%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP062^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:14 AM UTC 2026
% Result : Theorem 18.24s 3.89s
% Output : Refutation 18.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 174 ( 64 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 1026 ( 37 ~; 16 |; 0 &; 964 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 121 ( 118 usr; 10 con; 0-4 aty)
% Number of variables : 51 ( 0 ^; 51 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
real: $tType ).
thf(type_def_8,type,
num: $tType ).
thf(type_def_9,type,
set_real: $tType ).
thf(func_def_0,type,
set_real: $tType ).
thf(func_def_1,type,
real: $tType ).
thf(func_def_2,type,
num: $tType ).
thf(func_def_3,type,
nat: $tType ).
thf(func_def_4,type,
genClo1161277105lle_PC: nat > real > real ).
thf(func_def_5,type,
genClo1144207539le_rho: real ).
thf(func_def_6,type,
genClo1015804716orrect: nat > real > $o ).
thf(func_def_7,type,
genClo293725281kRead1: ( nat > real ) > real > ( nat > $o ) > $o ).
thf(func_def_8,type,
genClo293725282kRead2: ( nat > real ) > ( nat > real ) > real > ( nat > $o ) > $o ).
thf(func_def_9,type,
genClo2108747022bound1: ( nat > real > real ) > $o ).
thf(func_def_10,type,
genClo2108747023bound2: ( nat > real > real ) > $o ).
thf(func_def_11,type,
abs_abs_real: real > real ).
thf(func_def_12,type,
minus_minus_nat: nat > nat > nat ).
thf(func_def_13,type,
minus_minus_real: real > real > real ).
thf(func_def_14,type,
one_one_nat: nat ).
thf(func_def_15,type,
one_one_real: real ).
thf(func_def_16,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_17,type,
plus_plus_num: num > num > num ).
thf(func_def_18,type,
plus_plus_real: real > real > real ).
thf(func_def_19,type,
times_times_nat: nat > nat > nat ).
thf(func_def_20,type,
times_times_num: num > num > num ).
thf(func_def_21,type,
times_times_real: real > real > real ).
thf(func_def_22,type,
neg_numeral_dbl_real: real > real ).
thf(func_def_23,type,
bit0: num > num ).
thf(func_def_24,type,
one: num ).
thf(func_def_25,type,
numeral_numeral_nat: num > nat ).
thf(func_def_26,type,
numeral_numeral_real: num > real ).
thf(func_def_27,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_28,type,
ord_less_eq_num: num > num > $o ).
thf(func_def_29,type,
ord_less_eq_real: real > real > $o ).
thf(func_def_30,type,
collect_real: ( real > $o ) > set_real ).
thf(func_def_31,type,
member_real: real > set_real > $o ).
thf(func_def_32,type,
c: nat > real > real ).
thf(func_def_33,type,
d: nat > real > real ).
thf(func_def_34,type,
p: nat ).
thf(func_def_35,type,
q: nat ).
thf(func_def_36,type,
s: real ).
thf(func_def_37,type,
t: real ).
thf(func_def_52,type,
sP0: num > num > num > $o ).
thf(func_def_53,type,
sP1: num > num > num > $o ).
thf(func_def_54,type,
sP2: num > num > num > $o ).
thf(func_def_55,type,
sP3: nat > nat > nat > $o ).
thf(func_def_56,type,
sP4: nat > nat > nat > $o ).
thf(func_def_57,type,
sP5: nat > nat > nat > $o ).
thf(func_def_58,type,
sP6: real > real > real > $o ).
thf(func_def_59,type,
sP7: real > real > real > $o ).
thf(func_def_60,type,
sP8: real > real > real > $o ).
thf(func_def_61,type,
sK9: ( real > num ) > real ).
thf(func_def_62,type,
sK10: ( real > num ) > real ).
thf(func_def_63,type,
sK11: ( num > real ) > num ).
thf(func_def_64,type,
sK12: ( num > real ) > num ).
thf(func_def_65,type,
sK13: ( nat > real ) > nat ).
thf(func_def_66,type,
sK14: ( nat > real ) > nat ).
thf(func_def_67,type,
sK15: ( real > num ) > real ).
thf(func_def_68,type,
sK16: ( real > num ) > real ).
thf(func_def_69,type,
sK17: ( nat > nat ) > nat ).
thf(func_def_70,type,
sK18: ( nat > nat ) > nat ).
thf(func_def_71,type,
sK19: ( nat > real ) > nat ).
thf(func_def_72,type,
sK20: ( nat > real ) > nat ).
thf(func_def_73,type,
sK21: ( num > num ) > num ).
thf(func_def_74,type,
sK22: ( num > num ) > num ).
thf(func_def_75,type,
sK23: ( num > num ) > num ).
thf(func_def_76,type,
sK24: ( num > num ) > num ).
thf(func_def_77,type,
sK25: ( real > nat ) > real ).
thf(func_def_78,type,
sK26: ( real > nat ) > real ).
thf(func_def_79,type,
sK27: ( nat > nat ) > nat ).
thf(func_def_80,type,
sK28: ( nat > nat ) > nat ).
thf(func_def_81,type,
sK29: ( nat > nat ) > nat ).
thf(func_def_82,type,
sK30: ( nat > nat ) > nat ).
thf(func_def_83,type,
sK31: ( real > nat ) > real ).
thf(func_def_84,type,
sK32: ( real > nat ) > real ).
thf(func_def_85,type,
sK33: ( real > real ) > real ).
thf(func_def_86,type,
sK34: ( real > real ) > real ).
thf(func_def_87,type,
sK35: ( num > num ) > num ).
thf(func_def_88,type,
sK36: ( num > num ) > num ).
thf(func_def_89,type,
sK37: ( num > nat ) > num ).
thf(func_def_90,type,
sK38: ( num > nat ) > num ).
thf(func_def_91,type,
sK39: ( num > real ) > num ).
thf(func_def_92,type,
sK40: ( num > real ) > num ).
thf(func_def_93,type,
sK41: ( nat > nat ) > nat ).
thf(func_def_94,type,
sK42: ( nat > nat ) > nat ).
thf(func_def_95,type,
sK43: ( num > nat ) > num ).
thf(func_def_96,type,
sK44: ( num > nat ) > num ).
thf(func_def_97,type,
sK45: ( nat > num ) > nat ).
thf(func_def_98,type,
sK46: ( nat > num ) > nat ).
thf(func_def_99,type,
sK47: ( real > nat ) > real ).
thf(func_def_100,type,
sK48: ( real > nat ) > real ).
thf(func_def_101,type,
sK49: ( real > nat ) > real ).
thf(func_def_102,type,
sK50: ( real > nat ) > real ).
thf(func_def_103,type,
sK51: ( nat > num ) > nat ).
thf(func_def_104,type,
sK52: ( nat > num ) > nat ).
thf(func_def_105,type,
sK53: ( nat > num ) > nat ).
thf(func_def_106,type,
sK54: ( nat > num ) > nat ).
thf(func_def_107,type,
sK55: ( real > num ) > real ).
thf(func_def_108,type,
sK56: ( real > num ) > real ).
thf(func_def_109,type,
sK57: ( real > real ) > real ).
thf(func_def_110,type,
sK58: ( real > real ) > real ).
thf(func_def_111,type,
sK59: ( num > nat ) > num ).
thf(func_def_112,type,
sK60: ( num > nat ) > num ).
thf(func_def_113,type,
sK61: ( num > nat ) > num ).
thf(func_def_114,type,
sK62: ( num > nat ) > num ).
thf(func_def_115,type,
sK63: ( num > num ) > num ).
thf(func_def_116,type,
sK64: ( num > num ) > num ).
thf(func_def_117,type,
sK65: ( nat > $o ) > nat ).
thf(func_def_118,type,
sK66: ( nat > $o ) > nat > nat ).
thf(func_def_119,type,
sK67: ( num > real ) > num ).
thf(func_def_120,type,
sK68: ( num > real ) > num ).
thf(func_def_121,type,
sK69: ( real > real ) > real ).
thf(func_def_122,type,
sK70: ( real > real ) > real ).
thf(func_def_123,type,
sK71: ( nat > real ) > nat ).
thf(func_def_124,type,
sK72: ( nat > real ) > nat ).
thf(func_def_125,type,
sK73: ( num > real ) > num ).
thf(func_def_126,type,
sK74: ( num > real ) > num ).
thf(func_def_127,type,
sK75: ( real > real ) > real ).
thf(func_def_128,type,
sK76: ( real > real ) > real ).
thf(func_def_129,type,
sK77: ( nat > num ) > nat ).
thf(func_def_130,type,
sK78: ( nat > num ) > nat ).
thf(func_def_131,type,
sK79: ( real > num ) > real ).
thf(func_def_132,type,
sK80: ( real > num ) > real ).
thf(func_def_133,type,
sK81: ( nat > real ) > nat ).
thf(func_def_134,type,
sK82: ( nat > real ) > nat ).
thf(func_def_136,type,
ph84:
!>[X0: $tType] : X0 ).
thf(f1697,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1696,f1469]) ).
thf(f1469,plain,
! [X1: real] :
( $true
= ( ord_less_eq_real @ X1 @ X1 ) ),
inference(equality_resolution,[status(thm)],[f1395]) ).
thf(f1395,plain,
! [X0: real,X1: real] :
( ( ( ord_less_eq_real @ X1 @ X0 )
= $true )
| ( X0 != X1 ) ),
inference(cnf_transformation,[status(thm)],[f867]) ).
thf(f867,plain,
! [X0: real,X1: real] :
( ( ( ord_less_eq_real @ X1 @ X0 )
= $true )
| ( X0 != X1 ) ),
inference(ennf_transformation,[status(thm)],[f479]) ).
thf(f479,plain,
! [X0: real,X1: real] :
( ( X0 = X1 )
=> ( ( ord_less_eq_real @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f478]) ).
thf(f478,plain,
! [X0: real,X1: real] :
( ( X0 = X1 )
=> ( ord_less_eq_real @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f298]) ).
thf(f298,axiom,
! [X33: real,X19: real] :
( ( X19 = X33 )
=> ( ord_less_eq_real @ X19 @ X33 ) ),
file('/export/starexec/sandbox/tmp/tmp.3sGo6IMQoe/DTF2THF_1172.p',fact_297_eq__refl) ).
thf(f1696,plain,
( $true
!= ( ord_less_eq_real @ ( times_times_real @ genClo1144207539le_rho @ ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( minus_minus_real @ t @ s ) ) ) @ ( times_times_real @ genClo1144207539le_rho @ ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( minus_minus_real @ t @ s ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1695,f1331]) ).
thf(f1331,plain,
( ( numeral_numeral_real @ ( bit0 @ one ) )
= ( plus_plus_real @ one_one_real @ one_one_real ) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
thf(f85,axiom,
( ( numeral_numeral_real @ ( bit0 @ one ) )
= ( plus_plus_real @ one_one_real @ one_one_real ) ),
file('/export/starexec/sandbox/tmp/tmp.3sGo6IMQoe/DTF2THF_1172.p',fact_84_one__add__one) ).
thf(f1695,plain,
( $true
!= ( ord_less_eq_real @ ( times_times_real @ genClo1144207539le_rho @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( minus_minus_real @ t @ s ) ) ) @ ( times_times_real @ genClo1144207539le_rho @ ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( minus_minus_real @ t @ s ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1694,f1185]) ).
thf(f1185,plain,
! [X2: real,X0: real,X1: real] :
( ( times_times_real @ X2 @ ( times_times_real @ X1 @ X0 ) )
= ( times_times_real @ X1 @ ( times_times_real @ X2 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f778]) ).
thf(f778,plain,
! [X0: real,X1: real,X2: real] :
( ( times_times_real @ X2 @ ( times_times_real @ X1 @ X0 ) )
= ( times_times_real @ X1 @ ( times_times_real @ X2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f164]) ).
thf(f164,axiom,
! [X3: real,X1: real,X0: real] :
( ( times_times_real @ X1 @ ( times_times_real @ X0 @ X3 ) )
= ( times_times_real @ X0 @ ( times_times_real @ X1 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3sGo6IMQoe/DTF2THF_1172.p',fact_163_mult_Oleft__commute) ).
thf(f1694,plain,
( $true
!= ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_real @ genClo1144207539le_rho @ ( minus_minus_real @ t @ s ) ) ) @ ( times_times_real @ genClo1144207539le_rho @ ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( minus_minus_real @ t @ s ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1693,f1203]) ).
thf(f1203,plain,
! [X2: real,X0: real,X1: real] :
( ( times_times_real @ ( times_times_real @ X0 @ X2 ) @ X1 )
= ( times_times_real @ X0 @ ( times_times_real @ X2 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f785]) ).
thf(f785,plain,
! [X0: real,X1: real,X2: real] :
( ( times_times_real @ ( times_times_real @ X0 @ X2 ) @ X1 )
= ( times_times_real @ X0 @ ( times_times_real @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f168]) ).
thf(f168,axiom,
! [X0: real,X3: real,X1: real] :
( ( times_times_real @ X0 @ ( times_times_real @ X1 @ X3 ) )
= ( times_times_real @ ( times_times_real @ X0 @ X1 ) @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.3sGo6IMQoe/DTF2THF_1172.p',fact_167_mult_Oassoc) ).
thf(f1693,plain,
( $true
!= ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) @ ( times_times_real @ genClo1144207539le_rho @ ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( minus_minus_real @ t @ s ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1692,f1283]) ).
thf(f1283,plain,
( ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) )
= ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,axiom,
( ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) )
= ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3sGo6IMQoe/DTF2THF_1172.p',fact_4_Eq4) ).
thf(f1692,plain,
( $true
!= ( ord_less_eq_real @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) ) @ ( times_times_real @ genClo1144207539le_rho @ ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( minus_minus_real @ t @ s ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1661]) ).
thf(f1661,plain,
( ( $true
!= ( ord_less_eq_real @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) ) @ ( times_times_real @ genClo1144207539le_rho @ ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( minus_minus_real @ t @ s ) ) ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1543,f1324]) ).
thf(f1324,plain,
( ( ord_less_eq_real @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f533]) ).
thf(f533,plain,
( ( ord_less_eq_real @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f532]) ).
thf(f532,plain,
ord_less_eq_real @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
ord_less_eq_real @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3sGo6IMQoe/DTF2THF_1172.p',fact_5_Eq3) ).
thf(f1543,plain,
! [X0: real] :
( ( $true
!= ( ord_less_eq_real @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ X0 ) )
| ( $true
!= ( ord_less_eq_real @ X0 @ ( times_times_real @ genClo1144207539le_rho @ ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( minus_minus_real @ t @ s ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1535]) ).
thf(f1535,plain,
! [X0: real] :
( ( $true
!= ( ord_less_eq_real @ X0 @ ( times_times_real @ genClo1144207539le_rho @ ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( minus_minus_real @ t @ s ) ) ) ) )
| ( $true
!= ( ord_less_eq_real @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1526,f1221]) ).
thf(f1221,plain,
! [X2: real,X0: real,X1: real] :
( ( $true
= ( ord_less_eq_real @ X2 @ X0 ) )
| ( ( ord_less_eq_real @ X1 @ X0 )
!= $true )
| ( $true
!= ( ord_less_eq_real @ X2 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f888]) ).
thf(f888,plain,
! [X0: real,X1: real,X2: real] :
( ( ( ord_less_eq_real @ X1 @ X0 )
!= $true )
| ( $true
!= ( ord_less_eq_real @ X2 @ X1 ) )
| ( $true
= ( ord_less_eq_real @ X2 @ X0 ) ) ),
inference(flattening,[status(thm)],[f887]) ).
thf(f887,plain,
! [X0: real,X1: real,X2: real] :
( ( $true
= ( ord_less_eq_real @ X2 @ X0 ) )
| ( ( ord_less_eq_real @ X1 @ X0 )
!= $true )
| ( $true
!= ( ord_less_eq_real @ X2 @ X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f723]) ).
thf(f723,plain,
! [X0: real,X1: real,X2: real] :
( ( $true
= ( ord_less_eq_real @ X2 @ X1 ) )
=> ( ( ( ord_less_eq_real @ X1 @ X0 )
= $true )
=> ( $true
= ( ord_less_eq_real @ X2 @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f722]) ).
thf(f722,plain,
! [X0: real,X1: real,X2: real] :
( ( ord_less_eq_real @ X2 @ X1 )
=> ( ( ord_less_eq_real @ X1 @ X0 )
=> ( ord_less_eq_real @ X2 @ X0 ) ) ),
inference(rectify,[status(thm)],[f304]) ).
thf(f304,axiom,
! [X3: real,X1: real,X0: real] :
( ( ord_less_eq_real @ X0 @ X1 )
=> ( ( ord_less_eq_real @ X1 @ X3 )
=> ( ord_less_eq_real @ X0 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3sGo6IMQoe/DTF2THF_1172.p',fact_303_order_Otrans) ).
thf(f1526,plain,
( $true
!= ( ord_less_eq_real @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( times_times_real @ genClo1144207539le_rho @ ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( minus_minus_real @ t @ s ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1502]) ).
thf(f1502,plain,
( ( $true != $true )
| ( $true
!= ( ord_less_eq_real @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( times_times_real @ genClo1144207539le_rho @ ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( minus_minus_real @ t @ s ) ) ) ) ) ),
inference(superposition,[status(thm)],[f1488,f1150]) ).
thf(f1150,plain,
( ( ord_less_eq_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f473]) ).
thf(f473,plain,
( ( ord_less_eq_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f472]) ).
thf(f472,plain,
ord_less_eq_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,axiom,
ord_less_eq_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3sGo6IMQoe/DTF2THF_1172.p',fact_9_Eq2) ).
thf(f1488,plain,
! [X0: real] :
( ( ( ord_less_eq_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ X0 )
!= $true )
| ( $true
!= ( ord_less_eq_real @ X0 @ ( times_times_real @ genClo1144207539le_rho @ ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( minus_minus_real @ t @ s ) ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1482]) ).
thf(f1482,plain,
! [X0: real] :
( ( $true
!= ( ord_less_eq_real @ X0 @ ( times_times_real @ genClo1144207539le_rho @ ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( minus_minus_real @ t @ s ) ) ) ) )
| ( $true != $true )
| ( ( ord_less_eq_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f1480,f1221]) ).
thf(f1480,plain,
( $true
!= ( ord_less_eq_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( times_times_real @ genClo1144207539le_rho @ ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( minus_minus_real @ t @ s ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1479,f1331]) ).
thf(f1479,plain,
( $true
!= ( ord_less_eq_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( times_times_real @ genClo1144207539le_rho @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( minus_minus_real @ t @ s ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1478,f1185]) ).
thf(f1478,plain,
( $true
!= ( ord_less_eq_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_real @ genClo1144207539le_rho @ ( minus_minus_real @ t @ s ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1477,f1203]) ).
thf(f1477,plain,
( $true
!= ( ord_less_eq_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ) ),
inference(forward_demodulation,[status(thm)],[f1141,f1212]) ).
thf(f1212,plain,
( ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) )
= ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) )
= ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.3sGo6IMQoe/DTF2THF_1172.p',fact_3_Eq1) ).
thf(f1141,plain,
( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f754]) ).
thf(f754,plain,
( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) )
!= $true ),
inference(flattening,[status(thm)],[f485]) ).
thf(f485,plain,
( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f484]) ).
thf(f484,plain,
~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ),
inference(rectify,[status(thm)],[f354]) ).
thf(f354,negated_conjecture,
~ ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ),
inference(negated_conjecture,[status(cth)],[f353]) ).
thf(f353,conjecture,
ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ),
file('/export/starexec/sandbox/tmp/tmp.3sGo6IMQoe/DTF2THF_1172.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP062^1 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n019.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:25:09 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : ITP062^1 : TPTP v9.2.1. Released v7.5.0.
% 0.29/0.46 % Domain : Interactive Theorem Proving
% 0.29/0.46 % Problem : Sledgehammer GenClock problem prob_249__3245100_1
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.29/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Des21]
% 0.29/0.46 % Names : GenClock/prob_249__3245100_1 [Des21]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.46 v8.1.0, 0.36 v7.5.0
% 0.29/0.46 % Syntax : Number of formulae : 391 ( 209 unt; 38 typ; 0 def)
% 0.29/0.46 % Number of atoms : 814 ( 343 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 12 ( 2 avg)
% 0.29/0.46 % Number of connectives : 3187 ( 36 ~; 10 |; 23 &;2807 @)
% 0.29/0.46 % ( 0 <=>; 311 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 14 ( 6 avg)
% 0.29/0.46 % Number of types : 5 ( 4 usr)
% 0.29/0.46 % Number of type conns : 104 ( 104 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 35 ( 34 usr; 8 con; 0-4 aty)
% 0.29/0.46 % Number of variables : 975 ( 33 ^; 937 !; 5 ?; 975 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:29:52.030
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % Could-be-implicit typings (4)
% 0.29/0.46 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 0.29/0.46 set_real: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Real__Oreal,type,
% 0.29/0.46 real: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Num__Onum,type,
% 0.29/0.46 num: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_n_t__Nat__Onat,type,
% 0.29/0.46 nat: $tType ).
% 0.29/0.46
% 0.29/0.46 % Explicit typings (34)
% 0.29/0.46 thf(sy_c_GenClock__Mirabelle__bsvkzpgbls_OPC,type,
% 0.29/0.46 genClo1161277105lle_PC: nat > real > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_GenClock__Mirabelle__bsvkzpgbls_O_092_060rho_062,type,
% 0.29/0.46 genClo1144207539le_rho: real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_GenClock__Mirabelle__bsvkzpgbls_Ocorrect,type,
% 0.29/0.46 genClo1015804716orrect: nat > real > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_GenClock__Mirabelle__bsvkzpgbls_OokRead1,type,
% 0.29/0.46 genClo293725281kRead1: ( nat > real ) > real > ( nat > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_GenClock__Mirabelle__bsvkzpgbls_OokRead2,type,
% 0.29/0.46 genClo293725282kRead2: ( nat > real ) > ( nat > real ) > real > ( nat > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_GenClock__Mirabelle__bsvkzpgbls_Orho__bound1,type,
% 0.29/0.46 genClo2108747022bound1: ( nat > real > real ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_GenClock__Mirabelle__bsvkzpgbls_Orho__bound2,type,
% 0.29/0.46 genClo2108747023bound2: ( nat > real > real ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal,type,
% 0.29/0.46 abs_abs_real: real > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 0.29/0.46 minus_minus_nat: nat > nat > nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal,type,
% 0.29/0.46 minus_minus_real: real > real > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 0.29/0.46 one_one_nat: nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal,type,
% 0.29/0.46 one_one_real: real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 0.29/0.46 plus_plus_nat: nat > nat > nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Oplus__class_Oplus_001t__Num__Onum,type,
% 0.29/0.46 plus_plus_num: num > num > num ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal,type,
% 0.29/0.46 plus_plus_real: real > real > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat,type,
% 0.29/0.46 times_times_nat: nat > nat > nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Otimes__class_Otimes_001t__Num__Onum,type,
% 0.29/0.46 times_times_num: num > num > num ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Otimes__class_Otimes_001t__Real__Oreal,type,
% 0.29/0.46 times_times_real: real > real > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 0.29/0.46 neg_numeral_dbl_real: real > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Num_Onum_OBit0,type,
% 0.29/0.46 bit0: num > num ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Num_Onum_OOne,type,
% 0.29/0.46 one: num ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
% 0.29/0.46 numeral_numeral_nat: num > nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal,type,
% 0.29/0.46 numeral_numeral_real: num > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.29/0.46 ord_less_eq_nat: nat > nat > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Num__Onum,type,
% 0.29/0.46 ord_less_eq_num: num > num > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 0.29/0.46 ord_less_eq_real: real > real > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
% 0.29/0.46 collect_real: ( real > $o ) > set_real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_member_001t__Real__Oreal,type,
% 0.29/0.46 member_real: real > set_real > $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_C,type,
% 0.29/0.46 c: nat > real > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_D,type,
% 0.29/0.46 d: nat > real > real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_p,type,
% 0.29/0.46 p: nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_q,type,
% 0.29/0.46 q: nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_s,type,
% 0.29/0.46 s: real ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_t,type,
% 0.29/0.46 t: real ).
% 0.29/0.46
% 0.29/0.46 % Relevant facts (352)
% 0.29/0.46 thf(fact_0_rb2,axiom,
% 0.29/0.46 genClo2108747023bound2 @ d ).
% 0.29/0.46
% 0.29/0.46 % rb2
% 0.29/0.46 thf(fact_1_rb1,axiom,
% 0.29/0.46 genClo2108747022bound1 @ c ).
% 0.29/0.46
% 0.29/0.46 % rb1
% 0.29/0.46 thf(fact_2_ie,axiom,
% 0.29/0.46 ord_less_eq_real @ s @ t ).
% 0.29/0.46
% 0.29/0.46 % ie
% 0.29/0.46 thf(fact_3_Eq1,axiom,
% 0.29/0.46 ( ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
% 0.29/0.46 = ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Eq1
% 0.29/0.46 thf(fact_4_Eq4,axiom,
% 0.29/0.46 ( ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) )
% 0.29/0.46 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Eq4
% 0.29/0.46 thf(fact_5_Eq3,axiom,
% 0.29/0.46 ord_less_eq_real @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Eq3
% 0.29/0.46 thf(fact_6_corr__q,axiom,
% 0.29/0.46 genClo1015804716orrect @ q @ t ).
% 0.29/0.46
% 0.29/0.46 % corr_q
% 0.29/0.46 thf(fact_7_PC__ie,axiom,
% 0.29/0.46 ord_less_eq_real @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) ).
% 0.29/0.46
% 0.29/0.46 % PC_ie
% 0.29/0.46 thf(fact_8_corr__p,axiom,
% 0.29/0.46 genClo1015804716orrect @ p @ t ).
% 0.29/0.46
% 0.29/0.46 % corr_p
% 0.29/0.46 thf(fact_9_Eq2,axiom,
% 0.29/0.46 ord_less_eq_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Eq2
% 0.29/0.46 thf(fact_10__092_060open_062_It_A_N_As_J_A_K_A_I1_A_N_A_092_060rho_062_J_A_092_060le_062_AD_Aq_At_A_N_AD_Aq_As_092_060close_062,axiom,
% 0.29/0.46 ord_less_eq_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ).
% 0.29/0.46
% 0.29/0.46 % \<open>(t - s) * (1 - \<rho>) \<le> D q t - D q s\<close>
% 0.29/0.46 thf(fact_11_left__diff__distrib__numeral,axiom,
% 0.29/0.46 ! [A: real,B: real,V: num] :
% 0.29/0.46 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 0.29/0.46 = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % left_diff_distrib_numeral
% 0.29/0.46 thf(fact_12_right__diff__distrib__numeral,axiom,
% 0.29/0.46 ! [V: num,B: real,C: real] :
% 0.29/0.46 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 0.29/0.46 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % right_diff_distrib_numeral
% 0.29/0.46 thf(fact_13_abs__numeral,axiom,
% 0.29/0.46 ! [N: num] :
% 0.29/0.46 ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 0.29/0.46 = ( numeral_numeral_real @ N ) ) ).
% 0.29/0.46
% 0.29/0.46 % abs_numeral
% 0.29/0.46 thf(fact_14_abs__mult__self__eq,axiom,
% 0.29/0.46 ! [A: real] :
% 0.29/0.46 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 0.29/0.46 = ( times_times_real @ A @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 % abs_mult_self_eq
% 0.29/0.46 thf(fact_15_semiring__norm_I85_J,axiom,
% 0.29/0.46 ! [M: num] :
% 0.29/0.46 ( ( bit0 @ M )
% 0.29/0.46 != one ) ).
% 0.29/0.46
% 0.29/0.46 % semiring_norm(85)
% 0.29/0.46 thf(fact_16_semiring__norm_I83_J,axiom,
% 0.29/0.46 ! [N: num] :
% 0.29/0.46 ( one
% 0.29/0.46 != ( bit0 @ N ) ) ).
% 0.29/0.46
% 0.29/0.46 % semiring_norm(83)
% 0.29/0.46 thf(fact_17_mult__numeral__left__semiring__numeral,axiom,
% 0.29/0.46 ! [V: num,W: num,Z: real] :
% 0.29/0.46 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 0.29/0.46 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_numeral_left_semiring_numeral
% 0.29/0.46 thf(fact_18_mult__numeral__left__semiring__numeral,axiom,
% 0.29/0.46 ! [V: num,W: num,Z: nat] :
% 0.29/0.46 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 0.29/0.46 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_numeral_left_semiring_numeral
% 0.29/0.46 thf(fact_19_numeral__times__numeral,axiom,
% 0.29/0.46 ! [M: num,N: num] :
% 0.29/0.46 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 0.29/0.46 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % numeral_times_numeral
% 0.29/0.46 thf(fact_20_numeral__times__numeral,axiom,
% 0.29/0.46 ! [M: num,N: num] :
% 0.29/0.46 ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.29/0.46 = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % numeral_times_numeral
% 0.29/0.46 thf(fact_21_numeral__le__iff,axiom,
% 0.29/0.46 ! [M: num,N: num] :
% 0.29/0.46 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 0.29/0.46 = ( ord_less_eq_num @ M @ N ) ) ).
% 0.29/0.46
% 0.29/0.46 % numeral_le_iff
% 0.29/0.46 thf(fact_22_numeral__le__iff,axiom,
% 0.29/0.46 ! [M: num,N: num] :
% 0.29/0.46 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.29/0.46 = ( ord_less_eq_num @ M @ N ) ) ).
% 0.29/0.46
% 0.29/0.46 % numeral_le_iff
% 0.29/0.46 thf(fact_23_okRead2__def,axiom,
% 0.29/0.46 ( genClo293725282kRead2
% 0.29/0.46 = ( ^ [F: nat > real,G: nat > real,X: real,Ppred: nat > $o] :
% 0.29/0.46 ! [P: nat] :
% 0.29/0.46 ( ( Ppred @ P )
% 0.29/0.46 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ P ) @ ( G @ P ) ) ) @ X ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % okRead2_def
% 0.29/0.46 thf(fact_24_abs__triangle__ineq2,axiom,
% 0.29/0.46 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % abs_triangle_ineq2
% 0.29/0.46 thf(fact_25_abs__triangle__ineq3,axiom,
% 0.29/0.46 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % abs_triangle_ineq3
% 0.29/0.46 thf(fact_26_numeral__eq__iff,axiom,
% 0.29/0.46 ! [M: num,N: num] :
% 0.29/0.46 ( ( ( numeral_numeral_real @ M )
% 0.29/0.46 = ( numeral_numeral_real @ N ) )
% 0.29/0.46 = ( M = N ) ) ).
% 0.29/0.46
% 0.29/0.46 % numeral_eq_iff
% 0.29/0.46 thf(fact_27_numeral__eq__iff,axiom,
% 0.29/0.46 ! [M: num,N: num] :
% 0.29/0.46 ( ( ( numeral_numeral_nat @ M )
% 0.29/0.46 = ( numeral_numeral_nat @ N ) )
% 0.29/0.46 = ( M = N ) ) ).
% 0.29/0.46
% 0.29/0.46 % numeral_eq_iff
% 0.29/0.46 thf(fact_28_add__left__cancel,axiom,
% 0.29/0.46 ! [A: real,B: real,C: real] :
% 0.29/0.46 ( ( ( plus_plus_real @ A @ B )
% 0.29/0.46 = ( plus_plus_real @ A @ C ) )
% 0.29/0.46 = ( B = C ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_left_cancel
% 0.29/0.46 thf(fact_29_add__left__cancel,axiom,
% 0.29/0.46 ! [A: nat,B: nat,C: nat] :
% 0.29/0.46 ( ( ( plus_plus_nat @ A @ B )
% 0.29/0.46 = ( plus_plus_nat @ A @ C ) )
% 0.29/0.46 = ( B = C ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_left_cancel
% 0.29/0.46 thf(fact_30_add__right__cancel,axiom,
% 0.29/0.46 ! [B: real,A: real,C: real] :
% 0.29/0.46 ( ( ( plus_plus_real @ B @ A )
% 0.29/0.46 = ( plus_plus_real @ C @ A ) )
% 0.29/0.46 = ( B = C ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_right_cancel
% 0.29/0.46 thf(fact_31_add__right__cancel,axiom,
% 0.29/0.46 ! [B: nat,A: nat,C: nat] :
% 0.29/0.46 ( ( ( plus_plus_nat @ B @ A )
% 0.29/0.46 = ( plus_plus_nat @ C @ A ) )
% 0.29/0.46 = ( B = C ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_right_cancel
% 0.29/0.46 thf(fact_32_semiring__norm_I87_J,axiom,
% 0.29/0.46 ! [M: num,N: num] :
% 0.29/0.46 ( ( ( bit0 @ M )
% 0.29/0.46 = ( bit0 @ N ) )
% 0.29/0.46 = ( M = N ) ) ).
% 0.29/0.46
% 0.29/0.46 % semiring_norm(87)
% 0.29/0.46 thf(fact_33_abs__idempotent,axiom,
% 0.29/0.46 ! [A: real] :
% 0.29/0.46 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 0.29/0.46 = ( abs_abs_real @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 % abs_idempotent
% 0.29/0.46 thf(fact_34_abs__abs,axiom,
% 0.29/0.46 ! [A: real] :
% 0.29/0.46 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 0.29/0.46 = ( abs_abs_real @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 % abs_abs
% 0.29/0.46 thf(fact_35_add__le__cancel__right,axiom,
% 0.29/0.46 ! [A: real,C: real,B: real] :
% 0.29/0.46 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.29/0.46 = ( ord_less_eq_real @ A @ B ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_le_cancel_right
% 0.29/0.46 thf(fact_36_add__le__cancel__right,axiom,
% 0.29/0.46 ! [A: nat,C: nat,B: nat] :
% 0.29/0.46 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.29/0.46 = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_le_cancel_right
% 0.29/0.46 thf(fact_37_add__le__cancel__left,axiom,
% 0.29/0.46 ! [C: real,A: real,B: real] :
% 0.29/0.46 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.29/0.46 = ( ord_less_eq_real @ A @ B ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_le_cancel_left
% 0.29/0.46 thf(fact_38_add__le__cancel__left,axiom,
% 0.29/0.46 ! [C: nat,A: nat,B: nat] :
% 0.29/0.46 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.29/0.46 = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_le_cancel_left
% 0.29/0.46 thf(fact_39_mult_Oright__neutral,axiom,
% 0.29/0.46 ! [A: real] :
% 0.29/0.46 ( ( times_times_real @ A @ one_one_real )
% 0.29/0.46 = A ) ).
% 0.29/0.46
% 0.29/0.46 % mult.right_neutral
% 0.29/0.46 thf(fact_40_mult_Oright__neutral,axiom,
% 0.29/0.46 ! [A: nat] :
% 0.29/0.46 ( ( times_times_nat @ A @ one_one_nat )
% 0.29/0.46 = A ) ).
% 0.29/0.46
% 0.29/0.46 % mult.right_neutral
% 0.29/0.46 thf(fact_41_mult_Oleft__neutral,axiom,
% 0.29/0.46 ! [A: real] :
% 0.29/0.46 ( ( times_times_real @ one_one_real @ A )
% 0.29/0.46 = A ) ).
% 0.29/0.46
% 0.29/0.46 % mult.left_neutral
% 0.29/0.46 thf(fact_42_mult_Oleft__neutral,axiom,
% 0.29/0.46 ! [A: nat] :
% 0.29/0.46 ( ( times_times_nat @ one_one_nat @ A )
% 0.29/0.46 = A ) ).
% 0.29/0.46
% 0.29/0.46 % mult.left_neutral
% 0.29/0.46 thf(fact_43_numeral__plus__numeral,axiom,
% 0.29/0.46 ! [M: num,N: num] :
% 0.29/0.46 ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 0.29/0.46 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % numeral_plus_numeral
% 0.29/0.46 thf(fact_44_numeral__plus__numeral,axiom,
% 0.29/0.46 ! [M: num,N: num] :
% 0.29/0.46 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.29/0.46 = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % numeral_plus_numeral
% 0.29/0.46 thf(fact_45_add__numeral__left,axiom,
% 0.29/0.46 ! [V: num,W: num,Z: real] :
% 0.29/0.46 ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 0.29/0.46 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_numeral_left
% 0.29/0.46 thf(fact_46_add__numeral__left,axiom,
% 0.29/0.46 ! [V: num,W: num,Z: nat] :
% 0.29/0.46 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 0.29/0.46 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_numeral_left
% 0.29/0.46 thf(fact_47_add__diff__cancel__right_H,axiom,
% 0.29/0.46 ! [A: real,B: real] :
% 0.29/0.46 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.29/0.46 = A ) ).
% 0.29/0.46
% 0.29/0.46 % add_diff_cancel_right'
% 0.29/0.46 thf(fact_48_add__diff__cancel__right_H,axiom,
% 0.29/0.46 ! [A: nat,B: nat] :
% 0.29/0.46 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.29/0.46 = A ) ).
% 0.29/0.46
% 0.29/0.46 % add_diff_cancel_right'
% 0.29/0.46 thf(fact_49_add__diff__cancel__right,axiom,
% 0.29/0.46 ! [A: real,C: real,B: real] :
% 0.29/0.46 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.29/0.46 = ( minus_minus_real @ A @ B ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_diff_cancel_right
% 0.29/0.46 thf(fact_50_add__diff__cancel__right,axiom,
% 0.29/0.46 ! [A: nat,C: nat,B: nat] :
% 0.29/0.46 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.29/0.46 = ( minus_minus_nat @ A @ B ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_diff_cancel_right
% 0.29/0.46 thf(fact_51_add__diff__cancel__left_H,axiom,
% 0.29/0.46 ! [A: real,B: real] :
% 0.29/0.46 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 0.29/0.46 = B ) ).
% 0.29/0.46
% 0.29/0.46 % add_diff_cancel_left'
% 0.29/0.46 thf(fact_52_add__diff__cancel__left_H,axiom,
% 0.29/0.46 ! [A: nat,B: nat] :
% 0.29/0.46 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 0.29/0.46 = B ) ).
% 0.29/0.46
% 0.29/0.46 % add_diff_cancel_left'
% 0.29/0.46 thf(fact_53_add__diff__cancel__left,axiom,
% 0.29/0.46 ! [C: real,A: real,B: real] :
% 0.29/0.46 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.29/0.46 = ( minus_minus_real @ A @ B ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_diff_cancel_left
% 0.29/0.46 thf(fact_54_add__diff__cancel__left,axiom,
% 0.29/0.46 ! [C: nat,A: nat,B: nat] :
% 0.29/0.46 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.29/0.46 = ( minus_minus_nat @ A @ B ) ) ).
% 0.29/0.46
% 0.29/0.46 % add_diff_cancel_left
% 0.29/0.46 thf(fact_55_diff__add__cancel,axiom,
% 0.29/0.46 ! [A: real,B: real] :
% 0.29/0.46 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 0.29/0.46 = A ) ).
% 0.29/0.46
% 0.29/0.46 % diff_add_cancel
% 0.29/0.46 thf(fact_56_add__diff__cancel,axiom,
% 0.29/0.46 ! [A: real,B: real] :
% 0.29/0.46 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.29/0.46 = A ) ).
% 0.29/0.46
% 0.29/0.46 % add_diff_cancel
% 0.29/0.46 thf(fact_57_abs__add__abs,axiom,
% 0.29/0.46 ! [A: real,B: real] :
% 0.29/0.46 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 0.29/0.46 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % abs_add_abs
% 0.29/0.46 thf(fact_58_abs__1,axiom,
% 0.29/0.46 ( ( abs_abs_real @ one_one_real )
% 0.29/0.46 = one_one_real ) ).
% 0.29/0.46
% 0.29/0.46 % abs_1
% 0.29/0.46 thf(fact_59_mem__Collect__eq,axiom,
% 0.29/0.46 ! [A: real,P2: real > $o] :
% 0.29/0.46 ( ( member_real @ A @ ( collect_real @ P2 ) )
% 0.29/0.46 = ( P2 @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 % mem_Collect_eq
% 0.29/0.46 thf(fact_60_Collect__mem__eq,axiom,
% 0.29/0.46 ! [A2: set_real] :
% 0.29/0.46 ( ( collect_real
% 0.29/0.46 @ ^ [X: real] : ( member_real @ X @ A2 ) )
% 0.29/0.46 = A2 ) ).
% 0.29/0.46
% 0.29/0.46 % Collect_mem_eq
% 0.29/0.46 thf(fact_61_semiring__norm_I13_J,axiom,
% 0.29/0.46 ! [M: num,N: num] :
% 0.29/0.46 ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.29/0.46 = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % semiring_norm(13)
% 0.29/0.46 thf(fact_62_semiring__norm_I11_J,axiom,
% 0.29/0.46 ! [M: num] :
% 0.29/0.46 ( ( times_times_num @ M @ one )
% 0.29/0.46 = M ) ).
% 0.29/0.46
% 0.29/0.46 % semiring_norm(11)
% 0.29/0.46 thf(fact_63_semiring__norm_I12_J,axiom,
% 0.29/0.46 ! [N: num] :
% 0.29/0.46 ( ( times_times_num @ one @ N )
% 0.29/0.46 = N ) ).
% 0.29/0.46
% 0.29/0.46 % semiring_norm(12)
% 0.29/0.46 thf(fact_64_semiring__norm_I71_J,axiom,
% 0.29/0.46 ! [M: num,N: num] :
% 0.29/0.46 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.29/0.46 = ( ord_less_eq_num @ M @ N ) ) ).
% 0.29/0.46
% 0.29/0.46 % semiring_norm(71)
% 0.29/0.46 thf(fact_65_semiring__norm_I68_J,axiom,
% 0.29/0.46 ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 0.29/0.46
% 0.29/0.46 % semiring_norm(68)
% 0.29/0.46 thf(fact_66_le__add__diff__inverse2,axiom,
% 0.29/0.46 ! [B: real,A: real] :
% 0.29/0.46 ( ( ord_less_eq_real @ B @ A )
% 0.29/0.46 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 0.29/0.46 = A ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_add_diff_inverse2
% 0.29/0.46 thf(fact_67_le__add__diff__inverse2,axiom,
% 0.29/0.46 ! [B: nat,A: nat] :
% 0.29/0.46 ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.46 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 0.29/0.46 = A ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_add_diff_inverse2
% 0.29/0.46 thf(fact_68_le__add__diff__inverse,axiom,
% 0.29/0.46 ! [B: real,A: real] :
% 0.29/0.46 ( ( ord_less_eq_real @ B @ A )
% 0.29/0.46 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 0.29/0.46 = A ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_add_diff_inverse
% 0.29/0.46 thf(fact_69_le__add__diff__inverse,axiom,
% 0.29/0.46 ! [B: nat,A: nat] :
% 0.29/0.46 ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.46 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 0.29/0.46 = A ) ) ).
% 0.29/0.46
% 0.29/0.46 % le_add_diff_inverse
% 0.29/0.46 thf(fact_70_distrib__right__numeral,axiom,
% 0.29/0.46 ! [A: real,B: real,V: num] :
% 0.29/0.46 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 0.29/0.46 = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % distrib_right_numeral
% 0.29/0.46 thf(fact_71_distrib__right__numeral,axiom,
% 0.29/0.46 ! [A: nat,B: nat,V: num] :
% 0.29/0.46 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 0.29/0.46 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % distrib_right_numeral
% 0.29/0.46 thf(fact_72_distrib__left__numeral,axiom,
% 0.29/0.46 ! [V: num,B: real,C: real] :
% 0.29/0.46 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 0.29/0.46 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % distrib_left_numeral
% 0.29/0.46 thf(fact_73_distrib__left__numeral,axiom,
% 0.29/0.46 ! [V: num,B: nat,C: nat] :
% 0.29/0.46 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 0.29/0.46 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % distrib_left_numeral
% 0.29/0.46 thf(fact_74_one__eq__numeral__iff,axiom,
% 0.29/0.46 ! [N: num] :
% 0.29/0.46 ( ( one_one_real
% 0.29/0.46 = ( numeral_numeral_real @ N ) )
% 0.29/0.46 = ( one = N ) ) ).
% 0.29/0.46
% 0.29/0.46 % one_eq_numeral_iff
% 0.29/0.46 thf(fact_75_one__eq__numeral__iff,axiom,
% 0.29/0.46 ! [N: num] :
% 0.29/0.46 ( ( one_one_nat
% 0.29/0.46 = ( numeral_numeral_nat @ N ) )
% 0.29/0.46 = ( one = N ) ) ).
% 0.29/0.46
% 0.29/0.46 % one_eq_numeral_iff
% 0.29/0.46 thf(fact_76_numeral__eq__one__iff,axiom,
% 0.29/0.46 ! [N: num] :
% 0.29/0.46 ( ( ( numeral_numeral_real @ N )
% 0.29/0.46 = one_one_real )
% 0.29/0.46 = ( N = one ) ) ).
% 0.29/0.46
% 0.29/0.46 % numeral_eq_one_iff
% 0.29/0.46 thf(fact_77_numeral__eq__one__iff,axiom,
% 0.29/0.46 ! [N: num] :
% 0.29/0.46 ( ( ( numeral_numeral_nat @ N )
% 0.29/0.46 = one_one_nat )
% 0.29/0.46 = ( N = one ) ) ).
% 0.29/0.46
% 0.29/0.46 % numeral_eq_one_iff
% 0.29/0.46 thf(fact_78_num__double,axiom,
% 0.29/0.46 ! [N: num] :
% 0.29/0.46 ( ( times_times_num @ ( bit0 @ one ) @ N )
% 0.29/0.46 = ( bit0 @ N ) ) ).
% 0.29/0.46
% 0.29/0.46 % num_double
% 0.29/0.46 thf(fact_79_semiring__norm_I69_J,axiom,
% 0.29/0.46 ! [M: num] :
% 0.29/0.46 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 0.29/0.46
% 0.29/0.46 % semiring_norm(69)
% 0.29/0.47 thf(fact_80_one__plus__numeral,axiom,
% 0.29/0.47 ! [N: num] :
% 0.29/0.47 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 0.29/0.47 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % one_plus_numeral
% 0.29/0.47 thf(fact_81_one__plus__numeral,axiom,
% 0.29/0.47 ! [N: num] :
% 0.29/0.47 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 0.29/0.47 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % one_plus_numeral
% 0.29/0.47 thf(fact_82_numeral__plus__one,axiom,
% 0.29/0.47 ! [N: num] :
% 0.29/0.47 ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 0.29/0.47 = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % numeral_plus_one
% 0.29/0.47 thf(fact_83_numeral__plus__one,axiom,
% 0.29/0.47 ! [N: num] :
% 0.29/0.47 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 0.29/0.47 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % numeral_plus_one
% 0.29/0.47 thf(fact_84_one__add__one,axiom,
% 0.29/0.47 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 0.29/0.47 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % one_add_one
% 0.29/0.47 thf(fact_85_one__add__one,axiom,
% 0.29/0.47 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.29/0.47 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % one_add_one
% 0.29/0.47 thf(fact_86_numeral__le__one__iff,axiom,
% 0.29/0.47 ! [N: num] :
% 0.29/0.47 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 0.29/0.47 = ( ord_less_eq_num @ N @ one ) ) ).
% 0.29/0.47
% 0.29/0.47 % numeral_le_one_iff
% 0.29/0.47 thf(fact_87_numeral__le__one__iff,axiom,
% 0.29/0.47 ! [N: num] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 0.29/0.47 = ( ord_less_eq_num @ N @ one ) ) ).
% 0.29/0.47
% 0.29/0.47 % numeral_le_one_iff
% 0.29/0.47 thf(fact_88_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.29/0.47 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ab_semigroup_add_class.add_ac(1)
% 0.29/0.47 thf(fact_89_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C: nat] :
% 0.29/0.47 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.29/0.47 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ab_semigroup_add_class.add_ac(1)
% 0.29/0.47 thf(fact_90_is__num__normalize_I1_J,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.29/0.47 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % is_num_normalize(1)
% 0.29/0.47 thf(fact_91_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.29/0.47 ! [I: real,J: real,K: real,L: real] :
% 0.29/0.47 ( ( ( I = J )
% 0.29/0.47 & ( K = L ) )
% 0.29/0.47 => ( ( plus_plus_real @ I @ K )
% 0.29/0.47 = ( plus_plus_real @ J @ L ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_mono_thms_linordered_semiring(4)
% 0.29/0.47 thf(fact_92_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.29/0.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.47 ( ( ( I = J )
% 0.29/0.47 & ( K = L ) )
% 0.29/0.47 => ( ( plus_plus_nat @ I @ K )
% 0.29/0.47 = ( plus_plus_nat @ J @ L ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_mono_thms_linordered_semiring(4)
% 0.29/0.47 thf(fact_93_one__reorient,axiom,
% 0.29/0.47 ! [X2: real] :
% 0.29/0.47 ( ( one_one_real = X2 )
% 0.29/0.47 = ( X2 = one_one_real ) ) ).
% 0.29/0.47
% 0.29/0.47 % one_reorient
% 0.29/0.47 thf(fact_94_one__reorient,axiom,
% 0.29/0.47 ! [X2: nat] :
% 0.29/0.47 ( ( one_one_nat = X2 )
% 0.29/0.47 = ( X2 = one_one_nat ) ) ).
% 0.29/0.47
% 0.29/0.47 % one_reorient
% 0.29/0.47 thf(fact_95_group__cancel_Oadd1,axiom,
% 0.29/0.47 ! [A2: real,K: real,A: real,B: real] :
% 0.29/0.47 ( ( A2
% 0.29/0.47 = ( plus_plus_real @ K @ A ) )
% 0.29/0.47 => ( ( plus_plus_real @ A2 @ B )
% 0.29/0.47 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % group_cancel.add1
% 0.29/0.47 thf(fact_96_group__cancel_Oadd1,axiom,
% 0.29/0.47 ! [A2: nat,K: nat,A: nat,B: nat] :
% 0.29/0.47 ( ( A2
% 0.29/0.47 = ( plus_plus_nat @ K @ A ) )
% 0.29/0.47 => ( ( plus_plus_nat @ A2 @ B )
% 0.29/0.47 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % group_cancel.add1
% 0.29/0.47 thf(fact_97_group__cancel_Oadd2,axiom,
% 0.29/0.47 ! [B2: real,K: real,B: real,A: real] :
% 0.29/0.47 ( ( B2
% 0.29/0.47 = ( plus_plus_real @ K @ B ) )
% 0.29/0.47 => ( ( plus_plus_real @ A @ B2 )
% 0.29/0.47 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % group_cancel.add2
% 0.29/0.47 thf(fact_98_group__cancel_Oadd2,axiom,
% 0.29/0.47 ! [B2: nat,K: nat,B: nat,A: nat] :
% 0.29/0.47 ( ( B2
% 0.29/0.47 = ( plus_plus_nat @ K @ B ) )
% 0.29/0.47 => ( ( plus_plus_nat @ A @ B2 )
% 0.29/0.47 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % group_cancel.add2
% 0.29/0.47 thf(fact_99_add_Oassoc,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.29/0.47 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add.assoc
% 0.29/0.47 thf(fact_100_add_Oassoc,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C: nat] :
% 0.29/0.47 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.29/0.47 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add.assoc
% 0.29/0.47 thf(fact_101_add_Oleft__cancel,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( ( plus_plus_real @ A @ B )
% 0.29/0.47 = ( plus_plus_real @ A @ C ) )
% 0.29/0.47 = ( B = C ) ) ).
% 0.29/0.47
% 0.29/0.47 % add.left_cancel
% 0.29/0.47 thf(fact_102_add_Oright__cancel,axiom,
% 0.29/0.47 ! [B: real,A: real,C: real] :
% 0.29/0.47 ( ( ( plus_plus_real @ B @ A )
% 0.29/0.47 = ( plus_plus_real @ C @ A ) )
% 0.29/0.47 = ( B = C ) ) ).
% 0.29/0.47
% 0.29/0.47 % add.right_cancel
% 0.29/0.47 thf(fact_103_add_Ocommute,axiom,
% 0.29/0.47 ( plus_plus_real
% 0.29/0.47 = ( ^ [A3: real,B3: real] : ( plus_plus_real @ B3 @ A3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add.commute
% 0.29/0.47 thf(fact_104_add_Ocommute,axiom,
% 0.29/0.47 ( plus_plus_nat
% 0.29/0.47 = ( ^ [A3: nat,B3: nat] : ( plus_plus_nat @ B3 @ A3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add.commute
% 0.29/0.47 thf(fact_105_add_Oleft__commute,axiom,
% 0.29/0.47 ! [B: real,A: real,C: real] :
% 0.29/0.47 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 0.29/0.47 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add.left_commute
% 0.29/0.47 thf(fact_106_add_Oleft__commute,axiom,
% 0.29/0.47 ! [B: nat,A: nat,C: nat] :
% 0.29/0.47 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 0.29/0.47 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add.left_commute
% 0.29/0.47 thf(fact_107_add__left__imp__eq,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( ( plus_plus_real @ A @ B )
% 0.29/0.47 = ( plus_plus_real @ A @ C ) )
% 0.29/0.47 => ( B = C ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_left_imp_eq
% 0.29/0.47 thf(fact_108_add__left__imp__eq,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C: nat] :
% 0.29/0.47 ( ( ( plus_plus_nat @ A @ B )
% 0.29/0.47 = ( plus_plus_nat @ A @ C ) )
% 0.29/0.47 => ( B = C ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_left_imp_eq
% 0.29/0.47 thf(fact_109_add__right__imp__eq,axiom,
% 0.29/0.47 ! [B: real,A: real,C: real] :
% 0.29/0.47 ( ( ( plus_plus_real @ B @ A )
% 0.29/0.47 = ( plus_plus_real @ C @ A ) )
% 0.29/0.47 => ( B = C ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_right_imp_eq
% 0.29/0.47 thf(fact_110_add__right__imp__eq,axiom,
% 0.29/0.47 ! [B: nat,A: nat,C: nat] :
% 0.29/0.47 ( ( ( plus_plus_nat @ B @ A )
% 0.29/0.47 = ( plus_plus_nat @ C @ A ) )
% 0.29/0.47 => ( B = C ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_right_imp_eq
% 0.29/0.47 thf(fact_111_le__num__One__iff,axiom,
% 0.29/0.47 ! [X2: num] :
% 0.29/0.47 ( ( ord_less_eq_num @ X2 @ one )
% 0.29/0.47 = ( X2 = one ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_num_One_iff
% 0.29/0.47 thf(fact_112_one__plus__numeral__commute,axiom,
% 0.29/0.47 ! [X2: num] :
% 0.29/0.47 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X2 ) )
% 0.29/0.47 = ( plus_plus_real @ ( numeral_numeral_real @ X2 ) @ one_one_real ) ) ).
% 0.29/0.47
% 0.29/0.47 % one_plus_numeral_commute
% 0.29/0.47 thf(fact_113_one__plus__numeral__commute,axiom,
% 0.29/0.47 ! [X2: num] :
% 0.29/0.47 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X2 ) )
% 0.29/0.47 = ( plus_plus_nat @ ( numeral_numeral_nat @ X2 ) @ one_one_nat ) ) ).
% 0.29/0.47
% 0.29/0.47 % one_plus_numeral_commute
% 0.29/0.47 thf(fact_114_correct__closed,axiom,
% 0.29/0.47 ! [P3: nat,S: real,T: real] :
% 0.29/0.47 ( ( ( ord_less_eq_real @ S @ T )
% 0.29/0.47 & ( genClo1015804716orrect @ P3 @ T ) )
% 0.29/0.47 => ( genClo1015804716orrect @ P3 @ S ) ) ).
% 0.29/0.47
% 0.29/0.47 % correct_closed
% 0.29/0.47 thf(fact_115_add__le__imp__le__right,axiom,
% 0.29/0.47 ! [A: real,C: real,B: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 0.29/0.47 => ( ord_less_eq_real @ A @ B ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_le_imp_le_right
% 0.29/0.47 thf(fact_116_add__le__imp__le__right,axiom,
% 0.29/0.47 ! [A: nat,C: nat,B: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.29/0.47 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_le_imp_le_right
% 0.29/0.47 thf(fact_117_add__le__imp__le__left,axiom,
% 0.29/0.47 ! [C: real,A: real,B: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 0.29/0.47 => ( ord_less_eq_real @ A @ B ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_le_imp_le_left
% 0.29/0.47 thf(fact_118_add__le__imp__le__left,axiom,
% 0.29/0.47 ! [C: nat,A: nat,B: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.29/0.47 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_le_imp_le_left
% 0.29/0.47 thf(fact_119_le__iff__add,axiom,
% 0.29/0.47 ( ord_less_eq_nat
% 0.29/0.47 = ( ^ [A3: nat,B3: nat] :
% 0.29/0.47 ? [C2: nat] :
% 0.29/0.47 ( B3
% 0.29/0.47 = ( plus_plus_nat @ A3 @ C2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_iff_add
% 0.29/0.47 thf(fact_120_add__right__mono,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ A @ B )
% 0.29/0.47 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_right_mono
% 0.29/0.47 thf(fact_121_add__right__mono,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_right_mono
% 0.29/0.47 thf(fact_122_less__eqE,axiom,
% 0.29/0.47 ! [A: nat,B: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ~ ! [C3: nat] :
% 0.29/0.47 ( B
% 0.29/0.47 != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_eqE
% 0.29/0.47 thf(fact_123_add__left__mono,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ A @ B )
% 0.29/0.47 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_left_mono
% 0.29/0.47 thf(fact_124_add__left__mono,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_left_mono
% 0.29/0.47 thf(fact_125_add__mono,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real,D: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_real @ C @ D )
% 0.29/0.47 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_mono
% 0.29/0.47 thf(fact_126_add__mono,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C: nat,D: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_nat @ C @ D )
% 0.29/0.47 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_mono
% 0.29/0.47 thf(fact_127_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.29/0.47 ! [I: real,J: real,K: real,L: real] :
% 0.29/0.47 ( ( ( ord_less_eq_real @ I @ J )
% 0.29/0.47 & ( ord_less_eq_real @ K @ L ) )
% 0.29/0.47 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_mono_thms_linordered_semiring(1)
% 0.29/0.47 thf(fact_128_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.29/0.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.47 ( ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.47 & ( ord_less_eq_nat @ K @ L ) )
% 0.29/0.47 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_mono_thms_linordered_semiring(1)
% 0.29/0.47 thf(fact_129_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.29/0.47 ! [I: real,J: real,K: real,L: real] :
% 0.29/0.47 ( ( ( I = J )
% 0.29/0.47 & ( ord_less_eq_real @ K @ L ) )
% 0.29/0.47 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_mono_thms_linordered_semiring(2)
% 0.29/0.47 thf(fact_130_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.29/0.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.47 ( ( ( I = J )
% 0.29/0.47 & ( ord_less_eq_nat @ K @ L ) )
% 0.29/0.47 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_mono_thms_linordered_semiring(2)
% 0.29/0.47 thf(fact_131_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.29/0.47 ! [I: real,J: real,K: real,L: real] :
% 0.29/0.47 ( ( ( ord_less_eq_real @ I @ J )
% 0.29/0.47 & ( K = L ) )
% 0.29/0.47 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_mono_thms_linordered_semiring(3)
% 0.29/0.47 thf(fact_132_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.29/0.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.47 ( ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.47 & ( K = L ) )
% 0.29/0.47 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_mono_thms_linordered_semiring(3)
% 0.29/0.47 thf(fact_133_combine__common__factor,axiom,
% 0.29/0.47 ! [A: real,E: real,B: real,C: real] :
% 0.29/0.47 ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C ) )
% 0.29/0.47 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C ) ) ).
% 0.29/0.47
% 0.29/0.47 % combine_common_factor
% 0.29/0.47 thf(fact_134_combine__common__factor,axiom,
% 0.29/0.47 ! [A: nat,E: nat,B: nat,C: nat] :
% 0.29/0.47 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 0.29/0.47 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 0.29/0.47
% 0.29/0.47 % combine_common_factor
% 0.29/0.47 thf(fact_135_distrib__right,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.29/0.47 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % distrib_right
% 0.29/0.47 thf(fact_136_distrib__right,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C: nat] :
% 0.29/0.47 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.29/0.47 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % distrib_right
% 0.29/0.47 thf(fact_137_distrib__left,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.29/0.47 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % distrib_left
% 0.29/0.47 thf(fact_138_distrib__left,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C: nat] :
% 0.29/0.47 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.29/0.47 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % distrib_left
% 0.29/0.47 thf(fact_139_comm__semiring__class_Odistrib,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.29/0.47 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % comm_semiring_class.distrib
% 0.29/0.47 thf(fact_140_comm__semiring__class_Odistrib,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C: nat] :
% 0.29/0.47 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.29/0.47 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % comm_semiring_class.distrib
% 0.29/0.47 thf(fact_141_ring__class_Oring__distribs_I1_J,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.29/0.47 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ring_class.ring_distribs(1)
% 0.29/0.47 thf(fact_142_ring__class_Oring__distribs_I2_J,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 0.29/0.47 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ring_class.ring_distribs(2)
% 0.29/0.47 thf(fact_143_le__numeral__extra_I4_J,axiom,
% 0.29/0.47 ord_less_eq_real @ one_one_real @ one_one_real ).
% 0.29/0.47
% 0.29/0.47 % le_numeral_extra(4)
% 0.29/0.47 thf(fact_144_le__numeral__extra_I4_J,axiom,
% 0.29/0.47 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 0.29/0.47
% 0.29/0.47 % le_numeral_extra(4)
% 0.29/0.47 thf(fact_145_add__implies__diff,axiom,
% 0.29/0.47 ! [C: real,B: real,A: real] :
% 0.29/0.47 ( ( ( plus_plus_real @ C @ B )
% 0.29/0.47 = A )
% 0.29/0.47 => ( C
% 0.29/0.47 = ( minus_minus_real @ A @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_implies_diff
% 0.29/0.47 thf(fact_146_add__implies__diff,axiom,
% 0.29/0.47 ! [C: nat,B: nat,A: nat] :
% 0.29/0.47 ( ( ( plus_plus_nat @ C @ B )
% 0.29/0.47 = A )
% 0.29/0.47 => ( C
% 0.29/0.47 = ( minus_minus_nat @ A @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_implies_diff
% 0.29/0.47 thf(fact_147_diff__diff__add,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.29/0.47 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % diff_diff_add
% 0.29/0.47 thf(fact_148_diff__diff__add,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C: nat] :
% 0.29/0.47 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 0.29/0.47 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % diff_diff_add
% 0.29/0.47 thf(fact_149_diff__add__eq__diff__diff__swap,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 0.29/0.47 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 0.29/0.47
% 0.29/0.47 % diff_add_eq_diff_diff_swap
% 0.29/0.47 thf(fact_150_diff__add__eq,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.29/0.47 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 0.29/0.47
% 0.29/0.47 % diff_add_eq
% 0.29/0.47 thf(fact_151_diff__diff__eq2,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.29/0.47 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 0.29/0.47
% 0.29/0.47 % diff_diff_eq2
% 0.29/0.47 thf(fact_152_add__diff__eq,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.29/0.47 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_diff_eq
% 0.29/0.47 thf(fact_153_eq__diff__eq,axiom,
% 0.29/0.47 ! [A: real,C: real,B: real] :
% 0.29/0.47 ( ( A
% 0.29/0.47 = ( minus_minus_real @ C @ B ) )
% 0.29/0.47 = ( ( plus_plus_real @ A @ B )
% 0.29/0.47 = C ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_diff_eq
% 0.29/0.47 thf(fact_154_diff__eq__eq,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( ( minus_minus_real @ A @ B )
% 0.29/0.47 = C )
% 0.29/0.47 = ( A
% 0.29/0.47 = ( plus_plus_real @ C @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % diff_eq_eq
% 0.29/0.47 thf(fact_155_group__cancel_Osub1,axiom,
% 0.29/0.47 ! [A2: real,K: real,A: real,B: real] :
% 0.29/0.47 ( ( A2
% 0.29/0.47 = ( plus_plus_real @ K @ A ) )
% 0.29/0.47 => ( ( minus_minus_real @ A2 @ B )
% 0.29/0.47 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % group_cancel.sub1
% 0.29/0.47 thf(fact_156_mult_Ocomm__neutral,axiom,
% 0.29/0.47 ! [A: real] :
% 0.29/0.47 ( ( times_times_real @ A @ one_one_real )
% 0.29/0.47 = A ) ).
% 0.29/0.47
% 0.29/0.47 % mult.comm_neutral
% 0.29/0.47 thf(fact_157_mult_Ocomm__neutral,axiom,
% 0.29/0.47 ! [A: nat] :
% 0.29/0.47 ( ( times_times_nat @ A @ one_one_nat )
% 0.29/0.47 = A ) ).
% 0.29/0.47
% 0.29/0.47 % mult.comm_neutral
% 0.29/0.47 thf(fact_158_comm__monoid__mult__class_Omult__1,axiom,
% 0.29/0.47 ! [A: real] :
% 0.29/0.47 ( ( times_times_real @ one_one_real @ A )
% 0.29/0.47 = A ) ).
% 0.29/0.47
% 0.29/0.47 % comm_monoid_mult_class.mult_1
% 0.29/0.47 thf(fact_159_comm__monoid__mult__class_Omult__1,axiom,
% 0.29/0.47 ! [A: nat] :
% 0.29/0.47 ( ( times_times_nat @ one_one_nat @ A )
% 0.29/0.47 = A ) ).
% 0.29/0.47
% 0.29/0.47 % comm_monoid_mult_class.mult_1
% 0.29/0.47 thf(fact_160_abs__one,axiom,
% 0.29/0.47 ( ( abs_abs_real @ one_one_real )
% 0.29/0.47 = one_one_real ) ).
% 0.29/0.47
% 0.29/0.47 % abs_one
% 0.29/0.47 thf(fact_161_square__diff__one__factored,axiom,
% 0.29/0.47 ! [X2: real] :
% 0.29/0.47 ( ( minus_minus_real @ ( times_times_real @ X2 @ X2 ) @ one_one_real )
% 0.29/0.47 = ( times_times_real @ ( plus_plus_real @ X2 @ one_one_real ) @ ( minus_minus_real @ X2 @ one_one_real ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % square_diff_one_factored
% 0.29/0.47 thf(fact_162_rho__bound1__def,axiom,
% 0.29/0.47 ( genClo2108747022bound1
% 0.29/0.47 = ( ^ [C4: nat > real > real] :
% 0.29/0.47 ! [P: nat,S2: real,T2: real] :
% 0.29/0.47 ( ( ( genClo1015804716orrect @ P @ T2 )
% 0.29/0.47 & ( ord_less_eq_real @ S2 @ T2 ) )
% 0.29/0.47 => ( ord_less_eq_real @ ( minus_minus_real @ ( C4 @ P @ T2 ) @ ( C4 @ P @ S2 ) ) @ ( times_times_real @ ( minus_minus_real @ T2 @ S2 ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % rho_bound1_def
% 0.29/0.47 thf(fact_163_mult_Oleft__commute,axiom,
% 0.29/0.47 ! [B: real,A: real,C: real] :
% 0.29/0.47 ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 0.29/0.47 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % mult.left_commute
% 0.29/0.47 thf(fact_164_mult_Oleft__commute,axiom,
% 0.29/0.47 ! [B: nat,A: nat,C: nat] :
% 0.29/0.47 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 0.29/0.47 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % mult.left_commute
% 0.29/0.47 thf(fact_165_mult_Ocommute,axiom,
% 0.29/0.47 ( times_times_real
% 0.29/0.47 = ( ^ [A3: real,B3: real] : ( times_times_real @ B3 @ A3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % mult.commute
% 0.29/0.47 thf(fact_166_mult_Ocommute,axiom,
% 0.29/0.47 ( times_times_nat
% 0.29/0.47 = ( ^ [A3: nat,B3: nat] : ( times_times_nat @ B3 @ A3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % mult.commute
% 0.29/0.47 thf(fact_167_mult_Oassoc,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 0.29/0.47 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % mult.assoc
% 0.29/0.47 thf(fact_168_mult_Oassoc,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C: nat] :
% 0.29/0.47 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.29/0.47 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % mult.assoc
% 0.29/0.47 thf(fact_169_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 0.29/0.47 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ab_semigroup_mult_class.mult_ac(1)
% 0.29/0.47 thf(fact_170_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C: nat] :
% 0.29/0.47 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.29/0.47 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ab_semigroup_mult_class.mult_ac(1)
% 0.29/0.47 thf(fact_171_diff__right__commute,axiom,
% 0.29/0.47 ! [A: real,C: real,B: real] :
% 0.29/0.47 ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 0.29/0.47 = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 0.29/0.47
% 0.29/0.47 % diff_right_commute
% 0.29/0.47 thf(fact_172_diff__right__commute,axiom,
% 0.29/0.47 ! [A: nat,C: nat,B: nat] :
% 0.29/0.47 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 0.29/0.47 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 0.29/0.47
% 0.29/0.47 % diff_right_commute
% 0.29/0.47 thf(fact_173_diff__eq__diff__eq,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real,D: real] :
% 0.29/0.47 ( ( ( minus_minus_real @ A @ B )
% 0.29/0.47 = ( minus_minus_real @ C @ D ) )
% 0.29/0.47 => ( ( A = B )
% 0.29/0.47 = ( C = D ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % diff_eq_diff_eq
% 0.29/0.47 thf(fact_174_rho__bound2__def,axiom,
% 0.29/0.47 ( genClo2108747023bound2
% 0.29/0.47 = ( ^ [C4: nat > real > real] :
% 0.29/0.47 ! [P: nat,S2: real,T2: real] :
% 0.29/0.47 ( ( ( genClo1015804716orrect @ P @ T2 )
% 0.29/0.47 & ( ord_less_eq_real @ S2 @ T2 ) )
% 0.29/0.47 => ( ord_less_eq_real @ ( times_times_real @ ( minus_minus_real @ T2 @ S2 ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( C4 @ P @ T2 ) @ ( C4 @ P @ S2 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % rho_bound2_def
% 0.29/0.47 thf(fact_175_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( ( minus_minus_nat @ B @ A )
% 0.29/0.47 = C )
% 0.29/0.47 = ( B
% 0.29/0.47 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 0.29/0.47 thf(fact_176_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 0.29/0.47 ! [A: nat,B: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 0.29/0.47 = B ) ) ).
% 0.29/0.47
% 0.29/0.47 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 0.29/0.47 thf(fact_177_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.29/0.47 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 0.29/0.47 thf(fact_178_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 0.29/0.47 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 0.29/0.47 thf(fact_179_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 0.29/0.47 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 0.29/0.47 thf(fact_180_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 0.29/0.47 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 0.29/0.47 thf(fact_181_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.29/0.47 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 0.29/0.47 thf(fact_182_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.29/0.47 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 0.29/0.47 thf(fact_183_le__add__diff,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_add_diff
% 0.29/0.47 thf(fact_184_add__le__add__imp__diff__le,axiom,
% 0.29/0.47 ! [I: real,K: real,N: real,J: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 0.29/0.47 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 0.29/0.47 => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 0.29/0.47 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 0.29/0.47 => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_le_add_imp_diff_le
% 0.29/0.47 thf(fact_185_add__le__add__imp__diff__le,axiom,
% 0.29/0.47 ! [I: nat,K: nat,N: nat,J: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 0.29/0.47 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 0.29/0.47 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 0.29/0.47 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 0.29/0.47 => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_le_add_imp_diff_le
% 0.29/0.47 thf(fact_186_diff__add,axiom,
% 0.29/0.47 ! [A: nat,B: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 0.29/0.47 = B ) ) ).
% 0.29/0.47
% 0.29/0.47 % diff_add
% 0.29/0.47 thf(fact_187_add__le__imp__le__diff,axiom,
% 0.29/0.47 ! [I: real,K: real,N: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 0.29/0.47 => ( ord_less_eq_real @ I @ ( minus_minus_real @ N @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_le_imp_le_diff
% 0.29/0.47 thf(fact_188_add__le__imp__le__diff,axiom,
% 0.29/0.47 ! [I: nat,K: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 0.29/0.47 => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_le_imp_le_diff
% 0.29/0.47 thf(fact_189_le__diff__eq,axiom,
% 0.29/0.47 ! [A: real,C: real,B: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 0.29/0.47 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_diff_eq
% 0.29/0.47 thf(fact_190_diff__le__eq,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.29/0.47 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % diff_le_eq
% 0.29/0.47 thf(fact_191_square__diff__square__factored,axiom,
% 0.29/0.47 ! [X2: real,Y: real] :
% 0.29/0.47 ( ( minus_minus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y @ Y ) )
% 0.29/0.47 = ( times_times_real @ ( plus_plus_real @ X2 @ Y ) @ ( minus_minus_real @ X2 @ Y ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % square_diff_square_factored
% 0.29/0.47 thf(fact_192_eq__add__iff2,axiom,
% 0.29/0.47 ! [A: real,E: real,C: real,B: real,D: real] :
% 0.29/0.47 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 0.29/0.47 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 0.29/0.47 = ( C
% 0.29/0.47 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_add_iff2
% 0.29/0.47 thf(fact_193_eq__add__iff1,axiom,
% 0.29/0.47 ! [A: real,E: real,C: real,B: real,D: real] :
% 0.29/0.47 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 0.29/0.47 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 0.29/0.47 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C )
% 0.29/0.47 = D ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_add_iff1
% 0.29/0.47 thf(fact_194_numeral__Bit0,axiom,
% 0.29/0.47 ! [N: num] :
% 0.29/0.47 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 0.29/0.47 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % numeral_Bit0
% 0.29/0.47 thf(fact_195_numeral__Bit0,axiom,
% 0.29/0.47 ! [N: num] :
% 0.29/0.47 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 0.29/0.47 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % numeral_Bit0
% 0.29/0.47 thf(fact_196_one__le__numeral,axiom,
% 0.29/0.47 ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 % one_le_numeral
% 0.29/0.47 thf(fact_197_one__le__numeral,axiom,
% 0.29/0.47 ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 % one_le_numeral
% 0.29/0.47 thf(fact_198_abs__triangle__ineq,axiom,
% 0.29/0.47 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % abs_triangle_ineq
% 0.29/0.47 thf(fact_199_numeral__One,axiom,
% 0.29/0.47 ( ( numeral_numeral_real @ one )
% 0.29/0.47 = one_one_real ) ).
% 0.29/0.47
% 0.29/0.47 % numeral_One
% 0.29/0.47 thf(fact_200_numeral__One,axiom,
% 0.29/0.47 ( ( numeral_numeral_nat @ one )
% 0.29/0.47 = one_one_nat ) ).
% 0.29/0.47
% 0.29/0.47 % numeral_One
% 0.29/0.47 thf(fact_201_ordered__ring__class_Ole__add__iff2,axiom,
% 0.29/0.47 ! [A: real,E: real,C: real,B: real,D: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 0.29/0.47 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ordered_ring_class.le_add_iff2
% 0.29/0.47 thf(fact_202_ordered__ring__class_Ole__add__iff1,axiom,
% 0.29/0.47 ! [A: real,E: real,C: real,B: real,D: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 0.29/0.47 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 0.29/0.47
% 0.29/0.47 % ordered_ring_class.le_add_iff1
% 0.29/0.47 thf(fact_203_abs__diff__triangle__ineq,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % abs_diff_triangle_ineq
% 0.29/0.47 thf(fact_204_abs__triangle__ineq4,axiom,
% 0.29/0.47 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % abs_triangle_ineq4
% 0.29/0.47 thf(fact_205_abs__diff__le__iff,axiom,
% 0.29/0.47 ! [X2: real,A: real,R: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ A ) ) @ R )
% 0.29/0.47 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R ) @ X2 )
% 0.29/0.47 & ( ord_less_eq_real @ X2 @ ( plus_plus_real @ A @ R ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % abs_diff_le_iff
% 0.29/0.47 thf(fact_206_diff__eq__diff__less__eq,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real,D: real] :
% 0.29/0.47 ( ( ( minus_minus_real @ A @ B )
% 0.29/0.47 = ( minus_minus_real @ C @ D ) )
% 0.29/0.47 => ( ( ord_less_eq_real @ A @ B )
% 0.29/0.47 = ( ord_less_eq_real @ C @ D ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % diff_eq_diff_less_eq
% 0.29/0.47 thf(fact_207_diff__right__mono,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ A @ B )
% 0.29/0.47 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % diff_right_mono
% 0.29/0.47 thf(fact_208_diff__left__mono,axiom,
% 0.29/0.47 ! [B: real,A: real,C: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ B @ A )
% 0.29/0.47 => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % diff_left_mono
% 0.29/0.47 thf(fact_209_diff__mono,axiom,
% 0.29/0.47 ! [A: real,B: real,D: real,C: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_real @ D @ C )
% 0.29/0.47 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % diff_mono
% 0.29/0.47 thf(fact_210_right__diff__distrib_H,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.29/0.47 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % right_diff_distrib'
% 0.29/0.47 thf(fact_211_right__diff__distrib_H,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C: nat] :
% 0.29/0.47 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 0.29/0.47 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % right_diff_distrib'
% 0.29/0.47 thf(fact_212_left__diff__distrib_H,axiom,
% 0.29/0.47 ! [B: real,C: real,A: real] :
% 0.29/0.47 ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 0.29/0.47 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % left_diff_distrib'
% 0.29/0.47 thf(fact_213_left__diff__distrib_H,axiom,
% 0.29/0.47 ! [B: nat,C: nat,A: nat] :
% 0.29/0.47 ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 0.29/0.47 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % left_diff_distrib'
% 0.29/0.47 thf(fact_214_right__diff__distrib,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 0.29/0.47 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % right_diff_distrib
% 0.29/0.47 thf(fact_215_left__diff__distrib,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 0.29/0.47 = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % left_diff_distrib
% 0.29/0.47 thf(fact_216_abs__ge__self,axiom,
% 0.29/0.47 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 0.29/0.47
% 0.29/0.47 % abs_ge_self
% 0.29/0.47 thf(fact_217_abs__le__D1,axiom,
% 0.29/0.47 ! [A: real,B: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 0.29/0.47 => ( ord_less_eq_real @ A @ B ) ) ).
% 0.29/0.47
% 0.29/0.47 % abs_le_D1
% 0.29/0.47 thf(fact_218_abs__mult,axiom,
% 0.29/0.47 ! [A: real,B: real] :
% 0.29/0.47 ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 0.29/0.47 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % abs_mult
% 0.29/0.47 thf(fact_219_abs__minus__commute,axiom,
% 0.29/0.47 ! [A: real,B: real] :
% 0.29/0.47 ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 0.29/0.47 = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % abs_minus_commute
% 0.29/0.47 thf(fact_220_left__add__twice,axiom,
% 0.29/0.47 ! [A: real,B: real] :
% 0.29/0.47 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.29/0.47 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.29/0.47
% 0.29/0.47 % left_add_twice
% 0.29/0.47 thf(fact_221_left__add__twice,axiom,
% 0.29/0.47 ! [A: nat,B: nat] :
% 0.29/0.47 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.29/0.47 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.29/0.47
% 0.29/0.47 % left_add_twice
% 0.29/0.47 thf(fact_222_mult__2__right,axiom,
% 0.29/0.47 ! [Z: real] :
% 0.29/0.47 ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.29/0.47 = ( plus_plus_real @ Z @ Z ) ) ).
% 0.29/0.47
% 0.29/0.47 % mult_2_right
% 0.29/0.47 thf(fact_223_mult__2__right,axiom,
% 0.29/0.47 ! [Z: nat] :
% 0.29/0.47 ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.29/0.47 = ( plus_plus_nat @ Z @ Z ) ) ).
% 0.29/0.47
% 0.29/0.47 % mult_2_right
% 0.29/0.47 thf(fact_224_mult__2,axiom,
% 0.29/0.47 ! [Z: real] :
% 0.29/0.47 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 0.29/0.47 = ( plus_plus_real @ Z @ Z ) ) ).
% 0.29/0.47
% 0.29/0.47 % mult_2
% 0.29/0.47 thf(fact_225_mult__2,axiom,
% 0.29/0.47 ! [Z: nat] :
% 0.29/0.47 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 0.29/0.47 = ( plus_plus_nat @ Z @ Z ) ) ).
% 0.29/0.47
% 0.29/0.47 % mult_2
% 0.29/0.47 thf(fact_226_mult__numeral__1__right,axiom,
% 0.29/0.47 ! [A: real] :
% 0.29/0.47 ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 0.29/0.47 = A ) ).
% 0.29/0.47
% 0.29/0.47 % mult_numeral_1_right
% 0.29/0.47 thf(fact_227_mult__numeral__1__right,axiom,
% 0.29/0.47 ! [A: nat] :
% 0.29/0.47 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 0.29/0.47 = A ) ).
% 0.29/0.47
% 0.29/0.47 % mult_numeral_1_right
% 0.29/0.47 thf(fact_228_mult__numeral__1,axiom,
% 0.29/0.47 ! [A: real] :
% 0.29/0.47 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 0.29/0.47 = A ) ).
% 0.29/0.47
% 0.29/0.47 % mult_numeral_1
% 0.29/0.47 thf(fact_229_mult__numeral__1,axiom,
% 0.29/0.47 ! [A: nat] :
% 0.29/0.47 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 0.29/0.47 = A ) ).
% 0.29/0.47
% 0.29/0.47 % mult_numeral_1
% 0.29/0.47 thf(fact_230_abs__triangle__ineq2__sym,axiom,
% 0.29/0.47 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % abs_triangle_ineq2_sym
% 0.29/0.47 thf(fact_231_sin__bound__lemma,axiom,
% 0.29/0.47 ! [X2: real,Y: real,U: real,V: real] :
% 0.29/0.47 ( ( X2 = Y )
% 0.29/0.47 => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 0.29/0.47 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X2 @ U ) @ Y ) ) @ V ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % sin_bound_lemma
% 0.29/0.47 thf(fact_232_rate__1,axiom,
% 0.29/0.47 ! [P3: nat,S: real,T: real] :
% 0.29/0.47 ( ( ( genClo1015804716orrect @ P3 @ T )
% 0.29/0.47 & ( ord_less_eq_real @ S @ T ) )
% 0.29/0.47 => ( ord_less_eq_real @ ( minus_minus_real @ ( genClo1161277105lle_PC @ P3 @ T ) @ ( genClo1161277105lle_PC @ P3 @ S ) ) @ ( times_times_real @ ( minus_minus_real @ T @ S ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % rate_1
% 0.29/0.47 thf(fact_233_rate__2,axiom,
% 0.29/0.47 ! [P3: nat,S: real,T: real] :
% 0.29/0.47 ( ( ( genClo1015804716orrect @ P3 @ T )
% 0.29/0.47 & ( ord_less_eq_real @ S @ T ) )
% 0.29/0.47 => ( ord_less_eq_real @ ( times_times_real @ ( minus_minus_real @ T @ S ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( genClo1161277105lle_PC @ P3 @ T ) @ ( genClo1161277105lle_PC @ P3 @ S ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % rate_2
% 0.29/0.47 thf(fact_234_dbl__simps_I3_J,axiom,
% 0.29/0.47 ( ( neg_numeral_dbl_real @ one_one_real )
% 0.29/0.47 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dbl_simps(3)
% 0.29/0.47 thf(fact_235_mult__diff__mult,axiom,
% 0.29/0.47 ! [X2: real,Y: real,A: real,B: real] :
% 0.29/0.47 ( ( minus_minus_real @ ( times_times_real @ X2 @ Y ) @ ( times_times_real @ A @ B ) )
% 0.29/0.47 = ( plus_plus_real @ ( times_times_real @ X2 @ ( minus_minus_real @ Y @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X2 @ A ) @ B ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % mult_diff_mult
% 0.29/0.47 thf(fact_236_verit__eq__simplify_I8_J,axiom,
% 0.29/0.47 ! [X22: num,Y2: num] :
% 0.29/0.47 ( ( ( bit0 @ X22 )
% 0.29/0.47 = ( bit0 @ Y2 ) )
% 0.29/0.47 = ( X22 = Y2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % verit_eq_simplify(8)
% 0.29/0.47 thf(fact_237_okRead1__def,axiom,
% 0.29/0.47 ( genClo293725281kRead1
% 0.29/0.47 = ( ^ [F: nat > real,X: real,Ppred: nat > $o] :
% 0.29/0.47 ! [L2: nat,M2: nat] :
% 0.29/0.47 ( ( ( Ppred @ L2 )
% 0.29/0.47 & ( Ppred @ M2 ) )
% 0.29/0.47 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ L2 ) @ ( F @ M2 ) ) ) @ X ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % okRead1_def
% 0.29/0.47 thf(fact_238_order__refl,axiom,
% 0.29/0.47 ! [X2: real] : ( ord_less_eq_real @ X2 @ X2 ) ).
% 0.29/0.47
% 0.29/0.47 % order_refl
% 0.29/0.47 thf(fact_239_order__refl,axiom,
% 0.29/0.47 ! [X2: num] : ( ord_less_eq_num @ X2 @ X2 ) ).
% 0.29/0.47
% 0.29/0.47 % order_refl
% 0.29/0.47 thf(fact_240_order__refl,axiom,
% 0.29/0.47 ! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ).
% 0.29/0.47
% 0.29/0.47 % order_refl
% 0.29/0.47 thf(fact_241_eq__diff__eq_H,axiom,
% 0.29/0.47 ! [X2: real,Y: real,Z: real] :
% 0.29/0.47 ( ( X2
% 0.29/0.47 = ( minus_minus_real @ Y @ Z ) )
% 0.29/0.47 = ( Y
% 0.29/0.47 = ( plus_plus_real @ X2 @ Z ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_diff_eq'
% 0.29/0.47 thf(fact_242_semiring__norm_I6_J,axiom,
% 0.29/0.47 ! [M: num,N: num] :
% 0.29/0.47 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.29/0.47 = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % semiring_norm(6)
% 0.29/0.47 thf(fact_243_semiring__norm_I2_J,axiom,
% 0.29/0.47 ( ( plus_plus_num @ one @ one )
% 0.29/0.47 = ( bit0 @ one ) ) ).
% 0.29/0.47
% 0.29/0.47 % semiring_norm(2)
% 0.29/0.47 thf(fact_244_dbl__simps_I5_J,axiom,
% 0.29/0.47 ! [K: num] :
% 0.29/0.47 ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 0.29/0.47 = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dbl_simps(5)
% 0.29/0.47 thf(fact_245_nat__1__add__1,axiom,
% 0.29/0.47 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.29/0.47 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_1_add_1
% 0.29/0.47 thf(fact_246_add__One__commute,axiom,
% 0.29/0.47 ! [N: num] :
% 0.29/0.47 ( ( plus_plus_num @ one @ N )
% 0.29/0.47 = ( plus_plus_num @ N @ one ) ) ).
% 0.29/0.47
% 0.29/0.47 % add_One_commute
% 0.29/0.47 thf(fact_247_numerals_I1_J,axiom,
% 0.29/0.47 ( ( numeral_numeral_nat @ one )
% 0.29/0.47 = one_one_nat ) ).
% 0.29/0.47
% 0.29/0.47 % numerals(1)
% 0.29/0.47 thf(fact_248_dbl__def,axiom,
% 0.29/0.47 ( neg_numeral_dbl_real
% 0.29/0.47 = ( ^ [X: real] : ( plus_plus_real @ X @ X ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dbl_def
% 0.29/0.47 thf(fact_249_order__subst1,axiom,
% 0.29/0.47 ! [A: real,F2: real > real,B: real,C: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ A @ ( F2 @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_real @ B @ C )
% 0.29/0.47 => ( ! [X3: real,Y3: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_real @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst1
% 0.29/0.47 thf(fact_250_order__subst1,axiom,
% 0.29/0.47 ! [A: real,F2: num > real,B: num,C: num] :
% 0.29/0.47 ( ( ord_less_eq_real @ A @ ( F2 @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_num @ B @ C )
% 0.29/0.47 => ( ! [X3: num,Y3: num] :
% 0.29/0.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_real @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst1
% 0.29/0.47 thf(fact_251_order__subst1,axiom,
% 0.29/0.47 ! [A: real,F2: nat > real,B: nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_real @ A @ ( F2 @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.47 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_real @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst1
% 0.29/0.47 thf(fact_252_order__subst1,axiom,
% 0.29/0.47 ! [A: num,F2: real > num,B: real,C: real] :
% 0.29/0.47 ( ( ord_less_eq_num @ A @ ( F2 @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_real @ B @ C )
% 0.29/0.47 => ( ! [X3: real,Y3: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_num @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst1
% 0.29/0.47 thf(fact_253_order__subst1,axiom,
% 0.29/0.47 ! [A: num,F2: num > num,B: num,C: num] :
% 0.29/0.47 ( ( ord_less_eq_num @ A @ ( F2 @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_num @ B @ C )
% 0.29/0.47 => ( ! [X3: num,Y3: num] :
% 0.29/0.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_num @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst1
% 0.29/0.47 thf(fact_254_order__subst1,axiom,
% 0.29/0.47 ! [A: num,F2: nat > num,B: nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_num @ A @ ( F2 @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.47 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_num @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst1
% 0.29/0.47 thf(fact_255_order__subst1,axiom,
% 0.29/0.47 ! [A: nat,F2: real > nat,B: real,C: real] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_real @ B @ C )
% 0.29/0.47 => ( ! [X3: real,Y3: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst1
% 0.29/0.47 thf(fact_256_order__subst1,axiom,
% 0.29/0.47 ! [A: nat,F2: num > nat,B: num,C: num] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_num @ B @ C )
% 0.29/0.47 => ( ! [X3: num,Y3: num] :
% 0.29/0.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst1
% 0.29/0.47 thf(fact_257_order__subst1,axiom,
% 0.29/0.47 ! [A: nat,F2: nat > nat,B: nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.47 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst1
% 0.29/0.47 thf(fact_258_order__subst2,axiom,
% 0.29/0.47 ! [A: real,B: real,F2: real > real,C: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_real @ ( F2 @ B ) @ C )
% 0.29/0.47 => ( ! [X3: real,Y3: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_real @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst2
% 0.29/0.47 thf(fact_259_order__subst2,axiom,
% 0.29/0.47 ! [A: real,B: real,F2: real > num,C: num] :
% 0.29/0.47 ( ( ord_less_eq_real @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_num @ ( F2 @ B ) @ C )
% 0.29/0.47 => ( ! [X3: real,Y3: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_num @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst2
% 0.29/0.47 thf(fact_260_order__subst2,axiom,
% 0.29/0.47 ! [A: real,B: real,F2: real > nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_real @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
% 0.29/0.47 => ( ! [X3: real,Y3: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst2
% 0.29/0.47 thf(fact_261_order__subst2,axiom,
% 0.29/0.47 ! [A: num,B: num,F2: num > real,C: real] :
% 0.29/0.47 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_real @ ( F2 @ B ) @ C )
% 0.29/0.47 => ( ! [X3: num,Y3: num] :
% 0.29/0.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_real @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst2
% 0.29/0.47 thf(fact_262_order__subst2,axiom,
% 0.29/0.47 ! [A: num,B: num,F2: num > num,C: num] :
% 0.29/0.47 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_num @ ( F2 @ B ) @ C )
% 0.29/0.47 => ( ! [X3: num,Y3: num] :
% 0.29/0.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_num @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst2
% 0.29/0.47 thf(fact_263_order__subst2,axiom,
% 0.29/0.47 ! [A: num,B: num,F2: num > nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
% 0.29/0.47 => ( ! [X3: num,Y3: num] :
% 0.29/0.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst2
% 0.29/0.47 thf(fact_264_order__subst2,axiom,
% 0.29/0.47 ! [A: nat,B: nat,F2: nat > real,C: real] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_real @ ( F2 @ B ) @ C )
% 0.29/0.47 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_real @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst2
% 0.29/0.47 thf(fact_265_order__subst2,axiom,
% 0.29/0.47 ! [A: nat,B: nat,F2: nat > num,C: num] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_num @ ( F2 @ B ) @ C )
% 0.29/0.47 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_num @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst2
% 0.29/0.47 thf(fact_266_order__subst2,axiom,
% 0.29/0.47 ! [A: nat,B: nat,F2: nat > nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
% 0.29/0.47 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order_subst2
% 0.29/0.47 thf(fact_267_verit__la__disequality,axiom,
% 0.29/0.47 ! [A: real,B: real] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 | ~ ( ord_less_eq_real @ A @ B )
% 0.29/0.47 | ~ ( ord_less_eq_real @ B @ A ) ) ).
% 0.29/0.47
% 0.29/0.47 % verit_la_disequality
% 0.29/0.47 thf(fact_268_verit__la__disequality,axiom,
% 0.29/0.47 ! [A: num,B: num] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 | ~ ( ord_less_eq_num @ A @ B )
% 0.29/0.47 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 0.29/0.47
% 0.29/0.47 % verit_la_disequality
% 0.29/0.47 thf(fact_269_verit__la__disequality,axiom,
% 0.29/0.47 ! [A: nat,B: nat] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 | ~ ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 0.29/0.47
% 0.29/0.47 % verit_la_disequality
% 0.29/0.47 thf(fact_270_ord__eq__le__subst,axiom,
% 0.29/0.47 ! [A: real,F2: real > real,B: real,C: real] :
% 0.29/0.47 ( ( A
% 0.29/0.47 = ( F2 @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_real @ B @ C )
% 0.29/0.47 => ( ! [X3: real,Y3: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_real @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_subst
% 0.29/0.47 thf(fact_271_ord__eq__le__subst,axiom,
% 0.29/0.47 ! [A: num,F2: real > num,B: real,C: real] :
% 0.29/0.47 ( ( A
% 0.29/0.47 = ( F2 @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_real @ B @ C )
% 0.29/0.47 => ( ! [X3: real,Y3: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_num @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_subst
% 0.29/0.47 thf(fact_272_ord__eq__le__subst,axiom,
% 0.29/0.47 ! [A: nat,F2: real > nat,B: real,C: real] :
% 0.29/0.47 ( ( A
% 0.29/0.47 = ( F2 @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_real @ B @ C )
% 0.29/0.47 => ( ! [X3: real,Y3: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_subst
% 0.29/0.47 thf(fact_273_ord__eq__le__subst,axiom,
% 0.29/0.47 ! [A: real,F2: num > real,B: num,C: num] :
% 0.29/0.47 ( ( A
% 0.29/0.47 = ( F2 @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_num @ B @ C )
% 0.29/0.47 => ( ! [X3: num,Y3: num] :
% 0.29/0.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_real @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_subst
% 0.29/0.47 thf(fact_274_ord__eq__le__subst,axiom,
% 0.29/0.47 ! [A: num,F2: num > num,B: num,C: num] :
% 0.29/0.47 ( ( A
% 0.29/0.47 = ( F2 @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_num @ B @ C )
% 0.29/0.47 => ( ! [X3: num,Y3: num] :
% 0.29/0.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_num @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_subst
% 0.29/0.47 thf(fact_275_ord__eq__le__subst,axiom,
% 0.29/0.47 ! [A: nat,F2: num > nat,B: num,C: num] :
% 0.29/0.47 ( ( A
% 0.29/0.47 = ( F2 @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_num @ B @ C )
% 0.29/0.47 => ( ! [X3: num,Y3: num] :
% 0.29/0.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_subst
% 0.29/0.47 thf(fact_276_ord__eq__le__subst,axiom,
% 0.29/0.47 ! [A: real,F2: nat > real,B: nat,C: nat] :
% 0.29/0.47 ( ( A
% 0.29/0.47 = ( F2 @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.47 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_real @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_subst
% 0.29/0.47 thf(fact_277_ord__eq__le__subst,axiom,
% 0.29/0.47 ! [A: num,F2: nat > num,B: nat,C: nat] :
% 0.29/0.47 ( ( A
% 0.29/0.47 = ( F2 @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.47 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_num @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_subst
% 0.29/0.47 thf(fact_278_ord__eq__le__subst,axiom,
% 0.29/0.47 ! [A: nat,F2: nat > nat,B: nat,C: nat] :
% 0.29/0.47 ( ( A
% 0.29/0.47 = ( F2 @ B ) )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.47 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_eq_le_subst
% 0.29/0.47 thf(fact_279_ord__le__eq__subst,axiom,
% 0.29/0.47 ! [A: real,B: real,F2: real > real,C: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ A @ B )
% 0.29/0.47 => ( ( ( F2 @ B )
% 0.29/0.47 = C )
% 0.29/0.47 => ( ! [X3: real,Y3: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_real @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_subst
% 0.29/0.47 thf(fact_280_ord__le__eq__subst,axiom,
% 0.29/0.47 ! [A: real,B: real,F2: real > num,C: num] :
% 0.29/0.47 ( ( ord_less_eq_real @ A @ B )
% 0.29/0.47 => ( ( ( F2 @ B )
% 0.29/0.47 = C )
% 0.29/0.47 => ( ! [X3: real,Y3: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_num @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_subst
% 0.29/0.47 thf(fact_281_ord__le__eq__subst,axiom,
% 0.29/0.47 ! [A: real,B: real,F2: real > nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_real @ A @ B )
% 0.29/0.47 => ( ( ( F2 @ B )
% 0.29/0.47 = C )
% 0.29/0.47 => ( ! [X3: real,Y3: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_subst
% 0.29/0.47 thf(fact_282_ord__le__eq__subst,axiom,
% 0.29/0.47 ! [A: num,B: num,F2: num > real,C: real] :
% 0.29/0.47 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.47 => ( ( ( F2 @ B )
% 0.29/0.47 = C )
% 0.29/0.47 => ( ! [X3: num,Y3: num] :
% 0.29/0.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_real @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_subst
% 0.29/0.47 thf(fact_283_ord__le__eq__subst,axiom,
% 0.29/0.47 ! [A: num,B: num,F2: num > num,C: num] :
% 0.29/0.47 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.47 => ( ( ( F2 @ B )
% 0.29/0.47 = C )
% 0.29/0.47 => ( ! [X3: num,Y3: num] :
% 0.29/0.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_num @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_subst
% 0.29/0.47 thf(fact_284_ord__le__eq__subst,axiom,
% 0.29/0.47 ! [A: num,B: num,F2: num > nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.47 => ( ( ( F2 @ B )
% 0.29/0.47 = C )
% 0.29/0.47 => ( ! [X3: num,Y3: num] :
% 0.29/0.47 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_subst
% 0.29/0.47 thf(fact_285_ord__le__eq__subst,axiom,
% 0.29/0.47 ! [A: nat,B: nat,F2: nat > real,C: real] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( ( F2 @ B )
% 0.29/0.47 = C )
% 0.29/0.47 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_real @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_subst
% 0.29/0.47 thf(fact_286_ord__le__eq__subst,axiom,
% 0.29/0.47 ! [A: nat,B: nat,F2: nat > num,C: num] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( ( F2 @ B )
% 0.29/0.47 = C )
% 0.29/0.47 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_num @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_subst
% 0.29/0.47 thf(fact_287_ord__le__eq__subst,axiom,
% 0.29/0.47 ! [A: nat,B: nat,F2: nat > nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( ( F2 @ B )
% 0.29/0.47 = C )
% 0.29/0.47 => ( ! [X3: nat,Y3: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.29/0.47 => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % ord_le_eq_subst
% 0.29/0.47 thf(fact_288_eq__iff,axiom,
% 0.29/0.47 ( ( ^ [Y4: real,Z2: real] : ( Y4 = Z2 ) )
% 0.29/0.47 = ( ^ [X: real,Y5: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ X @ Y5 )
% 0.29/0.47 & ( ord_less_eq_real @ Y5 @ X ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_iff
% 0.29/0.47 thf(fact_289_eq__iff,axiom,
% 0.29/0.47 ( ( ^ [Y4: num,Z2: num] : ( Y4 = Z2 ) )
% 0.29/0.47 = ( ^ [X: num,Y5: num] :
% 0.29/0.47 ( ( ord_less_eq_num @ X @ Y5 )
% 0.29/0.47 & ( ord_less_eq_num @ Y5 @ X ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_iff
% 0.29/0.47 thf(fact_290_eq__iff,axiom,
% 0.29/0.47 ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 0.29/0.47 = ( ^ [X: nat,Y5: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X @ Y5 )
% 0.29/0.47 & ( ord_less_eq_nat @ Y5 @ X ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_iff
% 0.29/0.47 thf(fact_291_antisym,axiom,
% 0.29/0.47 ! [X2: real,Y: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ X2 @ Y )
% 0.29/0.47 => ( ( ord_less_eq_real @ Y @ X2 )
% 0.29/0.47 => ( X2 = Y ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % antisym
% 0.29/0.47 thf(fact_292_antisym,axiom,
% 0.29/0.47 ! [X2: num,Y: num] :
% 0.29/0.47 ( ( ord_less_eq_num @ X2 @ Y )
% 0.29/0.47 => ( ( ord_less_eq_num @ Y @ X2 )
% 0.29/0.47 => ( X2 = Y ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % antisym
% 0.29/0.47 thf(fact_293_antisym,axiom,
% 0.29/0.47 ! [X2: nat,Y: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X2 @ Y )
% 0.29/0.47 => ( ( ord_less_eq_nat @ Y @ X2 )
% 0.29/0.47 => ( X2 = Y ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % antisym
% 0.29/0.47 thf(fact_294_linear,axiom,
% 0.29/0.47 ! [X2: real,Y: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ X2 @ Y )
% 0.29/0.47 | ( ord_less_eq_real @ Y @ X2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % linear
% 0.29/0.47 thf(fact_295_linear,axiom,
% 0.29/0.47 ! [X2: num,Y: num] :
% 0.29/0.47 ( ( ord_less_eq_num @ X2 @ Y )
% 0.29/0.47 | ( ord_less_eq_num @ Y @ X2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % linear
% 0.29/0.47 thf(fact_296_linear,axiom,
% 0.29/0.47 ! [X2: nat,Y: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ X2 @ Y )
% 0.29/0.47 | ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % linear
% 0.29/0.47 thf(fact_297_eq__refl,axiom,
% 0.29/0.47 ! [X2: real,Y: real] :
% 0.29/0.47 ( ( X2 = Y )
% 0.29/0.47 => ( ord_less_eq_real @ X2 @ Y ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_refl
% 0.29/0.47 thf(fact_298_eq__refl,axiom,
% 0.29/0.47 ! [X2: num,Y: num] :
% 0.29/0.47 ( ( X2 = Y )
% 0.29/0.47 => ( ord_less_eq_num @ X2 @ Y ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_refl
% 0.29/0.47 thf(fact_299_eq__refl,axiom,
% 0.29/0.47 ! [X2: nat,Y: nat] :
% 0.29/0.47 ( ( X2 = Y )
% 0.29/0.47 => ( ord_less_eq_nat @ X2 @ Y ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_refl
% 0.29/0.47 thf(fact_300_le__cases,axiom,
% 0.29/0.47 ! [X2: real,Y: real] :
% 0.29/0.47 ( ~ ( ord_less_eq_real @ X2 @ Y )
% 0.29/0.47 => ( ord_less_eq_real @ Y @ X2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_cases
% 0.29/0.47 thf(fact_301_le__cases,axiom,
% 0.29/0.47 ! [X2: num,Y: num] :
% 0.29/0.47 ( ~ ( ord_less_eq_num @ X2 @ Y )
% 0.29/0.47 => ( ord_less_eq_num @ Y @ X2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_cases
% 0.29/0.47 thf(fact_302_le__cases,axiom,
% 0.29/0.47 ! [X2: nat,Y: nat] :
% 0.29/0.47 ( ~ ( ord_less_eq_nat @ X2 @ Y )
% 0.29/0.47 => ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_cases
% 0.29/0.47 thf(fact_303_order_Otrans,axiom,
% 0.29/0.47 ! [A: real,B: real,C: real] :
% 0.29/0.47 ( ( ord_less_eq_real @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_real @ B @ C )
% 0.29/0.47 => ( ord_less_eq_real @ A @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.trans
% 0.29/0.47 thf(fact_304_order_Otrans,axiom,
% 0.29/0.47 ! [A: num,B: num,C: num] :
% 0.29/0.47 ( ( ord_less_eq_num @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_num @ B @ C )
% 0.29/0.47 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.trans
% 0.29/0.47 thf(fact_305_order_Otrans,axiom,
% 0.29/0.47 ! [A: nat,B: nat,C: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.47 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % order.trans
% 0.29/0.47 thf(fact_306_le__cases3,axiom,
% 0.29/0.47 ! [X2: real,Y: real,Z: real] :
% 0.29/0.47 ( ( ( ord_less_eq_real @ X2 @ Y )
% 0.29/0.47 => ~ ( ord_less_eq_real @ Y @ Z ) )
% 0.29/0.47 => ( ( ( ord_less_eq_real @ Y @ X2 )
% 0.29/0.47 => ~ ( ord_less_eq_real @ X2 @ Z ) )
% 0.29/0.47 => ( ( ( ord_less_eq_real @ X2 @ Z )
% 0.29/0.47 => ~ ( ord_less_eq_real @ Z @ Y ) )
% 0.29/0.47 => ( ( ( ord_less_eq_real @ Z @ Y )
% 0.29/0.47 => ~ ( ord_less_eq_real @ Y @ X2 ) )
% 0.29/0.47 => ( ( ( ord_less_eq_real @ Y @ Z )
% 0.29/0.47 => ~ ( ord_less_eq_real @ Z @ X2 ) )
% 0.29/0.47 => ~ ( ( ord_less_eq_real @ Z @ X2 )
% 0.29/0.47 => ~ ( ord_less_eq_real @ X2 @ Y ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_cases3
% 0.29/0.47 thf(fact_307_le__cases3,axiom,
% 0.29/0.47 ! [X2: num,Y: num,Z: num] :
% 0.29/0.47 ( ( ( ord_less_eq_num @ X2 @ Y )
% 0.29/0.47 => ~ ( ord_less_eq_num @ Y @ Z ) )
% 0.29/0.47 => ( ( ( ord_less_eq_num @ Y @ X2 )
% 0.29/0.47 => ~ ( ord_less_eq_num @ X2 @ Z ) )
% 0.29/0.47 => ( ( ( ord_less_eq_num @ X2 @ Z )
% 0.29/0.47 => ~ ( ord_less_eq_num @ Z @ Y ) )
% 0.29/0.47 => ( ( ( ord_less_eq_num @ Z @ Y )
% 0.29/0.47 => ~ ( ord_less_eq_num @ Y @ X2 ) )
% 0.29/0.47 => ( ( ( ord_less_eq_num @ Y @ Z )
% 0.29/0.47 => ~ ( ord_less_eq_num @ Z @ X2 ) )
% 0.29/0.47 => ~ ( ( ord_less_eq_num @ Z @ X2 )
% 0.29/0.47 => ~ ( ord_less_eq_num @ X2 @ Y ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_cases3
% 0.29/0.47 thf(fact_308_le__cases3,axiom,
% 0.29/0.47 ! [X2: nat,Y: nat,Z: nat] :
% 0.29/0.47 ( ( ( ord_less_eq_nat @ X2 @ Y )
% 0.29/0.47 => ~ ( ord_less_eq_nat @ Y @ Z ) )
% 0.29/0.47 => ( ( ( ord_less_eq_nat @ Y @ X2 )
% 0.29/0.47 => ~ ( ord_less_eq_nat @ X2 @ Z ) )
% 0.29/0.47 => ( ( ( ord_less_eq_nat @ X2 @ Z )
% 0.29/0.47 => ~ ( ord_less_eq_nat @ Z @ Y ) )
% 0.29/0.47 => ( ( ( ord_less_eq_nat @ Z @ Y )
% 0.29/0.47 => ~ ( ord_less_eq_nat @ Y @ X2 ) )
% 0.29/0.47 => ( ( ( ord_less_eq_nat @ Y @ Z )
% 0.29/0.47 => ~ ( ord_less_eq_nat @ Z @ X2 ) )
% 0.29/0.47 => ~ ( ( ord_less_eq_nat @ Z @ X2 )
% 0.29/0.47 => ~ ( ord_less_eq_nat @ X2 @ Y ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_cases3
% 0.29/0.47 thf(fact_309_antisym__conv,axiom,
% 0.29/0.47 ! [Y: num,X2: num] :
% 0.29/0.47 ( ( ord_less_eq_num @ Y @ X2 )
% 0.29/0.47 => ( ( ord_less_eq_num @ X2 @ Y )
% 0.29/0.47 = ( X2 = Y ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % antisym_conv
% 0.29/0.47 thf(fact_310_antisym__conv,axiom,
% 0.29/0.47 ! [Y: nat,X2: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ Y @ X2 )
% 0.29/0.47 => ( ( ord_less_eq_nat @ X2 @ Y )
% 0.29/0.47 = ( X2 = Y ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % antisym_conv
% 0.29/0.47 thf(fact_311_complete__real,axiom,
% 0.29/0.47 ! [S3: set_real] :
% 0.29/0.47 ( ? [X4: real] : ( member_real @ X4 @ S3 )
% 0.29/0.47 => ( ? [Z3: real] :
% 0.29/0.47 ! [X3: real] :
% 0.29/0.47 ( ( member_real @ X3 @ S3 )
% 0.29/0.47 => ( ord_less_eq_real @ X3 @ Z3 ) )
% 0.29/0.47 => ? [Y3: real] :
% 0.29/0.47 ( ! [X4: real] :
% 0.29/0.47 ( ( member_real @ X4 @ S3 )
% 0.29/0.47 => ( ord_less_eq_real @ X4 @ Y3 ) )
% 0.29/0.47 & ! [Z3: real] :
% 0.29/0.47 ( ! [X3: real] :
% 0.29/0.47 ( ( member_real @ X3 @ S3 )
% 0.29/0.47 => ( ord_less_eq_real @ X3 @ Z3 ) )
% 0.29/0.47 => ( ord_less_eq_real @ Y3 @ Z3 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % complete_real
% 0.29/0.47 thf(fact_312_PC__monotone,axiom,
% 0.29/0.47 ! [P3: nat,S: real,T: real] :
% 0.29/0.47 ( ( ( genClo1015804716orrect @ P3 @ T )
% 0.29/0.47 & ( ord_less_eq_real @ S @ T ) )
% 0.29/0.47 => ( ord_less_eq_real @ ( genClo1161277105lle_PC @ P3 @ S ) @ ( genClo1161277105lle_PC @ P3 @ T ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % PC_monotone
% 0.29/0.47 thf(fact_313_verit__eq__simplify_I10_J,axiom,
% 0.29/0.47 ! [X22: num] :
% 0.29/0.47 ( one
% 0.29/0.47 != ( bit0 @ X22 ) ) ).
% 0.29/0.47
% 0.29/0.47 % verit_eq_simplify(10)
% 0.29/0.47 thf(fact_314_nat__eq__add__iff1,axiom,
% 0.29/0.47 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ J @ I )
% 0.29/0.47 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 0.29/0.47 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.29/0.47 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M )
% 0.29/0.47 = N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_eq_add_iff1
% 0.29/0.47 thf(fact_315_nat__eq__add__iff2,axiom,
% 0.29/0.47 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.47 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 0.29/0.47 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.29/0.47 = ( M
% 0.29/0.47 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_eq_add_iff2
% 0.29/0.47 thf(fact_316_nat__le__add__iff1,axiom,
% 0.29/0.47 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ J @ I )
% 0.29/0.47 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.29/0.47 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_le_add_iff1
% 0.29/0.47 thf(fact_317_nat__le__add__iff2,axiom,
% 0.29/0.47 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.47 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.29/0.47 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_le_add_iff2
% 0.29/0.47 thf(fact_318_nat__diff__add__eq1,axiom,
% 0.29/0.47 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ J @ I )
% 0.29/0.47 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.29/0.47 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_diff_add_eq1
% 0.29/0.47 thf(fact_319_nat__diff__add__eq2,axiom,
% 0.29/0.47 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.47 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.29/0.47 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_diff_add_eq2
% 0.29/0.47 thf(fact_320_left__add__mult__distrib,axiom,
% 0.29/0.47 ! [I: nat,U: nat,J: nat,K: nat] :
% 0.29/0.47 ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 0.29/0.47 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 0.29/0.47
% 0.29/0.47 % left_add_mult_distrib
% 0.29/0.47 thf(fact_321_nat__1__eq__mult__iff,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( one_one_nat
% 0.29/0.47 = ( times_times_nat @ M @ N ) )
% 0.29/0.47 = ( ( M = one_one_nat )
% 0.29/0.47 & ( N = one_one_nat ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_1_eq_mult_iff
% 0.29/0.47 thf(fact_322_nat__mult__eq__1__iff,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ( times_times_nat @ M @ N )
% 0.29/0.47 = one_one_nat )
% 0.29/0.47 = ( ( M = one_one_nat )
% 0.29/0.47 & ( N = one_one_nat ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_mult_eq_1_iff
% 0.29/0.47 thf(fact_323_nat__add__left__cancel__le,axiom,
% 0.29/0.47 ! [K: nat,M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.29/0.47 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_add_left_cancel_le
% 0.29/0.47 thf(fact_324_diff__diff__cancel,axiom,
% 0.29/0.47 ! [I: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ N )
% 0.29/0.47 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 0.29/0.47 = I ) ) ).
% 0.29/0.47
% 0.29/0.47 % diff_diff_cancel
% 0.29/0.47 thf(fact_325_diff__diff__left,axiom,
% 0.29/0.47 ! [I: nat,J: nat,K: nat] :
% 0.29/0.47 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 0.29/0.47 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % diff_diff_left
% 0.29/0.47 thf(fact_326_Nat_Odiff__diff__right,axiom,
% 0.29/0.47 ! [K: nat,J: nat,I: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.47 => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.29/0.47 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Nat.diff_diff_right
% 0.29/0.47 thf(fact_327_Nat_Oadd__diff__assoc2,axiom,
% 0.29/0.47 ! [K: nat,J: nat,I: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.47 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 0.29/0.47 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Nat.add_diff_assoc2
% 0.29/0.47 thf(fact_328_Nat_Oadd__diff__assoc,axiom,
% 0.29/0.47 ! [K: nat,J: nat,I: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ K @ J )
% 0.29/0.47 => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 0.29/0.47 = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Nat.add_diff_assoc
% 0.29/0.47 thf(fact_329_eq__diff__iff,axiom,
% 0.29/0.47 ! [K: nat,M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.47 => ( ( ord_less_eq_nat @ K @ N )
% 0.29/0.47 => ( ( ( minus_minus_nat @ M @ K )
% 0.29/0.47 = ( minus_minus_nat @ N @ K ) )
% 0.29/0.47 = ( M = N ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_diff_iff
% 0.29/0.47 thf(fact_330_le__diff__iff,axiom,
% 0.29/0.47 ! [K: nat,M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.47 => ( ( ord_less_eq_nat @ K @ N )
% 0.29/0.47 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.29/0.47 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_diff_iff
% 0.29/0.47 thf(fact_331_Nat_Odiff__diff__eq,axiom,
% 0.29/0.47 ! [K: nat,M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ K @ M )
% 0.29/0.47 => ( ( ord_less_eq_nat @ K @ N )
% 0.29/0.47 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.29/0.47 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Nat.diff_diff_eq
% 0.29/0.47 thf(fact_332_diff__le__mono,axiom,
% 0.29/0.47 ! [M: nat,N: nat,L: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.47 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % diff_le_mono
% 0.29/0.47 thf(fact_333_diff__le__self,axiom,
% 0.29/0.47 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 0.29/0.47
% 0.29/0.47 % diff_le_self
% 0.29/0.47 thf(fact_334_le__diff__iff_H,axiom,
% 0.29/0.47 ! [A: nat,C: nat,B: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ A @ C )
% 0.29/0.47 => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.47 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 0.29/0.47 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_diff_iff'
% 0.29/0.47 thf(fact_335_diff__le__mono2,axiom,
% 0.29/0.47 ! [M: nat,N: nat,L: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.47 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % diff_le_mono2
% 0.29/0.47 thf(fact_336_Nat_Oex__has__greatest__nat,axiom,
% 0.29/0.47 ! [P2: nat > $o,K: nat,B: nat] :
% 0.29/0.47 ( ( P2 @ K )
% 0.29/0.47 => ( ! [Y3: nat] :
% 0.29/0.47 ( ( P2 @ Y3 )
% 0.29/0.47 => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.29/0.47 => ? [X3: nat] :
% 0.29/0.47 ( ( P2 @ X3 )
% 0.29/0.47 & ! [Y6: nat] :
% 0.29/0.47 ( ( P2 @ Y6 )
% 0.29/0.47 => ( ord_less_eq_nat @ Y6 @ X3 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Nat.ex_has_greatest_nat
% 0.29/0.47 thf(fact_337_nat__le__linear,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.47 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_le_linear
% 0.29/0.47 thf(fact_338_mult__le__mono2,axiom,
% 0.29/0.47 ! [I: nat,J: nat,K: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.47 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % mult_le_mono2
% 0.29/0.47 thf(fact_339_mult__le__mono1,axiom,
% 0.29/0.47 ! [I: nat,J: nat,K: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.47 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % mult_le_mono1
% 0.29/0.47 thf(fact_340_mult__le__mono,axiom,
% 0.29/0.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.47 => ( ( ord_less_eq_nat @ K @ L )
% 0.29/0.47 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % mult_le_mono
% 0.29/0.47 thf(fact_341_le__antisym,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ M @ N )
% 0.29/0.47 => ( ( ord_less_eq_nat @ N @ M )
% 0.29/0.47 => ( M = N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_antisym
% 0.29/0.47 thf(fact_342_le__square,axiom,
% 0.29/0.47 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_square
% 0.29/0.47 thf(fact_343_eq__imp__le,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( M = N )
% 0.29/0.47 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.29/0.47
% 0.29/0.47 % eq_imp_le
% 0.29/0.47 thf(fact_344_le__trans,axiom,
% 0.29/0.47 ! [I: nat,J: nat,K: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.47 => ( ( ord_less_eq_nat @ J @ K )
% 0.29/0.47 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_trans
% 0.29/0.47 thf(fact_345_le__refl,axiom,
% 0.29/0.47 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.29/0.47
% 0.29/0.47 % le_refl
% 0.29/0.47 thf(fact_346_le__cube,axiom,
% 0.29/0.47 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_cube
% 0.29/0.47 thf(fact_347_diff__mult__distrib2,axiom,
% 0.29/0.47 ! [K: nat,M: nat,N: nat] :
% 0.29/0.47 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 0.29/0.47 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % diff_mult_distrib2
% 0.29/0.47 thf(fact_348_diff__mult__distrib,axiom,
% 0.29/0.47 ! [M: nat,N: nat,K: nat] :
% 0.29/0.47 ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 0.29/0.47 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % diff_mult_distrib
% 0.29/0.47 thf(fact_349_diff__commute,axiom,
% 0.29/0.47 ! [I: nat,J: nat,K: nat] :
% 0.29/0.47 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 0.29/0.47 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 0.29/0.47
% 0.29/0.47 % diff_commute
% 0.29/0.47 thf(fact_350_Nat_Ole__imp__diff__is__add,axiom,
% 0.29/0.47 ! [I: nat,J: nat,K: nat] :
% 0.29/0.47 ( ( ord_less_eq_nat @ I @ J )
% 0.29/0.47 => ( ( ( minus_minus_nat @ J @ I )
% 0.29/0.47 = K )
% 0.29/0.47 = ( J
% 0.29/0.47 = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Nat.le_imp_diff_is_add
% 0.29/0.47 thf(fact_351_diff__add__inverse2,axiom,
% 0.29/0.47 ! [M: nat,N: nat] :
% 0.29/0.47 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 0.29/0.47 = M ) ).
% 0.29/0.47
% 0.29/0.47 % diff_add_inverse2
% 0.29/0.47
% 0.29/0.47 % Conjectures (1)
% 0.29/0.47 thf(conj_0,conjecture,
% 0.29/0.47 ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 2.61/1.46 ---- Embedded in THF ---
% 2.61/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.61/1.46 %%% Generated on Tue Feb 24 08:25:10 EST 2026
% 2.61/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 2.61/1.46 %%% Logic specification used:
% 2.61/1.46 %%% thf(spec, logic, $$dhol).
% 2.61/1.46
% 2.61/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.3sGo6IMQoe/DTF2DTF1172.p
% See solution above
% 2.61/1.46 ------------------------
% 2.61/1.49 ---- Cleaned THF ---
% 2.61/1.49 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 2.61/1.49 set_real: $tType ).
% 2.61/1.49
% 2.61/1.49 thf(ty_n_t__Real__Oreal,type,
% 2.61/1.49 real: $tType ).
% 2.61/1.49
% 2.61/1.49 thf(ty_n_t__Num__Onum,type,
% 2.61/1.49 num: $tType ).
% 2.61/1.49
% 2.61/1.49 thf(ty_n_t__Nat__Onat,type,
% 2.61/1.49 nat: $tType ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_GenClock__Mirabelle__bsvkzpgbls_OPC,type,
% 2.61/1.49 genClo1161277105lle_PC: nat > real > real ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_GenClock__Mirabelle__bsvkzpgbls_O_092_060rho_062,type,
% 2.61/1.49 genClo1144207539le_rho: real ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_GenClock__Mirabelle__bsvkzpgbls_Ocorrect,type,
% 2.61/1.49 genClo1015804716orrect: nat > real > $o ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_GenClock__Mirabelle__bsvkzpgbls_OokRead1,type,
% 2.61/1.49 genClo293725281kRead1: ( nat > real ) > real > ( nat > $o ) > $o ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_GenClock__Mirabelle__bsvkzpgbls_OokRead2,type,
% 2.61/1.49 genClo293725282kRead2: ( nat > real ) > ( nat > real ) > real > ( nat > $o ) > $o ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_GenClock__Mirabelle__bsvkzpgbls_Orho__bound1,type,
% 2.61/1.49 genClo2108747022bound1: ( nat > real > real ) > $o ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_GenClock__Mirabelle__bsvkzpgbls_Orho__bound2,type,
% 2.61/1.49 genClo2108747023bound2: ( nat > real > real ) > $o ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal,type,
% 2.61/1.49 abs_abs_real: real > real ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 2.61/1.49 minus_minus_nat: nat > nat > nat ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal,type,
% 2.61/1.49 minus_minus_real: real > real > real ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 2.61/1.49 one_one_nat: nat ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal,type,
% 2.61/1.49 one_one_real: real ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 2.61/1.49 plus_plus_nat: nat > nat > nat ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_Groups_Oplus__class_Oplus_001t__Num__Onum,type,
% 2.61/1.49 plus_plus_num: num > num > num ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal,type,
% 2.61/1.49 plus_plus_real: real > real > real ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat,type,
% 2.61/1.49 times_times_nat: nat > nat > nat ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_Groups_Otimes__class_Otimes_001t__Num__Onum,type,
% 2.61/1.49 times_times_num: num > num > num ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_Groups_Otimes__class_Otimes_001t__Real__Oreal,type,
% 2.61/1.49 times_times_real: real > real > real ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 2.61/1.49 neg_numeral_dbl_real: real > real ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_Num_Onum_OBit0,type,
% 2.61/1.49 bit0: num > num ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_Num_Onum_OOne,type,
% 2.61/1.49 one: num ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
% 2.61/1.49 numeral_numeral_nat: num > nat ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal,type,
% 2.61/1.49 numeral_numeral_real: num > real ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 2.61/1.49 ord_less_eq_nat: nat > nat > $o ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Num__Onum,type,
% 2.61/1.49 ord_less_eq_num: num > num > $o ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 2.61/1.49 ord_less_eq_real: real > real > $o ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
% 2.61/1.49 collect_real: ( real > $o ) > set_real ).
% 2.61/1.49
% 2.61/1.49 thf(sy_c_member_001t__Real__Oreal,type,
% 2.61/1.49 member_real: real > set_real > $o ).
% 2.61/1.49
% 2.61/1.49 thf(sy_v_C,type,
% 2.61/1.49 c: nat > real > real ).
% 2.61/1.49
% 2.61/1.49 thf(sy_v_D,type,
% 2.61/1.49 d: nat > real > real ).
% 2.61/1.49
% 2.61/1.49 thf(sy_v_p,type,
% 2.61/1.49 p: nat ).
% 2.61/1.49
% 2.61/1.49 thf(sy_v_q,type,
% 2.61/1.49 q: nat ).
% 2.61/1.49
% 2.61/1.49 thf(sy_v_s,type,
% 2.61/1.49 s: real ).
% 2.61/1.49
% 2.61/1.49 thf(sy_v_t,type,
% 2.61/1.49 t: real ).
% 2.61/1.49
% 2.61/1.49 thf(fact_0_rb2,axiom,
% 2.61/1.49 genClo2108747023bound2 @ d ).
% 2.61/1.49
% 2.61/1.49 thf(fact_1_rb1,axiom,
% 2.61/1.49 genClo2108747022bound1 @ c ).
% 2.61/1.49
% 2.61/1.49 thf(fact_2_ie,axiom,
% 2.61/1.49 ord_less_eq_real @ s @ t ).
% 2.61/1.49
% 2.61/1.49 thf(fact_3_Eq1,axiom,
% 2.61/1.49 ( ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
% 2.61/1.49 = ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_4_Eq4,axiom,
% 2.61/1.49 ( ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) )
% 2.61/1.49 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_5_Eq3,axiom,
% 2.61/1.49 ord_less_eq_real @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_6_corr__q,axiom,
% 2.61/1.49 genClo1015804716orrect @ q @ t ).
% 2.61/1.49
% 2.61/1.49 thf(fact_7_PC__ie,axiom,
% 2.61/1.49 ord_less_eq_real @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_8_corr__p,axiom,
% 2.61/1.49 genClo1015804716orrect @ p @ t ).
% 2.61/1.49
% 2.61/1.49 thf(fact_9_Eq2,axiom,
% 2.61/1.49 ord_less_eq_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_10__092_060open_062_It_A_N_As_J_A_K_A_I1_A_N_A_092_060rho_062_J_A_092_060le_062_AD_Aq_At_A_N_AD_Aq_As_092_060close_062,axiom,
% 2.61/1.49 ord_less_eq_real @ ( times_times_real @ ( minus_minus_real @ t @ s ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_11_left__diff__distrib__numeral,axiom,
% 2.61/1.49 ! [A: real,B: real,V: num] :
% 2.61/1.49 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 2.61/1.49 = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_12_right__diff__distrib__numeral,axiom,
% 2.61/1.49 ! [V: num,B: real,C: real] :
% 2.61/1.49 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 2.61/1.49 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_13_abs__numeral,axiom,
% 2.61/1.49 ! [N: num] :
% 2.61/1.49 ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 2.61/1.49 = ( numeral_numeral_real @ N ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_14_abs__mult__self__eq,axiom,
% 2.61/1.49 ! [A: real] :
% 2.61/1.49 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 2.61/1.49 = ( times_times_real @ A @ A ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_15_semiring__norm_I85_J,axiom,
% 2.61/1.49 ! [M: num] :
% 2.61/1.49 ( ( bit0 @ M )
% 2.61/1.49 != one ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_16_semiring__norm_I83_J,axiom,
% 2.61/1.49 ! [N: num] :
% 2.61/1.49 ( one
% 2.61/1.49 != ( bit0 @ N ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_17_mult__numeral__left__semiring__numeral,axiom,
% 2.61/1.49 ! [V: num,W: num,Z: real] :
% 2.61/1.49 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 2.61/1.49 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_18_mult__numeral__left__semiring__numeral,axiom,
% 2.61/1.49 ! [V: num,W: num,Z: nat] :
% 2.61/1.49 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 2.61/1.49 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_19_numeral__times__numeral,axiom,
% 2.61/1.49 ! [M: num,N: num] :
% 2.61/1.49 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 2.61/1.49 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_20_numeral__times__numeral,axiom,
% 2.61/1.49 ! [M: num,N: num] :
% 2.61/1.49 ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 2.61/1.49 = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_21_numeral__le__iff,axiom,
% 2.61/1.49 ! [M: num,N: num] :
% 2.61/1.49 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 2.61/1.49 = ( ord_less_eq_num @ M @ N ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_22_numeral__le__iff,axiom,
% 2.61/1.49 ! [M: num,N: num] :
% 2.61/1.49 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 2.61/1.49 = ( ord_less_eq_num @ M @ N ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_23_okRead2__def,axiom,
% 2.61/1.49 ( genClo293725282kRead2
% 2.61/1.49 = ( ^ [F: nat > real,G: nat > real,X: real,Ppred: nat > $o] :
% 2.61/1.49 ! [P: nat] :
% 2.61/1.49 ( ( Ppred @ P )
% 2.61/1.49 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ P ) @ ( G @ P ) ) ) @ X ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_24_abs__triangle__ineq2,axiom,
% 2.61/1.49 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_25_abs__triangle__ineq3,axiom,
% 2.61/1.49 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_26_numeral__eq__iff,axiom,
% 2.61/1.49 ! [M: num,N: num] :
% 2.61/1.49 ( ( ( numeral_numeral_real @ M )
% 2.61/1.49 = ( numeral_numeral_real @ N ) )
% 2.61/1.49 = ( M = N ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_27_numeral__eq__iff,axiom,
% 2.61/1.49 ! [M: num,N: num] :
% 2.61/1.49 ( ( ( numeral_numeral_nat @ M )
% 2.61/1.49 = ( numeral_numeral_nat @ N ) )
% 2.61/1.49 = ( M = N ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_28_add__left__cancel,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( ( plus_plus_real @ A @ B )
% 2.61/1.49 = ( plus_plus_real @ A @ C ) )
% 2.61/1.49 = ( B = C ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_29_add__left__cancel,axiom,
% 2.61/1.49 ! [A: nat,B: nat,C: nat] :
% 2.61/1.49 ( ( ( plus_plus_nat @ A @ B )
% 2.61/1.49 = ( plus_plus_nat @ A @ C ) )
% 2.61/1.49 = ( B = C ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_30_add__right__cancel,axiom,
% 2.61/1.49 ! [B: real,A: real,C: real] :
% 2.61/1.49 ( ( ( plus_plus_real @ B @ A )
% 2.61/1.49 = ( plus_plus_real @ C @ A ) )
% 2.61/1.49 = ( B = C ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_31_add__right__cancel,axiom,
% 2.61/1.49 ! [B: nat,A: nat,C: nat] :
% 2.61/1.49 ( ( ( plus_plus_nat @ B @ A )
% 2.61/1.49 = ( plus_plus_nat @ C @ A ) )
% 2.61/1.49 = ( B = C ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_32_semiring__norm_I87_J,axiom,
% 2.61/1.49 ! [M: num,N: num] :
% 2.61/1.49 ( ( ( bit0 @ M )
% 2.61/1.49 = ( bit0 @ N ) )
% 2.61/1.49 = ( M = N ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_33_abs__idempotent,axiom,
% 2.61/1.49 ! [A: real] :
% 2.61/1.49 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 2.61/1.49 = ( abs_abs_real @ A ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_34_abs__abs,axiom,
% 2.61/1.49 ! [A: real] :
% 2.61/1.49 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 2.61/1.49 = ( abs_abs_real @ A ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_35_add__le__cancel__right,axiom,
% 2.61/1.49 ! [A: real,C: real,B: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 2.61/1.49 = ( ord_less_eq_real @ A @ B ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_36_add__le__cancel__right,axiom,
% 2.61/1.49 ! [A: nat,C: nat,B: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 2.61/1.49 = ( ord_less_eq_nat @ A @ B ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_37_add__le__cancel__left,axiom,
% 2.61/1.49 ! [C: real,A: real,B: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 2.61/1.49 = ( ord_less_eq_real @ A @ B ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_38_add__le__cancel__left,axiom,
% 2.61/1.49 ! [C: nat,A: nat,B: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 2.61/1.49 = ( ord_less_eq_nat @ A @ B ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_39_mult_Oright__neutral,axiom,
% 2.61/1.49 ! [A: real] :
% 2.61/1.49 ( ( times_times_real @ A @ one_one_real )
% 2.61/1.49 = A ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_40_mult_Oright__neutral,axiom,
% 2.61/1.49 ! [A: nat] :
% 2.61/1.49 ( ( times_times_nat @ A @ one_one_nat )
% 2.61/1.49 = A ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_41_mult_Oleft__neutral,axiom,
% 2.61/1.49 ! [A: real] :
% 2.61/1.49 ( ( times_times_real @ one_one_real @ A )
% 2.61/1.49 = A ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_42_mult_Oleft__neutral,axiom,
% 2.61/1.49 ! [A: nat] :
% 2.61/1.49 ( ( times_times_nat @ one_one_nat @ A )
% 2.61/1.49 = A ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_43_numeral__plus__numeral,axiom,
% 2.61/1.49 ! [M: num,N: num] :
% 2.61/1.49 ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 2.61/1.49 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_44_numeral__plus__numeral,axiom,
% 2.61/1.49 ! [M: num,N: num] :
% 2.61/1.49 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 2.61/1.49 = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_45_add__numeral__left,axiom,
% 2.61/1.49 ! [V: num,W: num,Z: real] :
% 2.61/1.49 ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 2.61/1.49 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_46_add__numeral__left,axiom,
% 2.61/1.49 ! [V: num,W: num,Z: nat] :
% 2.61/1.49 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 2.61/1.49 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_47_add__diff__cancel__right_H,axiom,
% 2.61/1.49 ! [A: real,B: real] :
% 2.61/1.49 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 2.61/1.49 = A ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_48_add__diff__cancel__right_H,axiom,
% 2.61/1.49 ! [A: nat,B: nat] :
% 2.61/1.49 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 2.61/1.49 = A ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_49_add__diff__cancel__right,axiom,
% 2.61/1.49 ! [A: real,C: real,B: real] :
% 2.61/1.49 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 2.61/1.49 = ( minus_minus_real @ A @ B ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_50_add__diff__cancel__right,axiom,
% 2.61/1.49 ! [A: nat,C: nat,B: nat] :
% 2.61/1.49 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 2.61/1.49 = ( minus_minus_nat @ A @ B ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_51_add__diff__cancel__left_H,axiom,
% 2.61/1.49 ! [A: real,B: real] :
% 2.61/1.49 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 2.61/1.49 = B ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_52_add__diff__cancel__left_H,axiom,
% 2.61/1.49 ! [A: nat,B: nat] :
% 2.61/1.49 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 2.61/1.49 = B ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_53_add__diff__cancel__left,axiom,
% 2.61/1.49 ! [C: real,A: real,B: real] :
% 2.61/1.49 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 2.61/1.49 = ( minus_minus_real @ A @ B ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_54_add__diff__cancel__left,axiom,
% 2.61/1.49 ! [C: nat,A: nat,B: nat] :
% 2.61/1.49 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 2.61/1.49 = ( minus_minus_nat @ A @ B ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_55_diff__add__cancel,axiom,
% 2.61/1.49 ! [A: real,B: real] :
% 2.61/1.49 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 2.61/1.49 = A ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_56_add__diff__cancel,axiom,
% 2.61/1.49 ! [A: real,B: real] :
% 2.61/1.49 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 2.61/1.49 = A ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_57_abs__add__abs,axiom,
% 2.61/1.49 ! [A: real,B: real] :
% 2.61/1.49 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 2.61/1.49 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_58_abs__1,axiom,
% 2.61/1.49 ( ( abs_abs_real @ one_one_real )
% 2.61/1.49 = one_one_real ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_59_mem__Collect__eq,axiom,
% 2.61/1.49 ! [A: real,P2: real > $o] :
% 2.61/1.49 ( ( member_real @ A @ ( collect_real @ P2 ) )
% 2.61/1.49 = ( P2 @ A ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_60_Collect__mem__eq,axiom,
% 2.61/1.49 ! [A2: set_real] :
% 2.61/1.49 ( ( collect_real
% 2.61/1.49 @ ^ [X: real] : ( member_real @ X @ A2 ) )
% 2.61/1.49 = A2 ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_61_semiring__norm_I13_J,axiom,
% 2.61/1.49 ! [M: num,N: num] :
% 2.61/1.49 ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 2.61/1.49 = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_62_semiring__norm_I11_J,axiom,
% 2.61/1.49 ! [M: num] :
% 2.61/1.49 ( ( times_times_num @ M @ one )
% 2.61/1.49 = M ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_63_semiring__norm_I12_J,axiom,
% 2.61/1.49 ! [N: num] :
% 2.61/1.49 ( ( times_times_num @ one @ N )
% 2.61/1.49 = N ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_64_semiring__norm_I71_J,axiom,
% 2.61/1.49 ! [M: num,N: num] :
% 2.61/1.49 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 2.61/1.49 = ( ord_less_eq_num @ M @ N ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_65_semiring__norm_I68_J,axiom,
% 2.61/1.49 ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_66_le__add__diff__inverse2,axiom,
% 2.61/1.49 ! [B: real,A: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ B @ A )
% 2.61/1.49 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 2.61/1.49 = A ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_67_le__add__diff__inverse2,axiom,
% 2.61/1.49 ! [B: nat,A: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ B @ A )
% 2.61/1.49 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 2.61/1.49 = A ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_68_le__add__diff__inverse,axiom,
% 2.61/1.49 ! [B: real,A: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ B @ A )
% 2.61/1.49 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 2.61/1.49 = A ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_69_le__add__diff__inverse,axiom,
% 2.61/1.49 ! [B: nat,A: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ B @ A )
% 2.61/1.49 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 2.61/1.49 = A ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_70_distrib__right__numeral,axiom,
% 2.61/1.49 ! [A: real,B: real,V: num] :
% 2.61/1.49 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 2.61/1.49 = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_71_distrib__right__numeral,axiom,
% 2.61/1.49 ! [A: nat,B: nat,V: num] :
% 2.61/1.49 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 2.61/1.49 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_72_distrib__left__numeral,axiom,
% 2.61/1.49 ! [V: num,B: real,C: real] :
% 2.61/1.49 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 2.61/1.49 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_73_distrib__left__numeral,axiom,
% 2.61/1.49 ! [V: num,B: nat,C: nat] :
% 2.61/1.49 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 2.61/1.49 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_74_one__eq__numeral__iff,axiom,
% 2.61/1.49 ! [N: num] :
% 2.61/1.49 ( ( one_one_real
% 2.61/1.49 = ( numeral_numeral_real @ N ) )
% 2.61/1.49 = ( one = N ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_75_one__eq__numeral__iff,axiom,
% 2.61/1.49 ! [N: num] :
% 2.61/1.49 ( ( one_one_nat
% 2.61/1.49 = ( numeral_numeral_nat @ N ) )
% 2.61/1.49 = ( one = N ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_76_numeral__eq__one__iff,axiom,
% 2.61/1.49 ! [N: num] :
% 2.61/1.49 ( ( ( numeral_numeral_real @ N )
% 2.61/1.49 = one_one_real )
% 2.61/1.49 = ( N = one ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_77_numeral__eq__one__iff,axiom,
% 2.61/1.49 ! [N: num] :
% 2.61/1.49 ( ( ( numeral_numeral_nat @ N )
% 2.61/1.49 = one_one_nat )
% 2.61/1.49 = ( N = one ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_78_num__double,axiom,
% 2.61/1.49 ! [N: num] :
% 2.61/1.49 ( ( times_times_num @ ( bit0 @ one ) @ N )
% 2.61/1.49 = ( bit0 @ N ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_79_semiring__norm_I69_J,axiom,
% 2.61/1.49 ! [M: num] :
% 2.61/1.49 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_80_one__plus__numeral,axiom,
% 2.61/1.49 ! [N: num] :
% 2.61/1.49 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 2.61/1.49 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_81_one__plus__numeral,axiom,
% 2.61/1.49 ! [N: num] :
% 2.61/1.49 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 2.61/1.49 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_82_numeral__plus__one,axiom,
% 2.61/1.49 ! [N: num] :
% 2.61/1.49 ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 2.61/1.49 = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_83_numeral__plus__one,axiom,
% 2.61/1.49 ! [N: num] :
% 2.61/1.49 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 2.61/1.49 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_84_one__add__one,axiom,
% 2.61/1.49 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 2.61/1.49 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_85_one__add__one,axiom,
% 2.61/1.49 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 2.61/1.49 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_86_numeral__le__one__iff,axiom,
% 2.61/1.49 ! [N: num] :
% 2.61/1.49 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 2.61/1.49 = ( ord_less_eq_num @ N @ one ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_87_numeral__le__one__iff,axiom,
% 2.61/1.49 ! [N: num] :
% 2.61/1.49 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 2.61/1.49 = ( ord_less_eq_num @ N @ one ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_88_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 2.61/1.49 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_89_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 2.61/1.49 ! [A: nat,B: nat,C: nat] :
% 2.61/1.49 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 2.61/1.49 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_90_is__num__normalize_I1_J,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 2.61/1.49 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_91_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.61/1.49 ! [I: real,J: real,K: real,L: real] :
% 2.61/1.49 ( ( ( I = J )
% 2.61/1.49 & ( K = L ) )
% 2.61/1.49 => ( ( plus_plus_real @ I @ K )
% 2.61/1.49 = ( plus_plus_real @ J @ L ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_92_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.61/1.49 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.61/1.49 ( ( ( I = J )
% 2.61/1.49 & ( K = L ) )
% 2.61/1.49 => ( ( plus_plus_nat @ I @ K )
% 2.61/1.49 = ( plus_plus_nat @ J @ L ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_93_one__reorient,axiom,
% 2.61/1.49 ! [X2: real] :
% 2.61/1.49 ( ( one_one_real = X2 )
% 2.61/1.49 = ( X2 = one_one_real ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_94_one__reorient,axiom,
% 2.61/1.49 ! [X2: nat] :
% 2.61/1.49 ( ( one_one_nat = X2 )
% 2.61/1.49 = ( X2 = one_one_nat ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_95_group__cancel_Oadd1,axiom,
% 2.61/1.49 ! [A2: real,K: real,A: real,B: real] :
% 2.61/1.49 ( ( A2
% 2.61/1.49 = ( plus_plus_real @ K @ A ) )
% 2.61/1.49 => ( ( plus_plus_real @ A2 @ B )
% 2.61/1.49 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_96_group__cancel_Oadd1,axiom,
% 2.61/1.49 ! [A2: nat,K: nat,A: nat,B: nat] :
% 2.61/1.49 ( ( A2
% 2.61/1.49 = ( plus_plus_nat @ K @ A ) )
% 2.61/1.49 => ( ( plus_plus_nat @ A2 @ B )
% 2.61/1.49 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_97_group__cancel_Oadd2,axiom,
% 2.61/1.49 ! [B2: real,K: real,B: real,A: real] :
% 2.61/1.49 ( ( B2
% 2.61/1.49 = ( plus_plus_real @ K @ B ) )
% 2.61/1.49 => ( ( plus_plus_real @ A @ B2 )
% 2.61/1.49 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_98_group__cancel_Oadd2,axiom,
% 2.61/1.49 ! [B2: nat,K: nat,B: nat,A: nat] :
% 2.61/1.49 ( ( B2
% 2.61/1.49 = ( plus_plus_nat @ K @ B ) )
% 2.61/1.49 => ( ( plus_plus_nat @ A @ B2 )
% 2.61/1.49 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_99_add_Oassoc,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 2.61/1.49 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_100_add_Oassoc,axiom,
% 2.61/1.49 ! [A: nat,B: nat,C: nat] :
% 2.61/1.49 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 2.61/1.49 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_101_add_Oleft__cancel,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( ( plus_plus_real @ A @ B )
% 2.61/1.49 = ( plus_plus_real @ A @ C ) )
% 2.61/1.49 = ( B = C ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_102_add_Oright__cancel,axiom,
% 2.61/1.49 ! [B: real,A: real,C: real] :
% 2.61/1.49 ( ( ( plus_plus_real @ B @ A )
% 2.61/1.49 = ( plus_plus_real @ C @ A ) )
% 2.61/1.49 = ( B = C ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_103_add_Ocommute,axiom,
% 2.61/1.49 ( plus_plus_real
% 2.61/1.49 = ( ^ [A3: real,B3: real] : ( plus_plus_real @ B3 @ A3 ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_104_add_Ocommute,axiom,
% 2.61/1.49 ( plus_plus_nat
% 2.61/1.49 = ( ^ [A3: nat,B3: nat] : ( plus_plus_nat @ B3 @ A3 ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_105_add_Oleft__commute,axiom,
% 2.61/1.49 ! [B: real,A: real,C: real] :
% 2.61/1.49 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 2.61/1.49 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_106_add_Oleft__commute,axiom,
% 2.61/1.49 ! [B: nat,A: nat,C: nat] :
% 2.61/1.49 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 2.61/1.49 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_107_add__left__imp__eq,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( ( plus_plus_real @ A @ B )
% 2.61/1.49 = ( plus_plus_real @ A @ C ) )
% 2.61/1.49 => ( B = C ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_108_add__left__imp__eq,axiom,
% 2.61/1.49 ! [A: nat,B: nat,C: nat] :
% 2.61/1.49 ( ( ( plus_plus_nat @ A @ B )
% 2.61/1.49 = ( plus_plus_nat @ A @ C ) )
% 2.61/1.49 => ( B = C ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_109_add__right__imp__eq,axiom,
% 2.61/1.49 ! [B: real,A: real,C: real] :
% 2.61/1.49 ( ( ( plus_plus_real @ B @ A )
% 2.61/1.49 = ( plus_plus_real @ C @ A ) )
% 2.61/1.49 => ( B = C ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_110_add__right__imp__eq,axiom,
% 2.61/1.49 ! [B: nat,A: nat,C: nat] :
% 2.61/1.49 ( ( ( plus_plus_nat @ B @ A )
% 2.61/1.49 = ( plus_plus_nat @ C @ A ) )
% 2.61/1.49 => ( B = C ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_111_le__num__One__iff,axiom,
% 2.61/1.49 ! [X2: num] :
% 2.61/1.49 ( ( ord_less_eq_num @ X2 @ one )
% 2.61/1.49 = ( X2 = one ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_112_one__plus__numeral__commute,axiom,
% 2.61/1.49 ! [X2: num] :
% 2.61/1.49 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X2 ) )
% 2.61/1.49 = ( plus_plus_real @ ( numeral_numeral_real @ X2 ) @ one_one_real ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_113_one__plus__numeral__commute,axiom,
% 2.61/1.49 ! [X2: num] :
% 2.61/1.49 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X2 ) )
% 2.61/1.49 = ( plus_plus_nat @ ( numeral_numeral_nat @ X2 ) @ one_one_nat ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_114_correct__closed,axiom,
% 2.61/1.49 ! [P3: nat,S: real,T: real] :
% 2.61/1.49 ( ( ( ord_less_eq_real @ S @ T )
% 2.61/1.49 & ( genClo1015804716orrect @ P3 @ T ) )
% 2.61/1.49 => ( genClo1015804716orrect @ P3 @ S ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_115_add__le__imp__le__right,axiom,
% 2.61/1.49 ! [A: real,C: real,B: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 2.61/1.49 => ( ord_less_eq_real @ A @ B ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_116_add__le__imp__le__right,axiom,
% 2.61/1.49 ! [A: nat,C: nat,B: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 2.61/1.49 => ( ord_less_eq_nat @ A @ B ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_117_add__le__imp__le__left,axiom,
% 2.61/1.49 ! [C: real,A: real,B: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 2.61/1.49 => ( ord_less_eq_real @ A @ B ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_118_add__le__imp__le__left,axiom,
% 2.61/1.49 ! [C: nat,A: nat,B: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 2.61/1.49 => ( ord_less_eq_nat @ A @ B ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_119_le__iff__add,axiom,
% 2.61/1.49 ( ord_less_eq_nat
% 2.61/1.49 = ( ^ [A3: nat,B3: nat] :
% 2.61/1.49 ? [C2: nat] :
% 2.61/1.49 ( B3
% 2.61/1.49 = ( plus_plus_nat @ A3 @ C2 ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_120_add__right__mono,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ A @ B )
% 2.61/1.49 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_121_add__right__mono,axiom,
% 2.61/1.49 ! [A: nat,B: nat,C: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ A @ B )
% 2.61/1.49 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_122_less__eqE,axiom,
% 2.61/1.49 ! [A: nat,B: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ A @ B )
% 2.61/1.49 => ~ ! [C3: nat] :
% 2.61/1.49 ( B
% 2.61/1.49 != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_123_add__left__mono,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ A @ B )
% 2.61/1.49 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_124_add__left__mono,axiom,
% 2.61/1.49 ! [A: nat,B: nat,C: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ A @ B )
% 2.61/1.49 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_125_add__mono,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real,D: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ A @ B )
% 2.61/1.49 => ( ( ord_less_eq_real @ C @ D )
% 2.61/1.49 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_126_add__mono,axiom,
% 2.61/1.49 ! [A: nat,B: nat,C: nat,D: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ A @ B )
% 2.61/1.49 => ( ( ord_less_eq_nat @ C @ D )
% 2.61/1.49 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_127_add__mono__thms__linordered__semiring_I1_J,axiom,
% 2.61/1.49 ! [I: real,J: real,K: real,L: real] :
% 2.61/1.49 ( ( ( ord_less_eq_real @ I @ J )
% 2.61/1.49 & ( ord_less_eq_real @ K @ L ) )
% 2.61/1.49 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_128_add__mono__thms__linordered__semiring_I1_J,axiom,
% 2.61/1.49 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.61/1.49 ( ( ( ord_less_eq_nat @ I @ J )
% 2.61/1.49 & ( ord_less_eq_nat @ K @ L ) )
% 2.61/1.49 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_129_add__mono__thms__linordered__semiring_I2_J,axiom,
% 2.61/1.49 ! [I: real,J: real,K: real,L: real] :
% 2.61/1.49 ( ( ( I = J )
% 2.61/1.49 & ( ord_less_eq_real @ K @ L ) )
% 2.61/1.49 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_130_add__mono__thms__linordered__semiring_I2_J,axiom,
% 2.61/1.49 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.61/1.49 ( ( ( I = J )
% 2.61/1.49 & ( ord_less_eq_nat @ K @ L ) )
% 2.61/1.49 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_131_add__mono__thms__linordered__semiring_I3_J,axiom,
% 2.61/1.49 ! [I: real,J: real,K: real,L: real] :
% 2.61/1.49 ( ( ( ord_less_eq_real @ I @ J )
% 2.61/1.49 & ( K = L ) )
% 2.61/1.49 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_132_add__mono__thms__linordered__semiring_I3_J,axiom,
% 2.61/1.49 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.61/1.49 ( ( ( ord_less_eq_nat @ I @ J )
% 2.61/1.49 & ( K = L ) )
% 2.61/1.49 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_133_combine__common__factor,axiom,
% 2.61/1.49 ! [A: real,E: real,B: real,C: real] :
% 2.61/1.49 ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C ) )
% 2.61/1.49 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_134_combine__common__factor,axiom,
% 2.61/1.49 ! [A: nat,E: nat,B: nat,C: nat] :
% 2.61/1.49 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 2.61/1.49 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_135_distrib__right,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 2.61/1.49 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_136_distrib__right,axiom,
% 2.61/1.49 ! [A: nat,B: nat,C: nat] :
% 2.61/1.49 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 2.61/1.49 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_137_distrib__left,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 2.61/1.49 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_138_distrib__left,axiom,
% 2.61/1.49 ! [A: nat,B: nat,C: nat] :
% 2.61/1.49 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 2.61/1.49 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_139_comm__semiring__class_Odistrib,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 2.61/1.49 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_140_comm__semiring__class_Odistrib,axiom,
% 2.61/1.49 ! [A: nat,B: nat,C: nat] :
% 2.61/1.49 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 2.61/1.49 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_141_ring__class_Oring__distribs_I1_J,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 2.61/1.49 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_142_ring__class_Oring__distribs_I2_J,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 2.61/1.49 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_143_le__numeral__extra_I4_J,axiom,
% 2.61/1.49 ord_less_eq_real @ one_one_real @ one_one_real ).
% 2.61/1.49
% 2.61/1.49 thf(fact_144_le__numeral__extra_I4_J,axiom,
% 2.61/1.49 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 2.61/1.49
% 2.61/1.49 thf(fact_145_add__implies__diff,axiom,
% 2.61/1.49 ! [C: real,B: real,A: real] :
% 2.61/1.49 ( ( ( plus_plus_real @ C @ B )
% 2.61/1.49 = A )
% 2.61/1.49 => ( C
% 2.61/1.49 = ( minus_minus_real @ A @ B ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_146_add__implies__diff,axiom,
% 2.61/1.49 ! [C: nat,B: nat,A: nat] :
% 2.61/1.49 ( ( ( plus_plus_nat @ C @ B )
% 2.61/1.49 = A )
% 2.61/1.49 => ( C
% 2.61/1.49 = ( minus_minus_nat @ A @ B ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_147_diff__diff__add,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 2.61/1.49 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_148_diff__diff__add,axiom,
% 2.61/1.49 ! [A: nat,B: nat,C: nat] :
% 2.61/1.49 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 2.61/1.49 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_149_diff__add__eq__diff__diff__swap,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 2.61/1.49 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_150_diff__add__eq,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 2.61/1.49 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_151_diff__diff__eq2,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 2.61/1.49 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_152_add__diff__eq,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 2.61/1.49 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_153_eq__diff__eq,axiom,
% 2.61/1.49 ! [A: real,C: real,B: real] :
% 2.61/1.49 ( ( A
% 2.61/1.49 = ( minus_minus_real @ C @ B ) )
% 2.61/1.49 = ( ( plus_plus_real @ A @ B )
% 2.61/1.49 = C ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_154_diff__eq__eq,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( ( minus_minus_real @ A @ B )
% 2.61/1.49 = C )
% 2.61/1.49 = ( A
% 2.61/1.49 = ( plus_plus_real @ C @ B ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_155_group__cancel_Osub1,axiom,
% 2.61/1.49 ! [A2: real,K: real,A: real,B: real] :
% 2.61/1.49 ( ( A2
% 2.61/1.49 = ( plus_plus_real @ K @ A ) )
% 2.61/1.49 => ( ( minus_minus_real @ A2 @ B )
% 2.61/1.49 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_156_mult_Ocomm__neutral,axiom,
% 2.61/1.49 ! [A: real] :
% 2.61/1.49 ( ( times_times_real @ A @ one_one_real )
% 2.61/1.49 = A ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_157_mult_Ocomm__neutral,axiom,
% 2.61/1.49 ! [A: nat] :
% 2.61/1.49 ( ( times_times_nat @ A @ one_one_nat )
% 2.61/1.49 = A ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_158_comm__monoid__mult__class_Omult__1,axiom,
% 2.61/1.49 ! [A: real] :
% 2.61/1.49 ( ( times_times_real @ one_one_real @ A )
% 2.61/1.49 = A ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_159_comm__monoid__mult__class_Omult__1,axiom,
% 2.61/1.49 ! [A: nat] :
% 2.61/1.49 ( ( times_times_nat @ one_one_nat @ A )
% 2.61/1.49 = A ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_160_abs__one,axiom,
% 2.61/1.49 ( ( abs_abs_real @ one_one_real )
% 2.61/1.49 = one_one_real ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_161_square__diff__one__factored,axiom,
% 2.61/1.49 ! [X2: real] :
% 2.61/1.49 ( ( minus_minus_real @ ( times_times_real @ X2 @ X2 ) @ one_one_real )
% 2.61/1.49 = ( times_times_real @ ( plus_plus_real @ X2 @ one_one_real ) @ ( minus_minus_real @ X2 @ one_one_real ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_162_rho__bound1__def,axiom,
% 2.61/1.49 ( genClo2108747022bound1
% 2.61/1.49 = ( ^ [C4: nat > real > real] :
% 2.61/1.49 ! [P: nat,S2: real,T2: real] :
% 2.61/1.49 ( ( ( genClo1015804716orrect @ P @ T2 )
% 2.61/1.49 & ( ord_less_eq_real @ S2 @ T2 ) )
% 2.61/1.49 => ( ord_less_eq_real @ ( minus_minus_real @ ( C4 @ P @ T2 ) @ ( C4 @ P @ S2 ) ) @ ( times_times_real @ ( minus_minus_real @ T2 @ S2 ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_163_mult_Oleft__commute,axiom,
% 2.61/1.49 ! [B: real,A: real,C: real] :
% 2.61/1.49 ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 2.61/1.49 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_164_mult_Oleft__commute,axiom,
% 2.61/1.49 ! [B: nat,A: nat,C: nat] :
% 2.61/1.49 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 2.61/1.49 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_165_mult_Ocommute,axiom,
% 2.61/1.49 ( times_times_real
% 2.61/1.49 = ( ^ [A3: real,B3: real] : ( times_times_real @ B3 @ A3 ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_166_mult_Ocommute,axiom,
% 2.61/1.49 ( times_times_nat
% 2.61/1.49 = ( ^ [A3: nat,B3: nat] : ( times_times_nat @ B3 @ A3 ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_167_mult_Oassoc,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 2.61/1.49 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_168_mult_Oassoc,axiom,
% 2.61/1.49 ! [A: nat,B: nat,C: nat] :
% 2.61/1.49 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 2.61/1.49 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_169_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 2.61/1.49 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_170_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 2.61/1.49 ! [A: nat,B: nat,C: nat] :
% 2.61/1.49 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 2.61/1.49 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_171_diff__right__commute,axiom,
% 2.61/1.49 ! [A: real,C: real,B: real] :
% 2.61/1.49 ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 2.61/1.49 = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_172_diff__right__commute,axiom,
% 2.61/1.49 ! [A: nat,C: nat,B: nat] :
% 2.61/1.49 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 2.61/1.49 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_173_diff__eq__diff__eq,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real,D: real] :
% 2.61/1.49 ( ( ( minus_minus_real @ A @ B )
% 2.61/1.49 = ( minus_minus_real @ C @ D ) )
% 2.61/1.49 => ( ( A = B )
% 2.61/1.49 = ( C = D ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_174_rho__bound2__def,axiom,
% 2.61/1.49 ( genClo2108747023bound2
% 2.61/1.49 = ( ^ [C4: nat > real > real] :
% 2.61/1.49 ! [P: nat,S2: real,T2: real] :
% 2.61/1.49 ( ( ( genClo1015804716orrect @ P @ T2 )
% 2.61/1.49 & ( ord_less_eq_real @ S2 @ T2 ) )
% 2.61/1.49 => ( ord_less_eq_real @ ( times_times_real @ ( minus_minus_real @ T2 @ S2 ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( C4 @ P @ T2 ) @ ( C4 @ P @ S2 ) ) ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_175_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 2.61/1.49 ! [A: nat,B: nat,C: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ A @ B )
% 2.61/1.49 => ( ( ord_less_eq_nat @ A @ B )
% 2.61/1.49 => ( ( ( minus_minus_nat @ B @ A )
% 2.61/1.49 = C )
% 2.61/1.49 = ( B
% 2.61/1.49 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_176_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 2.61/1.49 ! [A: nat,B: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ A @ B )
% 2.61/1.49 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 2.61/1.49 = B ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_177_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 2.61/1.49 ! [A: nat,B: nat,C: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ A @ B )
% 2.61/1.49 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 2.61/1.49 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_178_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 2.61/1.49 ! [A: nat,B: nat,C: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ A @ B )
% 2.61/1.49 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 2.61/1.49 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_179_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 2.61/1.49 ! [A: nat,B: nat,C: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ A @ B )
% 2.61/1.49 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 2.61/1.49 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_180_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 2.61/1.49 ! [A: nat,B: nat,C: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ A @ B )
% 2.61/1.49 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 2.61/1.49 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_181_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 2.61/1.49 ! [A: nat,B: nat,C: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ A @ B )
% 2.61/1.49 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 2.61/1.49 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_182_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 2.61/1.49 ! [A: nat,B: nat,C: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ A @ B )
% 2.61/1.49 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 2.61/1.49 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_183_le__add__diff,axiom,
% 2.61/1.49 ! [A: nat,B: nat,C: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ A @ B )
% 2.61/1.49 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_184_add__le__add__imp__diff__le,axiom,
% 2.61/1.49 ! [I: real,K: real,N: real,J: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 2.61/1.49 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 2.61/1.49 => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 2.61/1.49 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 2.61/1.49 => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J ) ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_185_add__le__add__imp__diff__le,axiom,
% 2.61/1.49 ! [I: nat,K: nat,N: nat,J: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 2.61/1.49 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 2.61/1.49 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 2.61/1.49 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 2.61/1.49 => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_186_diff__add,axiom,
% 2.61/1.49 ! [A: nat,B: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ A @ B )
% 2.61/1.49 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 2.61/1.49 = B ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_187_add__le__imp__le__diff,axiom,
% 2.61/1.49 ! [I: real,K: real,N: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 2.61/1.49 => ( ord_less_eq_real @ I @ ( minus_minus_real @ N @ K ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_188_add__le__imp__le__diff,axiom,
% 2.61/1.49 ! [I: nat,K: nat,N: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 2.61/1.49 => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_189_le__diff__eq,axiom,
% 2.61/1.49 ! [A: real,C: real,B: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 2.61/1.49 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_190_diff__le__eq,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 2.61/1.49 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_191_square__diff__square__factored,axiom,
% 2.61/1.49 ! [X2: real,Y: real] :
% 2.61/1.49 ( ( minus_minus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y @ Y ) )
% 2.61/1.49 = ( times_times_real @ ( plus_plus_real @ X2 @ Y ) @ ( minus_minus_real @ X2 @ Y ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_192_eq__add__iff2,axiom,
% 2.61/1.49 ! [A: real,E: real,C: real,B: real,D: real] :
% 2.61/1.49 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 2.61/1.49 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 2.61/1.49 = ( C
% 2.61/1.49 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_193_eq__add__iff1,axiom,
% 2.61/1.49 ! [A: real,E: real,C: real,B: real,D: real] :
% 2.61/1.49 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 2.61/1.49 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 2.61/1.49 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C )
% 2.61/1.49 = D ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_194_numeral__Bit0,axiom,
% 2.61/1.49 ! [N: num] :
% 2.61/1.49 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 2.61/1.49 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_195_numeral__Bit0,axiom,
% 2.61/1.49 ! [N: num] :
% 2.61/1.49 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 2.61/1.49 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_196_one__le__numeral,axiom,
% 2.61/1.49 ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_197_one__le__numeral,axiom,
% 2.61/1.49 ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_198_abs__triangle__ineq,axiom,
% 2.61/1.49 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_199_numeral__One,axiom,
% 2.61/1.49 ( ( numeral_numeral_real @ one )
% 2.61/1.49 = one_one_real ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_200_numeral__One,axiom,
% 2.61/1.49 ( ( numeral_numeral_nat @ one )
% 2.61/1.49 = one_one_nat ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_201_ordered__ring__class_Ole__add__iff2,axiom,
% 2.61/1.49 ! [A: real,E: real,C: real,B: real,D: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 2.61/1.49 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_202_ordered__ring__class_Ole__add__iff1,axiom,
% 2.61/1.49 ! [A: real,E: real,C: real,B: real,D: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 2.61/1.49 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_203_abs__diff__triangle__ineq,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_204_abs__triangle__ineq4,axiom,
% 2.61/1.49 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_205_abs__diff__le__iff,axiom,
% 2.61/1.49 ! [X2: real,A: real,R: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ A ) ) @ R )
% 2.61/1.49 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R ) @ X2 )
% 2.61/1.49 & ( ord_less_eq_real @ X2 @ ( plus_plus_real @ A @ R ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_206_diff__eq__diff__less__eq,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real,D: real] :
% 2.61/1.49 ( ( ( minus_minus_real @ A @ B )
% 2.61/1.49 = ( minus_minus_real @ C @ D ) )
% 2.61/1.49 => ( ( ord_less_eq_real @ A @ B )
% 2.61/1.49 = ( ord_less_eq_real @ C @ D ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_207_diff__right__mono,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ A @ B )
% 2.61/1.49 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_208_diff__left__mono,axiom,
% 2.61/1.49 ! [B: real,A: real,C: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ B @ A )
% 2.61/1.49 => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_209_diff__mono,axiom,
% 2.61/1.49 ! [A: real,B: real,D: real,C: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ A @ B )
% 2.61/1.49 => ( ( ord_less_eq_real @ D @ C )
% 2.61/1.49 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_210_right__diff__distrib_H,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 2.61/1.49 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_211_right__diff__distrib_H,axiom,
% 2.61/1.49 ! [A: nat,B: nat,C: nat] :
% 2.61/1.49 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 2.61/1.49 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_212_left__diff__distrib_H,axiom,
% 2.61/1.49 ! [B: real,C: real,A: real] :
% 2.61/1.49 ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 2.61/1.49 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_213_left__diff__distrib_H,axiom,
% 2.61/1.49 ! [B: nat,C: nat,A: nat] :
% 2.61/1.49 ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 2.61/1.49 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_214_right__diff__distrib,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 2.61/1.49 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_215_left__diff__distrib,axiom,
% 2.61/1.49 ! [A: real,B: real,C: real] :
% 2.61/1.49 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 2.61/1.49 = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_216_abs__ge__self,axiom,
% 2.61/1.49 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_217_abs__le__D1,axiom,
% 2.61/1.49 ! [A: real,B: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 2.61/1.49 => ( ord_less_eq_real @ A @ B ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_218_abs__mult,axiom,
% 2.61/1.49 ! [A: real,B: real] :
% 2.61/1.49 ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 2.61/1.49 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_219_abs__minus__commute,axiom,
% 2.61/1.49 ! [A: real,B: real] :
% 2.61/1.49 ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 2.61/1.49 = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_220_left__add__twice,axiom,
% 2.61/1.49 ! [A: real,B: real] :
% 2.61/1.49 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 2.61/1.49 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_221_left__add__twice,axiom,
% 2.61/1.49 ! [A: nat,B: nat] :
% 2.61/1.49 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 2.61/1.49 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_222_mult__2__right,axiom,
% 2.61/1.49 ! [Z: real] :
% 2.61/1.49 ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 2.61/1.49 = ( plus_plus_real @ Z @ Z ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_223_mult__2__right,axiom,
% 2.61/1.49 ! [Z: nat] :
% 2.61/1.49 ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 2.61/1.49 = ( plus_plus_nat @ Z @ Z ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_224_mult__2,axiom,
% 2.61/1.49 ! [Z: real] :
% 2.61/1.49 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 2.61/1.49 = ( plus_plus_real @ Z @ Z ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_225_mult__2,axiom,
% 2.61/1.49 ! [Z: nat] :
% 2.61/1.49 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 2.61/1.49 = ( plus_plus_nat @ Z @ Z ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_226_mult__numeral__1__right,axiom,
% 2.61/1.49 ! [A: real] :
% 2.61/1.49 ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 2.61/1.49 = A ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_227_mult__numeral__1__right,axiom,
% 2.61/1.49 ! [A: nat] :
% 2.61/1.49 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 2.61/1.49 = A ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_228_mult__numeral__1,axiom,
% 2.61/1.49 ! [A: real] :
% 2.61/1.49 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 2.61/1.49 = A ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_229_mult__numeral__1,axiom,
% 2.61/1.49 ! [A: nat] :
% 2.61/1.49 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 2.61/1.49 = A ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_230_abs__triangle__ineq2__sym,axiom,
% 2.61/1.49 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_231_sin__bound__lemma,axiom,
% 2.61/1.49 ! [X2: real,Y: real,U: real,V: real] :
% 2.61/1.49 ( ( X2 = Y )
% 2.61/1.49 => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 2.61/1.49 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X2 @ U ) @ Y ) ) @ V ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_232_rate__1,axiom,
% 2.61/1.49 ! [P3: nat,S: real,T: real] :
% 2.61/1.49 ( ( ( genClo1015804716orrect @ P3 @ T )
% 2.61/1.49 & ( ord_less_eq_real @ S @ T ) )
% 2.61/1.49 => ( ord_less_eq_real @ ( minus_minus_real @ ( genClo1161277105lle_PC @ P3 @ T ) @ ( genClo1161277105lle_PC @ P3 @ S ) ) @ ( times_times_real @ ( minus_minus_real @ T @ S ) @ ( plus_plus_real @ one_one_real @ genClo1144207539le_rho ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_233_rate__2,axiom,
% 2.61/1.49 ! [P3: nat,S: real,T: real] :
% 2.61/1.49 ( ( ( genClo1015804716orrect @ P3 @ T )
% 2.61/1.49 & ( ord_less_eq_real @ S @ T ) )
% 2.61/1.49 => ( ord_less_eq_real @ ( times_times_real @ ( minus_minus_real @ T @ S ) @ ( minus_minus_real @ one_one_real @ genClo1144207539le_rho ) ) @ ( minus_minus_real @ ( genClo1161277105lle_PC @ P3 @ T ) @ ( genClo1161277105lle_PC @ P3 @ S ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_234_dbl__simps_I3_J,axiom,
% 2.61/1.49 ( ( neg_numeral_dbl_real @ one_one_real )
% 2.61/1.49 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_235_mult__diff__mult,axiom,
% 2.61/1.49 ! [X2: real,Y: real,A: real,B: real] :
% 2.61/1.49 ( ( minus_minus_real @ ( times_times_real @ X2 @ Y ) @ ( times_times_real @ A @ B ) )
% 2.61/1.49 = ( plus_plus_real @ ( times_times_real @ X2 @ ( minus_minus_real @ Y @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X2 @ A ) @ B ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_236_verit__eq__simplify_I8_J,axiom,
% 2.61/1.49 ! [X22: num,Y2: num] :
% 2.61/1.49 ( ( ( bit0 @ X22 )
% 2.61/1.49 = ( bit0 @ Y2 ) )
% 2.61/1.49 = ( X22 = Y2 ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_237_okRead1__def,axiom,
% 2.61/1.49 ( genClo293725281kRead1
% 2.61/1.49 = ( ^ [F: nat > real,X: real,Ppred: nat > $o] :
% 2.61/1.49 ! [L2: nat,M2: nat] :
% 2.61/1.49 ( ( ( Ppred @ L2 )
% 2.61/1.49 & ( Ppred @ M2 ) )
% 2.61/1.49 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ L2 ) @ ( F @ M2 ) ) ) @ X ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_238_order__refl,axiom,
% 2.61/1.49 ! [X2: real] : ( ord_less_eq_real @ X2 @ X2 ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_239_order__refl,axiom,
% 2.61/1.49 ! [X2: num] : ( ord_less_eq_num @ X2 @ X2 ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_240_order__refl,axiom,
% 2.61/1.49 ! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_241_eq__diff__eq_H,axiom,
% 2.61/1.49 ! [X2: real,Y: real,Z: real] :
% 2.61/1.49 ( ( X2
% 2.61/1.49 = ( minus_minus_real @ Y @ Z ) )
% 2.61/1.49 = ( Y
% 2.61/1.49 = ( plus_plus_real @ X2 @ Z ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_242_semiring__norm_I6_J,axiom,
% 2.61/1.49 ! [M: num,N: num] :
% 2.61/1.49 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 2.61/1.49 = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_243_semiring__norm_I2_J,axiom,
% 2.61/1.49 ( ( plus_plus_num @ one @ one )
% 2.61/1.49 = ( bit0 @ one ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_244_dbl__simps_I5_J,axiom,
% 2.61/1.49 ! [K: num] :
% 2.61/1.49 ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 2.61/1.49 = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_245_nat__1__add__1,axiom,
% 2.61/1.49 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 2.61/1.49 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_246_add__One__commute,axiom,
% 2.61/1.49 ! [N: num] :
% 2.61/1.49 ( ( plus_plus_num @ one @ N )
% 2.61/1.49 = ( plus_plus_num @ N @ one ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_247_numerals_I1_J,axiom,
% 2.61/1.49 ( ( numeral_numeral_nat @ one )
% 2.61/1.49 = one_one_nat ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_248_dbl__def,axiom,
% 2.61/1.49 ( neg_numeral_dbl_real
% 2.61/1.49 = ( ^ [X: real] : ( plus_plus_real @ X @ X ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_249_order__subst1,axiom,
% 2.61/1.49 ! [A: real,F2: real > real,B: real,C: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ A @ ( F2 @ B ) )
% 2.61/1.49 => ( ( ord_less_eq_real @ B @ C )
% 2.61/1.49 => ( ! [X3: real,Y3: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_real @ A @ ( F2 @ C ) ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_250_order__subst1,axiom,
% 2.61/1.49 ! [A: real,F2: num > real,B: num,C: num] :
% 2.61/1.49 ( ( ord_less_eq_real @ A @ ( F2 @ B ) )
% 2.61/1.49 => ( ( ord_less_eq_num @ B @ C )
% 2.61/1.49 => ( ! [X3: num,Y3: num] :
% 2.61/1.49 ( ( ord_less_eq_num @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_real @ A @ ( F2 @ C ) ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_251_order__subst1,axiom,
% 2.61/1.49 ! [A: real,F2: nat > real,B: nat,C: nat] :
% 2.61/1.49 ( ( ord_less_eq_real @ A @ ( F2 @ B ) )
% 2.61/1.49 => ( ( ord_less_eq_nat @ B @ C )
% 2.61/1.49 => ( ! [X3: nat,Y3: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_real @ A @ ( F2 @ C ) ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_252_order__subst1,axiom,
% 2.61/1.49 ! [A: num,F2: real > num,B: real,C: real] :
% 2.61/1.49 ( ( ord_less_eq_num @ A @ ( F2 @ B ) )
% 2.61/1.49 => ( ( ord_less_eq_real @ B @ C )
% 2.61/1.49 => ( ! [X3: real,Y3: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_num @ A @ ( F2 @ C ) ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_253_order__subst1,axiom,
% 2.61/1.49 ! [A: num,F2: num > num,B: num,C: num] :
% 2.61/1.49 ( ( ord_less_eq_num @ A @ ( F2 @ B ) )
% 2.61/1.49 => ( ( ord_less_eq_num @ B @ C )
% 2.61/1.49 => ( ! [X3: num,Y3: num] :
% 2.61/1.49 ( ( ord_less_eq_num @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_num @ A @ ( F2 @ C ) ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_254_order__subst1,axiom,
% 2.61/1.49 ! [A: num,F2: nat > num,B: nat,C: nat] :
% 2.61/1.49 ( ( ord_less_eq_num @ A @ ( F2 @ B ) )
% 2.61/1.49 => ( ( ord_less_eq_nat @ B @ C )
% 2.61/1.49 => ( ! [X3: nat,Y3: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_num @ A @ ( F2 @ C ) ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_255_order__subst1,axiom,
% 2.61/1.49 ! [A: nat,F2: real > nat,B: real,C: real] :
% 2.61/1.49 ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 2.61/1.49 => ( ( ord_less_eq_real @ B @ C )
% 2.61/1.49 => ( ! [X3: real,Y3: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_256_order__subst1,axiom,
% 2.61/1.49 ! [A: nat,F2: num > nat,B: num,C: num] :
% 2.61/1.49 ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 2.61/1.49 => ( ( ord_less_eq_num @ B @ C )
% 2.61/1.49 => ( ! [X3: num,Y3: num] :
% 2.61/1.49 ( ( ord_less_eq_num @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_257_order__subst1,axiom,
% 2.61/1.49 ! [A: nat,F2: nat > nat,B: nat,C: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 2.61/1.49 => ( ( ord_less_eq_nat @ B @ C )
% 2.61/1.49 => ( ! [X3: nat,Y3: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_258_order__subst2,axiom,
% 2.61/1.49 ! [A: real,B: real,F2: real > real,C: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ A @ B )
% 2.61/1.49 => ( ( ord_less_eq_real @ ( F2 @ B ) @ C )
% 2.61/1.49 => ( ! [X3: real,Y3: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_real @ ( F2 @ A ) @ C ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_259_order__subst2,axiom,
% 2.61/1.49 ! [A: real,B: real,F2: real > num,C: num] :
% 2.61/1.49 ( ( ord_less_eq_real @ A @ B )
% 2.61/1.49 => ( ( ord_less_eq_num @ ( F2 @ B ) @ C )
% 2.61/1.49 => ( ! [X3: real,Y3: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_num @ ( F2 @ A ) @ C ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_260_order__subst2,axiom,
% 2.61/1.49 ! [A: real,B: real,F2: real > nat,C: nat] :
% 2.61/1.49 ( ( ord_less_eq_real @ A @ B )
% 2.61/1.49 => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
% 2.61/1.49 => ( ! [X3: real,Y3: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_261_order__subst2,axiom,
% 2.61/1.49 ! [A: num,B: num,F2: num > real,C: real] :
% 2.61/1.49 ( ( ord_less_eq_num @ A @ B )
% 2.61/1.49 => ( ( ord_less_eq_real @ ( F2 @ B ) @ C )
% 2.61/1.49 => ( ! [X3: num,Y3: num] :
% 2.61/1.49 ( ( ord_less_eq_num @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_real @ ( F2 @ A ) @ C ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_262_order__subst2,axiom,
% 2.61/1.49 ! [A: num,B: num,F2: num > num,C: num] :
% 2.61/1.49 ( ( ord_less_eq_num @ A @ B )
% 2.61/1.49 => ( ( ord_less_eq_num @ ( F2 @ B ) @ C )
% 2.61/1.49 => ( ! [X3: num,Y3: num] :
% 2.61/1.49 ( ( ord_less_eq_num @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_num @ ( F2 @ A ) @ C ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_263_order__subst2,axiom,
% 2.61/1.49 ! [A: num,B: num,F2: num > nat,C: nat] :
% 2.61/1.49 ( ( ord_less_eq_num @ A @ B )
% 2.61/1.49 => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
% 2.61/1.49 => ( ! [X3: num,Y3: num] :
% 2.61/1.49 ( ( ord_less_eq_num @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_264_order__subst2,axiom,
% 2.61/1.49 ! [A: nat,B: nat,F2: nat > real,C: real] :
% 2.61/1.49 ( ( ord_less_eq_nat @ A @ B )
% 2.61/1.49 => ( ( ord_less_eq_real @ ( F2 @ B ) @ C )
% 2.61/1.49 => ( ! [X3: nat,Y3: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_real @ ( F2 @ A ) @ C ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_265_order__subst2,axiom,
% 2.61/1.49 ! [A: nat,B: nat,F2: nat > num,C: num] :
% 2.61/1.49 ( ( ord_less_eq_nat @ A @ B )
% 2.61/1.49 => ( ( ord_less_eq_num @ ( F2 @ B ) @ C )
% 2.61/1.49 => ( ! [X3: nat,Y3: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_num @ ( F2 @ A ) @ C ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_266_order__subst2,axiom,
% 2.61/1.49 ! [A: nat,B: nat,F2: nat > nat,C: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ A @ B )
% 2.61/1.49 => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
% 2.61/1.49 => ( ! [X3: nat,Y3: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_267_verit__la__disequality,axiom,
% 2.61/1.49 ! [A: real,B: real] :
% 2.61/1.49 ( ( A = B )
% 2.61/1.49 | ~ ( ord_less_eq_real @ A @ B )
% 2.61/1.49 | ~ ( ord_less_eq_real @ B @ A ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_268_verit__la__disequality,axiom,
% 2.61/1.49 ! [A: num,B: num] :
% 2.61/1.49 ( ( A = B )
% 2.61/1.49 | ~ ( ord_less_eq_num @ A @ B )
% 2.61/1.49 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_269_verit__la__disequality,axiom,
% 2.61/1.49 ! [A: nat,B: nat] :
% 2.61/1.49 ( ( A = B )
% 2.61/1.49 | ~ ( ord_less_eq_nat @ A @ B )
% 2.61/1.49 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_270_ord__eq__le__subst,axiom,
% 2.61/1.49 ! [A: real,F2: real > real,B: real,C: real] :
% 2.61/1.49 ( ( A
% 2.61/1.49 = ( F2 @ B ) )
% 2.61/1.49 => ( ( ord_less_eq_real @ B @ C )
% 2.61/1.49 => ( ! [X3: real,Y3: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_real @ A @ ( F2 @ C ) ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_271_ord__eq__le__subst,axiom,
% 2.61/1.49 ! [A: num,F2: real > num,B: real,C: real] :
% 2.61/1.49 ( ( A
% 2.61/1.49 = ( F2 @ B ) )
% 2.61/1.49 => ( ( ord_less_eq_real @ B @ C )
% 2.61/1.49 => ( ! [X3: real,Y3: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_num @ A @ ( F2 @ C ) ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_272_ord__eq__le__subst,axiom,
% 2.61/1.49 ! [A: nat,F2: real > nat,B: real,C: real] :
% 2.61/1.49 ( ( A
% 2.61/1.49 = ( F2 @ B ) )
% 2.61/1.49 => ( ( ord_less_eq_real @ B @ C )
% 2.61/1.49 => ( ! [X3: real,Y3: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_273_ord__eq__le__subst,axiom,
% 2.61/1.49 ! [A: real,F2: num > real,B: num,C: num] :
% 2.61/1.49 ( ( A
% 2.61/1.49 = ( F2 @ B ) )
% 2.61/1.49 => ( ( ord_less_eq_num @ B @ C )
% 2.61/1.49 => ( ! [X3: num,Y3: num] :
% 2.61/1.49 ( ( ord_less_eq_num @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_real @ A @ ( F2 @ C ) ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_274_ord__eq__le__subst,axiom,
% 2.61/1.49 ! [A: num,F2: num > num,B: num,C: num] :
% 2.61/1.49 ( ( A
% 2.61/1.49 = ( F2 @ B ) )
% 2.61/1.49 => ( ( ord_less_eq_num @ B @ C )
% 2.61/1.49 => ( ! [X3: num,Y3: num] :
% 2.61/1.49 ( ( ord_less_eq_num @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_num @ A @ ( F2 @ C ) ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_275_ord__eq__le__subst,axiom,
% 2.61/1.49 ! [A: nat,F2: num > nat,B: num,C: num] :
% 2.61/1.49 ( ( A
% 2.61/1.49 = ( F2 @ B ) )
% 2.61/1.49 => ( ( ord_less_eq_num @ B @ C )
% 2.61/1.49 => ( ! [X3: num,Y3: num] :
% 2.61/1.49 ( ( ord_less_eq_num @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_276_ord__eq__le__subst,axiom,
% 2.61/1.49 ! [A: real,F2: nat > real,B: nat,C: nat] :
% 2.61/1.49 ( ( A
% 2.61/1.49 = ( F2 @ B ) )
% 2.61/1.49 => ( ( ord_less_eq_nat @ B @ C )
% 2.61/1.49 => ( ! [X3: nat,Y3: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_real @ A @ ( F2 @ C ) ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_277_ord__eq__le__subst,axiom,
% 2.61/1.49 ! [A: num,F2: nat > num,B: nat,C: nat] :
% 2.61/1.49 ( ( A
% 2.61/1.49 = ( F2 @ B ) )
% 2.61/1.49 => ( ( ord_less_eq_nat @ B @ C )
% 2.61/1.49 => ( ! [X3: nat,Y3: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_num @ A @ ( F2 @ C ) ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_278_ord__eq__le__subst,axiom,
% 2.61/1.49 ! [A: nat,F2: nat > nat,B: nat,C: nat] :
% 2.61/1.49 ( ( A
% 2.61/1.49 = ( F2 @ B ) )
% 2.61/1.49 => ( ( ord_less_eq_nat @ B @ C )
% 2.61/1.49 => ( ! [X3: nat,Y3: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_279_ord__le__eq__subst,axiom,
% 2.61/1.49 ! [A: real,B: real,F2: real > real,C: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ A @ B )
% 2.61/1.49 => ( ( ( F2 @ B )
% 2.61/1.49 = C )
% 2.61/1.49 => ( ! [X3: real,Y3: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_real @ ( F2 @ A ) @ C ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_280_ord__le__eq__subst,axiom,
% 2.61/1.49 ! [A: real,B: real,F2: real > num,C: num] :
% 2.61/1.49 ( ( ord_less_eq_real @ A @ B )
% 2.61/1.49 => ( ( ( F2 @ B )
% 2.61/1.49 = C )
% 2.61/1.49 => ( ! [X3: real,Y3: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_num @ ( F2 @ A ) @ C ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_281_ord__le__eq__subst,axiom,
% 2.61/1.49 ! [A: real,B: real,F2: real > nat,C: nat] :
% 2.61/1.49 ( ( ord_less_eq_real @ A @ B )
% 2.61/1.49 => ( ( ( F2 @ B )
% 2.61/1.49 = C )
% 2.61/1.49 => ( ! [X3: real,Y3: real] :
% 2.61/1.49 ( ( ord_less_eq_real @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_282_ord__le__eq__subst,axiom,
% 2.61/1.49 ! [A: num,B: num,F2: num > real,C: real] :
% 2.61/1.49 ( ( ord_less_eq_num @ A @ B )
% 2.61/1.49 => ( ( ( F2 @ B )
% 2.61/1.49 = C )
% 2.61/1.49 => ( ! [X3: num,Y3: num] :
% 2.61/1.49 ( ( ord_less_eq_num @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_real @ ( F2 @ A ) @ C ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_283_ord__le__eq__subst,axiom,
% 2.61/1.49 ! [A: num,B: num,F2: num > num,C: num] :
% 2.61/1.49 ( ( ord_less_eq_num @ A @ B )
% 2.61/1.49 => ( ( ( F2 @ B )
% 2.61/1.49 = C )
% 2.61/1.49 => ( ! [X3: num,Y3: num] :
% 2.61/1.49 ( ( ord_less_eq_num @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_num @ ( F2 @ A ) @ C ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_284_ord__le__eq__subst,axiom,
% 2.61/1.49 ! [A: num,B: num,F2: num > nat,C: nat] :
% 2.61/1.49 ( ( ord_less_eq_num @ A @ B )
% 2.61/1.49 => ( ( ( F2 @ B )
% 2.61/1.49 = C )
% 2.61/1.49 => ( ! [X3: num,Y3: num] :
% 2.61/1.49 ( ( ord_less_eq_num @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.49 => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 2.61/1.49
% 2.61/1.49 thf(fact_285_ord__le__eq__subst,axiom,
% 2.61/1.49 ! [A: nat,B: nat,F2: nat > real,C: real] :
% 2.61/1.49 ( ( ord_less_eq_nat @ A @ B )
% 2.61/1.49 => ( ( ( F2 @ B )
% 2.61/1.49 = C )
% 2.61/1.49 => ( ! [X3: nat,Y3: nat] :
% 2.61/1.49 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.61/1.49 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.50 => ( ord_less_eq_real @ ( F2 @ A ) @ C ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_286_ord__le__eq__subst,axiom,
% 2.61/1.50 ! [A: nat,B: nat,F2: nat > num,C: num] :
% 2.61/1.50 ( ( ord_less_eq_nat @ A @ B )
% 2.61/1.50 => ( ( ( F2 @ B )
% 2.61/1.50 = C )
% 2.61/1.50 => ( ! [X3: nat,Y3: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.61/1.50 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.50 => ( ord_less_eq_num @ ( F2 @ A ) @ C ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_287_ord__le__eq__subst,axiom,
% 2.61/1.50 ! [A: nat,B: nat,F2: nat > nat,C: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ A @ B )
% 2.61/1.50 => ( ( ( F2 @ B )
% 2.61/1.50 = C )
% 2.61/1.50 => ( ! [X3: nat,Y3: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 2.61/1.50 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 2.61/1.50 => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_288_eq__iff,axiom,
% 2.61/1.50 ( ( ^ [Y4: real,Z2: real] : ( Y4 = Z2 ) )
% 2.61/1.50 = ( ^ [X: real,Y5: real] :
% 2.61/1.50 ( ( ord_less_eq_real @ X @ Y5 )
% 2.61/1.50 & ( ord_less_eq_real @ Y5 @ X ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_289_eq__iff,axiom,
% 2.61/1.50 ( ( ^ [Y4: num,Z2: num] : ( Y4 = Z2 ) )
% 2.61/1.50 = ( ^ [X: num,Y5: num] :
% 2.61/1.50 ( ( ord_less_eq_num @ X @ Y5 )
% 2.61/1.50 & ( ord_less_eq_num @ Y5 @ X ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_290_eq__iff,axiom,
% 2.61/1.50 ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 2.61/1.50 = ( ^ [X: nat,Y5: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ X @ Y5 )
% 2.61/1.50 & ( ord_less_eq_nat @ Y5 @ X ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_291_antisym,axiom,
% 2.61/1.50 ! [X2: real,Y: real] :
% 2.61/1.50 ( ( ord_less_eq_real @ X2 @ Y )
% 2.61/1.50 => ( ( ord_less_eq_real @ Y @ X2 )
% 2.61/1.50 => ( X2 = Y ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_292_antisym,axiom,
% 2.61/1.50 ! [X2: num,Y: num] :
% 2.61/1.50 ( ( ord_less_eq_num @ X2 @ Y )
% 2.61/1.50 => ( ( ord_less_eq_num @ Y @ X2 )
% 2.61/1.50 => ( X2 = Y ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_293_antisym,axiom,
% 2.61/1.50 ! [X2: nat,Y: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ X2 @ Y )
% 2.61/1.50 => ( ( ord_less_eq_nat @ Y @ X2 )
% 2.61/1.50 => ( X2 = Y ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_294_linear,axiom,
% 2.61/1.50 ! [X2: real,Y: real] :
% 2.61/1.50 ( ( ord_less_eq_real @ X2 @ Y )
% 2.61/1.50 | ( ord_less_eq_real @ Y @ X2 ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_295_linear,axiom,
% 2.61/1.50 ! [X2: num,Y: num] :
% 2.61/1.50 ( ( ord_less_eq_num @ X2 @ Y )
% 2.61/1.50 | ( ord_less_eq_num @ Y @ X2 ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_296_linear,axiom,
% 2.61/1.50 ! [X2: nat,Y: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ X2 @ Y )
% 2.61/1.50 | ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_297_eq__refl,axiom,
% 2.61/1.50 ! [X2: real,Y: real] :
% 2.61/1.50 ( ( X2 = Y )
% 2.61/1.50 => ( ord_less_eq_real @ X2 @ Y ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_298_eq__refl,axiom,
% 2.61/1.50 ! [X2: num,Y: num] :
% 2.61/1.50 ( ( X2 = Y )
% 2.61/1.50 => ( ord_less_eq_num @ X2 @ Y ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_299_eq__refl,axiom,
% 2.61/1.50 ! [X2: nat,Y: nat] :
% 2.61/1.50 ( ( X2 = Y )
% 2.61/1.50 => ( ord_less_eq_nat @ X2 @ Y ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_300_le__cases,axiom,
% 2.61/1.50 ! [X2: real,Y: real] :
% 2.61/1.50 ( ~ ( ord_less_eq_real @ X2 @ Y )
% 2.61/1.50 => ( ord_less_eq_real @ Y @ X2 ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_301_le__cases,axiom,
% 2.61/1.50 ! [X2: num,Y: num] :
% 2.61/1.50 ( ~ ( ord_less_eq_num @ X2 @ Y )
% 2.61/1.50 => ( ord_less_eq_num @ Y @ X2 ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_302_le__cases,axiom,
% 2.61/1.50 ! [X2: nat,Y: nat] :
% 2.61/1.50 ( ~ ( ord_less_eq_nat @ X2 @ Y )
% 2.61/1.50 => ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_303_order_Otrans,axiom,
% 2.61/1.50 ! [A: real,B: real,C: real] :
% 2.61/1.50 ( ( ord_less_eq_real @ A @ B )
% 2.61/1.50 => ( ( ord_less_eq_real @ B @ C )
% 2.61/1.50 => ( ord_less_eq_real @ A @ C ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_304_order_Otrans,axiom,
% 2.61/1.50 ! [A: num,B: num,C: num] :
% 2.61/1.50 ( ( ord_less_eq_num @ A @ B )
% 2.61/1.50 => ( ( ord_less_eq_num @ B @ C )
% 2.61/1.50 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_305_order_Otrans,axiom,
% 2.61/1.50 ! [A: nat,B: nat,C: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ A @ B )
% 2.61/1.50 => ( ( ord_less_eq_nat @ B @ C )
% 2.61/1.50 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_306_le__cases3,axiom,
% 2.61/1.50 ! [X2: real,Y: real,Z: real] :
% 2.61/1.50 ( ( ( ord_less_eq_real @ X2 @ Y )
% 2.61/1.50 => ~ ( ord_less_eq_real @ Y @ Z ) )
% 2.61/1.50 => ( ( ( ord_less_eq_real @ Y @ X2 )
% 2.61/1.50 => ~ ( ord_less_eq_real @ X2 @ Z ) )
% 2.61/1.50 => ( ( ( ord_less_eq_real @ X2 @ Z )
% 2.61/1.50 => ~ ( ord_less_eq_real @ Z @ Y ) )
% 2.61/1.50 => ( ( ( ord_less_eq_real @ Z @ Y )
% 2.61/1.50 => ~ ( ord_less_eq_real @ Y @ X2 ) )
% 2.61/1.50 => ( ( ( ord_less_eq_real @ Y @ Z )
% 2.61/1.50 => ~ ( ord_less_eq_real @ Z @ X2 ) )
% 2.61/1.50 => ~ ( ( ord_less_eq_real @ Z @ X2 )
% 2.61/1.50 => ~ ( ord_less_eq_real @ X2 @ Y ) ) ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_307_le__cases3,axiom,
% 2.61/1.50 ! [X2: num,Y: num,Z: num] :
% 2.61/1.50 ( ( ( ord_less_eq_num @ X2 @ Y )
% 2.61/1.50 => ~ ( ord_less_eq_num @ Y @ Z ) )
% 2.61/1.50 => ( ( ( ord_less_eq_num @ Y @ X2 )
% 2.61/1.50 => ~ ( ord_less_eq_num @ X2 @ Z ) )
% 2.61/1.50 => ( ( ( ord_less_eq_num @ X2 @ Z )
% 2.61/1.50 => ~ ( ord_less_eq_num @ Z @ Y ) )
% 2.61/1.50 => ( ( ( ord_less_eq_num @ Z @ Y )
% 2.61/1.50 => ~ ( ord_less_eq_num @ Y @ X2 ) )
% 2.61/1.50 => ( ( ( ord_less_eq_num @ Y @ Z )
% 2.61/1.50 => ~ ( ord_less_eq_num @ Z @ X2 ) )
% 2.61/1.50 => ~ ( ( ord_less_eq_num @ Z @ X2 )
% 2.61/1.50 => ~ ( ord_less_eq_num @ X2 @ Y ) ) ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_308_le__cases3,axiom,
% 2.61/1.50 ! [X2: nat,Y: nat,Z: nat] :
% 2.61/1.50 ( ( ( ord_less_eq_nat @ X2 @ Y )
% 2.61/1.50 => ~ ( ord_less_eq_nat @ Y @ Z ) )
% 2.61/1.50 => ( ( ( ord_less_eq_nat @ Y @ X2 )
% 2.61/1.50 => ~ ( ord_less_eq_nat @ X2 @ Z ) )
% 2.61/1.50 => ( ( ( ord_less_eq_nat @ X2 @ Z )
% 2.61/1.50 => ~ ( ord_less_eq_nat @ Z @ Y ) )
% 2.61/1.50 => ( ( ( ord_less_eq_nat @ Z @ Y )
% 2.61/1.50 => ~ ( ord_less_eq_nat @ Y @ X2 ) )
% 2.61/1.50 => ( ( ( ord_less_eq_nat @ Y @ Z )
% 2.61/1.50 => ~ ( ord_less_eq_nat @ Z @ X2 ) )
% 2.61/1.50 => ~ ( ( ord_less_eq_nat @ Z @ X2 )
% 2.61/1.50 => ~ ( ord_less_eq_nat @ X2 @ Y ) ) ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_309_antisym__conv,axiom,
% 2.61/1.50 ! [Y: num,X2: num] :
% 2.61/1.50 ( ( ord_less_eq_num @ Y @ X2 )
% 2.61/1.50 => ( ( ord_less_eq_num @ X2 @ Y )
% 2.61/1.50 = ( X2 = Y ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_310_antisym__conv,axiom,
% 2.61/1.50 ! [Y: nat,X2: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ Y @ X2 )
% 2.61/1.50 => ( ( ord_less_eq_nat @ X2 @ Y )
% 2.61/1.50 = ( X2 = Y ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_311_complete__real,axiom,
% 2.61/1.50 ! [S3: set_real] :
% 2.61/1.50 ( ? [X4: real] : ( member_real @ X4 @ S3 )
% 2.61/1.50 => ( ? [Z3: real] :
% 2.61/1.50 ! [X3: real] :
% 2.61/1.50 ( ( member_real @ X3 @ S3 )
% 2.61/1.50 => ( ord_less_eq_real @ X3 @ Z3 ) )
% 2.61/1.50 => ? [Y3: real] :
% 2.61/1.50 ( ! [X4: real] :
% 2.61/1.50 ( ( member_real @ X4 @ S3 )
% 2.61/1.50 => ( ord_less_eq_real @ X4 @ Y3 ) )
% 2.61/1.50 & ! [Z3: real] :
% 2.61/1.50 ( ! [X3: real] :
% 2.61/1.50 ( ( member_real @ X3 @ S3 )
% 2.61/1.50 => ( ord_less_eq_real @ X3 @ Z3 ) )
% 2.61/1.50 => ( ord_less_eq_real @ Y3 @ Z3 ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_312_PC__monotone,axiom,
% 2.61/1.50 ! [P3: nat,S: real,T: real] :
% 2.61/1.50 ( ( ( genClo1015804716orrect @ P3 @ T )
% 2.61/1.50 & ( ord_less_eq_real @ S @ T ) )
% 2.61/1.50 => ( ord_less_eq_real @ ( genClo1161277105lle_PC @ P3 @ S ) @ ( genClo1161277105lle_PC @ P3 @ T ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_313_verit__eq__simplify_I10_J,axiom,
% 2.61/1.50 ! [X22: num] :
% 2.61/1.50 ( one
% 2.61/1.50 != ( bit0 @ X22 ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_314_nat__eq__add__iff1,axiom,
% 2.61/1.50 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ J @ I )
% 2.61/1.50 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 2.61/1.50 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 2.61/1.50 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M )
% 2.61/1.50 = N ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_315_nat__eq__add__iff2,axiom,
% 2.61/1.50 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ I @ J )
% 2.61/1.50 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 2.61/1.50 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 2.61/1.50 = ( M
% 2.61/1.50 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_316_nat__le__add__iff1,axiom,
% 2.61/1.50 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ J @ I )
% 2.61/1.50 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 2.61/1.50 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_317_nat__le__add__iff2,axiom,
% 2.61/1.50 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ I @ J )
% 2.61/1.50 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 2.61/1.50 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_318_nat__diff__add__eq1,axiom,
% 2.61/1.50 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ J @ I )
% 2.61/1.50 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 2.61/1.50 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_319_nat__diff__add__eq2,axiom,
% 2.61/1.50 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ I @ J )
% 2.61/1.50 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 2.61/1.50 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_320_left__add__mult__distrib,axiom,
% 2.61/1.50 ! [I: nat,U: nat,J: nat,K: nat] :
% 2.61/1.50 ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 2.61/1.50 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_321_nat__1__eq__mult__iff,axiom,
% 2.61/1.50 ! [M: nat,N: nat] :
% 2.61/1.50 ( ( one_one_nat
% 2.61/1.50 = ( times_times_nat @ M @ N ) )
% 2.61/1.50 = ( ( M = one_one_nat )
% 2.61/1.50 & ( N = one_one_nat ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_322_nat__mult__eq__1__iff,axiom,
% 2.61/1.50 ! [M: nat,N: nat] :
% 2.61/1.50 ( ( ( times_times_nat @ M @ N )
% 2.61/1.50 = one_one_nat )
% 2.61/1.50 = ( ( M = one_one_nat )
% 2.61/1.50 & ( N = one_one_nat ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_323_nat__add__left__cancel__le,axiom,
% 2.61/1.50 ! [K: nat,M: nat,N: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 2.61/1.50 = ( ord_less_eq_nat @ M @ N ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_324_diff__diff__cancel,axiom,
% 2.61/1.50 ! [I: nat,N: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ I @ N )
% 2.61/1.50 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 2.61/1.50 = I ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_325_diff__diff__left,axiom,
% 2.61/1.50 ! [I: nat,J: nat,K: nat] :
% 2.61/1.50 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 2.61/1.50 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_326_Nat_Odiff__diff__right,axiom,
% 2.61/1.50 ! [K: nat,J: nat,I: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ K @ J )
% 2.61/1.50 => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 2.61/1.50 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_327_Nat_Oadd__diff__assoc2,axiom,
% 2.61/1.50 ! [K: nat,J: nat,I: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ K @ J )
% 2.61/1.50 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 2.61/1.50 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_328_Nat_Oadd__diff__assoc,axiom,
% 2.61/1.50 ! [K: nat,J: nat,I: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ K @ J )
% 2.61/1.50 => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 2.61/1.50 = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_329_eq__diff__iff,axiom,
% 2.61/1.50 ! [K: nat,M: nat,N: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ K @ M )
% 2.61/1.50 => ( ( ord_less_eq_nat @ K @ N )
% 2.61/1.50 => ( ( ( minus_minus_nat @ M @ K )
% 2.61/1.50 = ( minus_minus_nat @ N @ K ) )
% 2.61/1.50 = ( M = N ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_330_le__diff__iff,axiom,
% 2.61/1.50 ! [K: nat,M: nat,N: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ K @ M )
% 2.61/1.50 => ( ( ord_less_eq_nat @ K @ N )
% 2.61/1.50 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 2.61/1.50 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_331_Nat_Odiff__diff__eq,axiom,
% 2.61/1.50 ! [K: nat,M: nat,N: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ K @ M )
% 2.61/1.50 => ( ( ord_less_eq_nat @ K @ N )
% 2.61/1.50 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 2.61/1.50 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_332_diff__le__mono,axiom,
% 2.61/1.50 ! [M: nat,N: nat,L: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ M @ N )
% 2.61/1.50 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_333_diff__le__self,axiom,
% 2.61/1.50 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_334_le__diff__iff_H,axiom,
% 2.61/1.50 ! [A: nat,C: nat,B: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ A @ C )
% 2.61/1.50 => ( ( ord_less_eq_nat @ B @ C )
% 2.61/1.50 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 2.61/1.50 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_335_diff__le__mono2,axiom,
% 2.61/1.50 ! [M: nat,N: nat,L: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ M @ N )
% 2.61/1.50 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_336_Nat_Oex__has__greatest__nat,axiom,
% 2.61/1.50 ! [P2: nat > $o,K: nat,B: nat] :
% 2.61/1.50 ( ( P2 @ K )
% 2.61/1.50 => ( ! [Y3: nat] :
% 2.61/1.50 ( ( P2 @ Y3 )
% 2.61/1.50 => ( ord_less_eq_nat @ Y3 @ B ) )
% 2.61/1.50 => ? [X3: nat] :
% 2.61/1.50 ( ( P2 @ X3 )
% 2.61/1.50 & ! [Y6: nat] :
% 2.61/1.50 ( ( P2 @ Y6 )
% 2.61/1.50 => ( ord_less_eq_nat @ Y6 @ X3 ) ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_337_nat__le__linear,axiom,
% 2.61/1.50 ! [M: nat,N: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ M @ N )
% 2.61/1.50 | ( ord_less_eq_nat @ N @ M ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_338_mult__le__mono2,axiom,
% 2.61/1.50 ! [I: nat,J: nat,K: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ I @ J )
% 2.61/1.50 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_339_mult__le__mono1,axiom,
% 2.61/1.50 ! [I: nat,J: nat,K: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ I @ J )
% 2.61/1.50 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_340_mult__le__mono,axiom,
% 2.61/1.50 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ I @ J )
% 2.61/1.50 => ( ( ord_less_eq_nat @ K @ L )
% 2.61/1.50 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_341_le__antisym,axiom,
% 2.61/1.50 ! [M: nat,N: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ M @ N )
% 2.61/1.50 => ( ( ord_less_eq_nat @ N @ M )
% 2.61/1.50 => ( M = N ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_342_le__square,axiom,
% 2.61/1.50 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_343_eq__imp__le,axiom,
% 2.61/1.50 ! [M: nat,N: nat] :
% 2.61/1.50 ( ( M = N )
% 2.61/1.50 => ( ord_less_eq_nat @ M @ N ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_344_le__trans,axiom,
% 2.61/1.50 ! [I: nat,J: nat,K: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ I @ J )
% 2.61/1.50 => ( ( ord_less_eq_nat @ J @ K )
% 2.61/1.50 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_345_le__refl,axiom,
% 2.61/1.50 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_346_le__cube,axiom,
% 2.61/1.50 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_347_diff__mult__distrib2,axiom,
% 2.61/1.50 ! [K: nat,M: nat,N: nat] :
% 2.61/1.50 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 2.61/1.50 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_348_diff__mult__distrib,axiom,
% 2.61/1.50 ! [M: nat,N: nat,K: nat] :
% 2.61/1.50 ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 2.61/1.50 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_349_diff__commute,axiom,
% 2.61/1.50 ! [I: nat,J: nat,K: nat] :
% 2.61/1.50 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 2.61/1.50 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_350_Nat_Ole__imp__diff__is__add,axiom,
% 2.61/1.50 ! [I: nat,J: nat,K: nat] :
% 2.61/1.50 ( ( ord_less_eq_nat @ I @ J )
% 2.61/1.50 => ( ( ( minus_minus_nat @ J @ I )
% 2.61/1.50 = K )
% 2.61/1.50 = ( J
% 2.61/1.50 = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 2.61/1.50
% 2.61/1.50 thf(fact_351_diff__add__inverse2,axiom,
% 2.61/1.50 ! [M: nat,N: nat] :
% 2.61/1.50 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 2.61/1.50 = M ) ).
% 2.61/1.50
% 2.61/1.50 thf(conj_0,conjecture,
% 2.61/1.50 ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( minus_minus_real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus_real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ genClo1144207539le_rho ) @ ( minus_minus_real @ t @ s ) ) ).
% 2.61/1.50 ------------------------
% 2.83/1.52 % (1371)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/18Mi)
% 2.83/1.52 % (1367)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/27Mi)
% 2.83/1.52 % (1368)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/2Mi)
% 2.83/1.52 % (1368)Instruction limit reached!
% 2.83/1.52 % (1368)------------------------------
% 2.83/1.52 % (1368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.52 % (1368)Termination reason: Unknown
% 2.83/1.52 % (1368)Termination phase: shuffling
% 2.83/1.52
% 2.83/1.52 % (1368)Memory used [KB]: 1407
% 2.83/1.52 % (1368)Time elapsed: 0.002 s
% 2.83/1.52 % (1368)Instructions burned: 2 (million)
% 2.83/1.52 % (1368)------------------------------
% 2.83/1.52 % (1368)------------------------------
% 2.83/1.52 % (1371)Instruction limit reached!
% 2.83/1.52 % (1371)------------------------------
% 2.83/1.52 % (1371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.52 % (1371)Termination reason: Unknown
% 2.83/1.52 % (1371)Termination phase: shuffling
% 2.83/1.52
% 2.83/1.52 % (1371)Memory used [KB]: 1663
% 2.83/1.52 % (1371)Time elapsed: 0.007 s
% 2.83/1.52 % (1371)Instructions burned: 18 (million)
% 2.83/1.52 % (1371)------------------------------
% 2.83/1.52 % (1371)------------------------------
% 2.83/1.52 % (1366)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/4Mi)
% 2.83/1.52 % (1370)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/275Mi)
% 2.83/1.52 % (1369)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/2Mi)
% 2.83/1.52 % (1369)Instruction limit reached!
% 2.83/1.52 % (1369)------------------------------
% 2.83/1.52 % (1369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.52 % (1369)Termination reason: Unknown
% 2.83/1.52 % (1369)Termination phase: shuffling
% 2.83/1.52
% 2.83/1.52 % (1369)Memory used [KB]: 1407
% 2.83/1.52 % (1369)Time elapsed: 0.002 s
% 2.83/1.52 % (1369)Instructions burned: 3 (million)
% 2.83/1.52 % (1369)------------------------------
% 2.83/1.52 % (1369)------------------------------
% 2.83/1.53 % (1366)Instruction limit reached!
% 2.83/1.53 % (1366)------------------------------
% 2.83/1.53 % (1366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.53 % (1366)Termination reason: Unknown
% 2.83/1.53 % (1366)Termination phase: shuffling
% 2.83/1.53
% 2.83/1.53 % (1366)Memory used [KB]: 1407
% 2.83/1.53 % (1366)Time elapsed: 0.004 s
% 2.83/1.53 % (1366)Instructions burned: 5 (million)
% 2.83/1.53 % (1366)------------------------------
% 2.83/1.53 % (1366)------------------------------
% 2.83/1.53 % (1365)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/183Mi)
% 2.83/1.53 % (1367)Instruction limit reached!
% 2.83/1.53 % (1367)------------------------------
% 2.83/1.53 % (1367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.53 % (1367)Termination reason: Unknown
% 2.83/1.53 % (1367)Termination phase: Property scanning
% 2.83/1.53
% 2.83/1.53 % (1367)Memory used [KB]: 1663
% 2.83/1.53 % (1367)Time elapsed: 0.010 s
% 2.83/1.53 % (1367)Instructions burned: 27 (million)
% 2.83/1.53 % (1367)------------------------------
% 2.83/1.53 % (1367)------------------------------
% 2.83/1.53 % (1372)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/3Mi)
% 2.83/1.53 % (1372)Instruction limit reached!
% 2.83/1.53 % (1372)------------------------------
% 2.83/1.53 % (1372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.53 % (1372)Termination reason: Unknown
% 2.83/1.53 % (1372)Termination phase: shuffling
% 2.83/1.53
% 2.83/1.53 % (1372)Memory used [KB]: 1407
% 2.83/1.53 % (1372)Time elapsed: 0.002 s
% 2.83/1.53 % (1372)Instructions burned: 3 (million)
% 2.83/1.53 % (1372)------------------------------
% 2.83/1.53 % (1372)------------------------------
% 2.83/1.53 % (1373)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/37Mi)
% 2.83/1.54 % (1374)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/15Mi)
% 2.83/1.54 % (1375)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/3Mi)
% 2.83/1.54 % (1375)Instruction limit reached!
% 2.83/1.54 % (1375)------------------------------
% 2.83/1.54 % (1375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.54 % (1375)Termination reason: Unknown
% 2.83/1.54 % (1375)Termination phase: shuffling
% 2.83/1.54
% 2.83/1.54 % (1375)Memory used [KB]: 1407
% 2.83/1.54 % (1375)Time elapsed: 0.003 s
% 2.83/1.54 % (1375)Instructions burned: 3 (million)
% 2.83/1.54 % (1375)------------------------------
% 2.83/1.54 % (1375)------------------------------
% 2.83/1.54 % (1377)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/7Mi)
% 2.83/1.54 % (1374)Instruction limit reached!
% 2.83/1.54 % (1374)------------------------------
% 2.83/1.54 % (1374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.54 % (1374)Termination reason: Unknown
% 2.83/1.54 % (1374)Termination phase: shuffling
% 2.83/1.54
% 2.83/1.54 % (1374)Memory used [KB]: 1663
% 2.83/1.54 % (1374)Time elapsed: 0.008 s
% 2.83/1.54 % (1374)Instructions burned: 17 (million)
% 2.83/1.54 % (1374)------------------------------
% 2.83/1.54 % (1374)------------------------------
% 2.83/1.54 % (1373)Instruction limit reached!
% 2.83/1.54 % (1373)------------------------------
% 2.83/1.54 % (1373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.54 % (1373)Termination reason: Unknown
% 2.83/1.54 % (1373)Termination phase: shuffling
% 2.83/1.54
% 2.83/1.54 % (1373)Memory used [KB]: 2046
% 2.83/1.54 % (1373)Time elapsed: 0.011 s
% 2.83/1.54 % (1373)Instructions burned: 38 (million)
% 2.83/1.54 % (1373)------------------------------
% 2.83/1.54 % (1373)------------------------------
% 2.83/1.54 % (1376)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/1041Mi)
% 2.83/1.54 % (1377)Instruction limit reached!
% 2.83/1.54 % (1377)------------------------------
% 2.83/1.54 % (1377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.54 % (1377)Termination reason: Unknown
% 2.83/1.54 % (1377)Termination phase: shuffling
% 2.83/1.54
% 2.83/1.54 % (1377)Memory used [KB]: 1535
% 2.83/1.54 % (1377)Time elapsed: 0.004 s
% 2.83/1.54 % (1377)Instructions burned: 9 (million)
% 2.83/1.54 % (1377)------------------------------
% 2.83/1.54 % (1377)------------------------------
% 2.83/1.55 % (1378)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/16Mi)
% 2.83/1.55 % (1380)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/3Mi)
% 2.83/1.55 % (1380)Instruction limit reached!
% 2.83/1.55 % (1380)------------------------------
% 2.83/1.55 % (1380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.55 % (1380)Termination reason: Unknown
% 2.83/1.55 % (1380)Termination phase: shuffling
% 2.83/1.55
% 2.83/1.55 % (1380)Memory used [KB]: 1407
% 2.83/1.55 % (1380)Time elapsed: 0.002 s
% 2.83/1.55 % (1380)Instructions burned: 3 (million)
% 2.83/1.55 % (1380)------------------------------
% 2.83/1.55 % (1380)------------------------------
% 2.83/1.55 % (1379)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/3Mi)
% 2.83/1.55 % (1378)Instruction limit reached!
% 2.83/1.55 % (1378)------------------------------
% 2.83/1.55 % (1378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.55 % (1378)Termination reason: Unknown
% 2.83/1.55 % (1378)Termination phase: shuffling
% 2.83/1.55
% 2.83/1.55 % (1378)Memory used [KB]: 1663
% 2.83/1.55 % (1378)Time elapsed: 0.008 s
% 2.83/1.55 % (1378)Instructions burned: 17 (million)
% 2.83/1.55 % (1378)------------------------------
% 2.83/1.55 % (1378)------------------------------
% 2.83/1.56 % (1379)Instruction limit reached!
% 2.83/1.56 % (1379)------------------------------
% 2.83/1.56 % (1379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.56 % (1379)Termination reason: Unknown
% 2.83/1.56 % (1379)Termination phase: shuffling
% 2.83/1.56
% 2.83/1.56 % (1379)Memory used [KB]: 1407
% 2.83/1.56 % (1379)Time elapsed: 0.003 s
% 2.83/1.56 % (1379)Instructions burned: 4 (million)
% 2.83/1.56 % (1379)------------------------------
% 2.83/1.56 % (1379)------------------------------
% 2.83/1.56 % (1381)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/7Mi)
% 2.83/1.56 % (1381)Instruction limit reached!
% 2.83/1.56 % (1381)------------------------------
% 2.83/1.56 % (1381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.56 % (1381)Termination reason: Unknown
% 2.83/1.56 % (1381)Termination phase: shuffling
% 2.83/1.56
% 2.83/1.56 % (1381)Memory used [KB]: 1407
% 2.83/1.56 % (1381)Time elapsed: 0.005 s
% 2.83/1.56 % (1381)Instructions burned: 9 (million)
% 2.83/1.56 % (1381)------------------------------
% 2.83/1.56 % (1381)------------------------------
% 2.83/1.56 % (1382)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/3Mi)
% 2.83/1.56 % (1382)Instruction limit reached!
% 2.83/1.56 % (1382)------------------------------
% 2.83/1.56 % (1382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.56 % (1382)Termination reason: Unknown
% 2.83/1.56 % (1382)Termination phase: shuffling
% 2.83/1.56
% 2.83/1.56 % (1382)Memory used [KB]: 1407
% 2.83/1.56 % (1382)Time elapsed: 0.002 s
% 2.83/1.56 % (1382)Instructions burned: 3 (million)
% 2.83/1.56 % (1382)------------------------------
% 2.83/1.56 % (1382)------------------------------
% 2.83/1.56 % (1383)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/4Mi)
% 2.83/1.57 % (1384)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/18Mi)
% 2.83/1.57 % (1383)Instruction limit reached!
% 2.83/1.57 % (1383)------------------------------
% 2.83/1.57 % (1383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.57 % (1383)Termination reason: Unknown
% 2.83/1.57 % (1383)Termination phase: shuffling
% 2.83/1.57
% 2.83/1.57 % (1383)Memory used [KB]: 1407
% 2.83/1.57 % (1383)Time elapsed: 0.004 s
% 2.83/1.57 % (1383)Instructions burned: 6 (million)
% 2.83/1.57 % (1383)------------------------------
% 2.83/1.57 % (1383)------------------------------
% 2.83/1.57 % (1385)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/710Mi)
% 2.83/1.57 % (1386)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/6Mi)
% 2.83/1.57 % (1386)Instruction limit reached!
% 2.83/1.57 % (1386)------------------------------
% 2.83/1.57 % (1386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.57 % (1386)Termination reason: Unknown
% 2.83/1.57 % (1386)Termination phase: shuffling
% 2.83/1.57
% 2.83/1.57 % (1386)Memory used [KB]: 1407
% 2.83/1.57 % (1386)Time elapsed: 0.003 s
% 2.83/1.57 % (1386)Instructions burned: 6 (million)
% 2.83/1.57 % (1386)------------------------------
% 2.83/1.57 % (1386)------------------------------
% 2.83/1.57 % (1384)Instruction limit reached!
% 2.83/1.57 % (1384)------------------------------
% 2.83/1.57 % (1384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.57 % (1384)Termination reason: Unknown
% 2.83/1.57 % (1384)Termination phase: shuffling
% 2.83/1.57
% 2.83/1.57 % (1384)Memory used [KB]: 1791
% 2.83/1.57 % (1384)Time elapsed: 0.010 s
% 2.83/1.57 % (1384)Instructions burned: 20 (million)
% 2.83/1.57 % (1384)------------------------------
% 2.83/1.57 % (1384)------------------------------
% 2.83/1.58 % (1387)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/902Mi)
% 2.83/1.58 % (1388)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/21Mi)
% 2.83/1.59 % (1389)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/5Mi)
% 2.83/1.59 % (1389)Instruction limit reached!
% 2.83/1.59 % (1389)------------------------------
% 2.83/1.59 % (1389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.59 % (1389)Termination reason: Unknown
% 2.83/1.59 % (1389)Termination phase: shuffling
% 2.83/1.59
% 2.83/1.59 % (1389)Memory used [KB]: 1535
% 2.83/1.59 % (1389)Time elapsed: 0.004 s
% 2.83/1.59 % (1389)Instructions burned: 7 (million)
% 2.83/1.59 % (1389)------------------------------
% 2.83/1.59 % (1389)------------------------------
% 2.83/1.59 % (1388)Instruction limit reached!
% 2.83/1.59 % (1388)------------------------------
% 2.83/1.59 % (1388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.59 % (1388)Termination reason: Unknown
% 2.83/1.59 % (1388)Termination phase: shuffling
% 2.83/1.59
% 2.83/1.59 % (1388)Memory used [KB]: 1663
% 2.83/1.59 % (1388)Time elapsed: 0.009 s
% 2.83/1.59 % (1388)Instructions burned: 21 (million)
% 2.83/1.59 % (1388)------------------------------
% 2.83/1.59 % (1388)------------------------------
% 2.83/1.60 % (1365)Instruction limit reached!
% 2.83/1.60 % (1365)------------------------------
% 2.83/1.60 % (1365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.60 % (1365)Termination reason: Unknown
% 2.83/1.60 % (1365)Termination phase: Saturation
% 2.83/1.60
% 2.83/1.60 % (1365)Memory used [KB]: 7164
% 2.83/1.60 % (1365)Time elapsed: 0.073 s
% 2.83/1.60 % (1365)Instructions burned: 184 (million)
% 2.83/1.60 % (1365)------------------------------
% 2.83/1.60 % (1365)------------------------------
% 2.83/1.60 % (1390)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/6Mi)
% 2.83/1.60 % (1391)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/377Mi)
% 2.83/1.60 % (1390)Instruction limit reached!
% 2.83/1.60 % (1390)------------------------------
% 2.83/1.60 % (1390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.60 % (1390)Termination reason: Unknown
% 2.83/1.60 % (1390)Termination phase: shuffling
% 2.83/1.60
% 2.83/1.60 % (1390)Memory used [KB]: 1407
% 2.83/1.60 % (1390)Time elapsed: 0.003 s
% 2.83/1.60 % (1390)Instructions burned: 6 (million)
% 2.83/1.60 % (1390)------------------------------
% 2.83/1.60 % (1390)------------------------------
% 2.83/1.61 % (1392)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/779Mi)
% 2.83/1.61 % (1393)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_1172 for (2999ds/19Mi)
% 2.83/1.62 % (1393)Instruction limit reached!
% 2.83/1.62 % (1393)------------------------------
% 2.83/1.62 % (1393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.62 % (1393)Termination reason: Unknown
% 2.83/1.62 % (1393)Termination phase: shuffling
% 2.83/1.62
% 2.83/1.62 % (1393)Memory used [KB]: 1663
% 2.83/1.62 % (1393)Time elapsed: 0.009 s
% 2.83/1.62 % (1393)Instructions burned: 19 (million)
% 2.83/1.62 % (1393)------------------------------
% 2.83/1.62 % (1393)------------------------------
% 2.83/1.63 % (1394)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_1172 for (2998ds/879Mi)
% 2.83/1.65 % (1370)Instruction limit reached!
% 2.83/1.65 % (1370)------------------------------
% 2.83/1.65 % (1370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.65 % (1370)Termination reason: Unknown
% 2.83/1.65 % (1370)Termination phase: Saturation
% 2.83/1.65
% 2.83/1.65 % (1370)Memory used [KB]: 7291
% 2.83/1.65 % (1370)Time elapsed: 0.127 s
% 2.83/1.65 % (1370)Instructions burned: 277 (million)
% 2.83/1.65 % (1370)------------------------------
% 2.83/1.65 % (1370)------------------------------
% 2.83/1.66 % (1400)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_1172 for (2998ds/17Mi)
% 2.83/1.66 % (1400)Instruction limit reached!
% 2.83/1.66 % (1400)------------------------------
% 2.83/1.66 % (1400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.66 % (1400)Termination reason: Unknown
% 2.83/1.66 % (1400)Termination phase: shuffling
% 2.83/1.66
% 2.83/1.66 % (1400)Memory used [KB]: 1663
% 2.83/1.66 % (1400)Time elapsed: 0.008 s
% 2.83/1.66 % (1400)Instructions burned: 17 (million)
% 2.83/1.66 % (1400)------------------------------
% 2.83/1.66 % (1400)------------------------------
% 2.83/1.68 % (1403)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_1172 for (2998ds/3Mi)
% 2.83/1.68 % (1403)Instruction limit reached!
% 2.83/1.68 % (1403)------------------------------
% 2.83/1.68 % (1403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.68 % (1403)Termination reason: Unknown
% 2.83/1.68 % (1403)Termination phase: shuffling
% 2.83/1.68
% 2.83/1.68 % (1403)Memory used [KB]: 1407
% 2.83/1.68 % (1403)Time elapsed: 0.004 s
% 2.83/1.68 % (1403)Instructions burned: 4 (million)
% 2.83/1.68 % (1403)------------------------------
% 2.83/1.68 % (1403)------------------------------
% 2.83/1.70 % (1411)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_1172 for (2998ds/30Mi)
% 2.83/1.71 % (1411)Instruction limit reached!
% 2.83/1.71 % (1411)------------------------------
% 2.83/1.71 % (1411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.71 % (1411)Termination reason: Unknown
% 2.83/1.71 % (1411)Termination phase: shuffling
% 2.83/1.71
% 2.83/1.71 % (1411)Memory used [KB]: 1791
% 2.83/1.71 % (1411)Time elapsed: 0.017 s
% 2.83/1.71 % (1411)Instructions burned: 30 (million)
% 2.83/1.71 % (1411)------------------------------
% 2.83/1.71 % (1411)------------------------------
% 2.83/1.73 % (1418)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_1172 for (2997ds/127Mi)
% 2.83/1.74 % (1391)Instruction limit reached!
% 2.83/1.74 % (1391)------------------------------
% 2.83/1.74 % (1391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.74 % (1391)Termination reason: Unknown
% 2.83/1.74 % (1391)Termination phase: Saturation
% 2.83/1.74
% 2.83/1.74 % (1391)Memory used [KB]: 8187
% 2.83/1.74 % (1391)Time elapsed: 0.136 s
% 2.83/1.74 % (1391)Instructions burned: 377 (million)
% 2.83/1.74 % (1391)------------------------------
% 2.83/1.74 % (1391)------------------------------
% 2.83/1.75 % (1423)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_1172 for (2997ds/100Mi)
% 2.83/1.78 % (1418)Instruction limit reached!
% 2.83/1.78 % (1418)------------------------------
% 2.83/1.78 % (1418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.78 % (1418)Termination reason: Unknown
% 2.83/1.78 % (1418)Termination phase: Saturation
% 2.83/1.78
% 2.83/1.78 % (1418)Memory used [KB]: 6908
% 2.83/1.78 % (1418)Time elapsed: 0.055 s
% 2.83/1.78 % (1418)Instructions burned: 127 (million)
% 2.83/1.78 % (1418)------------------------------
% 2.83/1.78 % (1418)------------------------------
% 2.83/1.79 % (1433)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_1172 for (2997ds/3Mi)
% 2.83/1.79 % (1433)Instruction limit reached!
% 2.83/1.79 % (1433)------------------------------
% 2.83/1.79 % (1433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.79 % (1433)Termination reason: Unknown
% 2.83/1.79 % (1433)Termination phase: shuffling
% 2.83/1.79
% 2.83/1.79 % (1433)Memory used [KB]: 1407
% 2.83/1.79 % (1433)Time elapsed: 0.003 s
% 2.83/1.79 % (1433)Instructions burned: 6 (million)
% 2.83/1.79 % (1433)------------------------------
% 2.83/1.79 % (1433)------------------------------
% 2.83/1.80 % (1423)Instruction limit reached!
% 2.83/1.80 % (1423)------------------------------
% 2.83/1.80 % (1423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.80 % (1423)Termination reason: Unknown
% 2.83/1.80 % (1423)Termination phase: Property scanning
% 2.83/1.80
% 2.83/1.80 % (1423)Memory used [KB]: 2430
% 2.83/1.80 % (1423)Time elapsed: 0.047 s
% 2.83/1.80 % (1423)Instructions burned: 101 (million)
% 2.83/1.80 % (1423)------------------------------
% 2.83/1.80 % (1423)------------------------------
% 2.83/1.80 % (1436)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_1172 for (2996ds/20Mi)
% 2.83/1.81 % (1436)Instruction limit reached!
% 2.83/1.81 % (1436)------------------------------
% 2.83/1.81 % (1436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.81 % (1436)Termination reason: Unknown
% 2.83/1.81 % (1436)Termination phase: Property scanning
% 2.83/1.81
% 2.83/1.81 % (1436)Memory used [KB]: 1791
% 2.83/1.81 % (1436)Time elapsed: 0.008 s
% 2.83/1.81 % (1436)Instructions burned: 21 (million)
% 2.83/1.81 % (1436)------------------------------
% 2.83/1.81 % (1436)------------------------------
% 2.83/1.82 % (1438)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_1172 for (2996ds/86Mi)
% 2.83/1.82 % (1439)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_1172 for (2996ds/107Mi)
% 2.83/1.85 % (1385)Instruction limit reached!
% 2.83/1.85 % (1385)------------------------------
% 2.83/1.85 % (1385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.85 % (1385)Termination reason: Unknown
% 2.83/1.85 % (1385)Termination phase: Saturation
% 2.83/1.85
% 2.83/1.85 % (1385)Memory used [KB]: 7931
% 2.83/1.85 % (1385)Time elapsed: 0.276 s
% 2.83/1.85 % (1385)Instructions burned: 711 (million)
% 2.83/1.85 % (1385)------------------------------
% 2.83/1.85 % (1385)------------------------------
% 2.83/1.85 % (1438)Instruction limit reached!
% 2.83/1.85 % (1438)------------------------------
% 2.83/1.85 % (1438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.85 % (1438)Termination reason: Unknown
% 2.83/1.85 % (1438)Termination phase: Property scanning
% 2.83/1.85
% 2.83/1.85 % (1438)Memory used [KB]: 2174
% 2.83/1.85 % (1438)Time elapsed: 0.038 s
% 2.83/1.85 % (1438)Instructions burned: 89 (million)
% 2.83/1.85 % (1438)------------------------------
% 2.83/1.85 % (1438)------------------------------
% 2.83/1.86 % (1439)Instruction limit reached!
% 2.83/1.86 % (1439)------------------------------
% 2.83/1.86 % (1439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.86 % (1439)Termination reason: Unknown
% 2.83/1.86 % (1439)Termination phase: Property scanning
% 2.83/1.86
% 2.83/1.86 % (1439)Memory used [KB]: 2174
% 2.83/1.86 % (1439)Time elapsed: 0.039 s
% 2.83/1.86 % (1439)Instructions burned: 107 (million)
% 2.83/1.86 % (1439)------------------------------
% 2.83/1.86 % (1439)------------------------------
% 2.83/1.86 % (1443)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_1172 for (2996ds/39Mi)
% 2.83/1.86 % (1444)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_1172 for (2996ds/448Mi)
% 2.83/1.87 % (1445)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_1172 for (2996ds/46Mi)
% 2.83/1.87 % (1443)Instruction limit reached!
% 2.83/1.87 % (1443)------------------------------
% 2.83/1.87 % (1443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.87 % (1443)Termination reason: Unknown
% 2.83/1.87 % (1443)Termination phase: shuffling
% 2.83/1.87
% 2.83/1.87 % (1443)Memory used [KB]: 2174
% 2.83/1.87 % (1443)Time elapsed: 0.012 s
% 2.83/1.87 % (1443)Instructions burned: 39 (million)
% 2.83/1.87 % (1443)------------------------------
% 2.83/1.87 % (1443)------------------------------
% 2.83/1.88 % (1446)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_1172 for (2996ds/98Mi)
% 2.83/1.88 % (1445)Instruction limit reached!
% 2.83/1.88 % (1445)------------------------------
% 2.83/1.88 % (1445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.88 % (1445)Termination reason: Unknown
% 2.83/1.88 % (1445)Termination phase: Preprocessing 1
% 2.83/1.88
% 2.83/1.88 % (1445)Memory used [KB]: 1791
% 2.83/1.88 % (1445)Time elapsed: 0.020 s
% 2.83/1.88 % (1445)Instructions burned: 48 (million)
% 2.83/1.88 % (1445)------------------------------
% 2.83/1.88 % (1445)------------------------------
% 2.83/1.89 % (1392)Instruction limit reached!
% 2.83/1.89 % (1392)------------------------------
% 2.83/1.89 % (1392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.89 % (1392)Termination reason: Unknown
% 2.83/1.89 % (1392)Termination phase: Saturation
% 2.83/1.89
% 2.83/1.89 % (1392)Memory used [KB]: 9210
% 2.83/1.89 % (1392)Time elapsed: 0.304 s
% 2.83/1.89 % (1392)Instructions burned: 780 (million)
% 2.83/1.89 % (1392)------------------------------
% 2.83/1.89 % (1392)------------------------------
% 2.83/1.89 % (1447)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_1172 for (2996ds/507Mi)
% 2.83/1.90 % (1387)Instruction limit reached!
% 2.83/1.90 % (1387)------------------------------
% 2.83/1.90 % (1387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.90 % (1387)Termination reason: Unknown
% 2.83/1.90 % (1387)Termination phase: Saturation
% 2.83/1.90
% 2.83/1.90 % (1387)Memory used [KB]: 7547
% 2.83/1.90 % (1387)Time elapsed: 0.317 s
% 2.83/1.90 % (1387)Instructions burned: 904 (million)
% 2.83/1.90 % (1387)------------------------------
% 2.83/1.90 % (1387)------------------------------
% 2.83/1.90 % (1448)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_1172 for (2996ds/149Mi)
% 2.83/1.90 % (1446)Instruction limit reached!
% 2.83/1.90 % (1446)------------------------------
% 2.83/1.90 % (1446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.90 % (1446)Termination reason: Unknown
% 2.83/1.90 % (1446)Termination phase: Property scanning
% 2.83/1.90
% 2.83/1.90 % (1446)Memory used [KB]: 2430
% 2.83/1.90 % (1446)Time elapsed: 0.027 s
% 2.83/1.90 % (1446)Instructions burned: 100 (million)
% 2.83/1.90 % (1446)------------------------------
% 2.83/1.90 % (1446)------------------------------
% 2.83/1.91 % (1449)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_1172 for (2995ds/39Mi)
% 2.83/1.91 % (1450)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_1172 for (2995ds/6Mi)
% 2.83/1.91 % (1450)Instruction limit reached!
% 2.83/1.91 % (1450)------------------------------
% 2.83/1.91 % (1450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.91 % (1450)Termination reason: Unknown
% 2.83/1.91 % (1450)Termination phase: shuffling
% 2.83/1.91
% 2.83/1.91 % (1450)Memory used [KB]: 1535
% 2.83/1.91 % (1450)Time elapsed: 0.003 s
% 2.83/1.91 % (1450)Instructions burned: 7 (million)
% 2.83/1.91 % (1450)------------------------------
% 2.83/1.91 % (1450)------------------------------
% 2.83/1.92 % (1449)Instruction limit reached!
% 2.83/1.92 % (1449)------------------------------
% 2.83/1.92 % (1449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.92 % (1449)Termination reason: Unknown
% 2.83/1.92 % (1449)Termination phase: Unused predicate definition removal
% 2.83/1.92
% 2.83/1.92 % (1449)Memory used [KB]: 1791
% 2.83/1.92 % (1449)Time elapsed: 0.013 s
% 2.83/1.92 % (1449)Instructions burned: 42 (million)
% 2.83/1.92 % (1449)------------------------------
% 2.83/1.92 % (1449)------------------------------
% 2.83/1.92 % (1451)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_1172 for (2995ds/1087Mi)
% 2.83/1.93 % (1452)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_1172 for (2995ds/47Mi)
% 2.83/1.93 % (1376)Instruction limit reached!
% 2.83/1.93 % (1376)------------------------------
% 2.83/1.93 % (1376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.93 % (1376)Termination reason: Unknown
% 2.83/1.93 % (1376)Termination phase: Saturation
% 2.83/1.93
% 2.83/1.93 % (1376)Memory used [KB]: 9850
% 2.83/1.93 % (1376)Time elapsed: 0.388 s
% 2.83/1.93 % (1376)Instructions burned: 1042 (million)
% 2.83/1.93 % (1376)------------------------------
% 2.83/1.93 % (1376)------------------------------
% 2.83/1.94 % (1453)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_1172 for (2995ds/44Mi)
% 2.83/1.94 % (1452)Instruction limit reached!
% 2.83/1.94 % (1452)------------------------------
% 2.83/1.94 % (1452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.94 % (1452)Termination reason: Unknown
% 2.83/1.94 % (1452)Termination phase: Preprocessing 3
% 2.83/1.94
% 2.83/1.94 % (1452)Memory used [KB]: 2046
% 2.83/1.94 % (1452)Time elapsed: 0.015 s
% 2.83/1.94 % (1452)Instructions burned: 48 (million)
% 2.83/1.94 % (1452)------------------------------
% 2.83/1.94 % (1452)------------------------------
% 2.83/1.95 % (1458)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_1172 for (2995ds/432Mi)
% 2.83/1.95 % (1453)Instruction limit reached!
% 2.83/1.95 % (1453)------------------------------
% 2.83/1.95 % (1453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.95 % (1453)Termination reason: Unknown
% 2.83/1.95 % (1453)Termination phase: shuffling
% 2.83/1.95
% 2.83/1.95 % (1453)Memory used [KB]: 2174
% 2.83/1.95 % (1453)Time elapsed: 0.013 s
% 2.83/1.95 % (1453)Instructions burned: 44 (million)
% 2.83/1.95 % (1453)------------------------------
% 2.83/1.95 % (1453)------------------------------
% 2.83/1.95 % (1448)Instruction limit reached!
% 2.83/1.95 % (1448)------------------------------
% 2.83/1.95 % (1448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.95 % (1448)Termination reason: Unknown
% 2.83/1.95 % (1448)Termination phase: Saturation
% 2.83/1.95
% 2.83/1.95 % (1448)Memory used [KB]: 6780
% 2.83/1.95 % (1448)Time elapsed: 0.052 s
% 2.83/1.95 % (1448)Instructions burned: 150 (million)
% 2.83/1.95 % (1448)------------------------------
% 2.83/1.95 % (1448)------------------------------
% 2.83/1.96 % (1464)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_1172 for (2995ds/62Mi)
% 2.83/1.96 % (1466)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_1172 for (2995ds/31Mi)
% 2.83/1.97 % (1466)Instruction limit reached!
% 2.83/1.97 % (1466)------------------------------
% 2.83/1.97 % (1466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.97 % (1466)Termination reason: Unknown
% 2.83/1.97 % (1466)Termination phase: Property scanning
% 2.83/1.97
% 2.83/1.97 % (1466)Memory used [KB]: 1791
% 2.83/1.97 % (1466)Time elapsed: 0.011 s
% 2.83/1.97 % (1466)Instructions burned: 31 (million)
% 2.83/1.97 % (1466)------------------------------
% 2.83/1.97 % (1466)------------------------------
% 2.83/1.98 % (1394)Instruction limit reached!
% 2.83/1.98 % (1394)------------------------------
% 2.83/1.98 % (1394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.98 % (1394)Termination reason: Unknown
% 2.83/1.98 % (1394)Termination phase: Saturation
% 2.83/1.98
% 2.83/1.98 % (1394)Memory used [KB]: 7931
% 2.83/1.98 % (1394)Time elapsed: 0.368 s
% 2.83/1.98 % (1394)Instructions burned: 879 (million)
% 2.83/1.98 % (1394)------------------------------
% 2.83/1.98 % (1394)------------------------------
% 2.83/1.98 % (1464)Instruction limit reached!
% 2.83/1.98 % (1464)------------------------------
% 2.83/1.98 % (1464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.98 % (1464)Termination reason: Unknown
% 2.83/1.98 % (1464)Termination phase: Property scanning
% 2.83/1.98
% 2.83/1.98 % (1464)Memory used [KB]: 2302
% 2.83/1.98 % (1464)Time elapsed: 0.018 s
% 2.83/1.98 % (1464)Instructions burned: 62 (million)
% 2.83/1.98 % (1464)------------------------------
% 2.83/1.98 % (1464)------------------------------
% 2.83/1.98 % (1476)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_1172 for (2995ds/96Mi)
% 2.83/1.99 % (1444)Instruction limit reached!
% 2.83/1.99 % (1444)------------------------------
% 2.83/1.99 % (1444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.99 % (1444)Termination reason: Unknown
% 2.83/1.99 % (1444)Termination phase: Saturation
% 2.83/1.99
% 2.83/1.99 % (1444)Memory used [KB]: 8187
% 2.83/1.99 % (1444)Time elapsed: 0.126 s
% 2.83/1.99 % (1444)Instructions burned: 448 (million)
% 2.83/1.99 % (1444)------------------------------
% 2.83/1.99 % (1444)------------------------------
% 2.83/1.99 % (1480)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_1172 for (2995ds/453Mi)
% 2.83/1.99 % (1481)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_1172 for (2995ds/71Mi)
% 2.83/2.00 % (1486)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_1172 for (2995ds/83Mi)
% 2.83/2.01 % (1481)Instruction limit reached!
% 2.83/2.01 % (1481)------------------------------
% 2.83/2.01 % (1481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/2.01 % (1481)Termination reason: Unknown
% 2.83/2.01 % (1481)Termination phase: Property scanning
% 2.83/2.01
% 2.83/2.01 % (1481)Memory used [KB]: 2046
% 2.83/2.01 % (1481)Time elapsed: 0.022 s
% 2.83/2.01 % (1481)Instructions burned: 74 (million)
% 2.83/2.01 % (1481)------------------------------
% 2.83/2.01 % (1481)------------------------------
% 6.26/2.02 % (1476)Instruction limit reached!
% 6.26/2.02 % (1476)------------------------------
% 6.26/2.02 % (1476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.02 % (1476)Termination reason: Unknown
% 6.26/2.02 % (1476)Termination phase: Property scanning
% 6.26/2.02
% 6.26/2.02 % (1476)Memory used [KB]: 2174
% 6.26/2.02 % (1476)Time elapsed: 0.029 s
% 6.26/2.02 % (1476)Instructions burned: 99 (million)
% 6.26/2.02 % (1476)------------------------------
% 6.26/2.02 % (1476)------------------------------
% 6.26/2.02 % (1500)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_1172 for (2994ds/11Mi)
% 6.26/2.02 % (1486)Instruction limit reached!
% 6.26/2.02 % (1486)------------------------------
% 6.26/2.02 % (1486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.02 % (1486)Termination reason: Unknown
% 6.26/2.02 % (1486)Termination phase: Property scanning
% 6.26/2.02
% 6.26/2.02 % (1486)Memory used [KB]: 2046
% 6.26/2.02 % (1486)Time elapsed: 0.024 s
% 6.26/2.02 % (1486)Instructions burned: 84 (million)
% 6.26/2.02 % (1486)------------------------------
% 6.26/2.02 % (1486)------------------------------
% 6.26/2.02 % (1500)Instruction limit reached!
% 6.26/2.02 % (1500)------------------------------
% 6.26/2.02 % (1500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.02 % (1500)Termination reason: Unknown
% 6.26/2.02 % (1500)Termination phase: shuffling
% 6.26/2.02
% 6.26/2.02 % (1500)Memory used [KB]: 1535
% 6.26/2.02 % (1500)Time elapsed: 0.004 s
% 6.26/2.02 % (1500)Instructions burned: 11 (million)
% 6.26/2.02 % (1500)------------------------------
% 6.26/2.02 % (1500)------------------------------
% 6.26/2.03 % (1503)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_1172 for (2994ds/41Mi)
% 6.26/2.03 % (1504)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_1172 for (2994ds/6Mi)
% 6.26/2.03 % (1505)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_1172 for (2994ds/150Mi)
% 6.26/2.03 % (1504)Instruction limit reached!
% 6.26/2.03 % (1504)------------------------------
% 6.26/2.03 % (1504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.03 % (1504)Termination reason: Unknown
% 6.26/2.03 % (1504)Termination phase: shuffling
% 6.26/2.03
% 6.26/2.03 % (1504)Memory used [KB]: 1407
% 6.26/2.03 % (1504)Time elapsed: 0.004 s
% 6.26/2.03 % (1504)Instructions burned: 8 (million)
% 6.26/2.03 % (1504)------------------------------
% 6.26/2.03 % (1504)------------------------------
% 6.26/2.04 % (1503)Instruction limit reached!
% 6.26/2.04 % (1503)------------------------------
% 6.26/2.04 % (1503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.04 % (1503)Termination reason: Unknown
% 6.26/2.04 % (1503)Termination phase: shuffling
% 6.26/2.04
% 6.26/2.04 % (1503)Memory used [KB]: 2174
% 6.26/2.04 % (1503)Time elapsed: 0.013 s
% 6.26/2.04 % (1503)Instructions burned: 43 (million)
% 6.26/2.04 % (1503)------------------------------
% 6.26/2.04 % (1503)------------------------------
% 6.26/2.04 % (1511)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_1172 for (2994ds/343Mi)
% 6.26/2.05 % (1447)Instruction limit reached!
% 6.26/2.05 % (1447)------------------------------
% 6.26/2.05 % (1447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.05 % (1447)Termination reason: Unknown
% 6.26/2.05 % (1447)Termination phase: Saturation
% 6.26/2.05
% 6.26/2.05 % (1447)Memory used [KB]: 8059
% 6.26/2.05 % (1447)Time elapsed: 0.153 s
% 6.26/2.05 % (1447)Instructions burned: 509 (million)
% 6.26/2.05 % (1447)------------------------------
% 6.26/2.05 % (1447)------------------------------
% 6.26/2.05 % (1516)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_1172 for (2994ds/109Mi)
% 6.26/2.06 % (1520)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_1172 for (2994ds/253Mi)
% 6.26/2.07 % (1505)Instruction limit reached!
% 6.26/2.07 % (1505)------------------------------
% 6.26/2.07 % (1505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.07 % (1505)Termination reason: Unknown
% 6.26/2.07 % (1505)Termination phase: Saturation
% 6.26/2.07
% 6.26/2.07 % (1505)Memory used [KB]: 7036
% 6.26/2.07 % (1505)Time elapsed: 0.042 s
% 6.26/2.07 % (1505)Instructions burned: 150 (million)
% 6.26/2.07 % (1505)------------------------------
% 6.26/2.07 % (1505)------------------------------
% 6.26/2.08 % (1458)Instruction limit reached!
% 6.26/2.08 % (1458)------------------------------
% 6.26/2.08 % (1458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.08 % (1458)Termination reason: Unknown
% 6.26/2.08 % (1458)Termination phase: Saturation
% 6.26/2.08
% 6.26/2.08 % (1458)Memory used [KB]: 3582
% 6.26/2.08 % (1458)Time elapsed: 0.127 s
% 6.26/2.08 % (1458)Instructions burned: 433 (million)
% 6.26/2.08 % (1458)------------------------------
% 6.26/2.08 % (1458)------------------------------
% 6.26/2.08 % (1516)Instruction limit reached!
% 6.26/2.08 % (1516)------------------------------
% 6.26/2.08 % (1516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.08 % (1516)Termination reason: Unknown
% 6.26/2.08 % (1516)Termination phase: Property scanning
% 6.26/2.08
% 6.26/2.08 % (1516)Memory used [KB]: 2174
% 6.26/2.08 % (1516)Time elapsed: 0.031 s
% 6.26/2.08 % (1516)Instructions burned: 110 (million)
% 6.26/2.08 % (1516)------------------------------
% 6.26/2.08 % (1516)------------------------------
% 6.26/2.08 % (1528)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_1172 for (2994ds/140Mi)
% 6.26/2.09 % (1531)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_1172 for (2994ds/614Mi)
% 6.26/2.09 % (1535)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_1172 for (2994ds/202Mi)
% 6.26/2.11 % (1480)Instruction limit reached!
% 6.26/2.11 % (1480)------------------------------
% 6.26/2.11 % (1480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.11 % (1480)Termination reason: Unknown
% 6.26/2.11 % (1480)Termination phase: Saturation
% 6.26/2.11
% 6.26/2.11 % (1480)Memory used [KB]: 7931
% 6.26/2.11 % (1480)Time elapsed: 0.125 s
% 6.26/2.11 % (1480)Instructions burned: 454 (million)
% 6.26/2.11 % (1480)------------------------------
% 6.26/2.11 % (1480)------------------------------
% 6.76/2.12 % (1551)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_1172 for (2993ds/339Mi)
% 6.76/2.12 % (1528)Instruction limit reached!
% 6.76/2.12 % (1528)------------------------------
% 6.76/2.12 % (1528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.12 % (1528)Termination reason: Unknown
% 6.76/2.12 % (1528)Termination phase: Saturation
% 6.76/2.12
% 6.76/2.12 % (1528)Memory used [KB]: 6908
% 6.76/2.12 % (1528)Time elapsed: 0.043 s
% 6.76/2.12 % (1528)Instructions burned: 141 (million)
% 6.76/2.12 % (1528)------------------------------
% 6.76/2.12 % (1528)------------------------------
% 6.76/2.13 % (1520)Instruction limit reached!
% 6.76/2.13 % (1520)------------------------------
% 6.76/2.13 % (1520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.13 % (1520)Termination reason: Unknown
% 6.76/2.13 % (1520)Termination phase: Saturation
% 6.76/2.13
% 6.76/2.13 % (1520)Memory used [KB]: 7547
% 6.76/2.13 % (1520)Time elapsed: 0.074 s
% 6.76/2.13 % (1520)Instructions burned: 254 (million)
% 6.76/2.13 % (1520)------------------------------
% 6.76/2.13 % (1520)------------------------------
% 6.76/2.13 % (1560)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_1172 for (2993ds/283Mi)
% 6.76/2.14 % (1561)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_1172 for (2993ds/134Mi)
% 6.76/2.14 % (1511)Instruction limit reached!
% 6.76/2.14 % (1511)------------------------------
% 6.76/2.14 % (1511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.14 % (1511)Termination reason: Unknown
% 6.76/2.14 % (1511)Termination phase: Saturation
% 6.76/2.14
% 6.76/2.14 % (1511)Memory used [KB]: 7547
% 6.76/2.14 % (1511)Time elapsed: 0.105 s
% 6.76/2.14 % (1511)Instructions burned: 345 (million)
% 6.76/2.14 % (1511)------------------------------
% 6.76/2.14 % (1511)------------------------------
% 6.76/2.15 % (1535)Instruction limit reached!
% 6.76/2.15 % (1535)------------------------------
% 6.76/2.15 % (1535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.15 % (1535)Termination reason: Unknown
% 6.76/2.15 % (1535)Termination phase: Saturation
% 6.76/2.15
% 6.76/2.15 % (1535)Memory used [KB]: 7291
% 6.76/2.15 % (1535)Time elapsed: 0.060 s
% 6.76/2.15 % (1535)Instructions burned: 202 (million)
% 6.76/2.15 % (1535)------------------------------
% 6.76/2.15 % (1535)------------------------------
% 6.76/2.15 % (1570)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_1172 for (2993ds/298Mi)
% 6.76/2.16 % (1573)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_1172 for (2993ds/192Mi)
% 6.76/2.17 % (1561)Instruction limit reached!
% 6.76/2.17 % (1561)------------------------------
% 6.76/2.17 % (1561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.76/2.17 % (1561)Termination reason: Unknown
% 6.76/2.17 % (1561)Termination phase: Saturation
% 6.76/2.17
% 6.76/2.17 % (1561)Memory used [KB]: 6908
% 6.76/2.17 % (1561)Time elapsed: 0.038 s
% 6.76/2.17 % (1561)Instructions burned: 136 (million)
% 6.76/2.17 % (1561)------------------------------
% 6.76/2.17 % (1561)------------------------------
% 6.76/2.18 % (1588)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_1172 for (2993ds/258Mi)
% 7.23/2.21 % (1560)Instruction limit reached!
% 7.23/2.21 % (1560)------------------------------
% 7.23/2.21 % (1560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.21 % (1560)Termination reason: Unknown
% 7.23/2.21 % (1560)Termination phase: Saturation
% 7.23/2.21
% 7.23/2.21 % (1560)Memory used [KB]: 7547
% 7.23/2.21 % (1560)Time elapsed: 0.080 s
% 7.23/2.21 % (1560)Instructions burned: 284 (million)
% 7.23/2.21 % (1560)------------------------------
% 7.23/2.21 % (1560)------------------------------
% 7.23/2.21 % (1573)Instruction limit reached!
% 7.23/2.21 % (1573)------------------------------
% 7.23/2.21 % (1573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.21 % (1573)Termination reason: Unknown
% 7.23/2.21 % (1573)Termination phase: Saturation
% 7.23/2.21
% 7.23/2.21 % (1573)Memory used [KB]: 3198
% 7.23/2.21 % (1573)Time elapsed: 0.058 s
% 7.23/2.21 % (1573)Instructions burned: 194 (million)
% 7.23/2.21 % (1573)------------------------------
% 7.23/2.21 % (1573)------------------------------
% 7.23/2.22 % (1551)Instruction limit reached!
% 7.23/2.22 % (1551)------------------------------
% 7.23/2.22 % (1551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.22 % (1551)Termination reason: Unknown
% 7.23/2.22 % (1551)Termination phase: Saturation
% 7.23/2.22
% 7.23/2.22 % (1551)Memory used [KB]: 7164
% 7.23/2.22 % (1551)Time elapsed: 0.099 s
% 7.23/2.22 % (1551)Instructions burned: 342 (million)
% 7.23/2.22 % (1551)------------------------------
% 7.23/2.22 % (1551)------------------------------
% 7.23/2.22 % (1605)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_1172 for (2992ds/90Mi)
% 7.23/2.22 % (1607)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_1172 for (2992ds/231Mi)
% 7.23/2.23 % (1610)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_1172 for (2992ds/458Mi)
% 7.23/2.23 % (1570)Instruction limit reached!
% 7.23/2.23 % (1570)------------------------------
% 7.23/2.23 % (1570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.23 % (1570)Termination reason: Unknown
% 7.23/2.23 % (1570)Termination phase: Saturation
% 7.23/2.23
% 7.23/2.23 % (1570)Memory used [KB]: 7803
% 7.23/2.23 % (1570)Time elapsed: 0.080 s
% 7.23/2.23 % (1570)Instructions burned: 299 (million)
% 7.23/2.23 % (1570)------------------------------
% 7.23/2.23 % (1570)------------------------------
% 7.23/2.24 % (1621)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_1172 for (2992ds/31Mi)
% 7.23/2.25 % (1605)Instruction limit reached!
% 7.23/2.25 % (1605)------------------------------
% 7.23/2.25 % (1605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.25 % (1605)Termination reason: Unknown
% 7.23/2.25 % (1605)Termination phase: Property scanning
% 7.23/2.25
% 7.23/2.25 % (1605)Memory used [KB]: 2174
% 7.23/2.25 % (1605)Time elapsed: 0.026 s
% 7.23/2.25 % (1605)Instructions burned: 90 (million)
% 7.23/2.25 % (1605)------------------------------
% 7.23/2.25 % (1605)------------------------------
% 7.23/2.25 % (1621)Instruction limit reached!
% 7.23/2.25 % (1621)------------------------------
% 7.23/2.25 % (1621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.25 % (1621)Termination reason: Unknown
% 7.23/2.25 % (1621)Termination phase: Property scanning
% 7.23/2.25
% 7.23/2.25 % (1621)Memory used [KB]: 1791
% 7.23/2.25 % (1621)Time elapsed: 0.011 s
% 7.23/2.25 % (1621)Instructions burned: 33 (million)
% 7.23/2.25 % (1621)------------------------------
% 7.23/2.25 % (1621)------------------------------
% 7.23/2.26 % (1625)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_1172 for (2992ds/297Mi)
% 7.23/2.26 % (1588)Instruction limit reached!
% 7.23/2.26 % (1588)------------------------------
% 7.23/2.26 % (1588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.26 % (1588)Termination reason: Unknown
% 7.23/2.26 % (1588)Termination phase: Saturation
% 7.23/2.26
% 7.23/2.26 % (1588)Memory used [KB]: 7675
% 7.23/2.26 % (1588)Time elapsed: 0.075 s
% 7.23/2.26 % (1588)Instructions burned: 258 (million)
% 7.23/2.26 % (1588)------------------------------
% 7.23/2.26 % (1588)------------------------------
% 7.23/2.26 % (1451)Instruction limit reached!
% 7.23/2.26 % (1451)------------------------------
% 7.23/2.26 % (1451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.26 % (1451)Termination reason: Unknown
% 7.23/2.26 % (1451)Termination phase: Saturation
% 7.23/2.26
% 7.23/2.26 % (1451)Memory used [KB]: 7803
% 7.23/2.26 % (1451)Time elapsed: 0.338 s
% 7.23/2.26 % (1451)Instructions burned: 1090 (million)
% 7.23/2.26 % (1451)------------------------------
% 7.23/2.26 % (1451)------------------------------
% 7.23/2.26 % (1630)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_1172 for (2992ds/987Mi)
% 7.23/2.27 % (1531)Instruction limit reached!
% 7.23/2.27 % (1531)------------------------------
% 7.23/2.27 % (1531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.27 % (1531)Termination reason: Unknown
% 7.23/2.27 % (1531)Termination phase: Saturation
% 7.23/2.27
% 7.23/2.27 % (1531)Memory used [KB]: 8955
% 7.23/2.27 % (1531)Time elapsed: 0.184 s
% 7.23/2.27 % (1531)Instructions burned: 616 (million)
% 7.23/2.27 % (1531)------------------------------
% 7.23/2.27 % (1531)------------------------------
% 7.23/2.27 % (1633)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_1172 for (2992ds/182Mi)
% 7.23/2.27 % (1635)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_1172 for (2992ds/182Mi)
% 7.23/2.28 % (1639)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_1172 for (2992ds/154Mi)
% 7.23/2.28 % (1607)Instruction limit reached!
% 7.23/2.28 % (1607)------------------------------
% 7.23/2.28 % (1607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.23/2.28 % (1607)Termination reason: Unknown
% 7.23/2.28 % (1607)Termination phase: Saturation
% 7.23/2.28
% 7.23/2.28 % (1607)Memory used [KB]: 7419
% 7.23/2.28 % (1607)Time elapsed: 0.062 s
% 7.23/2.28 % (1607)Instructions burned: 232 (million)
% 7.23/2.28 % (1607)------------------------------
% 7.23/2.28 % (1607)------------------------------
% 7.23/2.29 % (1644)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_1172 for (2992ds/79Mi)
% 8.05/2.32 % (1644)Instruction limit reached!
% 8.05/2.32 % (1644)------------------------------
% 8.05/2.32 % (1644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.32 % (1644)Termination reason: Unknown
% 8.05/2.32 % (1644)Termination phase: Property scanning
% 8.05/2.32
% 8.05/2.32 % (1644)Memory used [KB]: 2174
% 8.05/2.32 % (1644)Time elapsed: 0.024 s
% 8.05/2.32 % (1644)Instructions burned: 80 (million)
% 8.05/2.32 % (1644)------------------------------
% 8.05/2.32 % (1644)------------------------------
% 8.05/2.32 % (1639)Instruction limit reached!
% 8.05/2.32 % (1639)------------------------------
% 8.05/2.32 % (1639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.32 % (1639)Termination reason: Unknown
% 8.05/2.32 % (1639)Termination phase: Property scanning
% 8.05/2.32
% 8.05/2.32 % (1639)Memory used [KB]: 2686
% 8.05/2.32 % (1639)Time elapsed: 0.041 s
% 8.05/2.32 % (1639)Instructions burned: 156 (million)
% 8.05/2.32 % (1639)------------------------------
% 8.05/2.32 % (1639)------------------------------
% 8.05/2.32 % (1633)Instruction limit reached!
% 8.05/2.32 % (1633)------------------------------
% 8.05/2.32 % (1633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.32 % (1633)Termination reason: Unknown
% 8.05/2.32 % (1633)Termination phase: Saturation
% 8.05/2.32
% 8.05/2.32 % (1633)Memory used [KB]: 7036
% 8.05/2.32 % (1633)Time elapsed: 0.051 s
% 8.05/2.32 % (1633)Instructions burned: 183 (million)
% 8.05/2.32 % (1633)------------------------------
% 8.05/2.32 % (1633)------------------------------
% 8.05/2.32 % (1635)Instruction limit reached!
% 8.05/2.32 % (1635)------------------------------
% 8.05/2.32 % (1635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.32 % (1635)Termination reason: Unknown
% 8.05/2.32 % (1635)Termination phase: Saturation
% 8.05/2.32
% 8.05/2.32 % (1635)Memory used [KB]: 6908
% 8.05/2.32 % (1635)Time elapsed: 0.056 s
% 8.05/2.32 % (1635)Instructions burned: 182 (million)
% 8.05/2.32 % (1635)------------------------------
% 8.05/2.32 % (1635)------------------------------
% 8.05/2.33 % (1661)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_1172 for (2991ds/216Mi)
% 8.05/2.33 % (1665)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_1172 for (2991ds/922Mi)
% 8.05/2.33 % (1667)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_1172 for (2991ds/182Mi)
% 8.05/2.34 % (1664)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_1172 for (2991ds/114Mi)
% 8.05/2.34 % (1625)Instruction limit reached!
% 8.05/2.34 % (1625)------------------------------
% 8.05/2.34 % (1625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.34 % (1625)Termination reason: Unknown
% 8.05/2.34 % (1625)Termination phase: Saturation
% 8.05/2.34
% 8.05/2.34 % (1625)Memory used [KB]: 7547
% 8.05/2.34 % (1625)Time elapsed: 0.108 s
% 8.05/2.34 % (1625)Instructions burned: 297 (million)
% 8.05/2.34 % (1625)------------------------------
% 8.05/2.34 % (1625)------------------------------
% 8.05/2.35 % (1671)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_1172 for (2991ds/164Mi)
% 8.05/2.37 % (1610)Instruction limit reached!
% 8.05/2.37 % (1610)------------------------------
% 8.05/2.37 % (1610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.37 % (1610)Termination reason: Unknown
% 8.05/2.37 % (1610)Termination phase: Saturation
% 8.05/2.37
% 8.05/2.37 % (1610)Memory used [KB]: 8187
% 8.05/2.37 % (1610)Time elapsed: 0.141 s
% 8.05/2.37 % (1610)Instructions burned: 459 (million)
% 8.05/2.37 % (1610)------------------------------
% 8.05/2.37 % (1610)------------------------------
% 8.05/2.38 % (1689)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_1172 for (2991ds/50Mi)
% 8.05/2.38 % (1667)Instruction limit reached!
% 8.05/2.38 % (1667)------------------------------
% 8.05/2.38 % (1667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.38 % (1667)Termination reason: Unknown
% 8.05/2.38 % (1667)Termination phase: Saturation
% 8.05/2.38
% 8.05/2.38 % (1667)Memory used [KB]: 7164
% 8.05/2.38 % (1667)Time elapsed: 0.047 s
% 8.05/2.38 % (1667)Instructions burned: 182 (million)
% 8.05/2.38 % (1667)------------------------------
% 8.05/2.38 % (1667)------------------------------
% 8.05/2.38 % (1661)Instruction limit reached!
% 8.05/2.38 % (1661)------------------------------
% 8.05/2.38 % (1661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.38 % (1661)Termination reason: Unknown
% 8.05/2.38 % (1661)Termination phase: Saturation
% 8.05/2.38
% 8.05/2.38 % (1661)Memory used [KB]: 7164
% 8.05/2.38 % (1661)Time elapsed: 0.057 s
% 8.05/2.38 % (1661)Instructions burned: 216 (million)
% 8.05/2.38 % (1661)------------------------------
% 8.05/2.38 % (1661)------------------------------
% 8.05/2.39 % (1692)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_1172 for (2991ds/368Mi)
% 8.05/2.39 % (1671)Instruction limit reached!
% 8.05/2.39 % (1671)------------------------------
% 8.05/2.39 % (1671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.39 % (1671)Termination reason: Unknown
% 8.05/2.39 % (1671)Termination phase: Saturation
% 8.05/2.39
% 8.05/2.39 % (1671)Memory used [KB]: 2430
% 8.05/2.39 % (1671)Time elapsed: 0.043 s
% 8.05/2.39 % (1671)Instructions burned: 165 (million)
% 8.05/2.39 % (1671)------------------------------
% 8.05/2.39 % (1671)------------------------------
% 8.05/2.39 % (1689)Instruction limit reached!
% 8.05/2.39 % (1689)------------------------------
% 8.05/2.39 % (1689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.39 % (1689)Termination reason: Unknown
% 8.05/2.39 % (1689)Termination phase: shuffling
% 8.05/2.39
% 8.05/2.39 % (1689)Memory used [KB]: 2302
% 8.05/2.39 % (1689)Time elapsed: 0.015 s
% 8.05/2.39 % (1689)Instructions burned: 53 (million)
% 8.05/2.39 % (1689)------------------------------
% 8.05/2.39 % (1689)------------------------------
% 8.05/2.39 % (1693)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_1172 for (2991ds/1021Mi)
% 8.05/2.40 % (1664)Instruction limit reached!
% 8.05/2.40 % (1664)------------------------------
% 8.05/2.40 % (1664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.05/2.40 % (1664)Termination reason: Unknown
% 8.05/2.40 % (1664)Termination phase: Saturation
% 8.05/2.40
% 8.05/2.40 % (1664)Memory used [KB]: 6652
% 8.05/2.40 % (1664)Time elapsed: 0.062 s
% 8.05/2.40 % (1664)Instructions burned: 114 (million)
% 8.05/2.40 % (1664)------------------------------
% 8.05/2.40 % (1664)------------------------------
% 8.69/2.40 % (1696)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_1172 for (2991ds/267Mi)
% 8.69/2.40 % (1697)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_1172 for (2991ds/204Mi)
% 8.69/2.41 % (1705)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_1172 for (2990ds/26Mi)
% 8.69/2.42 % (1705)Instruction limit reached!
% 8.69/2.42 % (1705)------------------------------
% 8.69/2.42 % (1705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.69/2.42 % (1705)Termination reason: Unknown
% 8.69/2.42 % (1705)Termination phase: shuffling
% 8.69/2.42
% 8.69/2.42 % (1705)Memory used [KB]: 1918
% 8.69/2.42 % (1705)Time elapsed: 0.009 s
% 8.69/2.42 % (1705)Instructions burned: 28 (million)
% 8.69/2.42 % (1705)------------------------------
% 8.69/2.42 % (1705)------------------------------
% 8.69/2.43 % (1722)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_1172 for (2990ds/53Mi)
% 8.69/2.44 % (1722)Instruction limit reached!
% 8.69/2.44 % (1722)------------------------------
% 8.69/2.44 % (1722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.69/2.44 % (1722)Termination reason: Unknown
% 8.69/2.44 % (1722)Termination phase: Property scanning
% 8.69/2.44
% 8.69/2.44 % (1722)Memory used [KB]: 2302
% 8.69/2.44 % (1722)Time elapsed: 0.017 s
% 8.69/2.44 % (1722)Instructions burned: 56 (million)
% 8.69/2.44 % (1722)------------------------------
% 8.69/2.44 % (1722)------------------------------
% 8.69/2.45 % (1738)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_1172 for (2990ds/4436Mi)
% 8.69/2.46 % (1697)Instruction limit reached!
% 8.69/2.46 % (1697)------------------------------
% 8.69/2.46 % (1697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.69/2.46 % (1697)Termination reason: Unknown
% 8.69/2.46 % (1697)Termination phase: Saturation
% 8.69/2.46
% 8.69/2.46 % (1697)Memory used [KB]: 7164
% 8.69/2.46 % (1697)Time elapsed: 0.058 s
% 8.69/2.46 % (1697)Instructions burned: 206 (million)
% 8.69/2.46 % (1697)------------------------------
% 8.69/2.46 % (1697)------------------------------
% 8.69/2.47 % (1744)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_1172 for (2990ds/1539Mi)
% 8.69/2.47 % (1696)Instruction limit reached!
% 8.69/2.47 % (1696)------------------------------
% 8.69/2.47 % (1696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.69/2.47 % (1696)Termination reason: Unknown
% 8.69/2.47 % (1696)Termination phase: Saturation
% 8.69/2.47
% 8.69/2.47 % (1696)Memory used [KB]: 7547
% 8.69/2.47 % (1696)Time elapsed: 0.074 s
% 8.69/2.47 % (1696)Instructions burned: 268 (million)
% 8.69/2.47 % (1696)------------------------------
% 8.69/2.47 % (1696)------------------------------
% 8.69/2.48 % (1745)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_1172 for (2990ds/408Mi)
% 8.69/2.49 % (1692)Instruction limit reached!
% 8.69/2.49 % (1692)------------------------------
% 8.69/2.49 % (1692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.69/2.49 % (1692)Termination reason: Unknown
% 8.69/2.49 % (1692)Termination phase: Saturation
% 8.69/2.49
% 8.69/2.49 % (1692)Memory used [KB]: 7675
% 8.69/2.49 % (1692)Time elapsed: 0.103 s
% 8.69/2.49 % (1692)Instructions burned: 368 (million)
% 8.69/2.49 % (1692)------------------------------
% 8.69/2.49 % (1692)------------------------------
% 9.07/2.50 % (1746)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_1172 for (2990ds/5205Mi)
% 9.07/2.56 % (1630)Instruction limit reached!
% 9.07/2.56 % (1630)------------------------------
% 9.07/2.56 % (1630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.07/2.56 % (1630)Termination reason: Unknown
% 9.07/2.56 % (1630)Termination phase: Saturation
% 9.07/2.56
% 9.07/2.56 % (1630)Memory used [KB]: 9594
% 9.07/2.56 % (1630)Time elapsed: 0.325 s
% 9.07/2.56 % (1630)Instructions burned: 987 (million)
% 9.07/2.56 % (1630)------------------------------
% 9.07/2.56 % (1630)------------------------------
% 9.07/2.57 % (1747)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_1172 for (2989ds/1913Mi)
% 9.39/2.60 % (1745)Instruction limit reached!
% 9.39/2.60 % (1745)------------------------------
% 9.39/2.60 % (1745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.39/2.60 % (1745)Termination reason: Unknown
% 9.39/2.60 % (1745)Termination phase: Saturation
% 9.39/2.60
% 9.39/2.60 % (1745)Memory used [KB]: 7803
% 9.39/2.60 % (1745)Time elapsed: 0.120 s
% 9.39/2.60 % (1745)Instructions burned: 411 (million)
% 9.39/2.60 % (1745)------------------------------
% 9.39/2.60 % (1745)------------------------------
% 9.39/2.61 % (1748)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_1172 for (2988ds/4350Mi)
% 9.39/2.61 % (1665)Instruction limit reached!
% 9.39/2.61 % (1665)------------------------------
% 9.39/2.61 % (1665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.39/2.61 % (1665)Termination reason: Unknown
% 9.39/2.61 % (1665)Termination phase: Saturation
% 9.39/2.61
% 9.39/2.61 % (1665)Memory used [KB]: 8315
% 9.39/2.61 % (1665)Time elapsed: 0.286 s
% 9.39/2.61 % (1665)Instructions burned: 923 (million)
% 9.39/2.61 % (1665)------------------------------
% 9.39/2.61 % (1665)------------------------------
% 9.39/2.62 % (1749)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_1172 for (2988ds/68Mi)
% 9.39/2.64 % (1749)Instruction limit reached!
% 9.39/2.64 % (1749)------------------------------
% 9.39/2.64 % (1749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.39/2.64 % (1749)Termination reason: Unknown
% 9.39/2.64 % (1749)Termination phase: Property scanning
% 9.39/2.64
% 9.39/2.64 % (1749)Memory used [KB]: 2046
% 9.39/2.64 % (1749)Time elapsed: 0.021 s
% 9.39/2.64 % (1749)Instructions burned: 71 (million)
% 9.39/2.64 % (1749)------------------------------
% 9.39/2.64 % (1749)------------------------------
% 9.39/2.65 % (1750)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_1172 for (2988ds/358Mi)
% 9.84/2.70 % (1693)Instruction limit reached!
% 9.84/2.70 % (1693)------------------------------
% 9.84/2.70 % (1693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.84/2.70 % (1693)Termination reason: Unknown
% 9.84/2.70 % (1693)Termination phase: Saturation
% 9.84/2.70
% 9.84/2.70 % (1693)Memory used [KB]: 8443
% 9.84/2.70 % (1693)Time elapsed: 0.311 s
% 9.84/2.70 % (1693)Instructions burned: 1022 (million)
% 9.84/2.70 % (1693)------------------------------
% 9.84/2.70 % (1693)------------------------------
% 9.84/2.71 % (1751)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_1172 for (2987ds/31Mi)
% 9.84/2.72 % (1751)Instruction limit reached!
% 9.84/2.72 % (1751)------------------------------
% 9.84/2.72 % (1751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.84/2.72 % (1751)Termination reason: Unknown
% 9.84/2.72 % (1751)Termination phase: Property scanning
% 9.84/2.72
% 9.84/2.72 % (1751)Memory used [KB]: 1663
% 9.84/2.72 % (1751)Time elapsed: 0.010 s
% 9.84/2.72 % (1751)Instructions burned: 31 (million)
% 9.84/2.72 % (1751)------------------------------
% 9.84/2.72 % (1751)------------------------------
% 9.84/2.73 % (1752)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_1172 for (2987ds/279Mi)
% 9.84/2.76 % (1750)Instruction limit reached!
% 9.84/2.76 % (1750)------------------------------
% 9.84/2.76 % (1750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.84/2.76 % (1750)Termination reason: Unknown
% 9.84/2.76 % (1750)Termination phase: Saturation
% 9.84/2.76
% 9.84/2.76 % (1750)Memory used [KB]: 7291
% 9.84/2.76 % (1750)Time elapsed: 0.109 s
% 9.84/2.76 % (1750)Instructions burned: 358 (million)
% 9.84/2.76 % (1750)------------------------------
% 9.84/2.76 % (1750)------------------------------
% 9.84/2.77 % (1753)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_1172 for (2987ds/258Mi)
% 9.84/2.77 % (1752)Refutation not found, incomplete strategy
% 9.84/2.77 % (1752)------------------------------
% 9.84/2.77 % (1752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.84/2.77 % (1752)Termination reason: Refutation not found, incomplete strategy
% 9.84/2.77
% 9.84/2.77
% 9.84/2.77 % (1752)Memory used [KB]: 7164
% 9.84/2.77 % (1752)Time elapsed: 0.043 s
% 9.84/2.77 % (1752)Instructions burned: 163 (million)
% 9.84/2.77 % (1752)------------------------------
% 9.84/2.77 % (1752)------------------------------
% 9.84/2.78 % (1754)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_1172 for (2987ds/26Mi)
% 9.84/2.79 % (1754)Instruction limit reached!
% 9.84/2.79 % (1754)------------------------------
% 9.84/2.79 % (1754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.84/2.79 % (1754)Termination reason: Unknown
% 9.84/2.79 % (1754)Termination phase: shuffling
% 9.84/2.79
% 9.84/2.79 % (1754)Memory used [KB]: 1918
% 9.84/2.79 % (1754)Time elapsed: 0.008 s
% 9.84/2.79 % (1754)Instructions burned: 27 (million)
% 9.84/2.79 % (1754)------------------------------
% 9.84/2.79 % (1754)------------------------------
% 10.37/2.80 % (1755)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_1172 for (2987ds/995Mi)
% 10.37/2.85 % (1753)Instruction limit reached!
% 10.37/2.85 % (1753)------------------------------
% 10.37/2.85 % (1753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.37/2.85 % (1753)Termination reason: Unknown
% 10.37/2.85 % (1753)Termination phase: Saturation
% 10.37/2.85
% 10.37/2.85 % (1753)Memory used [KB]: 7419
% 10.37/2.85 % (1753)Time elapsed: 0.080 s
% 10.37/2.85 % (1753)Instructions burned: 259 (million)
% 10.37/2.85 % (1753)------------------------------
% 10.37/2.85 % (1753)------------------------------
% 10.37/2.86 % (1756)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_1172 for (2986ds/373Mi)
% 10.46/2.94 % (1744)Instruction limit reached!
% 10.46/2.94 % (1744)------------------------------
% 10.46/2.94 % (1744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.46/2.94 % (1744)Termination reason: Unknown
% 10.46/2.94 % (1744)Termination phase: Saturation
% 10.46/2.94
% 10.46/2.94 % (1744)Memory used [KB]: 10106
% 10.46/2.94 % (1744)Time elapsed: 0.478 s
% 10.46/2.94 % (1744)Instructions burned: 1540 (million)
% 10.46/2.94 % (1744)------------------------------
% 10.46/2.94 % (1744)------------------------------
% 10.46/2.95 % (1757)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_1172 for (2985ds/253Mi)
% 10.46/2.97 % (1756)Instruction limit reached!
% 10.46/2.97 % (1756)------------------------------
% 10.46/2.97 % (1756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.46/2.97 % (1756)Termination reason: Unknown
% 10.46/2.97 % (1756)Termination phase: Saturation
% 10.46/2.97
% 10.46/2.97 % (1756)Memory used [KB]: 7675
% 10.46/2.97 % (1756)Time elapsed: 0.111 s
% 10.46/2.97 % (1756)Instructions burned: 375 (million)
% 10.46/2.97 % (1756)------------------------------
% 10.46/2.97 % (1756)------------------------------
% 10.46/2.98 % (1758)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_1172 for (2985ds/832Mi)
% 13.27/3.02 % (1757)Instruction limit reached!
% 13.27/3.02 % (1757)------------------------------
% 13.27/3.02 % (1757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.27/3.02 % (1757)Termination reason: Unknown
% 13.27/3.02 % (1757)Termination phase: Saturation
% 13.27/3.02
% 13.27/3.02 % (1757)Memory used [KB]: 7803
% 13.27/3.02 % (1757)Time elapsed: 0.066 s
% 13.27/3.02 % (1757)Instructions burned: 254 (million)
% 13.27/3.02 % (1757)------------------------------
% 13.27/3.02 % (1757)------------------------------
% 13.27/3.03 % (1759)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_1172 for (2984ds/668Mi)
% 13.27/3.10 % (1755)Instruction limit reached!
% 13.27/3.10 % (1755)------------------------------
% 13.27/3.10 % (1755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.27/3.10 % (1755)Termination reason: Unknown
% 13.27/3.10 % (1755)Termination phase: Saturation
% 13.27/3.10
% 13.27/3.10 % (1755)Memory used [KB]: 9850
% 13.27/3.10 % (1755)Time elapsed: 0.298 s
% 13.27/3.10 % (1755)Instructions burned: 996 (million)
% 13.27/3.10 % (1755)------------------------------
% 13.27/3.10 % (1755)------------------------------
% 13.27/3.10 % (1760)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_1172 for (2984ds/40Mi)
% 13.92/3.12 % (1760)Instruction limit reached!
% 13.92/3.12 % (1760)------------------------------
% 13.92/3.12 % (1760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.92/3.12 % (1760)Termination reason: Unknown
% 13.92/3.12 % (1760)Termination phase: shuffling
% 13.92/3.12
% 13.92/3.12 % (1760)Memory used [KB]: 2174
% 13.92/3.12 % (1760)Time elapsed: 0.012 s
% 13.92/3.12 % (1760)Instructions burned: 41 (million)
% 13.92/3.12 % (1760)------------------------------
% 13.92/3.12 % (1760)------------------------------
% 13.92/3.13 % (1761)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_1172 for (2983ds/294Mi)
% 13.92/3.14 % (1747)Instruction limit reached!
% 13.92/3.14 % (1747)------------------------------
% 13.92/3.14 % (1747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.92/3.14 % (1747)Termination reason: Unknown
% 13.92/3.14 % (1747)Termination phase: Saturation
% 13.92/3.14
% 13.92/3.14 % (1747)Memory used [KB]: 4093
% 13.92/3.14 % (1747)Time elapsed: 0.565 s
% 13.92/3.14 % (1747)Instructions burned: 1913 (million)
% 13.92/3.14 % (1747)------------------------------
% 13.92/3.14 % (1747)------------------------------
% 13.92/3.15 % (1762)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_1172 for (2983ds/187Mi)
% 13.92/3.16 % (1761)Refutation not found, incomplete strategy
% 13.92/3.16 % (1761)------------------------------
% 13.92/3.16 % (1761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.92/3.16 % (1761)Termination reason: Refutation not found, incomplete strategy
% 13.92/3.16
% 13.92/3.16
% 13.92/3.16 % (1761)Memory used [KB]: 7164
% 13.92/3.16 % (1761)Time elapsed: 0.038 s
% 13.92/3.16 % (1761)Instructions burned: 141 (million)
% 13.92/3.16 % (1761)------------------------------
% 13.92/3.16 % (1761)------------------------------
% 13.92/3.17 % (1763)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_1172 for (2983ds/371Mi)
% 13.92/3.20 % (1762)Instruction limit reached!
% 13.92/3.20 % (1762)------------------------------
% 13.92/3.20 % (1762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.92/3.20 % (1762)Termination reason: Unknown
% 13.92/3.20 % (1762)Termination phase: Saturation
% 13.92/3.20
% 13.92/3.20 % (1762)Memory used [KB]: 7164
% 13.92/3.20 % (1762)Time elapsed: 0.052 s
% 13.92/3.20 % (1762)Instructions burned: 187 (million)
% 13.92/3.20 % (1762)------------------------------
% 13.92/3.20 % (1762)------------------------------
% 14.34/3.21 % (1764)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_1172 for (2982ds/1827Mi)
% 14.34/3.22 % (1759)Instruction limit reached!
% 14.34/3.22 % (1759)------------------------------
% 14.34/3.22 % (1759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.34/3.22 % (1759)Termination reason: Unknown
% 14.34/3.22 % (1759)Termination phase: Saturation
% 14.34/3.22
% 14.34/3.22 % (1759)Memory used [KB]: 14200
% 14.34/3.22 % (1759)Time elapsed: 0.195 s
% 14.34/3.22 % (1759)Instructions burned: 668 (million)
% 14.34/3.22 % (1759)------------------------------
% 14.34/3.22 % (1759)------------------------------
% 14.34/3.23 % (1758)Instruction limit reached!
% 14.34/3.23 % (1758)------------------------------
% 14.34/3.23 % (1758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.34/3.23 % (1758)Termination reason: Unknown
% 14.34/3.23 % (1758)Termination phase: Saturation
% 14.34/3.23
% 14.34/3.23 % (1758)Memory used [KB]: 7931
% 14.34/3.23 % (1758)Time elapsed: 0.250 s
% 14.34/3.23 % (1758)Instructions burned: 834 (million)
% 14.34/3.23 % (1758)------------------------------
% 14.34/3.23 % (1758)------------------------------
% 14.34/3.23 % (1765)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_1172 for (2982ds/70Mi)
% 14.34/3.24 % (1766)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_1172 for (2982ds/316Mi)
% 14.34/3.25 % (1765)Instruction limit reached!
% 14.34/3.25 % (1765)------------------------------
% 14.34/3.25 % (1765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.34/3.25 % (1765)Termination reason: Unknown
% 14.34/3.25 % (1765)Termination phase: Property scanning
% 14.34/3.25
% 14.34/3.25 % (1765)Memory used [KB]: 2302
% 14.34/3.25 % (1765)Time elapsed: 0.020 s
% 14.34/3.25 % (1765)Instructions burned: 73 (million)
% 14.34/3.25 % (1765)------------------------------
% 14.34/3.25 % (1765)------------------------------
% 14.34/3.26 % (1767)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_1172 for (2982ds/932Mi)
% 14.34/3.29 % (1763)Instruction limit reached!
% 14.34/3.29 % (1763)------------------------------
% 14.34/3.29 % (1763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.34/3.29 % (1763)Termination reason: Unknown
% 14.34/3.29 % (1763)Termination phase: Saturation
% 14.34/3.29
% 14.34/3.29 % (1763)Memory used [KB]: 7547
% 14.34/3.29 % (1763)Time elapsed: 0.135 s
% 14.34/3.29 % (1763)Instructions burned: 372 (million)
% 14.34/3.29 % (1763)------------------------------
% 14.34/3.29 % (1763)------------------------------
% 14.34/3.30 % (1768)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_1172 for (2982ds/4714Mi)
% 15.08/3.30 % (1766)Refutation not found, incomplete strategy
% 15.08/3.30 % (1766)------------------------------
% 15.08/3.30 % (1766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.08/3.30 % (1766)Termination reason: Refutation not found, incomplete strategy
% 15.08/3.30
% 15.08/3.30
% 15.08/3.30 % (1766)Memory used [KB]: 7547
% 15.08/3.30 % (1766)Time elapsed: 0.064 s
% 15.08/3.30 % (1766)Instructions burned: 237 (million)
% 15.08/3.30 % (1766)------------------------------
% 15.08/3.30 % (1766)------------------------------
% 15.08/3.31 % (1769)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_1172 for (2981ds/8250Mi)
% 15.08/3.36 % (1768)Refutation not found, incomplete strategy
% 15.08/3.36 % (1768)------------------------------
% 15.08/3.36 % (1768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.08/3.36 % (1768)Termination reason: Refutation not found, incomplete strategy
% 15.08/3.36
% 15.08/3.36
% 15.08/3.36 % (1768)Memory used [KB]: 7803
% 15.08/3.36 % (1768)Time elapsed: 0.065 s
% 15.08/3.36 % (1768)Instructions burned: 244 (million)
% 15.08/3.36 % (1768)------------------------------
% 15.08/3.36 % (1768)------------------------------
% 15.08/3.37 % (1770)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_1172 for (2981ds/770Mi)
% 15.84/3.53 % (1767)Instruction limit reached!
% 15.84/3.53 % (1767)------------------------------
% 15.84/3.53 % (1767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.84/3.53 % (1767)Termination reason: Unknown
% 15.84/3.53 % (1767)Termination phase: Saturation
% 15.84/3.53
% 15.84/3.53 % (1767)Memory used [KB]: 8699
% 15.84/3.53 % (1767)Time elapsed: 0.270 s
% 15.84/3.53 % (1767)Instructions burned: 935 (million)
% 15.84/3.53 % (1767)------------------------------
% 15.84/3.53 % (1767)------------------------------
% 15.84/3.54 % (1771)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_1172 for (2979ds/794Mi)
% 15.84/3.60 % (1770)Instruction limit reached!
% 15.84/3.60 % (1770)------------------------------
% 15.84/3.60 % (1770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.84/3.60 % (1770)Termination reason: Unknown
% 15.84/3.60 % (1770)Termination phase: Saturation
% 15.84/3.60
% 15.84/3.60 % (1770)Memory used [KB]: 8059
% 15.84/3.60 % (1770)Time elapsed: 0.227 s
% 15.84/3.60 % (1770)Instructions burned: 773 (million)
% 15.84/3.60 % (1770)------------------------------
% 15.84/3.60 % (1770)------------------------------
% 16.42/3.61 % (1772)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_1172 for (2978ds/464Mi)
% 16.95/3.74 % (1772)Instruction limit reached!
% 16.95/3.74 % (1772)------------------------------
% 16.95/3.74 % (1772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.95/3.74 % (1772)Termination reason: Unknown
% 16.95/3.74 % (1772)Termination phase: Saturation
% 16.95/3.74
% 16.95/3.74 % (1772)Memory used [KB]: 7675
% 16.95/3.74 % (1772)Time elapsed: 0.140 s
% 16.95/3.74 % (1772)Instructions burned: 464 (million)
% 16.95/3.74 % (1772)------------------------------
% 16.95/3.74 % (1772)------------------------------
% 16.95/3.75 % (1773)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_1172 for (2977ds/1376Mi)
% 16.95/3.77 % (1764)Instruction limit reached!
% 16.95/3.77 % (1764)------------------------------
% 16.95/3.77 % (1764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.95/3.77 % (1764)Termination reason: Unknown
% 16.95/3.77 % (1764)Termination phase: Saturation
% 16.95/3.77
% 16.95/3.77 % (1764)Memory used [KB]: 9210
% 16.95/3.77 % (1764)Time elapsed: 0.568 s
% 16.95/3.77 % (1764)Instructions burned: 1828 (million)
% 16.95/3.77 % (1764)------------------------------
% 16.95/3.77 % (1764)------------------------------
% 16.95/3.78 % (1774)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_1172 for (2977ds/906Mi)
% 16.95/3.79 % (1771)Instruction limit reached!
% 16.95/3.79 % (1771)------------------------------
% 16.95/3.79 % (1771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.95/3.79 % (1771)Termination reason: Unknown
% 16.95/3.79 % (1771)Termination phase: Saturation
% 16.95/3.79
% 16.95/3.79 % (1771)Memory used [KB]: 5117
% 16.95/3.79 % (1771)Time elapsed: 0.248 s
% 16.95/3.79 % (1771)Instructions burned: 795 (million)
% 16.95/3.79 % (1771)------------------------------
% 16.95/3.79 % (1771)------------------------------
% 16.95/3.80 % (1775)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_1172 for (2977ds/434Mi)
% 18.24/3.84 % (1738)Instruction limit reached!
% 18.24/3.84 % (1738)------------------------------
% 18.24/3.84 % (1738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.24/3.84 % (1738)Termination reason: Unknown
% 18.24/3.84 % (1738)Termination phase: Saturation
% 18.24/3.84
% 18.24/3.84 % (1738)Memory used [KB]: 11897
% 18.24/3.84 % (1738)Time elapsed: 1.397 s
% 18.24/3.84 % (1738)Instructions burned: 4438 (million)
% 18.24/3.84 % (1738)------------------------------
% 18.24/3.84 % (1738)------------------------------
% 18.24/3.85 % (1776)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_1172 for (2976ds/865Mi)
% 18.24/3.89 % (1775)First to succeed.
% 18.24/3.89 % (1775)Refutation found. Thanks to Tanya!
% 18.24/3.89 % SZS status Theorem for DTF2THF_1172
% 18.24/3.89 % SZS output start Proof for DTF2THF_1172
% 18.24/3.89 thf(type_def_5, type, nat: $tType).
% 18.24/3.89 thf(type_def_6, type, real: $tType).
% 18.24/3.89 thf(type_def_8, type, num: $tType).
% 18.24/3.89 thf(type_def_9, type, set_real: $tType).
% 18.24/3.89 thf(func_def_0, type, set_real: $tType).
% 18.24/3.89 thf(func_def_1, type, real: $tType).
% 18.24/3.89 thf(func_def_2, type, num: $tType).
% 18.24/3.89 thf(func_def_3, type, nat: $tType).
% 18.24/3.89 thf(func_def_4, type, genClo1161277105lle_PC: nat > real > real).
% 18.24/3.89 thf(func_def_5, type, genClo1144207539le_rho: real).
% 18.24/3.89 thf(func_def_6, type, genClo1015804716orrect: nat > real > $o).
% 18.24/3.89 thf(func_def_7, type, genClo293725281kRead1: (nat > real) > real > (nat > $o) > $o).
% 18.24/3.89 thf(func_def_8, type, genClo293725282kRead2: (nat > real) > (nat > real) > real > (nat > $o) > $o).
% 18.24/3.89 thf(func_def_9, type, genClo2108747022bound1: (nat > real > real) > $o).
% 18.24/3.89 thf(func_def_10, type, genClo2108747023bound2: (nat > real > real) > $o).
% 18.24/3.89 thf(func_def_11, type, abs_abs_real: real > real).
% 18.24/3.89 thf(func_def_12, type, minus_minus_nat: nat > nat > nat).
% 18.24/3.89 thf(func_def_13, type, minus_minus_real: real > real > real).
% 18.24/3.89 thf(func_def_14, type, one_one_nat: nat).
% 18.24/3.89 thf(func_def_15, type, one_one_real: real).
% 18.24/3.89 thf(func_def_16, type, plus_plus_nat: nat > nat > nat).
% 18.24/3.89 thf(func_def_17, type, plus_plus_num: num > num > num).
% 18.24/3.89 thf(func_def_18, type, plus_plus_real: real > real > real).
% 18.24/3.89 thf(func_def_19, type, times_times_nat: nat > nat > nat).
% 18.24/3.89 thf(func_def_20, type, times_times_num: num > num > num).
% 18.24/3.89 thf(func_def_21, type, times_times_real: real > real > real).
% 18.24/3.89 thf(func_def_22, type, neg_numeral_dbl_real: real > real).
% 18.24/3.89 thf(func_def_23, type, bit0: num > num).
% 18.24/3.89 thf(func_def_24, type, one: num).
% 18.24/3.89 thf(func_def_25, type, numeral_numeral_nat: num > nat).
% 18.24/3.89 thf(func_def_26, type, numeral_numeral_real: num > real).
% 18.24/3.89 thf(func_def_27, type, ord_less_eq_nat: nat > nat > $o).
% 18.24/3.89 thf(func_def_28, type, ord_less_eq_num: num > num > $o).
% 18.24/3.89 thf(func_def_29, type, ord_less_eq_real: real > real > $o).
% 18.24/3.89 thf(func_def_30, type, collect_real: (real > $o) > set_real).
% 18.24/3.89 thf(func_def_31, type, member_real: real > set_real > $o).
% 18.24/3.89 thf(func_def_32, type, c: nat > real > real).
% 18.24/3.89 thf(func_def_33, type, d: nat > real > real).
% 18.24/3.89 thf(func_def_34, type, p: nat).
% 18.24/3.89 thf(func_def_35, type, q: nat).
% 18.24/3.89 thf(func_def_36, type, s: real).
% 18.24/3.89 thf(func_def_37, type, t: real).
% 18.24/3.89 thf(func_def_52, type, sP0: num > num > num > $o).
% 18.24/3.89 thf(func_def_53, type, sP1: num > num > num > $o).
% 18.24/3.89 thf(func_def_54, type, sP2: num > num > num > $o).
% 18.24/3.89 thf(func_def_55, type, sP3: nat > nat > nat > $o).
% 18.24/3.89 thf(func_def_56, type, sP4: nat > nat > nat > $o).
% 18.24/3.89 thf(func_def_57, type, sP5: nat > nat > nat > $o).
% 18.24/3.89 thf(func_def_58, type, sP6: real > real > real > $o).
% 18.24/3.89 thf(func_def_59, type, sP7: real > real > real > $o).
% 18.24/3.89 thf(func_def_60, type, sP8: real > real > real > $o).
% 18.24/3.89 thf(func_def_61, type, sK9: (real > num) > real).
% 18.24/3.89 thf(func_def_62, type, sK10: (real > num) > real).
% 18.24/3.89 thf(func_def_63, type, sK11: (num > real) > num).
% 18.24/3.89 thf(func_def_64, type, sK12: (num > real) > num).
% 18.24/3.89 thf(func_def_65, type, sK13: (nat > real) > nat).
% 18.24/3.89 thf(func_def_66, type, sK14: (nat > real) > nat).
% 18.24/3.89 thf(func_def_67, type, sK15: (real > num) > real).
% 18.24/3.89 thf(func_def_68, type, sK16: (real > num) > real).
% 18.24/3.89 thf(func_def_69, type, sK17: (nat > nat) > nat).
% 18.24/3.89 thf(func_def_70, type, sK18: (nat > nat) > nat).
% 18.24/3.89 thf(func_def_71, type, sK19: (nat > real) > nat).
% 18.24/3.89 thf(func_def_72, type, sK20: (nat > real) > nat).
% 18.24/3.89 thf(func_def_73, type, sK21: (num > num) > num).
% 18.24/3.89 thf(func_def_74, type, sK22: (num > num) > num).
% 18.24/3.89 thf(func_def_75, type, sK23: (num > num) > num).
% 18.24/3.89 thf(func_def_76, type, sK24: (num > num) > num).
% 18.24/3.89 thf(func_def_77, type, sK25: (real > nat) > real).
% 18.24/3.89 thf(func_def_78, type, sK26: (real > nat) > real).
% 18.24/3.89 thf(func_def_79, type, sK27: (nat > nat) > nat).
% 18.24/3.89 thf(func_def_80, type, sK28: (nat > nat) > nat).
% 18.24/3.89 thf(func_def_81, type, sK29: (nat > nat) > nat).
% 18.24/3.89 thf(func_def_82, type, sK30: (nat > nat) > nat).
% 18.24/3.89 thf(func_def_83, type, sK31: (real > nat) > real).
% 18.24/3.89 thf(func_def_84, type, sK32: (real > nat) > real).
% 18.24/3.89 thf(func_def_85, type, sK33: (real > real) > real).
% 18.24/3.89 thf(func_def_86, type, sK34: (real > real) > real).
% 18.24/3.89 thf(func_def_87, type, sK35: (num > num) > num).
% 18.24/3.89 thf(func_def_88, type, sK36: (num > num) > num).
% 18.24/3.89 thf(func_def_89, type, sK37: (num > nat) > num).
% 18.24/3.89 thf(func_def_90, type, sK38: (num > nat) > num).
% 18.24/3.89 thf(func_def_91, type, sK39: (num > real) > num).
% 18.24/3.89 thf(func_def_92, type, sK40: (num > real) > num).
% 18.24/3.89 thf(func_def_93, type, sK41: (nat > nat) > nat).
% 18.24/3.89 thf(func_def_94, type, sK42: (nat > nat) > nat).
% 18.24/3.89 thf(func_def_95, type, sK43: (num > nat) > num).
% 18.24/3.89 thf(func_def_96, type, sK44: (num > nat) > num).
% 18.24/3.89 thf(func_def_97, type, sK45: (nat > num) > nat).
% 18.24/3.89 thf(func_def_98, type, sK46: (nat > num) > nat).
% 18.24/3.89 thf(func_def_99, type, sK47: (real > nat) > real).
% 18.24/3.89 thf(func_def_100, type, sK48: (real > nat) > real).
% 18.24/3.89 thf(func_def_101, type, sK49: (real > nat) > real).
% 18.24/3.89 thf(func_def_102, type, sK50: (real > nat) > real).
% 18.24/3.89 thf(func_def_103, type, sK51: (nat > num) > nat).
% 18.24/3.89 thf(func_def_104, type, sK52: (nat > num) > nat).
% 18.24/3.89 thf(func_def_105, type, sK53: (nat > num) > nat).
% 18.24/3.89 thf(func_def_106, type, sK54: (nat > num) > nat).
% 18.24/3.89 thf(func_def_107, type, sK55: (real > num) > real).
% 18.24/3.89 thf(func_def_108, type, sK56: (real > num) > real).
% 18.24/3.89 thf(func_def_109, type, sK57: (real > real) > real).
% 18.24/3.89 thf(func_def_110, type, sK58: (real > real) > real).
% 18.24/3.89 thf(func_def_111, type, sK59: (num > nat) > num).
% 18.24/3.89 thf(func_def_112, type, sK60: (num > nat) > num).
% 18.24/3.89 thf(func_def_113, type, sK61: (num > nat) > num).
% 18.24/3.89 thf(func_def_114, type, sK62: (num > nat) > num).
% 18.24/3.89 thf(func_def_115, type, sK63: (num > num) > num).
% 18.24/3.89 thf(func_def_116, type, sK64: (num > num) > num).
% 18.24/3.89 thf(func_def_117, type, sK65: (nat > $o) > nat).
% 18.24/3.89 thf(func_def_118, type, sK66: (nat > $o) > nat > nat).
% 18.24/3.89 thf(func_def_119, type, sK67: (num > real) > num).
% 18.24/3.89 thf(func_def_120, type, sK68: (num > real) > num).
% 18.24/3.89 thf(func_def_121, type, sK69: (real > real) > real).
% 18.24/3.89 thf(func_def_122, type, sK70: (real > real) > real).
% 18.24/3.89 thf(func_def_123, type, sK71: (nat > real) > nat).
% 18.24/3.89 thf(func_def_124, type, sK72: (nat > real) > nat).
% 18.24/3.89 thf(func_def_125, type, sK73: (num > real) > num).
% 18.24/3.89 thf(func_def_126, type, sK74: (num > real) > num).
% 18.24/3.89 thf(func_def_127, type, sK75: (real > real) > real).
% 18.24/3.89 thf(func_def_128, type, sK76: (real > real) > real).
% 18.24/3.89 thf(func_def_129, type, sK77: (nat > num) > nat).
% 18.24/3.89 thf(func_def_130, type, sK78: (nat > num) > nat).
% 18.24/3.89 thf(func_def_131, type, sK79: (real > num) > real).
% 18.24/3.89 thf(func_def_132, type, sK80: (real > num) > real).
% 18.24/3.89 thf(func_def_133, type, sK81: (nat > real) > nat).
% 18.24/3.89 thf(func_def_134, type, sK82: (nat > real) > nat).
% 18.24/3.89 thf(func_def_136, type, ph84: !>[X0: $tType]:(X0)).
% 18.24/3.89 thf(f1697,plain,(
% 18.24/3.89 $false),
% 18.24/3.89 inference(subsumption_resolution,[status(thm)],[f1696,f1469])).
% 18.24/3.89 thf(f1469,plain,(
% 18.24/3.89 ( ! [X1 : real] : (($true = (ord_less_eq_real @ X1 @ X1))) )),
% 18.24/3.89 inference(equality_resolution,[status(thm)],[f1395])).
% 18.24/3.89 thf(f1395,plain,(
% 18.24/3.89 ( ! [X0 : real,X1 : real] : (((ord_less_eq_real @ X1 @ X0) = $true) | (X0 != X1)) )),
% 18.24/3.89 inference(cnf_transformation,[status(thm)],[f867])).
% 18.24/3.89 thf(f867,plain,(
% 18.24/3.89 ! [X0 : real,X1 : real] : (((ord_less_eq_real @ X1 @ X0) = $true) | (X0 != X1))),
% 18.24/3.89 inference(ennf_transformation,[status(thm)],[f479])).
% 18.24/3.89 thf(f479,plain,(
% 18.24/3.89 ! [X0 : real,X1 : real] : ((X0 = X1) => ((ord_less_eq_real @ X1 @ X0) = $true))),
% 18.24/3.89 inference(fool_elimination,[status(thm)],[f478])).
% 18.24/3.89 thf(f478,plain,(
% 18.24/3.89 ! [X0 : real,X1 : real] : ((X0 = X1) => (ord_less_eq_real @ X1 @ X0))),
% 18.24/3.89 inference(rectify,[status(thm)],[f298])).
% 18.24/3.89 thf(f298,axiom,(
% 18.24/3.89 ! [X33 : real,X19 : real] : ((X19 = X33) => (ord_less_eq_real @ X19 @ X33))),
% 18.24/3.89 file('/export/starexec/sandbox/tmp/tmp.3sGo6IMQoe/DTF2THF_1172.p',fact_297_eq__refl)).
% 18.24/3.89 thf(f1696,plain,(
% 18.24/3.89 ($true != (ord_less_eq_real @ (times_times_real @ genClo1144207539le_rho @ (times_times_real @ (plus_plus_real @ one_one_real @ one_one_real) @ (minus_minus_real @ t @ s))) @ (times_times_real @ genClo1144207539le_rho @ (times_times_real @ (plus_plus_real @ one_one_real @ one_one_real) @ (minus_minus_real @ t @ s)))))),
% 18.24/3.89 inference(forward_demodulation,[status(thm)],[f1695,f1331])).
% 18.24/3.89 thf(f1331,plain,(
% 18.24/3.89 ((numeral_numeral_real @ (bit0 @ one)) = (plus_plus_real @ one_one_real @ one_one_real))),
% 18.24/3.89 inference(cnf_transformation,[status(thm)],[f85])).
% 18.24/3.89 thf(f85,axiom,(
% 18.24/3.89 ((numeral_numeral_real @ (bit0 @ one)) = (plus_plus_real @ one_one_real @ one_one_real))),
% 18.24/3.89 file('/export/starexec/sandbox/tmp/tmp.3sGo6IMQoe/DTF2THF_1172.p',fact_84_one__add__one)).
% 18.24/3.89 thf(f1695,plain,(
% 18.24/3.89 ($true != (ord_less_eq_real @ (times_times_real @ genClo1144207539le_rho @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (minus_minus_real @ t @ s))) @ (times_times_real @ genClo1144207539le_rho @ (times_times_real @ (plus_plus_real @ one_one_real @ one_one_real) @ (minus_minus_real @ t @ s)))))),
% 18.24/3.89 inference(forward_demodulation,[status(thm)],[f1694,f1185])).
% 18.24/3.89 thf(f1185,plain,(
% 18.24/3.89 ( ! [X2 : real,X0 : real,X1 : real] : (((times_times_real @ X2 @ (times_times_real @ X1 @ X0)) = (times_times_real @ X1 @ (times_times_real @ X2 @ X0)))) )),
% 18.24/3.89 inference(cnf_transformation,[status(thm)],[f778])).
% 18.24/3.89 thf(f778,plain,(
% 18.24/3.89 ! [X0 : real,X1 : real,X2 : real] : ((times_times_real @ X2 @ (times_times_real @ X1 @ X0)) = (times_times_real @ X1 @ (times_times_real @ X2 @ X0)))),
% 18.24/3.89 inference(rectify,[status(thm)],[f164])).
% 18.24/3.89 thf(f164,axiom,(
% 18.24/3.89 ! [X3 : real,X1 : real,X0 : real] : ((times_times_real @ X1 @ (times_times_real @ X0 @ X3)) = (times_times_real @ X0 @ (times_times_real @ X1 @ X3)))),
% 18.24/3.89 file('/export/starexec/sandbox/tmp/tmp.3sGo6IMQoe/DTF2THF_1172.p',fact_163_mult_Oleft__commute)).
% 18.24/3.89 thf(f1694,plain,(
% 18.24/3.89 ($true != (ord_less_eq_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (times_times_real @ genClo1144207539le_rho @ (minus_minus_real @ t @ s))) @ (times_times_real @ genClo1144207539le_rho @ (times_times_real @ (plus_plus_real @ one_one_real @ one_one_real) @ (minus_minus_real @ t @ s)))))),
% 18.24/3.89 inference(forward_demodulation,[status(thm)],[f1693,f1203])).
% 18.24/3.89 thf(f1203,plain,(
% 18.24/3.89 ( ! [X2 : real,X0 : real,X1 : real] : (((times_times_real @ (times_times_real @ X0 @ X2) @ X1) = (times_times_real @ X0 @ (times_times_real @ X2 @ X1)))) )),
% 18.24/3.89 inference(cnf_transformation,[status(thm)],[f785])).
% 18.24/3.89 thf(f785,plain,(
% 18.24/3.89 ! [X0 : real,X1 : real,X2 : real] : ((times_times_real @ (times_times_real @ X0 @ X2) @ X1) = (times_times_real @ X0 @ (times_times_real @ X2 @ X1)))),
% 18.24/3.89 inference(rectify,[status(thm)],[f168])).
% 18.24/3.89 thf(f168,axiom,(
% 18.24/3.89 ! [X0 : real,X3 : real,X1 : real] : ((times_times_real @ X0 @ (times_times_real @ X1 @ X3)) = (times_times_real @ (times_times_real @ X0 @ X1) @ X3))),
% 18.24/3.89 file('/export/starexec/sandbox/tmp/tmp.3sGo6IMQoe/DTF2THF_1172.p',fact_167_mult_Oassoc)).
% 18.24/3.89 thf(f1693,plain,(
% 18.24/3.89 ($true != (ord_less_eq_real @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)) @ (times_times_real @ genClo1144207539le_rho @ (times_times_real @ (plus_plus_real @ one_one_real @ one_one_real) @ (minus_minus_real @ t @ s)))))),
% 18.24/3.89 inference(forward_demodulation,[status(thm)],[f1692,f1283])).
% 18.24/3.89 thf(f1283,plain,(
% 18.24/3.89 ((minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (times_times_real @ (minus_minus_real @ t @ s) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho))) = (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)))),
% 18.24/3.89 inference(cnf_transformation,[status(thm)],[f5])).
% 18.24/3.89 thf(f5,axiom,(
% 18.24/3.89 ((minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (times_times_real @ (minus_minus_real @ t @ s) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho))) = (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)))),
% 18.24/3.89 file('/export/starexec/sandbox/tmp/tmp.3sGo6IMQoe/DTF2THF_1172.p',fact_4_Eq4)).
% 18.24/3.89 thf(f1692,plain,(
% 18.24/3.89 ($true != (ord_less_eq_real @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (times_times_real @ (minus_minus_real @ t @ s) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho))) @ (times_times_real @ genClo1144207539le_rho @ (times_times_real @ (plus_plus_real @ one_one_real @ one_one_real) @ (minus_minus_real @ t @ s)))))),
% 18.24/3.89 inference(trivial_inequality_removal,[status(thm)],[f1661])).
% 18.24/3.89 thf(f1661,plain,(
% 18.24/3.89 ($true != (ord_less_eq_real @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (times_times_real @ (minus_minus_real @ t @ s) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho))) @ (times_times_real @ genClo1144207539le_rho @ (times_times_real @ (plus_plus_real @ one_one_real @ one_one_real) @ (minus_minus_real @ t @ s))))) | ($true != $true)),
% 18.24/3.89 inference(superposition,[status(thm)],[f1543,f1324])).
% 18.24/3.89 thf(f1324,plain,(
% 18.24/3.89 ((ord_less_eq_real @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (times_times_real @ (minus_minus_real @ t @ s) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho)))) = $true)),
% 18.24/3.89 inference(cnf_transformation,[status(thm)],[f533])).
% 18.24/3.89 thf(f533,plain,(
% 18.24/3.89 ((ord_less_eq_real @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (times_times_real @ (minus_minus_real @ t @ s) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho)))) = $true)),
% 18.24/3.89 inference(fool_elimination,[status(thm)],[f532])).
% 18.24/3.89 thf(f532,plain,(
% 18.24/3.89 (ord_less_eq_real @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (times_times_real @ (minus_minus_real @ t @ s) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho))))),
% 18.24/3.89 inference(rectify,[status(thm)],[f6])).
% 18.24/3.89 thf(f6,axiom,(
% 18.24/3.89 (ord_less_eq_real @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (times_times_real @ (minus_minus_real @ t @ s) @ (minus_minus_real @ one_one_real @ genClo1144207539le_rho))))),
% 18.24/3.89 file('/export/starexec/sandbox/tmp/tmp.3sGo6IMQoe/DTF2THF_1172.p',fact_5_Eq3)).
% 18.24/3.89 thf(f1543,plain,(
% 18.24/3.89 ( ! [X0 : real] : (($true != (ord_less_eq_real @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ X0)) | ($true != (ord_less_eq_real @ X0 @ (times_times_real @ genClo1144207539le_rho @ (times_times_real @ (plus_plus_real @ one_one_real @ one_one_real) @ (minus_minus_real @ t @ s)))))) )),
% 18.24/3.89 inference(trivial_inequality_removal,[status(thm)],[f1535])).
% 18.24/3.89 thf(f1535,plain,(
% 18.24/3.89 ( ! [X0 : real] : (($true != (ord_less_eq_real @ X0 @ (times_times_real @ genClo1144207539le_rho @ (times_times_real @ (plus_plus_real @ one_one_real @ one_one_real) @ (minus_minus_real @ t @ s))))) | ($true != (ord_less_eq_real @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ X0)) | ($true != $true)) )),
% 18.24/3.89 inference(superposition,[status(thm)],[f1526,f1221])).
% 18.24/3.89 thf(f1221,plain,(
% 18.24/3.89 ( ! [X2 : real,X0 : real,X1 : real] : (($true = (ord_less_eq_real @ X2 @ X0)) | ((ord_less_eq_real @ X1 @ X0) != $true) | ($true != (ord_less_eq_real @ X2 @ X1))) )),
% 18.24/3.89 inference(cnf_transformation,[status(thm)],[f888])).
% 18.24/3.89 thf(f888,plain,(
% 18.24/3.89 ! [X0 : real,X1 : real,X2 : real] : (((ord_less_eq_real @ X1 @ X0) != $true) | ($true != (ord_less_eq_real @ X2 @ X1)) | ($true = (ord_less_eq_real @ X2 @ X0)))),
% 18.24/3.89 inference(flattening,[status(thm)],[f887])).
% 18.24/3.89 thf(f887,plain,(
% 18.24/3.89 ! [X0 : real,X1 : real,X2 : real] : ((($true = (ord_less_eq_real @ X2 @ X0)) | ((ord_less_eq_real @ X1 @ X0) != $true)) | ($true != (ord_less_eq_real @ X2 @ X1)))),
% 18.24/3.89 inference(ennf_transformation,[status(thm)],[f723])).
% 18.24/3.89 thf(f723,plain,(
% 18.24/3.89 ! [X0 : real,X1 : real,X2 : real] : (($true = (ord_less_eq_real @ X2 @ X1)) => (((ord_less_eq_real @ X1 @ X0) = $true) => ($true = (ord_less_eq_real @ X2 @ X0))))),
% 18.24/3.89 inference(fool_elimination,[status(thm)],[f722])).
% 18.24/3.89 thf(f722,plain,(
% 18.24/3.89 ! [X0 : real,X1 : real,X2 : real] : ((ord_less_eq_real @ X2 @ X1) => ((ord_less_eq_real @ X1 @ X0) => (ord_less_eq_real @ X2 @ X0)))),
% 18.24/3.89 inference(rectify,[status(thm)],[f304])).
% 18.24/3.89 thf(f304,axiom,(
% 18.24/3.89 ! [X3 : real,X1 : real,X0 : real] : ((ord_less_eq_real @ X0 @ X1) => ((ord_less_eq_real @ X1 @ X3) => (ord_less_eq_real @ X0 @ X3)))),
% 18.24/3.89 file('/export/starexec/sandbox/tmp/tmp.3sGo6IMQoe/DTF2THF_1172.p',fact_303_order_Otrans)).
% 18.24/3.89 thf(f1526,plain,(
% 18.24/3.89 ($true != (ord_less_eq_real @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ (times_times_real @ genClo1144207539le_rho @ (times_times_real @ (plus_plus_real @ one_one_real @ one_one_real) @ (minus_minus_real @ t @ s)))))),
% 18.24/3.89 inference(trivial_inequality_removal,[status(thm)],[f1502])).
% 18.24/3.89 thf(f1502,plain,(
% 18.24/3.89 ($true != $true) | ($true != (ord_less_eq_real @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ (times_times_real @ genClo1144207539le_rho @ (times_times_real @ (plus_plus_real @ one_one_real @ one_one_real) @ (minus_minus_real @ t @ s)))))),
% 18.24/3.89 inference(superposition,[status(thm)],[f1488,f1150])).
% 18.24/3.89 thf(f1150,plain,(
% 18.24/3.89 ((ord_less_eq_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) = $true)),
% 18.24/3.89 inference(cnf_transformation,[status(thm)],[f473])).
% 18.24/3.89 thf(f473,plain,(
% 18.24/3.89 ((ord_less_eq_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) = $true)),
% 18.24/3.89 inference(fool_elimination,[status(thm)],[f472])).
% 18.24/3.89 thf(f472,plain,(
% 18.24/3.89 (ord_less_eq_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))))),
% 18.24/3.89 inference(rectify,[status(thm)],[f10])).
% 18.24/3.89 thf(f10,axiom,(
% 18.24/3.89 (ord_less_eq_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus_real @ (times_times_real @ (minus_minus_real @ t @ s) @ (plus_plus_real @ one_one_real @ genClo1144207539le_rho)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))))),
% 18.24/3.89 file('/export/starexec/sandbox/tmp/tmp.3sGo6IMQoe/DTF2THF_1172.p',fact_9_Eq2)).
% 18.24/3.89 thf(f1488,plain,(
% 18.24/3.89 ( ! [X0 : real] : (((ord_less_eq_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ X0) != $true) | ($true != (ord_less_eq_real @ X0 @ (times_times_real @ genClo1144207539le_rho @ (times_times_real @ (plus_plus_real @ one_one_real @ one_one_real) @ (minus_minus_real @ t @ s)))))) )),
% 18.24/3.89 inference(trivial_inequality_removal,[status(thm)],[f1482])).
% 18.24/3.89 thf(f1482,plain,(
% 18.24/3.89 ( ! [X0 : real] : (($true != (ord_less_eq_real @ X0 @ (times_times_real @ genClo1144207539le_rho @ (times_times_real @ (plus_plus_real @ one_one_real @ one_one_real) @ (minus_minus_real @ t @ s))))) | ($true != $true) | ((ord_less_eq_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ X0) != $true)) )),
% 18.24/3.89 inference(superposition,[status(thm)],[f1480,f1221])).
% 18.24/3.89 thf(f1480,plain,(
% 18.24/3.89 ($true != (ord_less_eq_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ (times_times_real @ genClo1144207539le_rho @ (times_times_real @ (plus_plus_real @ one_one_real @ one_one_real) @ (minus_minus_real @ t @ s)))))),
% 18.24/3.89 inference(forward_demodulation,[status(thm)],[f1479,f1331])).
% 18.24/3.89 thf(f1479,plain,(
% 18.24/3.89 ($true != (ord_less_eq_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ (times_times_real @ genClo1144207539le_rho @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (minus_minus_real @ t @ s)))))),
% 18.24/3.89 inference(forward_demodulation,[status(thm)],[f1478,f1185])).
% 18.24/3.89 thf(f1478,plain,(
% 18.24/3.89 ($true != (ord_less_eq_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ (times_times_real @ genClo1144207539le_rho @ (minus_minus_real @ t @ s)))))),
% 18.24/3.89 inference(forward_demodulation,[status(thm)],[f1477,f1203])).
% 18.24/3.89 thf(f1477,plain,(
% 18.24/3.89 ($true != (ord_less_eq_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s))))),
% 18.24/3.89 inference(forward_demodulation,[status(thm)],[f1141,f1212])).
% 18.24/3.89 thf(f1212,plain,(
% 18.24/3.89 ((minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) = (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))))),
% 18.24/3.89 inference(cnf_transformation,[status(thm)],[f4])).
% 18.24/3.89 thf(f4,axiom,(
% 18.24/3.89 ((minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s))) = (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))))),
% 18.24/3.89 file('/export/starexec/sandbox/tmp/tmp.3sGo6IMQoe/DTF2THF_1172.p',fact_3_Eq1)).
% 18.24/3.89 thf(f1141,plain,(
% 18.24/3.89 ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s))) != $true)),
% 18.24/3.89 inference(cnf_transformation,[status(thm)],[f754])).
% 18.24/3.89 thf(f754,plain,(
% 18.24/3.89 ((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s))) != $true)),
% 18.24/3.89 inference(flattening,[status(thm)],[f485])).
% 18.24/3.89 thf(f485,plain,(
% 18.24/3.89 ~((ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s))) = $true)),
% 18.24/3.89 inference(fool_elimination,[status(thm)],[f484])).
% 18.24/3.89 thf(f484,plain,(
% 18.24/3.89 ~(ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)))),
% 18.24/3.89 inference(rectify,[status(thm)],[f354])).
% 18.24/3.89 thf(f354,negated_conjecture,(
% 18.24/3.89 ~(ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)))),
% 18.24/3.89 inference(negated_conjecture,[status(cth)],[f353])).
% 18.24/3.89 thf(f353,conjecture,(
% 18.24/3.89 (ord_less_eq_real @ (abs_abs_real @ (minus_minus_real @ (minus_minus_real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus_real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ genClo1144207539le_rho) @ (minus_minus_real @ t @ s)))),
% 18.24/3.89 file('/export/starexec/sandbox/tmp/tmp.3sGo6IMQoe/DTF2THF_1172.p',conj_0)).
% 18.24/3.89 % SZS output end Proof for DTF2THF_1172
% 18.24/3.89 % (1775)------------------------------
% 18.24/3.89 % (1775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.24/3.89 % (1775)Termination reason: Refutation
% 18.24/3.89
% 18.24/3.89 % (1775)Memory used [KB]: 7419
% 18.24/3.89 % (1775)Time elapsed: 0.096 s
% 18.24/3.89 % (1775)Instructions burned: 322 (million)
% 18.24/3.89 % (1775)------------------------------
% 18.24/3.89 % (1775)------------------------------
% 18.24/3.89 % (1364)Success in time 2.399 s
%------------------------------------------------------------------------------