
thf(1175,plain,
! [SV237: $i,SV28: $i] :
( ( ( ( power_power @ SV28 @ ( number_number_of @ SV28 @ SV237 ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ SV28 @ ( number_number_of @ SV28 @ SV237 ) @ ( number_number_of @ SV28 @ SV237 ) ) )
= $true )
| ( ( monoid_mult @ SV28 )
= $false )
| ( ( number @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1176,plain,
! [SV204: $i,SV182: $i,SV51: $i] :
( ( ( ( ( number_number_of @ SV51 @ SV182 )
!= ( ti @ SV51 @ SV204 ) )
| ( ( ti @ SV51 @ SV204 )
= ( number_number_of @ SV51 @ SV182 ) ) )
= $true )
| ( ( number @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1133]) ).
thf(1177,plain,
! [SV182: $i,SV204: $i,SV51: $i] :
( ( ( ( ( ti @ SV51 @ SV204 )
!= ( number_number_of @ SV51 @ SV182 ) )
| ( ( number_number_of @ SV51 @ SV182 )
= ( ti @ SV51 @ SV204 ) ) )
= $true )
| ( ( number @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1134]) ).
thf(1178,plain,
! [SV238: $i,SV52: $i] :
( ( ( ! [SY470: $i] :
~ ( ~ ( ~ ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SV238 ) @ ( number_number_of @ SV52 @ SY470 ) )
| ( ord_less_eq @ int @ SV238 @ SY470 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV238 @ SY470 )
| ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SV238 ) @ ( number_number_of @ SV52 @ SY470 ) ) ) ) )
= $true )
| ( ( number_ring @ SV52 )
= $false )
| ( ( linordered_idom @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1179,plain,
! [SV132: $i,SV58: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV58 @ SV132 )
| ~ ( ( SV58 != SV132 ) ) )
= $false )
| ( ( ord_less @ int @ SV58 @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1141]) ).
thf(1180,plain,
! [SV132: $i,SV58: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV58 @ SV132 )
| ~ ( ( SV58 != SV132 ) ) )
= $true )
| ( ( ord_less @ int @ SV58 @ SV132 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1142]) ).
thf(1181,plain,
! [SV239: $i,SV72: $i] :
( ( ( ! [SY471: $i] :
~ ( ~ ( ~ ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SV239 ) @ ( number_number_of @ SV72 @ SY471 ) )
| ( ord_less @ int @ SV239 @ SY471 ) )
| ~ ( ~ ( ord_less @ int @ SV239 @ SY471 )
| ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SV239 ) @ ( number_number_of @ SV72 @ SY471 ) ) ) ) )
= $true )
| ( ( number_ring @ SV72 )
= $false )
| ( ( linordered_idom @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1182,plain,
( ( ( ( plus_plus @ int @ ( power_power @ int @ sK3_SX0 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ sK5_SY438 @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ ( one_one @ int ) ) )
= $true )
| ( ( t
= ( one_one @ int ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1158]) ).
thf(1183,plain,
! [SV192: $i,SV169: $i,SV142: $i,SV78: $i] :
( ( ( ord_less_eq @ int @ SV78 @ SV142 )
= $false )
| ( ( ord_less @ int @ ( plus_plus @ int @ SV169 @ SV78 ) @ ( plus_plus @ int @ SV192 @ SV142 ) )
= $true )
| ( ( ord_less @ int @ SV169 @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1159]) ).
thf(1184,plain,
! [SV240: $i,SV91: $i] :
( ( ( ! [SY472: $i] :
~ ( ~ ( ( ( number_number_of @ SV91 @ SV240 )
!= ( number_number_of @ SV91 @ SY472 ) )
| ( SV240 = SY472 ) )
| ~ ( ( SV240 != SY472 )
| ( ( number_number_of @ SV91 @ SV240 )
= ( number_number_of @ SV91 @ SY472 ) ) ) ) )
= $true )
| ( ( number_ring @ SV91 )
= $false )
| ( ( ring_char_0 @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1185,plain,
! [SV92: $i,SV149: $i] :
( ( ( ord_less @ int @ SV149 @ pls )
= $true )
| ( ( ~ ( ~ ( ~ ( ord_less @ int @ SV92 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ SV149 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV92 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV149 @ SV92 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1168]) ).
thf(1186,plain,
! [SV204: $i,SV182: $i,SV51: $i] :
( ( ( ( number_number_of @ SV51 @ SV182 )
!= ( ti @ SV51 @ SV204 ) )
= $true )
| ( ( ( ti @ SV51 @ SV204 )
= ( number_number_of @ SV51 @ SV182 ) )
= $true )
| ( ( number @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1176]) ).
thf(1187,plain,
! [SV182: $i,SV204: $i,SV51: $i] :
( ( ( ( ti @ SV51 @ SV204 )
!= ( number_number_of @ SV51 @ SV182 ) )
= $true )
| ( ( ( number_number_of @ SV51 @ SV182 )
= ( ti @ SV51 @ SV204 ) )
= $true )
| ( ( number @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1177]) ).
thf(1188,plain,
! [SV241: $i,SV238: $i,SV52: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SV238 ) @ ( number_number_of @ SV52 @ SV241 ) )
| ( ord_less_eq @ int @ SV238 @ SV241 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV238 @ SV241 )
| ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SV238 ) @ ( number_number_of @ SV52 @ SV241 ) ) ) ) )
= $true )
| ( ( number_ring @ SV52 )
= $false )
| ( ( linordered_idom @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1189,plain,
! [SV132: $i,SV58: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV58 @ SV132 ) )
= $false )
| ( ( ord_less @ int @ SV58 @ SV132 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1179]) ).
thf(1190,plain,
! [SV132: $i,SV58: $i] :
( ( ( ~ ( ( SV58 != SV132 ) ) )
= $false )
| ( ( ord_less @ int @ SV58 @ SV132 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1179]) ).
thf(1191,plain,
! [SV132: $i,SV58: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV58 @ SV132 ) )
= $true )
| ( ( ~ ( ( SV58 != SV132 ) ) )
= $true )
| ( ( ord_less @ int @ SV58 @ SV132 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1180]) ).
thf(1192,plain,
! [SV242: $i,SV239: $i,SV72: $i] :
( ( ( ~ ( ~ ( ~ ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SV239 ) @ ( number_number_of @ SV72 @ SV242 ) )
| ( ord_less @ int @ SV239 @ SV242 ) )
| ~ ( ~ ( ord_less @ int @ SV239 @ SV242 )
| ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SV239 ) @ ( number_number_of @ SV72 @ SV242 ) ) ) ) )
= $true )
| ( ( number_ring @ SV72 )
= $false )
| ( ( linordered_idom @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1193,plain,
! [SV243: $i,SV240: $i,SV91: $i] :
( ( ( ~ ( ~ ( ( ( number_number_of @ SV91 @ SV240 )
!= ( number_number_of @ SV91 @ SV243 ) )
| ( SV240 = SV243 ) )
| ~ ( ( SV240 != SV243 )
| ( ( number_number_of @ SV91 @ SV240 )
= ( number_number_of @ SV91 @ SV243 ) ) ) ) )
= $true )
| ( ( number_ring @ SV91 )
= $false )
| ( ( ring_char_0 @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1194,plain,
! [SV149: $i,SV92: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ SV92 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ SV149 ) ) )
| ~ ( ~ ~ ( ord_less @ int @ SV92 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV149 @ SV92 ) ) ) ) )
= $false )
| ( ( ord_less @ int @ SV149 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1195,plain,
! [SV204: $i,SV182: $i,SV51: $i] :
( ( ( ( number_number_of @ SV51 @ SV182 )
= ( ti @ SV51 @ SV204 ) )
= $false )
| ( ( ( ti @ SV51 @ SV204 )
= ( number_number_of @ SV51 @ SV182 ) )
= $true )
| ( ( number @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1196,plain,
! [SV182: $i,SV204: $i,SV51: $i] :
( ( ( ( ti @ SV51 @ SV204 )
= ( number_number_of @ SV51 @ SV182 ) )
= $false )
| ( ( ( number_number_of @ SV51 @ SV182 )
= ( ti @ SV51 @ SV204 ) )
= $true )
| ( ( number @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1187]) ).
thf(1197,plain,
! [SV241: $i,SV238: $i,SV52: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SV238 ) @ ( number_number_of @ SV52 @ SV241 ) )
| ( ord_less_eq @ int @ SV238 @ SV241 ) )
| ~ ( ~ ( ord_less_eq @ int @ SV238 @ SV241 )
| ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SV238 ) @ ( number_number_of @ SV52 @ SV241 ) ) ) )
= $false )
| ( ( number_ring @ SV52 )
= $false )
| ( ( linordered_idom @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1188]) ).
thf(1198,plain,
! [SV132: $i,SV58: $i] :
( ( ( ord_less_eq @ int @ SV58 @ SV132 )
= $true )
| ( ( ord_less @ int @ SV58 @ SV132 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1189]) ).
thf(1199,plain,
! [SV132: $i,SV58: $i] :
( ( ( SV58 != SV132 )
= $true )
| ( ( ord_less @ int @ SV58 @ SV132 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1190]) ).
thf(1200,plain,
! [SV132: $i,SV58: $i] :
( ( ( ord_less_eq @ int @ SV58 @ SV132 )
= $false )
| ( ( ~ ( ( SV58 != SV132 ) ) )
= $true )
| ( ( ord_less @ int @ SV58 @ SV132 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1201,plain,
! [SV242: $i,SV239: $i,SV72: $i] :
( ( ( ~ ( ~ ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SV239 ) @ ( number_number_of @ SV72 @ SV242 ) )
| ( ord_less @ int @ SV239 @ SV242 ) )
| ~ ( ~ ( ord_less @ int @ SV239 @ SV242 )
| ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SV239 ) @ ( number_number_of @ SV72 @ SV242 ) ) ) )
= $false )
| ( ( number_ring @ SV72 )
= $false )
| ( ( linordered_idom @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1202,plain,
! [SV243: $i,SV240: $i,SV91: $i] :
( ( ( ~ ( ( ( number_number_of @ SV91 @ SV240 )
!= ( number_number_of @ SV91 @ SV243 ) )
| ( SV240 = SV243 ) )
| ~ ( ( SV240 != SV243 )
| ( ( number_number_of @ SV91 @ SV240 )
= ( number_number_of @ SV91 @ SV243 ) ) ) )
= $false )
| ( ( number_ring @ SV91 )
= $false )
| ( ( ring_char_0 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1193]) ).
thf(1203,plain,
! [SV149: $i,SV92: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ SV92 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ SV149 ) ) ) )
= $false )
| ( ( ord_less @ int @ SV149 @ pls )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1194]) ).
thf(1204,plain,
! [SV149: $i,SV92: $i] :
( ( ( ~ ( ~ ~ ( ord_less @ int @ SV92 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV149 @ SV92 ) ) ) ) )
= $false )
| ( ( ord_less @ int @ SV149 @ pls )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1194]) ).
thf(1205,plain,
! [SV241: $i,SV238: $i,SV52: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SV238 ) @ ( number_number_of @ SV52 @ SV241 ) )
| ( ord_less_eq @ int @ SV238 @ SV241 ) ) )
= $false )
| ( ( number_ring @ SV52 )
= $false )
| ( ( linordered_idom @ SV52 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1197]) ).
thf(1206,plain,
! [SV52: $i,SV241: $i,SV238: $i] :
( ( ( ~ ( ~ ( ord_less_eq @ int @ SV238 @ SV241 )
| ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SV238 ) @ ( number_number_of @ SV52 @ SV241 ) ) ) )
= $false )
| ( ( number_ring @ SV52 )
= $false )
| ( ( linordered_idom @ SV52 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1197]) ).
thf(1207,plain,
! [SV132: $i,SV58: $i] :
( ( ( SV58 = SV132 )
= $false )
| ( ( ord_less @ int @ SV58 @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1208,plain,
! [SV132: $i,SV58: $i] :
( ( ( SV58 != SV132 )
= $false )
| ( ( ord_less_eq @ int @ SV58 @ SV132 )
= $false )
| ( ( ord_less @ int @ SV58 @ SV132 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1209,plain,
! [SV242: $i,SV239: $i,SV72: $i] :
( ( ( ~ ( ~ ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SV239 ) @ ( number_number_of @ SV72 @ SV242 ) )
| ( ord_less @ int @ SV239 @ SV242 ) ) )
= $false )
| ( ( number_ring @ SV72 )
= $false )
| ( ( linordered_idom @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1201]) ).
thf(1210,plain,
! [SV72: $i,SV242: $i,SV239: $i] :
( ( ( ~ ( ~ ( ord_less @ int @ SV239 @ SV242 )
| ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SV239 ) @ ( number_number_of @ SV72 @ SV242 ) ) ) )
= $false )
| ( ( number_ring @ SV72 )
= $false )
| ( ( linordered_idom @ SV72 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1201]) ).
thf(1211,plain,
! [SV243: $i,SV240: $i,SV91: $i] :
( ( ( ~ ( ( ( number_number_of @ SV91 @ SV240 )
!= ( number_number_of @ SV91 @ SV243 ) )
| ( SV240 = SV243 ) ) )
= $false )
| ( ( number_ring @ SV91 )
= $false )
| ( ( ring_char_0 @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1202]) ).
thf(1212,plain,
! [SV91: $i,SV243: $i,SV240: $i] :
( ( ( ~ ( ( SV240 != SV243 )
| ( ( number_number_of @ SV91 @ SV240 )
= ( number_number_of @ SV91 @ SV243 ) ) ) )
= $false )
| ( ( number_ring @ SV91 )
= $false )
| ( ( ring_char_0 @ SV91 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1202]) ).
thf(1213,plain,
! [SV149: $i,SV92: $i] :
( ( ( ~ ( ord_less @ int @ SV92 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ SV149 ) ) )
= $true )
| ( ( ord_less @ int @ SV149 @ pls )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1203]) ).
thf(1214,plain,
! [SV149: $i,SV92: $i] :
( ( ( ~ ~ ( ord_less @ int @ SV92 @ pls )
| ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV149 @ SV92 ) ) ) )
= $true )
| ( ( ord_less @ int @ SV149 @ pls )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1204]) ).
thf(1215,plain,
! [SV241: $i,SV238: $i,SV52: $i] :
( ( ( ~ ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SV238 ) @ ( number_number_of @ SV52 @ SV241 ) )
| ( ord_less_eq @ int @ SV238 @ SV241 ) )
= $true )
| ( ( number_ring @ SV52 )
= $false )
| ( ( linordered_idom @ SV52 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1205]) ).
thf(1216,plain,
! [SV52: $i,SV241: $i,SV238: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV238 @ SV241 )
| ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SV238 ) @ ( number_number_of @ SV52 @ SV241 ) ) )
= $true )
| ( ( number_ring @ SV52 )
= $false )
| ( ( linordered_idom @ SV52 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1206]) ).
thf(1217,plain,
! [SV132: $i,SV58: $i] :
( ( ( SV58 = SV132 )
= $true )
| ( ( ord_less_eq @ int @ SV58 @ SV132 )
= $false )
| ( ( ord_less @ int @ SV58 @ SV132 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1208]) ).
thf(1218,plain,
! [SV242: $i,SV239: $i,SV72: $i] :
( ( ( ~ ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SV239 ) @ ( number_number_of @ SV72 @ SV242 ) )
| ( ord_less @ int @ SV239 @ SV242 ) )
= $true )
| ( ( number_ring @ SV72 )
= $false )
| ( ( linordered_idom @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1209]) ).
thf(1219,plain,
! [SV72: $i,SV242: $i,SV239: $i] :
( ( ( ~ ( ord_less @ int @ SV239 @ SV242 )
| ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SV239 ) @ ( number_number_of @ SV72 @ SV242 ) ) )
= $true )
| ( ( number_ring @ SV72 )
= $false )
| ( ( linordered_idom @ SV72 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1210]) ).
thf(1220,plain,
! [SV243: $i,SV240: $i,SV91: $i] :
( ( ( ( ( number_number_of @ SV91 @ SV240 )
!= ( number_number_of @ SV91 @ SV243 ) )
| ( SV240 = SV243 ) )
= $true )
| ( ( number_ring @ SV91 )
= $false )
| ( ( ring_char_0 @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1211]) ).
thf(1221,plain,
! [SV91: $i,SV243: $i,SV240: $i] :
( ( ( ( SV240 != SV243 )
| ( ( number_number_of @ SV91 @ SV240 )
= ( number_number_of @ SV91 @ SV243 ) ) )
= $true )
| ( ( number_ring @ SV91 )
= $false )
| ( ( ring_char_0 @ SV91 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1212]) ).
thf(1222,plain,
! [SV149: $i,SV92: $i] :
( ( ( ~ ( ord_less @ int @ SV92 @ pls ) )
= $true )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ SV149 ) )
= $true )
| ( ( ord_less @ int @ SV149 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1213]) ).
thf(1223,plain,
! [SV149: $i,SV92: $i] :
( ( ( ~ ~ ( ord_less @ int @ SV92 @ pls ) )
= $true )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV149 @ SV92 ) ) )
= $true )
| ( ( ord_less @ int @ SV149 @ pls )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1214]) ).
thf(1224,plain,
! [SV241: $i,SV238: $i,SV52: $i] :
( ( ( ~ ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SV238 ) @ ( number_number_of @ SV52 @ SV241 ) ) )
= $true )
| ( ( ord_less_eq @ int @ SV238 @ SV241 )
= $true )
| ( ( number_ring @ SV52 )
= $false )
| ( ( linordered_idom @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1215]) ).
thf(1225,plain,
! [SV52: $i,SV241: $i,SV238: $i] :
( ( ( ~ ( ord_less_eq @ int @ SV238 @ SV241 ) )
= $true )
| ( ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SV238 ) @ ( number_number_of @ SV52 @ SV241 ) )
= $true )
| ( ( number_ring @ SV52 )
= $false )
| ( ( linordered_idom @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1216]) ).
thf(1226,plain,
! [SV242: $i,SV239: $i,SV72: $i] :
( ( ( ~ ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SV239 ) @ ( number_number_of @ SV72 @ SV242 ) ) )
= $true )
| ( ( ord_less @ int @ SV239 @ SV242 )
= $true )
| ( ( number_ring @ SV72 )
= $false )
| ( ( linordered_idom @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1218]) ).
thf(1227,plain,
! [SV72: $i,SV242: $i,SV239: $i] :
( ( ( ~ ( ord_less @ int @ SV239 @ SV242 ) )
= $true )
| ( ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SV239 ) @ ( number_number_of @ SV72 @ SV242 ) )
= $true )
| ( ( number_ring @ SV72 )
= $false )
| ( ( linordered_idom @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1219]) ).
thf(1228,plain,
! [SV243: $i,SV240: $i,SV91: $i] :
( ( ( ( number_number_of @ SV91 @ SV240 )
!= ( number_number_of @ SV91 @ SV243 ) )
= $true )
| ( ( SV240 = SV243 )
= $true )
| ( ( number_ring @ SV91 )
= $false )
| ( ( ring_char_0 @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1220]) ).
thf(1229,plain,
! [SV91: $i,SV243: $i,SV240: $i] :
( ( ( SV240 != SV243 )
= $true )
| ( ( ( number_number_of @ SV91 @ SV240 )
= ( number_number_of @ SV91 @ SV243 ) )
= $true )
| ( ( number_ring @ SV91 )
= $false )
| ( ( ring_char_0 @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1221]) ).
thf(1230,plain,
! [SV149: $i,SV92: $i] :
( ( ( ord_less @ int @ SV92 @ pls )
= $false )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ SV149 ) )
= $true )
| ( ( ord_less @ int @ SV149 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1231,plain,
! [SV149: $i,SV92: $i] :
( ( ( ~ ( ord_less @ int @ SV92 @ pls ) )
= $false )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV149 @ SV92 ) ) )
= $true )
| ( ( ord_less @ int @ SV149 @ pls )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1232,plain,
! [SV241: $i,SV238: $i,SV52: $i] :
( ( ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SV238 ) @ ( number_number_of @ SV52 @ SV241 ) )
= $false )
| ( ( ord_less_eq @ int @ SV238 @ SV241 )
= $true )
| ( ( number_ring @ SV52 )
= $false )
| ( ( linordered_idom @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1224]) ).
thf(1233,plain,
! [SV52: $i,SV241: $i,SV238: $i] :
( ( ( ord_less_eq @ int @ SV238 @ SV241 )
= $false )
| ( ( ord_less_eq @ SV52 @ ( number_number_of @ SV52 @ SV238 ) @ ( number_number_of @ SV52 @ SV241 ) )
= $true )
| ( ( number_ring @ SV52 )
= $false )
| ( ( linordered_idom @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1225]) ).
thf(1234,plain,
! [SV242: $i,SV239: $i,SV72: $i] :
( ( ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SV239 ) @ ( number_number_of @ SV72 @ SV242 ) )
= $false )
| ( ( ord_less @ int @ SV239 @ SV242 )
= $true )
| ( ( number_ring @ SV72 )
= $false )
| ( ( linordered_idom @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1226]) ).
thf(1235,plain,
! [SV72: $i,SV242: $i,SV239: $i] :
( ( ( ord_less @ int @ SV239 @ SV242 )
= $false )
| ( ( ord_less @ SV72 @ ( number_number_of @ SV72 @ SV239 ) @ ( number_number_of @ SV72 @ SV242 ) )
= $true )
| ( ( number_ring @ SV72 )
= $false )
| ( ( linordered_idom @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1227]) ).
thf(1236,plain,
! [SV243: $i,SV240: $i,SV91: $i] :
( ( ( ( number_number_of @ SV91 @ SV240 )
= ( number_number_of @ SV91 @ SV243 ) )
= $false )
| ( ( SV240 = SV243 )
= $true )
| ( ( number_ring @ SV91 )
= $false )
| ( ( ring_char_0 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1237,plain,
! [SV91: $i,SV243: $i,SV240: $i] :
( ( ( SV240 = SV243 )
= $false )
| ( ( ( number_number_of @ SV91 @ SV240 )
= ( number_number_of @ SV91 @ SV243 ) )
= $true )
| ( ( number_ring @ SV91 )
= $false )
| ( ( ring_char_0 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1229]) ).
thf(1238,plain,
! [SV149: $i,SV92: $i] :
( ( ( ord_less @ int @ SV92 @ pls )
= $true )
| ( ( ( plus_plus @ nat @ ( number_number_of @ nat @ SV149 ) @ ( number_number_of @ nat @ SV92 ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ SV149 @ SV92 ) ) )
= $true )
| ( ( ord_less @ int @ SV149 @ pls )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1231]) ).
thf(1239,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[284,1238,1237,1236,1235,1234,1233,1232,1230,1217,1207,1198,1196,1195,1183,1182,1175,1174,1173,1172,1171,1170,1169,1167,1165,1164,1163,1162,1161,1160,1157,1156,1155,1153,1152,1151,1150,1149,1148,1147,1146,1145,1144,1143,1140,1139,1138,1137,1136,1132,1131,1130,1129,1128,1127,1126,1125,1124,1123,1122,1121,1120,1119,1118,1117,1115,1114,1112,1111,1110,1109,1108,1104,1103,1100,1096,1095,1094,1087,1085,1083,1082,1067,1066,1065,1064,1056,1054,1051,1050,1049,1039,1035,1034,1029,1028,1021,1017,1005,997,996,991,972,968,954,953,944,935,932,919,917,916,904,887,886,863,850,843,835,810,802,781,764,763,741,708,707,706,705,704,702,616,613,607,606,517,514,513,512,507,506,503,502,501,500,413,412,411,410,409,408,407,406,405,404,403,402,401,400,399,365,355,354,346,338,308,307,306,305,302,301,300,285]) ).
thf(1240,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1239]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM926+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.09 % Computer : n012.cluster.edu
% 0.00/0.09 % Model : x86_64 x86_64
% 0.00/0.09 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.09 % Memory : 8046.5625MB
% 0.00/0.09 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Oct 6 13:45:00 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.08/1.15 .
% 6.08/1.15
% 6.08/1.15 No.of.Axioms: 134
% 6.08/1.15
% 6.08/1.15 Length.of.Defs: 0
% 6.08/1.15
% 6.08/1.15 Contains.Choice.Funs: false
% 6.08/1.15 ..............................................
% 6.08/1.15
% 6.08/1.15 ********************************
% 6.08/1.15 * All subproblems solved! *
% 6.08/1.15 ********************************
% 6.08/1.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:134,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:1239,loop_count:0,foatp_calls:1,translation:fof_full)
% 6.08/1.15
% 6.08/1.15 %**** Beginning of derivation protocol ****
% 6.08/1.15 % SZS output start CNFRefutation
% See solution above
% 6.08/1.16
% 6.08/1.16 %**** End of derivation protocol ****
% 6.08/1.16 %**** no. of clauses in derivation: 1233 ****
% 6.08/1.16 %**** clause counter: 1239 ****
% 6.08/1.16
% 6.08/1.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:134,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:1239,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------