%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP105^1 : 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 : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:35 AM UTC 2026
% Result : Theorem 3.66s 2.56s
% Output : Refutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 86 ( 62 unt; 0 typ; 0 def)
% Number of atoms : 183 ( 108 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 475 ( 41 ~; 19 |; 0 &; 401 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 14 ( 13 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 119 ( 116 usr; 10 con; 0-3 aty)
% Number of variables : 79 ( 14 ^; 65 !; 0 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
real: $tType ).
thf(type_def_7,type,
int: $tType ).
thf(type_def_8,type,
nat: $tType ).
thf(type_def_9,type,
list_list_a: $tType ).
thf(type_def_10,type,
list_list_list_a: $tType ).
thf(type_def_11,type,
list_a: $tType ).
thf(type_def_12,type,
a: $tType ).
thf(type_def_13,type,
list_l2071841302list_a: $tType ).
thf(type_def_14,type,
option_list_list_a: $tType ).
thf(type_def_15,type,
option_list_a: $tType ).
thf(type_def_16,type,
option_a: $tType ).
thf(type_def_17,type,
set_nat: $tType ).
thf(type_def_18,type,
set_real: $tType ).
thf(func_def_0,type,
list_l2071841302list_a: $tType ).
thf(func_def_1,type,
option_list_list_a: $tType ).
thf(func_def_2,type,
list_list_list_a: $tType ).
thf(func_def_3,type,
option_list_a: $tType ).
thf(func_def_4,type,
list_list_a: $tType ).
thf(func_def_5,type,
set_real: $tType ).
thf(func_def_6,type,
set_nat: $tType ).
thf(func_def_7,type,
option_a: $tType ).
thf(func_def_8,type,
list_a: $tType ).
thf(func_def_9,type,
real: $tType ).
thf(func_def_10,type,
nat: $tType ).
thf(func_def_11,type,
int: $tType ).
thf(func_def_12,type,
a: $tType ).
thf(func_def_13,type,
inverse_inverse_real: real > real ).
thf(func_def_14,type,
zero_zero_int: int ).
thf(func_def_15,type,
zero_zero_nat: nat ).
thf(func_def_16,type,
zero_zero_real: real ).
thf(func_def_17,type,
if_nat: $o > nat > nat > nat ).
thf(func_def_18,type,
listSl162220270list_a: list_list_a > nat > list_list_list_a ).
thf(func_def_19,type,
listSl97544552lice_a: list_a > nat > list_list_a ).
thf(func_def_20,type,
listSl856612276list_a: list_list_a > nat > nat > list_list_list_a ).
thf(func_def_21,type,
listSl1495374126_aux_a: list_a > nat > nat > list_list_a ).
thf(func_def_22,type,
bind_l311701255list_a: list_list_list_a > ( list_list_a > list_list_list_a ) > list_list_list_a ).
thf(func_def_23,type,
bind_l94945665list_a: list_list_list_a > ( list_list_a > list_list_a ) > list_list_a ).
thf(func_def_24,type,
bind_list_list_a_a: list_list_list_a > ( list_list_a > list_a ) > list_a ).
thf(func_def_25,type,
bind_l971853709list_a: list_list_a > ( list_a > list_list_list_a ) > list_list_list_a ).
thf(func_def_26,type,
bind_list_a_list_a: list_list_a > ( list_a > list_list_a ) > list_list_a ).
thf(func_def_27,type,
bind_list_a_a: list_list_a > ( list_a > list_a ) > list_a ).
thf(func_def_28,type,
bind_a_list_list_a: list_a > ( a > list_list_list_a ) > list_list_list_a ).
thf(func_def_29,type,
bind_a_list_a: list_a > ( a > list_list_a ) > list_list_a ).
thf(func_def_30,type,
bind_a_a: list_a > ( a > list_a ) > list_a ).
thf(func_def_31,type,
concat_list_list_a: list_l2071841302list_a > list_list_list_a ).
thf(func_def_32,type,
concat_list_a: list_list_list_a > list_list_a ).
thf(func_def_33,type,
concat_a: list_list_a > list_a ).
thf(func_def_34,type,
count_429956358list_a: list_list_list_a > list_list_a > nat ).
thf(func_def_35,type,
count_list_list_a: list_list_a > list_a > nat ).
thf(func_def_36,type,
count_list_a: list_a > a > nat ).
thf(func_def_37,type,
gen_le840878749list_a: nat > list_list_list_a > nat ).
thf(func_def_38,type,
gen_length_list_a: nat > list_list_a > nat ).
thf(func_def_39,type,
gen_length_a: nat > list_a > nat ).
thf(func_def_40,type,
nil_list_list_list_a: list_l2071841302list_a ).
thf(func_def_41,type,
nil_list_list_a: list_list_list_a ).
thf(func_def_42,type,
nil_list_a: list_list_a ).
thf(func_def_43,type,
nil_a: list_a ).
thf(func_def_44,type,
list_ex1_list_list_a: ( list_list_a > $o ) > list_list_list_a > $o ).
thf(func_def_45,type,
list_ex1_list_a: ( list_a > $o ) > list_list_a > $o ).
thf(func_def_46,type,
list_ex1_a: ( a > $o ) > list_a > $o ).
thf(func_def_47,type,
map_fi824137674list_a: ( list_list_a > option_list_list_a ) > list_list_list_a > list_list_list_a ).
thf(func_def_48,type,
map_fi213215172list_a: ( list_list_a > option_list_a ) > list_list_list_a > list_list_a ).
thf(func_def_49,type,
map_fi1574988606st_a_a: ( list_list_a > option_a ) > list_list_list_a > list_a ).
thf(func_def_50,type,
map_fi1090123216list_a: ( list_a > option_list_list_a ) > list_list_a > list_list_list_a ).
thf(func_def_51,type,
map_fi461586634list_a: ( list_a > option_list_a ) > list_list_a > list_list_a ).
thf(func_def_52,type,
map_filter_list_a_a: ( list_a > option_a ) > list_list_a > list_a ).
thf(func_def_53,type,
map_fi2089402454list_a: ( a > option_list_list_a ) > list_a > list_list_list_a ).
thf(func_def_54,type,
map_filter_a_list_a: ( a > option_list_a ) > list_a > list_list_a ).
thf(func_def_55,type,
map_filter_a_a: ( a > option_a ) > list_a > list_a ).
thf(func_def_56,type,
maps_l57963201list_a: ( list_list_a > list_list_list_a ) > list_list_list_a > list_list_list_a ).
thf(func_def_57,type,
maps_l2025957947list_a: ( list_list_a > list_list_a ) > list_list_list_a > list_list_a ).
thf(func_def_58,type,
maps_list_list_a_a: ( list_list_a > list_a ) > list_list_list_a > list_a ).
thf(func_def_59,type,
maps_l755382343list_a: ( list_a > list_list_list_a ) > list_list_a > list_list_list_a ).
thf(func_def_60,type,
maps_list_a_list_a: ( list_a > list_list_a ) > list_list_a > list_list_a ).
thf(func_def_61,type,
maps_list_a_a: ( list_a > list_a ) > list_list_a > list_a ).
thf(func_def_62,type,
maps_a_list_list_a: ( a > list_list_list_a ) > list_a > list_list_list_a ).
thf(func_def_63,type,
maps_a_list_a: ( a > list_list_a ) > list_a > list_list_a ).
thf(func_def_64,type,
maps_a_a: ( a > list_a ) > list_a > list_a ).
thf(func_def_65,type,
member_list_list_a: list_list_list_a > list_list_a > $o ).
thf(func_def_66,type,
member_list_a: list_list_a > list_a > $o ).
thf(func_def_67,type,
member_a: list_a > a > $o ).
thf(func_def_68,type,
null_list_list_a: list_list_list_a > $o ).
thf(func_def_69,type,
null_list_a: list_list_a > $o ).
thf(func_def_70,type,
null_a: list_a > $o ).
thf(func_def_71,type,
semiri2019852685at_int: nat > int ).
thf(func_def_72,type,
semiri1382578993at_nat: nat > nat ).
thf(func_def_73,type,
semiri2110766477t_real: nat > real ).
thf(func_def_74,type,
size_s575106428list_a: list_list_list_a > nat ).
thf(func_def_75,type,
size_s1427607542list_a: list_list_a > nat ).
thf(func_def_76,type,
size_size_list_a: list_a > nat ).
thf(func_def_77,type,
ord_less_int: int > int > $o ).
thf(func_def_78,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_79,type,
ord_less_real: real > real > $o ).
thf(func_def_80,type,
ord_less_eq_int: int > int > $o ).
thf(func_def_81,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_82,type,
ord_less_eq_real: real > real > $o ).
thf(func_def_83,type,
power_power_int: int > nat > int ).
thf(func_def_84,type,
power_power_nat: nat > nat > nat ).
thf(func_def_85,type,
power_power_real: real > nat > real ).
thf(func_def_86,type,
divide_divide_int: int > int > int ).
thf(func_def_87,type,
divide_divide_nat: nat > nat > nat ).
thf(func_def_88,type,
divide_divide_real: real > real > real ).
thf(func_def_89,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_90,type,
collect_real: ( real > $o ) > set_real ).
thf(func_def_91,type,
member_nat: nat > set_nat > $o ).
thf(func_def_92,type,
member_real: real > set_real > $o ).
thf(func_def_93,type,
k: nat ).
thf(func_def_108,type,
sK0:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_109,type,
sK1:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_110,type,
sK2: real > nat ).
thf(func_def_111,type,
sK3: int > nat ).
thf(func_def_112,type,
sK4: real > real ).
thf(func_def_113,type,
sK5: set_nat > ( nat > $o ) > nat ).
thf(func_def_114,type,
sK6: int > nat ).
thf(func_def_115,type,
sK7: ( nat > $o ) > nat ).
thf(func_def_116,type,
sK8: set_nat > ( nat > $o ) > nat ).
thf(func_def_117,type,
sK9: real > nat ).
thf(func_def_118,type,
sK10: int > nat ).
thf(func_def_119,type,
sK11: nat > list_a ).
thf(func_def_120,type,
sK12: ( nat > $o ) > nat > nat ).
thf(func_def_121,type,
sK13: ( nat > $o ) > nat ).
thf(func_def_122,type,
sK14: real > real > real ).
thf(func_def_123,type,
sK15: real > nat > real ).
thf(func_def_124,type,
sK16: real > real ).
thf(func_def_125,type,
sK17: real > set_real > real ).
thf(func_def_126,type,
sK18: set_real > real ).
thf(func_def_127,type,
sK19: real > set_real > real ).
thf(func_def_128,type,
sK20: real > nat ).
thf(func_def_129,type,
sK21: ( nat > $o ) > set_nat > nat ).
thf(func_def_130,type,
sK22: ( nat > $o ) > nat ).
thf(func_def_131,type,
sK23: ( list_a > $o ) > list_a ).
thf(func_def_132,type,
sK24: set_nat > ( nat > $o ) > nat ).
thf(func_def_133,type,
sK25: ( nat > $o ) > nat ).
thf(func_def_134,type,
sK26: nat > ( nat > $o ) > nat ).
thf(func_def_135,type,
sK27: ( nat > nat ) > nat ).
thf(func_def_136,type,
sK28: ( nat > nat ) > nat ).
thf(func_def_137,type,
sK29: real > nat > real ).
thf(func_def_138,type,
sK30: ( real > $o ) > nat ).
thf(func_def_139,type,
sK31: ( real > $o ) > real ).
thf(func_def_140,type,
sK32: ( real > $o ) > real ).
thf(func_def_141,type,
sK33: int > nat ).
thf(func_def_143,type,
ph35:
!>[X0: $tType] : X0 ).
thf(f2686,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f2685,f2313]) ).
thf(f2313,plain,
( ( listSl1495374126_aux_a @ ( concat_a @ ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ) @ k @ ( divide_divide_nat @ k @ k ) )
!= ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ),
inference(superposition,[status(thm)],[f2192,f2214]) ).
thf(f2214,plain,
( k
= ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ),
inference(subsumption_resolution,[status(thm)],[f2212,f1763]) ).
thf(f1763,plain,
! [X0: nat] :
( ( ord_less_nat @ X0 @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f1374,f1709]) ).
thf(f1709,plain,
( zero_zero_nat
= ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ),
inference(definition_unfolding,[status(thm)],[f1416,f1329]) ).
thf(f1329,plain,
( nil_list_list_a
= ( concat_list_list_a @ nil_list_list_list_a ) ),
inference(cnf_transformation,[status(thm)],[f480]) ).
thf(f480,plain,
( nil_list_list_a
= ( concat_list_list_a @ nil_list_list_list_a ) ),
inference(fool_elimination,[status(thm)],[f3]) ).
thf(f3,axiom,
( nil_list_list_a
= ( concat_list_list_a @ nil_list_list_list_a ) ),
file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_2_concat_Osimps_I1_J) ).
thf(f1416,plain,
( zero_zero_nat
= ( size_s575106428list_a @ nil_list_list_a ) ),
inference(cnf_transformation,[status(thm)],[f916]) ).
thf(f916,plain,
( zero_zero_nat
= ( size_s575106428list_a @ nil_list_list_a ) ),
inference(fool_elimination,[status(thm)],[f57]) ).
thf(f57,axiom,
( zero_zero_nat
= ( size_s575106428list_a @ nil_list_list_a ) ),
file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_56_list_Osize_I3_J) ).
thf(f1374,plain,
! [X0: nat] :
( ( ord_less_nat @ X0 @ zero_zero_nat )
!= $true ),
inference(cnf_transformation,[status(thm)],[f1070]) ).
thf(f1070,plain,
! [X0: nat] :
( ( ord_less_nat @ X0 @ zero_zero_nat )
!= $true ),
inference(flattening,[status(thm)],[f981]) ).
thf(f981,plain,
! [X0: nat] :
( ( ord_less_nat @ X0 @ zero_zero_nat )
!= $true ),
inference(fool_elimination,[status(thm)],[f980]) ).
thf(f980,plain,
! [X0: nat] :
~ ( ord_less_nat @ X0 @ zero_zero_nat ),
inference(rectify,[status(thm)],[f74]) ).
thf(f74,axiom,
! [X5: nat] :
~ ( ord_less_nat @ X5 @ zero_zero_nat ),
file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_73_less__zeroE) ).
thf(f2212,plain,
( ( k
= ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) )
| ( ( ord_less_nat @ k @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f2207]) ).
thf(f2207,plain,
( ( $true != $true )
| ( ( ord_less_nat @ k @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) )
= $true )
| ( k
= ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ) ),
inference(superposition,[status(thm)],[f2198,f1445]) ).
thf(f1445,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_nat @ X1 @ X0 )
= $true )
| ( X0 = X1 )
| ( ( ord_less_nat @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f1209]) ).
thf(f1209,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_nat @ X0 @ X1 )
= $true )
| ( X0 = X1 )
| ( ( ord_less_nat @ X1 @ X0 )
= $true ) ),
inference(flattening,[status(thm)],[f1208]) ).
thf(f1208,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_nat @ X1 @ X0 )
= $true )
| ( ( ord_less_nat @ X0 @ X1 )
= $true )
| ( X0 = X1 ) ),
inference(ennf_transformation,[status(thm)],[f1066]) ).
thf(f1066,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ( ( ord_less_nat @ X0 @ X1 )
!= $true )
=> ( ( ord_less_nat @ X1 @ X0 )
= $true ) ) ),
inference(flattening,[status(thm)],[f923]) ).
thf(f923,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ( ( ord_less_nat @ X0 @ X1 )
!= $true )
=> ( ( ord_less_nat @ X1 @ X0 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f922]) ).
thf(f922,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ~ ( ord_less_nat @ X0 @ X1 )
=> ( ord_less_nat @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f79]) ).
thf(f79,axiom,
! [X11: nat,X4: nat] :
( ( X4 != X11 )
=> ( ~ ( ord_less_nat @ X11 @ X4 )
=> ( ord_less_nat @ X4 @ X11 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_78_linorder__neqE__nat) ).
thf(f2198,plain,
( $true
!= ( ord_less_nat @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) @ k ) ),
inference(superposition,[status(thm)],[f2196,f1953]) ).
thf(f1953,plain,
! [X0: nat] :
( ( gen_length_a @ X0 @ ( concat_a @ ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ) )
= X0 ),
inference(definition_unfolding,[status(thm)],[f1624,f1713]) ).
thf(f1713,plain,
( nil_a
= ( concat_a @ ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1546,f1712]) ).
thf(f1712,plain,
( nil_list_a
= ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ),
inference(definition_unfolding,[status(thm)],[f1362,f1329]) ).
thf(f1362,plain,
( nil_list_a
= ( concat_list_a @ nil_list_list_a ) ),
inference(cnf_transformation,[status(thm)],[f741]) ).
thf(f741,plain,
( nil_list_a
= ( concat_list_a @ nil_list_list_a ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,axiom,
( nil_list_a
= ( concat_list_a @ nil_list_list_a ) ),
file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_3_concat_Osimps_I1_J) ).
thf(f1546,plain,
( ( concat_a @ nil_list_a )
= nil_a ),
inference(cnf_transformation,[status(thm)],[f903]) ).
thf(f903,plain,
( ( concat_a @ nil_list_a )
= nil_a ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,axiom,
( ( concat_a @ nil_list_a )
= nil_a ),
file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_4_concat_Osimps_I1_J) ).
thf(f1624,plain,
! [X0: nat] :
( ( gen_length_a @ X0 @ nil_a )
= X0 ),
inference(cnf_transformation,[status(thm)],[f548]) ).
thf(f548,plain,
! [X0: nat] :
( ( gen_length_a @ X0 @ nil_a )
= X0 ),
inference(fool_elimination,[status(thm)],[f547]) ).
thf(f547,plain,
! [X0: nat] :
( ( gen_length_a @ X0 @ nil_a )
= X0 ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,axiom,
! [X5: nat] :
( ( gen_length_a @ X5 @ nil_a )
= X5 ),
file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_23_gen__length__code_I1_J) ).
thf(f2196,plain,
( ( ord_less_nat @ ( gen_length_a @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) @ ( concat_a @ ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ) ) @ k )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f2193,f1891]) ).
thf(f1891,plain,
! [X0: nat,X1: list_a] :
( ( listSl1495374126_aux_a @ X1 @ X0 @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) )
= ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ),
inference(definition_unfolding,[status(thm)],[f1536,f1712,f1709]) ).
thf(f1536,plain,
! [X0: nat,X1: list_a] :
( nil_list_a
= ( listSl1495374126_aux_a @ X1 @ X0 @ zero_zero_nat ) ),
inference(cnf_transformation,[status(thm)],[f919]) ).
thf(f919,plain,
! [X0: nat,X1: list_a] :
( nil_list_a
= ( listSl1495374126_aux_a @ X1 @ X0 @ zero_zero_nat ) ),
inference(fool_elimination,[status(thm)],[f918]) ).
thf(f918,plain,
! [X0: nat,X1: list_a] :
( nil_list_a
= ( listSl1495374126_aux_a @ X1 @ X0 @ zero_zero_nat ) ),
inference(rectify,[status(thm)],[f103]) ).
thf(f103,axiom,
! [X2: nat,X0: list_a] :
( nil_list_a
= ( listSl1495374126_aux_a @ X0 @ X2 @ zero_zero_nat ) ),
file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_102_list__slice__aux_Osimps_I1_J) ).
thf(f2193,plain,
( ( ( ord_less_nat @ ( gen_length_a @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) @ ( concat_a @ ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ) ) @ k )
!= $true )
| ( ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) )
!= ( listSl1495374126_aux_a @ ( concat_a @ ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ) @ k @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ) ) ),
inference(superposition,[status(thm)],[f2190,f1977]) ).
thf(f1977,plain,
! [X0: nat,X1: nat] :
( ( ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) )
= ( divide_divide_nat @ X0 @ X1 ) )
| ( ( ord_less_nat @ X0 @ X1 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f1655,f1709]) ).
thf(f1655,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat
= ( divide_divide_nat @ X0 @ X1 ) )
| ( ( ord_less_nat @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1169]) ).
thf(f1169,plain,
! [X0: nat,X1: nat] :
( ( zero_zero_nat
= ( divide_divide_nat @ X0 @ X1 ) )
| ( ( ord_less_nat @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f358]) ).
thf(f358,plain,
! [X0: nat,X1: nat] :
( ( ( ord_less_nat @ X0 @ X1 )
= $true )
=> ( zero_zero_nat
= ( divide_divide_nat @ X0 @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f357]) ).
thf(f357,plain,
! [X0: nat,X1: nat] :
( ( ord_less_nat @ X0 @ X1 )
=> ( zero_zero_nat
= ( divide_divide_nat @ X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f261]) ).
thf(f261,axiom,
! [X10: nat,X5: nat] :
( ( ord_less_nat @ X10 @ X5 )
=> ( zero_zero_nat
= ( divide_divide_nat @ X10 @ X5 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_260_div__less) ).
thf(f2190,plain,
( ( listSl1495374126_aux_a @ ( concat_a @ ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ) @ k @ ( divide_divide_nat @ ( gen_length_a @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) @ ( concat_a @ ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ) ) @ k ) )
!= ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1917]) ).
thf(f1917,plain,
( ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) )
!= ( ^ [Y0: list_a,Y1: nat] : ( listSl1495374126_aux_a @ Y0 @ Y1 @ ( divide_divide_nat @ ( gen_length_a @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) @ Y0 ) @ Y1 ) )
@ ( concat_a @ ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) )
@ k ) ),
inference(definition_unfolding,[status(thm)],[f1578,f1712,f1716,f1713]) ).
thf(f1716,plain,
( listSl97544552lice_a
= ( ^ [Y0: list_a,Y1: nat] : ( listSl1495374126_aux_a @ Y0 @ Y1 @ ( divide_divide_nat @ ( gen_length_a @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) @ Y0 ) @ Y1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1358,f1715]) ).
thf(f1715,plain,
( size_size_list_a
= ( gen_length_a @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1404,f1709]) ).
thf(f1404,plain,
( size_size_list_a
= ( gen_length_a @ zero_zero_nat ) ),
inference(cnf_transformation,[status(thm)],[f968]) ).
thf(f968,plain,
( size_size_list_a
= ( gen_length_a @ zero_zero_nat ) ),
inference(fool_elimination,[status(thm)],[f60]) ).
thf(f60,axiom,
( size_size_list_a
= ( gen_length_a @ zero_zero_nat ) ),
file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_59_length__code) ).
thf(f1358,plain,
( listSl97544552lice_a
= ( ^ [Y0: list_a,Y1: nat] : ( listSl1495374126_aux_a @ Y0 @ Y1 @ ( divide_divide_nat @ ( size_size_list_a @ Y0 ) @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f779]) ).
thf(f779,plain,
( listSl97544552lice_a
= ( ^ [Y0: list_a,Y1: nat] : ( listSl1495374126_aux_a @ Y0 @ Y1 @ ( divide_divide_nat @ ( size_size_list_a @ Y0 ) @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f778]) ).
thf(f778,plain,
( listSl97544552lice_a
= ( ^ [X0: list_a,X1: nat] : ( listSl1495374126_aux_a @ X0 @ X1 @ ( divide_divide_nat @ ( size_size_list_a @ X0 ) @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f142]) ).
thf(f142,axiom,
( listSl97544552lice_a
= ( ^ [X26: list_a,X27: nat] : ( listSl1495374126_aux_a @ X26 @ X27 @ ( divide_divide_nat @ ( size_size_list_a @ X26 ) @ X27 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_141_list__slice__def) ).
thf(f1578,plain,
( nil_list_a
!= ( listSl97544552lice_a @ nil_a @ k ) ),
inference(cnf_transformation,[status(thm)],[f1065]) ).
thf(f1065,plain,
( nil_list_a
!= ( listSl97544552lice_a @ nil_a @ k ) ),
inference(flattening,[status(thm)],[f917]) ).
thf(f917,plain,
( nil_list_a
!= ( listSl97544552lice_a @ nil_a @ k ) ),
inference(fool_elimination,[status(thm)],[f351]) ).
thf(f351,negated_conjecture,
( nil_list_a
!= ( listSl97544552lice_a @ nil_a @ k ) ),
inference(negated_conjecture,[status(cth)],[f350]) ).
thf(f350,conjecture,
( nil_list_a
= ( listSl97544552lice_a @ nil_a @ k ) ),
file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',conj_0) ).
thf(f2192,plain,
( ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) )
!= ( listSl1495374126_aux_a @ ( concat_a @ ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ) @ k @ ( divide_divide_nat @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) @ k ) ) ),
inference(superposition,[status(thm)],[f2190,f1953]) ).
thf(f2685,plain,
( ( listSl1495374126_aux_a @ ( concat_a @ ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ) @ k @ ( divide_divide_nat @ k @ k ) )
= ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ),
inference(superposition,[status(thm)],[f2326,f2214]) ).
thf(f2326,plain,
( ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) )
= ( listSl1495374126_aux_a @ ( concat_a @ ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ) @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) @ ( divide_divide_nat @ k @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ) ) ),
inference(superposition,[status(thm)],[f2173,f2203]) ).
thf(f2203,plain,
( k
= ( gen_length_a @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) @ ( concat_a @ ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f2201,f2038]) ).
thf(f2038,plain,
! [X0: nat] :
( ( ord_less_nat @ X0 @ ( gen_length_a @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) @ ( concat_a @ ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ) ) )
!= $true ),
inference(equality_resolution,[status(thm)],[f1973]) ).
thf(f1973,plain,
! [X0: nat,X1: list_a] :
( ( ( concat_a @ ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) )
!= X1 )
| ( $true
!= ( ord_less_nat @ X0 @ ( gen_length_a @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) @ X1 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1651,f1713,f1715]) ).
thf(f1651,plain,
! [X0: nat,X1: list_a] :
( ( nil_a != X1 )
| ( $true
!= ( ord_less_nat @ X0 @ ( size_size_list_a @ X1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f1096]) ).
thf(f1096,plain,
! [X0: nat,X1: list_a] :
( ( nil_a != X1 )
| ( $true
!= ( ord_less_nat @ X0 @ ( size_size_list_a @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f772]) ).
thf(f772,plain,
! [X0: nat,X1: list_a] :
( ( $true
= ( ord_less_nat @ X0 @ ( size_size_list_a @ X1 ) ) )
=> ( nil_a != X1 ) ),
inference(fool_elimination,[status(thm)],[f771]) ).
thf(f771,plain,
! [X0: nat,X1: list_a] :
( ( ord_less_nat @ X0 @ ( size_size_list_a @ X1 ) )
=> ( nil_a != X1 ) ),
inference(rectify,[status(thm)],[f70]) ).
thf(f70,axiom,
! [X5: nat,X0: list_a] :
( ( ord_less_nat @ X5 @ ( size_size_list_a @ X0 ) )
=> ( nil_a != X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_69_length__greater__imp__not__empty) ).
thf(f2201,plain,
( ( k
= ( gen_length_a @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) @ ( concat_a @ ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ) ) )
| ( ( ord_less_nat @ k @ ( gen_length_a @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) @ ( concat_a @ ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ) ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f2199]) ).
thf(f2199,plain,
( ( k
= ( gen_length_a @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) @ ( concat_a @ ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ) ) )
| ( ( ord_less_nat @ k @ ( gen_length_a @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) @ ( concat_a @ ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ) ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f2196,f1445]) ).
thf(f2173,plain,
! [X0: list_a] :
( ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) )
= ( listSl1495374126_aux_a @ X0 @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) @ ( divide_divide_nat @ ( gen_length_a @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) @ X0 ) @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1906]) ).
thf(f1906,plain,
! [X0: list_a] :
( ( ^ [Y0: list_a,Y1: nat] : ( listSl1495374126_aux_a @ Y0 @ Y1 @ ( divide_divide_nat @ ( gen_length_a @ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) @ Y0 ) @ Y1 ) )
@ X0
@ ( size_s575106428list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) )
= ( concat_list_a @ ( concat_list_list_a @ nil_list_list_list_a ) ) ),
inference(definition_unfolding,[status(thm)],[f1554,f1716,f1709,f1712]) ).
thf(f1554,plain,
! [X0: list_a] :
( ( listSl97544552lice_a @ X0 @ zero_zero_nat )
= nil_list_a ),
inference(cnf_transformation,[status(thm)],[f590]) ).
thf(f590,plain,
! [X0: list_a] :
( ( listSl97544552lice_a @ X0 @ zero_zero_nat )
= nil_list_a ),
inference(fool_elimination,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: list_a] :
( ( listSl97544552lice_a @ X0 @ zero_zero_nat )
= nil_list_a ),
file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_1_list__slice__0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP105^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.32 % Computer : n008.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue Feb 24 08:26:09 EST 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.44 ---- Original DTF file ---
% 0.18/0.44 thf(spec,logic,$$dhol).
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 % File : ITP105^1 : TPTP v9.2.1. Released v7.5.0.
% 0.18/0.44 % Domain : Interactive Theorem Proving
% 0.18/0.44 % Problem : Sledgehammer ListSlice problem prob_61__5615344_1
% 0.18/0.44 % Version : Especial.
% 0.18/0.44 % English :
% 0.18/0.44
% 0.18/0.44 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.18/0.44 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.18/0.44 % Source : [Des21]
% 0.18/0.44 % Names : ListSlice/prob_61__5615344_1 [Des21]
% 0.18/0.44
% 0.18/0.44 % Status : Theorem
% 0.18/0.44 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% 0.18/0.44 % Syntax : Number of formulae : 444 ( 223 unt; 94 typ; 0 def)
% 0.18/0.44 % Number of atoms : 887 ( 375 equ; 0 cnn)
% 0.18/0.44 % Maximal formula atoms : 8 ( 2 avg)
% 0.18/0.44 % Number of connectives : 2086 ( 85 ~; 26 |; 46 &;1677 @)
% 0.18/0.44 % ( 0 <=>; 252 =>; 0 <=; 0 <~>)
% 0.18/0.44 % Maximal formula depth : 14 ( 5 avg)
% 0.18/0.44 % Number of types : 14 ( 13 usr)
% 0.18/0.44 % Number of type conns : 210 ( 210 >; 0 *; 0 +; 0 <<)
% 0.18/0.44 % Number of symbols : 84 ( 81 usr; 10 con; 0-3 aty)
% 0.18/0.44 % Number of variables : 646 ( 42 ^; 582 !; 22 ?; 646 :)
% 0.18/0.44 % SPC : TH0_THM_EQU_NAR
% 0.18/0.44
% 0.18/0.44 % Comments : This file was generated by Sledgehammer 2021-02-23 15:29:59.697
% 0.18/0.44 %------------------------------------------------------------------------------
% 0.18/0.44 % Could-be-implicit typings (13)
% 0.18/0.44 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J_J,type,
% 0.18/0.44 list_l2071841302list_a: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(ty_n_t__Option__Ooption_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 0.18/0.44 option_list_list_a: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 0.18/0.44 list_list_list_a: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(ty_n_t__Option__Ooption_It__List__Olist_Itf__a_J_J,type,
% 0.18/0.44 option_list_a: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(ty_n_t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.18/0.44 list_list_a: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 0.18/0.44 set_real: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.18/0.44 set_nat: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(ty_n_t__Option__Ooption_Itf__a_J,type,
% 0.18/0.44 option_a: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 0.18/0.44 list_a: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(ty_n_t__Real__Oreal,type,
% 0.18/0.44 real: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(ty_n_t__Nat__Onat,type,
% 0.18/0.44 nat: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(ty_n_t__Int__Oint,type,
% 0.18/0.44 int: $tType ).
% 0.18/0.44
% 0.18/0.44 thf(ty_n_tf__a,type,
% 0.18/0.44 a: $tType ).
% 0.18/0.44
% 0.18/0.44 % Explicit typings (81)
% 0.18/0.44 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Real__Oreal,type,
% 0.18/0.44 inverse_inverse_real: real > real ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
% 0.18/0.44 zero_zero_int: int ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.18/0.44 zero_zero_nat: nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
% 0.18/0.44 zero_zero_real: real ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_If_001t__Nat__Onat,type,
% 0.18/0.44 if_nat: $o > nat > nat > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice_001t__List__Olist_Itf__a_J,type,
% 0.18/0.44 listSl162220270list_a: list_list_a > nat > list_list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice_001tf__a,type,
% 0.18/0.44 listSl97544552lice_a: list_a > nat > list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice__aux_001t__List__Olist_Itf__a_J,type,
% 0.18/0.44 listSl856612276list_a: list_list_a > nat > nat > list_list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice__aux_001tf__a,type,
% 0.18/0.44 listSl1495374126_aux_a: list_a > nat > nat > list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Obind_001t__List__Olist_It__List__Olist_Itf__a_J_J_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.18/0.44 bind_l311701255list_a: list_list_list_a > ( list_list_a > list_list_list_a ) > list_list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Obind_001t__List__Olist_It__List__Olist_Itf__a_J_J_001t__List__Olist_Itf__a_J,type,
% 0.18/0.44 bind_l94945665list_a: list_list_list_a > ( list_list_a > list_list_a ) > list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Obind_001t__List__Olist_It__List__Olist_Itf__a_J_J_001tf__a,type,
% 0.18/0.44 bind_list_list_a_a: list_list_list_a > ( list_list_a > list_a ) > list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Obind_001t__List__Olist_Itf__a_J_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.18/0.44 bind_l971853709list_a: list_list_a > ( list_a > list_list_list_a ) > list_list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Obind_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
% 0.18/0.44 bind_list_a_list_a: list_list_a > ( list_a > list_list_a ) > list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Obind_001t__List__Olist_Itf__a_J_001tf__a,type,
% 0.18/0.44 bind_list_a_a: list_list_a > ( list_a > list_a ) > list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Obind_001tf__a_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.18/0.44 bind_a_list_list_a: list_a > ( a > list_list_list_a ) > list_list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Obind_001tf__a_001t__List__Olist_Itf__a_J,type,
% 0.18/0.44 bind_a_list_a: list_a > ( a > list_list_a ) > list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Obind_001tf__a_001tf__a,type,
% 0.18/0.44 bind_a_a: list_a > ( a > list_a ) > list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Oconcat_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.18/0.44 concat_list_list_a: list_l2071841302list_a > list_list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Oconcat_001t__List__Olist_Itf__a_J,type,
% 0.18/0.44 concat_list_a: list_list_list_a > list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Oconcat_001tf__a,type,
% 0.18/0.44 concat_a: list_list_a > list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Ocount__list_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.18/0.44 count_429956358list_a: list_list_list_a > list_list_a > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Ocount__list_001t__List__Olist_Itf__a_J,type,
% 0.18/0.44 count_list_list_a: list_list_a > list_a > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Ocount__list_001tf__a,type,
% 0.18/0.44 count_list_a: list_a > a > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Ogen__length_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.18/0.44 gen_le840878749list_a: nat > list_list_list_a > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Ogen__length_001t__List__Olist_Itf__a_J,type,
% 0.18/0.44 gen_length_list_a: nat > list_list_a > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Ogen__length_001tf__a,type,
% 0.18/0.44 gen_length_a: nat > list_a > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 0.18/0.44 nil_list_list_list_a: list_l2071841302list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.18/0.44 nil_list_list_a: list_list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Olist_ONil_001t__List__Olist_Itf__a_J,type,
% 0.18/0.44 nil_list_a: list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Olist_ONil_001tf__a,type,
% 0.18/0.44 nil_a: list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Olist__ex1_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.18/0.44 list_ex1_list_list_a: ( list_list_a > $o ) > list_list_list_a > $o ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Olist__ex1_001t__List__Olist_Itf__a_J,type,
% 0.18/0.44 list_ex1_list_a: ( list_a > $o ) > list_list_a > $o ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Olist__ex1_001tf__a,type,
% 0.18/0.44 list_ex1_a: ( a > $o ) > list_a > $o ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Omap__filter_001t__List__Olist_It__List__Olist_Itf__a_J_J_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.18/0.44 map_fi824137674list_a: ( list_list_a > option_list_list_a ) > list_list_list_a > list_list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Omap__filter_001t__List__Olist_It__List__Olist_Itf__a_J_J_001t__List__Olist_Itf__a_J,type,
% 0.18/0.44 map_fi213215172list_a: ( list_list_a > option_list_a ) > list_list_list_a > list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Omap__filter_001t__List__Olist_It__List__Olist_Itf__a_J_J_001tf__a,type,
% 0.18/0.44 map_fi1574988606st_a_a: ( list_list_a > option_a ) > list_list_list_a > list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Omap__filter_001t__List__Olist_Itf__a_J_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.18/0.44 map_fi1090123216list_a: ( list_a > option_list_list_a ) > list_list_a > list_list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Omap__filter_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
% 0.18/0.44 map_fi461586634list_a: ( list_a > option_list_a ) > list_list_a > list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Omap__filter_001t__List__Olist_Itf__a_J_001tf__a,type,
% 0.18/0.44 map_filter_list_a_a: ( list_a > option_a ) > list_list_a > list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Omap__filter_001tf__a_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.18/0.44 map_fi2089402454list_a: ( a > option_list_list_a ) > list_a > list_list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Omap__filter_001tf__a_001t__List__Olist_Itf__a_J,type,
% 0.18/0.44 map_filter_a_list_a: ( a > option_list_a ) > list_a > list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Omap__filter_001tf__a_001tf__a,type,
% 0.18/0.44 map_filter_a_a: ( a > option_a ) > list_a > list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Omaps_001t__List__Olist_It__List__Olist_Itf__a_J_J_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.18/0.44 maps_l57963201list_a: ( list_list_a > list_list_list_a ) > list_list_list_a > list_list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Omaps_001t__List__Olist_It__List__Olist_Itf__a_J_J_001t__List__Olist_Itf__a_J,type,
% 0.18/0.44 maps_l2025957947list_a: ( list_list_a > list_list_a ) > list_list_list_a > list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Omaps_001t__List__Olist_It__List__Olist_Itf__a_J_J_001tf__a,type,
% 0.18/0.44 maps_list_list_a_a: ( list_list_a > list_a ) > list_list_list_a > list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Omaps_001t__List__Olist_Itf__a_J_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.18/0.44 maps_l755382343list_a: ( list_a > list_list_list_a ) > list_list_a > list_list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Omaps_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
% 0.18/0.44 maps_list_a_list_a: ( list_a > list_list_a ) > list_list_a > list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Omaps_001t__List__Olist_Itf__a_J_001tf__a,type,
% 0.18/0.44 maps_list_a_a: ( list_a > list_a ) > list_list_a > list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Omaps_001tf__a_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.18/0.44 maps_a_list_list_a: ( a > list_list_list_a ) > list_a > list_list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Omaps_001tf__a_001t__List__Olist_Itf__a_J,type,
% 0.18/0.44 maps_a_list_a: ( a > list_list_a ) > list_a > list_list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Omaps_001tf__a_001tf__a,type,
% 0.18/0.44 maps_a_a: ( a > list_a ) > list_a > list_a ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Omember_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.18/0.44 member_list_list_a: list_list_list_a > list_list_a > $o ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Omember_001t__List__Olist_Itf__a_J,type,
% 0.18/0.44 member_list_a: list_list_a > list_a > $o ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Omember_001tf__a,type,
% 0.18/0.44 member_a: list_a > a > $o ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Onull_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.18/0.44 null_list_list_a: list_list_list_a > $o ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Onull_001t__List__Olist_Itf__a_J,type,
% 0.18/0.44 null_list_a: list_list_a > $o ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_List_Onull_001tf__a,type,
% 0.18/0.44 null_a: list_a > $o ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 0.18/0.44 semiri2019852685at_int: nat > int ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 0.18/0.44 semiri1382578993at_nat: nat > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 0.18/0.44 semiri2110766477t_real: nat > real ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 0.18/0.44 size_s575106428list_a: list_list_list_a > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.18/0.44 size_s1427607542list_a: list_list_a > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_Itf__a_J,type,
% 0.18/0.44 size_size_list_a: list_a > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 0.18/0.44 ord_less_int: int > int > $o ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.18/0.44 ord_less_nat: nat > nat > $o ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
% 0.18/0.44 ord_less_real: real > real > $o ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
% 0.18/0.44 ord_less_eq_int: int > int > $o ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.18/0.44 ord_less_eq_nat: nat > nat > $o ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 0.18/0.44 ord_less_eq_real: real > real > $o ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Power_Opower__class_Opower_001t__Int__Oint,type,
% 0.18/0.44 power_power_int: int > nat > int ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat,type,
% 0.18/0.44 power_power_nat: nat > nat > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Power_Opower__class_Opower_001t__Real__Oreal,type,
% 0.18/0.44 power_power_real: real > nat > real ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
% 0.18/0.44 divide_divide_int: int > int > int ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 0.18/0.44 divide_divide_nat: nat > nat > nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 0.18/0.44 divide_divide_real: real > real > real ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.18/0.44 collect_nat: ( nat > $o ) > set_nat ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
% 0.18/0.44 collect_real: ( real > $o ) > set_real ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_member_001t__Nat__Onat,type,
% 0.18/0.44 member_nat: nat > set_nat > $o ).
% 0.18/0.44
% 0.18/0.44 thf(sy_c_member_001t__Real__Oreal,type,
% 0.18/0.44 member_real: real > set_real > $o ).
% 0.18/0.44
% 0.18/0.44 thf(sy_v_k,type,
% 0.18/0.44 k: nat ).
% 0.18/0.44
% 0.18/0.44 % Relevant facts (346)
% 0.18/0.44 thf(fact_0_list__slice__0,axiom,
% 0.18/0.44 ! [Xs: list_list_a] :
% 0.18/0.44 ( ( listSl162220270list_a @ Xs @ zero_zero_nat )
% 0.18/0.44 = nil_list_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % list_slice_0
% 0.18/0.44 thf(fact_1_list__slice__0,axiom,
% 0.18/0.44 ! [Xs: list_a] :
% 0.18/0.44 ( ( listSl97544552lice_a @ Xs @ zero_zero_nat )
% 0.18/0.44 = nil_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % list_slice_0
% 0.18/0.44 thf(fact_2_concat_Osimps_I1_J,axiom,
% 0.18/0.44 ( ( concat_list_list_a @ nil_list_list_list_a )
% 0.18/0.44 = nil_list_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % concat.simps(1)
% 0.18/0.44 thf(fact_3_concat_Osimps_I1_J,axiom,
% 0.18/0.44 ( ( concat_list_a @ nil_list_list_a )
% 0.18/0.44 = nil_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % concat.simps(1)
% 0.18/0.44 thf(fact_4_concat_Osimps_I1_J,axiom,
% 0.18/0.44 ( ( concat_a @ nil_list_a )
% 0.18/0.44 = nil_a ) ).
% 0.18/0.44
% 0.18/0.44 % concat.simps(1)
% 0.18/0.44 thf(fact_5_list__ex1__simps_I1_J,axiom,
% 0.18/0.44 ! [P: list_list_a > $o] :
% 0.18/0.44 ~ ( list_ex1_list_list_a @ P @ nil_list_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % list_ex1_simps(1)
% 0.18/0.44 thf(fact_6_list__ex1__simps_I1_J,axiom,
% 0.18/0.44 ! [P: a > $o] :
% 0.18/0.44 ~ ( list_ex1_a @ P @ nil_a ) ).
% 0.18/0.44
% 0.18/0.44 % list_ex1_simps(1)
% 0.18/0.44 thf(fact_7_list__ex1__simps_I1_J,axiom,
% 0.18/0.44 ! [P: list_a > $o] :
% 0.18/0.44 ~ ( list_ex1_list_a @ P @ nil_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % list_ex1_simps(1)
% 0.18/0.44 thf(fact_8_list__slice__less,axiom,
% 0.18/0.44 ! [Xs: list_list_a,K: nat] :
% 0.18/0.44 ( ( ord_less_nat @ ( size_s1427607542list_a @ Xs ) @ K )
% 0.18/0.44 => ( ( listSl162220270list_a @ Xs @ K )
% 0.18/0.44 = nil_list_list_a ) ) ).
% 0.18/0.44
% 0.18/0.44 % list_slice_less
% 0.18/0.44 thf(fact_9_list__slice__less,axiom,
% 0.18/0.44 ! [Xs: list_a,K: nat] :
% 0.18/0.44 ( ( ord_less_nat @ ( size_size_list_a @ Xs ) @ K )
% 0.18/0.44 => ( ( listSl97544552lice_a @ Xs @ K )
% 0.18/0.44 = nil_list_a ) ) ).
% 0.18/0.44
% 0.18/0.44 % list_slice_less
% 0.18/0.44 thf(fact_10_bind__simps_I1_J,axiom,
% 0.18/0.44 ! [F: a > list_list_list_a] :
% 0.18/0.44 ( ( bind_a_list_list_a @ nil_a @ F )
% 0.18/0.44 = nil_list_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % bind_simps(1)
% 0.18/0.44 thf(fact_11_bind__simps_I1_J,axiom,
% 0.18/0.44 ! [F: list_a > list_list_list_a] :
% 0.18/0.44 ( ( bind_l971853709list_a @ nil_list_a @ F )
% 0.18/0.44 = nil_list_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % bind_simps(1)
% 0.18/0.44 thf(fact_12_bind__simps_I1_J,axiom,
% 0.18/0.44 ! [F: list_list_a > list_a] :
% 0.18/0.44 ( ( bind_list_list_a_a @ nil_list_list_a @ F )
% 0.18/0.44 = nil_a ) ).
% 0.18/0.44
% 0.18/0.44 % bind_simps(1)
% 0.18/0.44 thf(fact_13_bind__simps_I1_J,axiom,
% 0.18/0.44 ! [F: list_list_a > list_list_a] :
% 0.18/0.44 ( ( bind_l94945665list_a @ nil_list_list_a @ F )
% 0.18/0.44 = nil_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % bind_simps(1)
% 0.18/0.44 thf(fact_14_bind__simps_I1_J,axiom,
% 0.18/0.44 ! [F: list_list_a > list_list_list_a] :
% 0.18/0.44 ( ( bind_l311701255list_a @ nil_list_list_a @ F )
% 0.18/0.44 = nil_list_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % bind_simps(1)
% 0.18/0.44 thf(fact_15_bind__simps_I1_J,axiom,
% 0.18/0.44 ! [F: a > list_a] :
% 0.18/0.44 ( ( bind_a_a @ nil_a @ F )
% 0.18/0.44 = nil_a ) ).
% 0.18/0.44
% 0.18/0.44 % bind_simps(1)
% 0.18/0.44 thf(fact_16_bind__simps_I1_J,axiom,
% 0.18/0.44 ! [F: a > list_list_a] :
% 0.18/0.44 ( ( bind_a_list_a @ nil_a @ F )
% 0.18/0.44 = nil_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % bind_simps(1)
% 0.18/0.44 thf(fact_17_bind__simps_I1_J,axiom,
% 0.18/0.44 ! [F: list_a > list_a] :
% 0.18/0.44 ( ( bind_list_a_a @ nil_list_a @ F )
% 0.18/0.44 = nil_a ) ).
% 0.18/0.44
% 0.18/0.44 % bind_simps(1)
% 0.18/0.44 thf(fact_18_bind__simps_I1_J,axiom,
% 0.18/0.44 ! [F: list_a > list_list_a] :
% 0.18/0.44 ( ( bind_list_a_list_a @ nil_list_a @ F )
% 0.18/0.44 = nil_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % bind_simps(1)
% 0.18/0.44 thf(fact_19_member__rec_I2_J,axiom,
% 0.18/0.44 ! [Y: list_list_a] :
% 0.18/0.44 ~ ( member_list_list_a @ nil_list_list_a @ Y ) ).
% 0.18/0.44
% 0.18/0.44 % member_rec(2)
% 0.18/0.44 thf(fact_20_member__rec_I2_J,axiom,
% 0.18/0.44 ! [Y: a] :
% 0.18/0.44 ~ ( member_a @ nil_a @ Y ) ).
% 0.18/0.44
% 0.18/0.44 % member_rec(2)
% 0.18/0.44 thf(fact_21_member__rec_I2_J,axiom,
% 0.18/0.44 ! [Y: list_a] :
% 0.18/0.44 ~ ( member_list_a @ nil_list_a @ Y ) ).
% 0.18/0.44
% 0.18/0.44 % member_rec(2)
% 0.18/0.44 thf(fact_22_gen__length__code_I1_J,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ( ( gen_le840878749list_a @ N @ nil_list_list_a )
% 0.18/0.44 = N ) ).
% 0.18/0.44
% 0.18/0.44 % gen_length_code(1)
% 0.18/0.44 thf(fact_23_gen__length__code_I1_J,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ( ( gen_length_a @ N @ nil_a )
% 0.18/0.44 = N ) ).
% 0.18/0.44
% 0.18/0.44 % gen_length_code(1)
% 0.18/0.44 thf(fact_24_gen__length__code_I1_J,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ( ( gen_length_list_a @ N @ nil_list_a )
% 0.18/0.44 = N ) ).
% 0.18/0.44
% 0.18/0.44 % gen_length_code(1)
% 0.18/0.44 thf(fact_25_maps__simps_I2_J,axiom,
% 0.18/0.44 ! [F: a > list_list_list_a] :
% 0.18/0.44 ( ( maps_a_list_list_a @ F @ nil_a )
% 0.18/0.44 = nil_list_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % maps_simps(2)
% 0.18/0.44 thf(fact_26_maps__simps_I2_J,axiom,
% 0.18/0.44 ! [F: list_a > list_list_list_a] :
% 0.18/0.44 ( ( maps_l755382343list_a @ F @ nil_list_a )
% 0.18/0.44 = nil_list_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % maps_simps(2)
% 0.18/0.44 thf(fact_27_maps__simps_I2_J,axiom,
% 0.18/0.44 ! [F: list_list_a > list_a] :
% 0.18/0.44 ( ( maps_list_list_a_a @ F @ nil_list_list_a )
% 0.18/0.44 = nil_a ) ).
% 0.18/0.44
% 0.18/0.44 % maps_simps(2)
% 0.18/0.44 thf(fact_28_maps__simps_I2_J,axiom,
% 0.18/0.44 ! [F: list_list_a > list_list_a] :
% 0.18/0.44 ( ( maps_l2025957947list_a @ F @ nil_list_list_a )
% 0.18/0.44 = nil_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % maps_simps(2)
% 0.18/0.44 thf(fact_29_maps__simps_I2_J,axiom,
% 0.18/0.44 ! [F: list_list_a > list_list_list_a] :
% 0.18/0.44 ( ( maps_l57963201list_a @ F @ nil_list_list_a )
% 0.18/0.44 = nil_list_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % maps_simps(2)
% 0.18/0.44 thf(fact_30_maps__simps_I2_J,axiom,
% 0.18/0.44 ! [F: a > list_a] :
% 0.18/0.44 ( ( maps_a_a @ F @ nil_a )
% 0.18/0.44 = nil_a ) ).
% 0.18/0.44
% 0.18/0.44 % maps_simps(2)
% 0.18/0.44 thf(fact_31_maps__simps_I2_J,axiom,
% 0.18/0.44 ! [F: a > list_list_a] :
% 0.18/0.44 ( ( maps_a_list_a @ F @ nil_a )
% 0.18/0.44 = nil_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % maps_simps(2)
% 0.18/0.44 thf(fact_32_maps__simps_I2_J,axiom,
% 0.18/0.44 ! [F: list_a > list_a] :
% 0.18/0.44 ( ( maps_list_a_a @ F @ nil_list_a )
% 0.18/0.44 = nil_a ) ).
% 0.18/0.44
% 0.18/0.44 % maps_simps(2)
% 0.18/0.44 thf(fact_33_maps__simps_I2_J,axiom,
% 0.18/0.44 ! [F: list_a > list_list_a] :
% 0.18/0.44 ( ( maps_list_a_list_a @ F @ nil_list_a )
% 0.18/0.44 = nil_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % maps_simps(2)
% 0.18/0.44 thf(fact_34_null__rec_I2_J,axiom,
% 0.18/0.44 null_list_list_a @ nil_list_list_a ).
% 0.18/0.44
% 0.18/0.44 % null_rec(2)
% 0.18/0.44 thf(fact_35_null__rec_I2_J,axiom,
% 0.18/0.44 null_a @ nil_a ).
% 0.18/0.44
% 0.18/0.44 % null_rec(2)
% 0.18/0.44 thf(fact_36_null__rec_I2_J,axiom,
% 0.18/0.44 null_list_a @ nil_list_a ).
% 0.18/0.44
% 0.18/0.44 % null_rec(2)
% 0.18/0.44 thf(fact_37_eq__Nil__null,axiom,
% 0.18/0.44 ! [Xs: list_a] :
% 0.18/0.44 ( ( Xs = nil_a )
% 0.18/0.44 = ( null_a @ Xs ) ) ).
% 0.18/0.44
% 0.18/0.44 % eq_Nil_null
% 0.18/0.44 thf(fact_38_eq__Nil__null,axiom,
% 0.18/0.44 ! [Xs: list_list_a] :
% 0.18/0.44 ( ( Xs = nil_list_a )
% 0.18/0.44 = ( null_list_a @ Xs ) ) ).
% 0.18/0.44
% 0.18/0.44 % eq_Nil_null
% 0.18/0.44 thf(fact_39_eq__Nil__null,axiom,
% 0.18/0.44 ! [Xs: list_list_list_a] :
% 0.18/0.44 ( ( Xs = nil_list_list_a )
% 0.18/0.44 = ( null_list_list_a @ Xs ) ) ).
% 0.18/0.44
% 0.18/0.44 % eq_Nil_null
% 0.18/0.44 thf(fact_40_map__filter__simps_I2_J,axiom,
% 0.18/0.44 ! [F: a > option_a] :
% 0.18/0.44 ( ( map_filter_a_a @ F @ nil_a )
% 0.18/0.44 = nil_a ) ).
% 0.18/0.44
% 0.18/0.44 % map_filter_simps(2)
% 0.18/0.44 thf(fact_41_map__filter__simps_I2_J,axiom,
% 0.18/0.44 ! [F: a > option_list_a] :
% 0.18/0.44 ( ( map_filter_a_list_a @ F @ nil_a )
% 0.18/0.44 = nil_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % map_filter_simps(2)
% 0.18/0.44 thf(fact_42_map__filter__simps_I2_J,axiom,
% 0.18/0.44 ! [F: a > option_list_list_a] :
% 0.18/0.44 ( ( map_fi2089402454list_a @ F @ nil_a )
% 0.18/0.44 = nil_list_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % map_filter_simps(2)
% 0.18/0.44 thf(fact_43_map__filter__simps_I2_J,axiom,
% 0.18/0.44 ! [F: list_a > option_a] :
% 0.18/0.44 ( ( map_filter_list_a_a @ F @ nil_list_a )
% 0.18/0.44 = nil_a ) ).
% 0.18/0.44
% 0.18/0.44 % map_filter_simps(2)
% 0.18/0.44 thf(fact_44_map__filter__simps_I2_J,axiom,
% 0.18/0.44 ! [F: list_a > option_list_a] :
% 0.18/0.44 ( ( map_fi461586634list_a @ F @ nil_list_a )
% 0.18/0.44 = nil_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % map_filter_simps(2)
% 0.18/0.44 thf(fact_45_map__filter__simps_I2_J,axiom,
% 0.18/0.44 ! [F: list_a > option_list_list_a] :
% 0.18/0.44 ( ( map_fi1090123216list_a @ F @ nil_list_a )
% 0.18/0.44 = nil_list_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % map_filter_simps(2)
% 0.18/0.44 thf(fact_46_map__filter__simps_I2_J,axiom,
% 0.18/0.44 ! [F: list_list_a > option_a] :
% 0.18/0.44 ( ( map_fi1574988606st_a_a @ F @ nil_list_list_a )
% 0.18/0.44 = nil_a ) ).
% 0.18/0.44
% 0.18/0.44 % map_filter_simps(2)
% 0.18/0.44 thf(fact_47_map__filter__simps_I2_J,axiom,
% 0.18/0.44 ! [F: list_list_a > option_list_a] :
% 0.18/0.44 ( ( map_fi213215172list_a @ F @ nil_list_list_a )
% 0.18/0.44 = nil_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % map_filter_simps(2)
% 0.18/0.44 thf(fact_48_map__filter__simps_I2_J,axiom,
% 0.18/0.44 ! [F: list_list_a > option_list_list_a] :
% 0.18/0.44 ( ( map_fi824137674list_a @ F @ nil_list_list_a )
% 0.18/0.44 = nil_list_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % map_filter_simps(2)
% 0.18/0.44 thf(fact_49_length__0__conv,axiom,
% 0.18/0.44 ! [Xs: list_list_a] :
% 0.18/0.44 ( ( ( size_s1427607542list_a @ Xs )
% 0.18/0.44 = zero_zero_nat )
% 0.18/0.44 = ( Xs = nil_list_a ) ) ).
% 0.18/0.44
% 0.18/0.44 % length_0_conv
% 0.18/0.44 thf(fact_50_length__0__conv,axiom,
% 0.18/0.44 ! [Xs: list_list_list_a] :
% 0.18/0.44 ( ( ( size_s575106428list_a @ Xs )
% 0.18/0.44 = zero_zero_nat )
% 0.18/0.44 = ( Xs = nil_list_list_a ) ) ).
% 0.18/0.44
% 0.18/0.44 % length_0_conv
% 0.18/0.44 thf(fact_51_length__0__conv,axiom,
% 0.18/0.44 ! [Xs: list_a] :
% 0.18/0.44 ( ( ( size_size_list_a @ Xs )
% 0.18/0.44 = zero_zero_nat )
% 0.18/0.44 = ( Xs = nil_a ) ) ).
% 0.18/0.44
% 0.18/0.44 % length_0_conv
% 0.18/0.44 thf(fact_52_length__greater__0__conv,axiom,
% 0.18/0.44 ! [Xs: list_list_a] :
% 0.18/0.44 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ Xs ) )
% 0.18/0.44 = ( Xs != nil_list_a ) ) ).
% 0.18/0.44
% 0.18/0.44 % length_greater_0_conv
% 0.18/0.44 thf(fact_53_length__greater__0__conv,axiom,
% 0.18/0.44 ! [Xs: list_list_list_a] :
% 0.18/0.44 ( ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ Xs ) )
% 0.18/0.44 = ( Xs != nil_list_list_a ) ) ).
% 0.18/0.44
% 0.18/0.44 % length_greater_0_conv
% 0.18/0.44 thf(fact_54_length__greater__0__conv,axiom,
% 0.18/0.44 ! [Xs: list_a] :
% 0.18/0.44 ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ Xs ) )
% 0.18/0.44 = ( Xs != nil_a ) ) ).
% 0.18/0.44
% 0.18/0.44 % length_greater_0_conv
% 0.18/0.44 thf(fact_55_list_Osize_I3_J,axiom,
% 0.18/0.44 ( ( size_s1427607542list_a @ nil_list_a )
% 0.18/0.44 = zero_zero_nat ) ).
% 0.18/0.44
% 0.18/0.44 % list.size(3)
% 0.18/0.44 thf(fact_56_list_Osize_I3_J,axiom,
% 0.18/0.44 ( ( size_s575106428list_a @ nil_list_list_a )
% 0.18/0.44 = zero_zero_nat ) ).
% 0.18/0.44
% 0.18/0.44 % list.size(3)
% 0.18/0.44 thf(fact_57_list_Osize_I3_J,axiom,
% 0.18/0.44 ( ( size_size_list_a @ nil_a )
% 0.18/0.44 = zero_zero_nat ) ).
% 0.18/0.44
% 0.18/0.44 % list.size(3)
% 0.18/0.44 thf(fact_58_length__code,axiom,
% 0.18/0.44 ( size_s1427607542list_a
% 0.18/0.44 = ( gen_length_list_a @ zero_zero_nat ) ) ).
% 0.18/0.44
% 0.18/0.44 % length_code
% 0.18/0.44 thf(fact_59_length__code,axiom,
% 0.18/0.44 ( size_size_list_a
% 0.18/0.44 = ( gen_length_a @ zero_zero_nat ) ) ).
% 0.18/0.44
% 0.18/0.44 % length_code
% 0.18/0.44 thf(fact_60_length__induct,axiom,
% 0.18/0.44 ! [P: list_a > $o,Xs: list_a] :
% 0.18/0.44 ( ! [Xs2: list_a] :
% 0.18/0.44 ( ! [Ys: list_a] :
% 0.18/0.44 ( ( ord_less_nat @ ( size_size_list_a @ Ys ) @ ( size_size_list_a @ Xs2 ) )
% 0.18/0.44 => ( P @ Ys ) )
% 0.18/0.44 => ( P @ Xs2 ) )
% 0.18/0.44 => ( P @ Xs ) ) ).
% 0.18/0.44
% 0.18/0.44 % length_induct
% 0.18/0.44 thf(fact_61_Ex__list__of__length,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ? [Xs2: list_a] :
% 0.18/0.44 ( ( size_size_list_a @ Xs2 )
% 0.18/0.44 = N ) ).
% 0.18/0.44
% 0.18/0.44 % Ex_list_of_length
% 0.18/0.44 thf(fact_62_neq__if__length__neq,axiom,
% 0.18/0.44 ! [Xs: list_a,Ys2: list_a] :
% 0.18/0.44 ( ( ( size_size_list_a @ Xs )
% 0.18/0.44 != ( size_size_list_a @ Ys2 ) )
% 0.18/0.44 => ( Xs != Ys2 ) ) ).
% 0.18/0.44
% 0.18/0.44 % neq_if_length_neq
% 0.18/0.44 thf(fact_63_neq0__conv,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ( ( N != zero_zero_nat )
% 0.18/0.44 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.18/0.44
% 0.18/0.44 % neq0_conv
% 0.18/0.44 thf(fact_64_less__nat__zero__code,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.18/0.44
% 0.18/0.44 % less_nat_zero_code
% 0.18/0.44 thf(fact_65_bot__nat__0_Onot__eq__extremum,axiom,
% 0.18/0.44 ! [A: nat] :
% 0.18/0.44 ( ( A != zero_zero_nat )
% 0.18/0.44 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 0.18/0.44
% 0.18/0.44 % bot_nat_0.not_eq_extremum
% 0.18/0.44 thf(fact_66_not__gr__zero,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.18/0.44 = ( N = zero_zero_nat ) ) ).
% 0.18/0.44
% 0.18/0.44 % not_gr_zero
% 0.18/0.44 thf(fact_67_length__greater__imp__not__empty,axiom,
% 0.18/0.44 ! [N: nat,Xs: list_list_a] :
% 0.18/0.44 ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 0.18/0.44 => ( Xs != nil_list_a ) ) ).
% 0.18/0.44
% 0.18/0.44 % length_greater_imp_not_empty
% 0.18/0.44 thf(fact_68_length__greater__imp__not__empty,axiom,
% 0.18/0.44 ! [N: nat,Xs: list_list_list_a] :
% 0.18/0.44 ( ( ord_less_nat @ N @ ( size_s575106428list_a @ Xs ) )
% 0.18/0.44 => ( Xs != nil_list_list_a ) ) ).
% 0.18/0.44
% 0.18/0.44 % length_greater_imp_not_empty
% 0.18/0.44 thf(fact_69_length__greater__imp__not__empty,axiom,
% 0.18/0.44 ! [N: nat,Xs: list_a] :
% 0.18/0.44 ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 0.18/0.44 => ( Xs != nil_a ) ) ).
% 0.18/0.44
% 0.18/0.44 % length_greater_imp_not_empty
% 0.18/0.44 thf(fact_70_gr0I,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ( ( N != zero_zero_nat )
% 0.18/0.44 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.18/0.44
% 0.18/0.44 % gr0I
% 0.18/0.44 thf(fact_71_not__gr0,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.18/0.44 = ( N = zero_zero_nat ) ) ).
% 0.18/0.44
% 0.18/0.44 % not_gr0
% 0.18/0.44 thf(fact_72_not__less0,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.18/0.44
% 0.18/0.44 % not_less0
% 0.18/0.44 thf(fact_73_less__zeroE,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.18/0.44
% 0.18/0.44 % less_zeroE
% 0.18/0.44 thf(fact_74_gr__implies__not0,axiom,
% 0.18/0.44 ! [M: nat,N: nat] :
% 0.18/0.44 ( ( ord_less_nat @ M @ N )
% 0.18/0.44 => ( N != zero_zero_nat ) ) ).
% 0.18/0.44
% 0.18/0.44 % gr_implies_not0
% 0.18/0.44 thf(fact_75_zero__reorient,axiom,
% 0.18/0.44 ! [X: nat] :
% 0.18/0.44 ( ( zero_zero_nat = X )
% 0.18/0.44 = ( X = zero_zero_nat ) ) ).
% 0.18/0.44
% 0.18/0.44 % zero_reorient
% 0.18/0.44 thf(fact_76_zero__reorient,axiom,
% 0.18/0.44 ! [X: int] :
% 0.18/0.44 ( ( zero_zero_int = X )
% 0.18/0.44 = ( X = zero_zero_int ) ) ).
% 0.18/0.44
% 0.18/0.44 % zero_reorient
% 0.18/0.44 thf(fact_77_zero__reorient,axiom,
% 0.18/0.44 ! [X: real] :
% 0.18/0.44 ( ( zero_zero_real = X )
% 0.18/0.44 = ( X = zero_zero_real ) ) ).
% 0.18/0.44
% 0.18/0.44 % zero_reorient
% 0.18/0.44 thf(fact_78_linorder__neqE__nat,axiom,
% 0.18/0.44 ! [X: nat,Y: nat] :
% 0.18/0.44 ( ( X != Y )
% 0.18/0.44 => ( ~ ( ord_less_nat @ X @ Y )
% 0.18/0.44 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % linorder_neqE_nat
% 0.18/0.44 thf(fact_79_infinite__descent,axiom,
% 0.18/0.44 ! [P: nat > $o,N: nat] :
% 0.18/0.44 ( ! [N2: nat] :
% 0.18/0.44 ( ~ ( P @ N2 )
% 0.18/0.44 => ? [M2: nat] :
% 0.18/0.44 ( ( ord_less_nat @ M2 @ N2 )
% 0.18/0.44 & ~ ( P @ M2 ) ) )
% 0.18/0.44 => ( P @ N ) ) ).
% 0.18/0.44
% 0.18/0.44 % infinite_descent
% 0.18/0.44 thf(fact_80_nat__less__induct,axiom,
% 0.18/0.44 ! [P: nat > $o,N: nat] :
% 0.18/0.44 ( ! [N2: nat] :
% 0.18/0.44 ( ! [M2: nat] :
% 0.18/0.44 ( ( ord_less_nat @ M2 @ N2 )
% 0.18/0.44 => ( P @ M2 ) )
% 0.18/0.44 => ( P @ N2 ) )
% 0.18/0.44 => ( P @ N ) ) ).
% 0.18/0.44
% 0.18/0.44 % nat_less_induct
% 0.18/0.44 thf(fact_81_less__irrefl__nat,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ~ ( ord_less_nat @ N @ N ) ).
% 0.18/0.44
% 0.18/0.44 % less_irrefl_nat
% 0.18/0.44 thf(fact_82_less__not__refl3,axiom,
% 0.18/0.44 ! [S: nat,T: nat] :
% 0.18/0.44 ( ( ord_less_nat @ S @ T )
% 0.18/0.44 => ( S != T ) ) ).
% 0.18/0.44
% 0.18/0.44 % less_not_refl3
% 0.18/0.44 thf(fact_83_less__not__refl2,axiom,
% 0.18/0.44 ! [N: nat,M: nat] :
% 0.18/0.44 ( ( ord_less_nat @ N @ M )
% 0.18/0.44 => ( M != N ) ) ).
% 0.18/0.44
% 0.18/0.44 % less_not_refl2
% 0.18/0.44 thf(fact_84_less__not__refl,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ~ ( ord_less_nat @ N @ N ) ).
% 0.18/0.44
% 0.18/0.44 % less_not_refl
% 0.18/0.44 thf(fact_85_nat__neq__iff,axiom,
% 0.18/0.44 ! [M: nat,N: nat] :
% 0.18/0.44 ( ( M != N )
% 0.18/0.44 = ( ( ord_less_nat @ M @ N )
% 0.18/0.44 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % nat_neq_iff
% 0.18/0.44 thf(fact_86_size__neq__size__imp__neq,axiom,
% 0.18/0.44 ! [X: list_a,Y: list_a] :
% 0.18/0.44 ( ( ( size_size_list_a @ X )
% 0.18/0.44 != ( size_size_list_a @ Y ) )
% 0.18/0.44 => ( X != Y ) ) ).
% 0.18/0.44
% 0.18/0.44 % size_neq_size_imp_neq
% 0.18/0.44 thf(fact_87_zero__less__iff__neq__zero,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.44 = ( N != zero_zero_nat ) ) ).
% 0.18/0.44
% 0.18/0.44 % zero_less_iff_neq_zero
% 0.18/0.44 thf(fact_88_mem__Collect__eq,axiom,
% 0.18/0.44 ! [A: nat,P: nat > $o] :
% 0.18/0.44 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 0.18/0.44 = ( P @ A ) ) ).
% 0.18/0.44
% 0.18/0.44 % mem_Collect_eq
% 0.18/0.44 thf(fact_89_mem__Collect__eq,axiom,
% 0.18/0.44 ! [A: real,P: real > $o] :
% 0.18/0.44 ( ( member_real @ A @ ( collect_real @ P ) )
% 0.18/0.44 = ( P @ A ) ) ).
% 0.18/0.44
% 0.18/0.44 % mem_Collect_eq
% 0.18/0.44 thf(fact_90_Collect__mem__eq,axiom,
% 0.18/0.44 ! [A2: set_nat] :
% 0.18/0.44 ( ( collect_nat
% 0.18/0.44 @ ^ [X2: nat] : ( member_nat @ X2 @ A2 ) )
% 0.18/0.44 = A2 ) ).
% 0.18/0.44
% 0.18/0.44 % Collect_mem_eq
% 0.18/0.44 thf(fact_91_Collect__mem__eq,axiom,
% 0.18/0.44 ! [A2: set_real] :
% 0.18/0.44 ( ( collect_real
% 0.18/0.44 @ ^ [X2: real] : ( member_real @ X2 @ A2 ) )
% 0.18/0.44 = A2 ) ).
% 0.18/0.44
% 0.18/0.44 % Collect_mem_eq
% 0.18/0.44 thf(fact_92_gr__implies__not__zero,axiom,
% 0.18/0.44 ! [M: nat,N: nat] :
% 0.18/0.44 ( ( ord_less_nat @ M @ N )
% 0.18/0.44 => ( N != zero_zero_nat ) ) ).
% 0.18/0.44
% 0.18/0.44 % gr_implies_not_zero
% 0.18/0.44 thf(fact_93_not__less__zero,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.18/0.44
% 0.18/0.44 % not_less_zero
% 0.18/0.44 thf(fact_94_gr__zeroI,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ( ( N != zero_zero_nat )
% 0.18/0.44 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.18/0.44
% 0.18/0.44 % gr_zeroI
% 0.18/0.44 thf(fact_95_bot__nat__0_Oextremum__strict,axiom,
% 0.18/0.44 ! [A: nat] :
% 0.18/0.44 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 0.18/0.44
% 0.18/0.44 % bot_nat_0.extremum_strict
% 0.18/0.44 thf(fact_96_infinite__descent0,axiom,
% 0.18/0.44 ! [P: nat > $o,N: nat] :
% 0.18/0.44 ( ( P @ zero_zero_nat )
% 0.18/0.44 => ( ! [N2: nat] :
% 0.18/0.44 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.18/0.44 => ( ~ ( P @ N2 )
% 0.18/0.44 => ? [M2: nat] :
% 0.18/0.44 ( ( ord_less_nat @ M2 @ N2 )
% 0.18/0.44 & ~ ( P @ M2 ) ) ) )
% 0.18/0.44 => ( P @ N ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % infinite_descent0
% 0.18/0.44 thf(fact_97_gr__implies__gr0,axiom,
% 0.18/0.44 ! [M: nat,N: nat] :
% 0.18/0.44 ( ( ord_less_nat @ M @ N )
% 0.18/0.44 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.18/0.44
% 0.18/0.44 % gr_implies_gr0
% 0.18/0.44 thf(fact_98_field__lbound__gt__zero,axiom,
% 0.18/0.44 ! [D1: real,D2: real] :
% 0.18/0.44 ( ( ord_less_real @ zero_zero_real @ D1 )
% 0.18/0.44 => ( ( ord_less_real @ zero_zero_real @ D2 )
% 0.18/0.44 => ? [E: real] :
% 0.18/0.44 ( ( ord_less_real @ zero_zero_real @ E )
% 0.18/0.44 & ( ord_less_real @ E @ D1 )
% 0.18/0.44 & ( ord_less_real @ E @ D2 ) ) ) ) ).
% 0.18/0.44
% 0.18/0.44 % field_lbound_gt_zero
% 0.18/0.44 thf(fact_99_less__numeral__extra_I3_J,axiom,
% 0.18/0.44 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.18/0.44
% 0.18/0.44 % less_numeral_extra(3)
% 0.18/0.44 thf(fact_100_less__numeral__extra_I3_J,axiom,
% 0.18/0.44 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.18/0.44
% 0.18/0.44 % less_numeral_extra(3)
% 0.18/0.44 thf(fact_101_less__numeral__extra_I3_J,axiom,
% 0.18/0.44 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 0.18/0.44
% 0.18/0.44 % less_numeral_extra(3)
% 0.18/0.44 thf(fact_102_list__slice__aux_Osimps_I1_J,axiom,
% 0.18/0.44 ! [Xs: list_a,K: nat] :
% 0.18/0.44 ( ( listSl1495374126_aux_a @ Xs @ K @ zero_zero_nat )
% 0.18/0.44 = nil_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % list_slice_aux.simps(1)
% 0.18/0.44 thf(fact_103_list__slice__aux_Osimps_I1_J,axiom,
% 0.18/0.44 ! [Xs: list_list_a,K: nat] :
% 0.18/0.44 ( ( listSl856612276list_a @ Xs @ K @ zero_zero_nat )
% 0.18/0.44 = nil_list_list_a ) ).
% 0.18/0.44
% 0.18/0.44 % list_slice_aux.simps(1)
% 0.18/0.44 thf(fact_104_of__nat__0__less__iff,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N ) )
% 0.18/0.44 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.18/0.44
% 0.18/0.44 % of_nat_0_less_iff
% 0.18/0.44 thf(fact_105_of__nat__0__less__iff,axiom,
% 0.18/0.44 ! [N: nat] :
% 0.18/0.44 ( ( ord_less_int @ zero_zero_int @ ( semiri2019852685at_int @ N ) )
% 0.18/0.44 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.18/0.44
% 0.18/0.44 % of_nat_0_less_iff
% 0.18/0.44 thf(fact_106_of__nat__0__less__iff,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ( ( ord_less_real @ zero_zero_real @ ( semiri2110766477t_real @ N ) )
% 0.18/0.45 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_0_less_iff
% 0.18/0.45 thf(fact_107_count__list_Osimps_I1_J,axiom,
% 0.18/0.45 ! [Y: a] :
% 0.18/0.45 ( ( count_list_a @ nil_a @ Y )
% 0.18/0.45 = zero_zero_nat ) ).
% 0.18/0.45
% 0.18/0.45 % count_list.simps(1)
% 0.18/0.45 thf(fact_108_count__list_Osimps_I1_J,axiom,
% 0.18/0.45 ! [Y: list_a] :
% 0.18/0.45 ( ( count_list_list_a @ nil_list_a @ Y )
% 0.18/0.45 = zero_zero_nat ) ).
% 0.18/0.45
% 0.18/0.45 % count_list.simps(1)
% 0.18/0.45 thf(fact_109_count__list_Osimps_I1_J,axiom,
% 0.18/0.45 ! [Y: list_list_a] :
% 0.18/0.45 ( ( count_429956358list_a @ nil_list_list_a @ Y )
% 0.18/0.45 = zero_zero_nat ) ).
% 0.18/0.45
% 0.18/0.45 % count_list.simps(1)
% 0.18/0.45 thf(fact_110_interval__induct__rule,axiom,
% 0.18/0.45 ! [I: set_nat,P: nat > $o,A: nat] :
% 0.18/0.45 ( ! [X3: nat] :
% 0.18/0.45 ( ! [Y2: nat] :
% 0.18/0.45 ( ( ( member_nat @ X3 @ I )
% 0.18/0.45 & ( member_nat @ Y2 @ I )
% 0.18/0.45 & ( ord_less_nat @ Y2 @ X3 ) )
% 0.18/0.45 => ( P @ Y2 ) )
% 0.18/0.45 => ( P @ X3 ) )
% 0.18/0.45 => ( P @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 % interval_induct_rule
% 0.18/0.45 thf(fact_111_interval__induct,axiom,
% 0.18/0.45 ! [I: set_nat,P: nat > $o,A: nat] :
% 0.18/0.45 ( ! [X3: nat] :
% 0.18/0.45 ( ! [Y2: nat] :
% 0.18/0.45 ( ( ( member_nat @ X3 @ I )
% 0.18/0.45 & ( member_nat @ Y2 @ I )
% 0.18/0.45 & ( ord_less_nat @ Y2 @ X3 ) )
% 0.18/0.45 => ( P @ Y2 ) )
% 0.18/0.45 => ( P @ X3 ) )
% 0.18/0.45 => ( P @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 % interval_induct
% 0.18/0.45 thf(fact_112_zero__natural_Orsp,axiom,
% 0.18/0.45 zero_zero_nat = zero_zero_nat ).
% 0.18/0.45
% 0.18/0.45 % zero_natural.rsp
% 0.18/0.45 thf(fact_113_of__nat__eq__iff,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ( semiri2019852685at_int @ M )
% 0.18/0.45 = ( semiri2019852685at_int @ N ) )
% 0.18/0.45 = ( M = N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_eq_iff
% 0.18/0.45 thf(fact_114_of__nat__eq__iff,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ( semiri2110766477t_real @ M )
% 0.18/0.45 = ( semiri2110766477t_real @ N ) )
% 0.18/0.45 = ( M = N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_eq_iff
% 0.18/0.45 thf(fact_115_of__nat__0,axiom,
% 0.18/0.45 ( ( semiri1382578993at_nat @ zero_zero_nat )
% 0.18/0.45 = zero_zero_nat ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_0
% 0.18/0.45 thf(fact_116_of__nat__0,axiom,
% 0.18/0.45 ( ( semiri2019852685at_int @ zero_zero_nat )
% 0.18/0.45 = zero_zero_int ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_0
% 0.18/0.45 thf(fact_117_of__nat__0,axiom,
% 0.18/0.45 ( ( semiri2110766477t_real @ zero_zero_nat )
% 0.18/0.45 = zero_zero_real ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_0
% 0.18/0.45 thf(fact_118_of__nat__0__eq__iff,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ( ( zero_zero_nat
% 0.18/0.45 = ( semiri1382578993at_nat @ N ) )
% 0.18/0.45 = ( zero_zero_nat = N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_0_eq_iff
% 0.18/0.45 thf(fact_119_of__nat__0__eq__iff,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ( ( zero_zero_int
% 0.18/0.45 = ( semiri2019852685at_int @ N ) )
% 0.18/0.45 = ( zero_zero_nat = N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_0_eq_iff
% 0.18/0.45 thf(fact_120_of__nat__0__eq__iff,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ( ( zero_zero_real
% 0.18/0.45 = ( semiri2110766477t_real @ N ) )
% 0.18/0.45 = ( zero_zero_nat = N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_0_eq_iff
% 0.18/0.45 thf(fact_121_of__nat__eq__0__iff,axiom,
% 0.18/0.45 ! [M: nat] :
% 0.18/0.45 ( ( ( semiri1382578993at_nat @ M )
% 0.18/0.45 = zero_zero_nat )
% 0.18/0.45 = ( M = zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_eq_0_iff
% 0.18/0.45 thf(fact_122_of__nat__eq__0__iff,axiom,
% 0.18/0.45 ! [M: nat] :
% 0.18/0.45 ( ( ( semiri2019852685at_int @ M )
% 0.18/0.45 = zero_zero_int )
% 0.18/0.45 = ( M = zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_eq_0_iff
% 0.18/0.45 thf(fact_123_of__nat__eq__0__iff,axiom,
% 0.18/0.45 ! [M: nat] :
% 0.18/0.45 ( ( ( semiri2110766477t_real @ M )
% 0.18/0.45 = zero_zero_real )
% 0.18/0.45 = ( M = zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_eq_0_iff
% 0.18/0.45 thf(fact_124_of__nat__less__iff,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) )
% 0.18/0.45 = ( ord_less_nat @ M @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_less_iff
% 0.18/0.45 thf(fact_125_of__nat__less__iff,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) )
% 0.18/0.45 = ( ord_less_nat @ M @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_less_iff
% 0.18/0.45 thf(fact_126_of__nat__less__iff,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_real @ ( semiri2110766477t_real @ M ) @ ( semiri2110766477t_real @ N ) )
% 0.18/0.45 = ( ord_less_nat @ M @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_less_iff
% 0.18/0.45 thf(fact_127_of__nat__less__0__iff,axiom,
% 0.18/0.45 ! [M: nat] :
% 0.18/0.45 ~ ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_less_0_iff
% 0.18/0.45 thf(fact_128_of__nat__less__0__iff,axiom,
% 0.18/0.45 ! [M: nat] :
% 0.18/0.45 ~ ( ord_less_int @ ( semiri2019852685at_int @ M ) @ zero_zero_int ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_less_0_iff
% 0.18/0.45 thf(fact_129_of__nat__less__0__iff,axiom,
% 0.18/0.45 ! [M: nat] :
% 0.18/0.45 ~ ( ord_less_real @ ( semiri2110766477t_real @ M ) @ zero_zero_real ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_less_0_iff
% 0.18/0.45 thf(fact_130_less__imp__of__nat__less,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ M @ N )
% 0.18/0.45 => ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_of_nat_less
% 0.18/0.45 thf(fact_131_less__imp__of__nat__less,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ M @ N )
% 0.18/0.45 => ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_of_nat_less
% 0.18/0.45 thf(fact_132_less__imp__of__nat__less,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ M @ N )
% 0.18/0.45 => ( ord_less_real @ ( semiri2110766477t_real @ M ) @ ( semiri2110766477t_real @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_of_nat_less
% 0.18/0.45 thf(fact_133_of__nat__less__imp__less,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) )
% 0.18/0.45 => ( ord_less_nat @ M @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_less_imp_less
% 0.18/0.45 thf(fact_134_of__nat__less__imp__less,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) )
% 0.18/0.45 => ( ord_less_nat @ M @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_less_imp_less
% 0.18/0.45 thf(fact_135_of__nat__less__imp__less,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_real @ ( semiri2110766477t_real @ M ) @ ( semiri2110766477t_real @ N ) )
% 0.18/0.45 => ( ord_less_nat @ M @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_less_imp_less
% 0.18/0.45 thf(fact_136_Collect__minI,axiom,
% 0.18/0.45 ! [K: nat,I: set_nat,P: nat > $o] :
% 0.18/0.45 ( ( member_nat @ K @ I )
% 0.18/0.45 => ( ( P @ K )
% 0.18/0.45 => ? [X3: nat] :
% 0.18/0.45 ( ( member_nat @ X3 @ I )
% 0.18/0.45 & ( P @ X3 )
% 0.18/0.45 & ! [Xa: nat] :
% 0.18/0.45 ( ( member_nat @ Xa @ I )
% 0.18/0.45 => ( ( ord_less_nat @ Xa @ X3 )
% 0.18/0.45 => ~ ( P @ Xa ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Collect_minI
% 0.18/0.45 thf(fact_137_Collect__minI__ex,axiom,
% 0.18/0.45 ! [I: set_nat,P: nat > $o] :
% 0.18/0.45 ( ? [X4: nat] :
% 0.18/0.45 ( ( member_nat @ X4 @ I )
% 0.18/0.45 & ( P @ X4 ) )
% 0.18/0.45 => ? [X3: nat] :
% 0.18/0.45 ( ( member_nat @ X3 @ I )
% 0.18/0.45 & ( P @ X3 )
% 0.18/0.45 & ! [Xa: nat] :
% 0.18/0.45 ( ( member_nat @ Xa @ I )
% 0.18/0.45 => ( ( ord_less_nat @ Xa @ X3 )
% 0.18/0.45 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Collect_minI_ex
% 0.18/0.45 thf(fact_138_zero__less__imp__eq__int,axiom,
% 0.18/0.45 ! [K: int] :
% 0.18/0.45 ( ( ord_less_int @ zero_zero_int @ K )
% 0.18/0.45 => ? [N2: nat] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.18/0.45 & ( K
% 0.18/0.45 = ( semiri2019852685at_int @ N2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % zero_less_imp_eq_int
% 0.18/0.45 thf(fact_139_pos__int__cases,axiom,
% 0.18/0.45 ! [K: int] :
% 0.18/0.45 ( ( ord_less_int @ zero_zero_int @ K )
% 0.18/0.45 => ~ ! [N2: nat] :
% 0.18/0.45 ( ( K
% 0.18/0.45 = ( semiri2019852685at_int @ N2 ) )
% 0.18/0.45 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % pos_int_cases
% 0.18/0.45 thf(fact_140_reals__Archimedean2,axiom,
% 0.18/0.45 ! [X: real] :
% 0.18/0.45 ? [N2: nat] : ( ord_less_real @ X @ ( semiri2110766477t_real @ N2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % reals_Archimedean2
% 0.18/0.45 thf(fact_141_list__slice__def,axiom,
% 0.18/0.45 ( listSl97544552lice_a
% 0.18/0.45 = ( ^ [Xs3: list_a,K2: nat] : ( listSl1495374126_aux_a @ Xs3 @ K2 @ ( divide_divide_nat @ ( size_size_list_a @ Xs3 ) @ K2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % list_slice_def
% 0.18/0.45 thf(fact_142_of__nat__zero__less__power__iff,axiom,
% 0.18/0.45 ! [X: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ X ) @ N ) )
% 0.18/0.45 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.18/0.45 | ( N = zero_zero_nat ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_zero_less_power_iff
% 0.18/0.45 thf(fact_143_of__nat__zero__less__power__iff,axiom,
% 0.18/0.45 ! [X: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri2019852685at_int @ X ) @ N ) )
% 0.18/0.45 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.18/0.45 | ( N = zero_zero_nat ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_zero_less_power_iff
% 0.18/0.45 thf(fact_144_of__nat__zero__less__power__iff,axiom,
% 0.18/0.45 ! [X: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri2110766477t_real @ X ) @ N ) )
% 0.18/0.45 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.18/0.45 | ( N = zero_zero_nat ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_zero_less_power_iff
% 0.18/0.45 thf(fact_145_of__nat__le__0__iff,axiom,
% 0.18/0.45 ! [M: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat )
% 0.18/0.45 = ( M = zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_le_0_iff
% 0.18/0.45 thf(fact_146_of__nat__le__0__iff,axiom,
% 0.18/0.45 ! [M: nat] :
% 0.18/0.45 ( ( ord_less_eq_int @ ( semiri2019852685at_int @ M ) @ zero_zero_int )
% 0.18/0.45 = ( M = zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_le_0_iff
% 0.18/0.45 thf(fact_147_of__nat__le__0__iff,axiom,
% 0.18/0.45 ! [M: nat] :
% 0.18/0.45 ( ( ord_less_eq_real @ ( semiri2110766477t_real @ M ) @ zero_zero_real )
% 0.18/0.45 = ( M = zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_le_0_iff
% 0.18/0.45 thf(fact_148_ex__inverse__of__nat__less,axiom,
% 0.18/0.45 ! [X: real] :
% 0.18/0.45 ( ( ord_less_real @ zero_zero_real @ X )
% 0.18/0.45 => ? [N2: nat] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.18/0.45 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri2110766477t_real @ N2 ) ) @ X ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ex_inverse_of_nat_less
% 0.18/0.45 thf(fact_149_bot__nat__0_Oextremum,axiom,
% 0.18/0.45 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 0.18/0.45
% 0.18/0.45 % bot_nat_0.extremum
% 0.18/0.45 thf(fact_150_le0,axiom,
% 0.18/0.45 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.18/0.45
% 0.18/0.45 % le0
% 0.18/0.45 thf(fact_151_le__zero__eq,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.18/0.45 = ( N = zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % le_zero_eq
% 0.18/0.45 thf(fact_152_of__nat__le__iff,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) )
% 0.18/0.45 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_le_iff
% 0.18/0.45 thf(fact_153_of__nat__le__iff,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_eq_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) )
% 0.18/0.45 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_le_iff
% 0.18/0.45 thf(fact_154_of__nat__le__iff,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_eq_real @ ( semiri2110766477t_real @ M ) @ ( semiri2110766477t_real @ N ) )
% 0.18/0.45 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_le_iff
% 0.18/0.45 thf(fact_155_nat__zero__less__power__iff,axiom,
% 0.18/0.45 ! [X: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
% 0.18/0.45 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.18/0.45 | ( N = zero_zero_nat ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % nat_zero_less_power_iff
% 0.18/0.45 thf(fact_156_of__nat__power,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( semiri1382578993at_nat @ ( power_power_nat @ M @ N ) )
% 0.18/0.45 = ( power_power_nat @ ( semiri1382578993at_nat @ M ) @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_power
% 0.18/0.45 thf(fact_157_of__nat__power,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( semiri2019852685at_int @ ( power_power_nat @ M @ N ) )
% 0.18/0.45 = ( power_power_int @ ( semiri2019852685at_int @ M ) @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_power
% 0.18/0.45 thf(fact_158_of__nat__power,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( semiri2110766477t_real @ ( power_power_nat @ M @ N ) )
% 0.18/0.45 = ( power_power_real @ ( semiri2110766477t_real @ M ) @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_power
% 0.18/0.45 thf(fact_159_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.18/0.45 ! [B: nat,W: nat,X: nat] :
% 0.18/0.45 ( ( ( power_power_nat @ ( semiri1382578993at_nat @ B ) @ W )
% 0.18/0.45 = ( semiri1382578993at_nat @ X ) )
% 0.18/0.45 = ( ( power_power_nat @ B @ W )
% 0.18/0.45 = X ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_eq_of_nat_power_cancel_iff
% 0.18/0.45 thf(fact_160_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.18/0.45 ! [B: nat,W: nat,X: nat] :
% 0.18/0.45 ( ( ( power_power_int @ ( semiri2019852685at_int @ B ) @ W )
% 0.18/0.45 = ( semiri2019852685at_int @ X ) )
% 0.18/0.45 = ( ( power_power_nat @ B @ W )
% 0.18/0.45 = X ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_eq_of_nat_power_cancel_iff
% 0.18/0.45 thf(fact_161_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 0.18/0.45 ! [B: nat,W: nat,X: nat] :
% 0.18/0.45 ( ( ( power_power_real @ ( semiri2110766477t_real @ B ) @ W )
% 0.18/0.45 = ( semiri2110766477t_real @ X ) )
% 0.18/0.45 = ( ( power_power_nat @ B @ W )
% 0.18/0.45 = X ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_eq_of_nat_power_cancel_iff
% 0.18/0.45 thf(fact_162_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.18/0.45 ! [X: nat,B: nat,W: nat] :
% 0.18/0.45 ( ( ( semiri1382578993at_nat @ X )
% 0.18/0.45 = ( power_power_nat @ ( semiri1382578993at_nat @ B ) @ W ) )
% 0.18/0.45 = ( X
% 0.18/0.45 = ( power_power_nat @ B @ W ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_power_eq_of_nat_cancel_iff
% 0.18/0.45 thf(fact_163_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.18/0.45 ! [X: nat,B: nat,W: nat] :
% 0.18/0.45 ( ( ( semiri2019852685at_int @ X )
% 0.18/0.45 = ( power_power_int @ ( semiri2019852685at_int @ B ) @ W ) )
% 0.18/0.45 = ( X
% 0.18/0.45 = ( power_power_nat @ B @ W ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_power_eq_of_nat_cancel_iff
% 0.18/0.45 thf(fact_164_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 0.18/0.45 ! [X: nat,B: nat,W: nat] :
% 0.18/0.45 ( ( ( semiri2110766477t_real @ X )
% 0.18/0.45 = ( power_power_real @ ( semiri2110766477t_real @ B ) @ W ) )
% 0.18/0.45 = ( X
% 0.18/0.45 = ( power_power_nat @ B @ W ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_power_eq_of_nat_cancel_iff
% 0.18/0.45 thf(fact_165_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.18/0.45 ! [B: nat,W: nat,X: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ B ) @ W ) @ ( semiri1382578993at_nat @ X ) )
% 0.18/0.45 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_le_of_nat_power_cancel_iff
% 0.18/0.45 thf(fact_166_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.18/0.45 ! [B: nat,W: nat,X: nat] :
% 0.18/0.45 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri2019852685at_int @ B ) @ W ) @ ( semiri2019852685at_int @ X ) )
% 0.18/0.45 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_le_of_nat_power_cancel_iff
% 0.18/0.45 thf(fact_167_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.18/0.45 ! [B: nat,W: nat,X: nat] :
% 0.18/0.45 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri2110766477t_real @ B ) @ W ) @ ( semiri2110766477t_real @ X ) )
% 0.18/0.45 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_le_of_nat_power_cancel_iff
% 0.18/0.45 thf(fact_168_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.18/0.45 ! [X: nat,B: nat,W: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ X ) @ ( power_power_nat @ ( semiri1382578993at_nat @ B ) @ W ) )
% 0.18/0.45 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_power_le_of_nat_cancel_iff
% 0.18/0.45 thf(fact_169_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.18/0.45 ! [X: nat,B: nat,W: nat] :
% 0.18/0.45 ( ( ord_less_eq_int @ ( semiri2019852685at_int @ X ) @ ( power_power_int @ ( semiri2019852685at_int @ B ) @ W ) )
% 0.18/0.45 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_power_le_of_nat_cancel_iff
% 0.18/0.45 thf(fact_170_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.18/0.45 ! [X: nat,B: nat,W: nat] :
% 0.18/0.45 ( ( ord_less_eq_real @ ( semiri2110766477t_real @ X ) @ ( power_power_real @ ( semiri2110766477t_real @ B ) @ W ) )
% 0.18/0.45 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_power_le_of_nat_cancel_iff
% 0.18/0.45 thf(fact_171_power__eq__0__iff,axiom,
% 0.18/0.45 ! [A: int,N: nat] :
% 0.18/0.45 ( ( ( power_power_int @ A @ N )
% 0.18/0.45 = zero_zero_int )
% 0.18/0.45 = ( ( A = zero_zero_int )
% 0.18/0.45 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_eq_0_iff
% 0.18/0.45 thf(fact_172_power__eq__0__iff,axiom,
% 0.18/0.45 ! [A: nat,N: nat] :
% 0.18/0.45 ( ( ( power_power_nat @ A @ N )
% 0.18/0.45 = zero_zero_nat )
% 0.18/0.45 = ( ( A = zero_zero_nat )
% 0.18/0.45 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_eq_0_iff
% 0.18/0.45 thf(fact_173_power__eq__0__iff,axiom,
% 0.18/0.45 ! [A: real,N: nat] :
% 0.18/0.45 ( ( ( power_power_real @ A @ N )
% 0.18/0.45 = zero_zero_real )
% 0.18/0.45 = ( ( A = zero_zero_real )
% 0.18/0.45 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_eq_0_iff
% 0.18/0.45 thf(fact_174_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.18/0.45 ! [X: nat,B: nat,W: nat] :
% 0.18/0.45 ( ( ord_less_nat @ ( semiri1382578993at_nat @ X ) @ ( power_power_nat @ ( semiri1382578993at_nat @ B ) @ W ) )
% 0.18/0.45 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_power_less_of_nat_cancel_iff
% 0.18/0.45 thf(fact_175_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.18/0.45 ! [X: nat,B: nat,W: nat] :
% 0.18/0.45 ( ( ord_less_int @ ( semiri2019852685at_int @ X ) @ ( power_power_int @ ( semiri2019852685at_int @ B ) @ W ) )
% 0.18/0.45 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_power_less_of_nat_cancel_iff
% 0.18/0.45 thf(fact_176_of__nat__power__less__of__nat__cancel__iff,axiom,
% 0.18/0.45 ! [X: nat,B: nat,W: nat] :
% 0.18/0.45 ( ( ord_less_real @ ( semiri2110766477t_real @ X ) @ ( power_power_real @ ( semiri2110766477t_real @ B ) @ W ) )
% 0.18/0.45 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_power_less_of_nat_cancel_iff
% 0.18/0.45 thf(fact_177_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.18/0.45 ! [B: nat,W: nat,X: nat] :
% 0.18/0.45 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ B ) @ W ) @ ( semiri1382578993at_nat @ X ) )
% 0.18/0.45 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_less_of_nat_power_cancel_iff
% 0.18/0.45 thf(fact_178_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.18/0.45 ! [B: nat,W: nat,X: nat] :
% 0.18/0.45 ( ( ord_less_int @ ( power_power_int @ ( semiri2019852685at_int @ B ) @ W ) @ ( semiri2019852685at_int @ X ) )
% 0.18/0.45 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_less_of_nat_power_cancel_iff
% 0.18/0.45 thf(fact_179_of__nat__less__of__nat__power__cancel__iff,axiom,
% 0.18/0.45 ! [B: nat,W: nat,X: nat] :
% 0.18/0.45 ( ( ord_less_real @ ( power_power_real @ ( semiri2110766477t_real @ B ) @ W ) @ ( semiri2110766477t_real @ X ) )
% 0.18/0.45 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_less_of_nat_power_cancel_iff
% 0.18/0.45 thf(fact_180_power__mono__iff,axiom,
% 0.18/0.45 ! [A: nat,B: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.18/0.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.18/0.45 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.45 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 0.18/0.45 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_mono_iff
% 0.18/0.45 thf(fact_181_power__mono__iff,axiom,
% 0.18/0.45 ! [A: int,B: int,N: nat] :
% 0.18/0.45 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.18/0.45 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.18/0.45 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.45 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 0.18/0.45 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_mono_iff
% 0.18/0.45 thf(fact_182_power__mono__iff,axiom,
% 0.18/0.45 ! [A: real,B: real,N: nat] :
% 0.18/0.45 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.18/0.45 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.18/0.45 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.45 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 0.18/0.45 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_mono_iff
% 0.18/0.45 thf(fact_183_nonneg__int__cases,axiom,
% 0.18/0.45 ! [K: int] :
% 0.18/0.45 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.18/0.45 => ~ ! [N2: nat] :
% 0.18/0.45 ( K
% 0.18/0.45 != ( semiri2019852685at_int @ N2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % nonneg_int_cases
% 0.18/0.45 thf(fact_184_zero__le__imp__eq__int,axiom,
% 0.18/0.45 ! [K: int] :
% 0.18/0.45 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.18/0.45 => ? [N2: nat] :
% 0.18/0.45 ( K
% 0.18/0.45 = ( semiri2019852685at_int @ N2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % zero_le_imp_eq_int
% 0.18/0.45 thf(fact_185_zero__integer_Orsp,axiom,
% 0.18/0.45 zero_zero_int = zero_zero_int ).
% 0.18/0.45
% 0.18/0.45 % zero_integer.rsp
% 0.18/0.45 thf(fact_186_of__nat__mono,axiom,
% 0.18/0.45 ! [I2: nat,J: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ I2 @ J )
% 0.18/0.45 => ( ord_less_eq_nat @ ( semiri1382578993at_nat @ I2 ) @ ( semiri1382578993at_nat @ J ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_mono
% 0.18/0.45 thf(fact_187_of__nat__mono,axiom,
% 0.18/0.45 ! [I2: nat,J: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ I2 @ J )
% 0.18/0.45 => ( ord_less_eq_int @ ( semiri2019852685at_int @ I2 ) @ ( semiri2019852685at_int @ J ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_mono
% 0.18/0.45 thf(fact_188_of__nat__mono,axiom,
% 0.18/0.45 ! [I2: nat,J: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ I2 @ J )
% 0.18/0.45 => ( ord_less_eq_real @ ( semiri2110766477t_real @ I2 ) @ ( semiri2110766477t_real @ J ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_mono
% 0.18/0.45 thf(fact_189_zle__int,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_eq_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) )
% 0.18/0.45 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % zle_int
% 0.18/0.45 thf(fact_190_int__int__eq,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ( semiri2019852685at_int @ M )
% 0.18/0.45 = ( semiri2019852685at_int @ N ) )
% 0.18/0.45 = ( M = N ) ) ).
% 0.18/0.45
% 0.18/0.45 % int_int_eq
% 0.18/0.45 thf(fact_191_real__arch__simple,axiom,
% 0.18/0.45 ! [X: real] :
% 0.18/0.45 ? [N2: nat] : ( ord_less_eq_real @ X @ ( semiri2110766477t_real @ N2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % real_arch_simple
% 0.18/0.45 thf(fact_192_power__less__imp__less__base,axiom,
% 0.18/0.45 ! [A: nat,N: nat,B: nat] :
% 0.18/0.45 ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 0.18/0.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.18/0.45 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_less_imp_less_base
% 0.18/0.45 thf(fact_193_power__less__imp__less__base,axiom,
% 0.18/0.45 ! [A: int,N: nat,B: int] :
% 0.18/0.45 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 0.18/0.45 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.18/0.45 => ( ord_less_int @ A @ B ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_less_imp_less_base
% 0.18/0.45 thf(fact_194_power__less__imp__less__base,axiom,
% 0.18/0.45 ! [A: real,N: nat,B: real] :
% 0.18/0.45 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 0.18/0.45 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.18/0.45 => ( ord_less_real @ A @ B ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_less_imp_less_base
% 0.18/0.45 thf(fact_195_power__inverse,axiom,
% 0.18/0.45 ! [A: real,N: nat] :
% 0.18/0.45 ( ( power_power_real @ ( inverse_inverse_real @ A ) @ N )
% 0.18/0.45 = ( inverse_inverse_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_inverse
% 0.18/0.45 thf(fact_196_power__divide,axiom,
% 0.18/0.45 ! [A: real,B: real,N: nat] :
% 0.18/0.45 ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N )
% 0.18/0.45 = ( divide_divide_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_divide
% 0.18/0.45 thf(fact_197_power__not__zero,axiom,
% 0.18/0.45 ! [A: int,N: nat] :
% 0.18/0.45 ( ( A != zero_zero_int )
% 0.18/0.45 => ( ( power_power_int @ A @ N )
% 0.18/0.45 != zero_zero_int ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_not_zero
% 0.18/0.45 thf(fact_198_power__not__zero,axiom,
% 0.18/0.45 ! [A: nat,N: nat] :
% 0.18/0.45 ( ( A != zero_zero_nat )
% 0.18/0.45 => ( ( power_power_nat @ A @ N )
% 0.18/0.45 != zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_not_zero
% 0.18/0.45 thf(fact_199_power__not__zero,axiom,
% 0.18/0.45 ! [A: real,N: nat] :
% 0.18/0.45 ( ( A != zero_zero_real )
% 0.18/0.45 => ( ( power_power_real @ A @ N )
% 0.18/0.45 != zero_zero_real ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_not_zero
% 0.18/0.45 thf(fact_200_zero__le__power,axiom,
% 0.18/0.45 ! [A: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.18/0.45 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % zero_le_power
% 0.18/0.45 thf(fact_201_zero__le__power,axiom,
% 0.18/0.45 ! [A: int,N: nat] :
% 0.18/0.45 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.18/0.45 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % zero_le_power
% 0.18/0.45 thf(fact_202_zero__le__power,axiom,
% 0.18/0.45 ! [A: real,N: nat] :
% 0.18/0.45 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.18/0.45 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % zero_le_power
% 0.18/0.45 thf(fact_203_power__mono,axiom,
% 0.18/0.45 ! [A: nat,B: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ A @ B )
% 0.18/0.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.18/0.45 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_mono
% 0.18/0.45 thf(fact_204_power__mono,axiom,
% 0.18/0.45 ! [A: int,B: int,N: nat] :
% 0.18/0.45 ( ( ord_less_eq_int @ A @ B )
% 0.18/0.45 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.18/0.45 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_mono
% 0.18/0.45 thf(fact_205_power__mono,axiom,
% 0.18/0.45 ! [A: real,B: real,N: nat] :
% 0.18/0.45 ( ( ord_less_eq_real @ A @ B )
% 0.18/0.45 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.18/0.45 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_mono
% 0.18/0.45 thf(fact_206_less__eq__int__code_I1_J,axiom,
% 0.18/0.45 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.18/0.45
% 0.18/0.45 % less_eq_int_code(1)
% 0.18/0.45 thf(fact_207_less__int__code_I1_J,axiom,
% 0.18/0.45 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.18/0.45
% 0.18/0.45 % less_int_code(1)
% 0.18/0.45 thf(fact_208_power__eq__imp__eq__base,axiom,
% 0.18/0.45 ! [A: nat,N: nat,B: nat] :
% 0.18/0.45 ( ( ( power_power_nat @ A @ N )
% 0.18/0.45 = ( power_power_nat @ B @ N ) )
% 0.18/0.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.18/0.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.18/0.45 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.45 => ( A = B ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_eq_imp_eq_base
% 0.18/0.45 thf(fact_209_power__eq__imp__eq__base,axiom,
% 0.18/0.45 ! [A: int,N: nat,B: int] :
% 0.18/0.45 ( ( ( power_power_int @ A @ N )
% 0.18/0.45 = ( power_power_int @ B @ N ) )
% 0.18/0.45 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.18/0.45 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.18/0.45 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.45 => ( A = B ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_eq_imp_eq_base
% 0.18/0.45 thf(fact_210_power__eq__imp__eq__base,axiom,
% 0.18/0.45 ! [A: real,N: nat,B: real] :
% 0.18/0.45 ( ( ( power_power_real @ A @ N )
% 0.18/0.45 = ( power_power_real @ B @ N ) )
% 0.18/0.45 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.18/0.45 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.18/0.45 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.45 => ( A = B ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_eq_imp_eq_base
% 0.18/0.45 thf(fact_211_power__eq__iff__eq__base,axiom,
% 0.18/0.45 ! [N: nat,A: nat,B: nat] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.18/0.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.18/0.45 => ( ( ( power_power_nat @ A @ N )
% 0.18/0.45 = ( power_power_nat @ B @ N ) )
% 0.18/0.45 = ( A = B ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_eq_iff_eq_base
% 0.18/0.45 thf(fact_212_power__eq__iff__eq__base,axiom,
% 0.18/0.45 ! [N: nat,A: int,B: int] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.45 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.18/0.45 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.18/0.45 => ( ( ( power_power_int @ A @ N )
% 0.18/0.45 = ( power_power_int @ B @ N ) )
% 0.18/0.45 = ( A = B ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_eq_iff_eq_base
% 0.18/0.45 thf(fact_213_power__eq__iff__eq__base,axiom,
% 0.18/0.45 ! [N: nat,A: real,B: real] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.45 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.18/0.45 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.18/0.45 => ( ( ( power_power_real @ A @ N )
% 0.18/0.45 = ( power_power_real @ B @ N ) )
% 0.18/0.45 = ( A = B ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_eq_iff_eq_base
% 0.18/0.45 thf(fact_214_real__arch__inverse,axiom,
% 0.18/0.45 ! [E2: real] :
% 0.18/0.45 ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.18/0.45 = ( ? [N3: nat] :
% 0.18/0.45 ( ( N3 != zero_zero_nat )
% 0.18/0.45 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri2110766477t_real @ N3 ) ) )
% 0.18/0.45 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri2110766477t_real @ N3 ) ) @ E2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % real_arch_inverse
% 0.18/0.45 thf(fact_215_forall__pos__mono,axiom,
% 0.18/0.45 ! [P: real > $o,E2: real] :
% 0.18/0.45 ( ! [D: real,E: real] :
% 0.18/0.45 ( ( ord_less_real @ D @ E )
% 0.18/0.45 => ( ( P @ D )
% 0.18/0.45 => ( P @ E ) ) )
% 0.18/0.45 => ( ! [N2: nat] :
% 0.18/0.45 ( ( N2 != zero_zero_nat )
% 0.18/0.45 => ( P @ ( inverse_inverse_real @ ( semiri2110766477t_real @ N2 ) ) ) )
% 0.18/0.45 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.18/0.45 => ( P @ E2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % forall_pos_mono
% 0.18/0.45 thf(fact_216_zero__le,axiom,
% 0.18/0.45 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 0.18/0.45
% 0.18/0.45 % zero_le
% 0.18/0.45 thf(fact_217_le__numeral__extra_I3_J,axiom,
% 0.18/0.45 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 0.18/0.45
% 0.18/0.45 % le_numeral_extra(3)
% 0.18/0.45 thf(fact_218_le__numeral__extra_I3_J,axiom,
% 0.18/0.45 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.18/0.45
% 0.18/0.45 % le_numeral_extra(3)
% 0.18/0.45 thf(fact_219_le__numeral__extra_I3_J,axiom,
% 0.18/0.45 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 0.18/0.45
% 0.18/0.45 % le_numeral_extra(3)
% 0.18/0.45 thf(fact_220_ge__less__neq__conv,axiom,
% 0.18/0.45 ( ord_less_eq_nat
% 0.18/0.45 = ( ^ [A3: nat,N3: nat] :
% 0.18/0.45 ! [X2: nat] :
% 0.18/0.45 ( ( ord_less_nat @ X2 @ A3 )
% 0.18/0.45 => ( N3 != X2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ge_less_neq_conv
% 0.18/0.45 thf(fact_221_ge__less__neq__conv,axiom,
% 0.18/0.45 ( ord_less_eq_int
% 0.18/0.45 = ( ^ [A3: int,N3: int] :
% 0.18/0.45 ! [X2: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ A3 )
% 0.18/0.45 => ( N3 != X2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ge_less_neq_conv
% 0.18/0.45 thf(fact_222_ge__less__neq__conv,axiom,
% 0.18/0.45 ( ord_less_eq_real
% 0.18/0.45 = ( ^ [A3: real,N3: real] :
% 0.18/0.45 ! [X2: real] :
% 0.18/0.45 ( ( ord_less_real @ X2 @ A3 )
% 0.18/0.45 => ( N3 != X2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ge_less_neq_conv
% 0.18/0.45 thf(fact_223_less__ge__neq__conv,axiom,
% 0.18/0.45 ( ord_less_nat
% 0.18/0.45 = ( ^ [N3: nat,A3: nat] :
% 0.18/0.45 ! [X2: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ A3 @ X2 )
% 0.18/0.45 => ( N3 != X2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_ge_neq_conv
% 0.18/0.45 thf(fact_224_less__ge__neq__conv,axiom,
% 0.18/0.45 ( ord_less_int
% 0.18/0.45 = ( ^ [N3: int,A3: int] :
% 0.18/0.45 ! [X2: int] :
% 0.18/0.45 ( ( ord_less_eq_int @ A3 @ X2 )
% 0.18/0.45 => ( N3 != X2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_ge_neq_conv
% 0.18/0.45 thf(fact_225_less__ge__neq__conv,axiom,
% 0.18/0.45 ( ord_less_real
% 0.18/0.45 = ( ^ [N3: real,A3: real] :
% 0.18/0.45 ! [X2: real] :
% 0.18/0.45 ( ( ord_less_eq_real @ A3 @ X2 )
% 0.18/0.45 => ( N3 != X2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_ge_neq_conv
% 0.18/0.45 thf(fact_226_greater__le__neq__conv,axiom,
% 0.18/0.45 ( ord_less_nat
% 0.18/0.45 = ( ^ [A3: nat,N3: nat] :
% 0.18/0.45 ! [X2: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ X2 @ A3 )
% 0.18/0.45 => ( N3 != X2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % greater_le_neq_conv
% 0.18/0.45 thf(fact_227_greater__le__neq__conv,axiom,
% 0.18/0.45 ( ord_less_int
% 0.18/0.45 = ( ^ [A3: int,N3: int] :
% 0.18/0.45 ! [X2: int] :
% 0.18/0.45 ( ( ord_less_eq_int @ X2 @ A3 )
% 0.18/0.45 => ( N3 != X2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % greater_le_neq_conv
% 0.18/0.45 thf(fact_228_greater__le__neq__conv,axiom,
% 0.18/0.45 ( ord_less_real
% 0.18/0.45 = ( ^ [A3: real,N3: real] :
% 0.18/0.45 ! [X2: real] :
% 0.18/0.45 ( ( ord_less_eq_real @ X2 @ A3 )
% 0.18/0.45 => ( N3 != X2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % greater_le_neq_conv
% 0.18/0.45 thf(fact_229_le__greater__neq__conv,axiom,
% 0.18/0.45 ( ord_less_eq_nat
% 0.18/0.45 = ( ^ [N3: nat,A3: nat] :
% 0.18/0.45 ! [X2: nat] :
% 0.18/0.45 ( ( ord_less_nat @ A3 @ X2 )
% 0.18/0.45 => ( N3 != X2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % le_greater_neq_conv
% 0.18/0.45 thf(fact_230_le__greater__neq__conv,axiom,
% 0.18/0.45 ( ord_less_eq_int
% 0.18/0.45 = ( ^ [N3: int,A3: int] :
% 0.18/0.45 ! [X2: int] :
% 0.18/0.45 ( ( ord_less_int @ A3 @ X2 )
% 0.18/0.45 => ( N3 != X2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % le_greater_neq_conv
% 0.18/0.45 thf(fact_231_le__greater__neq__conv,axiom,
% 0.18/0.45 ( ord_less_eq_real
% 0.18/0.45 = ( ^ [N3: real,A3: real] :
% 0.18/0.45 ! [X2: real] :
% 0.18/0.45 ( ( ord_less_real @ A3 @ X2 )
% 0.18/0.45 => ( N3 != X2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % le_greater_neq_conv
% 0.18/0.45 thf(fact_232_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.18/0.45 ! [A: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.18/0.45 => ( A = zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % bot_nat_0.extremum_uniqueI
% 0.18/0.45 thf(fact_233_bot__nat__0_Oextremum__unique,axiom,
% 0.18/0.45 ! [A: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.18/0.45 = ( A = zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % bot_nat_0.extremum_unique
% 0.18/0.45 thf(fact_234_le__0__eq,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.18/0.45 = ( N = zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % le_0_eq
% 0.18/0.45 thf(fact_235_less__eq__nat_Osimps_I1_J,axiom,
% 0.18/0.45 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.18/0.45
% 0.18/0.45 % less_eq_nat.simps(1)
% 0.18/0.45 thf(fact_236_less__mono__imp__le__mono,axiom,
% 0.18/0.45 ! [F: nat > nat,I2: nat,J: nat] :
% 0.18/0.45 ( ! [I3: nat,J2: nat] :
% 0.18/0.45 ( ( ord_less_nat @ I3 @ J2 )
% 0.18/0.45 => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 0.18/0.45 => ( ( ord_less_eq_nat @ I2 @ J )
% 0.18/0.45 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_mono_imp_le_mono
% 0.18/0.45 thf(fact_237_le__neq__implies__less,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ M @ N )
% 0.18/0.45 => ( ( M != N )
% 0.18/0.45 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % le_neq_implies_less
% 0.18/0.45 thf(fact_238_less__or__eq__imp__le,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ( ord_less_nat @ M @ N )
% 0.18/0.45 | ( M = N ) )
% 0.18/0.45 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_or_eq_imp_le
% 0.18/0.45 thf(fact_239_le__eq__less__or__eq,axiom,
% 0.18/0.45 ( ord_less_eq_nat
% 0.18/0.45 = ( ^ [M3: nat,N3: nat] :
% 0.18/0.45 ( ( ord_less_nat @ M3 @ N3 )
% 0.18/0.45 | ( M3 = N3 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % le_eq_less_or_eq
% 0.18/0.45 thf(fact_240_less__imp__le__nat,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ M @ N )
% 0.18/0.45 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_le_nat
% 0.18/0.45 thf(fact_241_nat__less__le,axiom,
% 0.18/0.45 ( ord_less_nat
% 0.18/0.45 = ( ^ [M3: nat,N3: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ M3 @ N3 )
% 0.18/0.45 & ( M3 != N3 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % nat_less_le
% 0.18/0.45 thf(fact_242_zero__less__power,axiom,
% 0.18/0.45 ! [A: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.18/0.45 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % zero_less_power
% 0.18/0.45 thf(fact_243_zero__less__power,axiom,
% 0.18/0.45 ! [A: int,N: nat] :
% 0.18/0.45 ( ( ord_less_int @ zero_zero_int @ A )
% 0.18/0.45 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % zero_less_power
% 0.18/0.45 thf(fact_244_zero__less__power,axiom,
% 0.18/0.45 ! [A: real,N: nat] :
% 0.18/0.45 ( ( ord_less_real @ zero_zero_real @ A )
% 0.18/0.45 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % zero_less_power
% 0.18/0.45 thf(fact_245_nat__power__less__imp__less,axiom,
% 0.18/0.45 ! [I2: nat,M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ I2 )
% 0.18/0.45 => ( ( ord_less_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N ) )
% 0.18/0.45 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % nat_power_less_imp_less
% 0.18/0.45 thf(fact_246_power__strict__mono,axiom,
% 0.18/0.45 ! [A: nat,B: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ A @ B )
% 0.18/0.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.18/0.45 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.45 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_strict_mono
% 0.18/0.45 thf(fact_247_power__strict__mono,axiom,
% 0.18/0.45 ! [A: int,B: int,N: nat] :
% 0.18/0.45 ( ( ord_less_int @ A @ B )
% 0.18/0.45 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.18/0.45 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.45 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_strict_mono
% 0.18/0.45 thf(fact_248_power__strict__mono,axiom,
% 0.18/0.45 ! [A: real,B: real,N: nat] :
% 0.18/0.45 ( ( ord_less_real @ A @ B )
% 0.18/0.45 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.18/0.45 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.45 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % power_strict_mono
% 0.18/0.45 thf(fact_249_zero__power,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.45 => ( ( power_power_int @ zero_zero_int @ N )
% 0.18/0.45 = zero_zero_int ) ) ).
% 0.18/0.45
% 0.18/0.45 % zero_power
% 0.18/0.45 thf(fact_250_zero__power,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.45 => ( ( power_power_nat @ zero_zero_nat @ N )
% 0.18/0.45 = zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % zero_power
% 0.18/0.45 thf(fact_251_zero__power,axiom,
% 0.18/0.45 ! [N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.45 => ( ( power_power_real @ zero_zero_real @ N )
% 0.18/0.45 = zero_zero_real ) ) ).
% 0.18/0.45
% 0.18/0.45 % zero_power
% 0.18/0.45 thf(fact_252_of__nat__0__le__iff,axiom,
% 0.18/0.45 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_0_le_iff
% 0.18/0.45 thf(fact_253_of__nat__0__le__iff,axiom,
% 0.18/0.45 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri2019852685at_int @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_0_le_iff
% 0.18/0.45 thf(fact_254_of__nat__0__le__iff,axiom,
% 0.18/0.45 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2110766477t_real @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % of_nat_0_le_iff
% 0.18/0.45 thf(fact_255_ex__least__nat__le,axiom,
% 0.18/0.45 ! [P: nat > $o,N: nat] :
% 0.18/0.45 ( ( P @ N )
% 0.18/0.45 => ( ~ ( P @ zero_zero_nat )
% 0.18/0.45 => ? [K3: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ K3 @ N )
% 0.18/0.45 & ! [I4: nat] :
% 0.18/0.45 ( ( ord_less_nat @ I4 @ K3 )
% 0.18/0.45 => ~ ( P @ I4 ) )
% 0.18/0.45 & ( P @ K3 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ex_least_nat_le
% 0.18/0.45 thf(fact_256_count__le__length,axiom,
% 0.18/0.45 ! [Xs: list_a,X: a] : ( ord_less_eq_nat @ ( count_list_a @ Xs @ X ) @ ( size_size_list_a @ Xs ) ) ).
% 0.18/0.45
% 0.18/0.45 % count_le_length
% 0.18/0.45 thf(fact_257_list__slice__length,axiom,
% 0.18/0.45 ! [Xs: list_a,K: nat] :
% 0.18/0.45 ( ( size_s1427607542list_a @ ( listSl97544552lice_a @ Xs @ K ) )
% 0.18/0.45 = ( divide_divide_nat @ ( size_size_list_a @ Xs ) @ K ) ) ).
% 0.18/0.45
% 0.18/0.45 % list_slice_length
% 0.18/0.45 thf(fact_258_inverse__le__iff__le,axiom,
% 0.18/0.45 ! [A: real,B: real] :
% 0.18/0.45 ( ( ord_less_real @ zero_zero_real @ A )
% 0.18/0.45 => ( ( ord_less_real @ zero_zero_real @ B )
% 0.18/0.45 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.18/0.45 = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % inverse_le_iff_le
% 0.18/0.45 thf(fact_259_inverse__le__iff__le__neg,axiom,
% 0.18/0.45 ! [A: real,B: real] :
% 0.18/0.45 ( ( ord_less_real @ A @ zero_zero_real )
% 0.18/0.45 => ( ( ord_less_real @ B @ zero_zero_real )
% 0.18/0.45 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.18/0.45 = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % inverse_le_iff_le_neg
% 0.18/0.45 thf(fact_260_div__less,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ M @ N )
% 0.18/0.45 => ( ( divide_divide_nat @ M @ N )
% 0.18/0.45 = zero_zero_nat ) ) ).
% 0.18/0.45
% 0.18/0.45 % div_less
% 0.18/0.45 thf(fact_261_inverse__positive__iff__positive,axiom,
% 0.18/0.45 ! [A: real] :
% 0.18/0.45 ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 0.18/0.45 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 % inverse_positive_iff_positive
% 0.18/0.45 thf(fact_262_inverse__negative__iff__negative,axiom,
% 0.18/0.45 ! [A: real] :
% 0.18/0.45 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 0.18/0.45 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.18/0.45
% 0.18/0.45 % inverse_negative_iff_negative
% 0.18/0.45 thf(fact_263_inverse__less__iff__less__neg,axiom,
% 0.18/0.45 ! [A: real,B: real] :
% 0.18/0.45 ( ( ord_less_real @ A @ zero_zero_real )
% 0.18/0.45 => ( ( ord_less_real @ B @ zero_zero_real )
% 0.18/0.45 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.18/0.45 = ( ord_less_real @ B @ A ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % inverse_less_iff_less_neg
% 0.18/0.45 thf(fact_264_inverse__eq__iff__eq,axiom,
% 0.18/0.45 ! [A: real,B: real] :
% 0.18/0.45 ( ( ( inverse_inverse_real @ A )
% 0.18/0.45 = ( inverse_inverse_real @ B ) )
% 0.18/0.45 = ( A = B ) ) ).
% 0.18/0.45
% 0.18/0.45 % inverse_eq_iff_eq
% 0.18/0.45 thf(fact_265_inverse__inverse__eq,axiom,
% 0.18/0.45 ! [A: real] :
% 0.18/0.45 ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 0.18/0.45 = A ) ).
% 0.18/0.45
% 0.18/0.45 % inverse_inverse_eq
% 0.18/0.45 thf(fact_266_division__ring__divide__zero,axiom,
% 0.18/0.45 ! [A: real] :
% 0.18/0.45 ( ( divide_divide_real @ A @ zero_zero_real )
% 0.18/0.45 = zero_zero_real ) ).
% 0.18/0.45
% 0.18/0.45 % division_ring_divide_zero
% 0.18/0.45 thf(fact_267_divide__cancel__right,axiom,
% 0.18/0.45 ! [A: real,C: real,B: real] :
% 0.18/0.45 ( ( ( divide_divide_real @ A @ C )
% 0.18/0.45 = ( divide_divide_real @ B @ C ) )
% 0.18/0.45 = ( ( C = zero_zero_real )
% 0.18/0.45 | ( A = B ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % divide_cancel_right
% 0.18/0.45 thf(fact_268_divide__cancel__left,axiom,
% 0.18/0.45 ! [C: real,A: real,B: real] :
% 0.18/0.45 ( ( ( divide_divide_real @ C @ A )
% 0.18/0.45 = ( divide_divide_real @ C @ B ) )
% 0.18/0.45 = ( ( C = zero_zero_real )
% 0.18/0.45 | ( A = B ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % divide_cancel_left
% 0.18/0.45 thf(fact_269_divide__eq__0__iff,axiom,
% 0.18/0.45 ! [A: real,B: real] :
% 0.18/0.45 ( ( ( divide_divide_real @ A @ B )
% 0.18/0.45 = zero_zero_real )
% 0.18/0.45 = ( ( A = zero_zero_real )
% 0.18/0.45 | ( B = zero_zero_real ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % divide_eq_0_iff
% 0.18/0.45 thf(fact_270_inverse__nonzero__iff__nonzero,axiom,
% 0.18/0.45 ! [A: real] :
% 0.18/0.45 ( ( ( inverse_inverse_real @ A )
% 0.18/0.45 = zero_zero_real )
% 0.18/0.45 = ( A = zero_zero_real ) ) ).
% 0.18/0.45
% 0.18/0.45 % inverse_nonzero_iff_nonzero
% 0.18/0.45 thf(fact_271_inverse__zero,axiom,
% 0.18/0.45 ( ( inverse_inverse_real @ zero_zero_real )
% 0.18/0.45 = zero_zero_real ) ).
% 0.18/0.45
% 0.18/0.45 % inverse_zero
% 0.18/0.45 thf(fact_272_inverse__divide,axiom,
% 0.18/0.45 ! [A: real,B: real] :
% 0.18/0.45 ( ( inverse_inverse_real @ ( divide_divide_real @ A @ B ) )
% 0.18/0.45 = ( divide_divide_real @ B @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 % inverse_divide
% 0.18/0.45 thf(fact_273_inverse__nonnegative__iff__nonnegative,axiom,
% 0.18/0.45 ! [A: real] :
% 0.18/0.45 ( ( ord_less_eq_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 0.18/0.45 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 % inverse_nonnegative_iff_nonnegative
% 0.18/0.45 thf(fact_274_inverse__nonpositive__iff__nonpositive,axiom,
% 0.18/0.45 ! [A: real] :
% 0.18/0.45 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 0.18/0.45 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.18/0.45
% 0.18/0.45 % inverse_nonpositive_iff_nonpositive
% 0.18/0.45 thf(fact_275_inverse__less__iff__less,axiom,
% 0.18/0.45 ! [A: real,B: real] :
% 0.18/0.45 ( ( ord_less_real @ zero_zero_real @ A )
% 0.18/0.45 => ( ( ord_less_real @ zero_zero_real @ B )
% 0.18/0.45 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.18/0.45 = ( ord_less_real @ B @ A ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % inverse_less_iff_less
% 0.18/0.45 thf(fact_276_div__neg__neg__trivial,axiom,
% 0.18/0.45 ! [K: int,L: int] :
% 0.18/0.45 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 0.18/0.45 => ( ( ord_less_int @ L @ K )
% 0.18/0.45 => ( ( divide_divide_int @ K @ L )
% 0.18/0.45 = zero_zero_int ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % div_neg_neg_trivial
% 0.18/0.45 thf(fact_277_div__pos__pos__trivial,axiom,
% 0.18/0.45 ! [K: int,L: int] :
% 0.18/0.45 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.18/0.45 => ( ( ord_less_int @ K @ L )
% 0.18/0.45 => ( ( divide_divide_int @ K @ L )
% 0.18/0.45 = zero_zero_int ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % div_pos_pos_trivial
% 0.18/0.45 thf(fact_278_less__eq__real__def,axiom,
% 0.18/0.45 ( ord_less_eq_real
% 0.18/0.45 = ( ^ [X2: real,Y3: real] :
% 0.18/0.45 ( ( ord_less_real @ X2 @ Y3 )
% 0.18/0.45 | ( X2 = Y3 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_eq_real_def
% 0.18/0.45 thf(fact_279_le__refl,axiom,
% 0.18/0.45 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.18/0.45
% 0.18/0.45 % le_refl
% 0.18/0.45 thf(fact_280_le__trans,axiom,
% 0.18/0.45 ! [I2: nat,J: nat,K: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ I2 @ J )
% 0.18/0.45 => ( ( ord_less_eq_nat @ J @ K )
% 0.18/0.45 => ( ord_less_eq_nat @ I2 @ K ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % le_trans
% 0.18/0.45 thf(fact_281_eq__imp__le,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( M = N )
% 0.18/0.45 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % eq_imp_le
% 0.18/0.45 thf(fact_282_le__antisym,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ M @ N )
% 0.18/0.45 => ( ( ord_less_eq_nat @ N @ M )
% 0.18/0.45 => ( M = N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % le_antisym
% 0.18/0.45 thf(fact_283_nat__le__linear,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ M @ N )
% 0.18/0.45 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.18/0.45
% 0.18/0.45 % nat_le_linear
% 0.18/0.45 thf(fact_284_Nat_Oex__has__greatest__nat,axiom,
% 0.18/0.45 ! [P: nat > $o,K: nat,B: nat] :
% 0.18/0.45 ( ( P @ K )
% 0.18/0.45 => ( ! [Y4: nat] :
% 0.18/0.45 ( ( P @ Y4 )
% 0.18/0.45 => ( ord_less_eq_nat @ Y4 @ B ) )
% 0.18/0.45 => ? [X3: nat] :
% 0.18/0.45 ( ( P @ X3 )
% 0.18/0.45 & ! [Y2: nat] :
% 0.18/0.45 ( ( P @ Y2 )
% 0.18/0.45 => ( ord_less_eq_nat @ Y2 @ X3 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Nat.ex_has_greatest_nat
% 0.18/0.45 thf(fact_285_real__of__nat__div4,axiom,
% 0.18/0.45 ! [N: nat,X: nat] : ( ord_less_eq_real @ ( semiri2110766477t_real @ ( divide_divide_nat @ N @ X ) ) @ ( divide_divide_real @ ( semiri2110766477t_real @ N ) @ ( semiri2110766477t_real @ X ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % real_of_nat_div4
% 0.18/0.45 thf(fact_286_linordered__field__no__lb,axiom,
% 0.18/0.45 ! [X4: real] :
% 0.18/0.45 ? [Y4: real] : ( ord_less_real @ Y4 @ X4 ) ).
% 0.18/0.45
% 0.18/0.45 % linordered_field_no_lb
% 0.18/0.45 thf(fact_287_linordered__field__no__ub,axiom,
% 0.18/0.45 ! [X4: real] :
% 0.18/0.45 ? [X_1: real] : ( ord_less_real @ X4 @ X_1 ) ).
% 0.18/0.45
% 0.18/0.45 % linordered_field_no_ub
% 0.18/0.45 thf(fact_288_inverse__eq__imp__eq,axiom,
% 0.18/0.45 ! [A: real,B: real] :
% 0.18/0.45 ( ( ( inverse_inverse_real @ A )
% 0.18/0.45 = ( inverse_inverse_real @ B ) )
% 0.18/0.45 => ( A = B ) ) ).
% 0.18/0.45
% 0.18/0.45 % inverse_eq_imp_eq
% 0.18/0.45 thf(fact_289_div__le__mono,axiom,
% 0.18/0.45 ! [M: nat,N: nat,K: nat] :
% 0.18/0.45 ( ( ord_less_eq_nat @ M @ N )
% 0.18/0.45 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % div_le_mono
% 0.18/0.45 thf(fact_290_div__le__dividend,axiom,
% 0.18/0.45 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 0.18/0.45
% 0.18/0.45 % div_le_dividend
% 0.18/0.45 thf(fact_291_nonzero__imp__inverse__nonzero,axiom,
% 0.18/0.45 ! [A: real] :
% 0.18/0.45 ( ( A != zero_zero_real )
% 0.18/0.45 => ( ( inverse_inverse_real @ A )
% 0.18/0.45 != zero_zero_real ) ) ).
% 0.18/0.45
% 0.18/0.45 % nonzero_imp_inverse_nonzero
% 0.18/0.45 thf(fact_292_nonzero__inverse__inverse__eq,axiom,
% 0.18/0.45 ! [A: real] :
% 0.18/0.45 ( ( A != zero_zero_real )
% 0.18/0.45 => ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 0.18/0.45 = A ) ) ).
% 0.18/0.45
% 0.18/0.45 % nonzero_inverse_inverse_eq
% 0.18/0.45 thf(fact_293_nonzero__inverse__eq__imp__eq,axiom,
% 0.18/0.45 ! [A: real,B: real] :
% 0.18/0.45 ( ( ( inverse_inverse_real @ A )
% 0.18/0.45 = ( inverse_inverse_real @ B ) )
% 0.18/0.45 => ( ( A != zero_zero_real )
% 0.18/0.45 => ( ( B != zero_zero_real )
% 0.18/0.45 => ( A = B ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % nonzero_inverse_eq_imp_eq
% 0.18/0.45 thf(fact_294_inverse__zero__imp__zero,axiom,
% 0.18/0.45 ! [A: real] :
% 0.18/0.45 ( ( ( inverse_inverse_real @ A )
% 0.18/0.45 = zero_zero_real )
% 0.18/0.45 => ( A = zero_zero_real ) ) ).
% 0.18/0.45
% 0.18/0.45 % inverse_zero_imp_zero
% 0.18/0.45 thf(fact_295_field__class_Ofield__inverse__zero,axiom,
% 0.18/0.45 ( ( inverse_inverse_real @ zero_zero_real )
% 0.18/0.45 = zero_zero_real ) ).
% 0.18/0.45
% 0.18/0.45 % field_class.field_inverse_zero
% 0.18/0.45 thf(fact_296_divide__le__0__iff,axiom,
% 0.18/0.45 ! [A: real,B: real] :
% 0.18/0.45 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 0.18/0.45 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.18/0.45 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 0.18/0.45 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.18/0.45 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % divide_le_0_iff
% 0.18/0.45 thf(fact_297_divide__right__mono,axiom,
% 0.18/0.45 ! [A: real,B: real,C: real] :
% 0.18/0.45 ( ( ord_less_eq_real @ A @ B )
% 0.18/0.45 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 0.18/0.45 => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % divide_right_mono
% 0.18/0.45 thf(fact_298_zero__le__divide__iff,axiom,
% 0.18/0.45 ! [A: real,B: real] :
% 0.18/0.45 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 0.18/0.45 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.18/0.45 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 0.18/0.45 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.18/0.45 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % zero_le_divide_iff
% 0.18/0.45 thf(fact_299_divide__nonneg__nonneg,axiom,
% 0.18/0.45 ! [X: real,Y: real] :
% 0.18/0.45 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.18/0.45 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.18/0.45 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % divide_nonneg_nonneg
% 0.18/0.45 thf(fact_300_divide__nonneg__nonpos,axiom,
% 0.18/0.45 ! [X: real,Y: real] :
% 0.18/0.45 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.18/0.45 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 0.18/0.45 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % divide_nonneg_nonpos
% 0.18/0.45 thf(fact_301_divide__nonpos__nonneg,axiom,
% 0.18/0.45 ! [X: real,Y: real] :
% 0.18/0.45 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.18/0.45 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.18/0.45 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % divide_nonpos_nonneg
% 0.18/0.45 thf(fact_302_divide__nonpos__nonpos,axiom,
% 0.18/0.45 ! [X: real,Y: real] :
% 0.18/0.45 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.18/0.45 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 0.18/0.45 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % divide_nonpos_nonpos
% 0.18/0.45 thf(fact_303_divide__right__mono__neg,axiom,
% 0.18/0.45 ! [A: real,B: real,C: real] :
% 0.18/0.45 ( ( ord_less_eq_real @ A @ B )
% 0.18/0.45 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 0.18/0.45 => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % divide_right_mono_neg
% 0.18/0.45 thf(fact_304_divide__neg__neg,axiom,
% 0.18/0.45 ! [X: real,Y: real] :
% 0.18/0.45 ( ( ord_less_real @ X @ zero_zero_real )
% 0.18/0.45 => ( ( ord_less_real @ Y @ zero_zero_real )
% 0.18/0.45 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % divide_neg_neg
% 0.18/0.45 thf(fact_305_divide__neg__pos,axiom,
% 0.18/0.45 ! [X: real,Y: real] :
% 0.18/0.45 ( ( ord_less_real @ X @ zero_zero_real )
% 0.18/0.45 => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.18/0.45 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % divide_neg_pos
% 0.18/0.45 thf(fact_306_divide__pos__neg,axiom,
% 0.18/0.45 ! [X: real,Y: real] :
% 0.18/0.45 ( ( ord_less_real @ zero_zero_real @ X )
% 0.18/0.45 => ( ( ord_less_real @ Y @ zero_zero_real )
% 0.18/0.45 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % divide_pos_neg
% 0.18/0.45 thf(fact_307_divide__pos__pos,axiom,
% 0.18/0.45 ! [X: real,Y: real] :
% 0.18/0.45 ( ( ord_less_real @ zero_zero_real @ X )
% 0.18/0.45 => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.18/0.45 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % divide_pos_pos
% 0.18/0.45 thf(fact_308_divide__less__0__iff,axiom,
% 0.18/0.45 ! [A: real,B: real] :
% 0.18/0.45 ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 0.18/0.45 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.18/0.45 & ( ord_less_real @ B @ zero_zero_real ) )
% 0.18/0.45 | ( ( ord_less_real @ A @ zero_zero_real )
% 0.18/0.45 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % divide_less_0_iff
% 0.18/0.45 thf(fact_309_divide__less__cancel,axiom,
% 0.18/0.45 ! [A: real,C: real,B: real] :
% 0.18/0.45 ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 0.18/0.45 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 0.18/0.45 => ( ord_less_real @ A @ B ) )
% 0.18/0.45 & ( ( ord_less_real @ C @ zero_zero_real )
% 0.18/0.45 => ( ord_less_real @ B @ A ) )
% 0.18/0.45 & ( C != zero_zero_real ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % divide_less_cancel
% 0.18/0.45 thf(fact_310_zero__less__divide__iff,axiom,
% 0.18/0.45 ! [A: real,B: real] :
% 0.18/0.45 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 0.18/0.45 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.18/0.45 & ( ord_less_real @ zero_zero_real @ B ) )
% 0.18/0.45 | ( ( ord_less_real @ A @ zero_zero_real )
% 0.18/0.45 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % zero_less_divide_iff
% 0.18/0.45 thf(fact_311_divide__strict__right__mono,axiom,
% 0.18/0.45 ! [A: real,B: real,C: real] :
% 0.18/0.45 ( ( ord_less_real @ A @ B )
% 0.18/0.45 => ( ( ord_less_real @ zero_zero_real @ C )
% 0.18/0.45 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % divide_strict_right_mono
% 0.18/0.45 thf(fact_312_divide__strict__right__mono__neg,axiom,
% 0.18/0.45 ! [B: real,A: real,C: real] :
% 0.18/0.45 ( ( ord_less_real @ B @ A )
% 0.18/0.45 => ( ( ord_less_real @ C @ zero_zero_real )
% 0.18/0.45 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % divide_strict_right_mono_neg
% 0.18/0.45 thf(fact_313_inverse__less__imp__less,axiom,
% 0.18/0.45 ! [A: real,B: real] :
% 0.18/0.45 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 0.18/0.45 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.18/0.45 => ( ord_less_real @ B @ A ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % inverse_less_imp_less
% 0.18/0.45 thf(fact_314_less__imp__inverse__less,axiom,
% 0.18/0.45 ! [A: real,B: real] :
% 0.18/0.45 ( ( ord_less_real @ A @ B )
% 0.18/0.45 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.18/0.45 => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_inverse_less
% 0.18/0.45 thf(fact_315_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ( divide_divide_nat @ M @ N )
% 0.18/0.45 = zero_zero_nat )
% 0.18/0.45 = ( ( ord_less_nat @ M @ N )
% 0.18/0.45 | ( N = zero_zero_nat ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Euclidean_Division.div_eq_0_iff
% 0.18/0.45 thf(fact_316_div__greater__zero__iff,axiom,
% 0.18/0.45 ! [M: nat,N: nat] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 0.18/0.45 = ( ( ord_less_eq_nat @ N @ M )
% 0.18/0.45 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % div_greater_zero_iff
% 0.18/0.45 thf(fact_317_div__le__mono2,axiom,
% 0.18/0.45 ! [M: nat,N: nat,K: nat] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.18/0.45 => ( ( ord_less_eq_nat @ M @ N )
% 0.18/0.45 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % div_le_mono2
% 0.18/0.45 thf(fact_318_complete__real,axiom,
% 0.18/0.45 ! [S2: set_real] :
% 0.18/0.45 ( ? [X4: real] : ( member_real @ X4 @ S2 )
% 0.18/0.45 => ( ? [Z: real] :
% 0.18/0.45 ! [X3: real] :
% 0.18/0.45 ( ( member_real @ X3 @ S2 )
% 0.18/0.45 => ( ord_less_eq_real @ X3 @ Z ) )
% 0.18/0.45 => ? [Y4: real] :
% 0.18/0.45 ( ! [X4: real] :
% 0.18/0.45 ( ( member_real @ X4 @ S2 )
% 0.18/0.45 => ( ord_less_eq_real @ X4 @ Y4 ) )
% 0.18/0.45 & ! [Z: real] :
% 0.18/0.45 ( ! [X3: real] :
% 0.18/0.45 ( ( member_real @ X3 @ S2 )
% 0.18/0.45 => ( ord_less_eq_real @ X3 @ Z ) )
% 0.18/0.45 => ( ord_less_eq_real @ Y4 @ Z ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % complete_real
% 0.18/0.45 thf(fact_319_nonneg1__imp__zdiv__pos__iff,axiom,
% 0.18/0.45 ! [A: int,B: int] :
% 0.18/0.45 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.18/0.45 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.18/0.45 = ( ( ord_less_eq_int @ B @ A )
% 0.18/0.45 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % nonneg1_imp_zdiv_pos_iff
% 0.18/0.45 thf(fact_320_pos__imp__zdiv__nonneg__iff,axiom,
% 0.18/0.45 ! [B: int,A: int] :
% 0.18/0.45 ( ( ord_less_int @ zero_zero_int @ B )
% 0.18/0.45 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.18/0.45 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % pos_imp_zdiv_nonneg_iff
% 0.18/0.45 thf(fact_321_div__neg__pos__less0,axiom,
% 0.18/0.45 ! [A: int,B: int] :
% 0.18/0.45 ( ( ord_less_int @ A @ zero_zero_int )
% 0.18/0.45 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.18/0.45 => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % div_neg_pos_less0
% 0.18/0.45 thf(fact_322_neg__imp__zdiv__neg__iff,axiom,
% 0.18/0.45 ! [B: int,A: int] :
% 0.18/0.45 ( ( ord_less_int @ B @ zero_zero_int )
% 0.18/0.45 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 0.18/0.45 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % neg_imp_zdiv_neg_iff
% 0.18/0.45 thf(fact_323_pos__imp__zdiv__neg__iff,axiom,
% 0.18/0.45 ! [B: int,A: int] :
% 0.18/0.45 ( ( ord_less_int @ zero_zero_int @ B )
% 0.18/0.45 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 0.18/0.45 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % pos_imp_zdiv_neg_iff
% 0.18/0.45 thf(fact_324_zdiv__int,axiom,
% 0.18/0.45 ! [A: nat,B: nat] :
% 0.18/0.45 ( ( semiri2019852685at_int @ ( divide_divide_nat @ A @ B ) )
% 0.18/0.45 = ( divide_divide_int @ ( semiri2019852685at_int @ A ) @ ( semiri2019852685at_int @ B ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % zdiv_int
% 0.18/0.45 thf(fact_325_zdiv__mono1,axiom,
% 0.18/0.45 ! [A: int,A4: int,B: int] :
% 0.18/0.45 ( ( ord_less_eq_int @ A @ A4 )
% 0.18/0.45 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.18/0.45 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A4 @ B ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % zdiv_mono1
% 0.18/0.45 thf(fact_326_zdiv__mono2,axiom,
% 0.18/0.45 ! [A: int,B2: int,B: int] :
% 0.18/0.45 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.18/0.45 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 0.18/0.45 => ( ( ord_less_eq_int @ B2 @ B )
% 0.18/0.45 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B2 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % zdiv_mono2
% 0.18/0.45 thf(fact_327_zdiv__eq__0__iff,axiom,
% 0.18/0.45 ! [I2: int,K: int] :
% 0.18/0.45 ( ( ( divide_divide_int @ I2 @ K )
% 0.18/0.45 = zero_zero_int )
% 0.18/0.45 = ( ( K = zero_zero_int )
% 0.18/0.45 | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 0.18/0.45 & ( ord_less_int @ I2 @ K ) )
% 0.18/0.45 | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 0.18/0.45 & ( ord_less_int @ K @ I2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % zdiv_eq_0_iff
% 0.18/0.45 thf(fact_328_zdiv__mono1__neg,axiom,
% 0.18/0.45 ! [A: int,A4: int,B: int] :
% 0.18/0.45 ( ( ord_less_eq_int @ A @ A4 )
% 0.18/0.45 => ( ( ord_less_int @ B @ zero_zero_int )
% 0.18/0.45 => ( ord_less_eq_int @ ( divide_divide_int @ A4 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % zdiv_mono1_neg
% 0.18/0.45 thf(fact_329_zdiv__mono2__neg,axiom,
% 0.18/0.45 ! [A: int,B2: int,B: int] :
% 0.18/0.45 ( ( ord_less_int @ A @ zero_zero_int )
% 0.18/0.45 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 0.18/0.45 => ( ( ord_less_eq_int @ B2 @ B )
% 0.18/0.45 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B2 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % zdiv_mono2_neg
% 0.18/0.45 thf(fact_330_div__int__pos__iff,axiom,
% 0.18/0.45 ! [K: int,L: int] :
% 0.18/0.45 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 0.18/0.45 = ( ( K = zero_zero_int )
% 0.18/0.45 | ( L = zero_zero_int )
% 0.18/0.45 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.18/0.45 & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 0.18/0.45 | ( ( ord_less_int @ K @ zero_zero_int )
% 0.18/0.45 & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % div_int_pos_iff
% 0.18/0.45 thf(fact_331_div__positive__int,axiom,
% 0.18/0.45 ! [L: int,K: int] :
% 0.18/0.45 ( ( ord_less_eq_int @ L @ K )
% 0.18/0.45 => ( ( ord_less_int @ zero_zero_int @ L )
% 0.18/0.45 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % div_positive_int
% 0.18/0.45 thf(fact_332_div__nonneg__neg__le0,axiom,
% 0.18/0.45 ! [A: int,B: int] :
% 0.18/0.45 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.18/0.45 => ( ( ord_less_int @ B @ zero_zero_int )
% 0.18/0.45 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % div_nonneg_neg_le0
% 0.18/0.45 thf(fact_333_div__nonpos__pos__le0,axiom,
% 0.18/0.45 ! [A: int,B: int] :
% 0.18/0.45 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.18/0.45 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.18/0.45 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % div_nonpos_pos_le0
% 0.18/0.45 thf(fact_334_pos__imp__zdiv__pos__iff,axiom,
% 0.18/0.45 ! [K: int,I2: int] :
% 0.18/0.45 ( ( ord_less_int @ zero_zero_int @ K )
% 0.18/0.45 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I2 @ K ) )
% 0.18/0.45 = ( ord_less_eq_int @ K @ I2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % pos_imp_zdiv_pos_iff
% 0.18/0.45 thf(fact_335_neg__imp__zdiv__nonneg__iff,axiom,
% 0.18/0.45 ! [B: int,A: int] :
% 0.18/0.45 ( ( ord_less_int @ B @ zero_zero_int )
% 0.18/0.45 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.18/0.45 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % neg_imp_zdiv_nonneg_iff
% 0.18/0.45 thf(fact_336_realpow__pos__nth__unique,axiom,
% 0.18/0.45 ! [N: nat,A: real] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.45 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.18/0.45 => ? [X3: real] :
% 0.18/0.45 ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.18/0.45 & ( ( power_power_real @ X3 @ N )
% 0.18/0.45 = A )
% 0.18/0.45 & ! [Y2: real] :
% 0.18/0.45 ( ( ( ord_less_real @ zero_zero_real @ Y2 )
% 0.18/0.45 & ( ( power_power_real @ Y2 @ N )
% 0.18/0.45 = A ) )
% 0.18/0.45 => ( Y2 = X3 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % realpow_pos_nth_unique
% 0.18/0.45 thf(fact_337_realpow__pos__nth,axiom,
% 0.18/0.45 ! [N: nat,A: real] :
% 0.18/0.45 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.18/0.45 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.18/0.45 => ? [R: real] :
% 0.18/0.45 ( ( ord_less_real @ zero_zero_real @ R )
% 0.18/0.45 & ( ( power_power_real @ R @ N )
% 0.18/0.45 = A ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % realpow_pos_nth
% 0.18/0.45 thf(fact_338_nat__int__comparison_I3_J,axiom,
% 0.18/0.45 ( ord_less_eq_nat
% 0.18/0.45 = ( ^ [A3: nat,B3: nat] : ( ord_less_eq_int @ ( semiri2019852685at_int @ A3 ) @ ( semiri2019852685at_int @ B3 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % nat_int_comparison(3)
% 0.18/0.45 thf(fact_339_nat__int__comparison_I2_J,axiom,
% 0.18/0.45 ( ord_less_nat
% 0.18/0.45 = ( ^ [A3: nat,B3: nat] : ( ord_less_int @ ( semiri2019852685at_int @ A3 ) @ ( semiri2019852685at_int @ B3 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % nat_int_comparison(2)
% 0.18/0.45 thf(fact_340_verit__la__generic,axiom,
% 0.18/0.45 ! [A: int,X: int] :
% 0.18/0.45 ( ( ord_less_eq_int @ A @ X )
% 0.18/0.45 | ( A = X )
% 0.18/0.45 | ( ord_less_eq_int @ X @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 % verit_la_generic
% 0.18/0.45 thf(fact_341_int__if,axiom,
% 0.18/0.45 ! [P: $o,A: nat,B: nat] :
% 0.18/0.45 ( ( P
% 0.18/0.45 => ( ( semiri2019852685at_int @ ( if_nat @ P @ A @ B ) )
% 0.18/0.45 = ( semiri2019852685at_int @ A ) ) )
% 0.18/0.45 & ( ~ P
% 0.18/0.45 => ( ( semiri2019852685at_int @ ( if_nat @ P @ A @ B ) )
% 0.18/0.45 = ( semiri2019852685at_int @ B ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % int_if
% 0.18/0.45 thf(fact_342_nat__int__comparison_I1_J,axiom,
% 0.18/0.45 ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 0.18/0.45 = ( ^ [A3: nat,B3: nat] :
% 0.18/0.45 ( ( semiri2019852685at_int @ A3 )
% 0.18/0.45 = ( semiri2019852685at_int @ B3 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % nat_int_comparison(1)
% 0.18/0.45 thf(fact_343_int__ops_I1_J,axiom,
% 0.18/0.45 ( ( semiri2019852685at_int @ zero_zero_nat )
% 0.18/0.45 = zero_zero_int ) ).
% 0.18/0.45
% 0.18/0.45 % int_ops(1)
% 0.18/0.45 thf(fact_344_div__gr__imp__gr__divisor,axiom,
% 0.18/0.45 ! [X: nat,N: nat,M: nat] :
% 0.18/0.45 ( ( ord_less_nat @ X @ ( divide_divide_nat @ N @ M ) )
% 0.18/0.45 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.18/0.45
% 0.18/0.45 % div_gr_imp_gr_divisor
% 0.18/0.45 thf(fact_345_div__eq__0__conv,axiom,
% 0.18/0.45 ! [N: nat,M: nat] :
% 0.18/0.45 ( ( ( divide_divide_nat @ N @ M )
% 0.18/0.45 = zero_zero_nat )
% 0.18/0.45 = ( ( M = zero_zero_nat )
% 0.18/0.45 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % div_eq_0_conv
% 0.18/0.45
% 0.18/0.45 % Helper facts (3)
% 0.18/0.45 thf(help_If_3_1_If_001t__Nat__Onat_T,axiom,
% 0.18/0.45 ! [P: $o] :
% 0.18/0.45 ( ( P = $true )
% 0.18/0.45 | ( P = $false ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 0.18/0.45 ! [X: nat,Y: nat] :
% 0.18/0.45 ( ( if_nat @ $false @ X @ Y )
% 0.18/0.45 = Y ) ).
% 0.18/0.45
% 0.18/0.45 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 0.18/0.45 ! [X: nat,Y: nat] :
% 0.18/0.45 ( ( if_nat @ $true @ X @ Y )
% 0.18/0.45 = X ) ).
% 0.18/0.45
% 0.18/0.45 % Conjectures (1)
% 0.18/0.45 thf(conj_0,conjecture,
% 0.18/0.45 ( ( listSl97544552lice_a @ nil_a @ k )
% 0.18/0.45 = nil_list_a ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 3.40/1.98 ---- Embedded in THF ---
% 3.40/1.98 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.40/1.98 %%% Generated on Tue Feb 24 08:26:11 EST 2026
% 3.40/1.98 %%% using '$$dhol' embedding, version 1.3.0.
% 3.40/1.98 %%% Logic specification used:
% 3.40/1.98 %%% thf(spec, logic, $$dhol).
% 3.40/1.98
% 3.40/1.98 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2DTF491.p
% See solution above
% 3.40/1.99 ------------------------
% 3.64/2.03 ---- Cleaned THF ---
% 3.64/2.03 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J_J,type,
% 3.64/2.03 list_l2071841302list_a: $tType ).
% 3.64/2.03
% 3.64/2.03 thf(ty_n_t__Option__Ooption_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 3.64/2.03 option_list_list_a: $tType ).
% 3.64/2.03
% 3.64/2.03 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 3.64/2.03 list_list_list_a: $tType ).
% 3.64/2.03
% 3.64/2.03 thf(ty_n_t__Option__Ooption_It__List__Olist_Itf__a_J_J,type,
% 3.64/2.03 option_list_a: $tType ).
% 3.64/2.03
% 3.64/2.03 thf(ty_n_t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 3.64/2.03 list_list_a: $tType ).
% 3.64/2.03
% 3.64/2.03 thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 3.64/2.03 set_real: $tType ).
% 3.64/2.03
% 3.64/2.03 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 3.64/2.03 set_nat: $tType ).
% 3.64/2.03
% 3.64/2.03 thf(ty_n_t__Option__Ooption_Itf__a_J,type,
% 3.64/2.03 option_a: $tType ).
% 3.64/2.03
% 3.64/2.03 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 3.64/2.03 list_a: $tType ).
% 3.64/2.03
% 3.64/2.03 thf(ty_n_t__Real__Oreal,type,
% 3.64/2.03 real: $tType ).
% 3.64/2.03
% 3.64/2.03 thf(ty_n_t__Nat__Onat,type,
% 3.64/2.03 nat: $tType ).
% 3.64/2.03
% 3.64/2.03 thf(ty_n_t__Int__Oint,type,
% 3.64/2.03 int: $tType ).
% 3.64/2.03
% 3.64/2.03 thf(ty_n_tf__a,type,
% 3.64/2.03 a: $tType ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Real__Oreal,type,
% 3.64/2.03 inverse_inverse_real: real > real ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
% 3.64/2.03 zero_zero_int: int ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 3.64/2.03 zero_zero_nat: nat ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
% 3.64/2.03 zero_zero_real: real ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_If_001t__Nat__Onat,type,
% 3.64/2.03 if_nat: $o > nat > nat > nat ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice_001t__List__Olist_Itf__a_J,type,
% 3.64/2.03 listSl162220270list_a: list_list_a > nat > list_list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice_001tf__a,type,
% 3.64/2.03 listSl97544552lice_a: list_a > nat > list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice__aux_001t__List__Olist_Itf__a_J,type,
% 3.64/2.03 listSl856612276list_a: list_list_a > nat > nat > list_list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_ListSlice__Mirabelle__csprijwpmv_Olist__slice__aux_001tf__a,type,
% 3.64/2.03 listSl1495374126_aux_a: list_a > nat > nat > list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Obind_001t__List__Olist_It__List__Olist_Itf__a_J_J_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 3.64/2.03 bind_l311701255list_a: list_list_list_a > ( list_list_a > list_list_list_a ) > list_list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Obind_001t__List__Olist_It__List__Olist_Itf__a_J_J_001t__List__Olist_Itf__a_J,type,
% 3.64/2.03 bind_l94945665list_a: list_list_list_a > ( list_list_a > list_list_a ) > list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Obind_001t__List__Olist_It__List__Olist_Itf__a_J_J_001tf__a,type,
% 3.64/2.03 bind_list_list_a_a: list_list_list_a > ( list_list_a > list_a ) > list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Obind_001t__List__Olist_Itf__a_J_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 3.64/2.03 bind_l971853709list_a: list_list_a > ( list_a > list_list_list_a ) > list_list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Obind_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
% 3.64/2.03 bind_list_a_list_a: list_list_a > ( list_a > list_list_a ) > list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Obind_001t__List__Olist_Itf__a_J_001tf__a,type,
% 3.64/2.03 bind_list_a_a: list_list_a > ( list_a > list_a ) > list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Obind_001tf__a_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 3.64/2.03 bind_a_list_list_a: list_a > ( a > list_list_list_a ) > list_list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Obind_001tf__a_001t__List__Olist_Itf__a_J,type,
% 3.64/2.03 bind_a_list_a: list_a > ( a > list_list_a ) > list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Obind_001tf__a_001tf__a,type,
% 3.64/2.03 bind_a_a: list_a > ( a > list_a ) > list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Oconcat_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 3.64/2.03 concat_list_list_a: list_l2071841302list_a > list_list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Oconcat_001t__List__Olist_Itf__a_J,type,
% 3.64/2.03 concat_list_a: list_list_list_a > list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Oconcat_001tf__a,type,
% 3.64/2.03 concat_a: list_list_a > list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Ocount__list_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 3.64/2.03 count_429956358list_a: list_list_list_a > list_list_a > nat ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Ocount__list_001t__List__Olist_Itf__a_J,type,
% 3.64/2.03 count_list_list_a: list_list_a > list_a > nat ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Ocount__list_001tf__a,type,
% 3.64/2.03 count_list_a: list_a > a > nat ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Ogen__length_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 3.64/2.03 gen_le840878749list_a: nat > list_list_list_a > nat ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Ogen__length_001t__List__Olist_Itf__a_J,type,
% 3.64/2.03 gen_length_list_a: nat > list_list_a > nat ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Ogen__length_001tf__a,type,
% 3.64/2.03 gen_length_a: nat > list_a > nat ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 3.64/2.03 nil_list_list_list_a: list_l2071841302list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 3.64/2.03 nil_list_list_a: list_list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Olist_ONil_001t__List__Olist_Itf__a_J,type,
% 3.64/2.03 nil_list_a: list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Olist_ONil_001tf__a,type,
% 3.64/2.03 nil_a: list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Olist__ex1_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 3.64/2.03 list_ex1_list_list_a: ( list_list_a > $o ) > list_list_list_a > $o ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Olist__ex1_001t__List__Olist_Itf__a_J,type,
% 3.64/2.03 list_ex1_list_a: ( list_a > $o ) > list_list_a > $o ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Olist__ex1_001tf__a,type,
% 3.64/2.03 list_ex1_a: ( a > $o ) > list_a > $o ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Omap__filter_001t__List__Olist_It__List__Olist_Itf__a_J_J_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 3.64/2.03 map_fi824137674list_a: ( list_list_a > option_list_list_a ) > list_list_list_a > list_list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Omap__filter_001t__List__Olist_It__List__Olist_Itf__a_J_J_001t__List__Olist_Itf__a_J,type,
% 3.64/2.03 map_fi213215172list_a: ( list_list_a > option_list_a ) > list_list_list_a > list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Omap__filter_001t__List__Olist_It__List__Olist_Itf__a_J_J_001tf__a,type,
% 3.64/2.03 map_fi1574988606st_a_a: ( list_list_a > option_a ) > list_list_list_a > list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Omap__filter_001t__List__Olist_Itf__a_J_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 3.64/2.03 map_fi1090123216list_a: ( list_a > option_list_list_a ) > list_list_a > list_list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Omap__filter_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
% 3.64/2.03 map_fi461586634list_a: ( list_a > option_list_a ) > list_list_a > list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Omap__filter_001t__List__Olist_Itf__a_J_001tf__a,type,
% 3.64/2.03 map_filter_list_a_a: ( list_a > option_a ) > list_list_a > list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Omap__filter_001tf__a_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 3.64/2.03 map_fi2089402454list_a: ( a > option_list_list_a ) > list_a > list_list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Omap__filter_001tf__a_001t__List__Olist_Itf__a_J,type,
% 3.64/2.03 map_filter_a_list_a: ( a > option_list_a ) > list_a > list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Omap__filter_001tf__a_001tf__a,type,
% 3.64/2.03 map_filter_a_a: ( a > option_a ) > list_a > list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Omaps_001t__List__Olist_It__List__Olist_Itf__a_J_J_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 3.64/2.03 maps_l57963201list_a: ( list_list_a > list_list_list_a ) > list_list_list_a > list_list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Omaps_001t__List__Olist_It__List__Olist_Itf__a_J_J_001t__List__Olist_Itf__a_J,type,
% 3.64/2.03 maps_l2025957947list_a: ( list_list_a > list_list_a ) > list_list_list_a > list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Omaps_001t__List__Olist_It__List__Olist_Itf__a_J_J_001tf__a,type,
% 3.64/2.03 maps_list_list_a_a: ( list_list_a > list_a ) > list_list_list_a > list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Omaps_001t__List__Olist_Itf__a_J_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 3.64/2.03 maps_l755382343list_a: ( list_a > list_list_list_a ) > list_list_a > list_list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Omaps_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
% 3.64/2.03 maps_list_a_list_a: ( list_a > list_list_a ) > list_list_a > list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Omaps_001t__List__Olist_Itf__a_J_001tf__a,type,
% 3.64/2.03 maps_list_a_a: ( list_a > list_a ) > list_list_a > list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Omaps_001tf__a_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 3.64/2.03 maps_a_list_list_a: ( a > list_list_list_a ) > list_a > list_list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Omaps_001tf__a_001t__List__Olist_Itf__a_J,type,
% 3.64/2.03 maps_a_list_a: ( a > list_list_a ) > list_a > list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Omaps_001tf__a_001tf__a,type,
% 3.64/2.03 maps_a_a: ( a > list_a ) > list_a > list_a ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Omember_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 3.64/2.03 member_list_list_a: list_list_list_a > list_list_a > $o ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Omember_001t__List__Olist_Itf__a_J,type,
% 3.64/2.03 member_list_a: list_list_a > list_a > $o ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Omember_001tf__a,type,
% 3.64/2.03 member_a: list_a > a > $o ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Onull_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 3.64/2.03 null_list_list_a: list_list_list_a > $o ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Onull_001t__List__Olist_Itf__a_J,type,
% 3.64/2.03 null_list_a: list_list_a > $o ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_List_Onull_001tf__a,type,
% 3.64/2.03 null_a: list_a > $o ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 3.64/2.03 semiri2019852685at_int: nat > int ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 3.64/2.03 semiri1382578993at_nat: nat > nat ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 3.64/2.03 semiri2110766477t_real: nat > real ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 3.64/2.03 size_s575106428list_a: list_list_list_a > nat ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 3.64/2.03 size_s1427607542list_a: list_list_a > nat ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_Itf__a_J,type,
% 3.64/2.03 size_size_list_a: list_a > nat ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 3.64/2.03 ord_less_int: int > int > $o ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 3.64/2.03 ord_less_nat: nat > nat > $o ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
% 3.64/2.03 ord_less_real: real > real > $o ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
% 3.64/2.03 ord_less_eq_int: int > int > $o ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 3.64/2.03 ord_less_eq_nat: nat > nat > $o ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 3.64/2.03 ord_less_eq_real: real > real > $o ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Power_Opower__class_Opower_001t__Int__Oint,type,
% 3.64/2.03 power_power_int: int > nat > int ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat,type,
% 3.64/2.03 power_power_nat: nat > nat > nat ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Power_Opower__class_Opower_001t__Real__Oreal,type,
% 3.64/2.03 power_power_real: real > nat > real ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
% 3.64/2.03 divide_divide_int: int > int > int ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 3.64/2.03 divide_divide_nat: nat > nat > nat ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 3.64/2.03 divide_divide_real: real > real > real ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 3.64/2.03 collect_nat: ( nat > $o ) > set_nat ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
% 3.64/2.03 collect_real: ( real > $o ) > set_real ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_member_001t__Nat__Onat,type,
% 3.64/2.03 member_nat: nat > set_nat > $o ).
% 3.64/2.03
% 3.64/2.03 thf(sy_c_member_001t__Real__Oreal,type,
% 3.64/2.03 member_real: real > set_real > $o ).
% 3.64/2.03
% 3.64/2.03 thf(sy_v_k,type,
% 3.64/2.03 k: nat ).
% 3.64/2.03
% 3.64/2.03 thf(fact_0_list__slice__0,axiom,
% 3.64/2.03 ! [Xs: list_list_a] :
% 3.64/2.03 ( ( listSl162220270list_a @ Xs @ zero_zero_nat )
% 3.64/2.03 = nil_list_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_1_list__slice__0,axiom,
% 3.64/2.03 ! [Xs: list_a] :
% 3.64/2.03 ( ( listSl97544552lice_a @ Xs @ zero_zero_nat )
% 3.64/2.03 = nil_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_2_concat_Osimps_I1_J,axiom,
% 3.64/2.03 ( ( concat_list_list_a @ nil_list_list_list_a )
% 3.64/2.03 = nil_list_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_3_concat_Osimps_I1_J,axiom,
% 3.64/2.03 ( ( concat_list_a @ nil_list_list_a )
% 3.64/2.03 = nil_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_4_concat_Osimps_I1_J,axiom,
% 3.64/2.03 ( ( concat_a @ nil_list_a )
% 3.64/2.03 = nil_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_5_list__ex1__simps_I1_J,axiom,
% 3.64/2.03 ! [P: list_list_a > $o] :
% 3.64/2.03 ~ ( list_ex1_list_list_a @ P @ nil_list_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_6_list__ex1__simps_I1_J,axiom,
% 3.64/2.03 ! [P: a > $o] :
% 3.64/2.03 ~ ( list_ex1_a @ P @ nil_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_7_list__ex1__simps_I1_J,axiom,
% 3.64/2.03 ! [P: list_a > $o] :
% 3.64/2.03 ~ ( list_ex1_list_a @ P @ nil_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_8_list__slice__less,axiom,
% 3.64/2.03 ! [Xs: list_list_a,K: nat] :
% 3.64/2.03 ( ( ord_less_nat @ ( size_s1427607542list_a @ Xs ) @ K )
% 3.64/2.03 => ( ( listSl162220270list_a @ Xs @ K )
% 3.64/2.03 = nil_list_list_a ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_9_list__slice__less,axiom,
% 3.64/2.03 ! [Xs: list_a,K: nat] :
% 3.64/2.03 ( ( ord_less_nat @ ( size_size_list_a @ Xs ) @ K )
% 3.64/2.03 => ( ( listSl97544552lice_a @ Xs @ K )
% 3.64/2.03 = nil_list_a ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_10_bind__simps_I1_J,axiom,
% 3.64/2.03 ! [F: a > list_list_list_a] :
% 3.64/2.03 ( ( bind_a_list_list_a @ nil_a @ F )
% 3.64/2.03 = nil_list_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_11_bind__simps_I1_J,axiom,
% 3.64/2.03 ! [F: list_a > list_list_list_a] :
% 3.64/2.03 ( ( bind_l971853709list_a @ nil_list_a @ F )
% 3.64/2.03 = nil_list_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_12_bind__simps_I1_J,axiom,
% 3.64/2.03 ! [F: list_list_a > list_a] :
% 3.64/2.03 ( ( bind_list_list_a_a @ nil_list_list_a @ F )
% 3.64/2.03 = nil_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_13_bind__simps_I1_J,axiom,
% 3.64/2.03 ! [F: list_list_a > list_list_a] :
% 3.64/2.03 ( ( bind_l94945665list_a @ nil_list_list_a @ F )
% 3.64/2.03 = nil_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_14_bind__simps_I1_J,axiom,
% 3.64/2.03 ! [F: list_list_a > list_list_list_a] :
% 3.64/2.03 ( ( bind_l311701255list_a @ nil_list_list_a @ F )
% 3.64/2.03 = nil_list_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_15_bind__simps_I1_J,axiom,
% 3.64/2.03 ! [F: a > list_a] :
% 3.64/2.03 ( ( bind_a_a @ nil_a @ F )
% 3.64/2.03 = nil_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_16_bind__simps_I1_J,axiom,
% 3.64/2.03 ! [F: a > list_list_a] :
% 3.64/2.03 ( ( bind_a_list_a @ nil_a @ F )
% 3.64/2.03 = nil_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_17_bind__simps_I1_J,axiom,
% 3.64/2.03 ! [F: list_a > list_a] :
% 3.64/2.03 ( ( bind_list_a_a @ nil_list_a @ F )
% 3.64/2.03 = nil_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_18_bind__simps_I1_J,axiom,
% 3.64/2.03 ! [F: list_a > list_list_a] :
% 3.64/2.03 ( ( bind_list_a_list_a @ nil_list_a @ F )
% 3.64/2.03 = nil_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_19_member__rec_I2_J,axiom,
% 3.64/2.03 ! [Y: list_list_a] :
% 3.64/2.03 ~ ( member_list_list_a @ nil_list_list_a @ Y ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_20_member__rec_I2_J,axiom,
% 3.64/2.03 ! [Y: a] :
% 3.64/2.03 ~ ( member_a @ nil_a @ Y ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_21_member__rec_I2_J,axiom,
% 3.64/2.03 ! [Y: list_a] :
% 3.64/2.03 ~ ( member_list_a @ nil_list_a @ Y ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_22_gen__length__code_I1_J,axiom,
% 3.64/2.03 ! [N: nat] :
% 3.64/2.03 ( ( gen_le840878749list_a @ N @ nil_list_list_a )
% 3.64/2.03 = N ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_23_gen__length__code_I1_J,axiom,
% 3.64/2.03 ! [N: nat] :
% 3.64/2.03 ( ( gen_length_a @ N @ nil_a )
% 3.64/2.03 = N ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_24_gen__length__code_I1_J,axiom,
% 3.64/2.03 ! [N: nat] :
% 3.64/2.03 ( ( gen_length_list_a @ N @ nil_list_a )
% 3.64/2.03 = N ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_25_maps__simps_I2_J,axiom,
% 3.64/2.03 ! [F: a > list_list_list_a] :
% 3.64/2.03 ( ( maps_a_list_list_a @ F @ nil_a )
% 3.64/2.03 = nil_list_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_26_maps__simps_I2_J,axiom,
% 3.64/2.03 ! [F: list_a > list_list_list_a] :
% 3.64/2.03 ( ( maps_l755382343list_a @ F @ nil_list_a )
% 3.64/2.03 = nil_list_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_27_maps__simps_I2_J,axiom,
% 3.64/2.03 ! [F: list_list_a > list_a] :
% 3.64/2.03 ( ( maps_list_list_a_a @ F @ nil_list_list_a )
% 3.64/2.03 = nil_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_28_maps__simps_I2_J,axiom,
% 3.64/2.03 ! [F: list_list_a > list_list_a] :
% 3.64/2.03 ( ( maps_l2025957947list_a @ F @ nil_list_list_a )
% 3.64/2.03 = nil_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_29_maps__simps_I2_J,axiom,
% 3.64/2.03 ! [F: list_list_a > list_list_list_a] :
% 3.64/2.03 ( ( maps_l57963201list_a @ F @ nil_list_list_a )
% 3.64/2.03 = nil_list_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_30_maps__simps_I2_J,axiom,
% 3.64/2.03 ! [F: a > list_a] :
% 3.64/2.03 ( ( maps_a_a @ F @ nil_a )
% 3.64/2.03 = nil_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_31_maps__simps_I2_J,axiom,
% 3.64/2.03 ! [F: a > list_list_a] :
% 3.64/2.03 ( ( maps_a_list_a @ F @ nil_a )
% 3.64/2.03 = nil_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_32_maps__simps_I2_J,axiom,
% 3.64/2.03 ! [F: list_a > list_a] :
% 3.64/2.03 ( ( maps_list_a_a @ F @ nil_list_a )
% 3.64/2.03 = nil_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_33_maps__simps_I2_J,axiom,
% 3.64/2.03 ! [F: list_a > list_list_a] :
% 3.64/2.03 ( ( maps_list_a_list_a @ F @ nil_list_a )
% 3.64/2.03 = nil_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_34_null__rec_I2_J,axiom,
% 3.64/2.03 null_list_list_a @ nil_list_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(fact_35_null__rec_I2_J,axiom,
% 3.64/2.03 null_a @ nil_a ).
% 3.64/2.03
% 3.64/2.03 thf(fact_36_null__rec_I2_J,axiom,
% 3.64/2.03 null_list_a @ nil_list_a ).
% 3.64/2.03
% 3.64/2.03 thf(fact_37_eq__Nil__null,axiom,
% 3.64/2.03 ! [Xs: list_a] :
% 3.64/2.03 ( ( Xs = nil_a )
% 3.64/2.03 = ( null_a @ Xs ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_38_eq__Nil__null,axiom,
% 3.64/2.03 ! [Xs: list_list_a] :
% 3.64/2.03 ( ( Xs = nil_list_a )
% 3.64/2.03 = ( null_list_a @ Xs ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_39_eq__Nil__null,axiom,
% 3.64/2.03 ! [Xs: list_list_list_a] :
% 3.64/2.03 ( ( Xs = nil_list_list_a )
% 3.64/2.03 = ( null_list_list_a @ Xs ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_40_map__filter__simps_I2_J,axiom,
% 3.64/2.03 ! [F: a > option_a] :
% 3.64/2.03 ( ( map_filter_a_a @ F @ nil_a )
% 3.64/2.03 = nil_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_41_map__filter__simps_I2_J,axiom,
% 3.64/2.03 ! [F: a > option_list_a] :
% 3.64/2.03 ( ( map_filter_a_list_a @ F @ nil_a )
% 3.64/2.03 = nil_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_42_map__filter__simps_I2_J,axiom,
% 3.64/2.03 ! [F: a > option_list_list_a] :
% 3.64/2.03 ( ( map_fi2089402454list_a @ F @ nil_a )
% 3.64/2.03 = nil_list_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_43_map__filter__simps_I2_J,axiom,
% 3.64/2.03 ! [F: list_a > option_a] :
% 3.64/2.03 ( ( map_filter_list_a_a @ F @ nil_list_a )
% 3.64/2.03 = nil_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_44_map__filter__simps_I2_J,axiom,
% 3.64/2.03 ! [F: list_a > option_list_a] :
% 3.64/2.03 ( ( map_fi461586634list_a @ F @ nil_list_a )
% 3.64/2.03 = nil_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_45_map__filter__simps_I2_J,axiom,
% 3.64/2.03 ! [F: list_a > option_list_list_a] :
% 3.64/2.03 ( ( map_fi1090123216list_a @ F @ nil_list_a )
% 3.64/2.03 = nil_list_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_46_map__filter__simps_I2_J,axiom,
% 3.64/2.03 ! [F: list_list_a > option_a] :
% 3.64/2.03 ( ( map_fi1574988606st_a_a @ F @ nil_list_list_a )
% 3.64/2.03 = nil_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_47_map__filter__simps_I2_J,axiom,
% 3.64/2.03 ! [F: list_list_a > option_list_a] :
% 3.64/2.03 ( ( map_fi213215172list_a @ F @ nil_list_list_a )
% 3.64/2.03 = nil_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_48_map__filter__simps_I2_J,axiom,
% 3.64/2.03 ! [F: list_list_a > option_list_list_a] :
% 3.64/2.03 ( ( map_fi824137674list_a @ F @ nil_list_list_a )
% 3.64/2.03 = nil_list_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_49_length__0__conv,axiom,
% 3.64/2.03 ! [Xs: list_list_a] :
% 3.64/2.03 ( ( ( size_s1427607542list_a @ Xs )
% 3.64/2.03 = zero_zero_nat )
% 3.64/2.03 = ( Xs = nil_list_a ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_50_length__0__conv,axiom,
% 3.64/2.03 ! [Xs: list_list_list_a] :
% 3.64/2.03 ( ( ( size_s575106428list_a @ Xs )
% 3.64/2.03 = zero_zero_nat )
% 3.64/2.03 = ( Xs = nil_list_list_a ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_51_length__0__conv,axiom,
% 3.64/2.03 ! [Xs: list_a] :
% 3.64/2.03 ( ( ( size_size_list_a @ Xs )
% 3.64/2.03 = zero_zero_nat )
% 3.64/2.03 = ( Xs = nil_a ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_52_length__greater__0__conv,axiom,
% 3.64/2.03 ! [Xs: list_list_a] :
% 3.64/2.03 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1427607542list_a @ Xs ) )
% 3.64/2.03 = ( Xs != nil_list_a ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_53_length__greater__0__conv,axiom,
% 3.64/2.03 ! [Xs: list_list_list_a] :
% 3.64/2.03 ( ( ord_less_nat @ zero_zero_nat @ ( size_s575106428list_a @ Xs ) )
% 3.64/2.03 = ( Xs != nil_list_list_a ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_54_length__greater__0__conv,axiom,
% 3.64/2.03 ! [Xs: list_a] :
% 3.64/2.03 ( ( ord_less_nat @ zero_zero_nat @ ( size_size_list_a @ Xs ) )
% 3.64/2.03 = ( Xs != nil_a ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_55_list_Osize_I3_J,axiom,
% 3.64/2.03 ( ( size_s1427607542list_a @ nil_list_a )
% 3.64/2.03 = zero_zero_nat ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_56_list_Osize_I3_J,axiom,
% 3.64/2.03 ( ( size_s575106428list_a @ nil_list_list_a )
% 3.64/2.03 = zero_zero_nat ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_57_list_Osize_I3_J,axiom,
% 3.64/2.03 ( ( size_size_list_a @ nil_a )
% 3.64/2.03 = zero_zero_nat ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_58_length__code,axiom,
% 3.64/2.03 ( size_s1427607542list_a
% 3.64/2.03 = ( gen_length_list_a @ zero_zero_nat ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_59_length__code,axiom,
% 3.64/2.03 ( size_size_list_a
% 3.64/2.03 = ( gen_length_a @ zero_zero_nat ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_60_length__induct,axiom,
% 3.64/2.03 ! [P: list_a > $o,Xs: list_a] :
% 3.64/2.03 ( ! [Xs2: list_a] :
% 3.64/2.03 ( ! [Ys: list_a] :
% 3.64/2.03 ( ( ord_less_nat @ ( size_size_list_a @ Ys ) @ ( size_size_list_a @ Xs2 ) )
% 3.64/2.03 => ( P @ Ys ) )
% 3.64/2.03 => ( P @ Xs2 ) )
% 3.64/2.03 => ( P @ Xs ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_61_Ex__list__of__length,axiom,
% 3.64/2.03 ! [N: nat] :
% 3.64/2.03 ? [Xs2: list_a] :
% 3.64/2.03 ( ( size_size_list_a @ Xs2 )
% 3.64/2.03 = N ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_62_neq__if__length__neq,axiom,
% 3.64/2.03 ! [Xs: list_a,Ys2: list_a] :
% 3.64/2.03 ( ( ( size_size_list_a @ Xs )
% 3.64/2.03 != ( size_size_list_a @ Ys2 ) )
% 3.64/2.03 => ( Xs != Ys2 ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_63_neq0__conv,axiom,
% 3.64/2.03 ! [N: nat] :
% 3.64/2.03 ( ( N != zero_zero_nat )
% 3.64/2.03 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_64_less__nat__zero__code,axiom,
% 3.64/2.03 ! [N: nat] :
% 3.64/2.03 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_65_bot__nat__0_Onot__eq__extremum,axiom,
% 3.64/2.03 ! [A: nat] :
% 3.64/2.03 ( ( A != zero_zero_nat )
% 3.64/2.03 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_66_not__gr__zero,axiom,
% 3.64/2.03 ! [N: nat] :
% 3.64/2.03 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 3.64/2.03 = ( N = zero_zero_nat ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_67_length__greater__imp__not__empty,axiom,
% 3.64/2.03 ! [N: nat,Xs: list_list_a] :
% 3.64/2.03 ( ( ord_less_nat @ N @ ( size_s1427607542list_a @ Xs ) )
% 3.64/2.03 => ( Xs != nil_list_a ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_68_length__greater__imp__not__empty,axiom,
% 3.64/2.03 ! [N: nat,Xs: list_list_list_a] :
% 3.64/2.03 ( ( ord_less_nat @ N @ ( size_s575106428list_a @ Xs ) )
% 3.64/2.03 => ( Xs != nil_list_list_a ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_69_length__greater__imp__not__empty,axiom,
% 3.64/2.03 ! [N: nat,Xs: list_a] :
% 3.64/2.03 ( ( ord_less_nat @ N @ ( size_size_list_a @ Xs ) )
% 3.64/2.03 => ( Xs != nil_a ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_70_gr0I,axiom,
% 3.64/2.03 ! [N: nat] :
% 3.64/2.03 ( ( N != zero_zero_nat )
% 3.64/2.03 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_71_not__gr0,axiom,
% 3.64/2.03 ! [N: nat] :
% 3.64/2.03 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 3.64/2.03 = ( N = zero_zero_nat ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_72_not__less0,axiom,
% 3.64/2.03 ! [N: nat] :
% 3.64/2.03 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_73_less__zeroE,axiom,
% 3.64/2.03 ! [N: nat] :
% 3.64/2.03 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_74_gr__implies__not0,axiom,
% 3.64/2.03 ! [M: nat,N: nat] :
% 3.64/2.03 ( ( ord_less_nat @ M @ N )
% 3.64/2.03 => ( N != zero_zero_nat ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_75_zero__reorient,axiom,
% 3.64/2.03 ! [X: nat] :
% 3.64/2.03 ( ( zero_zero_nat = X )
% 3.64/2.03 = ( X = zero_zero_nat ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_76_zero__reorient,axiom,
% 3.64/2.03 ! [X: int] :
% 3.64/2.03 ( ( zero_zero_int = X )
% 3.64/2.03 = ( X = zero_zero_int ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_77_zero__reorient,axiom,
% 3.64/2.03 ! [X: real] :
% 3.64/2.03 ( ( zero_zero_real = X )
% 3.64/2.03 = ( X = zero_zero_real ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_78_linorder__neqE__nat,axiom,
% 3.64/2.03 ! [X: nat,Y: nat] :
% 3.64/2.03 ( ( X != Y )
% 3.64/2.03 => ( ~ ( ord_less_nat @ X @ Y )
% 3.64/2.03 => ( ord_less_nat @ Y @ X ) ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_79_infinite__descent,axiom,
% 3.64/2.03 ! [P: nat > $o,N: nat] :
% 3.64/2.03 ( ! [N2: nat] :
% 3.64/2.03 ( ~ ( P @ N2 )
% 3.64/2.03 => ? [M2: nat] :
% 3.64/2.03 ( ( ord_less_nat @ M2 @ N2 )
% 3.64/2.03 & ~ ( P @ M2 ) ) )
% 3.64/2.03 => ( P @ N ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_80_nat__less__induct,axiom,
% 3.64/2.03 ! [P: nat > $o,N: nat] :
% 3.64/2.03 ( ! [N2: nat] :
% 3.64/2.03 ( ! [M2: nat] :
% 3.64/2.03 ( ( ord_less_nat @ M2 @ N2 )
% 3.64/2.03 => ( P @ M2 ) )
% 3.64/2.03 => ( P @ N2 ) )
% 3.64/2.03 => ( P @ N ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_81_less__irrefl__nat,axiom,
% 3.64/2.03 ! [N: nat] :
% 3.64/2.03 ~ ( ord_less_nat @ N @ N ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_82_less__not__refl3,axiom,
% 3.64/2.03 ! [S: nat,T: nat] :
% 3.64/2.03 ( ( ord_less_nat @ S @ T )
% 3.64/2.03 => ( S != T ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_83_less__not__refl2,axiom,
% 3.64/2.03 ! [N: nat,M: nat] :
% 3.64/2.03 ( ( ord_less_nat @ N @ M )
% 3.64/2.03 => ( M != N ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_84_less__not__refl,axiom,
% 3.64/2.03 ! [N: nat] :
% 3.64/2.03 ~ ( ord_less_nat @ N @ N ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_85_nat__neq__iff,axiom,
% 3.64/2.03 ! [M: nat,N: nat] :
% 3.64/2.03 ( ( M != N )
% 3.64/2.03 = ( ( ord_less_nat @ M @ N )
% 3.64/2.03 | ( ord_less_nat @ N @ M ) ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_86_size__neq__size__imp__neq,axiom,
% 3.64/2.03 ! [X: list_a,Y: list_a] :
% 3.64/2.03 ( ( ( size_size_list_a @ X )
% 3.64/2.03 != ( size_size_list_a @ Y ) )
% 3.64/2.03 => ( X != Y ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_87_zero__less__iff__neq__zero,axiom,
% 3.64/2.03 ! [N: nat] :
% 3.64/2.03 ( ( ord_less_nat @ zero_zero_nat @ N )
% 3.64/2.03 = ( N != zero_zero_nat ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_88_mem__Collect__eq,axiom,
% 3.64/2.03 ! [A: nat,P: nat > $o] :
% 3.64/2.03 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 3.64/2.03 = ( P @ A ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_89_mem__Collect__eq,axiom,
% 3.64/2.03 ! [A: real,P: real > $o] :
% 3.64/2.03 ( ( member_real @ A @ ( collect_real @ P ) )
% 3.64/2.03 = ( P @ A ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_90_Collect__mem__eq,axiom,
% 3.64/2.03 ! [A2: set_nat] :
% 3.64/2.03 ( ( collect_nat
% 3.64/2.03 @ ^ [X2: nat] : ( member_nat @ X2 @ A2 ) )
% 3.64/2.03 = A2 ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_91_Collect__mem__eq,axiom,
% 3.64/2.03 ! [A2: set_real] :
% 3.64/2.03 ( ( collect_real
% 3.64/2.03 @ ^ [X2: real] : ( member_real @ X2 @ A2 ) )
% 3.64/2.03 = A2 ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_92_gr__implies__not__zero,axiom,
% 3.64/2.03 ! [M: nat,N: nat] :
% 3.64/2.03 ( ( ord_less_nat @ M @ N )
% 3.64/2.03 => ( N != zero_zero_nat ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_93_not__less__zero,axiom,
% 3.64/2.03 ! [N: nat] :
% 3.64/2.03 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_94_gr__zeroI,axiom,
% 3.64/2.03 ! [N: nat] :
% 3.64/2.03 ( ( N != zero_zero_nat )
% 3.64/2.03 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_95_bot__nat__0_Oextremum__strict,axiom,
% 3.64/2.03 ! [A: nat] :
% 3.64/2.03 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_96_infinite__descent0,axiom,
% 3.64/2.03 ! [P: nat > $o,N: nat] :
% 3.64/2.03 ( ( P @ zero_zero_nat )
% 3.64/2.03 => ( ! [N2: nat] :
% 3.64/2.03 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.64/2.03 => ( ~ ( P @ N2 )
% 3.64/2.03 => ? [M2: nat] :
% 3.64/2.03 ( ( ord_less_nat @ M2 @ N2 )
% 3.64/2.03 & ~ ( P @ M2 ) ) ) )
% 3.64/2.03 => ( P @ N ) ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_97_gr__implies__gr0,axiom,
% 3.64/2.03 ! [M: nat,N: nat] :
% 3.64/2.03 ( ( ord_less_nat @ M @ N )
% 3.64/2.03 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_98_field__lbound__gt__zero,axiom,
% 3.64/2.03 ! [D1: real,D2: real] :
% 3.64/2.03 ( ( ord_less_real @ zero_zero_real @ D1 )
% 3.64/2.03 => ( ( ord_less_real @ zero_zero_real @ D2 )
% 3.64/2.03 => ? [E: real] :
% 3.64/2.03 ( ( ord_less_real @ zero_zero_real @ E )
% 3.64/2.03 & ( ord_less_real @ E @ D1 )
% 3.64/2.03 & ( ord_less_real @ E @ D2 ) ) ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_99_less__numeral__extra_I3_J,axiom,
% 3.64/2.03 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_100_less__numeral__extra_I3_J,axiom,
% 3.64/2.03 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_101_less__numeral__extra_I3_J,axiom,
% 3.64/2.03 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_102_list__slice__aux_Osimps_I1_J,axiom,
% 3.64/2.03 ! [Xs: list_a,K: nat] :
% 3.64/2.03 ( ( listSl1495374126_aux_a @ Xs @ K @ zero_zero_nat )
% 3.64/2.03 = nil_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_103_list__slice__aux_Osimps_I1_J,axiom,
% 3.64/2.03 ! [Xs: list_list_a,K: nat] :
% 3.64/2.03 ( ( listSl856612276list_a @ Xs @ K @ zero_zero_nat )
% 3.64/2.03 = nil_list_list_a ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_104_of__nat__0__less__iff,axiom,
% 3.64/2.03 ! [N: nat] :
% 3.64/2.03 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N ) )
% 3.64/2.03 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_105_of__nat__0__less__iff,axiom,
% 3.64/2.03 ! [N: nat] :
% 3.64/2.03 ( ( ord_less_int @ zero_zero_int @ ( semiri2019852685at_int @ N ) )
% 3.64/2.03 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_106_of__nat__0__less__iff,axiom,
% 3.64/2.03 ! [N: nat] :
% 3.64/2.03 ( ( ord_less_real @ zero_zero_real @ ( semiri2110766477t_real @ N ) )
% 3.64/2.03 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_107_count__list_Osimps_I1_J,axiom,
% 3.64/2.03 ! [Y: a] :
% 3.64/2.03 ( ( count_list_a @ nil_a @ Y )
% 3.64/2.03 = zero_zero_nat ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_108_count__list_Osimps_I1_J,axiom,
% 3.64/2.03 ! [Y: list_a] :
% 3.64/2.03 ( ( count_list_list_a @ nil_list_a @ Y )
% 3.64/2.03 = zero_zero_nat ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_109_count__list_Osimps_I1_J,axiom,
% 3.64/2.03 ! [Y: list_list_a] :
% 3.64/2.03 ( ( count_429956358list_a @ nil_list_list_a @ Y )
% 3.64/2.03 = zero_zero_nat ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_110_interval__induct__rule,axiom,
% 3.64/2.03 ! [I: set_nat,P: nat > $o,A: nat] :
% 3.64/2.03 ( ! [X3: nat] :
% 3.64/2.03 ( ! [Y2: nat] :
% 3.64/2.03 ( ( ( member_nat @ X3 @ I )
% 3.64/2.03 & ( member_nat @ Y2 @ I )
% 3.64/2.03 & ( ord_less_nat @ Y2 @ X3 ) )
% 3.64/2.03 => ( P @ Y2 ) )
% 3.64/2.03 => ( P @ X3 ) )
% 3.64/2.03 => ( P @ A ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_111_interval__induct,axiom,
% 3.64/2.03 ! [I: set_nat,P: nat > $o,A: nat] :
% 3.64/2.03 ( ! [X3: nat] :
% 3.64/2.03 ( ! [Y2: nat] :
% 3.64/2.03 ( ( ( member_nat @ X3 @ I )
% 3.64/2.03 & ( member_nat @ Y2 @ I )
% 3.64/2.03 & ( ord_less_nat @ Y2 @ X3 ) )
% 3.64/2.03 => ( P @ Y2 ) )
% 3.64/2.03 => ( P @ X3 ) )
% 3.64/2.03 => ( P @ A ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_112_zero__natural_Orsp,axiom,
% 3.64/2.03 zero_zero_nat = zero_zero_nat ).
% 3.64/2.03
% 3.64/2.03 thf(fact_113_of__nat__eq__iff,axiom,
% 3.64/2.03 ! [M: nat,N: nat] :
% 3.64/2.03 ( ( ( semiri2019852685at_int @ M )
% 3.64/2.03 = ( semiri2019852685at_int @ N ) )
% 3.64/2.03 = ( M = N ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_114_of__nat__eq__iff,axiom,
% 3.64/2.03 ! [M: nat,N: nat] :
% 3.64/2.03 ( ( ( semiri2110766477t_real @ M )
% 3.64/2.03 = ( semiri2110766477t_real @ N ) )
% 3.64/2.03 = ( M = N ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_115_of__nat__0,axiom,
% 3.64/2.03 ( ( semiri1382578993at_nat @ zero_zero_nat )
% 3.64/2.03 = zero_zero_nat ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_116_of__nat__0,axiom,
% 3.64/2.03 ( ( semiri2019852685at_int @ zero_zero_nat )
% 3.64/2.03 = zero_zero_int ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_117_of__nat__0,axiom,
% 3.64/2.03 ( ( semiri2110766477t_real @ zero_zero_nat )
% 3.64/2.03 = zero_zero_real ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_118_of__nat__0__eq__iff,axiom,
% 3.64/2.03 ! [N: nat] :
% 3.64/2.03 ( ( zero_zero_nat
% 3.64/2.03 = ( semiri1382578993at_nat @ N ) )
% 3.64/2.03 = ( zero_zero_nat = N ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_119_of__nat__0__eq__iff,axiom,
% 3.64/2.03 ! [N: nat] :
% 3.64/2.03 ( ( zero_zero_int
% 3.64/2.03 = ( semiri2019852685at_int @ N ) )
% 3.64/2.03 = ( zero_zero_nat = N ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_120_of__nat__0__eq__iff,axiom,
% 3.64/2.03 ! [N: nat] :
% 3.64/2.03 ( ( zero_zero_real
% 3.64/2.03 = ( semiri2110766477t_real @ N ) )
% 3.64/2.03 = ( zero_zero_nat = N ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_121_of__nat__eq__0__iff,axiom,
% 3.64/2.03 ! [M: nat] :
% 3.64/2.03 ( ( ( semiri1382578993at_nat @ M )
% 3.64/2.03 = zero_zero_nat )
% 3.64/2.03 = ( M = zero_zero_nat ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_122_of__nat__eq__0__iff,axiom,
% 3.64/2.03 ! [M: nat] :
% 3.64/2.03 ( ( ( semiri2019852685at_int @ M )
% 3.64/2.03 = zero_zero_int )
% 3.64/2.03 = ( M = zero_zero_nat ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_123_of__nat__eq__0__iff,axiom,
% 3.64/2.03 ! [M: nat] :
% 3.64/2.03 ( ( ( semiri2110766477t_real @ M )
% 3.64/2.03 = zero_zero_real )
% 3.64/2.03 = ( M = zero_zero_nat ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_124_of__nat__less__iff,axiom,
% 3.64/2.03 ! [M: nat,N: nat] :
% 3.64/2.03 ( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) )
% 3.64/2.03 = ( ord_less_nat @ M @ N ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_125_of__nat__less__iff,axiom,
% 3.64/2.03 ! [M: nat,N: nat] :
% 3.64/2.03 ( ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) )
% 3.64/2.03 = ( ord_less_nat @ M @ N ) ) ).
% 3.64/2.03
% 3.64/2.03 thf(fact_126_of__nat__less__iff,axiom,
% 3.64/2.03 ! [M: nat,N: nat] :
% 3.64/2.03 ( ( ord_less_real @ ( semiri2110766477t_real @ M ) @ ( semiri2110766477t_real @ N ) )
% 3.64/2.03 = ( ord_less_nat @ M @ N ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_127_of__nat__less__0__iff,axiom,
% 3.64/2.04 ! [M: nat] :
% 3.64/2.04 ~ ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_128_of__nat__less__0__iff,axiom,
% 3.64/2.04 ! [M: nat] :
% 3.64/2.04 ~ ( ord_less_int @ ( semiri2019852685at_int @ M ) @ zero_zero_int ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_129_of__nat__less__0__iff,axiom,
% 3.64/2.04 ! [M: nat] :
% 3.64/2.04 ~ ( ord_less_real @ ( semiri2110766477t_real @ M ) @ zero_zero_real ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_130_less__imp__of__nat__less,axiom,
% 3.64/2.04 ! [M: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_nat @ M @ N )
% 3.64/2.04 => ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_131_less__imp__of__nat__less,axiom,
% 3.64/2.04 ! [M: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_nat @ M @ N )
% 3.64/2.04 => ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_132_less__imp__of__nat__less,axiom,
% 3.64/2.04 ! [M: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_nat @ M @ N )
% 3.64/2.04 => ( ord_less_real @ ( semiri2110766477t_real @ M ) @ ( semiri2110766477t_real @ N ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_133_of__nat__less__imp__less,axiom,
% 3.64/2.04 ! [M: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) )
% 3.64/2.04 => ( ord_less_nat @ M @ N ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_134_of__nat__less__imp__less,axiom,
% 3.64/2.04 ! [M: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) )
% 3.64/2.04 => ( ord_less_nat @ M @ N ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_135_of__nat__less__imp__less,axiom,
% 3.64/2.04 ! [M: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_real @ ( semiri2110766477t_real @ M ) @ ( semiri2110766477t_real @ N ) )
% 3.64/2.04 => ( ord_less_nat @ M @ N ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_136_Collect__minI,axiom,
% 3.64/2.04 ! [K: nat,I: set_nat,P: nat > $o] :
% 3.64/2.04 ( ( member_nat @ K @ I )
% 3.64/2.04 => ( ( P @ K )
% 3.64/2.04 => ? [X3: nat] :
% 3.64/2.04 ( ( member_nat @ X3 @ I )
% 3.64/2.04 & ( P @ X3 )
% 3.64/2.04 & ! [Xa: nat] :
% 3.64/2.04 ( ( member_nat @ Xa @ I )
% 3.64/2.04 => ( ( ord_less_nat @ Xa @ X3 )
% 3.64/2.04 => ~ ( P @ Xa ) ) ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_137_Collect__minI__ex,axiom,
% 3.64/2.04 ! [I: set_nat,P: nat > $o] :
% 3.64/2.04 ( ? [X4: nat] :
% 3.64/2.04 ( ( member_nat @ X4 @ I )
% 3.64/2.04 & ( P @ X4 ) )
% 3.64/2.04 => ? [X3: nat] :
% 3.64/2.04 ( ( member_nat @ X3 @ I )
% 3.64/2.04 & ( P @ X3 )
% 3.64/2.04 & ! [Xa: nat] :
% 3.64/2.04 ( ( member_nat @ Xa @ I )
% 3.64/2.04 => ( ( ord_less_nat @ Xa @ X3 )
% 3.64/2.04 => ~ ( P @ Xa ) ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_138_zero__less__imp__eq__int,axiom,
% 3.64/2.04 ! [K: int] :
% 3.64/2.04 ( ( ord_less_int @ zero_zero_int @ K )
% 3.64/2.04 => ? [N2: nat] :
% 3.64/2.04 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.64/2.04 & ( K
% 3.64/2.04 = ( semiri2019852685at_int @ N2 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_139_pos__int__cases,axiom,
% 3.64/2.04 ! [K: int] :
% 3.64/2.04 ( ( ord_less_int @ zero_zero_int @ K )
% 3.64/2.04 => ~ ! [N2: nat] :
% 3.64/2.04 ( ( K
% 3.64/2.04 = ( semiri2019852685at_int @ N2 ) )
% 3.64/2.04 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_140_reals__Archimedean2,axiom,
% 3.64/2.04 ! [X: real] :
% 3.64/2.04 ? [N2: nat] : ( ord_less_real @ X @ ( semiri2110766477t_real @ N2 ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_141_list__slice__def,axiom,
% 3.64/2.04 ( listSl97544552lice_a
% 3.64/2.04 = ( ^ [Xs3: list_a,K2: nat] : ( listSl1495374126_aux_a @ Xs3 @ K2 @ ( divide_divide_nat @ ( size_size_list_a @ Xs3 ) @ K2 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_142_of__nat__zero__less__power__iff,axiom,
% 3.64/2.04 ! [X: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ X ) @ N ) )
% 3.64/2.04 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 3.64/2.04 | ( N = zero_zero_nat ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_143_of__nat__zero__less__power__iff,axiom,
% 3.64/2.04 ! [X: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri2019852685at_int @ X ) @ N ) )
% 3.64/2.04 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 3.64/2.04 | ( N = zero_zero_nat ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_144_of__nat__zero__less__power__iff,axiom,
% 3.64/2.04 ! [X: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri2110766477t_real @ X ) @ N ) )
% 3.64/2.04 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 3.64/2.04 | ( N = zero_zero_nat ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_145_of__nat__le__0__iff,axiom,
% 3.64/2.04 ! [M: nat] :
% 3.64/2.04 ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat )
% 3.64/2.04 = ( M = zero_zero_nat ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_146_of__nat__le__0__iff,axiom,
% 3.64/2.04 ! [M: nat] :
% 3.64/2.04 ( ( ord_less_eq_int @ ( semiri2019852685at_int @ M ) @ zero_zero_int )
% 3.64/2.04 = ( M = zero_zero_nat ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_147_of__nat__le__0__iff,axiom,
% 3.64/2.04 ! [M: nat] :
% 3.64/2.04 ( ( ord_less_eq_real @ ( semiri2110766477t_real @ M ) @ zero_zero_real )
% 3.64/2.04 = ( M = zero_zero_nat ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_148_ex__inverse__of__nat__less,axiom,
% 3.64/2.04 ! [X: real] :
% 3.64/2.04 ( ( ord_less_real @ zero_zero_real @ X )
% 3.64/2.04 => ? [N2: nat] :
% 3.64/2.04 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 3.64/2.04 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri2110766477t_real @ N2 ) ) @ X ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_149_bot__nat__0_Oextremum,axiom,
% 3.64/2.04 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_150_le0,axiom,
% 3.64/2.04 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_151_le__zero__eq,axiom,
% 3.64/2.04 ! [N: nat] :
% 3.64/2.04 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 3.64/2.04 = ( N = zero_zero_nat ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_152_of__nat__le__iff,axiom,
% 3.64/2.04 ! [M: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) )
% 3.64/2.04 = ( ord_less_eq_nat @ M @ N ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_153_of__nat__le__iff,axiom,
% 3.64/2.04 ! [M: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_eq_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) )
% 3.64/2.04 = ( ord_less_eq_nat @ M @ N ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_154_of__nat__le__iff,axiom,
% 3.64/2.04 ! [M: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_eq_real @ ( semiri2110766477t_real @ M ) @ ( semiri2110766477t_real @ N ) )
% 3.64/2.04 = ( ord_less_eq_nat @ M @ N ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_155_nat__zero__less__power__iff,axiom,
% 3.64/2.04 ! [X: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
% 3.64/2.04 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 3.64/2.04 | ( N = zero_zero_nat ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_156_of__nat__power,axiom,
% 3.64/2.04 ! [M: nat,N: nat] :
% 3.64/2.04 ( ( semiri1382578993at_nat @ ( power_power_nat @ M @ N ) )
% 3.64/2.04 = ( power_power_nat @ ( semiri1382578993at_nat @ M ) @ N ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_157_of__nat__power,axiom,
% 3.64/2.04 ! [M: nat,N: nat] :
% 3.64/2.04 ( ( semiri2019852685at_int @ ( power_power_nat @ M @ N ) )
% 3.64/2.04 = ( power_power_int @ ( semiri2019852685at_int @ M ) @ N ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_158_of__nat__power,axiom,
% 3.64/2.04 ! [M: nat,N: nat] :
% 3.64/2.04 ( ( semiri2110766477t_real @ ( power_power_nat @ M @ N ) )
% 3.64/2.04 = ( power_power_real @ ( semiri2110766477t_real @ M ) @ N ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_159_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 3.64/2.04 ! [B: nat,W: nat,X: nat] :
% 3.64/2.04 ( ( ( power_power_nat @ ( semiri1382578993at_nat @ B ) @ W )
% 3.64/2.04 = ( semiri1382578993at_nat @ X ) )
% 3.64/2.04 = ( ( power_power_nat @ B @ W )
% 3.64/2.04 = X ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_160_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 3.64/2.04 ! [B: nat,W: nat,X: nat] :
% 3.64/2.04 ( ( ( power_power_int @ ( semiri2019852685at_int @ B ) @ W )
% 3.64/2.04 = ( semiri2019852685at_int @ X ) )
% 3.64/2.04 = ( ( power_power_nat @ B @ W )
% 3.64/2.04 = X ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_161_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 3.64/2.04 ! [B: nat,W: nat,X: nat] :
% 3.64/2.04 ( ( ( power_power_real @ ( semiri2110766477t_real @ B ) @ W )
% 3.64/2.04 = ( semiri2110766477t_real @ X ) )
% 3.64/2.04 = ( ( power_power_nat @ B @ W )
% 3.64/2.04 = X ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_162_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 3.64/2.04 ! [X: nat,B: nat,W: nat] :
% 3.64/2.04 ( ( ( semiri1382578993at_nat @ X )
% 3.64/2.04 = ( power_power_nat @ ( semiri1382578993at_nat @ B ) @ W ) )
% 3.64/2.04 = ( X
% 3.64/2.04 = ( power_power_nat @ B @ W ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_163_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 3.64/2.04 ! [X: nat,B: nat,W: nat] :
% 3.64/2.04 ( ( ( semiri2019852685at_int @ X )
% 3.64/2.04 = ( power_power_int @ ( semiri2019852685at_int @ B ) @ W ) )
% 3.64/2.04 = ( X
% 3.64/2.04 = ( power_power_nat @ B @ W ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_164_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 3.64/2.04 ! [X: nat,B: nat,W: nat] :
% 3.64/2.04 ( ( ( semiri2110766477t_real @ X )
% 3.64/2.04 = ( power_power_real @ ( semiri2110766477t_real @ B ) @ W ) )
% 3.64/2.04 = ( X
% 3.64/2.04 = ( power_power_nat @ B @ W ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_165_of__nat__le__of__nat__power__cancel__iff,axiom,
% 3.64/2.04 ! [B: nat,W: nat,X: nat] :
% 3.64/2.04 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ B ) @ W ) @ ( semiri1382578993at_nat @ X ) )
% 3.64/2.04 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_166_of__nat__le__of__nat__power__cancel__iff,axiom,
% 3.64/2.04 ! [B: nat,W: nat,X: nat] :
% 3.64/2.04 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri2019852685at_int @ B ) @ W ) @ ( semiri2019852685at_int @ X ) )
% 3.64/2.04 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_167_of__nat__le__of__nat__power__cancel__iff,axiom,
% 3.64/2.04 ! [B: nat,W: nat,X: nat] :
% 3.64/2.04 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri2110766477t_real @ B ) @ W ) @ ( semiri2110766477t_real @ X ) )
% 3.64/2.04 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_168_of__nat__power__le__of__nat__cancel__iff,axiom,
% 3.64/2.04 ! [X: nat,B: nat,W: nat] :
% 3.64/2.04 ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ X ) @ ( power_power_nat @ ( semiri1382578993at_nat @ B ) @ W ) )
% 3.64/2.04 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_169_of__nat__power__le__of__nat__cancel__iff,axiom,
% 3.64/2.04 ! [X: nat,B: nat,W: nat] :
% 3.64/2.04 ( ( ord_less_eq_int @ ( semiri2019852685at_int @ X ) @ ( power_power_int @ ( semiri2019852685at_int @ B ) @ W ) )
% 3.64/2.04 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_170_of__nat__power__le__of__nat__cancel__iff,axiom,
% 3.64/2.04 ! [X: nat,B: nat,W: nat] :
% 3.64/2.04 ( ( ord_less_eq_real @ ( semiri2110766477t_real @ X ) @ ( power_power_real @ ( semiri2110766477t_real @ B ) @ W ) )
% 3.64/2.04 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_171_power__eq__0__iff,axiom,
% 3.64/2.04 ! [A: int,N: nat] :
% 3.64/2.04 ( ( ( power_power_int @ A @ N )
% 3.64/2.04 = zero_zero_int )
% 3.64/2.04 = ( ( A = zero_zero_int )
% 3.64/2.04 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_172_power__eq__0__iff,axiom,
% 3.64/2.04 ! [A: nat,N: nat] :
% 3.64/2.04 ( ( ( power_power_nat @ A @ N )
% 3.64/2.04 = zero_zero_nat )
% 3.64/2.04 = ( ( A = zero_zero_nat )
% 3.64/2.04 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_173_power__eq__0__iff,axiom,
% 3.64/2.04 ! [A: real,N: nat] :
% 3.64/2.04 ( ( ( power_power_real @ A @ N )
% 3.64/2.04 = zero_zero_real )
% 3.64/2.04 = ( ( A = zero_zero_real )
% 3.64/2.04 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_174_of__nat__power__less__of__nat__cancel__iff,axiom,
% 3.64/2.04 ! [X: nat,B: nat,W: nat] :
% 3.64/2.04 ( ( ord_less_nat @ ( semiri1382578993at_nat @ X ) @ ( power_power_nat @ ( semiri1382578993at_nat @ B ) @ W ) )
% 3.64/2.04 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_175_of__nat__power__less__of__nat__cancel__iff,axiom,
% 3.64/2.04 ! [X: nat,B: nat,W: nat] :
% 3.64/2.04 ( ( ord_less_int @ ( semiri2019852685at_int @ X ) @ ( power_power_int @ ( semiri2019852685at_int @ B ) @ W ) )
% 3.64/2.04 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_176_of__nat__power__less__of__nat__cancel__iff,axiom,
% 3.64/2.04 ! [X: nat,B: nat,W: nat] :
% 3.64/2.04 ( ( ord_less_real @ ( semiri2110766477t_real @ X ) @ ( power_power_real @ ( semiri2110766477t_real @ B ) @ W ) )
% 3.64/2.04 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_177_of__nat__less__of__nat__power__cancel__iff,axiom,
% 3.64/2.04 ! [B: nat,W: nat,X: nat] :
% 3.64/2.04 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1382578993at_nat @ B ) @ W ) @ ( semiri1382578993at_nat @ X ) )
% 3.64/2.04 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_178_of__nat__less__of__nat__power__cancel__iff,axiom,
% 3.64/2.04 ! [B: nat,W: nat,X: nat] :
% 3.64/2.04 ( ( ord_less_int @ ( power_power_int @ ( semiri2019852685at_int @ B ) @ W ) @ ( semiri2019852685at_int @ X ) )
% 3.64/2.04 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_179_of__nat__less__of__nat__power__cancel__iff,axiom,
% 3.64/2.04 ! [B: nat,W: nat,X: nat] :
% 3.64/2.04 ( ( ord_less_real @ ( power_power_real @ ( semiri2110766477t_real @ B ) @ W ) @ ( semiri2110766477t_real @ X ) )
% 3.64/2.04 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_180_power__mono__iff,axiom,
% 3.64/2.04 ! [A: nat,B: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.64/2.04 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 3.64/2.04 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 3.64/2.04 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 3.64/2.04 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_181_power__mono__iff,axiom,
% 3.64/2.04 ! [A: int,B: int,N: nat] :
% 3.64/2.04 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.64/2.04 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 3.64/2.04 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 3.64/2.04 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 3.64/2.04 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_182_power__mono__iff,axiom,
% 3.64/2.04 ! [A: real,B: real,N: nat] :
% 3.64/2.04 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.64/2.04 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 3.64/2.04 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 3.64/2.04 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 3.64/2.04 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_183_nonneg__int__cases,axiom,
% 3.64/2.04 ! [K: int] :
% 3.64/2.04 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 3.64/2.04 => ~ ! [N2: nat] :
% 3.64/2.04 ( K
% 3.64/2.04 != ( semiri2019852685at_int @ N2 ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_184_zero__le__imp__eq__int,axiom,
% 3.64/2.04 ! [K: int] :
% 3.64/2.04 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 3.64/2.04 => ? [N2: nat] :
% 3.64/2.04 ( K
% 3.64/2.04 = ( semiri2019852685at_int @ N2 ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_185_zero__integer_Orsp,axiom,
% 3.64/2.04 zero_zero_int = zero_zero_int ).
% 3.64/2.04
% 3.64/2.04 thf(fact_186_of__nat__mono,axiom,
% 3.64/2.04 ! [I2: nat,J: nat] :
% 3.64/2.04 ( ( ord_less_eq_nat @ I2 @ J )
% 3.64/2.04 => ( ord_less_eq_nat @ ( semiri1382578993at_nat @ I2 ) @ ( semiri1382578993at_nat @ J ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_187_of__nat__mono,axiom,
% 3.64/2.04 ! [I2: nat,J: nat] :
% 3.64/2.04 ( ( ord_less_eq_nat @ I2 @ J )
% 3.64/2.04 => ( ord_less_eq_int @ ( semiri2019852685at_int @ I2 ) @ ( semiri2019852685at_int @ J ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_188_of__nat__mono,axiom,
% 3.64/2.04 ! [I2: nat,J: nat] :
% 3.64/2.04 ( ( ord_less_eq_nat @ I2 @ J )
% 3.64/2.04 => ( ord_less_eq_real @ ( semiri2110766477t_real @ I2 ) @ ( semiri2110766477t_real @ J ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_189_zle__int,axiom,
% 3.64/2.04 ! [M: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_eq_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) )
% 3.64/2.04 = ( ord_less_eq_nat @ M @ N ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_190_int__int__eq,axiom,
% 3.64/2.04 ! [M: nat,N: nat] :
% 3.64/2.04 ( ( ( semiri2019852685at_int @ M )
% 3.64/2.04 = ( semiri2019852685at_int @ N ) )
% 3.64/2.04 = ( M = N ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_191_real__arch__simple,axiom,
% 3.64/2.04 ! [X: real] :
% 3.64/2.04 ? [N2: nat] : ( ord_less_eq_real @ X @ ( semiri2110766477t_real @ N2 ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_192_power__less__imp__less__base,axiom,
% 3.64/2.04 ! [A: nat,N: nat,B: nat] :
% 3.64/2.04 ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 3.64/2.04 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 3.64/2.04 => ( ord_less_nat @ A @ B ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_193_power__less__imp__less__base,axiom,
% 3.64/2.04 ! [A: int,N: nat,B: int] :
% 3.64/2.04 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 3.64/2.04 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 3.64/2.04 => ( ord_less_int @ A @ B ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_194_power__less__imp__less__base,axiom,
% 3.64/2.04 ! [A: real,N: nat,B: real] :
% 3.64/2.04 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 3.64/2.04 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 3.64/2.04 => ( ord_less_real @ A @ B ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_195_power__inverse,axiom,
% 3.64/2.04 ! [A: real,N: nat] :
% 3.64/2.04 ( ( power_power_real @ ( inverse_inverse_real @ A ) @ N )
% 3.64/2.04 = ( inverse_inverse_real @ ( power_power_real @ A @ N ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_196_power__divide,axiom,
% 3.64/2.04 ! [A: real,B: real,N: nat] :
% 3.64/2.04 ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N )
% 3.64/2.04 = ( divide_divide_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_197_power__not__zero,axiom,
% 3.64/2.04 ! [A: int,N: nat] :
% 3.64/2.04 ( ( A != zero_zero_int )
% 3.64/2.04 => ( ( power_power_int @ A @ N )
% 3.64/2.04 != zero_zero_int ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_198_power__not__zero,axiom,
% 3.64/2.04 ! [A: nat,N: nat] :
% 3.64/2.04 ( ( A != zero_zero_nat )
% 3.64/2.04 => ( ( power_power_nat @ A @ N )
% 3.64/2.04 != zero_zero_nat ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_199_power__not__zero,axiom,
% 3.64/2.04 ! [A: real,N: nat] :
% 3.64/2.04 ( ( A != zero_zero_real )
% 3.64/2.04 => ( ( power_power_real @ A @ N )
% 3.64/2.04 != zero_zero_real ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_200_zero__le__power,axiom,
% 3.64/2.04 ! [A: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.64/2.04 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_201_zero__le__power,axiom,
% 3.64/2.04 ! [A: int,N: nat] :
% 3.64/2.04 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.64/2.04 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_202_zero__le__power,axiom,
% 3.64/2.04 ! [A: real,N: nat] :
% 3.64/2.04 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.64/2.04 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_203_power__mono,axiom,
% 3.64/2.04 ! [A: nat,B: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_eq_nat @ A @ B )
% 3.64/2.04 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.64/2.04 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_204_power__mono,axiom,
% 3.64/2.04 ! [A: int,B: int,N: nat] :
% 3.64/2.04 ( ( ord_less_eq_int @ A @ B )
% 3.64/2.04 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.64/2.04 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_205_power__mono,axiom,
% 3.64/2.04 ! [A: real,B: real,N: nat] :
% 3.64/2.04 ( ( ord_less_eq_real @ A @ B )
% 3.64/2.04 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.64/2.04 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_206_less__eq__int__code_I1_J,axiom,
% 3.64/2.04 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 3.64/2.04
% 3.64/2.04 thf(fact_207_less__int__code_I1_J,axiom,
% 3.64/2.04 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_208_power__eq__imp__eq__base,axiom,
% 3.64/2.04 ! [A: nat,N: nat,B: nat] :
% 3.64/2.04 ( ( ( power_power_nat @ A @ N )
% 3.64/2.04 = ( power_power_nat @ B @ N ) )
% 3.64/2.04 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.64/2.04 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 3.64/2.04 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 3.64/2.04 => ( A = B ) ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_209_power__eq__imp__eq__base,axiom,
% 3.64/2.04 ! [A: int,N: nat,B: int] :
% 3.64/2.04 ( ( ( power_power_int @ A @ N )
% 3.64/2.04 = ( power_power_int @ B @ N ) )
% 3.64/2.04 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.64/2.04 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 3.64/2.04 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 3.64/2.04 => ( A = B ) ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_210_power__eq__imp__eq__base,axiom,
% 3.64/2.04 ! [A: real,N: nat,B: real] :
% 3.64/2.04 ( ( ( power_power_real @ A @ N )
% 3.64/2.04 = ( power_power_real @ B @ N ) )
% 3.64/2.04 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.64/2.04 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 3.64/2.04 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 3.64/2.04 => ( A = B ) ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_211_power__eq__iff__eq__base,axiom,
% 3.64/2.04 ! [N: nat,A: nat,B: nat] :
% 3.64/2.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 3.64/2.04 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.64/2.04 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 3.64/2.04 => ( ( ( power_power_nat @ A @ N )
% 3.64/2.04 = ( power_power_nat @ B @ N ) )
% 3.64/2.04 = ( A = B ) ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_212_power__eq__iff__eq__base,axiom,
% 3.64/2.04 ! [N: nat,A: int,B: int] :
% 3.64/2.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 3.64/2.04 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.64/2.04 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 3.64/2.04 => ( ( ( power_power_int @ A @ N )
% 3.64/2.04 = ( power_power_int @ B @ N ) )
% 3.64/2.04 = ( A = B ) ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_213_power__eq__iff__eq__base,axiom,
% 3.64/2.04 ! [N: nat,A: real,B: real] :
% 3.64/2.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 3.64/2.04 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.64/2.04 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 3.64/2.04 => ( ( ( power_power_real @ A @ N )
% 3.64/2.04 = ( power_power_real @ B @ N ) )
% 3.64/2.04 = ( A = B ) ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_214_real__arch__inverse,axiom,
% 3.64/2.04 ! [E2: real] :
% 3.64/2.04 ( ( ord_less_real @ zero_zero_real @ E2 )
% 3.64/2.04 = ( ? [N3: nat] :
% 3.64/2.04 ( ( N3 != zero_zero_nat )
% 3.64/2.04 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri2110766477t_real @ N3 ) ) )
% 3.64/2.04 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri2110766477t_real @ N3 ) ) @ E2 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_215_forall__pos__mono,axiom,
% 3.64/2.04 ! [P: real > $o,E2: real] :
% 3.64/2.04 ( ! [D: real,E: real] :
% 3.64/2.04 ( ( ord_less_real @ D @ E )
% 3.64/2.04 => ( ( P @ D )
% 3.64/2.04 => ( P @ E ) ) )
% 3.64/2.04 => ( ! [N2: nat] :
% 3.64/2.04 ( ( N2 != zero_zero_nat )
% 3.64/2.04 => ( P @ ( inverse_inverse_real @ ( semiri2110766477t_real @ N2 ) ) ) )
% 3.64/2.04 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 3.64/2.04 => ( P @ E2 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_216_zero__le,axiom,
% 3.64/2.04 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_217_le__numeral__extra_I3_J,axiom,
% 3.64/2.04 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 3.64/2.04
% 3.64/2.04 thf(fact_218_le__numeral__extra_I3_J,axiom,
% 3.64/2.04 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 3.64/2.04
% 3.64/2.04 thf(fact_219_le__numeral__extra_I3_J,axiom,
% 3.64/2.04 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 3.64/2.04
% 3.64/2.04 thf(fact_220_ge__less__neq__conv,axiom,
% 3.64/2.04 ( ord_less_eq_nat
% 3.64/2.04 = ( ^ [A3: nat,N3: nat] :
% 3.64/2.04 ! [X2: nat] :
% 3.64/2.04 ( ( ord_less_nat @ X2 @ A3 )
% 3.64/2.04 => ( N3 != X2 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_221_ge__less__neq__conv,axiom,
% 3.64/2.04 ( ord_less_eq_int
% 3.64/2.04 = ( ^ [A3: int,N3: int] :
% 3.64/2.04 ! [X2: int] :
% 3.64/2.04 ( ( ord_less_int @ X2 @ A3 )
% 3.64/2.04 => ( N3 != X2 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_222_ge__less__neq__conv,axiom,
% 3.64/2.04 ( ord_less_eq_real
% 3.64/2.04 = ( ^ [A3: real,N3: real] :
% 3.64/2.04 ! [X2: real] :
% 3.64/2.04 ( ( ord_less_real @ X2 @ A3 )
% 3.64/2.04 => ( N3 != X2 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_223_less__ge__neq__conv,axiom,
% 3.64/2.04 ( ord_less_nat
% 3.64/2.04 = ( ^ [N3: nat,A3: nat] :
% 3.64/2.04 ! [X2: nat] :
% 3.64/2.04 ( ( ord_less_eq_nat @ A3 @ X2 )
% 3.64/2.04 => ( N3 != X2 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_224_less__ge__neq__conv,axiom,
% 3.64/2.04 ( ord_less_int
% 3.64/2.04 = ( ^ [N3: int,A3: int] :
% 3.64/2.04 ! [X2: int] :
% 3.64/2.04 ( ( ord_less_eq_int @ A3 @ X2 )
% 3.64/2.04 => ( N3 != X2 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_225_less__ge__neq__conv,axiom,
% 3.64/2.04 ( ord_less_real
% 3.64/2.04 = ( ^ [N3: real,A3: real] :
% 3.64/2.04 ! [X2: real] :
% 3.64/2.04 ( ( ord_less_eq_real @ A3 @ X2 )
% 3.64/2.04 => ( N3 != X2 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_226_greater__le__neq__conv,axiom,
% 3.64/2.04 ( ord_less_nat
% 3.64/2.04 = ( ^ [A3: nat,N3: nat] :
% 3.64/2.04 ! [X2: nat] :
% 3.64/2.04 ( ( ord_less_eq_nat @ X2 @ A3 )
% 3.64/2.04 => ( N3 != X2 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_227_greater__le__neq__conv,axiom,
% 3.64/2.04 ( ord_less_int
% 3.64/2.04 = ( ^ [A3: int,N3: int] :
% 3.64/2.04 ! [X2: int] :
% 3.64/2.04 ( ( ord_less_eq_int @ X2 @ A3 )
% 3.64/2.04 => ( N3 != X2 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_228_greater__le__neq__conv,axiom,
% 3.64/2.04 ( ord_less_real
% 3.64/2.04 = ( ^ [A3: real,N3: real] :
% 3.64/2.04 ! [X2: real] :
% 3.64/2.04 ( ( ord_less_eq_real @ X2 @ A3 )
% 3.64/2.04 => ( N3 != X2 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_229_le__greater__neq__conv,axiom,
% 3.64/2.04 ( ord_less_eq_nat
% 3.64/2.04 = ( ^ [N3: nat,A3: nat] :
% 3.64/2.04 ! [X2: nat] :
% 3.64/2.04 ( ( ord_less_nat @ A3 @ X2 )
% 3.64/2.04 => ( N3 != X2 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_230_le__greater__neq__conv,axiom,
% 3.64/2.04 ( ord_less_eq_int
% 3.64/2.04 = ( ^ [N3: int,A3: int] :
% 3.64/2.04 ! [X2: int] :
% 3.64/2.04 ( ( ord_less_int @ A3 @ X2 )
% 3.64/2.04 => ( N3 != X2 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_231_le__greater__neq__conv,axiom,
% 3.64/2.04 ( ord_less_eq_real
% 3.64/2.04 = ( ^ [N3: real,A3: real] :
% 3.64/2.04 ! [X2: real] :
% 3.64/2.04 ( ( ord_less_real @ A3 @ X2 )
% 3.64/2.04 => ( N3 != X2 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_232_bot__nat__0_Oextremum__uniqueI,axiom,
% 3.64/2.04 ! [A: nat] :
% 3.64/2.04 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 3.64/2.04 => ( A = zero_zero_nat ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_233_bot__nat__0_Oextremum__unique,axiom,
% 3.64/2.04 ! [A: nat] :
% 3.64/2.04 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 3.64/2.04 = ( A = zero_zero_nat ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_234_le__0__eq,axiom,
% 3.64/2.04 ! [N: nat] :
% 3.64/2.04 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 3.64/2.04 = ( N = zero_zero_nat ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_235_less__eq__nat_Osimps_I1_J,axiom,
% 3.64/2.04 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_236_less__mono__imp__le__mono,axiom,
% 3.64/2.04 ! [F: nat > nat,I2: nat,J: nat] :
% 3.64/2.04 ( ! [I3: nat,J2: nat] :
% 3.64/2.04 ( ( ord_less_nat @ I3 @ J2 )
% 3.64/2.04 => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 3.64/2.04 => ( ( ord_less_eq_nat @ I2 @ J )
% 3.64/2.04 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_237_le__neq__implies__less,axiom,
% 3.64/2.04 ! [M: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_eq_nat @ M @ N )
% 3.64/2.04 => ( ( M != N )
% 3.64/2.04 => ( ord_less_nat @ M @ N ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_238_less__or__eq__imp__le,axiom,
% 3.64/2.04 ! [M: nat,N: nat] :
% 3.64/2.04 ( ( ( ord_less_nat @ M @ N )
% 3.64/2.04 | ( M = N ) )
% 3.64/2.04 => ( ord_less_eq_nat @ M @ N ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_239_le__eq__less__or__eq,axiom,
% 3.64/2.04 ( ord_less_eq_nat
% 3.64/2.04 = ( ^ [M3: nat,N3: nat] :
% 3.64/2.04 ( ( ord_less_nat @ M3 @ N3 )
% 3.64/2.04 | ( M3 = N3 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_240_less__imp__le__nat,axiom,
% 3.64/2.04 ! [M: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_nat @ M @ N )
% 3.64/2.04 => ( ord_less_eq_nat @ M @ N ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_241_nat__less__le,axiom,
% 3.64/2.04 ( ord_less_nat
% 3.64/2.04 = ( ^ [M3: nat,N3: nat] :
% 3.64/2.04 ( ( ord_less_eq_nat @ M3 @ N3 )
% 3.64/2.04 & ( M3 != N3 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_242_zero__less__power,axiom,
% 3.64/2.04 ! [A: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_nat @ zero_zero_nat @ A )
% 3.64/2.04 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_243_zero__less__power,axiom,
% 3.64/2.04 ! [A: int,N: nat] :
% 3.64/2.04 ( ( ord_less_int @ zero_zero_int @ A )
% 3.64/2.04 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_244_zero__less__power,axiom,
% 3.64/2.04 ! [A: real,N: nat] :
% 3.64/2.04 ( ( ord_less_real @ zero_zero_real @ A )
% 3.64/2.04 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_245_nat__power__less__imp__less,axiom,
% 3.64/2.04 ! [I2: nat,M: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_nat @ zero_zero_nat @ I2 )
% 3.64/2.04 => ( ( ord_less_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N ) )
% 3.64/2.04 => ( ord_less_nat @ M @ N ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_246_power__strict__mono,axiom,
% 3.64/2.04 ! [A: nat,B: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_nat @ A @ B )
% 3.64/2.04 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 3.64/2.04 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 3.64/2.04 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_247_power__strict__mono,axiom,
% 3.64/2.04 ! [A: int,B: int,N: nat] :
% 3.64/2.04 ( ( ord_less_int @ A @ B )
% 3.64/2.04 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.64/2.04 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 3.64/2.04 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_248_power__strict__mono,axiom,
% 3.64/2.04 ! [A: real,B: real,N: nat] :
% 3.64/2.04 ( ( ord_less_real @ A @ B )
% 3.64/2.04 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.64/2.04 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 3.64/2.04 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_249_zero__power,axiom,
% 3.64/2.04 ! [N: nat] :
% 3.64/2.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 3.64/2.04 => ( ( power_power_int @ zero_zero_int @ N )
% 3.64/2.04 = zero_zero_int ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_250_zero__power,axiom,
% 3.64/2.04 ! [N: nat] :
% 3.64/2.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 3.64/2.04 => ( ( power_power_nat @ zero_zero_nat @ N )
% 3.64/2.04 = zero_zero_nat ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_251_zero__power,axiom,
% 3.64/2.04 ! [N: nat] :
% 3.64/2.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 3.64/2.04 => ( ( power_power_real @ zero_zero_real @ N )
% 3.64/2.04 = zero_zero_real ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_252_of__nat__0__le__iff,axiom,
% 3.64/2.04 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_253_of__nat__0__le__iff,axiom,
% 3.64/2.04 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri2019852685at_int @ N ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_254_of__nat__0__le__iff,axiom,
% 3.64/2.04 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2110766477t_real @ N ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_255_ex__least__nat__le,axiom,
% 3.64/2.04 ! [P: nat > $o,N: nat] :
% 3.64/2.04 ( ( P @ N )
% 3.64/2.04 => ( ~ ( P @ zero_zero_nat )
% 3.64/2.04 => ? [K3: nat] :
% 3.64/2.04 ( ( ord_less_eq_nat @ K3 @ N )
% 3.64/2.04 & ! [I4: nat] :
% 3.64/2.04 ( ( ord_less_nat @ I4 @ K3 )
% 3.64/2.04 => ~ ( P @ I4 ) )
% 3.64/2.04 & ( P @ K3 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_256_count__le__length,axiom,
% 3.64/2.04 ! [Xs: list_a,X: a] : ( ord_less_eq_nat @ ( count_list_a @ Xs @ X ) @ ( size_size_list_a @ Xs ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_257_list__slice__length,axiom,
% 3.64/2.04 ! [Xs: list_a,K: nat] :
% 3.64/2.04 ( ( size_s1427607542list_a @ ( listSl97544552lice_a @ Xs @ K ) )
% 3.64/2.04 = ( divide_divide_nat @ ( size_size_list_a @ Xs ) @ K ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_258_inverse__le__iff__le,axiom,
% 3.64/2.04 ! [A: real,B: real] :
% 3.64/2.04 ( ( ord_less_real @ zero_zero_real @ A )
% 3.64/2.04 => ( ( ord_less_real @ zero_zero_real @ B )
% 3.64/2.04 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 3.64/2.04 = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_259_inverse__le__iff__le__neg,axiom,
% 3.64/2.04 ! [A: real,B: real] :
% 3.64/2.04 ( ( ord_less_real @ A @ zero_zero_real )
% 3.64/2.04 => ( ( ord_less_real @ B @ zero_zero_real )
% 3.64/2.04 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 3.64/2.04 = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_260_div__less,axiom,
% 3.64/2.04 ! [M: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_nat @ M @ N )
% 3.64/2.04 => ( ( divide_divide_nat @ M @ N )
% 3.64/2.04 = zero_zero_nat ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_261_inverse__positive__iff__positive,axiom,
% 3.64/2.04 ! [A: real] :
% 3.64/2.04 ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 3.64/2.04 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_262_inverse__negative__iff__negative,axiom,
% 3.64/2.04 ! [A: real] :
% 3.64/2.04 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 3.64/2.04 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_263_inverse__less__iff__less__neg,axiom,
% 3.64/2.04 ! [A: real,B: real] :
% 3.64/2.04 ( ( ord_less_real @ A @ zero_zero_real )
% 3.64/2.04 => ( ( ord_less_real @ B @ zero_zero_real )
% 3.64/2.04 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 3.64/2.04 = ( ord_less_real @ B @ A ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_264_inverse__eq__iff__eq,axiom,
% 3.64/2.04 ! [A: real,B: real] :
% 3.64/2.04 ( ( ( inverse_inverse_real @ A )
% 3.64/2.04 = ( inverse_inverse_real @ B ) )
% 3.64/2.04 = ( A = B ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_265_inverse__inverse__eq,axiom,
% 3.64/2.04 ! [A: real] :
% 3.64/2.04 ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 3.64/2.04 = A ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_266_division__ring__divide__zero,axiom,
% 3.64/2.04 ! [A: real] :
% 3.64/2.04 ( ( divide_divide_real @ A @ zero_zero_real )
% 3.64/2.04 = zero_zero_real ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_267_divide__cancel__right,axiom,
% 3.64/2.04 ! [A: real,C: real,B: real] :
% 3.64/2.04 ( ( ( divide_divide_real @ A @ C )
% 3.64/2.04 = ( divide_divide_real @ B @ C ) )
% 3.64/2.04 = ( ( C = zero_zero_real )
% 3.64/2.04 | ( A = B ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_268_divide__cancel__left,axiom,
% 3.64/2.04 ! [C: real,A: real,B: real] :
% 3.64/2.04 ( ( ( divide_divide_real @ C @ A )
% 3.64/2.04 = ( divide_divide_real @ C @ B ) )
% 3.64/2.04 = ( ( C = zero_zero_real )
% 3.64/2.04 | ( A = B ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_269_divide__eq__0__iff,axiom,
% 3.64/2.04 ! [A: real,B: real] :
% 3.64/2.04 ( ( ( divide_divide_real @ A @ B )
% 3.64/2.04 = zero_zero_real )
% 3.64/2.04 = ( ( A = zero_zero_real )
% 3.64/2.04 | ( B = zero_zero_real ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_270_inverse__nonzero__iff__nonzero,axiom,
% 3.64/2.04 ! [A: real] :
% 3.64/2.04 ( ( ( inverse_inverse_real @ A )
% 3.64/2.04 = zero_zero_real )
% 3.64/2.04 = ( A = zero_zero_real ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_271_inverse__zero,axiom,
% 3.64/2.04 ( ( inverse_inverse_real @ zero_zero_real )
% 3.64/2.04 = zero_zero_real ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_272_inverse__divide,axiom,
% 3.64/2.04 ! [A: real,B: real] :
% 3.64/2.04 ( ( inverse_inverse_real @ ( divide_divide_real @ A @ B ) )
% 3.64/2.04 = ( divide_divide_real @ B @ A ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_273_inverse__nonnegative__iff__nonnegative,axiom,
% 3.64/2.04 ! [A: real] :
% 3.64/2.04 ( ( ord_less_eq_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 3.64/2.04 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_274_inverse__nonpositive__iff__nonpositive,axiom,
% 3.64/2.04 ! [A: real] :
% 3.64/2.04 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 3.64/2.04 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_275_inverse__less__iff__less,axiom,
% 3.64/2.04 ! [A: real,B: real] :
% 3.64/2.04 ( ( ord_less_real @ zero_zero_real @ A )
% 3.64/2.04 => ( ( ord_less_real @ zero_zero_real @ B )
% 3.64/2.04 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 3.64/2.04 = ( ord_less_real @ B @ A ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_276_div__neg__neg__trivial,axiom,
% 3.64/2.04 ! [K: int,L: int] :
% 3.64/2.04 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 3.64/2.04 => ( ( ord_less_int @ L @ K )
% 3.64/2.04 => ( ( divide_divide_int @ K @ L )
% 3.64/2.04 = zero_zero_int ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_277_div__pos__pos__trivial,axiom,
% 3.64/2.04 ! [K: int,L: int] :
% 3.64/2.04 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 3.64/2.04 => ( ( ord_less_int @ K @ L )
% 3.64/2.04 => ( ( divide_divide_int @ K @ L )
% 3.64/2.04 = zero_zero_int ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_278_less__eq__real__def,axiom,
% 3.64/2.04 ( ord_less_eq_real
% 3.64/2.04 = ( ^ [X2: real,Y3: real] :
% 3.64/2.04 ( ( ord_less_real @ X2 @ Y3 )
% 3.64/2.04 | ( X2 = Y3 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_279_le__refl,axiom,
% 3.64/2.04 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_280_le__trans,axiom,
% 3.64/2.04 ! [I2: nat,J: nat,K: nat] :
% 3.64/2.04 ( ( ord_less_eq_nat @ I2 @ J )
% 3.64/2.04 => ( ( ord_less_eq_nat @ J @ K )
% 3.64/2.04 => ( ord_less_eq_nat @ I2 @ K ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_281_eq__imp__le,axiom,
% 3.64/2.04 ! [M: nat,N: nat] :
% 3.64/2.04 ( ( M = N )
% 3.64/2.04 => ( ord_less_eq_nat @ M @ N ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_282_le__antisym,axiom,
% 3.64/2.04 ! [M: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_eq_nat @ M @ N )
% 3.64/2.04 => ( ( ord_less_eq_nat @ N @ M )
% 3.64/2.04 => ( M = N ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_283_nat__le__linear,axiom,
% 3.64/2.04 ! [M: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_eq_nat @ M @ N )
% 3.64/2.04 | ( ord_less_eq_nat @ N @ M ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_284_Nat_Oex__has__greatest__nat,axiom,
% 3.64/2.04 ! [P: nat > $o,K: nat,B: nat] :
% 3.64/2.04 ( ( P @ K )
% 3.64/2.04 => ( ! [Y4: nat] :
% 3.64/2.04 ( ( P @ Y4 )
% 3.64/2.04 => ( ord_less_eq_nat @ Y4 @ B ) )
% 3.64/2.04 => ? [X3: nat] :
% 3.64/2.04 ( ( P @ X3 )
% 3.64/2.04 & ! [Y2: nat] :
% 3.64/2.04 ( ( P @ Y2 )
% 3.64/2.04 => ( ord_less_eq_nat @ Y2 @ X3 ) ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_285_real__of__nat__div4,axiom,
% 3.64/2.04 ! [N: nat,X: nat] : ( ord_less_eq_real @ ( semiri2110766477t_real @ ( divide_divide_nat @ N @ X ) ) @ ( divide_divide_real @ ( semiri2110766477t_real @ N ) @ ( semiri2110766477t_real @ X ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_286_linordered__field__no__lb,axiom,
% 3.64/2.04 ! [X4: real] :
% 3.64/2.04 ? [Y4: real] : ( ord_less_real @ Y4 @ X4 ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_287_linordered__field__no__ub,axiom,
% 3.64/2.04 ! [X4: real] :
% 3.64/2.04 ? [X_1: real] : ( ord_less_real @ X4 @ X_1 ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_288_inverse__eq__imp__eq,axiom,
% 3.64/2.04 ! [A: real,B: real] :
% 3.64/2.04 ( ( ( inverse_inverse_real @ A )
% 3.64/2.04 = ( inverse_inverse_real @ B ) )
% 3.64/2.04 => ( A = B ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_289_div__le__mono,axiom,
% 3.64/2.04 ! [M: nat,N: nat,K: nat] :
% 3.64/2.04 ( ( ord_less_eq_nat @ M @ N )
% 3.64/2.04 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_290_div__le__dividend,axiom,
% 3.64/2.04 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_291_nonzero__imp__inverse__nonzero,axiom,
% 3.64/2.04 ! [A: real] :
% 3.64/2.04 ( ( A != zero_zero_real )
% 3.64/2.04 => ( ( inverse_inverse_real @ A )
% 3.64/2.04 != zero_zero_real ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_292_nonzero__inverse__inverse__eq,axiom,
% 3.64/2.04 ! [A: real] :
% 3.64/2.04 ( ( A != zero_zero_real )
% 3.64/2.04 => ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 3.64/2.04 = A ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_293_nonzero__inverse__eq__imp__eq,axiom,
% 3.64/2.04 ! [A: real,B: real] :
% 3.64/2.04 ( ( ( inverse_inverse_real @ A )
% 3.64/2.04 = ( inverse_inverse_real @ B ) )
% 3.64/2.04 => ( ( A != zero_zero_real )
% 3.64/2.04 => ( ( B != zero_zero_real )
% 3.64/2.04 => ( A = B ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_294_inverse__zero__imp__zero,axiom,
% 3.64/2.04 ! [A: real] :
% 3.64/2.04 ( ( ( inverse_inverse_real @ A )
% 3.64/2.04 = zero_zero_real )
% 3.64/2.04 => ( A = zero_zero_real ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_295_field__class_Ofield__inverse__zero,axiom,
% 3.64/2.04 ( ( inverse_inverse_real @ zero_zero_real )
% 3.64/2.04 = zero_zero_real ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_296_divide__le__0__iff,axiom,
% 3.64/2.04 ! [A: real,B: real] :
% 3.64/2.04 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 3.64/2.04 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.64/2.04 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 3.64/2.04 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 3.64/2.04 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_297_divide__right__mono,axiom,
% 3.64/2.04 ! [A: real,B: real,C: real] :
% 3.64/2.04 ( ( ord_less_eq_real @ A @ B )
% 3.64/2.04 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 3.64/2.04 => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_298_zero__le__divide__iff,axiom,
% 3.64/2.04 ! [A: real,B: real] :
% 3.64/2.04 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 3.64/2.04 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 3.64/2.04 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 3.64/2.04 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 3.64/2.04 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_299_divide__nonneg__nonneg,axiom,
% 3.64/2.04 ! [X: real,Y: real] :
% 3.64/2.04 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.64/2.04 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 3.64/2.04 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_300_divide__nonneg__nonpos,axiom,
% 3.64/2.04 ! [X: real,Y: real] :
% 3.64/2.04 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 3.64/2.04 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 3.64/2.04 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_301_divide__nonpos__nonneg,axiom,
% 3.64/2.04 ! [X: real,Y: real] :
% 3.64/2.04 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 3.64/2.04 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 3.64/2.04 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_302_divide__nonpos__nonpos,axiom,
% 3.64/2.04 ! [X: real,Y: real] :
% 3.64/2.04 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 3.64/2.04 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 3.64/2.04 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_303_divide__right__mono__neg,axiom,
% 3.64/2.04 ! [A: real,B: real,C: real] :
% 3.64/2.04 ( ( ord_less_eq_real @ A @ B )
% 3.64/2.04 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 3.64/2.04 => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_304_divide__neg__neg,axiom,
% 3.64/2.04 ! [X: real,Y: real] :
% 3.64/2.04 ( ( ord_less_real @ X @ zero_zero_real )
% 3.64/2.04 => ( ( ord_less_real @ Y @ zero_zero_real )
% 3.64/2.04 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_305_divide__neg__pos,axiom,
% 3.64/2.04 ! [X: real,Y: real] :
% 3.64/2.04 ( ( ord_less_real @ X @ zero_zero_real )
% 3.64/2.04 => ( ( ord_less_real @ zero_zero_real @ Y )
% 3.64/2.04 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_306_divide__pos__neg,axiom,
% 3.64/2.04 ! [X: real,Y: real] :
% 3.64/2.04 ( ( ord_less_real @ zero_zero_real @ X )
% 3.64/2.04 => ( ( ord_less_real @ Y @ zero_zero_real )
% 3.64/2.04 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_307_divide__pos__pos,axiom,
% 3.64/2.04 ! [X: real,Y: real] :
% 3.64/2.04 ( ( ord_less_real @ zero_zero_real @ X )
% 3.64/2.04 => ( ( ord_less_real @ zero_zero_real @ Y )
% 3.64/2.04 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_308_divide__less__0__iff,axiom,
% 3.64/2.04 ! [A: real,B: real] :
% 3.64/2.04 ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 3.64/2.04 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 3.64/2.04 & ( ord_less_real @ B @ zero_zero_real ) )
% 3.64/2.04 | ( ( ord_less_real @ A @ zero_zero_real )
% 3.64/2.04 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_309_divide__less__cancel,axiom,
% 3.64/2.04 ! [A: real,C: real,B: real] :
% 3.64/2.04 ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 3.64/2.04 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 3.64/2.04 => ( ord_less_real @ A @ B ) )
% 3.64/2.04 & ( ( ord_less_real @ C @ zero_zero_real )
% 3.64/2.04 => ( ord_less_real @ B @ A ) )
% 3.64/2.04 & ( C != zero_zero_real ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_310_zero__less__divide__iff,axiom,
% 3.64/2.04 ! [A: real,B: real] :
% 3.64/2.04 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 3.64/2.04 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 3.64/2.04 & ( ord_less_real @ zero_zero_real @ B ) )
% 3.64/2.04 | ( ( ord_less_real @ A @ zero_zero_real )
% 3.64/2.04 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_311_divide__strict__right__mono,axiom,
% 3.64/2.04 ! [A: real,B: real,C: real] :
% 3.64/2.04 ( ( ord_less_real @ A @ B )
% 3.64/2.04 => ( ( ord_less_real @ zero_zero_real @ C )
% 3.64/2.04 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_312_divide__strict__right__mono__neg,axiom,
% 3.64/2.04 ! [B: real,A: real,C: real] :
% 3.64/2.04 ( ( ord_less_real @ B @ A )
% 3.64/2.04 => ( ( ord_less_real @ C @ zero_zero_real )
% 3.64/2.04 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_313_inverse__less__imp__less,axiom,
% 3.64/2.04 ! [A: real,B: real] :
% 3.64/2.04 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 3.64/2.04 => ( ( ord_less_real @ zero_zero_real @ A )
% 3.64/2.04 => ( ord_less_real @ B @ A ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_314_less__imp__inverse__less,axiom,
% 3.64/2.04 ! [A: real,B: real] :
% 3.64/2.04 ( ( ord_less_real @ A @ B )
% 3.64/2.04 => ( ( ord_less_real @ zero_zero_real @ A )
% 3.64/2.04 => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_315_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 3.64/2.04 ! [M: nat,N: nat] :
% 3.64/2.04 ( ( ( divide_divide_nat @ M @ N )
% 3.64/2.04 = zero_zero_nat )
% 3.64/2.04 = ( ( ord_less_nat @ M @ N )
% 3.64/2.04 | ( N = zero_zero_nat ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_316_div__greater__zero__iff,axiom,
% 3.64/2.04 ! [M: nat,N: nat] :
% 3.64/2.04 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 3.64/2.04 = ( ( ord_less_eq_nat @ N @ M )
% 3.64/2.04 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_317_div__le__mono2,axiom,
% 3.64/2.04 ! [M: nat,N: nat,K: nat] :
% 3.64/2.04 ( ( ord_less_nat @ zero_zero_nat @ M )
% 3.64/2.04 => ( ( ord_less_eq_nat @ M @ N )
% 3.64/2.04 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_318_complete__real,axiom,
% 3.64/2.04 ! [S2: set_real] :
% 3.64/2.04 ( ? [X4: real] : ( member_real @ X4 @ S2 )
% 3.64/2.04 => ( ? [Z: real] :
% 3.64/2.04 ! [X3: real] :
% 3.64/2.04 ( ( member_real @ X3 @ S2 )
% 3.64/2.04 => ( ord_less_eq_real @ X3 @ Z ) )
% 3.64/2.04 => ? [Y4: real] :
% 3.64/2.04 ( ! [X4: real] :
% 3.64/2.04 ( ( member_real @ X4 @ S2 )
% 3.64/2.04 => ( ord_less_eq_real @ X4 @ Y4 ) )
% 3.64/2.04 & ! [Z: real] :
% 3.64/2.04 ( ! [X3: real] :
% 3.64/2.04 ( ( member_real @ X3 @ S2 )
% 3.64/2.04 => ( ord_less_eq_real @ X3 @ Z ) )
% 3.64/2.04 => ( ord_less_eq_real @ Y4 @ Z ) ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_319_nonneg1__imp__zdiv__pos__iff,axiom,
% 3.64/2.04 ! [A: int,B: int] :
% 3.64/2.04 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.64/2.04 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 3.64/2.04 = ( ( ord_less_eq_int @ B @ A )
% 3.64/2.04 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_320_pos__imp__zdiv__nonneg__iff,axiom,
% 3.64/2.04 ! [B: int,A: int] :
% 3.64/2.04 ( ( ord_less_int @ zero_zero_int @ B )
% 3.64/2.04 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 3.64/2.04 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_321_div__neg__pos__less0,axiom,
% 3.64/2.04 ! [A: int,B: int] :
% 3.64/2.04 ( ( ord_less_int @ A @ zero_zero_int )
% 3.64/2.04 => ( ( ord_less_int @ zero_zero_int @ B )
% 3.64/2.04 => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_322_neg__imp__zdiv__neg__iff,axiom,
% 3.64/2.04 ! [B: int,A: int] :
% 3.64/2.04 ( ( ord_less_int @ B @ zero_zero_int )
% 3.64/2.04 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 3.64/2.04 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_323_pos__imp__zdiv__neg__iff,axiom,
% 3.64/2.04 ! [B: int,A: int] :
% 3.64/2.04 ( ( ord_less_int @ zero_zero_int @ B )
% 3.64/2.04 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 3.64/2.04 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_324_zdiv__int,axiom,
% 3.64/2.04 ! [A: nat,B: nat] :
% 3.64/2.04 ( ( semiri2019852685at_int @ ( divide_divide_nat @ A @ B ) )
% 3.64/2.04 = ( divide_divide_int @ ( semiri2019852685at_int @ A ) @ ( semiri2019852685at_int @ B ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_325_zdiv__mono1,axiom,
% 3.64/2.04 ! [A: int,A4: int,B: int] :
% 3.64/2.04 ( ( ord_less_eq_int @ A @ A4 )
% 3.64/2.04 => ( ( ord_less_int @ zero_zero_int @ B )
% 3.64/2.04 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A4 @ B ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_326_zdiv__mono2,axiom,
% 3.64/2.04 ! [A: int,B2: int,B: int] :
% 3.64/2.04 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.64/2.04 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 3.64/2.04 => ( ( ord_less_eq_int @ B2 @ B )
% 3.64/2.04 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B2 ) ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_327_zdiv__eq__0__iff,axiom,
% 3.64/2.04 ! [I2: int,K: int] :
% 3.64/2.04 ( ( ( divide_divide_int @ I2 @ K )
% 3.64/2.04 = zero_zero_int )
% 3.64/2.04 = ( ( K = zero_zero_int )
% 3.64/2.04 | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 3.64/2.04 & ( ord_less_int @ I2 @ K ) )
% 3.64/2.04 | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 3.64/2.04 & ( ord_less_int @ K @ I2 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_328_zdiv__mono1__neg,axiom,
% 3.64/2.04 ! [A: int,A4: int,B: int] :
% 3.64/2.04 ( ( ord_less_eq_int @ A @ A4 )
% 3.64/2.04 => ( ( ord_less_int @ B @ zero_zero_int )
% 3.64/2.04 => ( ord_less_eq_int @ ( divide_divide_int @ A4 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_329_zdiv__mono2__neg,axiom,
% 3.64/2.04 ! [A: int,B2: int,B: int] :
% 3.64/2.04 ( ( ord_less_int @ A @ zero_zero_int )
% 3.64/2.04 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 3.64/2.04 => ( ( ord_less_eq_int @ B2 @ B )
% 3.64/2.04 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B2 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_330_div__int__pos__iff,axiom,
% 3.64/2.04 ! [K: int,L: int] :
% 3.64/2.04 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 3.64/2.04 = ( ( K = zero_zero_int )
% 3.64/2.04 | ( L = zero_zero_int )
% 3.64/2.04 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 3.64/2.04 & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 3.64/2.04 | ( ( ord_less_int @ K @ zero_zero_int )
% 3.64/2.04 & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_331_div__positive__int,axiom,
% 3.64/2.04 ! [L: int,K: int] :
% 3.64/2.04 ( ( ord_less_eq_int @ L @ K )
% 3.64/2.04 => ( ( ord_less_int @ zero_zero_int @ L )
% 3.64/2.04 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_332_div__nonneg__neg__le0,axiom,
% 3.64/2.04 ! [A: int,B: int] :
% 3.64/2.04 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 3.64/2.04 => ( ( ord_less_int @ B @ zero_zero_int )
% 3.64/2.04 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_333_div__nonpos__pos__le0,axiom,
% 3.64/2.04 ! [A: int,B: int] :
% 3.64/2.04 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 3.64/2.04 => ( ( ord_less_int @ zero_zero_int @ B )
% 3.64/2.04 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_334_pos__imp__zdiv__pos__iff,axiom,
% 3.64/2.04 ! [K: int,I2: int] :
% 3.64/2.04 ( ( ord_less_int @ zero_zero_int @ K )
% 3.64/2.04 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I2 @ K ) )
% 3.64/2.04 = ( ord_less_eq_int @ K @ I2 ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_335_neg__imp__zdiv__nonneg__iff,axiom,
% 3.64/2.04 ! [B: int,A: int] :
% 3.64/2.04 ( ( ord_less_int @ B @ zero_zero_int )
% 3.64/2.04 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 3.64/2.04 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_336_realpow__pos__nth__unique,axiom,
% 3.64/2.04 ! [N: nat,A: real] :
% 3.64/2.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 3.64/2.04 => ( ( ord_less_real @ zero_zero_real @ A )
% 3.64/2.04 => ? [X3: real] :
% 3.64/2.04 ( ( ord_less_real @ zero_zero_real @ X3 )
% 3.64/2.04 & ( ( power_power_real @ X3 @ N )
% 3.64/2.04 = A )
% 3.64/2.04 & ! [Y2: real] :
% 3.64/2.04 ( ( ( ord_less_real @ zero_zero_real @ Y2 )
% 3.64/2.04 & ( ( power_power_real @ Y2 @ N )
% 3.64/2.04 = A ) )
% 3.64/2.04 => ( Y2 = X3 ) ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_337_realpow__pos__nth,axiom,
% 3.64/2.04 ! [N: nat,A: real] :
% 3.64/2.04 ( ( ord_less_nat @ zero_zero_nat @ N )
% 3.64/2.04 => ( ( ord_less_real @ zero_zero_real @ A )
% 3.64/2.04 => ? [R: real] :
% 3.64/2.04 ( ( ord_less_real @ zero_zero_real @ R )
% 3.64/2.04 & ( ( power_power_real @ R @ N )
% 3.64/2.04 = A ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_338_nat__int__comparison_I3_J,axiom,
% 3.64/2.04 ( ord_less_eq_nat
% 3.64/2.04 = ( ^ [A3: nat,B3: nat] : ( ord_less_eq_int @ ( semiri2019852685at_int @ A3 ) @ ( semiri2019852685at_int @ B3 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_339_nat__int__comparison_I2_J,axiom,
% 3.64/2.04 ( ord_less_nat
% 3.64/2.04 = ( ^ [A3: nat,B3: nat] : ( ord_less_int @ ( semiri2019852685at_int @ A3 ) @ ( semiri2019852685at_int @ B3 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_340_verit__la__generic,axiom,
% 3.64/2.04 ! [A: int,X: int] :
% 3.64/2.04 ( ( ord_less_eq_int @ A @ X )
% 3.64/2.04 | ( A = X )
% 3.64/2.04 | ( ord_less_eq_int @ X @ A ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_341_int__if,axiom,
% 3.64/2.04 ! [P: $o,A: nat,B: nat] :
% 3.64/2.04 ( ( P
% 3.64/2.04 => ( ( semiri2019852685at_int @ ( if_nat @ P @ A @ B ) )
% 3.64/2.04 = ( semiri2019852685at_int @ A ) ) )
% 3.64/2.04 & ( ~ P
% 3.64/2.04 => ( ( semiri2019852685at_int @ ( if_nat @ P @ A @ B ) )
% 3.64/2.04 = ( semiri2019852685at_int @ B ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_342_nat__int__comparison_I1_J,axiom,
% 3.64/2.04 ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 3.64/2.04 = ( ^ [A3: nat,B3: nat] :
% 3.64/2.04 ( ( semiri2019852685at_int @ A3 )
% 3.64/2.04 = ( semiri2019852685at_int @ B3 ) ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_343_int__ops_I1_J,axiom,
% 3.64/2.04 ( ( semiri2019852685at_int @ zero_zero_nat )
% 3.64/2.04 = zero_zero_int ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_344_div__gr__imp__gr__divisor,axiom,
% 3.64/2.04 ! [X: nat,N: nat,M: nat] :
% 3.64/2.04 ( ( ord_less_nat @ X @ ( divide_divide_nat @ N @ M ) )
% 3.64/2.04 => ( ord_less_eq_nat @ M @ N ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(fact_345_div__eq__0__conv,axiom,
% 3.64/2.04 ! [N: nat,M: nat] :
% 3.64/2.04 ( ( ( divide_divide_nat @ N @ M )
% 3.64/2.04 = zero_zero_nat )
% 3.64/2.04 = ( ( M = zero_zero_nat )
% 3.64/2.04 | ( ord_less_nat @ N @ M ) ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(help_If_3_1_If_001t__Nat__Onat_T,axiom,
% 3.64/2.04 ! [P: $o] :
% 3.64/2.04 ( ( P = $true )
% 3.64/2.04 | ( P = $false ) ) ).
% 3.64/2.04
% 3.64/2.04 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 3.64/2.04 ! [X: nat,Y: nat] :
% 3.64/2.04 ( ( if_nat @ $false @ X @ Y )
% 3.64/2.04 = Y ) ).
% 3.64/2.04
% 3.64/2.04 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 3.64/2.04 ! [X: nat,Y: nat] :
% 3.64/2.04 ( ( if_nat @ $true @ X @ Y )
% 3.64/2.04 = X ) ).
% 3.64/2.04
% 3.64/2.04 thf(conj_0,conjecture,
% 3.64/2.04 ( ( listSl97544552lice_a @ nil_a @ k )
% 3.64/2.04 = nil_list_a ) ).
% 3.64/2.04 ------------------------
% 3.64/2.08 % (608)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_491 for (2999ds/2Mi)
% 3.64/2.08 % (605)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_491 for (2999ds/4Mi)
% 3.64/2.08 % (606)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_491 for (2999ds/27Mi)
% 3.64/2.08 % (609)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_491 for (2999ds/275Mi)
% 3.64/2.08 % (604)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_491 for (2999ds/183Mi)
% 3.64/2.08 % (607)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_491 for (2999ds/2Mi)
% 3.64/2.08 % (610)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_491 for (2999ds/18Mi)
% 3.64/2.08 % (607)Instruction limit reached!
% 3.64/2.08 % (607)------------------------------
% 3.64/2.08 % (607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.64/2.08 % (607)Termination reason: Unknown
% 3.64/2.08 % (607)Termination phase: shuffling
% 3.64/2.08 % (608)Instruction limit reached!
% 3.64/2.08 % (608)------------------------------
% 3.64/2.08 % (608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.64/2.08 % (608)Termination reason: Unknown
% 3.64/2.08 % (608)Termination phase: shuffling
% 3.64/2.08
% 3.64/2.08 % (608)Memory used [KB]: 1407
% 3.64/2.08 % (608)Time elapsed: 0.003 s
% 3.64/2.08 % (608)Instructions burned: 3 (million)
% 3.64/2.08 % (608)------------------------------
% 3.64/2.08 % (608)------------------------------
% 3.64/2.08
% 3.64/2.08 % (607)Memory used [KB]: 1407
% 3.64/2.08 % (607)Time elapsed: 0.003 s
% 3.64/2.08 % (607)Instructions burned: 3 (million)
% 3.64/2.08 % (607)------------------------------
% 3.64/2.08 % (607)------------------------------
% 3.64/2.08 % (605)Instruction limit reached!
% 3.64/2.08 % (605)------------------------------
% 3.64/2.08 % (605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.64/2.08 % (605)Termination reason: Unknown
% 3.64/2.08 % (605)Termination phase: shuffling
% 3.64/2.08
% 3.64/2.08 % (605)Memory used [KB]: 1407
% 3.64/2.08 % (605)Time elapsed: 0.004 s
% 3.64/2.08 % (605)Instructions burned: 4 (million)
% 3.64/2.08 % (605)------------------------------
% 3.64/2.08 % (605)------------------------------
% 3.64/2.09 % (610)Instruction limit reached!
% 3.64/2.09 % (610)------------------------------
% 3.64/2.09 % (610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.64/2.09 % (610)Termination reason: Unknown
% 3.64/2.09 % (610)Termination phase: Property scanning
% 3.64/2.09
% 3.64/2.09 % (610)Memory used [KB]: 1663
% 3.64/2.09 % (610)Time elapsed: 0.012 s
% 3.64/2.09 % (610)Instructions burned: 18 (million)
% 3.64/2.09 % (610)------------------------------
% 3.64/2.09 % (610)------------------------------
% 3.64/2.09 % (606)Instruction limit reached!
% 3.64/2.09 % (606)------------------------------
% 3.64/2.09 % (606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.64/2.09 % (606)Termination reason: Unknown
% 3.64/2.09 % (606)Termination phase: Property scanning
% 3.64/2.09
% 3.64/2.09 % (606)Memory used [KB]: 1663
% 3.64/2.09 % (606)Time elapsed: 0.017 s
% 3.64/2.09 % (606)Instructions burned: 28 (million)
% 3.64/2.09 % (606)------------------------------
% 3.64/2.09 % (606)------------------------------
% 3.64/2.10 % (612)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_491 for (2999ds/37Mi)
% 3.64/2.10 % (611)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_491 for (2999ds/3Mi)
% 3.64/2.10 % (614)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_491 for (2999ds/15Mi)
% 3.64/2.10 % (611)Instruction limit reached!
% 3.64/2.10 % (611)------------------------------
% 3.64/2.10 % (611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.64/2.10 % (611)Termination reason: Unknown
% 3.64/2.10 % (611)Termination phase: shuffling
% 3.64/2.10
% 3.64/2.10 % (611)Memory used [KB]: 1407
% 3.64/2.10 % (611)Time elapsed: 0.003 s
% 3.64/2.10 % (611)Instructions burned: 3 (million)
% 3.64/2.10 % (611)------------------------------
% 3.64/2.10 % (611)------------------------------
% 3.64/2.10 % (609)Refutation not found, incomplete strategy
% 3.64/2.10 % (609)------------------------------
% 3.64/2.10 % (609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.64/2.10 % (609)Termination reason: Refutation not found, incomplete strategy
% 3.64/2.10
% 3.64/2.10
% 3.64/2.10 % (609)Memory used [KB]: 6268
% 3.64/2.10 % (609)Time elapsed: 0.026 s
% 3.64/2.10 % (609)Instructions burned: 40 (million)
% 3.64/2.10 % (609)------------------------------
% 3.64/2.10 % (609)------------------------------
% 3.64/2.11 % (614)Instruction limit reached!
% 3.64/2.11 % (614)------------------------------
% 3.64/2.11 % (614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.64/2.11 % (614)Termination reason: Unknown
% 3.64/2.11 % (614)Termination phase: shuffling
% 3.64/2.11
% 3.64/2.11 % (614)Memory used [KB]: 1535
% 3.64/2.11 % (614)Time elapsed: 0.010 s
% 3.64/2.11 % (614)Instructions burned: 15 (million)
% 3.64/2.11 % (614)------------------------------
% 3.64/2.11 % (614)------------------------------
% 3.64/2.11 % (615)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_491 for (2999ds/3Mi)
% 3.64/2.11 % (615)Instruction limit reached!
% 3.64/2.11 % (615)------------------------------
% 3.64/2.11 % (615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.64/2.11 % (615)Termination reason: Unknown
% 3.64/2.11 % (615)Termination phase: shuffling
% 3.64/2.11
% 3.64/2.11 % (615)Memory used [KB]: 1407
% 3.64/2.11 % (615)Time elapsed: 0.003 s
% 3.64/2.11 % (615)Instructions burned: 3 (million)
% 3.64/2.11 % (615)------------------------------
% 3.64/2.11 % (615)------------------------------
% 3.64/2.11 % (616)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_491 for (2999ds/1041Mi)
% 3.64/2.12 % (612)Instruction limit reached!
% 3.64/2.12 % (612)------------------------------
% 3.64/2.12 % (612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.64/2.12 % (612)Termination reason: Unknown
% 3.64/2.12 % (612)Termination phase: shuffling
% 3.64/2.12
% 3.64/2.12 % (612)Memory used [KB]: 2174
% 3.64/2.12 % (612)Time elapsed: 0.021 s
% 3.64/2.12 % (612)Instructions burned: 37 (million)
% 3.64/2.12 % (612)------------------------------
% 3.64/2.12 % (612)------------------------------
% 3.64/2.12 % (618)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_491 for (2999ds/7Mi)
% 3.64/2.12 % (621)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_491 for (2999ds/16Mi)
% 3.64/2.12 % (618)Instruction limit reached!
% 3.64/2.12 % (618)------------------------------
% 3.64/2.12 % (618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.64/2.12 % (618)Termination reason: Unknown
% 3.64/2.12 % (618)Termination phase: shuffling
% 3.64/2.12
% 3.64/2.12 % (618)Memory used [KB]: 1407
% 3.64/2.12 % (618)Time elapsed: 0.006 s
% 3.64/2.12 % (618)Instructions burned: 8 (million)
% 3.64/2.12 % (618)------------------------------
% 3.64/2.12 % (618)------------------------------
% 3.64/2.12 % (622)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_491 for (2999ds/3Mi)
% 3.64/2.13 % (623)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_491 for (2999ds/3Mi)
% 3.64/2.13 % (622)Instruction limit reached!
% 3.64/2.13 % (622)------------------------------
% 3.64/2.13 % (622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.64/2.13 % (622)Termination reason: Unknown
% 3.64/2.13 % (622)Termination phase: shuffling
% 3.64/2.13
% 3.64/2.13 % (622)Memory used [KB]: 1407
% 3.64/2.13 % (622)Time elapsed: 0.003 s
% 3.64/2.13 % (622)Instructions burned: 3 (million)
% 3.64/2.13 % (622)------------------------------
% 3.64/2.13 % (622)------------------------------
% 3.64/2.13 % (623)Instruction limit reached!
% 3.64/2.13 % (623)------------------------------
% 3.64/2.13 % (623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.64/2.13 % (623)Termination reason: Unknown
% 3.64/2.13 % (623)Termination phase: shuffling
% 3.64/2.13
% 3.64/2.13 % (623)Memory used [KB]: 1407
% 3.64/2.13 % (623)Time elapsed: 0.004 s
% 3.64/2.13 % (623)Instructions burned: 3 (million)
% 3.64/2.13 % (623)------------------------------
% 3.64/2.13 % (623)------------------------------
% 3.66/2.13 % (621)Instruction limit reached!
% 3.66/2.13 % (621)------------------------------
% 3.66/2.13 % (621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.13 % (621)Termination reason: Unknown
% 3.66/2.13 % (621)Termination phase: shuffling
% 3.66/2.13
% 3.66/2.13 % (621)Memory used [KB]: 1663
% 3.66/2.13 % (621)Time elapsed: 0.011 s
% 3.66/2.13 % (621)Instructions burned: 17 (million)
% 3.66/2.13 % (621)------------------------------
% 3.66/2.13 % (621)------------------------------
% 3.66/2.14 % (624)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_491 for (2999ds/7Mi)
% 3.66/2.14 % (624)Instruction limit reached!
% 3.66/2.14 % (624)------------------------------
% 3.66/2.14 % (624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.14 % (624)Termination reason: Unknown
% 3.66/2.14 % (624)Termination phase: shuffling
% 3.66/2.14
% 3.66/2.14 % (624)Memory used [KB]: 1407
% 3.66/2.14 % (624)Time elapsed: 0.005 s
% 3.66/2.14 % (624)Instructions burned: 7 (million)
% 3.66/2.14 % (624)------------------------------
% 3.66/2.14 % (624)------------------------------
% 3.66/2.14 % (625)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_491 for (2999ds/3Mi)
% 3.66/2.14 % (625)Instruction limit reached!
% 3.66/2.14 % (625)------------------------------
% 3.66/2.14 % (625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.14 % (625)Termination reason: Unknown
% 3.66/2.14 % (625)Termination phase: shuffling
% 3.66/2.14
% 3.66/2.14 % (625)Memory used [KB]: 1407
% 3.66/2.14 % (625)Time elapsed: 0.003 s
% 3.66/2.14 % (625)Instructions burned: 3 (million)
% 3.66/2.14 % (625)------------------------------
% 3.66/2.14 % (625)------------------------------
% 3.66/2.15 % (626)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_491 for (2999ds/4Mi)
% 3.66/2.15 % (627)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_491 for (2999ds/18Mi)
% 3.66/2.15 % (628)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_491 for (2999ds/710Mi)
% 3.66/2.15 % (626)Instruction limit reached!
% 3.66/2.15 % (626)------------------------------
% 3.66/2.15 % (626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.15 % (626)Termination reason: Unknown
% 3.66/2.15 % (626)Termination phase: shuffling
% 3.66/2.15
% 3.66/2.15 % (626)Memory used [KB]: 1407
% 3.66/2.15 % (626)Time elapsed: 0.004 s
% 3.66/2.15 % (626)Instructions burned: 5 (million)
% 3.66/2.15 % (626)------------------------------
% 3.66/2.15 % (626)------------------------------
% 3.66/2.16 % (627)Instruction limit reached!
% 3.66/2.16 % (627)------------------------------
% 3.66/2.16 % (627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.16 % (627)Termination reason: Unknown
% 3.66/2.16 % (627)Termination phase: Property scanning
% 3.66/2.16
% 3.66/2.16 % (627)Memory used [KB]: 1663
% 3.66/2.16 % (627)Time elapsed: 0.012 s
% 3.66/2.16 % (627)Instructions burned: 19 (million)
% 3.66/2.16 % (627)------------------------------
% 3.66/2.16 % (627)------------------------------
% 3.66/2.16 % (629)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_491 for (2999ds/6Mi)
% 3.66/2.16 % (630)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_491 for (2999ds/902Mi)
% 3.66/2.16 % (629)Instruction limit reached!
% 3.66/2.16 % (629)------------------------------
% 3.66/2.16 % (629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.16 % (629)Termination reason: Unknown
% 3.66/2.16 % (629)Termination phase: shuffling
% 3.66/2.16
% 3.66/2.16 % (629)Memory used [KB]: 1407
% 3.66/2.16 % (629)Time elapsed: 0.005 s
% 3.66/2.16 % (629)Instructions burned: 7 (million)
% 3.66/2.16 % (629)------------------------------
% 3.66/2.16 % (629)------------------------------
% 3.66/2.17 % (628)Refutation not found, incomplete strategy
% 3.66/2.17 % (628)------------------------------
% 3.66/2.17 % (628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.17 % (628)Termination reason: Refutation not found, incomplete strategy
% 3.66/2.17
% 3.66/2.17 % (632)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_491 for (2998ds/21Mi)
% 3.66/2.17
% 3.66/2.17 % (628)Memory used [KB]: 6140
% 3.66/2.17 % (628)Time elapsed: 0.020 s
% 3.66/2.17 % (628)Instructions burned: 34 (million)
% 3.66/2.17 % (628)------------------------------
% 3.66/2.17 % (628)------------------------------
% 3.66/2.18 % (633)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_491 for (2998ds/5Mi)
% 3.66/2.18 % (604)Instruction limit reached!
% 3.66/2.18 % (604)------------------------------
% 3.66/2.18 % (604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.18 % (604)Termination reason: Unknown
% 3.66/2.18 % (604)Termination phase: Saturation
% 3.66/2.18
% 3.66/2.18 % (604)Memory used [KB]: 7291
% 3.66/2.18 % (604)Time elapsed: 0.103 s
% 3.66/2.18 % (604)Instructions burned: 184 (million)
% 3.66/2.18 % (604)------------------------------
% 3.66/2.18 % (604)------------------------------
% 3.66/2.18 % (632)Instruction limit reached!
% 3.66/2.18 % (632)------------------------------
% 3.66/2.18 % (632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.18 % (632)Termination reason: Unknown
% 3.66/2.18 % (632)Termination phase: shuffling
% 3.66/2.18
% 3.66/2.18 % (632)Memory used [KB]: 1791
% 3.66/2.18 % (632)Time elapsed: 0.013 s
% 3.66/2.18 % (632)Instructions burned: 21 (million)
% 3.66/2.18 % (632)------------------------------
% 3.66/2.18 % (632)------------------------------
% 3.66/2.18 % (633)Instruction limit reached!
% 3.66/2.18 % (633)------------------------------
% 3.66/2.18 % (633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.18 % (633)Termination reason: Unknown
% 3.66/2.18 % (633)Termination phase: shuffling
% 3.66/2.18
% 3.66/2.18 % (633)Memory used [KB]: 1407
% 3.66/2.18 % (633)Time elapsed: 0.004 s
% 3.66/2.18 % (633)Instructions burned: 5 (million)
% 3.66/2.18 % (633)------------------------------
% 3.66/2.18 % (633)------------------------------
% 3.66/2.18 % (634)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_491 for (2998ds/6Mi)
% 3.66/2.18 % (634)Instruction limit reached!
% 3.66/2.18 % (634)------------------------------
% 3.66/2.18 % (634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.18 % (634)Termination reason: Unknown
% 3.66/2.18 % (634)Termination phase: shuffling
% 3.66/2.18
% 3.66/2.18 % (634)Memory used [KB]: 1407
% 3.66/2.18 % (634)Time elapsed: 0.005 s
% 3.66/2.18 % (634)Instructions burned: 7 (million)
% 3.66/2.18 % (634)------------------------------
% 3.66/2.18 % (634)------------------------------
% 3.66/2.19 % (636)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_491 for (2998ds/377Mi)
% 3.66/2.20 % (637)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_491 for (2998ds/779Mi)
% 3.66/2.20 % (641)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_491 for (2998ds/19Mi)
% 3.66/2.20 % (642)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_491 for (2998ds/879Mi)
% 3.66/2.20 % (644)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_491 for (2998ds/17Mi)
% 3.66/2.21 % (641)Instruction limit reached!
% 3.66/2.21 % (641)------------------------------
% 3.66/2.21 % (641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.21 % (641)Termination reason: Unknown
% 3.66/2.21 % (641)Termination phase: shuffling
% 3.66/2.21
% 3.66/2.21 % (641)Memory used [KB]: 1791
% 3.66/2.21 % (641)Time elapsed: 0.012 s
% 3.66/2.21 % (641)Instructions burned: 20 (million)
% 3.66/2.21 % (641)------------------------------
% 3.66/2.21 % (641)------------------------------
% 3.66/2.21 % (644)Instruction limit reached!
% 3.66/2.21 % (644)------------------------------
% 3.66/2.21 % (644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.21 % (644)Termination reason: Unknown
% 3.66/2.21 % (644)Termination phase: Property scanning
% 3.66/2.21
% 3.66/2.21 % (644)Memory used [KB]: 1663
% 3.66/2.21 % (644)Time elapsed: 0.012 s
% 3.66/2.21 % (644)Instructions burned: 18 (million)
% 3.66/2.21 % (644)------------------------------
% 3.66/2.21 % (644)------------------------------
% 3.66/2.22 % (630)Refutation not found, incomplete strategy
% 3.66/2.22 % (630)------------------------------
% 3.66/2.22 % (630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.22 % (630)Termination reason: Refutation not found, incomplete strategy
% 3.66/2.22
% 3.66/2.22
% 3.66/2.22 % (630)Memory used [KB]: 6908
% 3.66/2.22 % (630)Time elapsed: 0.055 s
% 3.66/2.22 % (630)Instructions burned: 95 (million)
% 3.66/2.22 % (630)------------------------------
% 3.66/2.22 % (630)------------------------------
% 3.66/2.23 % (645)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_491 for (2998ds/3Mi)
% 3.66/2.23 % (645)Instruction limit reached!
% 3.66/2.23 % (645)------------------------------
% 3.66/2.23 % (645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.23 % (645)Termination reason: Unknown
% 3.66/2.23 % (645)Termination phase: shuffling
% 3.66/2.23
% 3.66/2.23 % (645)Memory used [KB]: 1407
% 3.66/2.23 % (645)Time elapsed: 0.004 s
% 3.66/2.23 % (645)Instructions burned: 4 (million)
% 3.66/2.23 % (645)------------------------------
% 3.66/2.23 % (645)------------------------------
% 3.66/2.23 % (646)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_491 for (2998ds/30Mi)
% 3.66/2.24 % (661)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_491 for (2998ds/127Mi)
% 3.66/2.25 % (662)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_491 for (2998ds/100Mi)
% 3.66/2.25 % (646)Instruction limit reached!
% 3.66/2.25 % (646)------------------------------
% 3.66/2.25 % (646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.25 % (646)Termination reason: Unknown
% 3.66/2.25 % (646)Termination phase: Property scanning
% 3.66/2.25
% 3.66/2.25 % (646)Memory used [KB]: 1791
% 3.66/2.25 % (646)Time elapsed: 0.018 s
% 3.66/2.25 % (646)Instructions burned: 30 (million)
% 3.66/2.25 % (646)------------------------------
% 3.66/2.25 % (646)------------------------------
% 3.66/2.27 % (663)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_491 for (2997ds/3Mi)
% 3.66/2.27 % (663)Instruction limit reached!
% 3.66/2.27 % (663)------------------------------
% 3.66/2.27 % (663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.27 % (663)Termination reason: Unknown
% 3.66/2.27 % (663)Termination phase: shuffling
% 3.66/2.27
% 3.66/2.27 % (663)Memory used [KB]: 1407
% 3.66/2.27 % (663)Time elapsed: 0.003 s
% 3.66/2.27 % (663)Instructions burned: 3 (million)
% 3.66/2.27 % (663)------------------------------
% 3.66/2.27 % (663)------------------------------
% 3.66/2.29 % (664)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_491 for (2997ds/20Mi)
% 3.66/2.30 % (664)Instruction limit reached!
% 3.66/2.30 % (664)------------------------------
% 3.66/2.30 % (664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.30 % (664)Termination reason: Unknown
% 3.66/2.30 % (664)Termination phase: Property scanning
% 3.66/2.30
% 3.66/2.30 % (664)Memory used [KB]: 1663
% 3.66/2.30 % (664)Time elapsed: 0.013 s
% 3.66/2.30 % (664)Instructions burned: 20 (million)
% 3.66/2.30 % (664)------------------------------
% 3.66/2.30 % (664)------------------------------
% 3.66/2.30 % (662)Instruction limit reached!
% 3.66/2.30 % (662)------------------------------
% 3.66/2.30 % (662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.30 % (662)Termination reason: Unknown
% 3.66/2.30 % (662)Termination phase: Property scanning
% 3.66/2.30
% 3.66/2.30 % (662)Memory used [KB]: 2430
% 3.66/2.30 % (662)Time elapsed: 0.055 s
% 3.66/2.30 % (662)Instructions burned: 101 (million)
% 3.66/2.30 % (662)------------------------------
% 3.66/2.30 % (662)------------------------------
% 3.66/2.30 % (661)Instruction limit reached!
% 3.66/2.30 % (661)------------------------------
% 3.66/2.30 % (661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.30 % (661)Termination reason: Unknown
% 3.66/2.30 % (661)Termination phase: Saturation
% 3.66/2.30
% 3.66/2.30 % (661)Memory used [KB]: 6780
% 3.66/2.30 % (661)Time elapsed: 0.070 s
% 3.66/2.30 % (661)Instructions burned: 127 (million)
% 3.66/2.30 % (661)------------------------------
% 3.66/2.30 % (661)------------------------------
% 3.66/2.32 % (665)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_491 for (2997ds/86Mi)
% 3.66/2.32 % (666)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_491 for (2997ds/107Mi)
% 3.66/2.32 % (667)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_491 for (2997ds/39Mi)
% 3.66/2.34 % (667)Instruction limit reached!
% 3.66/2.34 % (667)------------------------------
% 3.66/2.34 % (667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.34 % (667)Termination reason: Unknown
% 3.66/2.34 % (667)Termination phase: Property scanning
% 3.66/2.34
% 3.66/2.34 % (667)Memory used [KB]: 2174
% 3.66/2.34 % (667)Time elapsed: 0.022 s
% 3.66/2.34 % (667)Instructions burned: 39 (million)
% 3.66/2.34 % (667)------------------------------
% 3.66/2.34 % (667)------------------------------
% 3.66/2.36 % (668)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_491 for (2996ds/448Mi)
% 3.66/2.37 % (665)Instruction limit reached!
% 3.66/2.37 % (665)------------------------------
% 3.66/2.37 % (665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.37 % (665)Termination reason: Unknown
% 3.66/2.37 % (665)Termination phase: Property scanning
% 3.66/2.37
% 3.66/2.37 % (665)Memory used [KB]: 2046
% 3.66/2.37 % (665)Time elapsed: 0.048 s
% 3.66/2.37 % (665)Instructions burned: 87 (million)
% 3.66/2.37 % (665)------------------------------
% 3.66/2.37 % (665)------------------------------
% 3.66/2.38 % (666)Instruction limit reached!
% 3.66/2.38 % (666)------------------------------
% 3.66/2.38 % (666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.38 % (666)Termination reason: Unknown
% 3.66/2.38 % (666)Termination phase: Saturation
% 3.66/2.38
% 3.66/2.38 % (666)Memory used [KB]: 6652
% 3.66/2.38 % (666)Time elapsed: 0.060 s
% 3.66/2.38 % (666)Instructions burned: 107 (million)
% 3.66/2.38 % (666)------------------------------
% 3.66/2.38 % (666)------------------------------
% 3.66/2.39 % (669)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_491 for (2996ds/46Mi)
% 3.66/2.40 % (670)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_491 for (2996ds/98Mi)
% 3.66/2.40 % (636)Instruction limit reached!
% 3.66/2.40 % (636)------------------------------
% 3.66/2.40 % (636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.40 % (636)Termination reason: Unknown
% 3.66/2.40 % (636)Termination phase: Saturation
% 3.66/2.40
% 3.66/2.40 % (636)Memory used [KB]: 8571
% 3.66/2.40 % (636)Time elapsed: 0.217 s
% 3.66/2.40 % (636)Instructions burned: 378 (million)
% 3.66/2.40 % (636)------------------------------
% 3.66/2.40 % (636)------------------------------
% 3.66/2.41 % (669)Instruction limit reached!
% 3.66/2.41 % (669)------------------------------
% 3.66/2.41 % (669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.41 % (669)Termination reason: Unknown
% 3.66/2.41 % (669)Termination phase: Property scanning
% 3.66/2.41
% 3.66/2.41 % (669)Memory used [KB]: 1918
% 3.66/2.41 % (669)Time elapsed: 0.028 s
% 3.66/2.41 % (669)Instructions burned: 47 (million)
% 3.66/2.41 % (669)------------------------------
% 3.66/2.41 % (669)------------------------------
% 3.66/2.42 % (671)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_491 for (2996ds/507Mi)
% 3.66/2.43 % (672)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_491 for (2996ds/149Mi)
% 3.66/2.45 % (670)Instruction limit reached!
% 3.66/2.45 % (670)------------------------------
% 3.66/2.45 % (670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.45 % (670)Termination reason: Unknown
% 3.66/2.45 % (670)Termination phase: Function definition elimination
% 3.66/2.45
% 3.66/2.45 % (670)Memory used [KB]: 2302
% 3.66/2.45 % (670)Time elapsed: 0.053 s
% 3.66/2.45 % (670)Instructions burned: 98 (million)
% 3.66/2.45 % (670)------------------------------
% 3.66/2.45 % (670)------------------------------
% 3.66/2.47 % (673)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_491 for (2995ds/39Mi)
% 3.66/2.49 % (673)Instruction limit reached!
% 3.66/2.49 % (673)------------------------------
% 3.66/2.49 % (673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.49 % (673)Termination reason: Unknown
% 3.66/2.49 % (673)Termination phase: Preprocessing 3
% 3.66/2.49
% 3.66/2.49 % (673)Memory used [KB]: 1918
% 3.66/2.49 % (673)Time elapsed: 0.023 s
% 3.66/2.49 % (673)Instructions burned: 39 (million)
% 3.66/2.49 % (673)------------------------------
% 3.66/2.49 % (673)------------------------------
% 3.66/2.51 % (674)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_491 for (2995ds/6Mi)
% 3.66/2.51 % (672)Instruction limit reached!
% 3.66/2.51 % (672)------------------------------
% 3.66/2.51 % (672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.51 % (672)Termination reason: Unknown
% 3.66/2.51 % (672)Termination phase: Saturation
% 3.66/2.51
% 3.66/2.51 % (672)Memory used [KB]: 7036
% 3.66/2.51 % (672)Time elapsed: 0.083 s
% 3.66/2.51 % (672)Instructions burned: 150 (million)
% 3.66/2.51 % (672)------------------------------
% 3.66/2.51 % (672)------------------------------
% 3.66/2.51 % (674)Instruction limit reached!
% 3.66/2.51 % (674)------------------------------
% 3.66/2.51 % (674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.51 % (674)Termination reason: Unknown
% 3.66/2.51 % (674)Termination phase: shuffling
% 3.66/2.51
% 3.66/2.51 % (674)Memory used [KB]: 1407
% 3.66/2.51 % (674)Time elapsed: 0.005 s
% 3.66/2.51 % (674)Instructions burned: 7 (million)
% 3.66/2.51 % (674)------------------------------
% 3.66/2.51 % (674)------------------------------
% 3.66/2.53 % (675)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_491 for (2995ds/1087Mi)
% 3.66/2.53 % (676)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_491 for (2995ds/47Mi)
% 3.66/2.56 % (671)First to succeed.
% 3.66/2.56 % (676)Instruction limit reached!
% 3.66/2.56 % (676)------------------------------
% 3.66/2.56 % (676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.56 % (676)Termination reason: Unknown
% 3.66/2.56 % (676)Termination phase: Property scanning
% 3.66/2.56
% 3.66/2.56 % (676)Memory used [KB]: 1918
% 3.66/2.56 % (676)Time elapsed: 0.028 s
% 3.66/2.56 % (676)Instructions burned: 47 (million)
% 3.66/2.56 % (676)------------------------------
% 3.66/2.56 % (676)------------------------------
% 3.66/2.56 % (671)Refutation found. Thanks to Tanya!
% 3.66/2.56 % SZS status Theorem for DTF2THF_491
% 3.66/2.56 % SZS output start Proof for DTF2THF_491
% 3.66/2.56 thf(type_def_5, type, real: $tType).
% 3.66/2.56 thf(type_def_7, type, int: $tType).
% 3.66/2.56 thf(type_def_8, type, nat: $tType).
% 3.66/2.56 thf(type_def_9, type, list_list_a: $tType).
% 3.66/2.56 thf(type_def_10, type, list_list_list_a: $tType).
% 3.66/2.56 thf(type_def_11, type, list_a: $tType).
% 3.66/2.56 thf(type_def_12, type, a: $tType).
% 3.66/2.56 thf(type_def_13, type, list_l2071841302list_a: $tType).
% 3.66/2.56 thf(type_def_14, type, option_list_list_a: $tType).
% 3.66/2.56 thf(type_def_15, type, option_list_a: $tType).
% 3.66/2.56 thf(type_def_16, type, option_a: $tType).
% 3.66/2.56 thf(type_def_17, type, set_nat: $tType).
% 3.66/2.56 thf(type_def_18, type, set_real: $tType).
% 3.66/2.56 thf(func_def_0, type, list_l2071841302list_a: $tType).
% 3.66/2.56 thf(func_def_1, type, option_list_list_a: $tType).
% 3.66/2.56 thf(func_def_2, type, list_list_list_a: $tType).
% 3.66/2.56 thf(func_def_3, type, option_list_a: $tType).
% 3.66/2.56 thf(func_def_4, type, list_list_a: $tType).
% 3.66/2.56 thf(func_def_5, type, set_real: $tType).
% 3.66/2.56 thf(func_def_6, type, set_nat: $tType).
% 3.66/2.56 thf(func_def_7, type, option_a: $tType).
% 3.66/2.56 thf(func_def_8, type, list_a: $tType).
% 3.66/2.56 thf(func_def_9, type, real: $tType).
% 3.66/2.56 thf(func_def_10, type, nat: $tType).
% 3.66/2.56 thf(func_def_11, type, int: $tType).
% 3.66/2.56 thf(func_def_12, type, a: $tType).
% 3.66/2.56 thf(func_def_13, type, inverse_inverse_real: real > real).
% 3.66/2.56 thf(func_def_14, type, zero_zero_int: int).
% 3.66/2.56 thf(func_def_15, type, zero_zero_nat: nat).
% 3.66/2.56 thf(func_def_16, type, zero_zero_real: real).
% 3.66/2.56 thf(func_def_17, type, if_nat: $o > nat > nat > nat).
% 3.66/2.56 thf(func_def_18, type, listSl162220270list_a: list_list_a > nat > list_list_list_a).
% 3.66/2.56 thf(func_def_19, type, listSl97544552lice_a: list_a > nat > list_list_a).
% 3.66/2.56 thf(func_def_20, type, listSl856612276list_a: list_list_a > nat > nat > list_list_list_a).
% 3.66/2.56 thf(func_def_21, type, listSl1495374126_aux_a: list_a > nat > nat > list_list_a).
% 3.66/2.56 thf(func_def_22, type, bind_l311701255list_a: list_list_list_a > (list_list_a > list_list_list_a) > list_list_list_a).
% 3.66/2.56 thf(func_def_23, type, bind_l94945665list_a: list_list_list_a > (list_list_a > list_list_a) > list_list_a).
% 3.66/2.56 thf(func_def_24, type, bind_list_list_a_a: list_list_list_a > (list_list_a > list_a) > list_a).
% 3.66/2.56 thf(func_def_25, type, bind_l971853709list_a: list_list_a > (list_a > list_list_list_a) > list_list_list_a).
% 3.66/2.56 thf(func_def_26, type, bind_list_a_list_a: list_list_a > (list_a > list_list_a) > list_list_a).
% 3.66/2.56 thf(func_def_27, type, bind_list_a_a: list_list_a > (list_a > list_a) > list_a).
% 3.66/2.56 thf(func_def_28, type, bind_a_list_list_a: list_a > (a > list_list_list_a) > list_list_list_a).
% 3.66/2.56 thf(func_def_29, type, bind_a_list_a: list_a > (a > list_list_a) > list_list_a).
% 3.66/2.56 thf(func_def_30, type, bind_a_a: list_a > (a > list_a) > list_a).
% 3.66/2.56 thf(func_def_31, type, concat_list_list_a: list_l2071841302list_a > list_list_list_a).
% 3.66/2.56 thf(func_def_32, type, concat_list_a: list_list_list_a > list_list_a).
% 3.66/2.56 thf(func_def_33, type, concat_a: list_list_a > list_a).
% 3.66/2.56 thf(func_def_34, type, count_429956358list_a: list_list_list_a > list_list_a > nat).
% 3.66/2.56 thf(func_def_35, type, count_list_list_a: list_list_a > list_a > nat).
% 3.66/2.56 thf(func_def_36, type, count_list_a: list_a > a > nat).
% 3.66/2.56 thf(func_def_37, type, gen_le840878749list_a: nat > list_list_list_a > nat).
% 3.66/2.56 thf(func_def_38, type, gen_length_list_a: nat > list_list_a > nat).
% 3.66/2.56 thf(func_def_39, type, gen_length_a: nat > list_a > nat).
% 3.66/2.56 thf(func_def_40, type, nil_list_list_list_a: list_l2071841302list_a).
% 3.66/2.56 thf(func_def_41, type, nil_list_list_a: list_list_list_a).
% 3.66/2.56 thf(func_def_42, type, nil_list_a: list_list_a).
% 3.66/2.56 thf(func_def_43, type, nil_a: list_a).
% 3.66/2.56 thf(func_def_44, type, list_ex1_list_list_a: (list_list_a > $o) > list_list_list_a > $o).
% 3.66/2.56 thf(func_def_45, type, list_ex1_list_a: (list_a > $o) > list_list_a > $o).
% 3.66/2.56 thf(func_def_46, type, list_ex1_a: (a > $o) > list_a > $o).
% 3.66/2.56 thf(func_def_47, type, map_fi824137674list_a: (list_list_a > option_list_list_a) > list_list_list_a > list_list_list_a).
% 3.66/2.56 thf(func_def_48, type, map_fi213215172list_a: (list_list_a > option_list_a) > list_list_list_a > list_list_a).
% 3.66/2.56 thf(func_def_49, type, map_fi1574988606st_a_a: (list_list_a > option_a) > list_list_list_a > list_a).
% 3.66/2.56 thf(func_def_50, type, map_fi1090123216list_a: (list_a > option_list_list_a) > list_list_a > list_list_list_a).
% 3.66/2.56 thf(func_def_51, type, map_fi461586634list_a: (list_a > option_list_a) > list_list_a > list_list_a).
% 3.66/2.56 thf(func_def_52, type, map_filter_list_a_a: (list_a > option_a) > list_list_a > list_a).
% 3.66/2.56 thf(func_def_53, type, map_fi2089402454list_a: (a > option_list_list_a) > list_a > list_list_list_a).
% 3.66/2.56 thf(func_def_54, type, map_filter_a_list_a: (a > option_list_a) > list_a > list_list_a).
% 3.66/2.56 thf(func_def_55, type, map_filter_a_a: (a > option_a) > list_a > list_a).
% 3.66/2.56 thf(func_def_56, type, maps_l57963201list_a: (list_list_a > list_list_list_a) > list_list_list_a > list_list_list_a).
% 3.66/2.56 thf(func_def_57, type, maps_l2025957947list_a: (list_list_a > list_list_a) > list_list_list_a > list_list_a).
% 3.66/2.56 thf(func_def_58, type, maps_list_list_a_a: (list_list_a > list_a) > list_list_list_a > list_a).
% 3.66/2.56 thf(func_def_59, type, maps_l755382343list_a: (list_a > list_list_list_a) > list_list_a > list_list_list_a).
% 3.66/2.56 thf(func_def_60, type, maps_list_a_list_a: (list_a > list_list_a) > list_list_a > list_list_a).
% 3.66/2.56 thf(func_def_61, type, maps_list_a_a: (list_a > list_a) > list_list_a > list_a).
% 3.66/2.56 thf(func_def_62, type, maps_a_list_list_a: (a > list_list_list_a) > list_a > list_list_list_a).
% 3.66/2.56 thf(func_def_63, type, maps_a_list_a: (a > list_list_a) > list_a > list_list_a).
% 3.66/2.56 thf(func_def_64, type, maps_a_a: (a > list_a) > list_a > list_a).
% 3.66/2.56 thf(func_def_65, type, member_list_list_a: list_list_list_a > list_list_a > $o).
% 3.66/2.56 thf(func_def_66, type, member_list_a: list_list_a > list_a > $o).
% 3.66/2.56 thf(func_def_67, type, member_a: list_a > a > $o).
% 3.66/2.56 thf(func_def_68, type, null_list_list_a: list_list_list_a > $o).
% 3.66/2.56 thf(func_def_69, type, null_list_a: list_list_a > $o).
% 3.66/2.56 thf(func_def_70, type, null_a: list_a > $o).
% 3.66/2.56 thf(func_def_71, type, semiri2019852685at_int: nat > int).
% 3.66/2.56 thf(func_def_72, type, semiri1382578993at_nat: nat > nat).
% 3.66/2.56 thf(func_def_73, type, semiri2110766477t_real: nat > real).
% 3.66/2.56 thf(func_def_74, type, size_s575106428list_a: list_list_list_a > nat).
% 3.66/2.56 thf(func_def_75, type, size_s1427607542list_a: list_list_a > nat).
% 3.66/2.56 thf(func_def_76, type, size_size_list_a: list_a > nat).
% 3.66/2.56 thf(func_def_77, type, ord_less_int: int > int > $o).
% 3.66/2.56 thf(func_def_78, type, ord_less_nat: nat > nat > $o).
% 3.66/2.56 thf(func_def_79, type, ord_less_real: real > real > $o).
% 3.66/2.56 thf(func_def_80, type, ord_less_eq_int: int > int > $o).
% 3.66/2.56 thf(func_def_81, type, ord_less_eq_nat: nat > nat > $o).
% 3.66/2.56 thf(func_def_82, type, ord_less_eq_real: real > real > $o).
% 3.66/2.56 thf(func_def_83, type, power_power_int: int > nat > int).
% 3.66/2.56 thf(func_def_84, type, power_power_nat: nat > nat > nat).
% 3.66/2.56 thf(func_def_85, type, power_power_real: real > nat > real).
% 3.66/2.56 thf(func_def_86, type, divide_divide_int: int > int > int).
% 3.66/2.56 thf(func_def_87, type, divide_divide_nat: nat > nat > nat).
% 3.66/2.56 thf(func_def_88, type, divide_divide_real: real > real > real).
% 3.66/2.56 thf(func_def_89, type, collect_nat: (nat > $o) > set_nat).
% 3.66/2.56 thf(func_def_90, type, collect_real: (real > $o) > set_real).
% 3.66/2.56 thf(func_def_91, type, member_nat: nat > set_nat > $o).
% 3.66/2.56 thf(func_def_92, type, member_real: real > set_real > $o).
% 3.66/2.56 thf(func_def_93, type, k: nat).
% 3.66/2.56 thf(func_def_108, type, sK0: !>[X0: $tType]:((X0 > $o) > X0)).
% 3.66/2.56 thf(func_def_109, type, sK1: !>[X0: $tType]:((X0 > $o) > X0)).
% 3.66/2.56 thf(func_def_110, type, sK2: real > nat).
% 3.66/2.56 thf(func_def_111, type, sK3: int > nat).
% 3.66/2.56 thf(func_def_112, type, sK4: real > real).
% 3.66/2.56 thf(func_def_113, type, sK5: set_nat > (nat > $o) > nat).
% 3.66/2.56 thf(func_def_114, type, sK6: int > nat).
% 3.66/2.56 thf(func_def_115, type, sK7: (nat > $o) > nat).
% 3.66/2.56 thf(func_def_116, type, sK8: set_nat > (nat > $o) > nat).
% 3.66/2.56 thf(func_def_117, type, sK9: real > nat).
% 3.66/2.56 thf(func_def_118, type, sK10: int > nat).
% 3.66/2.56 thf(func_def_119, type, sK11: nat > list_a).
% 3.66/2.56 thf(func_def_120, type, sK12: (nat > $o) > nat > nat).
% 3.66/2.56 thf(func_def_121, type, sK13: (nat > $o) > nat).
% 3.66/2.56 thf(func_def_122, type, sK14: real > real > real).
% 3.66/2.56 thf(func_def_123, type, sK15: real > nat > real).
% 3.66/2.56 thf(func_def_124, type, sK16: real > real).
% 3.66/2.56 thf(func_def_125, type, sK17: real > set_real > real).
% 3.66/2.56 thf(func_def_126, type, sK18: set_real > real).
% 3.66/2.56 thf(func_def_127, type, sK19: real > set_real > real).
% 3.66/2.56 thf(func_def_128, type, sK20: real > nat).
% 3.66/2.56 thf(func_def_129, type, sK21: (nat > $o) > set_nat > nat).
% 3.66/2.56 thf(func_def_130, type, sK22: (nat > $o) > nat).
% 3.66/2.56 thf(func_def_131, type, sK23: (list_a > $o) > list_a).
% 3.66/2.56 thf(func_def_132, type, sK24: set_nat > (nat > $o) > nat).
% 3.66/2.56 thf(func_def_133, type, sK25: (nat > $o) > nat).
% 3.66/2.56 thf(func_def_134, type, sK26: nat > (nat > $o) > nat).
% 3.66/2.56 thf(func_def_135, type, sK27: (nat > nat) > nat).
% 3.66/2.56 thf(func_def_136, type, sK28: (nat > nat) > nat).
% 3.66/2.56 thf(func_def_137, type, sK29: real > nat > real).
% 3.66/2.56 thf(func_def_138, type, sK30: (real > $o) > nat).
% 3.66/2.56 thf(func_def_139, type, sK31: (real > $o) > real).
% 3.66/2.56 thf(func_def_140, type, sK32: (real > $o) > real).
% 3.66/2.56 thf(func_def_141, type, sK33: int > nat).
% 3.66/2.56 thf(func_def_143, type, ph35: !>[X0: $tType]:(X0)).
% 3.66/2.56 thf(f2686,plain,(
% 3.66/2.56 $false),
% 3.66/2.56 inference(subsumption_resolution,[status(thm)],[f2685,f2313])).
% 3.66/2.56 thf(f2313,plain,(
% 3.66/2.56 ((listSl1495374126_aux_a @ (concat_a @ (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a))) @ k @ (divide_divide_nat @ k @ k)) != (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a)))),
% 3.66/2.56 inference(superposition,[status(thm)],[f2192,f2214])).
% 3.66/2.56 thf(f2214,plain,(
% 3.66/2.56 (k = (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)))),
% 3.66/2.56 inference(subsumption_resolution,[status(thm)],[f2212,f1763])).
% 3.66/2.56 thf(f1763,plain,(
% 3.66/2.56 ( ! [X0 : nat] : (((ord_less_nat @ X0 @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a))) != $true)) )),
% 3.66/2.56 inference(definition_unfolding,[status(thm)],[f1374,f1709])).
% 3.66/2.56 thf(f1709,plain,(
% 3.66/2.56 (zero_zero_nat = (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)))),
% 3.66/2.56 inference(definition_unfolding,[status(thm)],[f1416,f1329])).
% 3.66/2.56 thf(f1329,plain,(
% 3.66/2.56 (nil_list_list_a = (concat_list_list_a @ nil_list_list_list_a))),
% 3.66/2.56 inference(cnf_transformation,[status(thm)],[f480])).
% 3.66/2.56 thf(f480,plain,(
% 3.66/2.56 (nil_list_list_a = (concat_list_list_a @ nil_list_list_list_a))),
% 3.66/2.56 inference(fool_elimination,[status(thm)],[f3])).
% 3.66/2.56 thf(f3,axiom,(
% 3.66/2.56 (nil_list_list_a = (concat_list_list_a @ nil_list_list_list_a))),
% 3.66/2.56 file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_2_concat_Osimps_I1_J)).
% 3.66/2.56 thf(f1416,plain,(
% 3.66/2.56 (zero_zero_nat = (size_s575106428list_a @ nil_list_list_a))),
% 3.66/2.56 inference(cnf_transformation,[status(thm)],[f916])).
% 3.66/2.56 thf(f916,plain,(
% 3.66/2.56 (zero_zero_nat = (size_s575106428list_a @ nil_list_list_a))),
% 3.66/2.56 inference(fool_elimination,[status(thm)],[f57])).
% 3.66/2.56 thf(f57,axiom,(
% 3.66/2.56 (zero_zero_nat = (size_s575106428list_a @ nil_list_list_a))),
% 3.66/2.56 file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_56_list_Osize_I3_J)).
% 3.66/2.56 thf(f1374,plain,(
% 3.66/2.56 ( ! [X0 : nat] : (((ord_less_nat @ X0 @ zero_zero_nat) != $true)) )),
% 3.66/2.56 inference(cnf_transformation,[status(thm)],[f1070])).
% 3.66/2.56 thf(f1070,plain,(
% 3.66/2.56 ! [X0 : nat] : ((ord_less_nat @ X0 @ zero_zero_nat) != $true)),
% 3.66/2.56 inference(flattening,[status(thm)],[f981])).
% 3.66/2.56 thf(f981,plain,(
% 3.66/2.56 ! [X0 : nat] : ~((ord_less_nat @ X0 @ zero_zero_nat) = $true)),
% 3.66/2.56 inference(fool_elimination,[status(thm)],[f980])).
% 3.66/2.56 thf(f980,plain,(
% 3.66/2.56 ! [X0 : nat] : ~(ord_less_nat @ X0 @ zero_zero_nat)),
% 3.66/2.56 inference(rectify,[status(thm)],[f74])).
% 3.66/2.56 thf(f74,axiom,(
% 3.66/2.56 ! [X5 : nat] : ~(ord_less_nat @ X5 @ zero_zero_nat)),
% 3.66/2.56 file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_73_less__zeroE)).
% 3.66/2.56 thf(f2212,plain,(
% 3.66/2.56 (k = (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a))) | ((ord_less_nat @ k @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a))) = $true)),
% 3.66/2.56 inference(trivial_inequality_removal,[status(thm)],[f2207])).
% 3.66/2.56 thf(f2207,plain,(
% 3.66/2.56 ($true != $true) | ((ord_less_nat @ k @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a))) = $true) | (k = (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)))),
% 3.66/2.56 inference(superposition,[status(thm)],[f2198,f1445])).
% 3.66/2.56 thf(f1445,plain,(
% 3.66/2.56 ( ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X1 @ X0) = $true) | (X0 = X1) | ((ord_less_nat @ X0 @ X1) = $true)) )),
% 3.66/2.56 inference(cnf_transformation,[status(thm)],[f1209])).
% 3.66/2.56 thf(f1209,plain,(
% 3.66/2.56 ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X0 @ X1) = $true) | (X0 = X1) | ((ord_less_nat @ X1 @ X0) = $true))),
% 3.66/2.56 inference(flattening,[status(thm)],[f1208])).
% 3.66/2.56 thf(f1208,plain,(
% 3.66/2.56 ! [X0 : nat,X1 : nat] : ((((ord_less_nat @ X1 @ X0) = $true) | ((ord_less_nat @ X0 @ X1) = $true)) | (X0 = X1))),
% 3.66/2.56 inference(ennf_transformation,[status(thm)],[f1066])).
% 3.66/2.56 thf(f1066,plain,(
% 3.66/2.56 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (((ord_less_nat @ X0 @ X1) != $true) => ((ord_less_nat @ X1 @ X0) = $true)))),
% 3.66/2.56 inference(flattening,[status(thm)],[f923])).
% 3.66/2.56 thf(f923,plain,(
% 3.66/2.56 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~((ord_less_nat @ X0 @ X1) = $true) => ((ord_less_nat @ X1 @ X0) = $true)))),
% 3.66/2.56 inference(fool_elimination,[status(thm)],[f922])).
% 3.66/2.56 thf(f922,plain,(
% 3.66/2.56 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~(ord_less_nat @ X0 @ X1) => (ord_less_nat @ X1 @ X0)))),
% 3.66/2.56 inference(rectify,[status(thm)],[f79])).
% 3.66/2.56 thf(f79,axiom,(
% 3.66/2.56 ! [X11 : nat,X4 : nat] : ((X4 != X11) => (~(ord_less_nat @ X11 @ X4) => (ord_less_nat @ X4 @ X11)))),
% 3.66/2.56 file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_78_linorder__neqE__nat)).
% 3.66/2.56 thf(f2198,plain,(
% 3.66/2.56 ($true != (ord_less_nat @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)) @ k))),
% 3.66/2.56 inference(superposition,[status(thm)],[f2196,f1953])).
% 3.66/2.56 thf(f1953,plain,(
% 3.66/2.56 ( ! [X0 : nat] : (((gen_length_a @ X0 @ (concat_a @ (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a)))) = X0)) )),
% 3.66/2.56 inference(definition_unfolding,[status(thm)],[f1624,f1713])).
% 3.66/2.56 thf(f1713,plain,(
% 3.66/2.56 (nil_a = (concat_a @ (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a))))),
% 3.66/2.56 inference(definition_unfolding,[status(thm)],[f1546,f1712])).
% 3.66/2.56 thf(f1712,plain,(
% 3.66/2.56 (nil_list_a = (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a)))),
% 3.66/2.56 inference(definition_unfolding,[status(thm)],[f1362,f1329])).
% 3.66/2.56 thf(f1362,plain,(
% 3.66/2.56 (nil_list_a = (concat_list_a @ nil_list_list_a))),
% 3.66/2.56 inference(cnf_transformation,[status(thm)],[f741])).
% 3.66/2.56 thf(f741,plain,(
% 3.66/2.56 (nil_list_a = (concat_list_a @ nil_list_list_a))),
% 3.66/2.56 inference(fool_elimination,[status(thm)],[f4])).
% 3.66/2.56 thf(f4,axiom,(
% 3.66/2.56 (nil_list_a = (concat_list_a @ nil_list_list_a))),
% 3.66/2.56 file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_3_concat_Osimps_I1_J)).
% 3.66/2.56 thf(f1546,plain,(
% 3.66/2.56 ((concat_a @ nil_list_a) = nil_a)),
% 3.66/2.56 inference(cnf_transformation,[status(thm)],[f903])).
% 3.66/2.56 thf(f903,plain,(
% 3.66/2.56 ((concat_a @ nil_list_a) = nil_a)),
% 3.66/2.56 inference(fool_elimination,[status(thm)],[f5])).
% 3.66/2.56 thf(f5,axiom,(
% 3.66/2.56 ((concat_a @ nil_list_a) = nil_a)),
% 3.66/2.56 file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_4_concat_Osimps_I1_J)).
% 3.66/2.56 thf(f1624,plain,(
% 3.66/2.56 ( ! [X0 : nat] : (((gen_length_a @ X0 @ nil_a) = X0)) )),
% 3.66/2.56 inference(cnf_transformation,[status(thm)],[f548])).
% 3.66/2.56 thf(f548,plain,(
% 3.66/2.56 ! [X0 : nat] : ((gen_length_a @ X0 @ nil_a) = X0)),
% 3.66/2.56 inference(fool_elimination,[status(thm)],[f547])).
% 3.66/2.56 thf(f547,plain,(
% 3.66/2.56 ! [X0 : nat] : ((gen_length_a @ X0 @ nil_a) = X0)),
% 3.66/2.56 inference(rectify,[status(thm)],[f24])).
% 3.66/2.56 thf(f24,axiom,(
% 3.66/2.56 ! [X5 : nat] : ((gen_length_a @ X5 @ nil_a) = X5)),
% 3.66/2.56 file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_23_gen__length__code_I1_J)).
% 3.66/2.56 thf(f2196,plain,(
% 3.66/2.56 ((ord_less_nat @ (gen_length_a @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)) @ (concat_a @ (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a)))) @ k) != $true)),
% 3.66/2.56 inference(subsumption_resolution,[status(thm)],[f2193,f1891])).
% 3.66/2.56 thf(f1891,plain,(
% 3.66/2.56 ( ! [X0 : nat,X1 : list_a] : (((listSl1495374126_aux_a @ X1 @ X0 @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a))) = (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a)))) )),
% 3.66/2.56 inference(definition_unfolding,[status(thm)],[f1536,f1712,f1709])).
% 3.66/2.56 thf(f1536,plain,(
% 3.66/2.56 ( ! [X0 : nat,X1 : list_a] : ((nil_list_a = (listSl1495374126_aux_a @ X1 @ X0 @ zero_zero_nat))) )),
% 3.66/2.56 inference(cnf_transformation,[status(thm)],[f919])).
% 3.66/2.56 thf(f919,plain,(
% 3.66/2.56 ! [X0 : nat,X1 : list_a] : (nil_list_a = (listSl1495374126_aux_a @ X1 @ X0 @ zero_zero_nat))),
% 3.66/2.56 inference(fool_elimination,[status(thm)],[f918])).
% 3.66/2.56 thf(f918,plain,(
% 3.66/2.56 ! [X0 : nat,X1 : list_a] : (nil_list_a = (listSl1495374126_aux_a @ X1 @ X0 @ zero_zero_nat))),
% 3.66/2.56 inference(rectify,[status(thm)],[f103])).
% 3.66/2.56 thf(f103,axiom,(
% 3.66/2.56 ! [X2 : nat,X0 : list_a] : (nil_list_a = (listSl1495374126_aux_a @ X0 @ X2 @ zero_zero_nat))),
% 3.66/2.56 file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_102_list__slice__aux_Osimps_I1_J)).
% 3.66/2.56 thf(f2193,plain,(
% 3.66/2.56 ((ord_less_nat @ (gen_length_a @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)) @ (concat_a @ (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a)))) @ k) != $true) | ((concat_list_a @ (concat_list_list_a @ nil_list_list_list_a)) != (listSl1495374126_aux_a @ (concat_a @ (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a))) @ k @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a))))),
% 3.66/2.56 inference(superposition,[status(thm)],[f2190,f1977])).
% 3.66/2.56 thf(f1977,plain,(
% 3.66/2.56 ( ! [X0 : nat,X1 : nat] : (((size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)) = (divide_divide_nat @ X0 @ X1)) | ((ord_less_nat @ X0 @ X1) != $true)) )),
% 3.66/2.56 inference(definition_unfolding,[status(thm)],[f1655,f1709])).
% 3.66/2.56 thf(f1655,plain,(
% 3.66/2.56 ( ! [X0 : nat,X1 : nat] : ((zero_zero_nat = (divide_divide_nat @ X0 @ X1)) | ((ord_less_nat @ X0 @ X1) != $true)) )),
% 3.66/2.56 inference(cnf_transformation,[status(thm)],[f1169])).
% 3.66/2.56 thf(f1169,plain,(
% 3.66/2.56 ! [X0 : nat,X1 : nat] : ((zero_zero_nat = (divide_divide_nat @ X0 @ X1)) | ((ord_less_nat @ X0 @ X1) != $true))),
% 3.66/2.56 inference(ennf_transformation,[status(thm)],[f358])).
% 3.66/2.56 thf(f358,plain,(
% 3.66/2.56 ! [X0 : nat,X1 : nat] : (((ord_less_nat @ X0 @ X1) = $true) => (zero_zero_nat = (divide_divide_nat @ X0 @ X1)))),
% 3.66/2.56 inference(fool_elimination,[status(thm)],[f357])).
% 3.66/2.56 thf(f357,plain,(
% 3.66/2.56 ! [X0 : nat,X1 : nat] : ((ord_less_nat @ X0 @ X1) => (zero_zero_nat = (divide_divide_nat @ X0 @ X1)))),
% 3.66/2.56 inference(rectify,[status(thm)],[f261])).
% 3.66/2.56 thf(f261,axiom,(
% 3.66/2.56 ! [X10 : nat,X5 : nat] : ((ord_less_nat @ X10 @ X5) => (zero_zero_nat = (divide_divide_nat @ X10 @ X5)))),
% 3.66/2.56 file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_260_div__less)).
% 3.66/2.56 thf(f2190,plain,(
% 3.66/2.56 ((listSl1495374126_aux_a @ (concat_a @ (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a))) @ k @ (divide_divide_nat @ (gen_length_a @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)) @ (concat_a @ (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a)))) @ k)) != (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a)))),
% 3.66/2.56 inference(beta_eta_normalization,[status(thm)],[f1917])).
% 3.66/2.56 thf(f1917,plain,(
% 3.66/2.56 ((concat_list_a @ (concat_list_list_a @ nil_list_list_list_a)) != ((^[Y0 : list_a]: ((^[Y1 : nat]: (listSl1495374126_aux_a @ Y0 @ Y1 @ (divide_divide_nat @ (gen_length_a @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)) @ Y0) @ Y1))))) @ (concat_a @ (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a))) @ k))),
% 3.66/2.56 inference(definition_unfolding,[status(thm)],[f1578,f1712,f1716,f1713])).
% 3.66/2.56 thf(f1716,plain,(
% 3.66/2.56 (listSl97544552lice_a = (^[Y0 : list_a]: ((^[Y1 : nat]: (listSl1495374126_aux_a @ Y0 @ Y1 @ (divide_divide_nat @ (gen_length_a @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)) @ Y0) @ Y1))))))),
% 3.66/2.56 inference(definition_unfolding,[status(thm)],[f1358,f1715])).
% 3.66/2.56 thf(f1715,plain,(
% 3.66/2.56 (size_size_list_a = (gen_length_a @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a))))),
% 3.66/2.56 inference(definition_unfolding,[status(thm)],[f1404,f1709])).
% 3.66/2.56 thf(f1404,plain,(
% 3.66/2.56 (size_size_list_a = (gen_length_a @ zero_zero_nat))),
% 3.66/2.56 inference(cnf_transformation,[status(thm)],[f968])).
% 3.66/2.56 thf(f968,plain,(
% 3.66/2.56 (size_size_list_a = (gen_length_a @ zero_zero_nat))),
% 3.66/2.56 inference(fool_elimination,[status(thm)],[f60])).
% 3.66/2.56 thf(f60,axiom,(
% 3.66/2.56 (size_size_list_a = (gen_length_a @ zero_zero_nat))),
% 3.66/2.56 file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_59_length__code)).
% 3.66/2.56 thf(f1358,plain,(
% 3.66/2.56 (listSl97544552lice_a = (^[Y0 : list_a]: ((^[Y1 : nat]: (listSl1495374126_aux_a @ Y0 @ Y1 @ (divide_divide_nat @ (size_size_list_a @ Y0) @ Y1))))))),
% 3.66/2.56 inference(cnf_transformation,[status(thm)],[f779])).
% 3.66/2.56 thf(f779,plain,(
% 3.66/2.56 (listSl97544552lice_a = (^[Y0 : list_a]: ((^[Y1 : nat]: (listSl1495374126_aux_a @ Y0 @ Y1 @ (divide_divide_nat @ (size_size_list_a @ Y0) @ Y1))))))),
% 3.66/2.56 inference(fool_elimination,[status(thm)],[f778])).
% 3.66/2.56 thf(f778,plain,(
% 3.66/2.56 (listSl97544552lice_a = (^[X0 : list_a, X1 : nat] : (listSl1495374126_aux_a @ X0 @ X1 @ (divide_divide_nat @ (size_size_list_a @ X0) @ X1))))),
% 3.66/2.56 inference(rectify,[status(thm)],[f142])).
% 3.66/2.56 thf(f142,axiom,(
% 3.66/2.56 (listSl97544552lice_a = (^[X26 : list_a, X27 : nat] : (listSl1495374126_aux_a @ X26 @ X27 @ (divide_divide_nat @ (size_size_list_a @ X26) @ X27))))),
% 3.66/2.56 file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_141_list__slice__def)).
% 3.66/2.56 thf(f1578,plain,(
% 3.66/2.56 (nil_list_a != (listSl97544552lice_a @ nil_a @ k))),
% 3.66/2.56 inference(cnf_transformation,[status(thm)],[f1065])).
% 3.66/2.56 thf(f1065,plain,(
% 3.66/2.56 (nil_list_a != (listSl97544552lice_a @ nil_a @ k))),
% 3.66/2.56 inference(flattening,[status(thm)],[f917])).
% 3.66/2.56 thf(f917,plain,(
% 3.66/2.56 ~(nil_list_a = (listSl97544552lice_a @ nil_a @ k))),
% 3.66/2.56 inference(fool_elimination,[status(thm)],[f351])).
% 3.66/2.56 thf(f351,negated_conjecture,(
% 3.66/2.56 ~(nil_list_a = (listSl97544552lice_a @ nil_a @ k))),
% 3.66/2.56 inference(negated_conjecture,[status(cth)],[f350])).
% 3.66/2.56 thf(f350,conjecture,(
% 3.66/2.56 (nil_list_a = (listSl97544552lice_a @ nil_a @ k))),
% 3.66/2.56 file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',conj_0)).
% 3.66/2.56 thf(f2192,plain,(
% 3.66/2.56 ((concat_list_a @ (concat_list_list_a @ nil_list_list_list_a)) != (listSl1495374126_aux_a @ (concat_a @ (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a))) @ k @ (divide_divide_nat @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)) @ k)))),
% 3.66/2.56 inference(superposition,[status(thm)],[f2190,f1953])).
% 3.66/2.56 thf(f2685,plain,(
% 3.66/2.56 ((listSl1495374126_aux_a @ (concat_a @ (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a))) @ k @ (divide_divide_nat @ k @ k)) = (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a)))),
% 3.66/2.56 inference(superposition,[status(thm)],[f2326,f2214])).
% 3.66/2.56 thf(f2326,plain,(
% 3.66/2.56 ((concat_list_a @ (concat_list_list_a @ nil_list_list_list_a)) = (listSl1495374126_aux_a @ (concat_a @ (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a))) @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)) @ (divide_divide_nat @ k @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)))))),
% 3.66/2.56 inference(superposition,[status(thm)],[f2173,f2203])).
% 3.66/2.56 thf(f2203,plain,(
% 3.66/2.56 (k = (gen_length_a @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)) @ (concat_a @ (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a)))))),
% 3.66/2.56 inference(subsumption_resolution,[status(thm)],[f2201,f2038])).
% 3.66/2.56 thf(f2038,plain,(
% 3.66/2.56 ( ! [X0 : nat] : (((ord_less_nat @ X0 @ (gen_length_a @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)) @ (concat_a @ (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a))))) != $true)) )),
% 3.66/2.56 inference(equality_resolution,[status(thm)],[f1973])).
% 3.66/2.56 thf(f1973,plain,(
% 3.66/2.56 ( ! [X0 : nat,X1 : list_a] : (((concat_a @ (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a))) != X1) | ($true != (ord_less_nat @ X0 @ (gen_length_a @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)) @ X1)))) )),
% 3.66/2.56 inference(definition_unfolding,[status(thm)],[f1651,f1713,f1715])).
% 3.66/2.56 thf(f1651,plain,(
% 3.66/2.56 ( ! [X0 : nat,X1 : list_a] : ((nil_a != X1) | ($true != (ord_less_nat @ X0 @ (size_size_list_a @ X1)))) )),
% 3.66/2.56 inference(cnf_transformation,[status(thm)],[f1096])).
% 3.66/2.56 thf(f1096,plain,(
% 3.66/2.56 ! [X0 : nat,X1 : list_a] : ((nil_a != X1) | ($true != (ord_less_nat @ X0 @ (size_size_list_a @ X1))))),
% 3.66/2.56 inference(ennf_transformation,[status(thm)],[f772])).
% 3.66/2.56 thf(f772,plain,(
% 3.66/2.56 ! [X0 : nat,X1 : list_a] : (($true = (ord_less_nat @ X0 @ (size_size_list_a @ X1))) => (nil_a != X1))),
% 3.66/2.56 inference(fool_elimination,[status(thm)],[f771])).
% 3.66/2.56 thf(f771,plain,(
% 3.66/2.56 ! [X0 : nat,X1 : list_a] : ((ord_less_nat @ X0 @ (size_size_list_a @ X1)) => (nil_a != X1))),
% 3.66/2.56 inference(rectify,[status(thm)],[f70])).
% 3.66/2.56 thf(f70,axiom,(
% 3.66/2.56 ! [X5 : nat,X0 : list_a] : ((ord_less_nat @ X5 @ (size_size_list_a @ X0)) => (nil_a != X0))),
% 3.66/2.56 file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_69_length__greater__imp__not__empty)).
% 3.66/2.56 thf(f2201,plain,(
% 3.66/2.56 (k = (gen_length_a @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)) @ (concat_a @ (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a))))) | ((ord_less_nat @ k @ (gen_length_a @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)) @ (concat_a @ (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a))))) = $true)),
% 3.66/2.56 inference(trivial_inequality_removal,[status(thm)],[f2199])).
% 3.66/2.56 thf(f2199,plain,(
% 3.66/2.56 (k = (gen_length_a @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)) @ (concat_a @ (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a))))) | ((ord_less_nat @ k @ (gen_length_a @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)) @ (concat_a @ (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a))))) = $true) | ($true != $true)),
% 3.66/2.56 inference(superposition,[status(thm)],[f2196,f1445])).
% 3.66/2.56 thf(f2173,plain,(
% 3.66/2.56 ( ! [X0 : list_a] : (((concat_list_a @ (concat_list_list_a @ nil_list_list_list_a)) = (listSl1495374126_aux_a @ X0 @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)) @ (divide_divide_nat @ (gen_length_a @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)) @ X0) @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)))))) )),
% 3.66/2.56 inference(beta_eta_normalization,[status(thm)],[f1906])).
% 3.66/2.56 thf(f1906,plain,(
% 3.66/2.56 ( ! [X0 : list_a] : ((((^[Y0 : list_a]: ((^[Y1 : nat]: (listSl1495374126_aux_a @ Y0 @ Y1 @ (divide_divide_nat @ (gen_length_a @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a)) @ Y0) @ Y1))))) @ X0 @ (size_s575106428list_a @ (concat_list_list_a @ nil_list_list_list_a))) = (concat_list_a @ (concat_list_list_a @ nil_list_list_list_a)))) )),
% 3.66/2.56 inference(definition_unfolding,[status(thm)],[f1554,f1716,f1709,f1712])).
% 3.66/2.56 thf(f1554,plain,(
% 3.66/2.56 ( ! [X0 : list_a] : (((listSl97544552lice_a @ X0 @ zero_zero_nat) = nil_list_a)) )),
% 3.66/2.56 inference(cnf_transformation,[status(thm)],[f590])).
% 3.66/2.56 thf(f590,plain,(
% 3.66/2.56 ! [X0 : list_a] : ((listSl97544552lice_a @ X0 @ zero_zero_nat) = nil_list_a)),
% 3.66/2.56 inference(fool_elimination,[status(thm)],[f2])).
% 3.66/2.56 thf(f2,axiom,(
% 3.66/2.56 ! [X0 : list_a] : ((listSl97544552lice_a @ X0 @ zero_zero_nat) = nil_list_a)),
% 3.66/2.56 file('/export/starexec/sandbox/tmp/tmp.n01nconuop/DTF2THF_491.p',fact_1_list__slice__0)).
% 3.66/2.56 % SZS output end Proof for DTF2THF_491
% 3.66/2.56 % (671)------------------------------
% 3.66/2.56 % (671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.66/2.56 % (671)Termination reason: Refutation
% 3.66/2.56
% 3.66/2.56 % (671)Memory used [KB]: 7675
% 3.66/2.56 % (671)Time elapsed: 0.138 s
% 3.66/2.56 % (671)Instructions burned: 232 (million)
% 3.66/2.56 % (671)------------------------------
% 3.66/2.56 % (671)------------------------------
% 3.66/2.56 % (603)Success in time 0.52 s
%------------------------------------------------------------------------------