%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP197^1 : 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 : n028.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 08:56:20 AM UTC 2026
% Result : Theorem 3.12s 1.98s
% Output : Refutation 3.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 18
% Syntax : Number of formulae : 164 ( 143 unt; 0 typ; 0 def)
% Number of atoms : 630 ( 316 equ; 9 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 973 ( 79 ~; 49 |; 0 &; 764 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 15 ( 14 usr)
% Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% Number of symbols : 102 ( 97 usr; 16 con; 0-3 aty)
% ( 55 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 252 ( 145 ^; 107 !; 0 ?; 252 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_7,type,
type_Mirabelle_typ: $tType ).
thf(type_def_8,type,
set_nat: $tType ).
thf(type_def_9,type,
list_nat_o: $tType ).
thf(type_def_10,type,
list_n396811828le_typ: $tType ).
thf(type_def_11,type,
list_l865305402le_typ: $tType ).
thf(type_def_12,type,
list_l1334080099scheme: $tType ).
thf(type_def_13,type,
list_l1704431731scheme: $tType ).
thf(type_def_14,type,
list_T1103309005le_typ: $tType ).
thf(type_def_15,type,
list_l1790670291le_typ: $tType ).
thf(type_def_16,type,
list_T247403987scheme: $tType ).
thf(type_def_17,type,
list_nat: $tType ).
thf(type_def_18,type,
list_set_nat: $tType ).
thf(type_def_19,type,
type_M1694694083scheme: $tType ).
thf(func_def_0,type,
list_l1704431731scheme: $tType ).
thf(func_def_1,type,
list_l865305402le_typ: $tType ).
thf(func_def_2,type,
list_l1334080099scheme: $tType ).
thf(func_def_3,type,
list_n396811828le_typ: $tType ).
thf(func_def_4,type,
list_l1790670291le_typ: $tType ).
thf(func_def_5,type,
list_T247403987scheme: $tType ).
thf(func_def_6,type,
list_T1103309005le_typ: $tType ).
thf(func_def_7,type,
type_M1694694083scheme: $tType ).
thf(func_def_8,type,
list_set_nat: $tType ).
thf(func_def_9,type,
list_nat_o: $tType ).
thf(func_def_10,type,
type_Mirabelle_typ: $tType ).
thf(func_def_11,type,
list_nat: $tType ).
thf(func_def_12,type,
set_nat: $tType ).
thf(func_def_13,type,
nat: $tType ).
thf(func_def_14,type,
the_nat: ( nat > $o ) > nat ).
thf(func_def_15,type,
if_nat: $o > nat > nat > nat ).
thf(func_def_16,type,
if_Typ1169047309le_typ: $o > type_Mirabelle_typ > type_Mirabelle_typ > type_Mirabelle_typ ).
thf(func_def_17,type,
semila1414375521_nat_o: ( ( nat > $o ) > ( nat > $o ) > nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_18,type,
semila1369944356et_nat: ( set_nat > set_nat > set_nat ) > set_nat > $o ).
thf(func_def_19,type,
sup_sup_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
thf(func_def_20,type,
sup_sup_nat: nat > nat > nat ).
thf(func_def_21,type,
sup_sup_set_nat: set_nat > set_nat > set_nat ).
thf(func_def_22,type,
cons_nat_o: ( nat > $o ) > list_nat_o > list_nat_o ).
thf(func_def_23,type,
cons_n499085924le_typ: ( nat > type_Mirabelle_typ ) > list_n396811828le_typ > list_n396811828le_typ ).
thf(func_def_24,type,
cons_l1800589546le_typ: list_n396811828le_typ > list_l865305402le_typ > list_l865305402le_typ ).
thf(func_def_25,type,
cons_l531914285scheme: list_l1334080099scheme > list_l1704431731scheme > list_l1704431731scheme ).
thf(func_def_26,type,
cons_l392684675le_typ: list_T1103309005le_typ > list_l1790670291le_typ > list_l1790670291le_typ ).
thf(func_def_27,type,
cons_l1910959773scheme: list_T247403987scheme > list_l1334080099scheme > list_l1334080099scheme ).
thf(func_def_28,type,
cons_nat: nat > list_nat > list_nat ).
thf(func_def_29,type,
cons_set_nat: set_nat > list_set_nat > list_set_nat ).
thf(func_def_30,type,
cons_T363929085le_typ: type_Mirabelle_typ > list_T1103309005le_typ > list_T1103309005le_typ ).
thf(func_def_31,type,
cons_T633159821scheme: type_M1694694083scheme > list_T247403987scheme > list_T247403987scheme ).
thf(func_def_32,type,
nil_nat_o: list_nat_o ).
thf(func_def_33,type,
nil_nat: list_nat ).
thf(func_def_34,type,
nil_set_nat: list_set_nat ).
thf(func_def_35,type,
nil_Ty61485117scheme: list_T247403987scheme ).
thf(func_def_36,type,
ord_lexordp_eq_nat_o: list_nat_o > list_nat_o > $o ).
thf(func_def_37,type,
ord_lexordp_eq_nat: list_nat > list_nat > $o ).
thf(func_def_38,type,
ord_le727790544et_nat: list_set_nat > list_set_nat > $o ).
thf(func_def_39,type,
bot_bot_nat_o: nat > $o ).
thf(func_def_41,type,
bot_bot_nat: nat ).
thf(func_def_42,type,
bot_bot_set_nat: set_nat ).
thf(func_def_43,type,
ord_less_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_44,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_45,type,
ord_less_set_nat: set_nat > set_nat > $o ).
thf(func_def_46,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_47,type,
insert_nat: nat > set_nat > set_nat ).
thf(func_def_48,type,
is_empty_nat: set_nat > $o ).
thf(func_def_49,type,
is_singleton_nat: set_nat > $o ).
thf(func_def_50,type,
the_elem_nat: set_nat > nat ).
thf(func_def_51,type,
type_Mirabelle_cod: ( nat > type_Mirabelle_typ ) > set_nat ).
thf(func_def_52,type,
type_Mirabelle_dom: ( nat > type_Mirabelle_typ ) > set_nat ).
thf(func_def_53,type,
type_M405566558_subst: nat > type_Mirabelle_typ ).
thf(func_def_54,type,
type_M1006385707scheme: type_Mirabelle_typ > type_M1694694083scheme ).
thf(func_def_55,type,
type_M1734147655le_typ: nat > ( nat > type_Mirabelle_typ ) > $o ).
thf(func_def_56,type,
type_M244876119le_typ: nat > list_n396811828le_typ > $o ).
thf(func_def_57,type,
type_M2086816231le_typ: nat > list_l865305402le_typ > $o ).
thf(func_def_58,type,
type_M1172169604scheme: nat > list_l1704431731scheme > $o ).
thf(func_def_59,type,
type_M1826376056le_typ: nat > list_l1790670291le_typ > $o ).
thf(func_def_60,type,
type_M1377662078scheme: nat > list_l1334080099scheme > $o ).
thf(func_def_61,type,
type_M263553000le_typ: nat > list_T1103309005le_typ > $o ).
thf(func_def_62,type,
type_M2064939256scheme: nat > list_T247403987scheme > $o ).
thf(func_def_63,type,
type_M1211611096le_typ: nat > type_Mirabelle_typ > $o ).
thf(func_def_64,type,
type_M1963061490scheme: nat > type_M1694694083scheme > $o ).
thf(func_def_65,type,
type_M1898948661at_nat: nat > nat ).
thf(func_def_66,type,
type_Mirabelle_Fun: type_Mirabelle_typ > type_Mirabelle_typ > type_Mirabelle_typ ).
thf(func_def_67,type,
type_Mirabelle_TVar: nat > type_Mirabelle_typ ).
thf(func_def_68,type,
type_M1743451154le_typ: type_Mirabelle_typ > type_Mirabelle_typ ).
thf(func_def_69,type,
type_M2048935292e_BVar: nat > type_M1694694083scheme ).
thf(func_def_70,type,
type_M876316792e_FVar: nat > type_M1694694083scheme ).
thf(func_def_71,type,
type_M155660035e_SFun: type_M1694694083scheme > type_M1694694083scheme > type_M1694694083scheme ).
thf(func_def_72,type,
type_M1158474302le_typ: ( nat > type_Mirabelle_typ ) > ( nat > type_Mirabelle_typ ) > nat > type_Mirabelle_typ ).
thf(func_def_73,type,
type_M737052622le_typ: ( nat > type_Mirabelle_typ ) > list_n396811828le_typ > list_n396811828le_typ ).
thf(func_def_74,type,
type_M1385924301scheme: ( nat > type_Mirabelle_typ ) > list_l1704431731scheme > list_l1704431731scheme ).
thf(func_def_75,type,
type_M1913464047le_typ: ( nat > type_Mirabelle_typ ) > list_l1790670291le_typ > list_l1790670291le_typ ).
thf(func_def_76,type,
type_M1061687367scheme: ( nat > type_Mirabelle_typ ) > list_l1334080099scheme > list_l1334080099scheme ).
thf(func_def_77,type,
type_M1440203487le_typ: ( nat > type_Mirabelle_typ ) > list_T1103309005le_typ > list_T1103309005le_typ ).
thf(func_def_78,type,
type_M1944210753scheme: ( nat > type_Mirabelle_typ ) > list_T247403987scheme > list_T247403987scheme ).
thf(func_def_79,type,
type_M784671311le_typ: ( nat > type_Mirabelle_typ ) > type_Mirabelle_typ > type_Mirabelle_typ ).
thf(func_def_80,type,
type_M1690910139scheme: ( nat > type_Mirabelle_typ ) > type_M1694694083scheme > type_M1694694083scheme ).
thf(func_def_81,type,
type_M772783356le_typ: ( nat > type_Mirabelle_typ ) > set_nat ).
thf(func_def_82,type,
type_M513401740le_typ: list_n396811828le_typ > set_nat ).
thf(func_def_83,type,
type_M1496178953scheme: list_l1334080099scheme > set_nat ).
thf(func_def_84,type,
type_M1539052445le_typ: list_T1103309005le_typ > set_nat ).
thf(func_def_85,type,
type_M961603331scheme: list_T247403987scheme > set_nat ).
thf(func_def_86,type,
type_M801073677le_typ: type_Mirabelle_typ > set_nat ).
thf(func_def_87,type,
type_M326705277scheme: type_M1694694083scheme > set_nat ).
thf(func_def_88,type,
type_M1715972684le_typ: ( nat > type_Mirabelle_typ ) > set_nat ).
thf(func_def_89,type,
type_M1691543772le_typ: list_n396811828le_typ > set_nat ).
thf(func_def_90,type,
type_M906078444le_typ: list_l865305402le_typ > set_nat ).
thf(func_def_91,type,
type_M1926053183scheme: list_l1704431731scheme > set_nat ).
thf(func_def_92,type,
type_M1418941437le_typ: list_l1790670291le_typ > set_nat ).
thf(func_def_93,type,
type_M1958029241scheme: list_l1334080099scheme > set_nat ).
thf(func_def_94,type,
type_M510873837le_typ: list_T1103309005le_typ > set_nat ).
thf(func_def_95,type,
type_M141510067scheme: list_T247403987scheme > set_nat ).
thf(func_def_96,type,
type_M49385309le_typ: type_Mirabelle_typ > set_nat ).
thf(func_def_97,type,
type_M1050318637scheme: type_M1694694083scheme > set_nat ).
thf(func_def_98,type,
member_nat: nat > set_nat > $o ).
thf(func_def_99,type,
s1: nat > type_Mirabelle_typ ).
thf(func_def_100,type,
s2: nat > type_Mirabelle_typ ).
thf(func_def_101,type,
n: nat ).
thf(func_def_102,type,
x: nat ).
thf(func_def_123,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_124,type,
sK2: nat > nat ).
thf(func_def_125,type,
sK3: nat ).
thf(func_def_126,type,
sK4: nat > nat ).
thf(func_def_127,type,
sK5: nat > nat ).
thf(func_def_128,type,
sK6: nat ).
thf(func_def_129,type,
sK7: nat ).
thf(func_def_130,type,
sK8: nat > nat ).
thf(f3967,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f3964,f3284]) ).
thf(f3284,plain,
( ( s1 @ n )
!= ( s2 @ n ) ),
inference(equality_proxy_clausification,[status(thm)],[f3269]) ).
thf(f3269,plain,
( $false
= ( ( s1 @ n )
= ( s2 @ n ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f3268]) ).
thf(f3268,plain,
( ( $false
= ( ( s1 @ n )
= ( s2 @ n ) ) )
| ( $false = $true ) ),
inference(boolean_simplification,[status(thm)],[f3267]) ).
thf(f3267,plain,
( ( $false
= ( ( s1 @ n )
= ( s2 @ n ) ) )
| ( $true = ( ~ $true ) ) ),
inference(boolean_simplification,[status(thm)],[f3266]) ).
thf(f3266,plain,
( ( $true
= ( ~ ( $true
| ~ ( member_nat @ n @ ( type_M49385309le_typ @ ( type_M405566558_subst @ x ) ) ) ) ) )
| ( $false
= ( ( s1 @ n )
= ( s2 @ n ) ) ) ),
inference(boolean_simplification,[status(thm)],[f3245]) ).
thf(f3245,plain,
( ( $false
= ( ( s1 @ n )
= ( s2 @ n ) ) )
| ( $true
= ( ~ ( ( ( type_M1006385707scheme @ ( s1 @ x ) )
!= ( type_M1006385707scheme @ ( s2 @ x ) ) )
| $true
| ~ ( member_nat @ n @ ( type_M49385309le_typ @ ( type_M405566558_subst @ x ) ) ) ) ) ) ),
inference(superposition,[status(thm)],[f2534,f2294]) ).
thf(f2294,plain,
! [X1: $o] :
( ( $true = X1 )
| ( $false = X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f2141]) ).
thf(f2141,plain,
! [X1: $o] :
( ( $true
= ( $false = X1 ) )
| ( $true = X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f2091]) ).
thf(f2091,plain,
! [X1: $o] :
( ( $true
= ( $true = X1 ) )
| ( $true
= ( $false = X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f2090]) ).
thf(f2090,plain,
! [X1: $o] :
( ( ( $false = X1 )
| ( $true = X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2089]) ).
thf(f2089,plain,
! [X1: $o] :
( ( ^ [Y0: $o] :
( ( $false = Y0 )
| ( $true = Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f1273]) ).
thf(f1273,plain,
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( ( $false = Y0 )
| ( $true = Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f781]) ).
thf(f781,plain,
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( ( $false = Y0 )
| ( $true = Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f780]) ).
thf(f780,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
inference(rectify,[status(thm)],[f357]) ).
thf(f357,axiom,
! [X33: $o] :
( ( $true = X33 )
| ( $false = X33 ) ),
file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',help_If_3_1_If_001t__Type____Mirabelle____lczmhmumaa__Otyp_T) ).
thf(f2534,plain,
( ( ~ ( ( ( type_M1006385707scheme @ ( s1 @ x ) )
!= ( type_M1006385707scheme @ ( s2 @ x ) ) )
| ( ( s1 @ n )
= ( s2 @ n ) )
| ~ ( member_nat @ n @ ( type_M49385309le_typ @ ( type_M405566558_subst @ x ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f2531,f2529]) ).
thf(f2529,plain,
! [X2: nat > type_Mirabelle_typ,X1: nat] :
( ( type_M1690910139scheme @ X2 @ ( type_M876316792e_FVar @ X1 ) )
= ( type_M1006385707scheme @ ( X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f2527]) ).
thf(f2527,plain,
! [X2: nat > type_Mirabelle_typ,X1: nat] :
( ( ( type_M1006385707scheme @ ( X2 @ X1 ) )
= ( type_M1690910139scheme @ X2 @ ( type_M876316792e_FVar @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2526]) ).
thf(f2526,plain,
! [X2: nat > type_Mirabelle_typ,X1: nat] :
( ( ^ [Y0: nat > type_Mirabelle_typ] :
( ( type_M1006385707scheme @ ( Y0 @ X1 ) )
= ( type_M1690910139scheme @ Y0 @ ( type_M876316792e_FVar @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f2522]) ).
thf(f2522,plain,
! [X1: nat] :
( ( !! @ ( nat > type_Mirabelle_typ )
@ ^ [Y0: nat > type_Mirabelle_typ] :
( ( type_M1006385707scheme @ ( Y0 @ X1 ) )
= ( type_M1690910139scheme @ Y0 @ ( type_M876316792e_FVar @ X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2521]) ).
thf(f2521,plain,
! [X1: nat] :
( $true
= ( ^ [Y0: nat] :
( !! @ ( nat > type_Mirabelle_typ )
@ ^ [Y1: nat > type_Mirabelle_typ] :
( ( type_M1006385707scheme @ ( Y1 @ Y0 ) )
= ( type_M1690910139scheme @ Y1 @ ( type_M876316792e_FVar @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f1373]) ).
thf(f1373,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ ( nat > type_Mirabelle_typ )
@ ^ [Y1: nat > type_Mirabelle_typ] :
( ( type_M1006385707scheme @ ( Y1 @ Y0 ) )
= ( type_M1690910139scheme @ Y1 @ ( type_M876316792e_FVar @ Y0 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f1066]) ).
thf(f1066,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ ( nat > type_Mirabelle_typ )
@ ^ [Y1: nat > type_Mirabelle_typ] :
( ( type_M1006385707scheme @ ( Y1 @ Y0 ) )
= ( type_M1690910139scheme @ Y1 @ ( type_M876316792e_FVar @ Y0 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f1065]) ).
thf(f1065,plain,
! [X0: nat > type_Mirabelle_typ,X1: nat] :
( ( type_M1006385707scheme @ ( X0 @ X1 ) )
= ( type_M1690910139scheme @ X0 @ ( type_M876316792e_FVar @ X1 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X6: nat > type_Mirabelle_typ,X9: nat] :
( ( type_M1690910139scheme @ X6 @ ( type_M876316792e_FVar @ X9 ) )
= ( type_M1006385707scheme @ ( X6 @ X9 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_3_app__subst__type__scheme_Osimps_I1_J) ).
thf(f2531,plain,
( ( ~ ( ( ( type_M1006385707scheme @ ( s1 @ x ) )
!= ( type_M1690910139scheme @ s2 @ ( type_M876316792e_FVar @ x ) ) )
| ( ( s1 @ n )
= ( s2 @ n ) )
| ~ ( member_nat @ n @ ( type_M49385309le_typ @ ( type_M405566558_subst @ x ) ) ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f2069,f2529]) ).
thf(f2069,plain,
( $true
= ( ~ ( ( ( type_M1690910139scheme @ s1 @ ( type_M876316792e_FVar @ x ) )
!= ( type_M1690910139scheme @ s2 @ ( type_M876316792e_FVar @ x ) ) )
| ( ( s1 @ n )
= ( s2 @ n ) )
| ~ ( member_nat @ n @ ( type_M49385309le_typ @ ( type_M405566558_subst @ x ) ) ) ) ) ),
inference(backward_demodulation,[status(thm)],[f1375,f2068]) ).
thf(f2068,plain,
! [X0: nat] :
( ( type_M1050318637scheme @ ( type_M876316792e_FVar @ X0 ) )
= ( type_M49385309le_typ @ ( type_M405566558_subst @ X0 ) ) ),
inference(superposition,[status(thm)],[f2060,f2065]) ).
thf(f2065,plain,
! [X1: nat] :
( ( type_M876316792e_FVar @ X1 )
= ( type_M1006385707scheme @ ( type_M405566558_subst @ X1 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f2064]) ).
thf(f2064,plain,
! [X1: nat] :
( $true
= ( ( type_M876316792e_FVar @ X1 )
= ( type_M1006385707scheme @ ( type_M405566558_subst @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2063]) ).
thf(f2063,plain,
! [X1: nat] :
( $true
= ( ^ [Y0: nat] :
( ( type_M876316792e_FVar @ Y0 )
= ( type_M1006385707scheme @ ( type_M405566558_subst @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f1470]) ).
thf(f1470,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( ( type_M876316792e_FVar @ Y0 )
= ( type_M1006385707scheme @ ( type_M405566558_subst @ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f1101,f1324]) ).
thf(f1324,plain,
type_Mirabelle_TVar = type_M405566558_subst,
inference(cnf_transformation,[status(thm)],[f1055]) ).
thf(f1055,plain,
type_Mirabelle_TVar = type_M405566558_subst,
inference(fool_elimination,[status(thm)],[f228]) ).
thf(f228,axiom,
type_Mirabelle_TVar = type_M405566558_subst,
file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_227_id__subst__def) ).
thf(f1101,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( ( type_M876316792e_FVar @ Y0 )
= ( type_M1006385707scheme @ ( type_Mirabelle_TVar @ Y0 ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f1017]) ).
thf(f1017,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( ( type_M876316792e_FVar @ Y0 )
= ( type_M1006385707scheme @ ( type_Mirabelle_TVar @ Y0 ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f1016]) ).
thf(f1016,plain,
! [X0: nat] :
( ( type_M876316792e_FVar @ X0 )
= ( type_M1006385707scheme @ ( type_Mirabelle_TVar @ X0 ) ) ),
inference(rectify,[status(thm)],[f220]) ).
thf(f220,axiom,
! [X9: nat] :
( ( type_M876316792e_FVar @ X9 )
= ( type_M1006385707scheme @ ( type_Mirabelle_TVar @ X9 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_219_mk__scheme_Osimps_I1_J) ).
thf(f2060,plain,
! [X1: type_Mirabelle_typ] :
( ( type_M1050318637scheme @ ( type_M1006385707scheme @ X1 ) )
= ( type_M49385309le_typ @ X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f2059]) ).
thf(f2059,plain,
! [X1: type_Mirabelle_typ] :
( ( ( type_M49385309le_typ @ X1 )
= ( type_M1050318637scheme @ ( type_M1006385707scheme @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2058]) ).
thf(f2058,plain,
! [X1: type_Mirabelle_typ] :
( $true
= ( ^ [Y0: type_Mirabelle_typ] :
( ( type_M49385309le_typ @ Y0 )
= ( type_M1050318637scheme @ ( type_M1006385707scheme @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f1166]) ).
thf(f1166,plain,
( ( !! @ type_Mirabelle_typ
@ ^ [Y0: type_Mirabelle_typ] :
( ( type_M49385309le_typ @ Y0 )
= ( type_M1050318637scheme @ ( type_M1006385707scheme @ Y0 ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f918]) ).
thf(f918,plain,
( ( !! @ type_Mirabelle_typ
@ ^ [Y0: type_Mirabelle_typ] :
( ( type_M49385309le_typ @ Y0 )
= ( type_M1050318637scheme @ ( type_M1006385707scheme @ Y0 ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f917]) ).
thf(f917,plain,
! [X0: type_Mirabelle_typ] :
( ( type_M49385309le_typ @ X0 )
= ( type_M1050318637scheme @ ( type_M1006385707scheme @ X0 ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,axiom,
! [X17: type_Mirabelle_typ] :
( ( type_M1050318637scheme @ ( type_M1006385707scheme @ X17 ) )
= ( type_M49385309le_typ @ X17 ) ),
file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_14_free__tv__mk__scheme) ).
thf(f1375,plain,
( $true
= ( ~ ( ( ( type_M1690910139scheme @ s1 @ ( type_M876316792e_FVar @ x ) )
!= ( type_M1690910139scheme @ s2 @ ( type_M876316792e_FVar @ x ) ) )
| ( ( s1 @ n )
= ( s2 @ n ) )
| ~ ( member_nat @ n @ ( type_M1050318637scheme @ ( type_M876316792e_FVar @ x ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f982]) ).
thf(f982,plain,
( $true
= ( ~ ( ( ( type_M1690910139scheme @ s1 @ ( type_M876316792e_FVar @ x ) )
!= ( type_M1690910139scheme @ s2 @ ( type_M876316792e_FVar @ x ) ) )
| ( ( s1 @ n )
= ( s2 @ n ) )
| ~ ( member_nat @ n @ ( type_M1050318637scheme @ ( type_M876316792e_FVar @ x ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f981]) ).
thf(f981,plain,
~ ( ~ ( member_nat @ n @ ( type_M1050318637scheme @ ( type_M876316792e_FVar @ x ) ) )
| ( ( s1 @ n )
= ( s2 @ n ) )
| ( ( type_M1690910139scheme @ s1 @ ( type_M876316792e_FVar @ x ) )
!= ( type_M1690910139scheme @ s2 @ ( type_M876316792e_FVar @ x ) ) ) ),
inference(rectify,[status(thm)],[f361]) ).
thf(f361,negated_conjecture,
~ ( ~ ( member_nat @ n @ ( type_M1050318637scheme @ ( type_M876316792e_FVar @ x ) ) )
| ( ( s1 @ n )
= ( s2 @ n ) )
| ( ( type_M1690910139scheme @ s1 @ ( type_M876316792e_FVar @ x ) )
!= ( type_M1690910139scheme @ s2 @ ( type_M876316792e_FVar @ x ) ) ) ),
inference(negated_conjecture,[status(cth)],[f360]) ).
thf(f360,conjecture,
( ~ ( member_nat @ n @ ( type_M1050318637scheme @ ( type_M876316792e_FVar @ x ) ) )
| ( ( s1 @ n )
= ( s2 @ n ) )
| ( ( type_M1690910139scheme @ s1 @ ( type_M876316792e_FVar @ x ) )
!= ( type_M1690910139scheme @ s2 @ ( type_M876316792e_FVar @ x ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',conj_0) ).
thf(f3964,plain,
( ( s1 @ n )
= ( s2 @ n ) ),
inference(backward_demodulation,[status(thm)],[f3821,f3941]) ).
thf(f3941,plain,
x = n,
inference(equality_proxy_clausification,[status(thm)],[f3930]) ).
thf(f3930,plain,
( ( x = n )
= $true ),
inference(superposition,[status(thm)],[f3299,f3896]) ).
thf(f3896,plain,
! [X0: nat,X1: nat] :
( ( member_nat @ X1 @ ( type_M49385309le_typ @ ( type_M405566558_subst @ X0 ) ) )
= ( X0 = X1 ) ),
inference(superposition,[status(thm)],[f2317,f3866]) ).
thf(f3866,plain,
! [X0: nat] :
( ( type_M49385309le_typ @ ( type_M405566558_subst @ X0 ) )
= ( collect_nat @ ( (=) @ X0 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f3548]) ).
thf(f3548,plain,
! [X0: nat] :
( ( ( type_M49385309le_typ @ ( type_M405566558_subst @ X0 ) )
= ( collect_nat @ ( (=) @ X0 ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f3547,f2082]) ).
thf(f2082,plain,
! [X1: set_nat] :
( ( collect_nat
@ ^ [Y0: nat] : ( member_nat @ Y0 @ X1 ) )
= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f2081]) ).
thf(f2081,plain,
! [X1: set_nat] :
( ( X1
= ( collect_nat
@ ^ [Y0: nat] : ( member_nat @ Y0 @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2080]) ).
thf(f2080,plain,
! [X1: set_nat] :
( ( ^ [Y0: set_nat] :
( Y0
= ( collect_nat
@ ^ [Y1: nat] : ( member_nat @ Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f1370]) ).
thf(f1370,plain,
( $true
= ( !! @ set_nat
@ ^ [Y0: set_nat] :
( Y0
= ( collect_nat
@ ^ [Y1: nat] : ( member_nat @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f366]) ).
thf(f366,plain,
( $true
= ( !! @ set_nat
@ ^ [Y0: set_nat] :
( Y0
= ( collect_nat
@ ^ [Y1: nat] : ( member_nat @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f365]) ).
thf(f365,plain,
! [X0: set_nat] :
( X0
= ( collect_nat
@ ^ [X1: nat] : ( member_nat @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f60]) ).
thf(f60,axiom,
! [X46: set_nat] :
( X46
= ( collect_nat
@ ^ [X41: nat] : ( member_nat @ X41 @ X46 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_59_Collect__mem__eq) ).
thf(f3547,plain,
! [X0: nat] :
( ( ( type_M49385309le_typ @ ( type_M405566558_subst @ X0 ) )
= ( collect_nat
@ ^ [Y0: nat] : ( member_nat @ Y0 @ ( collect_nat @ ( (=) @ X0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f3546,f2282]) ).
thf(f2282,plain,
! [X1: nat > $o] :
( ( sup_sup_nat_o @ X1
@ ^ [Y0: nat] : bot_bot_o )
= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f2280]) ).
thf(f2280,plain,
! [X1: nat > $o] :
( ( ( sup_sup_nat_o @ X1
@ ^ [Y0: nat] : bot_bot_o )
= X1 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2279]) ).
thf(f2279,plain,
! [X1: nat > $o] :
( ( ^ [Y0: nat > $o] :
( ( sup_sup_nat_o @ Y0
@ ^ [Y1: nat] : bot_bot_o )
= Y0 )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f1616]) ).
thf(f1616,plain,
( $true
= ( !! @ ( nat > $o )
@ ^ [Y0: nat > $o] :
( ( sup_sup_nat_o @ Y0
@ ^ [Y1: nat] : bot_bot_o )
= Y0 ) ) ),
inference(definition_unfolding,[status(thm)],[f1296,f1284]) ).
thf(f1284,plain,
( bot_bot_nat_o
= ( ^ [Y0: nat] : bot_bot_o ) ),
inference(cnf_transformation,[status(thm)],[f573]) ).
thf(f573,plain,
( bot_bot_nat_o
= ( ^ [Y0: nat] : bot_bot_o ) ),
inference(fool_elimination,[status(thm)],[f572]) ).
thf(f572,plain,
( ( ^ [X0: nat] : bot_bot_o )
= bot_bot_nat_o ),
inference(rectify,[status(thm)],[f219]) ).
thf(f219,axiom,
( ( ^ [X41: nat] : bot_bot_o )
= bot_bot_nat_o ),
file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_218_bot__fun__def) ).
thf(f1296,plain,
( $true
= ( !! @ ( nat > $o )
@ ^ [Y0: nat > $o] :
( ( sup_sup_nat_o @ Y0 @ bot_bot_nat_o )
= Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f960]) ).
thf(f960,plain,
( $true
= ( !! @ ( nat > $o )
@ ^ [Y0: nat > $o] :
( ( sup_sup_nat_o @ Y0 @ bot_bot_nat_o )
= Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f959]) ).
thf(f959,plain,
! [X0: nat > $o] :
( ( sup_sup_nat_o @ X0 @ bot_bot_nat_o )
= X0 ),
inference(rectify,[status(thm)],[f294]) ).
thf(f294,axiom,
! [X15: nat > $o] :
( ( sup_sup_nat_o @ X15 @ bot_bot_nat_o )
= X15 ),
file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_293_sup__bot__right) ).
thf(f3546,plain,
! [X0: nat] :
( ( ( type_M49385309le_typ @ ( type_M405566558_subst @ X0 ) )
= ( collect_nat
@ ( sup_sup_nat_o
@ ^ [Y0: nat] : ( member_nat @ Y0 @ ( collect_nat @ ( (=) @ X0 ) ) )
@ ^ [Y0: nat] : bot_bot_o ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f3545,f1712]) ).
thf(f1712,plain,
( ( ^ [Y0: nat] : ( member_nat @ Y0 @ ( type_M141510067scheme @ nil_Ty61485117scheme ) ) )
= ( ^ [Y0: nat] : bot_bot_o ) ),
inference(definition_unfolding,[status(thm)],[f1420,f1284,f1124]) ).
thf(f1124,plain,
( bot_bot_set_nat
= ( type_M141510067scheme @ nil_Ty61485117scheme ) ),
inference(cnf_transformation,[status(thm)],[f745]) ).
thf(f745,plain,
( bot_bot_set_nat
= ( type_M141510067scheme @ nil_Ty61485117scheme ) ),
inference(fool_elimination,[status(thm)],[f353]) ).
thf(f353,axiom,
( bot_bot_set_nat
= ( type_M141510067scheme @ nil_Ty61485117scheme ) ),
file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_352_free__tv__list_Osimps_I1_J) ).
thf(f1420,plain,
( bot_bot_nat_o
= ( ^ [Y0: nat] : ( member_nat @ Y0 @ bot_bot_set_nat ) ) ),
inference(cnf_transformation,[status(thm)],[f698]) ).
thf(f698,plain,
( bot_bot_nat_o
= ( ^ [Y0: nat] : ( member_nat @ Y0 @ bot_bot_set_nat ) ) ),
inference(fool_elimination,[status(thm)],[f697]) ).
thf(f697,plain,
( bot_bot_nat_o
= ( ^ [X0: nat] : ( member_nat @ X0 @ bot_bot_set_nat ) ) ),
inference(rectify,[status(thm)],[f251]) ).
thf(f251,axiom,
( bot_bot_nat_o
= ( ^ [X41: nat] : ( member_nat @ X41 @ bot_bot_set_nat ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_250_bot__empty__eq) ).
thf(f3545,plain,
! [X0: nat] :
( ( ( type_M49385309le_typ @ ( type_M405566558_subst @ X0 ) )
= ( collect_nat
@ ( sup_sup_nat_o
@ ^ [Y0: nat] : ( member_nat @ Y0 @ ( collect_nat @ ( (=) @ X0 ) ) )
@ ^ [Y0: nat] : ( member_nat @ Y0 @ ( type_M141510067scheme @ nil_Ty61485117scheme ) ) ) ) )
= $true ),
inference(forward_demodulation,[status(thm)],[f3544,f2068]) ).
thf(f3544,plain,
! [X0: nat] :
( $true
= ( ( type_M1050318637scheme @ ( type_M876316792e_FVar @ X0 ) )
= ( collect_nat
@ ( sup_sup_nat_o
@ ^ [Y0: nat] : ( member_nat @ Y0 @ ( collect_nat @ ( (=) @ X0 ) ) )
@ ^ [Y0: nat] : ( member_nat @ Y0 @ ( type_M141510067scheme @ nil_Ty61485117scheme ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f3543]) ).
thf(f3543,plain,
! [X0: nat] :
( $true
= ( $true
=> ( ( type_M1050318637scheme @ ( type_M876316792e_FVar @ X0 ) )
= ( collect_nat
@ ( sup_sup_nat_o
@ ^ [Y0: nat] : ( member_nat @ Y0 @ ( collect_nat @ ( (=) @ X0 ) ) )
@ ^ [Y0: nat] : ( member_nat @ Y0 @ ( type_M141510067scheme @ nil_Ty61485117scheme ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3541]) ).
thf(f3541,plain,
! [X0: nat] :
( $true
= ( $true
=> ( ^ [Y0: nat] :
( ( type_M1050318637scheme @ ( type_M876316792e_FVar @ Y0 ) )
= ( collect_nat
@ ( sup_sup_nat_o
@ ^ [Y1: nat] : ( member_nat @ Y1 @ ( collect_nat @ ( (=) @ Y0 ) ) )
@ ^ [Y1: nat] : ( member_nat @ Y1 @ ( type_M141510067scheme @ nil_Ty61485117scheme ) ) ) ) )
@ X0 ) ) ),
inference(superposition,[status(thm)],[f2618,f1779]) ).
thf(f1779,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( ( type_M1050318637scheme @ ( type_M876316792e_FVar @ Y0 ) )
= ( collect_nat
@ ( sup_sup_nat_o
@ ^ [Y1: nat] : ( member_nat @ Y1 @ ( collect_nat @ ( (=) @ Y0 ) ) )
@ ^ [Y1: nat] : ( member_nat @ Y1 @ ( type_M141510067scheme @ nil_Ty61485117scheme ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1557]) ).
thf(f1557,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( ( type_M1050318637scheme @ ( type_M876316792e_FVar @ Y0 ) )
= ( ^ [Y1: nat] :
( ^ [Y2: set_nat,Y3: set_nat] :
( collect_nat
@ ( sup_sup_nat_o
@ ^ [Y4: nat] : ( member_nat @ Y4 @ Y2 )
@ ^ [Y4: nat] : ( member_nat @ Y4 @ Y3 ) ) )
@ ( collect_nat
@ ^ [Y2: nat] : ( Y1 = Y2 ) ) )
@ Y0
@ ( type_M141510067scheme @ nil_Ty61485117scheme ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1214,f1442,f1124]) ).
thf(f1442,plain,
( insert_nat
= ( ^ [Y0: nat] :
( ^ [Y1: set_nat,Y2: set_nat] :
( collect_nat
@ ( sup_sup_nat_o
@ ^ [Y3: nat] : ( member_nat @ Y3 @ Y1 )
@ ^ [Y3: nat] : ( member_nat @ Y3 @ Y2 ) ) )
@ ( collect_nat
@ ^ [Y1: nat] : ( Y0 = Y1 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1281,f1344]) ).
thf(f1344,plain,
( sup_sup_set_nat
= ( ^ [Y0: set_nat,Y1: set_nat] :
( collect_nat
@ ( sup_sup_nat_o
@ ^ [Y2: nat] : ( member_nat @ Y2 @ Y0 )
@ ^ [Y2: nat] : ( member_nat @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f749]) ).
thf(f749,plain,
( sup_sup_set_nat
= ( ^ [Y0: set_nat,Y1: set_nat] :
( collect_nat
@ ( sup_sup_nat_o
@ ^ [Y2: nat] : ( member_nat @ Y2 @ Y0 )
@ ^ [Y2: nat] : ( member_nat @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f748]) ).
thf(f748,plain,
( sup_sup_set_nat
= ( ^ [X0: set_nat,X1: set_nat] :
( collect_nat
@ ( sup_sup_nat_o
@ ^ [X2: nat] : ( member_nat @ X2 @ X0 )
@ ^ [X3: nat] : ( member_nat @ X3 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f309]) ).
thf(f309,axiom,
( sup_sup_set_nat
= ( ^ [X61: set_nat,X59: set_nat] :
( collect_nat
@ ( sup_sup_nat_o
@ ^ [X41: nat] : ( member_nat @ X41 @ X61 )
@ ^ [X41: nat] : ( member_nat @ X41 @ X59 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_308_sup__set__def) ).
thf(f1281,plain,
( insert_nat
= ( ^ [Y0: nat] :
( sup_sup_set_nat
@ ( collect_nat
@ ^ [Y1: nat] : ( Y0 = Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f655]) ).
thf(f655,plain,
( insert_nat
= ( ^ [Y0: nat] :
( sup_sup_set_nat
@ ( collect_nat
@ ^ [Y1: nat] : ( Y0 = Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f654]) ).
thf(f654,plain,
( insert_nat
= ( ^ [X0: nat] :
( sup_sup_set_nat
@ ( collect_nat
@ ^ [X1: nat] : ( X0 = X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f271]) ).
thf(f271,axiom,
( insert_nat
= ( ^ [X58: nat] :
( sup_sup_set_nat
@ ( collect_nat
@ ^ [X41: nat] : ( X41 = X58 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_270_insert__def) ).
thf(f1214,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( ( type_M1050318637scheme @ ( type_M876316792e_FVar @ Y0 ) )
= ( insert_nat @ Y0 @ bot_bot_set_nat ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f659]) ).
thf(f659,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( ( type_M1050318637scheme @ ( type_M876316792e_FVar @ Y0 ) )
= ( insert_nat @ Y0 @ bot_bot_set_nat ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f658]) ).
thf(f658,plain,
! [X0: nat] :
( ( type_M1050318637scheme @ ( type_M876316792e_FVar @ X0 ) )
= ( insert_nat @ X0 @ bot_bot_set_nat ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,axiom,
! [X18: nat] :
( ( type_M1050318637scheme @ ( type_M876316792e_FVar @ X18 ) )
= ( insert_nat @ X18 @ bot_bot_set_nat ) ),
file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_15_free__tv__type__scheme_Osimps_I1_J) ).
thf(f2618,plain,
! [X0: nat,X1: nat > $o] :
( $true
= ( ( !! @ nat @ X1 )
=> ( X1 @ X0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2617]) ).
thf(f2617,plain,
! [X0: nat,X1: nat > $o] :
( ( ( !! @ nat
@ ^ [Y0: nat] : ( X1 @ Y0 ) )
=> ( X1 @ X0 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2616]) ).
thf(f2616,plain,
! [X0: nat,X1: nat > $o] :
( ( ( !! @ nat
@ ^ [Y0: nat] :
~ ~ ( X1 @ Y0 ) )
=> ( X1 @ X0 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2614]) ).
thf(f2614,plain,
! [X0: nat,X1: nat > $o] :
( $true
= ( ( !! @ nat
@ ^ [Y0: nat] :
~ ( ^ [Y1: nat] :
~ ( X1 @ Y1 )
@ Y0 ) )
=> ( X1 @ X0 ) ) ),
inference(backward_demodulation,[status(thm)],[f2415,f2593]) ).
thf(f2593,plain,
! [X1: nat > $o] :
( ( ( type_M141510067scheme @ nil_Ty61485117scheme )
= ( collect_nat @ X1 ) )
= ( !! @ nat
@ ^ [Y0: nat] :
~ ( X1 @ Y0 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f2591]) ).
thf(f2591,plain,
! [X1: nat > $o] :
( $true
= ( ( !! @ nat
@ ^ [Y0: nat] :
~ ( X1 @ Y0 ) )
= ( ( type_M141510067scheme @ nil_Ty61485117scheme )
= ( collect_nat @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2590]) ).
thf(f2590,plain,
! [X1: nat > $o] :
( ( ^ [Y0: nat > $o] :
( ( !! @ nat
@ ^ [Y1: nat] :
~ ( Y0 @ Y1 ) )
= ( ( type_M141510067scheme @ nil_Ty61485117scheme )
= ( collect_nat @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f1594]) ).
thf(f1594,plain,
( $true
= ( !! @ ( nat > $o )
@ ^ [Y0: nat > $o] :
( ( !! @ nat
@ ^ [Y1: nat] :
~ ( Y0 @ Y1 ) )
= ( ( type_M141510067scheme @ nil_Ty61485117scheme )
= ( collect_nat @ Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1265,f1124]) ).
thf(f1265,plain,
( $true
= ( !! @ ( nat > $o )
@ ^ [Y0: nat > $o] :
( ( !! @ nat
@ ^ [Y1: nat] :
~ ( Y0 @ Y1 ) )
= ( bot_bot_set_nat
= ( collect_nat @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f775]) ).
thf(f775,plain,
( $true
= ( !! @ ( nat > $o )
@ ^ [Y0: nat > $o] :
( ( !! @ nat
@ ^ [Y1: nat] :
~ ( Y0 @ Y1 ) )
= ( bot_bot_set_nat
= ( collect_nat @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f774]) ).
thf(f774,plain,
! [X0: nat > $o,X1: nat] :
( ( ~ ( X0 @ X1 ) )
= ( bot_bot_set_nat
= ( collect_nat @ X0 ) ) ),
inference(rectify,[status(thm)],[f64]) ).
thf(f64,axiom,
! [X33: nat > $o,X41: nat] :
( ( ~ ( X33 @ X41 ) )
= ( bot_bot_set_nat
= ( collect_nat @ X33 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_63_empty__Collect__eq) ).
thf(f2415,plain,
! [X0: nat,X1: nat > $o] :
( ( ( ( type_M141510067scheme @ nil_Ty61485117scheme )
= ( collect_nat
@ ^ [Y0: nat] :
~ ( X1 @ Y0 ) ) )
=> ( X1 @ X0 ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f2414]) ).
thf(f2414,plain,
! [X0: nat,X1: nat > $o] :
( ( ( ( type_M141510067scheme @ nil_Ty61485117scheme )
= ( collect_nat
@ ^ [Y0: nat] :
~ ( X1 @ Y0 ) ) )
=> ~ ~ ( X1 @ X0 ) )
= $true ),
inference(superposition,[status(thm)],[f2206,f2354]) ).
thf(f2354,plain,
! [X1: nat,X5: nat > $o] :
( ( member_nat @ X1
@ ( collect_nat
@ ^ [Y0: nat] :
~ ( X5 @ Y0 ) ) )
= ( ~ ( X5 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2348]) ).
thf(f2348,plain,
! [X1: nat,X5: nat > $o] :
( ( member_nat @ X1
@ ( collect_nat
@ ^ [Y0: nat] :
~ ( X5 @ Y0 ) ) )
= ( ^ [Y0: nat] :
~ ( X5 @ Y0 )
@ X1 ) ),
inference(primitive_instantiation,[status(thm)],[f2317]) ).
thf(f2206,plain,
! [X2: set_nat,X1: nat] :
( ( ( ( type_M141510067scheme @ nil_Ty61485117scheme )
= X2 )
=> ~ ( member_nat @ X1 @ X2 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2205]) ).
thf(f2205,plain,
! [X2: set_nat,X1: nat] :
( $true
= ( ^ [Y0: set_nat] :
( ( ( type_M141510067scheme @ nil_Ty61485117scheme )
= Y0 )
=> ~ ( member_nat @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f2204]) ).
thf(f2204,plain,
! [X1: nat] :
( $true
= ( !! @ set_nat
@ ^ [Y0: set_nat] :
( ( ( type_M141510067scheme @ nil_Ty61485117scheme )
= Y0 )
=> ~ ( member_nat @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2203]) ).
thf(f2203,plain,
! [X1: nat] :
( $true
= ( ^ [Y0: nat] :
( !! @ set_nat
@ ^ [Y1: set_nat] :
( ( ( type_M141510067scheme @ nil_Ty61485117scheme )
= Y1 )
=> ~ ( member_nat @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f1505]) ).
thf(f1505,plain,
( $true
= ( !! @ nat
@ ^ [Y0: nat] :
( !! @ set_nat
@ ^ [Y1: set_nat] :
( ( ( type_M141510067scheme @ nil_Ty61485117scheme )
= Y1 )
=> ~ ( member_nat @ Y0 @ Y1 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1148,f1124]) ).
thf(f1148,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ set_nat
@ ^ [Y1: set_nat] :
( ( bot_bot_set_nat = Y1 )
=> ~ ( member_nat @ Y0 @ Y1 ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f686]) ).
thf(f686,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ set_nat
@ ^ [Y1: set_nat] :
( ( bot_bot_set_nat = Y1 )
=> ~ ( member_nat @ Y0 @ Y1 ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f685]) ).
thf(f685,plain,
! [X0: set_nat,X1: nat] :
( ( bot_bot_set_nat = X0 )
=> ~ ( member_nat @ X1 @ X0 ) ),
inference(rectify,[status(thm)],[f68]) ).
thf(f68,axiom,
! [X46: set_nat,X40: nat] :
( ( bot_bot_set_nat = X46 )
=> ~ ( member_nat @ X40 @ X46 ) ),
file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_67_equals0D) ).
thf(f2317,plain,
! [X2: nat > $o,X1: nat] :
( ( X2 @ X1 )
= ( member_nat @ X1 @ ( collect_nat @ X2 ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f2316]) ).
thf(f2316,plain,
! [X2: nat > $o,X1: nat] :
( ( ( member_nat @ X1 @ ( collect_nat @ X2 ) )
= ( X2 @ X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f2315]) ).
thf(f2315,plain,
! [X2: nat > $o,X1: nat] :
( $true
= ( ^ [Y0: nat > $o] :
( ( member_nat @ X1 @ ( collect_nat @ Y0 ) )
= ( Y0 @ X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f2310]) ).
thf(f2310,plain,
! [X1: nat] :
( $true
= ( !! @ ( nat > $o )
@ ^ [Y0: nat > $o] :
( ( member_nat @ X1 @ ( collect_nat @ Y0 ) )
= ( Y0 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2309]) ).
thf(f2309,plain,
! [X1: nat] :
( ( ^ [Y0: nat] :
( !! @ ( nat > $o )
@ ^ [Y1: nat > $o] :
( ( member_nat @ Y0 @ ( collect_nat @ Y1 ) )
= ( Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f1161]) ).
thf(f1161,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ ( nat > $o )
@ ^ [Y1: nat > $o] :
( ( member_nat @ Y0 @ ( collect_nat @ Y1 ) )
= ( Y1 @ Y0 ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f515]) ).
thf(f515,plain,
( ( !! @ nat
@ ^ [Y0: nat] :
( !! @ ( nat > $o )
@ ^ [Y1: nat > $o] :
( ( member_nat @ Y0 @ ( collect_nat @ Y1 ) )
= ( Y1 @ Y0 ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f514]) ).
thf(f514,plain,
! [X0: nat > $o,X1: nat] :
( ( member_nat @ X1 @ ( collect_nat @ X0 ) )
= ( X0 @ X1 ) ),
inference(rectify,[status(thm)],[f59]) ).
thf(f59,axiom,
! [X33: nat > $o,X40: nat] :
( ( member_nat @ X40 @ ( collect_nat @ X33 ) )
= ( X33 @ X40 ) ),
file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_58_mem__Collect__eq) ).
thf(f3299,plain,
( ( member_nat @ n @ ( type_M49385309le_typ @ ( type_M405566558_subst @ x ) ) )
= $true ),
inference(not_proxy_clausification,[status(thm)],[f3263]) ).
thf(f3263,plain,
( $false
= ( ~ ( member_nat @ n @ ( type_M49385309le_typ @ ( type_M405566558_subst @ x ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f3262]) ).
thf(f3262,plain,
( ( $false
= ( ~ ( member_nat @ n @ ( type_M49385309le_typ @ ( type_M405566558_subst @ x ) ) ) ) )
| ( $false = $true ) ),
inference(boolean_simplification,[status(thm)],[f3261]) ).
thf(f3261,plain,
( ( $false
= ( ~ ( member_nat @ n @ ( type_M49385309le_typ @ ( type_M405566558_subst @ x ) ) ) ) )
| ( $true = ( ~ $true ) ) ),
inference(boolean_simplification,[status(thm)],[f3244]) ).
thf(f3244,plain,
( ( $false
= ( ~ ( member_nat @ n @ ( type_M49385309le_typ @ ( type_M405566558_subst @ x ) ) ) ) )
| ( $true
= ( ~ ( ( ( type_M1006385707scheme @ ( s1 @ x ) )
!= ( type_M1006385707scheme @ ( s2 @ x ) ) )
| ( ( s1 @ n )
= ( s2 @ n ) )
| $true ) ) ) ),
inference(superposition,[status(thm)],[f2534,f2294]) ).
thf(f3821,plain,
( ( s2 @ x )
= ( s1 @ x ) ),
inference(equality_proxy_clausification,[status(thm)],[f3790]) ).
thf(f3790,plain,
( ( ( s1 @ x )
= ( s2 @ x ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f3789]) ).
thf(f3789,plain,
( ( $true
=> ( ( s1 @ x )
= ( s2 @ x ) ) )
= $true ),
inference(superposition,[status(thm)],[f2269,f3758]) ).
thf(f3758,plain,
( ( ( type_M1006385707scheme @ ( s1 @ x ) )
= ( type_M1006385707scheme @ ( s2 @ x ) ) )
= $true ),
inference(not_proxy_clausification,[status(thm)],[f3277]) ).
thf(f3277,plain,
( ( ( type_M1006385707scheme @ ( s1 @ x ) )
!= ( type_M1006385707scheme @ ( s2 @ x ) ) )
= $false ),
inference(boolean_simplification,[status(thm)],[f3276]) ).
thf(f3276,plain,
( $false
= ( ( ( type_M1006385707scheme @ ( s1 @ x ) )
!= ( type_M1006385707scheme @ ( s2 @ x ) ) )
| $false ) ),
inference(backward_demodulation,[status(thm)],[f3273,f3263]) ).
thf(f3273,plain,
( $false
= ( ( ( type_M1006385707scheme @ ( s1 @ x ) )
!= ( type_M1006385707scheme @ ( s2 @ x ) ) )
| ~ ( member_nat @ n @ ( type_M49385309le_typ @ ( type_M405566558_subst @ x ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f3272]) ).
thf(f3272,plain,
( $false
= ( ( ( type_M1006385707scheme @ ( s1 @ x ) )
!= ( type_M1006385707scheme @ ( s2 @ x ) ) )
| $false
| ~ ( member_nat @ n @ ( type_M49385309le_typ @ ( type_M405566558_subst @ x ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f3265,f3269]) ).
thf(f3265,plain,
( $false
= ( ( ( type_M1006385707scheme @ ( s1 @ x ) )
!= ( type_M1006385707scheme @ ( s2 @ x ) ) )
| ( ( s1 @ n )
= ( s2 @ n ) )
| ~ ( member_nat @ n @ ( type_M49385309le_typ @ ( type_M405566558_subst @ x ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f3264]) ).
thf(f3264,plain,
( ( $false = $true )
| ( $false
= ( ( ( type_M1006385707scheme @ ( s1 @ x ) )
!= ( type_M1006385707scheme @ ( s2 @ x ) ) )
| ( ( s1 @ n )
= ( s2 @ n ) )
| ~ ( member_nat @ n @ ( type_M49385309le_typ @ ( type_M405566558_subst @ x ) ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f3249]) ).
thf(f3249,plain,
( ( $false
= ( ( ( type_M1006385707scheme @ ( s1 @ x ) )
!= ( type_M1006385707scheme @ ( s2 @ x ) ) )
| ( ( s1 @ n )
= ( s2 @ n ) )
| ~ ( member_nat @ n @ ( type_M49385309le_typ @ ( type_M405566558_subst @ x ) ) ) ) )
| ( $true = ( ~ $true ) ) ),
inference(superposition,[status(thm)],[f2534,f2294]) ).
thf(f2269,plain,
! [X2: type_Mirabelle_typ,X1: type_Mirabelle_typ] :
( $true
= ( ( ( type_M1006385707scheme @ X2 )
= ( type_M1006385707scheme @ X1 ) )
=> ( X2 = X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2268]) ).
thf(f2268,plain,
! [X2: type_Mirabelle_typ,X1: type_Mirabelle_typ] :
( ( ^ [Y0: type_Mirabelle_typ] :
( ( ( type_M1006385707scheme @ Y0 )
= ( type_M1006385707scheme @ X1 ) )
=> ( Y0 = X1 ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f2267]) ).
thf(f2267,plain,
! [X1: type_Mirabelle_typ] :
( $true
= ( !! @ type_Mirabelle_typ
@ ^ [Y0: type_Mirabelle_typ] :
( ( ( type_M1006385707scheme @ Y0 )
= ( type_M1006385707scheme @ X1 ) )
=> ( Y0 = X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2266]) ).
thf(f2266,plain,
! [X1: type_Mirabelle_typ] :
( ( ^ [Y0: type_Mirabelle_typ] :
( !! @ type_Mirabelle_typ
@ ^ [Y1: type_Mirabelle_typ] :
( ( ( type_M1006385707scheme @ Y1 )
= ( type_M1006385707scheme @ Y0 ) )
=> ( Y1 = Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f1396]) ).
thf(f1396,plain,
( $true
= ( !! @ type_Mirabelle_typ
@ ^ [Y0: type_Mirabelle_typ] :
( !! @ type_Mirabelle_typ
@ ^ [Y1: type_Mirabelle_typ] :
( ( ( type_M1006385707scheme @ Y1 )
= ( type_M1006385707scheme @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f998]) ).
thf(f998,plain,
( $true
= ( !! @ type_Mirabelle_typ
@ ^ [Y0: type_Mirabelle_typ] :
( !! @ type_Mirabelle_typ
@ ^ [Y1: type_Mirabelle_typ] :
( ( ( type_M1006385707scheme @ Y1 )
= ( type_M1006385707scheme @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f997]) ).
thf(f997,plain,
! [X0: type_Mirabelle_typ,X1: type_Mirabelle_typ] :
( ( ( type_M1006385707scheme @ X0 )
= ( type_M1006385707scheme @ X1 ) )
=> ( X0 = X1 ) ),
inference(rectify,[status(thm)],[f36]) ).
thf(f36,axiom,
! [X17: type_Mirabelle_typ,X27: type_Mirabelle_typ] :
( ( ( type_M1006385707scheme @ X17 )
= ( type_M1006385707scheme @ X27 ) )
=> ( X17 = X27 ) ),
file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_35_mk__scheme__injective) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : ITP197^1 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.14 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.35 % Computer : n028.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Feb 24 08:30:27 EST 2026
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.48 ---- Original DTF file ---
% 0.31/0.48 thf(spec,logic,$$dhol).
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 % File : ITP197^1 : TPTP v9.2.1. Released v7.5.0.
% 0.31/0.48 % Domain : Interactive Theorem Proving
% 0.31/0.48 % Problem : Sledgehammer Type problem prob_386__3259180_1
% 0.31/0.48 % Version : Especial.
% 0.31/0.48 % English :
% 0.31/0.48
% 0.31/0.48 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.31/0.48 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.31/0.48 % Source : [Des21]
% 0.31/0.48 % Names : Type/prob_386__3259180_1 [Des21]
% 0.31/0.48
% 0.31/0.48 % Status : Theorem
% 0.31/0.48 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0
% 0.31/0.48 % Syntax : Number of formulae : 463 ( 194 unt; 103 typ; 0 def)
% 0.31/0.48 % Number of atoms : 1024 ( 428 equ; 0 cnn)
% 0.31/0.48 % Maximal formula atoms : 10 ( 2 avg)
% 0.31/0.48 % Number of connectives : 2773 ( 147 ~; 28 |; 82 &;2109 @)
% 0.31/0.48 % ( 0 <=>; 407 =>; 0 <=; 0 <~>)
% 0.31/0.48 % Maximal formula depth : 20 ( 6 avg)
% 0.31/0.48 % Number of types : 15 ( 14 usr)
% 0.31/0.48 % Number of type conns : 442 ( 442 >; 0 *; 0 +; 0 <<)
% 0.31/0.48 % Number of symbols : 92 ( 89 usr; 11 con; 0-3 aty)
% 0.31/0.48 % Number of variables : 1070 ( 86 ^; 935 !; 49 ?;1070 :)
% 0.31/0.48 % SPC : TH0_THM_EQU_NAR
% 0.31/0.48
% 0.31/0.48 % Comments : This file was generated by Sledgehammer 2021-02-23 15:34:01.522
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 % Could-be-implicit typings (14)
% 0.31/0.48 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J_J_J,type,
% 0.31/0.48 list_l1704431731scheme: $tType ).
% 0.31/0.48
% 0.31/0.48 thf(ty_n_t__List__Olist_It__List__Olist_I_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J_J_J,type,
% 0.31/0.48 list_l865305402le_typ: $tType ).
% 0.31/0.48
% 0.31/0.48 thf(ty_n_t__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J_J,type,
% 0.31/0.48 list_l1334080099scheme: $tType ).
% 0.31/0.48
% 0.31/0.48 thf(ty_n_t__List__Olist_I_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J_J,type,
% 0.31/0.48 list_n396811828le_typ: $tType ).
% 0.31/0.48
% 0.31/0.48 thf(ty_n_t__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otyp_J_J,type,
% 0.31/0.48 list_l1790670291le_typ: $tType ).
% 0.31/0.48
% 0.31/0.48 thf(ty_n_t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J,type,
% 0.31/0.48 list_T247403987scheme: $tType ).
% 0.31/0.48
% 0.31/0.48 thf(ty_n_t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otyp_J,type,
% 0.31/0.48 list_T1103309005le_typ: $tType ).
% 0.31/0.48
% 0.31/0.48 thf(ty_n_t__Type____Mirabelle____lczmhmumaa__Otype____scheme,type,
% 0.31/0.48 type_M1694694083scheme: $tType ).
% 0.31/0.48
% 0.31/0.48 thf(ty_n_t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.31/0.48 list_set_nat: $tType ).
% 0.31/0.48
% 0.31/0.48 thf(ty_n_t__List__Olist_I_062_It__Nat__Onat_M_Eo_J_J,type,
% 0.31/0.48 list_nat_o: $tType ).
% 0.31/0.48
% 0.31/0.48 thf(ty_n_t__Type____Mirabelle____lczmhmumaa__Otyp,type,
% 0.31/0.48 type_Mirabelle_typ: $tType ).
% 0.31/0.48
% 0.31/0.48 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 0.31/0.48 list_nat: $tType ).
% 0.31/0.48
% 0.31/0.48 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.31/0.48 set_nat: $tType ).
% 0.31/0.48
% 0.31/0.48 thf(ty_n_t__Nat__Onat,type,
% 0.31/0.48 nat: $tType ).
% 0.31/0.48
% 0.31/0.48 % Explicit typings (89)
% 0.31/0.48 thf(sy_c_HOL_OThe_001t__Nat__Onat,type,
% 0.31/0.48 the_nat: ( nat > $o ) > nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_If_001t__Nat__Onat,type,
% 0.31/0.48 if_nat: $o > nat > nat > nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_If_001t__Type____Mirabelle____lczmhmumaa__Otyp,type,
% 0.31/0.48 if_Typ1169047309le_typ: $o > type_Mirabelle_typ > type_Mirabelle_typ > type_Mirabelle_typ ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Lattices_Osemilattice__neutr_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.31/0.48 semila1414375521_nat_o: ( ( nat > $o ) > ( nat > $o ) > nat > $o ) > ( nat > $o ) > $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Lattices_Osemilattice__neutr_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.31/0.48 semila1369944356et_nat: ( set_nat > set_nat > set_nat ) > set_nat > $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.31/0.48 sup_sup_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 0.31/0.48 sup_sup_nat: nat > nat > nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.31/0.48 sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Olist_OCons_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.31/0.48 cons_nat_o: ( nat > $o ) > list_nat_o > list_nat_o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Olist_OCons_001_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J,type,
% 0.31/0.48 cons_n499085924le_typ: ( nat > type_Mirabelle_typ ) > list_n396811828le_typ > list_n396811828le_typ ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Olist_OCons_001t__List__Olist_I_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J_J,type,
% 0.31/0.48 cons_l1800589546le_typ: list_n396811828le_typ > list_l865305402le_typ > list_l865305402le_typ ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J_J,type,
% 0.31/0.48 cons_l531914285scheme: list_l1334080099scheme > list_l1704431731scheme > list_l1704431731scheme ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otyp_J,type,
% 0.31/0.48 cons_l392684675le_typ: list_T1103309005le_typ > list_l1790670291le_typ > list_l1790670291le_typ ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J,type,
% 0.31/0.48 cons_l1910959773scheme: list_T247403987scheme > list_l1334080099scheme > list_l1334080099scheme ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 0.31/0.48 cons_nat: nat > list_nat > list_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Olist_OCons_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.31/0.48 cons_set_nat: set_nat > list_set_nat > list_set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Olist_OCons_001t__Type____Mirabelle____lczmhmumaa__Otyp,type,
% 0.31/0.48 cons_T363929085le_typ: type_Mirabelle_typ > list_T1103309005le_typ > list_T1103309005le_typ ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Olist_OCons_001t__Type____Mirabelle____lczmhmumaa__Otype____scheme,type,
% 0.31/0.48 cons_T633159821scheme: type_M1694694083scheme > list_T247403987scheme > list_T247403987scheme ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Olist_ONil_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.31/0.48 nil_nat_o: list_nat_o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 0.31/0.48 nil_nat: list_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Olist_ONil_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.31/0.48 nil_set_nat: list_set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Olist_ONil_001t__Type____Mirabelle____lczmhmumaa__Otype____scheme,type,
% 0.31/0.48 nil_Ty61485117scheme: list_T247403987scheme ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Oord__class_Olexordp__eq_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.31/0.48 ord_lexordp_eq_nat_o: list_nat_o > list_nat_o > $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Oord__class_Olexordp__eq_001t__Nat__Onat,type,
% 0.31/0.48 ord_lexordp_eq_nat: list_nat > list_nat > $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Oord__class_Olexordp__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.31/0.48 ord_le727790544et_nat: list_set_nat > list_set_nat > $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.31/0.48 bot_bot_nat_o: nat > $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Orderings_Obot__class_Obot_001_Eo,type,
% 0.31/0.48 bot_bot_o: $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Orderings_Obot__class_Obot_001t__Nat__Onat,type,
% 0.31/0.48 bot_bot_nat: nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.31/0.48 bot_bot_set_nat: set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Orderings_Oord__class_Oless_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.31/0.48 ord_less_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.31/0.48 ord_less_nat: nat > nat > $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.31/0.48 ord_less_set_nat: set_nat > set_nat > $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.31/0.48 collect_nat: ( nat > $o ) > set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 0.31/0.48 insert_nat: nat > set_nat > set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Set_Ois__empty_001t__Nat__Onat,type,
% 0.31/0.48 is_empty_nat: set_nat > $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Set_Ois__singleton_001t__Nat__Onat,type,
% 0.31/0.48 is_singleton_nat: set_nat > $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Set_Othe__elem_001t__Nat__Onat,type,
% 0.31/0.48 the_elem_nat: set_nat > nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Ocod,type,
% 0.31/0.48 type_Mirabelle_cod: ( nat > type_Mirabelle_typ ) > set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Odom,type,
% 0.31/0.48 type_Mirabelle_dom: ( nat > type_Mirabelle_typ ) > set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Oid__subst,type,
% 0.31/0.48 type_M405566558_subst: nat > type_Mirabelle_typ ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Omk__scheme,type,
% 0.31/0.48 type_M1006385707scheme: type_Mirabelle_typ > type_M1694694083scheme ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Onew__tv_001_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J,type,
% 0.31/0.48 type_M1734147655le_typ: nat > ( nat > type_Mirabelle_typ ) > $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Onew__tv_001t__List__Olist_I_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J_J,type,
% 0.31/0.48 type_M244876119le_typ: nat > list_n396811828le_typ > $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Onew__tv_001t__List__Olist_It__List__Olist_I_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J_J_J,type,
% 0.31/0.48 type_M2086816231le_typ: nat > list_l865305402le_typ > $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Onew__tv_001t__List__Olist_It__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J_J_J,type,
% 0.31/0.48 type_M1172169604scheme: nat > list_l1704431731scheme > $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Onew__tv_001t__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otyp_J_J,type,
% 0.31/0.48 type_M1826376056le_typ: nat > list_l1790670291le_typ > $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Onew__tv_001t__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J_J,type,
% 0.31/0.48 type_M1377662078scheme: nat > list_l1334080099scheme > $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Onew__tv_001t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otyp_J,type,
% 0.31/0.48 type_M263553000le_typ: nat > list_T1103309005le_typ > $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Onew__tv_001t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J,type,
% 0.31/0.48 type_M2064939256scheme: nat > list_T247403987scheme > $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Onew__tv_001t__Type____Mirabelle____lczmhmumaa__Otyp,type,
% 0.31/0.48 type_M1211611096le_typ: nat > type_Mirabelle_typ > $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Onew__tv_001t__Type____Mirabelle____lczmhmumaa__Otype____scheme,type,
% 0.31/0.48 type_M1963061490scheme: nat > type_M1694694083scheme > $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Oof__nat__class_Oof__nat_001t__Nat__Onat,type,
% 0.31/0.48 type_M1898948661at_nat: nat > nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otyp_OFun,type,
% 0.31/0.48 type_Mirabelle_Fun: type_Mirabelle_typ > type_Mirabelle_typ > type_Mirabelle_typ ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otyp_OTVar,type,
% 0.31/0.48 type_Mirabelle_TVar: nat > type_Mirabelle_typ ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otyp__of__class_Otyp__of_001t__Type____Mirabelle____lczmhmumaa__Otyp,type,
% 0.31/0.48 type_M1743451154le_typ: type_Mirabelle_typ > type_Mirabelle_typ ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__scheme_OBVar,type,
% 0.31/0.48 type_M2048935292e_BVar: nat > type_M1694694083scheme ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__scheme_OFVar,type,
% 0.31/0.48 type_M876316792e_FVar: nat > type_M1694694083scheme ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__scheme_OSFun,type,
% 0.31/0.48 type_M155660035e_SFun: type_M1694694083scheme > type_M1694694083scheme > type_M1694694083scheme ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Oapp__subst_001_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J,type,
% 0.31/0.48 type_M1158474302le_typ: ( nat > type_Mirabelle_typ ) > ( nat > type_Mirabelle_typ ) > nat > type_Mirabelle_typ ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Oapp__subst_001t__List__Olist_I_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J_J,type,
% 0.31/0.48 type_M737052622le_typ: ( nat > type_Mirabelle_typ ) > list_n396811828le_typ > list_n396811828le_typ ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Oapp__subst_001t__List__Olist_It__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J_J_J,type,
% 0.31/0.48 type_M1385924301scheme: ( nat > type_Mirabelle_typ ) > list_l1704431731scheme > list_l1704431731scheme ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Oapp__subst_001t__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otyp_J_J,type,
% 0.31/0.48 type_M1913464047le_typ: ( nat > type_Mirabelle_typ ) > list_l1790670291le_typ > list_l1790670291le_typ ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Oapp__subst_001t__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J_J,type,
% 0.31/0.48 type_M1061687367scheme: ( nat > type_Mirabelle_typ ) > list_l1334080099scheme > list_l1334080099scheme ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Oapp__subst_001t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otyp_J,type,
% 0.31/0.48 type_M1440203487le_typ: ( nat > type_Mirabelle_typ ) > list_T1103309005le_typ > list_T1103309005le_typ ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Oapp__subst_001t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J,type,
% 0.31/0.48 type_M1944210753scheme: ( nat > type_Mirabelle_typ ) > list_T247403987scheme > list_T247403987scheme ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Oapp__subst_001t__Type____Mirabelle____lczmhmumaa__Otyp,type,
% 0.31/0.48 type_M784671311le_typ: ( nat > type_Mirabelle_typ ) > type_Mirabelle_typ > type_Mirabelle_typ ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Oapp__subst_001t__Type____Mirabelle____lczmhmumaa__Otype____scheme,type,
% 0.31/0.48 type_M1690910139scheme: ( nat > type_Mirabelle_typ ) > type_M1694694083scheme > type_M1694694083scheme ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Obound__tv_001_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J,type,
% 0.31/0.48 type_M772783356le_typ: ( nat > type_Mirabelle_typ ) > set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Obound__tv_001t__List__Olist_I_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J_J,type,
% 0.31/0.48 type_M513401740le_typ: list_n396811828le_typ > set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Obound__tv_001t__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J_J,type,
% 0.31/0.48 type_M1496178953scheme: list_l1334080099scheme > set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Obound__tv_001t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otyp_J,type,
% 0.31/0.48 type_M1539052445le_typ: list_T1103309005le_typ > set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Obound__tv_001t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J,type,
% 0.31/0.48 type_M961603331scheme: list_T247403987scheme > set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Obound__tv_001t__Type____Mirabelle____lczmhmumaa__Otyp,type,
% 0.31/0.48 type_M801073677le_typ: type_Mirabelle_typ > set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Obound__tv_001t__Type____Mirabelle____lczmhmumaa__Otype____scheme,type,
% 0.31/0.48 type_M326705277scheme: type_M1694694083scheme > set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Ofree__tv_001_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J,type,
% 0.31/0.48 type_M1715972684le_typ: ( nat > type_Mirabelle_typ ) > set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Ofree__tv_001t__List__Olist_I_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J_J,type,
% 0.31/0.48 type_M1691543772le_typ: list_n396811828le_typ > set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Ofree__tv_001t__List__Olist_It__List__Olist_I_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J_J_J,type,
% 0.31/0.48 type_M906078444le_typ: list_l865305402le_typ > set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Ofree__tv_001t__List__Olist_It__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J_J_J,type,
% 0.31/0.48 type_M1926053183scheme: list_l1704431731scheme > set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Ofree__tv_001t__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otyp_J_J,type,
% 0.31/0.48 type_M1418941437le_typ: list_l1790670291le_typ > set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Ofree__tv_001t__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J_J,type,
% 0.31/0.48 type_M1958029241scheme: list_l1334080099scheme > set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Ofree__tv_001t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otyp_J,type,
% 0.31/0.48 type_M510873837le_typ: list_T1103309005le_typ > set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Ofree__tv_001t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J,type,
% 0.31/0.48 type_M141510067scheme: list_T247403987scheme > set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Ofree__tv_001t__Type____Mirabelle____lczmhmumaa__Otyp,type,
% 0.31/0.48 type_M49385309le_typ: type_Mirabelle_typ > set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Ofree__tv_001t__Type____Mirabelle____lczmhmumaa__Otype____scheme,type,
% 0.31/0.48 type_M1050318637scheme: type_M1694694083scheme > set_nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_member_001t__Nat__Onat,type,
% 0.31/0.48 member_nat: nat > set_nat > $o ).
% 0.31/0.48
% 0.31/0.48 thf(sy_v_S1,type,
% 0.31/0.48 s1: nat > type_Mirabelle_typ ).
% 0.31/0.48
% 0.31/0.48 thf(sy_v_S2,type,
% 0.31/0.48 s2: nat > type_Mirabelle_typ ).
% 0.31/0.48
% 0.31/0.48 thf(sy_v_n,type,
% 0.31/0.48 n: nat ).
% 0.31/0.48
% 0.31/0.48 thf(sy_v_x,type,
% 0.31/0.48 x: nat ).
% 0.31/0.48
% 0.31/0.48 % Relevant facts (354)
% 0.31/0.48 thf(fact_0_type__scheme_Oinject_I1_J,axiom,
% 0.31/0.48 ! [X1: nat,Y1: nat] :
% 0.31/0.48 ( ( ( type_M876316792e_FVar @ X1 )
% 0.31/0.48 = ( type_M876316792e_FVar @ Y1 ) )
% 0.31/0.48 = ( X1 = Y1 ) ) ).
% 0.31/0.48
% 0.31/0.48 % type_scheme.inject(1)
% 0.31/0.48 thf(fact_1_eq__free__eq__subst__type__scheme,axiom,
% 0.31/0.48 ! [Sch: type_M1694694083scheme,S1: nat > type_Mirabelle_typ,S2: nat > type_Mirabelle_typ] :
% 0.31/0.48 ( ! [N: nat] :
% 0.31/0.48 ( ( member_nat @ N @ ( type_M1050318637scheme @ Sch ) )
% 0.31/0.48 => ( ( S1 @ N )
% 0.31/0.48 = ( S2 @ N ) ) )
% 0.31/0.48 => ( ( type_M1690910139scheme @ S1 @ Sch )
% 0.31/0.48 = ( type_M1690910139scheme @ S2 @ Sch ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % eq_free_eq_subst_type_scheme
% 0.31/0.48 thf(fact_2_scheme__substitutions__only__on__free__variables,axiom,
% 0.31/0.48 ! [Sch: type_M1694694083scheme,S: nat > type_Mirabelle_typ,S3: nat > type_Mirabelle_typ] :
% 0.31/0.48 ( ! [X: nat] :
% 0.31/0.48 ( ( member_nat @ X @ ( type_M1050318637scheme @ Sch ) )
% 0.31/0.48 => ( ( S @ X )
% 0.31/0.48 = ( S3 @ X ) ) )
% 0.31/0.48 => ( ( type_M1690910139scheme @ S @ Sch )
% 0.31/0.48 = ( type_M1690910139scheme @ S3 @ Sch ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % scheme_substitutions_only_on_free_variables
% 0.31/0.48 thf(fact_3_app__subst__type__scheme_Osimps_I1_J,axiom,
% 0.31/0.48 ! [S: nat > type_Mirabelle_typ,N2: nat] :
% 0.31/0.48 ( ( type_M1690910139scheme @ S @ ( type_M876316792e_FVar @ N2 ) )
% 0.31/0.48 = ( type_M1006385707scheme @ ( S @ N2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % app_subst_type_scheme.simps(1)
% 0.31/0.48 thf(fact_4_app__subst__type__scheme_Osimps_I2_J,axiom,
% 0.31/0.48 ! [S: nat > type_Mirabelle_typ,N2: nat] :
% 0.31/0.48 ( ( type_M1690910139scheme @ S @ ( type_M2048935292e_BVar @ N2 ) )
% 0.31/0.48 = ( type_M2048935292e_BVar @ N2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % app_subst_type_scheme.simps(2)
% 0.31/0.48 thf(fact_5_app__subst__type__scheme_Osimps_I3_J,axiom,
% 0.31/0.48 ! [S: nat > type_Mirabelle_typ,Sch1: type_M1694694083scheme,Sch2: type_M1694694083scheme] :
% 0.31/0.48 ( ( type_M1690910139scheme @ S @ ( type_M155660035e_SFun @ Sch1 @ Sch2 ) )
% 0.31/0.48 = ( type_M155660035e_SFun @ ( type_M1690910139scheme @ S @ Sch1 ) @ ( type_M1690910139scheme @ S @ Sch2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % app_subst_type_scheme.simps(3)
% 0.31/0.48 thf(fact_6_type__scheme_Odistinct_I1_J,axiom,
% 0.31/0.48 ! [X1: nat,X2: nat] :
% 0.31/0.48 ( ( type_M876316792e_FVar @ X1 )
% 0.31/0.48 != ( type_M2048935292e_BVar @ X2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % type_scheme.distinct(1)
% 0.31/0.48 thf(fact_7_type__scheme_Odistinct_I3_J,axiom,
% 0.31/0.48 ! [X1: nat,X31: type_M1694694083scheme,X32: type_M1694694083scheme] :
% 0.31/0.48 ( ( type_M876316792e_FVar @ X1 )
% 0.31/0.48 != ( type_M155660035e_SFun @ X31 @ X32 ) ) ).
% 0.31/0.48
% 0.31/0.48 % type_scheme.distinct(3)
% 0.31/0.48 thf(fact_8_app__subst__Cons,axiom,
% 0.31/0.48 ! [S: nat > type_Mirabelle_typ,X3: nat > type_Mirabelle_typ,L: list_n396811828le_typ] :
% 0.31/0.48 ( ( type_M737052622le_typ @ S @ ( cons_n499085924le_typ @ X3 @ L ) )
% 0.31/0.48 = ( cons_n499085924le_typ @ ( type_M1158474302le_typ @ S @ X3 ) @ ( type_M737052622le_typ @ S @ L ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % app_subst_Cons
% 0.31/0.48 thf(fact_9_app__subst__Cons,axiom,
% 0.31/0.48 ! [S: nat > type_Mirabelle_typ,X3: list_l1334080099scheme,L: list_l1704431731scheme] :
% 0.31/0.48 ( ( type_M1385924301scheme @ S @ ( cons_l531914285scheme @ X3 @ L ) )
% 0.31/0.48 = ( cons_l531914285scheme @ ( type_M1061687367scheme @ S @ X3 ) @ ( type_M1385924301scheme @ S @ L ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % app_subst_Cons
% 0.31/0.48 thf(fact_10_app__subst__Cons,axiom,
% 0.31/0.48 ! [S: nat > type_Mirabelle_typ,X3: list_T1103309005le_typ,L: list_l1790670291le_typ] :
% 0.31/0.48 ( ( type_M1913464047le_typ @ S @ ( cons_l392684675le_typ @ X3 @ L ) )
% 0.31/0.48 = ( cons_l392684675le_typ @ ( type_M1440203487le_typ @ S @ X3 ) @ ( type_M1913464047le_typ @ S @ L ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % app_subst_Cons
% 0.31/0.48 thf(fact_11_app__subst__Cons,axiom,
% 0.31/0.48 ! [S: nat > type_Mirabelle_typ,X3: type_Mirabelle_typ,L: list_T1103309005le_typ] :
% 0.31/0.48 ( ( type_M1440203487le_typ @ S @ ( cons_T363929085le_typ @ X3 @ L ) )
% 0.31/0.48 = ( cons_T363929085le_typ @ ( type_M784671311le_typ @ S @ X3 ) @ ( type_M1440203487le_typ @ S @ L ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % app_subst_Cons
% 0.31/0.48 thf(fact_12_app__subst__Cons,axiom,
% 0.31/0.48 ! [S: nat > type_Mirabelle_typ,X3: list_T247403987scheme,L: list_l1334080099scheme] :
% 0.31/0.48 ( ( type_M1061687367scheme @ S @ ( cons_l1910959773scheme @ X3 @ L ) )
% 0.31/0.48 = ( cons_l1910959773scheme @ ( type_M1944210753scheme @ S @ X3 ) @ ( type_M1061687367scheme @ S @ L ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % app_subst_Cons
% 0.31/0.48 thf(fact_13_app__subst__Cons,axiom,
% 0.31/0.48 ! [S: nat > type_Mirabelle_typ,X3: type_M1694694083scheme,L: list_T247403987scheme] :
% 0.31/0.48 ( ( type_M1944210753scheme @ S @ ( cons_T633159821scheme @ X3 @ L ) )
% 0.31/0.48 = ( cons_T633159821scheme @ ( type_M1690910139scheme @ S @ X3 ) @ ( type_M1944210753scheme @ S @ L ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % app_subst_Cons
% 0.31/0.48 thf(fact_14_free__tv__mk__scheme,axiom,
% 0.31/0.48 ! [T: type_Mirabelle_typ] :
% 0.31/0.48 ( ( type_M1050318637scheme @ ( type_M1006385707scheme @ T ) )
% 0.31/0.48 = ( type_M49385309le_typ @ T ) ) ).
% 0.31/0.48
% 0.31/0.48 % free_tv_mk_scheme
% 0.31/0.48 thf(fact_15_free__tv__type__scheme_Osimps_I1_J,axiom,
% 0.31/0.48 ! [M: nat] :
% 0.31/0.48 ( ( type_M1050318637scheme @ ( type_M876316792e_FVar @ M ) )
% 0.31/0.48 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 0.31/0.48
% 0.31/0.48 % free_tv_type_scheme.simps(1)
% 0.31/0.48 thf(fact_16_new__if__subst__type__scheme,axiom,
% 0.31/0.48 ! [N2: nat,Sch: type_M1694694083scheme,S: nat > type_Mirabelle_typ,S3: nat > type_Mirabelle_typ] :
% 0.31/0.48 ( ( type_M1963061490scheme @ N2 @ Sch )
% 0.31/0.48 => ( ( type_M1690910139scheme
% 0.31/0.48 @ ^ [K: nat] : ( if_Typ1169047309le_typ @ ( ord_less_nat @ K @ N2 ) @ ( S @ K ) @ ( S3 @ K ) )
% 0.31/0.48 @ Sch )
% 0.31/0.48 = ( type_M1690910139scheme @ S @ Sch ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % new_if_subst_type_scheme
% 0.31/0.48 thf(fact_17_type__scheme_Oinject_I3_J,axiom,
% 0.31/0.48 ! [X31: type_M1694694083scheme,X32: type_M1694694083scheme,Y31: type_M1694694083scheme,Y32: type_M1694694083scheme] :
% 0.31/0.48 ( ( ( type_M155660035e_SFun @ X31 @ X32 )
% 0.31/0.48 = ( type_M155660035e_SFun @ Y31 @ Y32 ) )
% 0.31/0.48 = ( ( X31 = Y31 )
% 0.31/0.48 & ( X32 = Y32 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % type_scheme.inject(3)
% 0.31/0.48 thf(fact_18_type__scheme_Oinject_I2_J,axiom,
% 0.31/0.48 ! [X2: nat,Y2: nat] :
% 0.31/0.48 ( ( ( type_M2048935292e_BVar @ X2 )
% 0.31/0.48 = ( type_M2048935292e_BVar @ Y2 ) )
% 0.31/0.48 = ( X2 = Y2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % type_scheme.inject(2)
% 0.31/0.48 thf(fact_19_new__tv__Cons,axiom,
% 0.31/0.48 ! [N2: nat,X3: list_n396811828le_typ,L: list_l865305402le_typ] :
% 0.31/0.48 ( ( type_M2086816231le_typ @ N2 @ ( cons_l1800589546le_typ @ X3 @ L ) )
% 0.31/0.48 = ( ( type_M244876119le_typ @ N2 @ X3 )
% 0.31/0.48 & ( type_M2086816231le_typ @ N2 @ L ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % new_tv_Cons
% 0.31/0.48 thf(fact_20_new__tv__Cons,axiom,
% 0.31/0.48 ! [N2: nat,X3: list_T1103309005le_typ,L: list_l1790670291le_typ] :
% 0.31/0.48 ( ( type_M1826376056le_typ @ N2 @ ( cons_l392684675le_typ @ X3 @ L ) )
% 0.31/0.48 = ( ( type_M263553000le_typ @ N2 @ X3 )
% 0.31/0.48 & ( type_M1826376056le_typ @ N2 @ L ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % new_tv_Cons
% 0.31/0.48 thf(fact_21_new__tv__Cons,axiom,
% 0.31/0.48 ! [N2: nat,X3: list_l1334080099scheme,L: list_l1704431731scheme] :
% 0.31/0.48 ( ( type_M1172169604scheme @ N2 @ ( cons_l531914285scheme @ X3 @ L ) )
% 0.31/0.48 = ( ( type_M1377662078scheme @ N2 @ X3 )
% 0.31/0.48 & ( type_M1172169604scheme @ N2 @ L ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % new_tv_Cons
% 0.31/0.48 thf(fact_22_new__tv__Cons,axiom,
% 0.31/0.48 ! [N2: nat,X3: list_T247403987scheme,L: list_l1334080099scheme] :
% 0.31/0.48 ( ( type_M1377662078scheme @ N2 @ ( cons_l1910959773scheme @ X3 @ L ) )
% 0.31/0.48 = ( ( type_M2064939256scheme @ N2 @ X3 )
% 0.31/0.48 & ( type_M1377662078scheme @ N2 @ L ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % new_tv_Cons
% 0.31/0.48 thf(fact_23_new__tv__Cons,axiom,
% 0.31/0.48 ! [N2: nat,X3: type_Mirabelle_typ,L: list_T1103309005le_typ] :
% 0.31/0.48 ( ( type_M263553000le_typ @ N2 @ ( cons_T363929085le_typ @ X3 @ L ) )
% 0.31/0.48 = ( ( type_M1211611096le_typ @ N2 @ X3 )
% 0.31/0.48 & ( type_M263553000le_typ @ N2 @ L ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % new_tv_Cons
% 0.31/0.48 thf(fact_24_new__tv__Cons,axiom,
% 0.31/0.48 ! [N2: nat,X3: nat > type_Mirabelle_typ,L: list_n396811828le_typ] :
% 0.31/0.48 ( ( type_M244876119le_typ @ N2 @ ( cons_n499085924le_typ @ X3 @ L ) )
% 0.31/0.48 = ( ( type_M1734147655le_typ @ N2 @ X3 )
% 0.31/0.48 & ( type_M244876119le_typ @ N2 @ L ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % new_tv_Cons
% 0.31/0.48 thf(fact_25_new__tv__Cons,axiom,
% 0.31/0.48 ! [N2: nat,X3: type_M1694694083scheme,L: list_T247403987scheme] :
% 0.31/0.48 ( ( type_M2064939256scheme @ N2 @ ( cons_T633159821scheme @ X3 @ L ) )
% 0.31/0.48 = ( ( type_M1963061490scheme @ N2 @ X3 )
% 0.31/0.48 & ( type_M2064939256scheme @ N2 @ L ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % new_tv_Cons
% 0.31/0.48 thf(fact_26_subst__mk__scheme,axiom,
% 0.31/0.48 ! [S: nat > type_Mirabelle_typ,T: type_Mirabelle_typ] :
% 0.31/0.48 ( ( type_M1690910139scheme @ S @ ( type_M1006385707scheme @ T ) )
% 0.31/0.48 = ( type_M1006385707scheme @ ( type_M784671311le_typ @ S @ T ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % subst_mk_scheme
% 0.31/0.48 thf(fact_27_new__tv__Fun2,axiom,
% 0.31/0.48 ! [N2: nat,T1: type_M1694694083scheme,T2: type_M1694694083scheme] :
% 0.31/0.48 ( ( type_M1963061490scheme @ N2 @ ( type_M155660035e_SFun @ T1 @ T2 ) )
% 0.31/0.48 = ( ( type_M1963061490scheme @ N2 @ T1 )
% 0.31/0.48 & ( type_M1963061490scheme @ N2 @ T2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % new_tv_Fun2
% 0.31/0.48 thf(fact_28_new__tv__BVar,axiom,
% 0.31/0.48 ! [N2: nat,M: nat] : ( type_M1963061490scheme @ N2 @ ( type_M2048935292e_BVar @ M ) ) ).
% 0.31/0.48
% 0.31/0.48 % new_tv_BVar
% 0.31/0.48 thf(fact_29_new__tv__FVar,axiom,
% 0.31/0.48 ! [N2: nat,M: nat] :
% 0.31/0.48 ( ( type_M1963061490scheme @ N2 @ ( type_M876316792e_FVar @ M ) )
% 0.31/0.48 = ( ord_less_nat @ M @ N2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % new_tv_FVar
% 0.31/0.48 thf(fact_30_type__scheme_Odistinct_I5_J,axiom,
% 0.31/0.48 ! [X2: nat,X31: type_M1694694083scheme,X32: type_M1694694083scheme] :
% 0.31/0.48 ( ( type_M2048935292e_BVar @ X2 )
% 0.31/0.48 != ( type_M155660035e_SFun @ X31 @ X32 ) ) ).
% 0.31/0.48
% 0.31/0.48 % type_scheme.distinct(5)
% 0.31/0.48 thf(fact_31_mk__scheme__Fun,axiom,
% 0.31/0.48 ! [T: type_Mirabelle_typ,Sch1: type_M1694694083scheme,Sch2: type_M1694694083scheme] :
% 0.31/0.48 ( ( ( type_M1006385707scheme @ T )
% 0.31/0.48 = ( type_M155660035e_SFun @ Sch1 @ Sch2 ) )
% 0.31/0.48 => ? [T12: type_Mirabelle_typ,T22: type_Mirabelle_typ] :
% 0.31/0.48 ( ( Sch1
% 0.31/0.48 = ( type_M1006385707scheme @ T12 ) )
% 0.31/0.48 & ( Sch2
% 0.31/0.48 = ( type_M1006385707scheme @ T22 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % mk_scheme_Fun
% 0.31/0.48 thf(fact_32_eq__free__eq__subst__te,axiom,
% 0.31/0.48 ! [T: type_Mirabelle_typ,S1: nat > type_Mirabelle_typ,S2: nat > type_Mirabelle_typ] :
% 0.31/0.48 ( ! [N: nat] :
% 0.31/0.48 ( ( member_nat @ N @ ( type_M49385309le_typ @ T ) )
% 0.31/0.48 => ( ( S1 @ N )
% 0.31/0.48 = ( S2 @ N ) ) )
% 0.31/0.48 => ( ( type_M784671311le_typ @ S1 @ T )
% 0.31/0.48 = ( type_M784671311le_typ @ S2 @ T ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % eq_free_eq_subst_te
% 0.31/0.48 thf(fact_33_eq__subst__te__eq__free,axiom,
% 0.31/0.48 ! [S1: nat > type_Mirabelle_typ,T: type_Mirabelle_typ,S2: nat > type_Mirabelle_typ,N2: nat] :
% 0.31/0.48 ( ( ( type_M784671311le_typ @ S1 @ T )
% 0.31/0.48 = ( type_M784671311le_typ @ S2 @ T ) )
% 0.31/0.48 => ( ( member_nat @ N2 @ ( type_M49385309le_typ @ T ) )
% 0.31/0.48 => ( ( S1 @ N2 )
% 0.31/0.48 = ( S2 @ N2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % eq_subst_te_eq_free
% 0.31/0.48 thf(fact_34_typ__substitutions__only__on__free__variables,axiom,
% 0.31/0.48 ! [T: type_Mirabelle_typ,S: nat > type_Mirabelle_typ,S3: nat > type_Mirabelle_typ] :
% 0.31/0.48 ( ! [X: nat] :
% 0.31/0.48 ( ( member_nat @ X @ ( type_M49385309le_typ @ T ) )
% 0.31/0.48 => ( ( S @ X )
% 0.31/0.48 = ( S3 @ X ) ) )
% 0.31/0.48 => ( ( type_M784671311le_typ @ S @ T )
% 0.31/0.48 = ( type_M784671311le_typ @ S3 @ T ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % typ_substitutions_only_on_free_variables
% 0.31/0.48 thf(fact_35_mk__scheme__injective,axiom,
% 0.31/0.48 ! [T: type_Mirabelle_typ,T3: type_Mirabelle_typ] :
% 0.31/0.48 ( ( ( type_M1006385707scheme @ T )
% 0.31/0.48 = ( type_M1006385707scheme @ T3 ) )
% 0.31/0.48 => ( T = T3 ) ) ).
% 0.31/0.48
% 0.31/0.48 % mk_scheme_injective
% 0.31/0.48 thf(fact_36_free__tv__type__scheme_Osimps_I2_J,axiom,
% 0.31/0.48 ! [M: nat] :
% 0.31/0.48 ( ( type_M1050318637scheme @ ( type_M2048935292e_BVar @ M ) )
% 0.31/0.48 = bot_bot_set_nat ) ).
% 0.31/0.48
% 0.31/0.48 % free_tv_type_scheme.simps(2)
% 0.31/0.48 thf(fact_37_type__scheme_Oexhaust,axiom,
% 0.31/0.48 ! [Y: type_M1694694083scheme] :
% 0.31/0.48 ( ! [X12: nat] :
% 0.31/0.48 ( Y
% 0.31/0.48 != ( type_M876316792e_FVar @ X12 ) )
% 0.31/0.48 => ( ! [X22: nat] :
% 0.31/0.48 ( Y
% 0.31/0.48 != ( type_M2048935292e_BVar @ X22 ) )
% 0.31/0.48 => ~ ! [X312: type_M1694694083scheme,X322: type_M1694694083scheme] :
% 0.31/0.48 ( Y
% 0.31/0.48 != ( type_M155660035e_SFun @ X312 @ X322 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % type_scheme.exhaust
% 0.31/0.48 thf(fact_38_type__scheme_Oinduct,axiom,
% 0.31/0.48 ! [P: type_M1694694083scheme > $o,Type_scheme: type_M1694694083scheme] :
% 0.31/0.48 ( ! [X: nat] : ( P @ ( type_M876316792e_FVar @ X ) )
% 0.31/0.48 => ( ! [X: nat] : ( P @ ( type_M2048935292e_BVar @ X ) )
% 0.31/0.48 => ( ! [X1a: type_M1694694083scheme,X2a: type_M1694694083scheme] :
% 0.31/0.48 ( ( P @ X1a )
% 0.31/0.48 => ( ( P @ X2a )
% 0.31/0.48 => ( P @ ( type_M155660035e_SFun @ X1a @ X2a ) ) ) )
% 0.31/0.48 => ( P @ Type_scheme ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % type_scheme.induct
% 0.31/0.48 thf(fact_39_new__tv__def,axiom,
% 0.31/0.48 ( type_M244876119le_typ
% 0.31/0.48 = ( ^ [N3: nat,Ts: list_n396811828le_typ] :
% 0.31/0.48 ! [M2: nat] :
% 0.31/0.48 ( ( member_nat @ M2 @ ( type_M1691543772le_typ @ Ts ) )
% 0.31/0.48 => ( ord_less_nat @ M2 @ N3 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % new_tv_def
% 0.31/0.48 thf(fact_40_new__tv__def,axiom,
% 0.31/0.48 ( type_M1377662078scheme
% 0.31/0.48 = ( ^ [N3: nat,Ts: list_l1334080099scheme] :
% 0.31/0.48 ! [M2: nat] :
% 0.31/0.48 ( ( member_nat @ M2 @ ( type_M1958029241scheme @ Ts ) )
% 0.31/0.48 => ( ord_less_nat @ M2 @ N3 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % new_tv_def
% 0.31/0.48 thf(fact_41_new__tv__def,axiom,
% 0.31/0.48 ( type_M263553000le_typ
% 0.31/0.48 = ( ^ [N3: nat,Ts: list_T1103309005le_typ] :
% 0.31/0.48 ! [M2: nat] :
% 0.31/0.48 ( ( member_nat @ M2 @ ( type_M510873837le_typ @ Ts ) )
% 0.31/0.48 => ( ord_less_nat @ M2 @ N3 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % new_tv_def
% 0.31/0.48 thf(fact_42_new__tv__def,axiom,
% 0.31/0.48 ( type_M1963061490scheme
% 0.31/0.48 = ( ^ [N3: nat,Ts: type_M1694694083scheme] :
% 0.31/0.48 ! [M2: nat] :
% 0.31/0.48 ( ( member_nat @ M2 @ ( type_M1050318637scheme @ Ts ) )
% 0.31/0.48 => ( ord_less_nat @ M2 @ N3 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % new_tv_def
% 0.31/0.48 thf(fact_43_new__tv__def,axiom,
% 0.31/0.48 ( type_M1211611096le_typ
% 0.31/0.48 = ( ^ [N3: nat,Ts: type_Mirabelle_typ] :
% 0.31/0.48 ! [M2: nat] :
% 0.31/0.48 ( ( member_nat @ M2 @ ( type_M49385309le_typ @ Ts ) )
% 0.31/0.48 => ( ord_less_nat @ M2 @ N3 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % new_tv_def
% 0.31/0.48 thf(fact_44_new__tv__def,axiom,
% 0.31/0.48 ( type_M2064939256scheme
% 0.31/0.48 = ( ^ [N3: nat,Ts: list_T247403987scheme] :
% 0.31/0.48 ! [M2: nat] :
% 0.31/0.48 ( ( member_nat @ M2 @ ( type_M141510067scheme @ Ts ) )
% 0.31/0.48 => ( ord_less_nat @ M2 @ N3 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % new_tv_def
% 0.31/0.48 thf(fact_45_new__tv__def,axiom,
% 0.31/0.48 ( type_M1734147655le_typ
% 0.31/0.48 = ( ^ [N3: nat,Ts: nat > type_Mirabelle_typ] :
% 0.31/0.48 ! [M2: nat] :
% 0.31/0.48 ( ( member_nat @ M2 @ ( type_M1715972684le_typ @ Ts ) )
% 0.31/0.48 => ( ord_less_nat @ M2 @ N3 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % new_tv_def
% 0.31/0.48 thf(fact_46_singleton__conv,axiom,
% 0.31/0.48 ! [A: nat] :
% 0.31/0.48 ( ( collect_nat
% 0.31/0.48 @ ^ [X4: nat] : ( X4 = A ) )
% 0.31/0.48 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 0.31/0.48
% 0.31/0.48 % singleton_conv
% 0.31/0.48 thf(fact_47_singleton__conv2,axiom,
% 0.31/0.48 ! [A: nat] :
% 0.31/0.48 ( ( collect_nat
% 0.31/0.48 @ ( ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.31/0.48 @ A ) )
% 0.31/0.48 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 0.31/0.48
% 0.31/0.48 % singleton_conv2
% 0.31/0.48 thf(fact_48_singletonI,axiom,
% 0.31/0.48 ! [A: nat] : ( member_nat @ A @ ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 0.31/0.48
% 0.31/0.48 % singletonI
% 0.31/0.48 thf(fact_49_insertCI,axiom,
% 0.31/0.48 ! [A: nat,B: set_nat,B2: nat] :
% 0.31/0.48 ( ( ~ ( member_nat @ A @ B )
% 0.31/0.48 => ( A = B2 ) )
% 0.31/0.48 => ( member_nat @ A @ ( insert_nat @ B2 @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insertCI
% 0.31/0.48 thf(fact_50_insert__iff,axiom,
% 0.31/0.48 ! [A: nat,B2: nat,A2: set_nat] :
% 0.31/0.48 ( ( member_nat @ A @ ( insert_nat @ B2 @ A2 ) )
% 0.31/0.48 = ( ( A = B2 )
% 0.31/0.48 | ( member_nat @ A @ A2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_iff
% 0.31/0.48 thf(fact_51_insert__absorb2,axiom,
% 0.31/0.48 ! [X3: nat,A2: set_nat] :
% 0.31/0.48 ( ( insert_nat @ X3 @ ( insert_nat @ X3 @ A2 ) )
% 0.31/0.48 = ( insert_nat @ X3 @ A2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_absorb2
% 0.31/0.48 thf(fact_52_list_Oinject,axiom,
% 0.31/0.48 ! [X21: type_M1694694083scheme,X222: list_T247403987scheme,Y21: type_M1694694083scheme,Y22: list_T247403987scheme] :
% 0.31/0.48 ( ( ( cons_T633159821scheme @ X21 @ X222 )
% 0.31/0.48 = ( cons_T633159821scheme @ Y21 @ Y22 ) )
% 0.31/0.48 = ( ( X21 = Y21 )
% 0.31/0.48 & ( X222 = Y22 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % list.inject
% 0.31/0.48 thf(fact_53_list_Oinject,axiom,
% 0.31/0.48 ! [X21: list_T247403987scheme,X222: list_l1334080099scheme,Y21: list_T247403987scheme,Y22: list_l1334080099scheme] :
% 0.31/0.48 ( ( ( cons_l1910959773scheme @ X21 @ X222 )
% 0.31/0.48 = ( cons_l1910959773scheme @ Y21 @ Y22 ) )
% 0.31/0.48 = ( ( X21 = Y21 )
% 0.31/0.48 & ( X222 = Y22 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % list.inject
% 0.31/0.48 thf(fact_54_list_Oinject,axiom,
% 0.31/0.48 ! [X21: type_Mirabelle_typ,X222: list_T1103309005le_typ,Y21: type_Mirabelle_typ,Y22: list_T1103309005le_typ] :
% 0.31/0.48 ( ( ( cons_T363929085le_typ @ X21 @ X222 )
% 0.31/0.48 = ( cons_T363929085le_typ @ Y21 @ Y22 ) )
% 0.31/0.48 = ( ( X21 = Y21 )
% 0.31/0.48 & ( X222 = Y22 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % list.inject
% 0.31/0.48 thf(fact_55_list_Oinject,axiom,
% 0.31/0.48 ! [X21: nat > type_Mirabelle_typ,X222: list_n396811828le_typ,Y21: nat > type_Mirabelle_typ,Y22: list_n396811828le_typ] :
% 0.31/0.48 ( ( ( cons_n499085924le_typ @ X21 @ X222 )
% 0.31/0.48 = ( cons_n499085924le_typ @ Y21 @ Y22 ) )
% 0.31/0.48 = ( ( X21 = Y21 )
% 0.31/0.48 & ( X222 = Y22 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % list.inject
% 0.31/0.48 thf(fact_56_list_Oinject,axiom,
% 0.31/0.48 ! [X21: nat,X222: list_nat,Y21: nat,Y22: list_nat] :
% 0.31/0.48 ( ( ( cons_nat @ X21 @ X222 )
% 0.31/0.48 = ( cons_nat @ Y21 @ Y22 ) )
% 0.31/0.48 = ( ( X21 = Y21 )
% 0.31/0.48 & ( X222 = Y22 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % list.inject
% 0.31/0.48 thf(fact_57_empty__iff,axiom,
% 0.31/0.48 ! [C: nat] :
% 0.31/0.48 ~ ( member_nat @ C @ bot_bot_set_nat ) ).
% 0.31/0.48
% 0.31/0.48 % empty_iff
% 0.31/0.48 thf(fact_58_mem__Collect__eq,axiom,
% 0.31/0.48 ! [A: nat,P: nat > $o] :
% 0.31/0.48 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 0.31/0.48 = ( P @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 % mem_Collect_eq
% 0.31/0.48 thf(fact_59_Collect__mem__eq,axiom,
% 0.31/0.48 ! [A2: set_nat] :
% 0.31/0.48 ( ( collect_nat
% 0.31/0.48 @ ^ [X4: nat] : ( member_nat @ X4 @ A2 ) )
% 0.31/0.48 = A2 ) ).
% 0.31/0.48
% 0.31/0.48 % Collect_mem_eq
% 0.31/0.48 thf(fact_60_Collect__cong,axiom,
% 0.31/0.48 ! [P: nat > $o,Q: nat > $o] :
% 0.31/0.48 ( ! [X: nat] :
% 0.31/0.48 ( ( P @ X )
% 0.31/0.48 = ( Q @ X ) )
% 0.31/0.48 => ( ( collect_nat @ P )
% 0.31/0.48 = ( collect_nat @ Q ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Collect_cong
% 0.31/0.48 thf(fact_61_all__not__in__conv,axiom,
% 0.31/0.48 ! [A2: set_nat] :
% 0.31/0.48 ( ( ! [X4: nat] :
% 0.31/0.48 ~ ( member_nat @ X4 @ A2 ) )
% 0.31/0.48 = ( A2 = bot_bot_set_nat ) ) ).
% 0.31/0.48
% 0.31/0.48 % all_not_in_conv
% 0.31/0.48 thf(fact_62_Collect__empty__eq,axiom,
% 0.31/0.48 ! [P: nat > $o] :
% 0.31/0.48 ( ( ( collect_nat @ P )
% 0.31/0.48 = bot_bot_set_nat )
% 0.31/0.48 = ( ! [X4: nat] :
% 0.31/0.48 ~ ( P @ X4 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Collect_empty_eq
% 0.31/0.48 thf(fact_63_empty__Collect__eq,axiom,
% 0.31/0.48 ! [P: nat > $o] :
% 0.31/0.48 ( ( bot_bot_set_nat
% 0.31/0.48 = ( collect_nat @ P ) )
% 0.31/0.48 = ( ! [X4: nat] :
% 0.31/0.48 ~ ( P @ X4 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % empty_Collect_eq
% 0.31/0.48 thf(fact_64_new__if__subst__type__scheme__list,axiom,
% 0.31/0.48 ! [N2: nat,A2: list_T247403987scheme,S: nat > type_Mirabelle_typ,S3: nat > type_Mirabelle_typ] :
% 0.31/0.48 ( ( type_M2064939256scheme @ N2 @ A2 )
% 0.31/0.48 => ( ( type_M1944210753scheme
% 0.31/0.48 @ ^ [K: nat] : ( if_Typ1169047309le_typ @ ( ord_less_nat @ K @ N2 ) @ ( S @ K ) @ ( S3 @ K ) )
% 0.31/0.48 @ A2 )
% 0.31/0.48 = ( type_M1944210753scheme @ S @ A2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % new_if_subst_type_scheme_list
% 0.31/0.48 thf(fact_65_ex__in__conv,axiom,
% 0.31/0.48 ! [A2: set_nat] :
% 0.31/0.48 ( ( ? [X4: nat] : ( member_nat @ X4 @ A2 ) )
% 0.31/0.48 = ( A2 != bot_bot_set_nat ) ) ).
% 0.31/0.48
% 0.31/0.48 % ex_in_conv
% 0.31/0.48 thf(fact_66_equals0I,axiom,
% 0.31/0.48 ! [A2: set_nat] :
% 0.31/0.48 ( ! [Y4: nat] :
% 0.31/0.48 ~ ( member_nat @ Y4 @ A2 )
% 0.31/0.48 => ( A2 = bot_bot_set_nat ) ) ).
% 0.31/0.48
% 0.31/0.48 % equals0I
% 0.31/0.48 thf(fact_67_equals0D,axiom,
% 0.31/0.48 ! [A2: set_nat,A: nat] :
% 0.31/0.48 ( ( A2 = bot_bot_set_nat )
% 0.31/0.48 => ~ ( member_nat @ A @ A2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % equals0D
% 0.31/0.48 thf(fact_68_emptyE,axiom,
% 0.31/0.48 ! [A: nat] :
% 0.31/0.48 ~ ( member_nat @ A @ bot_bot_set_nat ) ).
% 0.31/0.48
% 0.31/0.48 % emptyE
% 0.31/0.48 thf(fact_69_not__Cons__self2,axiom,
% 0.31/0.48 ! [X3: type_M1694694083scheme,Xs: list_T247403987scheme] :
% 0.31/0.48 ( ( cons_T633159821scheme @ X3 @ Xs )
% 0.31/0.48 != Xs ) ).
% 0.31/0.48
% 0.31/0.48 % not_Cons_self2
% 0.31/0.48 thf(fact_70_not__Cons__self2,axiom,
% 0.31/0.48 ! [X3: list_T247403987scheme,Xs: list_l1334080099scheme] :
% 0.31/0.48 ( ( cons_l1910959773scheme @ X3 @ Xs )
% 0.31/0.48 != Xs ) ).
% 0.31/0.48
% 0.31/0.48 % not_Cons_self2
% 0.31/0.48 thf(fact_71_not__Cons__self2,axiom,
% 0.31/0.48 ! [X3: type_Mirabelle_typ,Xs: list_T1103309005le_typ] :
% 0.31/0.48 ( ( cons_T363929085le_typ @ X3 @ Xs )
% 0.31/0.48 != Xs ) ).
% 0.31/0.48
% 0.31/0.48 % not_Cons_self2
% 0.31/0.48 thf(fact_72_not__Cons__self2,axiom,
% 0.31/0.48 ! [X3: nat > type_Mirabelle_typ,Xs: list_n396811828le_typ] :
% 0.31/0.48 ( ( cons_n499085924le_typ @ X3 @ Xs )
% 0.31/0.48 != Xs ) ).
% 0.31/0.48
% 0.31/0.48 % not_Cons_self2
% 0.31/0.48 thf(fact_73_not__Cons__self2,axiom,
% 0.31/0.48 ! [X3: nat,Xs: list_nat] :
% 0.31/0.48 ( ( cons_nat @ X3 @ Xs )
% 0.31/0.48 != Xs ) ).
% 0.31/0.48
% 0.31/0.48 % not_Cons_self2
% 0.31/0.48 thf(fact_74_mk__disjoint__insert,axiom,
% 0.31/0.48 ! [A: nat,A2: set_nat] :
% 0.31/0.48 ( ( member_nat @ A @ A2 )
% 0.31/0.48 => ? [B3: set_nat] :
% 0.31/0.48 ( ( A2
% 0.31/0.48 = ( insert_nat @ A @ B3 ) )
% 0.31/0.48 & ~ ( member_nat @ A @ B3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % mk_disjoint_insert
% 0.31/0.48 thf(fact_75_insert__commute,axiom,
% 0.31/0.48 ! [X3: nat,Y: nat,A2: set_nat] :
% 0.31/0.48 ( ( insert_nat @ X3 @ ( insert_nat @ Y @ A2 ) )
% 0.31/0.48 = ( insert_nat @ Y @ ( insert_nat @ X3 @ A2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_commute
% 0.31/0.48 thf(fact_76_insert__eq__iff,axiom,
% 0.31/0.48 ! [A: nat,A2: set_nat,B2: nat,B: set_nat] :
% 0.31/0.48 ( ~ ( member_nat @ A @ A2 )
% 0.31/0.48 => ( ~ ( member_nat @ B2 @ B )
% 0.31/0.48 => ( ( ( insert_nat @ A @ A2 )
% 0.31/0.48 = ( insert_nat @ B2 @ B ) )
% 0.31/0.48 = ( ( ( A = B2 )
% 0.31/0.48 => ( A2 = B ) )
% 0.31/0.48 & ( ( A != B2 )
% 0.31/0.48 => ? [C2: set_nat] :
% 0.31/0.48 ( ( A2
% 0.31/0.48 = ( insert_nat @ B2 @ C2 ) )
% 0.31/0.48 & ~ ( member_nat @ B2 @ C2 )
% 0.31/0.48 & ( B
% 0.31/0.48 = ( insert_nat @ A @ C2 ) )
% 0.31/0.48 & ~ ( member_nat @ A @ C2 ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_eq_iff
% 0.31/0.48 thf(fact_77_insert__absorb,axiom,
% 0.31/0.48 ! [A: nat,A2: set_nat] :
% 0.31/0.48 ( ( member_nat @ A @ A2 )
% 0.31/0.48 => ( ( insert_nat @ A @ A2 )
% 0.31/0.48 = A2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_absorb
% 0.31/0.48 thf(fact_78_insert__ident,axiom,
% 0.31/0.48 ! [X3: nat,A2: set_nat,B: set_nat] :
% 0.31/0.48 ( ~ ( member_nat @ X3 @ A2 )
% 0.31/0.48 => ( ~ ( member_nat @ X3 @ B )
% 0.31/0.48 => ( ( ( insert_nat @ X3 @ A2 )
% 0.31/0.48 = ( insert_nat @ X3 @ B ) )
% 0.31/0.48 = ( A2 = B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_ident
% 0.31/0.48 thf(fact_79_Set_Oset__insert,axiom,
% 0.31/0.48 ! [X3: nat,A2: set_nat] :
% 0.31/0.48 ( ( member_nat @ X3 @ A2 )
% 0.31/0.48 => ~ ! [B3: set_nat] :
% 0.31/0.48 ( ( A2
% 0.31/0.48 = ( insert_nat @ X3 @ B3 ) )
% 0.31/0.48 => ( member_nat @ X3 @ B3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Set.set_insert
% 0.31/0.48 thf(fact_80_insertI2,axiom,
% 0.31/0.48 ! [A: nat,B: set_nat,B2: nat] :
% 0.31/0.48 ( ( member_nat @ A @ B )
% 0.31/0.48 => ( member_nat @ A @ ( insert_nat @ B2 @ B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insertI2
% 0.31/0.48 thf(fact_81_insertI1,axiom,
% 0.31/0.48 ! [A: nat,B: set_nat] : ( member_nat @ A @ ( insert_nat @ A @ B ) ) ).
% 0.31/0.48
% 0.31/0.48 % insertI1
% 0.31/0.48 thf(fact_82_insertE,axiom,
% 0.31/0.48 ! [A: nat,B2: nat,A2: set_nat] :
% 0.31/0.48 ( ( member_nat @ A @ ( insert_nat @ B2 @ A2 ) )
% 0.31/0.48 => ( ( A != B2 )
% 0.31/0.48 => ( member_nat @ A @ A2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insertE
% 0.31/0.48 thf(fact_83_empty__def,axiom,
% 0.31/0.48 ( bot_bot_set_nat
% 0.31/0.48 = ( collect_nat
% 0.31/0.48 @ ^ [X4: nat] : $false ) ) ).
% 0.31/0.48
% 0.31/0.48 % empty_def
% 0.31/0.48 thf(fact_84_insert__Collect,axiom,
% 0.31/0.48 ! [A: nat,P: nat > $o] :
% 0.31/0.48 ( ( insert_nat @ A @ ( collect_nat @ P ) )
% 0.31/0.48 = ( collect_nat
% 0.31/0.48 @ ^ [U: nat] :
% 0.31/0.48 ( ( U != A )
% 0.31/0.48 => ( P @ U ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_Collect
% 0.31/0.48 thf(fact_85_insert__compr,axiom,
% 0.31/0.48 ( insert_nat
% 0.31/0.48 = ( ^ [A3: nat,B4: set_nat] :
% 0.31/0.48 ( collect_nat
% 0.31/0.48 @ ^ [X4: nat] :
% 0.31/0.48 ( ( X4 = A3 )
% 0.31/0.48 | ( member_nat @ X4 @ B4 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % insert_compr
% 0.31/0.48 thf(fact_86_singleton__inject,axiom,
% 0.31/0.48 ! [A: nat,B2: nat] :
% 0.31/0.48 ( ( ( insert_nat @ A @ bot_bot_set_nat )
% 0.31/0.48 = ( insert_nat @ B2 @ bot_bot_set_nat ) )
% 0.31/0.48 => ( A = B2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % singleton_inject
% 0.31/0.48 thf(fact_87_insert__not__empty,axiom,
% 0.31/0.48 ! [A: nat,A2: set_nat] :
% 0.31/0.48 ( ( insert_nat @ A @ A2 )
% 0.31/0.48 != bot_bot_set_nat ) ).
% 0.31/0.48
% 0.31/0.48 % insert_not_empty
% 0.31/0.48 thf(fact_88_doubleton__eq__iff,axiom,
% 0.31/0.48 ! [A: nat,B2: nat,C: nat,D: nat] :
% 0.31/0.48 ( ( ( insert_nat @ A @ ( insert_nat @ B2 @ bot_bot_set_nat ) )
% 0.31/0.48 = ( insert_nat @ C @ ( insert_nat @ D @ bot_bot_set_nat ) ) )
% 0.31/0.48 = ( ( ( A = C )
% 0.31/0.48 & ( B2 = D ) )
% 0.31/0.48 | ( ( A = D )
% 0.31/0.48 & ( B2 = C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % doubleton_eq_iff
% 0.31/0.48 thf(fact_89_singleton__iff,axiom,
% 0.31/0.48 ! [B2: nat,A: nat] :
% 0.31/0.48 ( ( member_nat @ B2 @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 0.31/0.48 = ( B2 = A ) ) ).
% 0.31/0.48
% 0.31/0.48 % singleton_iff
% 0.31/0.48 thf(fact_90_singletonD,axiom,
% 0.31/0.48 ! [B2: nat,A: nat] :
% 0.31/0.48 ( ( member_nat @ B2 @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 0.31/0.48 => ( B2 = A ) ) ).
% 0.31/0.48
% 0.31/0.48 % singletonD
% 0.31/0.48 thf(fact_91_Collect__conv__if2,axiom,
% 0.31/0.48 ! [P: nat > $o,A: nat] :
% 0.31/0.48 ( ( ( P @ A )
% 0.31/0.48 => ( ( collect_nat
% 0.31/0.48 @ ^ [X4: nat] :
% 0.31/0.48 ( ( A = X4 )
% 0.31/0.48 & ( P @ X4 ) ) )
% 0.31/0.48 = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.31/0.48 & ( ~ ( P @ A )
% 0.31/0.48 => ( ( collect_nat
% 0.31/0.48 @ ^ [X4: nat] :
% 0.31/0.48 ( ( A = X4 )
% 0.31/0.48 & ( P @ X4 ) ) )
% 0.31/0.48 = bot_bot_set_nat ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Collect_conv_if2
% 0.31/0.48 thf(fact_92_Collect__conv__if,axiom,
% 0.31/0.48 ! [P: nat > $o,A: nat] :
% 0.31/0.48 ( ( ( P @ A )
% 0.31/0.48 => ( ( collect_nat
% 0.31/0.48 @ ^ [X4: nat] :
% 0.31/0.48 ( ( X4 = A )
% 0.31/0.48 & ( P @ X4 ) ) )
% 0.31/0.48 = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.31/0.48 & ( ~ ( P @ A )
% 0.31/0.48 => ( ( collect_nat
% 0.31/0.48 @ ^ [X4: nat] :
% 0.31/0.48 ( ( X4 = A )
% 0.31/0.48 & ( P @ X4 ) ) )
% 0.31/0.48 = bot_bot_set_nat ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Collect_conv_if
% 0.31/0.48 thf(fact_93_the__elem__eq,axiom,
% 0.31/0.48 ! [X3: nat] :
% 0.31/0.48 ( ( the_elem_nat @ ( insert_nat @ X3 @ bot_bot_set_nat ) )
% 0.31/0.48 = X3 ) ).
% 0.31/0.48
% 0.31/0.48 % the_elem_eq
% 0.31/0.48 thf(fact_94_bot__apply,axiom,
% 0.31/0.48 ( bot_bot_nat_o
% 0.31/0.48 = ( ^ [X4: nat] : bot_bot_o ) ) ).
% 0.31/0.48
% 0.31/0.48 % bot_apply
% 0.31/0.48 thf(fact_95_bound__tv__type__scheme_Osimps_I2_J,axiom,
% 0.31/0.48 ! [M: nat] :
% 0.31/0.48 ( ( type_M326705277scheme @ ( type_M2048935292e_BVar @ M ) )
% 0.31/0.48 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 0.31/0.48
% 0.31/0.48 % bound_tv_type_scheme.simps(2)
% 0.31/0.48 thf(fact_96_is__singletonI,axiom,
% 0.31/0.48 ! [X3: nat] : ( is_singleton_nat @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) ).
% 0.31/0.48
% 0.31/0.48 % is_singletonI
% 0.31/0.48 thf(fact_97_bot_Onot__eq__extremum,axiom,
% 0.31/0.48 ! [A: nat > $o] :
% 0.31/0.48 ( ( A != bot_bot_nat_o )
% 0.31/0.48 = ( ord_less_nat_o @ bot_bot_nat_o @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 % bot.not_eq_extremum
% 0.31/0.48 thf(fact_98_bot_Onot__eq__extremum,axiom,
% 0.31/0.48 ! [A: set_nat] :
% 0.31/0.48 ( ( A != bot_bot_set_nat )
% 0.31/0.48 = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 % bot.not_eq_extremum
% 0.31/0.48 thf(fact_99_bot_Onot__eq__extremum,axiom,
% 0.31/0.48 ! [A: nat] :
% 0.31/0.48 ( ( A != bot_bot_nat )
% 0.31/0.48 = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 % bot.not_eq_extremum
% 0.31/0.48 thf(fact_100_bot_Oextremum__strict,axiom,
% 0.31/0.48 ! [A: nat > $o] :
% 0.31/0.48 ~ ( ord_less_nat_o @ A @ bot_bot_nat_o ) ).
% 0.31/0.48
% 0.31/0.48 % bot.extremum_strict
% 0.31/0.48 thf(fact_101_bot_Oextremum__strict,axiom,
% 0.31/0.48 ! [A: set_nat] :
% 0.31/0.48 ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 0.31/0.48
% 0.31/0.48 % bot.extremum_strict
% 0.31/0.48 thf(fact_102_bot_Oextremum__strict,axiom,
% 0.31/0.48 ! [A: nat] :
% 0.31/0.48 ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 0.31/0.48
% 0.31/0.48 % bot.extremum_strict
% 0.31/0.48 thf(fact_103_free__tv__TVar,axiom,
% 0.31/0.48 ! [M: nat] :
% 0.31/0.48 ( ( type_M49385309le_typ @ ( type_Mirabelle_TVar @ M ) )
% 0.31/0.48 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 0.31/0.48
% 0.31/0.48 % free_tv_TVar
% 0.31/0.48 thf(fact_104_bound__tv__type__scheme_Osimps_I1_J,axiom,
% 0.31/0.48 ! [M: nat] :
% 0.31/0.48 ( ( type_M326705277scheme @ ( type_M876316792e_FVar @ M ) )
% 0.31/0.48 = bot_bot_set_nat ) ).
% 0.31/0.48
% 0.31/0.48 % bound_tv_type_scheme.simps(1)
% 0.31/0.48 thf(fact_105_typ_Oinject_I1_J,axiom,
% 0.31/0.48 ! [X1: nat,Y1: nat] :
% 0.31/0.48 ( ( ( type_Mirabelle_TVar @ X1 )
% 0.31/0.48 = ( type_Mirabelle_TVar @ Y1 ) )
% 0.31/0.48 = ( X1 = Y1 ) ) ).
% 0.31/0.48
% 0.31/0.48 % typ.inject(1)
% 0.31/0.48 thf(fact_106_new__tv__TVar,axiom,
% 0.31/0.48 ! [N2: nat,M: nat] :
% 0.31/0.48 ( ( type_M1211611096le_typ @ N2 @ ( type_Mirabelle_TVar @ M ) )
% 0.31/0.48 = ( ord_less_nat @ M @ N2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % new_tv_TVar
% 0.31/0.48 thf(fact_107_new__tv__TVar__subst,axiom,
% 0.31/0.48 ! [N2: nat] : ( type_M1734147655le_typ @ N2 @ type_Mirabelle_TVar ) ).
% 0.31/0.48
% 0.31/0.48 % new_tv_TVar_subst
% 0.31/0.48 thf(fact_108_eq__free__eq__subst__scheme__list,axiom,
% 0.31/0.48 ! [A2: list_T247403987scheme,S1: nat > type_Mirabelle_typ,S2: nat > type_Mirabelle_typ] :
% 0.31/0.48 ( ! [N: nat] :
% 0.31/0.48 ( ( member_nat @ N @ ( type_M141510067scheme @ A2 ) )
% 0.31/0.48 => ( ( S1 @ N )
% 0.31/0.48 = ( S2 @ N ) ) )
% 0.31/0.48 => ( ( type_M1944210753scheme @ S1 @ A2 )
% 0.31/0.48 = ( type_M1944210753scheme @ S2 @ A2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % eq_free_eq_subst_scheme_list
% 0.31/0.48 thf(fact_109_scheme__list__substitutions__only__on__free__variables,axiom,
% 0.31/0.48 ! [A2: list_T247403987scheme,S: nat > type_Mirabelle_typ,S3: nat > type_Mirabelle_typ] :
% 0.31/0.48 ( ! [X: nat] :
% 0.31/0.48 ( ( member_nat @ X @ ( type_M141510067scheme @ A2 ) )
% 0.31/0.48 => ( ( S @ X )
% 0.31/0.48 = ( S3 @ X ) ) )
% 0.31/0.48 => ( ( type_M1944210753scheme @ S @ A2 )
% 0.31/0.48 = ( type_M1944210753scheme @ S3 @ A2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % scheme_list_substitutions_only_on_free_variables
% 0.31/0.48 thf(fact_110_bot__set__def,axiom,
% 0.31/0.48 ( bot_bot_set_nat
% 0.31/0.48 = ( collect_nat @ bot_bot_nat_o ) ) ).
% 0.31/0.48
% 0.31/0.48 % bot_set_def
% 0.31/0.48 thf(fact_111_not__psubset__empty,axiom,
% 0.31/0.48 ! [A2: set_nat] :
% 0.31/0.48 ~ ( ord_less_set_nat @ A2 @ bot_bot_set_nat ) ).
% 0.31/0.48
% 0.31/0.48 % not_psubset_empty
% 0.31/0.48 thf(fact_112_app__subst__TVar,axiom,
% 0.31/0.48 ! [S: nat > type_Mirabelle_typ,N2: nat] :
% 0.31/0.48 ( ( type_M784671311le_typ @ S @ ( type_Mirabelle_TVar @ N2 ) )
% 0.31/0.48 = ( S @ N2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % app_subst_TVar
% 0.31/0.48 thf(fact_113_is__singleton__the__elem,axiom,
% 0.31/0.48 ( is_singleton_nat
% 0.31/0.48 = ( ^ [A4: set_nat] :
% 0.31/0.48 ( A4
% 0.31/0.48 = ( insert_nat @ ( the_elem_nat @ A4 ) @ bot_bot_set_nat ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % is_singleton_the_elem
% 0.31/0.48 thf(fact_114_is__singletonI_H,axiom,
% 0.31/0.48 ! [A2: set_nat] :
% 0.31/0.48 ( ( A2 != bot_bot_set_nat )
% 0.31/0.48 => ( ! [X: nat,Y4: nat] :
% 0.31/0.48 ( ( member_nat @ X @ A2 )
% 0.31/0.48 => ( ( member_nat @ Y4 @ A2 )
% 0.31/0.48 => ( X = Y4 ) ) )
% 0.31/0.48 => ( is_singleton_nat @ A2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % is_singletonI'
% 0.31/0.48 thf(fact_115_ord__eq__less__subst,axiom,
% 0.31/0.48 ! [A: set_nat,F: nat > set_nat,B2: nat,C: nat] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( F @ B2 ) )
% 0.31/0.48 => ( ( ord_less_nat @ B2 @ C )
% 0.31/0.48 => ( ! [X: nat,Y4: nat] :
% 0.31/0.48 ( ( ord_less_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_set_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ord_eq_less_subst
% 0.31/0.48 thf(fact_116_ord__eq__less__subst,axiom,
% 0.31/0.48 ! [A: nat > $o,F: nat > nat > $o,B2: nat,C: nat] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( F @ B2 ) )
% 0.31/0.48 => ( ( ord_less_nat @ B2 @ C )
% 0.31/0.48 => ( ! [X: nat,Y4: nat] :
% 0.31/0.48 ( ( ord_less_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ord_eq_less_subst
% 0.31/0.48 thf(fact_117_ord__eq__less__subst,axiom,
% 0.31/0.48 ! [A: nat,F: set_nat > nat,B2: set_nat,C: set_nat] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( F @ B2 ) )
% 0.31/0.48 => ( ( ord_less_set_nat @ B2 @ C )
% 0.31/0.48 => ( ! [X: set_nat,Y4: set_nat] :
% 0.31/0.48 ( ( ord_less_set_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ord_eq_less_subst
% 0.31/0.48 thf(fact_118_ord__eq__less__subst,axiom,
% 0.31/0.48 ! [A: set_nat,F: set_nat > set_nat,B2: set_nat,C: set_nat] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( F @ B2 ) )
% 0.31/0.48 => ( ( ord_less_set_nat @ B2 @ C )
% 0.31/0.48 => ( ! [X: set_nat,Y4: set_nat] :
% 0.31/0.48 ( ( ord_less_set_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_set_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ord_eq_less_subst
% 0.31/0.48 thf(fact_119_ord__eq__less__subst,axiom,
% 0.31/0.48 ! [A: nat > $o,F: set_nat > nat > $o,B2: set_nat,C: set_nat] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( F @ B2 ) )
% 0.31/0.48 => ( ( ord_less_set_nat @ B2 @ C )
% 0.31/0.48 => ( ! [X: set_nat,Y4: set_nat] :
% 0.31/0.48 ( ( ord_less_set_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ord_eq_less_subst
% 0.31/0.48 thf(fact_120_ord__eq__less__subst,axiom,
% 0.31/0.48 ! [A: nat,F: ( nat > $o ) > nat,B2: nat > $o,C: nat > $o] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( F @ B2 ) )
% 0.31/0.48 => ( ( ord_less_nat_o @ B2 @ C )
% 0.31/0.48 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.31/0.48 ( ( ord_less_nat_o @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ord_eq_less_subst
% 0.31/0.48 thf(fact_121_ord__eq__less__subst,axiom,
% 0.31/0.48 ! [A: set_nat,F: ( nat > $o ) > set_nat,B2: nat > $o,C: nat > $o] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( F @ B2 ) )
% 0.31/0.48 => ( ( ord_less_nat_o @ B2 @ C )
% 0.31/0.48 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.31/0.48 ( ( ord_less_nat_o @ X @ Y4 )
% 0.31/0.48 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_set_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ord_eq_less_subst
% 0.31/0.48 thf(fact_122_ord__eq__less__subst,axiom,
% 0.31/0.48 ! [A: nat > $o,F: ( nat > $o ) > nat > $o,B2: nat > $o,C: nat > $o] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( F @ B2 ) )
% 0.31/0.48 => ( ( ord_less_nat_o @ B2 @ C )
% 0.31/0.48 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.31/0.48 ( ( ord_less_nat_o @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ord_eq_less_subst
% 0.31/0.48 thf(fact_123_ord__eq__less__subst,axiom,
% 0.31/0.48 ! [A: nat,F: nat > nat,B2: nat,C: nat] :
% 0.31/0.48 ( ( A
% 0.31/0.48 = ( F @ B2 ) )
% 0.31/0.48 => ( ( ord_less_nat @ B2 @ C )
% 0.31/0.48 => ( ! [X: nat,Y4: nat] :
% 0.31/0.48 ( ( ord_less_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ord_eq_less_subst
% 0.31/0.48 thf(fact_124_ord__less__eq__subst,axiom,
% 0.31/0.48 ! [A: nat,B2: nat,F: nat > set_nat,C: set_nat] :
% 0.31/0.48 ( ( ord_less_nat @ A @ B2 )
% 0.31/0.48 => ( ( ( F @ B2 )
% 0.31/0.48 = C )
% 0.31/0.48 => ( ! [X: nat,Y4: nat] :
% 0.31/0.48 ( ( ord_less_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_set_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ord_less_eq_subst
% 0.31/0.48 thf(fact_125_ord__less__eq__subst,axiom,
% 0.31/0.48 ! [A: nat,B2: nat,F: nat > nat > $o,C: nat > $o] :
% 0.31/0.48 ( ( ord_less_nat @ A @ B2 )
% 0.31/0.48 => ( ( ( F @ B2 )
% 0.31/0.48 = C )
% 0.31/0.48 => ( ! [X: nat,Y4: nat] :
% 0.31/0.48 ( ( ord_less_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ord_less_eq_subst
% 0.31/0.48 thf(fact_126_ord__less__eq__subst,axiom,
% 0.31/0.48 ! [A: set_nat,B2: set_nat,F: set_nat > nat,C: nat] :
% 0.31/0.48 ( ( ord_less_set_nat @ A @ B2 )
% 0.31/0.48 => ( ( ( F @ B2 )
% 0.31/0.48 = C )
% 0.31/0.48 => ( ! [X: set_nat,Y4: set_nat] :
% 0.31/0.48 ( ( ord_less_set_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ord_less_eq_subst
% 0.31/0.48 thf(fact_127_ord__less__eq__subst,axiom,
% 0.31/0.48 ! [A: set_nat,B2: set_nat,F: set_nat > set_nat,C: set_nat] :
% 0.31/0.48 ( ( ord_less_set_nat @ A @ B2 )
% 0.31/0.48 => ( ( ( F @ B2 )
% 0.31/0.48 = C )
% 0.31/0.48 => ( ! [X: set_nat,Y4: set_nat] :
% 0.31/0.48 ( ( ord_less_set_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_set_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ord_less_eq_subst
% 0.31/0.48 thf(fact_128_ord__less__eq__subst,axiom,
% 0.31/0.48 ! [A: set_nat,B2: set_nat,F: set_nat > nat > $o,C: nat > $o] :
% 0.31/0.48 ( ( ord_less_set_nat @ A @ B2 )
% 0.31/0.48 => ( ( ( F @ B2 )
% 0.31/0.48 = C )
% 0.31/0.48 => ( ! [X: set_nat,Y4: set_nat] :
% 0.31/0.48 ( ( ord_less_set_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ord_less_eq_subst
% 0.31/0.48 thf(fact_129_ord__less__eq__subst,axiom,
% 0.31/0.48 ! [A: nat > $o,B2: nat > $o,F: ( nat > $o ) > nat,C: nat] :
% 0.31/0.48 ( ( ord_less_nat_o @ A @ B2 )
% 0.31/0.48 => ( ( ( F @ B2 )
% 0.31/0.48 = C )
% 0.31/0.48 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.31/0.48 ( ( ord_less_nat_o @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ord_less_eq_subst
% 0.31/0.48 thf(fact_130_ord__less__eq__subst,axiom,
% 0.31/0.48 ! [A: nat > $o,B2: nat > $o,F: ( nat > $o ) > set_nat,C: set_nat] :
% 0.31/0.48 ( ( ord_less_nat_o @ A @ B2 )
% 0.31/0.48 => ( ( ( F @ B2 )
% 0.31/0.48 = C )
% 0.31/0.48 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.31/0.48 ( ( ord_less_nat_o @ X @ Y4 )
% 0.31/0.48 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_set_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ord_less_eq_subst
% 0.31/0.48 thf(fact_131_ord__less__eq__subst,axiom,
% 0.31/0.48 ! [A: nat > $o,B2: nat > $o,F: ( nat > $o ) > nat > $o,C: nat > $o] :
% 0.31/0.48 ( ( ord_less_nat_o @ A @ B2 )
% 0.31/0.48 => ( ( ( F @ B2 )
% 0.31/0.48 = C )
% 0.31/0.48 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.31/0.48 ( ( ord_less_nat_o @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ord_less_eq_subst
% 0.31/0.48 thf(fact_132_ord__less__eq__subst,axiom,
% 0.31/0.48 ! [A: nat,B2: nat,F: nat > nat,C: nat] :
% 0.31/0.48 ( ( ord_less_nat @ A @ B2 )
% 0.31/0.48 => ( ( ( F @ B2 )
% 0.31/0.48 = C )
% 0.31/0.48 => ( ! [X: nat,Y4: nat] :
% 0.31/0.48 ( ( ord_less_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ord_less_eq_subst
% 0.31/0.48 thf(fact_133_order__less__subst1,axiom,
% 0.31/0.48 ! [A: nat,F: set_nat > nat,B2: set_nat,C: set_nat] :
% 0.31/0.48 ( ( ord_less_nat @ A @ ( F @ B2 ) )
% 0.31/0.48 => ( ( ord_less_set_nat @ B2 @ C )
% 0.31/0.48 => ( ! [X: set_nat,Y4: set_nat] :
% 0.31/0.48 ( ( ord_less_set_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % order_less_subst1
% 0.31/0.48 thf(fact_134_order__less__subst1,axiom,
% 0.31/0.48 ! [A: nat,F: ( nat > $o ) > nat,B2: nat > $o,C: nat > $o] :
% 0.31/0.48 ( ( ord_less_nat @ A @ ( F @ B2 ) )
% 0.31/0.48 => ( ( ord_less_nat_o @ B2 @ C )
% 0.31/0.48 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.31/0.48 ( ( ord_less_nat_o @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % order_less_subst1
% 0.31/0.48 thf(fact_135_order__less__subst1,axiom,
% 0.31/0.48 ! [A: set_nat,F: nat > set_nat,B2: nat,C: nat] :
% 0.31/0.48 ( ( ord_less_set_nat @ A @ ( F @ B2 ) )
% 0.31/0.48 => ( ( ord_less_nat @ B2 @ C )
% 0.31/0.48 => ( ! [X: nat,Y4: nat] :
% 0.31/0.48 ( ( ord_less_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_set_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % order_less_subst1
% 0.31/0.48 thf(fact_136_order__less__subst1,axiom,
% 0.31/0.48 ! [A: set_nat,F: set_nat > set_nat,B2: set_nat,C: set_nat] :
% 0.31/0.48 ( ( ord_less_set_nat @ A @ ( F @ B2 ) )
% 0.31/0.48 => ( ( ord_less_set_nat @ B2 @ C )
% 0.31/0.48 => ( ! [X: set_nat,Y4: set_nat] :
% 0.31/0.48 ( ( ord_less_set_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_set_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % order_less_subst1
% 0.31/0.48 thf(fact_137_order__less__subst1,axiom,
% 0.31/0.48 ! [A: set_nat,F: ( nat > $o ) > set_nat,B2: nat > $o,C: nat > $o] :
% 0.31/0.48 ( ( ord_less_set_nat @ A @ ( F @ B2 ) )
% 0.31/0.48 => ( ( ord_less_nat_o @ B2 @ C )
% 0.31/0.48 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.31/0.48 ( ( ord_less_nat_o @ X @ Y4 )
% 0.31/0.48 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_set_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % order_less_subst1
% 0.31/0.48 thf(fact_138_order__less__subst1,axiom,
% 0.31/0.48 ! [A: nat > $o,F: nat > nat > $o,B2: nat,C: nat] :
% 0.31/0.48 ( ( ord_less_nat_o @ A @ ( F @ B2 ) )
% 0.31/0.48 => ( ( ord_less_nat @ B2 @ C )
% 0.31/0.48 => ( ! [X: nat,Y4: nat] :
% 0.31/0.48 ( ( ord_less_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % order_less_subst1
% 0.31/0.48 thf(fact_139_order__less__subst1,axiom,
% 0.31/0.48 ! [A: nat > $o,F: set_nat > nat > $o,B2: set_nat,C: set_nat] :
% 0.31/0.48 ( ( ord_less_nat_o @ A @ ( F @ B2 ) )
% 0.31/0.48 => ( ( ord_less_set_nat @ B2 @ C )
% 0.31/0.48 => ( ! [X: set_nat,Y4: set_nat] :
% 0.31/0.48 ( ( ord_less_set_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % order_less_subst1
% 0.31/0.48 thf(fact_140_order__less__subst1,axiom,
% 0.31/0.48 ! [A: nat > $o,F: ( nat > $o ) > nat > $o,B2: nat > $o,C: nat > $o] :
% 0.31/0.48 ( ( ord_less_nat_o @ A @ ( F @ B2 ) )
% 0.31/0.48 => ( ( ord_less_nat_o @ B2 @ C )
% 0.31/0.48 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.31/0.48 ( ( ord_less_nat_o @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % order_less_subst1
% 0.31/0.48 thf(fact_141_order__less__subst1,axiom,
% 0.31/0.48 ! [A: nat,F: nat > nat,B2: nat,C: nat] :
% 0.31/0.48 ( ( ord_less_nat @ A @ ( F @ B2 ) )
% 0.31/0.48 => ( ( ord_less_nat @ B2 @ C )
% 0.31/0.48 => ( ! [X: nat,Y4: nat] :
% 0.31/0.48 ( ( ord_less_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % order_less_subst1
% 0.31/0.48 thf(fact_142_order__less__subst2,axiom,
% 0.31/0.48 ! [A: nat,B2: nat,F: nat > set_nat,C: set_nat] :
% 0.31/0.48 ( ( ord_less_nat @ A @ B2 )
% 0.31/0.48 => ( ( ord_less_set_nat @ ( F @ B2 ) @ C )
% 0.31/0.48 => ( ! [X: nat,Y4: nat] :
% 0.31/0.48 ( ( ord_less_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_set_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % order_less_subst2
% 0.31/0.48 thf(fact_143_order__less__subst2,axiom,
% 0.31/0.48 ! [A: nat,B2: nat,F: nat > nat > $o,C: nat > $o] :
% 0.31/0.48 ( ( ord_less_nat @ A @ B2 )
% 0.31/0.48 => ( ( ord_less_nat_o @ ( F @ B2 ) @ C )
% 0.31/0.48 => ( ! [X: nat,Y4: nat] :
% 0.31/0.48 ( ( ord_less_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % order_less_subst2
% 0.31/0.48 thf(fact_144_order__less__subst2,axiom,
% 0.31/0.48 ! [A: set_nat,B2: set_nat,F: set_nat > nat,C: nat] :
% 0.31/0.48 ( ( ord_less_set_nat @ A @ B2 )
% 0.31/0.48 => ( ( ord_less_nat @ ( F @ B2 ) @ C )
% 0.31/0.48 => ( ! [X: set_nat,Y4: set_nat] :
% 0.31/0.48 ( ( ord_less_set_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % order_less_subst2
% 0.31/0.48 thf(fact_145_order__less__subst2,axiom,
% 0.31/0.48 ! [A: set_nat,B2: set_nat,F: set_nat > set_nat,C: set_nat] :
% 0.31/0.48 ( ( ord_less_set_nat @ A @ B2 )
% 0.31/0.48 => ( ( ord_less_set_nat @ ( F @ B2 ) @ C )
% 0.31/0.48 => ( ! [X: set_nat,Y4: set_nat] :
% 0.31/0.48 ( ( ord_less_set_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_set_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % order_less_subst2
% 0.31/0.48 thf(fact_146_order__less__subst2,axiom,
% 0.31/0.48 ! [A: set_nat,B2: set_nat,F: set_nat > nat > $o,C: nat > $o] :
% 0.31/0.48 ( ( ord_less_set_nat @ A @ B2 )
% 0.31/0.48 => ( ( ord_less_nat_o @ ( F @ B2 ) @ C )
% 0.31/0.48 => ( ! [X: set_nat,Y4: set_nat] :
% 0.31/0.48 ( ( ord_less_set_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % order_less_subst2
% 0.31/0.48 thf(fact_147_order__less__subst2,axiom,
% 0.31/0.48 ! [A: nat > $o,B2: nat > $o,F: ( nat > $o ) > nat,C: nat] :
% 0.31/0.48 ( ( ord_less_nat_o @ A @ B2 )
% 0.31/0.48 => ( ( ord_less_nat @ ( F @ B2 ) @ C )
% 0.31/0.48 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.31/0.48 ( ( ord_less_nat_o @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % order_less_subst2
% 0.31/0.48 thf(fact_148_order__less__subst2,axiom,
% 0.31/0.48 ! [A: nat > $o,B2: nat > $o,F: ( nat > $o ) > set_nat,C: set_nat] :
% 0.31/0.48 ( ( ord_less_nat_o @ A @ B2 )
% 0.31/0.48 => ( ( ord_less_set_nat @ ( F @ B2 ) @ C )
% 0.31/0.48 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.31/0.48 ( ( ord_less_nat_o @ X @ Y4 )
% 0.31/0.48 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_set_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % order_less_subst2
% 0.31/0.48 thf(fact_149_order__less__subst2,axiom,
% 0.31/0.48 ! [A: nat > $o,B2: nat > $o,F: ( nat > $o ) > nat > $o,C: nat > $o] :
% 0.31/0.48 ( ( ord_less_nat_o @ A @ B2 )
% 0.31/0.48 => ( ( ord_less_nat_o @ ( F @ B2 ) @ C )
% 0.31/0.48 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.31/0.48 ( ( ord_less_nat_o @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % order_less_subst2
% 0.31/0.48 thf(fact_150_order__less__subst2,axiom,
% 0.31/0.48 ! [A: nat,B2: nat,F: nat > nat,C: nat] :
% 0.31/0.48 ( ( ord_less_nat @ A @ B2 )
% 0.31/0.48 => ( ( ord_less_nat @ ( F @ B2 ) @ C )
% 0.31/0.48 => ( ! [X: nat,Y4: nat] :
% 0.31/0.48 ( ( ord_less_nat @ X @ Y4 )
% 0.31/0.48 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.31/0.48 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % order_less_subst2
% 0.31/0.48 thf(fact_151_gt__ex,axiom,
% 0.31/0.48 ! [X3: nat] :
% 0.31/0.48 ? [X_1: nat] : ( ord_less_nat @ X3 @ X_1 ) ).
% 0.31/0.48
% 0.31/0.48 % gt_ex
% 0.31/0.48 thf(fact_152_neqE,axiom,
% 0.31/0.48 ! [X3: nat,Y: nat] :
% 0.31/0.48 ( ( X3 != Y )
% 0.31/0.48 => ( ~ ( ord_less_nat @ X3 @ Y )
% 0.31/0.48 => ( ord_less_nat @ Y @ X3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % neqE
% 0.31/0.48 thf(fact_153_neq__iff,axiom,
% 0.31/0.48 ! [X3: nat,Y: nat] :
% 0.31/0.48 ( ( X3 != Y )
% 0.31/0.48 = ( ( ord_less_nat @ X3 @ Y )
% 0.31/0.48 | ( ord_less_nat @ Y @ X3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % neq_iff
% 0.31/0.48 thf(fact_154_order_Oasym,axiom,
% 0.31/0.48 ! [A: set_nat,B2: set_nat] :
% 0.31/0.48 ( ( ord_less_set_nat @ A @ B2 )
% 0.31/0.48 => ~ ( ord_less_set_nat @ B2 @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 % order.asym
% 0.31/0.48 thf(fact_155_order_Oasym,axiom,
% 0.31/0.48 ! [A: nat > $o,B2: nat > $o] :
% 0.31/0.48 ( ( ord_less_nat_o @ A @ B2 )
% 0.31/0.48 => ~ ( ord_less_nat_o @ B2 @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 % order.asym
% 0.31/0.48 thf(fact_156_order_Oasym,axiom,
% 0.31/0.48 ! [A: nat,B2: nat] :
% 0.31/0.48 ( ( ord_less_nat @ A @ B2 )
% 0.31/0.48 => ~ ( ord_less_nat @ B2 @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 % order.asym
% 0.31/0.48 thf(fact_157_less__imp__neq,axiom,
% 0.31/0.48 ! [X3: set_nat,Y: set_nat] :
% 0.31/0.48 ( ( ord_less_set_nat @ X3 @ Y )
% 0.31/0.48 => ( X3 != Y ) ) ).
% 0.31/0.48
% 0.31/0.48 % less_imp_neq
% 0.31/0.48 thf(fact_158_less__imp__neq,axiom,
% 0.31/0.48 ! [X3: nat > $o,Y: nat > $o] :
% 0.31/0.48 ( ( ord_less_nat_o @ X3 @ Y )
% 0.31/0.48 => ( X3 != Y ) ) ).
% 0.31/0.48
% 0.31/0.48 % less_imp_neq
% 0.31/0.48 thf(fact_159_less__imp__neq,axiom,
% 0.31/0.48 ! [X3: nat,Y: nat] :
% 0.31/0.48 ( ( ord_less_nat @ X3 @ Y )
% 0.31/0.48 => ( X3 != Y ) ) ).
% 0.31/0.48
% 0.31/0.48 % less_imp_neq
% 0.31/0.48 thf(fact_160_less__asym,axiom,
% 0.31/0.48 ! [X3: set_nat,Y: set_nat] :
% 0.31/0.48 ( ( ord_less_set_nat @ X3 @ Y )
% 0.31/0.48 => ~ ( ord_less_set_nat @ Y @ X3 ) ) ).
% 0.31/0.48
% 0.31/0.48 % less_asym
% 0.31/0.48 thf(fact_161_less__asym,axiom,
% 0.31/0.48 ! [X3: nat > $o,Y: nat > $o] :
% 0.31/0.48 ( ( ord_less_nat_o @ X3 @ Y )
% 0.31/0.48 => ~ ( ord_less_nat_o @ Y @ X3 ) ) ).
% 0.31/0.48
% 0.31/0.48 % less_asym
% 0.31/0.48 thf(fact_162_less__asym,axiom,
% 0.31/0.48 ! [X3: nat,Y: nat] :
% 0.31/0.48 ( ( ord_less_nat @ X3 @ Y )
% 0.31/0.48 => ~ ( ord_less_nat @ Y @ X3 ) ) ).
% 0.31/0.48
% 0.31/0.48 % less_asym
% 0.31/0.48 thf(fact_163_less__asym_H,axiom,
% 0.31/0.48 ! [A: set_nat,B2: set_nat] :
% 0.31/0.48 ( ( ord_less_set_nat @ A @ B2 )
% 0.31/0.48 => ~ ( ord_less_set_nat @ B2 @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 % less_asym'
% 0.31/0.48 thf(fact_164_less__asym_H,axiom,
% 0.31/0.48 ! [A: nat > $o,B2: nat > $o] :
% 0.31/0.48 ( ( ord_less_nat_o @ A @ B2 )
% 0.31/0.48 => ~ ( ord_less_nat_o @ B2 @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 % less_asym'
% 0.31/0.48 thf(fact_165_less__asym_H,axiom,
% 0.31/0.48 ! [A: nat,B2: nat] :
% 0.31/0.48 ( ( ord_less_nat @ A @ B2 )
% 0.31/0.48 => ~ ( ord_less_nat @ B2 @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 % less_asym'
% 0.31/0.49 thf(fact_166_less__trans,axiom,
% 0.31/0.49 ! [X3: set_nat,Y: set_nat,Z2: set_nat] :
% 0.31/0.49 ( ( ord_less_set_nat @ X3 @ Y )
% 0.31/0.49 => ( ( ord_less_set_nat @ Y @ Z2 )
% 0.31/0.49 => ( ord_less_set_nat @ X3 @ Z2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_trans
% 0.31/0.49 thf(fact_167_less__trans,axiom,
% 0.31/0.49 ! [X3: nat > $o,Y: nat > $o,Z2: nat > $o] :
% 0.31/0.49 ( ( ord_less_nat_o @ X3 @ Y )
% 0.31/0.49 => ( ( ord_less_nat_o @ Y @ Z2 )
% 0.31/0.49 => ( ord_less_nat_o @ X3 @ Z2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_trans
% 0.31/0.49 thf(fact_168_less__trans,axiom,
% 0.31/0.49 ! [X3: nat,Y: nat,Z2: nat] :
% 0.31/0.49 ( ( ord_less_nat @ X3 @ Y )
% 0.31/0.49 => ( ( ord_less_nat @ Y @ Z2 )
% 0.31/0.49 => ( ord_less_nat @ X3 @ Z2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_trans
% 0.31/0.49 thf(fact_169_less__linear,axiom,
% 0.31/0.49 ! [X3: nat,Y: nat] :
% 0.31/0.49 ( ( ord_less_nat @ X3 @ Y )
% 0.31/0.49 | ( X3 = Y )
% 0.31/0.49 | ( ord_less_nat @ Y @ X3 ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_linear
% 0.31/0.49 thf(fact_170_less__irrefl,axiom,
% 0.31/0.49 ! [X3: set_nat] :
% 0.31/0.49 ~ ( ord_less_set_nat @ X3 @ X3 ) ).
% 0.31/0.49
% 0.31/0.49 % less_irrefl
% 0.31/0.49 thf(fact_171_less__irrefl,axiom,
% 0.31/0.49 ! [X3: nat > $o] :
% 0.31/0.49 ~ ( ord_less_nat_o @ X3 @ X3 ) ).
% 0.31/0.49
% 0.31/0.49 % less_irrefl
% 0.31/0.49 thf(fact_172_less__irrefl,axiom,
% 0.31/0.49 ! [X3: nat] :
% 0.31/0.49 ~ ( ord_less_nat @ X3 @ X3 ) ).
% 0.31/0.49
% 0.31/0.49 % less_irrefl
% 0.31/0.49 thf(fact_173_ord__eq__less__trans,axiom,
% 0.31/0.49 ! [A: set_nat,B2: set_nat,C: set_nat] :
% 0.31/0.49 ( ( A = B2 )
% 0.31/0.49 => ( ( ord_less_set_nat @ B2 @ C )
% 0.31/0.49 => ( ord_less_set_nat @ A @ C ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % ord_eq_less_trans
% 0.31/0.49 thf(fact_174_ord__eq__less__trans,axiom,
% 0.31/0.49 ! [A: nat > $o,B2: nat > $o,C: nat > $o] :
% 0.31/0.49 ( ( A = B2 )
% 0.31/0.49 => ( ( ord_less_nat_o @ B2 @ C )
% 0.31/0.49 => ( ord_less_nat_o @ A @ C ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % ord_eq_less_trans
% 0.31/0.49 thf(fact_175_ord__eq__less__trans,axiom,
% 0.31/0.49 ! [A: nat,B2: nat,C: nat] :
% 0.31/0.49 ( ( A = B2 )
% 0.31/0.49 => ( ( ord_less_nat @ B2 @ C )
% 0.31/0.49 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % ord_eq_less_trans
% 0.31/0.49 thf(fact_176_ord__less__eq__trans,axiom,
% 0.31/0.49 ! [A: set_nat,B2: set_nat,C: set_nat] :
% 0.31/0.49 ( ( ord_less_set_nat @ A @ B2 )
% 0.31/0.49 => ( ( B2 = C )
% 0.31/0.49 => ( ord_less_set_nat @ A @ C ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % ord_less_eq_trans
% 0.31/0.49 thf(fact_177_ord__less__eq__trans,axiom,
% 0.31/0.49 ! [A: nat > $o,B2: nat > $o,C: nat > $o] :
% 0.31/0.49 ( ( ord_less_nat_o @ A @ B2 )
% 0.31/0.49 => ( ( B2 = C )
% 0.31/0.49 => ( ord_less_nat_o @ A @ C ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % ord_less_eq_trans
% 0.31/0.49 thf(fact_178_ord__less__eq__trans,axiom,
% 0.31/0.49 ! [A: nat,B2: nat,C: nat] :
% 0.31/0.49 ( ( ord_less_nat @ A @ B2 )
% 0.31/0.49 => ( ( B2 = C )
% 0.31/0.49 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % ord_less_eq_trans
% 0.31/0.49 thf(fact_179_dual__order_Oasym,axiom,
% 0.31/0.49 ! [B2: set_nat,A: set_nat] :
% 0.31/0.49 ( ( ord_less_set_nat @ B2 @ A )
% 0.31/0.49 => ~ ( ord_less_set_nat @ A @ B2 ) ) ).
% 0.31/0.49
% 0.31/0.49 % dual_order.asym
% 0.31/0.49 thf(fact_180_dual__order_Oasym,axiom,
% 0.31/0.49 ! [B2: nat > $o,A: nat > $o] :
% 0.31/0.49 ( ( ord_less_nat_o @ B2 @ A )
% 0.31/0.49 => ~ ( ord_less_nat_o @ A @ B2 ) ) ).
% 0.31/0.49
% 0.31/0.49 % dual_order.asym
% 0.31/0.49 thf(fact_181_dual__order_Oasym,axiom,
% 0.31/0.49 ! [B2: nat,A: nat] :
% 0.31/0.49 ( ( ord_less_nat @ B2 @ A )
% 0.31/0.49 => ~ ( ord_less_nat @ A @ B2 ) ) ).
% 0.31/0.49
% 0.31/0.49 % dual_order.asym
% 0.31/0.49 thf(fact_182_less__imp__not__eq,axiom,
% 0.31/0.49 ! [X3: set_nat,Y: set_nat] :
% 0.31/0.49 ( ( ord_less_set_nat @ X3 @ Y )
% 0.31/0.49 => ( X3 != Y ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_imp_not_eq
% 0.31/0.49 thf(fact_183_less__imp__not__eq,axiom,
% 0.31/0.49 ! [X3: nat > $o,Y: nat > $o] :
% 0.31/0.49 ( ( ord_less_nat_o @ X3 @ Y )
% 0.31/0.49 => ( X3 != Y ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_imp_not_eq
% 0.31/0.49 thf(fact_184_less__imp__not__eq,axiom,
% 0.31/0.49 ! [X3: nat,Y: nat] :
% 0.31/0.49 ( ( ord_less_nat @ X3 @ Y )
% 0.31/0.49 => ( X3 != Y ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_imp_not_eq
% 0.31/0.49 thf(fact_185_less__not__sym,axiom,
% 0.31/0.49 ! [X3: set_nat,Y: set_nat] :
% 0.31/0.49 ( ( ord_less_set_nat @ X3 @ Y )
% 0.31/0.49 => ~ ( ord_less_set_nat @ Y @ X3 ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_not_sym
% 0.31/0.49 thf(fact_186_less__not__sym,axiom,
% 0.31/0.49 ! [X3: nat > $o,Y: nat > $o] :
% 0.31/0.49 ( ( ord_less_nat_o @ X3 @ Y )
% 0.31/0.49 => ~ ( ord_less_nat_o @ Y @ X3 ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_not_sym
% 0.31/0.49 thf(fact_187_less__not__sym,axiom,
% 0.31/0.49 ! [X3: nat,Y: nat] :
% 0.31/0.49 ( ( ord_less_nat @ X3 @ Y )
% 0.31/0.49 => ~ ( ord_less_nat @ Y @ X3 ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_not_sym
% 0.31/0.49 thf(fact_188_less__induct,axiom,
% 0.31/0.49 ! [P: nat > $o,A: nat] :
% 0.31/0.49 ( ! [X: nat] :
% 0.31/0.49 ( ! [Y5: nat] :
% 0.31/0.49 ( ( ord_less_nat @ Y5 @ X )
% 0.31/0.49 => ( P @ Y5 ) )
% 0.31/0.49 => ( P @ X ) )
% 0.31/0.49 => ( P @ A ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_induct
% 0.31/0.49 thf(fact_189_antisym__conv3,axiom,
% 0.31/0.49 ! [Y: nat,X3: nat] :
% 0.31/0.49 ( ~ ( ord_less_nat @ Y @ X3 )
% 0.31/0.49 => ( ( ~ ( ord_less_nat @ X3 @ Y ) )
% 0.31/0.49 = ( X3 = Y ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % antisym_conv3
% 0.31/0.49 thf(fact_190_less__imp__not__eq2,axiom,
% 0.31/0.49 ! [X3: set_nat,Y: set_nat] :
% 0.31/0.49 ( ( ord_less_set_nat @ X3 @ Y )
% 0.31/0.49 => ( Y != X3 ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_imp_not_eq2
% 0.31/0.49 thf(fact_191_less__imp__not__eq2,axiom,
% 0.31/0.49 ! [X3: nat > $o,Y: nat > $o] :
% 0.31/0.49 ( ( ord_less_nat_o @ X3 @ Y )
% 0.31/0.49 => ( Y != X3 ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_imp_not_eq2
% 0.31/0.49 thf(fact_192_less__imp__not__eq2,axiom,
% 0.31/0.49 ! [X3: nat,Y: nat] :
% 0.31/0.49 ( ( ord_less_nat @ X3 @ Y )
% 0.31/0.49 => ( Y != X3 ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_imp_not_eq2
% 0.31/0.49 thf(fact_193_less__imp__triv,axiom,
% 0.31/0.49 ! [X3: set_nat,Y: set_nat,P: $o] :
% 0.31/0.49 ( ( ord_less_set_nat @ X3 @ Y )
% 0.31/0.49 => ( ( ord_less_set_nat @ Y @ X3 )
% 0.31/0.49 => P ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_imp_triv
% 0.31/0.49 thf(fact_194_less__imp__triv,axiom,
% 0.31/0.49 ! [X3: nat > $o,Y: nat > $o,P: $o] :
% 0.31/0.49 ( ( ord_less_nat_o @ X3 @ Y )
% 0.31/0.49 => ( ( ord_less_nat_o @ Y @ X3 )
% 0.31/0.49 => P ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_imp_triv
% 0.31/0.49 thf(fact_195_less__imp__triv,axiom,
% 0.31/0.49 ! [X3: nat,Y: nat,P: $o] :
% 0.31/0.49 ( ( ord_less_nat @ X3 @ Y )
% 0.31/0.49 => ( ( ord_less_nat @ Y @ X3 )
% 0.31/0.49 => P ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_imp_triv
% 0.31/0.49 thf(fact_196_linorder__cases,axiom,
% 0.31/0.49 ! [X3: nat,Y: nat] :
% 0.31/0.49 ( ~ ( ord_less_nat @ X3 @ Y )
% 0.31/0.49 => ( ( X3 != Y )
% 0.31/0.49 => ( ord_less_nat @ Y @ X3 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % linorder_cases
% 0.31/0.49 thf(fact_197_dual__order_Oirrefl,axiom,
% 0.31/0.49 ! [A: set_nat] :
% 0.31/0.49 ~ ( ord_less_set_nat @ A @ A ) ).
% 0.31/0.49
% 0.31/0.49 % dual_order.irrefl
% 0.31/0.49 thf(fact_198_dual__order_Oirrefl,axiom,
% 0.31/0.49 ! [A: nat > $o] :
% 0.31/0.49 ~ ( ord_less_nat_o @ A @ A ) ).
% 0.31/0.49
% 0.31/0.49 % dual_order.irrefl
% 0.31/0.49 thf(fact_199_dual__order_Oirrefl,axiom,
% 0.31/0.49 ! [A: nat] :
% 0.31/0.49 ~ ( ord_less_nat @ A @ A ) ).
% 0.31/0.49
% 0.31/0.49 % dual_order.irrefl
% 0.31/0.49 thf(fact_200_order_Ostrict__trans,axiom,
% 0.31/0.49 ! [A: set_nat,B2: set_nat,C: set_nat] :
% 0.31/0.49 ( ( ord_less_set_nat @ A @ B2 )
% 0.31/0.49 => ( ( ord_less_set_nat @ B2 @ C )
% 0.31/0.49 => ( ord_less_set_nat @ A @ C ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % order.strict_trans
% 0.31/0.49 thf(fact_201_order_Ostrict__trans,axiom,
% 0.31/0.49 ! [A: nat > $o,B2: nat > $o,C: nat > $o] :
% 0.31/0.49 ( ( ord_less_nat_o @ A @ B2 )
% 0.31/0.49 => ( ( ord_less_nat_o @ B2 @ C )
% 0.31/0.49 => ( ord_less_nat_o @ A @ C ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % order.strict_trans
% 0.31/0.49 thf(fact_202_order_Ostrict__trans,axiom,
% 0.31/0.49 ! [A: nat,B2: nat,C: nat] :
% 0.31/0.49 ( ( ord_less_nat @ A @ B2 )
% 0.31/0.49 => ( ( ord_less_nat @ B2 @ C )
% 0.31/0.49 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % order.strict_trans
% 0.31/0.49 thf(fact_203_less__imp__not__less,axiom,
% 0.31/0.49 ! [X3: set_nat,Y: set_nat] :
% 0.31/0.49 ( ( ord_less_set_nat @ X3 @ Y )
% 0.31/0.49 => ~ ( ord_less_set_nat @ Y @ X3 ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_imp_not_less
% 0.31/0.49 thf(fact_204_less__imp__not__less,axiom,
% 0.31/0.49 ! [X3: nat > $o,Y: nat > $o] :
% 0.31/0.49 ( ( ord_less_nat_o @ X3 @ Y )
% 0.31/0.49 => ~ ( ord_less_nat_o @ Y @ X3 ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_imp_not_less
% 0.31/0.49 thf(fact_205_less__imp__not__less,axiom,
% 0.31/0.49 ! [X3: nat,Y: nat] :
% 0.31/0.49 ( ( ord_less_nat @ X3 @ Y )
% 0.31/0.49 => ~ ( ord_less_nat @ Y @ X3 ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_imp_not_less
% 0.31/0.49 thf(fact_206_exists__least__iff,axiom,
% 0.31/0.49 ( ( ^ [P2: nat > $o] :
% 0.31/0.49 ? [X5: nat] : ( P2 @ X5 ) )
% 0.31/0.49 = ( ^ [P3: nat > $o] :
% 0.31/0.49 ? [N3: nat] :
% 0.31/0.49 ( ( P3 @ N3 )
% 0.31/0.49 & ! [M2: nat] :
% 0.31/0.49 ( ( ord_less_nat @ M2 @ N3 )
% 0.31/0.49 => ~ ( P3 @ M2 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % exists_least_iff
% 0.31/0.49 thf(fact_207_linorder__less__wlog,axiom,
% 0.31/0.49 ! [P: nat > nat > $o,A: nat,B2: nat] :
% 0.31/0.49 ( ! [A5: nat,B5: nat] :
% 0.31/0.49 ( ( ord_less_nat @ A5 @ B5 )
% 0.31/0.49 => ( P @ A5 @ B5 ) )
% 0.31/0.49 => ( ! [A5: nat] : ( P @ A5 @ A5 )
% 0.31/0.49 => ( ! [A5: nat,B5: nat] :
% 0.31/0.49 ( ( P @ B5 @ A5 )
% 0.31/0.49 => ( P @ A5 @ B5 ) )
% 0.31/0.49 => ( P @ A @ B2 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % linorder_less_wlog
% 0.31/0.49 thf(fact_208_dual__order_Ostrict__trans,axiom,
% 0.31/0.49 ! [B2: set_nat,A: set_nat,C: set_nat] :
% 0.31/0.49 ( ( ord_less_set_nat @ B2 @ A )
% 0.31/0.49 => ( ( ord_less_set_nat @ C @ B2 )
% 0.31/0.49 => ( ord_less_set_nat @ C @ A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % dual_order.strict_trans
% 0.31/0.49 thf(fact_209_dual__order_Ostrict__trans,axiom,
% 0.31/0.49 ! [B2: nat > $o,A: nat > $o,C: nat > $o] :
% 0.31/0.49 ( ( ord_less_nat_o @ B2 @ A )
% 0.31/0.49 => ( ( ord_less_nat_o @ C @ B2 )
% 0.31/0.49 => ( ord_less_nat_o @ C @ A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % dual_order.strict_trans
% 0.31/0.49 thf(fact_210_dual__order_Ostrict__trans,axiom,
% 0.31/0.49 ! [B2: nat,A: nat,C: nat] :
% 0.31/0.49 ( ( ord_less_nat @ B2 @ A )
% 0.31/0.49 => ( ( ord_less_nat @ C @ B2 )
% 0.31/0.49 => ( ord_less_nat @ C @ A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % dual_order.strict_trans
% 0.31/0.49 thf(fact_211_not__less__iff__gr__or__eq,axiom,
% 0.31/0.49 ! [X3: nat,Y: nat] :
% 0.31/0.49 ( ( ~ ( ord_less_nat @ X3 @ Y ) )
% 0.31/0.49 = ( ( ord_less_nat @ Y @ X3 )
% 0.31/0.49 | ( X3 = Y ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % not_less_iff_gr_or_eq
% 0.31/0.49 thf(fact_212_order_Ostrict__implies__not__eq,axiom,
% 0.31/0.49 ! [A: set_nat,B2: set_nat] :
% 0.31/0.49 ( ( ord_less_set_nat @ A @ B2 )
% 0.31/0.49 => ( A != B2 ) ) ).
% 0.31/0.49
% 0.31/0.49 % order.strict_implies_not_eq
% 0.31/0.49 thf(fact_213_order_Ostrict__implies__not__eq,axiom,
% 0.31/0.49 ! [A: nat > $o,B2: nat > $o] :
% 0.31/0.49 ( ( ord_less_nat_o @ A @ B2 )
% 0.31/0.49 => ( A != B2 ) ) ).
% 0.31/0.49
% 0.31/0.49 % order.strict_implies_not_eq
% 0.31/0.49 thf(fact_214_order_Ostrict__implies__not__eq,axiom,
% 0.31/0.49 ! [A: nat,B2: nat] :
% 0.31/0.49 ( ( ord_less_nat @ A @ B2 )
% 0.31/0.49 => ( A != B2 ) ) ).
% 0.31/0.49
% 0.31/0.49 % order.strict_implies_not_eq
% 0.31/0.49 thf(fact_215_dual__order_Ostrict__implies__not__eq,axiom,
% 0.31/0.49 ! [B2: set_nat,A: set_nat] :
% 0.31/0.49 ( ( ord_less_set_nat @ B2 @ A )
% 0.31/0.49 => ( A != B2 ) ) ).
% 0.31/0.49
% 0.31/0.49 % dual_order.strict_implies_not_eq
% 0.31/0.49 thf(fact_216_dual__order_Ostrict__implies__not__eq,axiom,
% 0.31/0.49 ! [B2: nat > $o,A: nat > $o] :
% 0.31/0.49 ( ( ord_less_nat_o @ B2 @ A )
% 0.31/0.49 => ( A != B2 ) ) ).
% 0.31/0.49
% 0.31/0.49 % dual_order.strict_implies_not_eq
% 0.31/0.49 thf(fact_217_dual__order_Ostrict__implies__not__eq,axiom,
% 0.31/0.49 ! [B2: nat,A: nat] :
% 0.31/0.49 ( ( ord_less_nat @ B2 @ A )
% 0.31/0.49 => ( A != B2 ) ) ).
% 0.31/0.49
% 0.31/0.49 % dual_order.strict_implies_not_eq
% 0.31/0.49 thf(fact_218_bot__fun__def,axiom,
% 0.31/0.49 ( bot_bot_nat_o
% 0.31/0.49 = ( ^ [X4: nat] : bot_bot_o ) ) ).
% 0.31/0.49
% 0.31/0.49 % bot_fun_def
% 0.31/0.49 thf(fact_219_mk__scheme_Osimps_I1_J,axiom,
% 0.31/0.49 ! [N2: nat] :
% 0.31/0.49 ( ( type_M1006385707scheme @ ( type_Mirabelle_TVar @ N2 ) )
% 0.31/0.49 = ( type_M876316792e_FVar @ N2 ) ) ).
% 0.31/0.49
% 0.31/0.49 % mk_scheme.simps(1)
% 0.31/0.49 thf(fact_220_is__singletonE,axiom,
% 0.31/0.49 ! [A2: set_nat] :
% 0.31/0.49 ( ( is_singleton_nat @ A2 )
% 0.31/0.49 => ~ ! [X: nat] :
% 0.31/0.49 ( A2
% 0.31/0.49 != ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % is_singletonE
% 0.31/0.49 thf(fact_221_is__singleton__def,axiom,
% 0.31/0.49 ( is_singleton_nat
% 0.31/0.49 = ( ^ [A4: set_nat] :
% 0.31/0.49 ? [X4: nat] :
% 0.31/0.49 ( A4
% 0.31/0.49 = ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % is_singleton_def
% 0.31/0.49 thf(fact_222_free__tv__id__subst,axiom,
% 0.31/0.49 ( ( type_M1715972684le_typ @ type_M405566558_subst )
% 0.31/0.49 = bot_bot_set_nat ) ).
% 0.31/0.49
% 0.31/0.49 % free_tv_id_subst
% 0.31/0.49 thf(fact_223_Set_Ois__empty__def,axiom,
% 0.31/0.49 ( is_empty_nat
% 0.31/0.49 = ( ^ [A4: set_nat] : ( A4 = bot_bot_set_nat ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % Set.is_empty_def
% 0.31/0.49 thf(fact_224_the__elem__def,axiom,
% 0.31/0.49 ( the_elem_nat
% 0.31/0.49 = ( ^ [X6: set_nat] :
% 0.31/0.49 ( the_nat
% 0.31/0.49 @ ^ [X4: nat] :
% 0.31/0.49 ( X6
% 0.31/0.49 = ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % the_elem_def
% 0.31/0.49 thf(fact_225_mk__scheme_Osimps_I2_J,axiom,
% 0.31/0.49 ! [T1: type_Mirabelle_typ,T2: type_Mirabelle_typ] :
% 0.31/0.49 ( ( type_M1006385707scheme @ ( type_Mirabelle_Fun @ T1 @ T2 ) )
% 0.31/0.49 = ( type_M155660035e_SFun @ ( type_M1006385707scheme @ T1 ) @ ( type_M1006385707scheme @ T2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % mk_scheme.simps(2)
% 0.31/0.49 thf(fact_226_Type__Mirabelle__lczmhmumaa_Odom__def,axiom,
% 0.31/0.49 ( type_Mirabelle_dom
% 0.31/0.49 = ( ^ [S4: nat > type_Mirabelle_typ] :
% 0.31/0.49 ( collect_nat
% 0.31/0.49 @ ^ [N3: nat] :
% 0.31/0.49 ( ( S4 @ N3 )
% 0.31/0.49 != ( type_Mirabelle_TVar @ N3 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % Type_Mirabelle_lczmhmumaa.dom_def
% 0.31/0.49 thf(fact_227_id__subst__def,axiom,
% 0.31/0.49 type_M405566558_subst = type_Mirabelle_TVar ).
% 0.31/0.49
% 0.31/0.49 % id_subst_def
% 0.31/0.49 thf(fact_228_typ_Oinject_I2_J,axiom,
% 0.31/0.49 ! [X21: type_Mirabelle_typ,X222: type_Mirabelle_typ,Y21: type_Mirabelle_typ,Y22: type_Mirabelle_typ] :
% 0.31/0.49 ( ( ( type_Mirabelle_Fun @ X21 @ X222 )
% 0.31/0.49 = ( type_Mirabelle_Fun @ Y21 @ Y22 ) )
% 0.31/0.49 = ( ( X21 = Y21 )
% 0.31/0.49 & ( X222 = Y22 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % typ.inject(2)
% 0.31/0.49 thf(fact_229_new__tv__Fun,axiom,
% 0.31/0.49 ! [N2: nat,T1: type_Mirabelle_typ,T2: type_Mirabelle_typ] :
% 0.31/0.49 ( ( type_M1211611096le_typ @ N2 @ ( type_Mirabelle_Fun @ T1 @ T2 ) )
% 0.31/0.49 = ( ( type_M1211611096le_typ @ N2 @ T1 )
% 0.31/0.49 & ( type_M1211611096le_typ @ N2 @ T2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % new_tv_Fun
% 0.31/0.49 thf(fact_230_dom__id__subst,axiom,
% 0.31/0.49 ( ( type_Mirabelle_dom @ type_M405566558_subst )
% 0.31/0.49 = bot_bot_set_nat ) ).
% 0.31/0.49
% 0.31/0.49 % dom_id_subst
% 0.31/0.49 thf(fact_231_psubsetD,axiom,
% 0.31/0.49 ! [A2: set_nat,B: set_nat,C: nat] :
% 0.31/0.49 ( ( ord_less_set_nat @ A2 @ B )
% 0.31/0.49 => ( ( member_nat @ C @ A2 )
% 0.31/0.49 => ( member_nat @ C @ B ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % psubsetD
% 0.31/0.49 thf(fact_232_less__set__def,axiom,
% 0.31/0.49 ( ord_less_set_nat
% 0.31/0.49 = ( ^ [A4: set_nat,B4: set_nat] :
% 0.31/0.49 ( ord_less_nat_o
% 0.31/0.49 @ ^ [X4: nat] : ( member_nat @ X4 @ A4 )
% 0.31/0.49 @ ^ [X4: nat] : ( member_nat @ X4 @ B4 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_set_def
% 0.31/0.49 thf(fact_233_psubset__trans,axiom,
% 0.31/0.49 ! [A2: set_nat,B: set_nat,C3: set_nat] :
% 0.31/0.49 ( ( ord_less_set_nat @ A2 @ B )
% 0.31/0.49 => ( ( ord_less_set_nat @ B @ C3 )
% 0.31/0.49 => ( ord_less_set_nat @ A2 @ C3 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % psubset_trans
% 0.31/0.49 thf(fact_234_new__tv__id__subst,axiom,
% 0.31/0.49 ! [N2: nat] : ( type_M1734147655le_typ @ N2 @ type_M405566558_subst ) ).
% 0.31/0.49
% 0.31/0.49 % new_tv_id_subst
% 0.31/0.49 thf(fact_235_app__subst__Fun,axiom,
% 0.31/0.49 ! [S: nat > type_Mirabelle_typ,T1: type_Mirabelle_typ,T2: type_Mirabelle_typ] :
% 0.31/0.49 ( ( type_M784671311le_typ @ S @ ( type_Mirabelle_Fun @ T1 @ T2 ) )
% 0.31/0.49 = ( type_Mirabelle_Fun @ ( type_M784671311le_typ @ S @ T1 ) @ ( type_M784671311le_typ @ S @ T2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % app_subst_Fun
% 0.31/0.49 thf(fact_236_typ_Oexhaust,axiom,
% 0.31/0.49 ! [Y: type_Mirabelle_typ] :
% 0.31/0.49 ( ! [X12: nat] :
% 0.31/0.49 ( Y
% 0.31/0.49 != ( type_Mirabelle_TVar @ X12 ) )
% 0.31/0.49 => ~ ! [X212: type_Mirabelle_typ,X223: type_Mirabelle_typ] :
% 0.31/0.49 ( Y
% 0.31/0.49 != ( type_Mirabelle_Fun @ X212 @ X223 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % typ.exhaust
% 0.31/0.49 thf(fact_237_typ_Oinduct,axiom,
% 0.31/0.49 ! [P: type_Mirabelle_typ > $o,Typ: type_Mirabelle_typ] :
% 0.31/0.49 ( ! [X: nat] : ( P @ ( type_Mirabelle_TVar @ X ) )
% 0.31/0.49 => ( ! [X1a: type_Mirabelle_typ,X22: type_Mirabelle_typ] :
% 0.31/0.49 ( ( P @ X1a )
% 0.31/0.49 => ( ( P @ X22 )
% 0.31/0.49 => ( P @ ( type_Mirabelle_Fun @ X1a @ X22 ) ) ) )
% 0.31/0.49 => ( P @ Typ ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % typ.induct
% 0.31/0.49 thf(fact_238_typ_Odistinct_I1_J,axiom,
% 0.31/0.49 ! [X1: nat,X21: type_Mirabelle_typ,X222: type_Mirabelle_typ] :
% 0.31/0.49 ( ( type_Mirabelle_TVar @ X1 )
% 0.31/0.49 != ( type_Mirabelle_Fun @ X21 @ X222 ) ) ).
% 0.31/0.49
% 0.31/0.49 % typ.distinct(1)
% 0.31/0.49 thf(fact_239_the__sym__eq__trivial,axiom,
% 0.31/0.49 ! [X3: nat] :
% 0.31/0.49 ( ( the_nat
% 0.31/0.49 @ ( ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.31/0.49 @ X3 ) )
% 0.31/0.49 = X3 ) ).
% 0.31/0.49
% 0.31/0.49 % the_sym_eq_trivial
% 0.31/0.49 thf(fact_240_the__eq__trivial,axiom,
% 0.31/0.49 ! [A: nat] :
% 0.31/0.49 ( ( the_nat
% 0.31/0.49 @ ^ [X4: nat] : ( X4 = A ) )
% 0.31/0.49 = A ) ).
% 0.31/0.49
% 0.31/0.49 % the_eq_trivial
% 0.31/0.49 thf(fact_241_the__equality,axiom,
% 0.31/0.49 ! [P: nat > $o,A: nat] :
% 0.31/0.49 ( ( P @ A )
% 0.31/0.49 => ( ! [X: nat] :
% 0.31/0.49 ( ( P @ X )
% 0.31/0.49 => ( X = A ) )
% 0.31/0.49 => ( ( the_nat @ P )
% 0.31/0.49 = A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % the_equality
% 0.31/0.49 thf(fact_242_cod__id__subst,axiom,
% 0.31/0.49 ( ( type_Mirabelle_cod @ type_M405566558_subst )
% 0.31/0.49 = bot_bot_set_nat ) ).
% 0.31/0.49
% 0.31/0.49 % cod_id_subst
% 0.31/0.49 thf(fact_243_theI,axiom,
% 0.31/0.49 ! [P: nat > $o,A: nat] :
% 0.31/0.49 ( ( P @ A )
% 0.31/0.49 => ( ! [X: nat] :
% 0.31/0.49 ( ( P @ X )
% 0.31/0.49 => ( X = A ) )
% 0.31/0.49 => ( P @ ( the_nat @ P ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % theI
% 0.31/0.49 thf(fact_244_theI_H,axiom,
% 0.31/0.49 ! [P: nat > $o] :
% 0.31/0.49 ( ? [X7: nat] :
% 0.31/0.49 ( ( P @ X7 )
% 0.31/0.49 & ! [Y4: nat] :
% 0.31/0.49 ( ( P @ Y4 )
% 0.31/0.49 => ( Y4 = X7 ) ) )
% 0.31/0.49 => ( P @ ( the_nat @ P ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % theI'
% 0.31/0.49 thf(fact_245_theI2,axiom,
% 0.31/0.49 ! [P: nat > $o,A: nat,Q: nat > $o] :
% 0.31/0.49 ( ( P @ A )
% 0.31/0.49 => ( ! [X: nat] :
% 0.31/0.49 ( ( P @ X )
% 0.31/0.49 => ( X = A ) )
% 0.31/0.49 => ( ! [X: nat] :
% 0.31/0.49 ( ( P @ X )
% 0.31/0.49 => ( Q @ X ) )
% 0.31/0.49 => ( Q @ ( the_nat @ P ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % theI2
% 0.31/0.49 thf(fact_246_If__def,axiom,
% 0.31/0.49 ( if_nat
% 0.31/0.49 = ( ^ [P3: $o,X4: nat,Y6: nat] :
% 0.31/0.49 ( the_nat
% 0.31/0.49 @ ^ [Z3: nat] :
% 0.31/0.49 ( ( P3
% 0.31/0.49 => ( Z3 = X4 ) )
% 0.31/0.49 & ( ~ P3
% 0.31/0.49 => ( Z3 = Y6 ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % If_def
% 0.31/0.49 thf(fact_247_the1I2,axiom,
% 0.31/0.49 ! [P: nat > $o,Q: nat > $o] :
% 0.31/0.49 ( ? [X7: nat] :
% 0.31/0.49 ( ( P @ X7 )
% 0.31/0.49 & ! [Y4: nat] :
% 0.31/0.49 ( ( P @ Y4 )
% 0.31/0.49 => ( Y4 = X7 ) ) )
% 0.31/0.49 => ( ! [X: nat] :
% 0.31/0.49 ( ( P @ X )
% 0.31/0.49 => ( Q @ X ) )
% 0.31/0.49 => ( Q @ ( the_nat @ P ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % the1I2
% 0.31/0.49 thf(fact_248_the1__equality,axiom,
% 0.31/0.49 ! [P: nat > $o,A: nat] :
% 0.31/0.49 ( ? [X7: nat] :
% 0.31/0.49 ( ( P @ X7 )
% 0.31/0.49 & ! [Y4: nat] :
% 0.31/0.49 ( ( P @ Y4 )
% 0.31/0.49 => ( Y4 = X7 ) ) )
% 0.31/0.49 => ( ( P @ A )
% 0.31/0.49 => ( ( the_nat @ P )
% 0.31/0.49 = A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % the1_equality
% 0.31/0.49 thf(fact_249_Collect__empty__eq__bot,axiom,
% 0.31/0.49 ! [P: nat > $o] :
% 0.31/0.49 ( ( ( collect_nat @ P )
% 0.31/0.49 = bot_bot_set_nat )
% 0.31/0.49 = ( P = bot_bot_nat_o ) ) ).
% 0.31/0.49
% 0.31/0.49 % Collect_empty_eq_bot
% 0.31/0.49 thf(fact_250_bot__empty__eq,axiom,
% 0.31/0.49 ( bot_bot_nat_o
% 0.31/0.49 = ( ^ [X4: nat] : ( member_nat @ X4 @ bot_bot_set_nat ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % bot_empty_eq
% 0.31/0.49 thf(fact_251_free__tv__subst,axiom,
% 0.31/0.49 ( type_M1715972684le_typ
% 0.31/0.49 = ( ^ [S4: nat > type_Mirabelle_typ] : ( sup_sup_set_nat @ ( type_Mirabelle_dom @ S4 ) @ ( type_Mirabelle_cod @ S4 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % free_tv_subst
% 0.31/0.49 thf(fact_252_UnCI,axiom,
% 0.31/0.49 ! [C: nat,B: set_nat,A2: set_nat] :
% 0.31/0.49 ( ( ~ ( member_nat @ C @ B )
% 0.31/0.49 => ( member_nat @ C @ A2 ) )
% 0.31/0.49 => ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % UnCI
% 0.31/0.49 thf(fact_253_Un__iff,axiom,
% 0.31/0.49 ! [C: nat,A2: set_nat,B: set_nat] :
% 0.31/0.49 ( ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B ) )
% 0.31/0.49 = ( ( member_nat @ C @ A2 )
% 0.31/0.49 | ( member_nat @ C @ B ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % Un_iff
% 0.31/0.49 thf(fact_254_Un__empty,axiom,
% 0.31/0.49 ! [A2: set_nat,B: set_nat] :
% 0.31/0.49 ( ( ( sup_sup_set_nat @ A2 @ B )
% 0.31/0.49 = bot_bot_set_nat )
% 0.31/0.49 = ( ( A2 = bot_bot_set_nat )
% 0.31/0.49 & ( B = bot_bot_set_nat ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % Un_empty
% 0.31/0.49 thf(fact_255_Un__insert__left,axiom,
% 0.31/0.49 ! [A: nat,B: set_nat,C3: set_nat] :
% 0.31/0.49 ( ( sup_sup_set_nat @ ( insert_nat @ A @ B ) @ C3 )
% 0.31/0.49 = ( insert_nat @ A @ ( sup_sup_set_nat @ B @ C3 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % Un_insert_left
% 0.31/0.49 thf(fact_256_Un__insert__right,axiom,
% 0.31/0.49 ! [A2: set_nat,A: nat,B: set_nat] :
% 0.31/0.49 ( ( sup_sup_set_nat @ A2 @ ( insert_nat @ A @ B ) )
% 0.31/0.49 = ( insert_nat @ A @ ( sup_sup_set_nat @ A2 @ B ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % Un_insert_right
% 0.31/0.49 thf(fact_257_weaken__asm__Un,axiom,
% 0.31/0.49 ! [A2: set_nat,P: nat > $o,Q: $o,B: set_nat] :
% 0.31/0.49 ( ( ! [X7: nat] :
% 0.31/0.49 ( ( member_nat @ X7 @ A2 )
% 0.31/0.49 => ( P @ X7 ) )
% 0.31/0.49 => Q )
% 0.31/0.49 => ( ! [X: nat] :
% 0.31/0.49 ( ( member_nat @ X @ ( sup_sup_set_nat @ A2 @ B ) )
% 0.31/0.49 => ( P @ X ) )
% 0.31/0.49 => Q ) ) ).
% 0.31/0.49
% 0.31/0.49 % weaken_asm_Un
% 0.31/0.49 thf(fact_258_UnE,axiom,
% 0.31/0.49 ! [C: nat,A2: set_nat,B: set_nat] :
% 0.31/0.49 ( ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B ) )
% 0.31/0.49 => ( ~ ( member_nat @ C @ A2 )
% 0.31/0.49 => ( member_nat @ C @ B ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % UnE
% 0.31/0.49 thf(fact_259_UnI1,axiom,
% 0.31/0.49 ! [C: nat,A2: set_nat,B: set_nat] :
% 0.31/0.49 ( ( member_nat @ C @ A2 )
% 0.31/0.49 => ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % UnI1
% 0.31/0.49 thf(fact_260_UnI2,axiom,
% 0.31/0.49 ! [C: nat,B: set_nat,A2: set_nat] :
% 0.31/0.49 ( ( member_nat @ C @ B )
% 0.31/0.49 => ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % UnI2
% 0.31/0.49 thf(fact_261_Un__def,axiom,
% 0.31/0.49 ( sup_sup_set_nat
% 0.31/0.49 = ( ^ [A4: set_nat,B4: set_nat] :
% 0.31/0.49 ( collect_nat
% 0.31/0.49 @ ^ [X4: nat] :
% 0.31/0.49 ( ( member_nat @ X4 @ A4 )
% 0.31/0.49 | ( member_nat @ X4 @ B4 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % Un_def
% 0.31/0.49 thf(fact_262_bex__Un,axiom,
% 0.31/0.49 ! [A2: set_nat,B: set_nat,P: nat > $o] :
% 0.31/0.49 ( ( ? [X4: nat] :
% 0.31/0.49 ( ( member_nat @ X4 @ ( sup_sup_set_nat @ A2 @ B ) )
% 0.31/0.49 & ( P @ X4 ) ) )
% 0.31/0.49 = ( ? [X4: nat] :
% 0.31/0.49 ( ( member_nat @ X4 @ A2 )
% 0.31/0.49 & ( P @ X4 ) )
% 0.31/0.49 | ? [X4: nat] :
% 0.31/0.49 ( ( member_nat @ X4 @ B )
% 0.31/0.49 & ( P @ X4 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % bex_Un
% 0.31/0.49 thf(fact_263_ball__Un,axiom,
% 0.31/0.49 ! [A2: set_nat,B: set_nat,P: nat > $o] :
% 0.31/0.49 ( ( ! [X4: nat] :
% 0.31/0.49 ( ( member_nat @ X4 @ ( sup_sup_set_nat @ A2 @ B ) )
% 0.31/0.49 => ( P @ X4 ) ) )
% 0.31/0.49 = ( ! [X4: nat] :
% 0.31/0.49 ( ( member_nat @ X4 @ A2 )
% 0.31/0.49 => ( P @ X4 ) )
% 0.31/0.49 & ! [X4: nat] :
% 0.31/0.49 ( ( member_nat @ X4 @ B )
% 0.31/0.49 => ( P @ X4 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % ball_Un
% 0.31/0.49 thf(fact_264_Un__assoc,axiom,
% 0.31/0.49 ! [A2: set_nat,B: set_nat,C3: set_nat] :
% 0.31/0.49 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A2 @ B ) @ C3 )
% 0.31/0.49 = ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ B @ C3 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % Un_assoc
% 0.31/0.49 thf(fact_265_Un__absorb,axiom,
% 0.31/0.49 ! [A2: set_nat] :
% 0.31/0.49 ( ( sup_sup_set_nat @ A2 @ A2 )
% 0.31/0.49 = A2 ) ).
% 0.31/0.49
% 0.31/0.49 % Un_absorb
% 0.31/0.49 thf(fact_266_Un__commute,axiom,
% 0.31/0.49 ( sup_sup_set_nat
% 0.31/0.49 = ( ^ [A4: set_nat,B4: set_nat] : ( sup_sup_set_nat @ B4 @ A4 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % Un_commute
% 0.31/0.49 thf(fact_267_Un__left__absorb,axiom,
% 0.31/0.49 ! [A2: set_nat,B: set_nat] :
% 0.31/0.49 ( ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ A2 @ B ) )
% 0.31/0.49 = ( sup_sup_set_nat @ A2 @ B ) ) ).
% 0.31/0.49
% 0.31/0.49 % Un_left_absorb
% 0.31/0.49 thf(fact_268_Collect__disj__eq,axiom,
% 0.31/0.49 ! [P: nat > $o,Q: nat > $o] :
% 0.31/0.49 ( ( collect_nat
% 0.31/0.49 @ ^ [X4: nat] :
% 0.31/0.49 ( ( P @ X4 )
% 0.31/0.49 | ( Q @ X4 ) ) )
% 0.31/0.49 = ( sup_sup_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % Collect_disj_eq
% 0.31/0.49 thf(fact_269_Un__left__commute,axiom,
% 0.31/0.49 ! [A2: set_nat,B: set_nat,C3: set_nat] :
% 0.31/0.49 ( ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ B @ C3 ) )
% 0.31/0.49 = ( sup_sup_set_nat @ B @ ( sup_sup_set_nat @ A2 @ C3 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % Un_left_commute
% 0.31/0.49 thf(fact_270_insert__def,axiom,
% 0.31/0.49 ( insert_nat
% 0.31/0.49 = ( ^ [A3: nat] :
% 0.31/0.49 ( sup_sup_set_nat
% 0.31/0.49 @ ( collect_nat
% 0.31/0.49 @ ^ [X4: nat] : ( X4 = A3 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % insert_def
% 0.31/0.49 thf(fact_271_Un__empty__left,axiom,
% 0.31/0.49 ! [B: set_nat] :
% 0.31/0.49 ( ( sup_sup_set_nat @ bot_bot_set_nat @ B )
% 0.31/0.49 = B ) ).
% 0.31/0.49
% 0.31/0.49 % Un_empty_left
% 0.31/0.49 thf(fact_272_Un__empty__right,axiom,
% 0.31/0.49 ! [A2: set_nat] :
% 0.31/0.49 ( ( sup_sup_set_nat @ A2 @ bot_bot_set_nat )
% 0.31/0.49 = A2 ) ).
% 0.31/0.49
% 0.31/0.49 % Un_empty_right
% 0.31/0.49 thf(fact_273_singleton__Un__iff,axiom,
% 0.31/0.49 ! [X3: nat,A2: set_nat,B: set_nat] :
% 0.31/0.49 ( ( ( insert_nat @ X3 @ bot_bot_set_nat )
% 0.31/0.49 = ( sup_sup_set_nat @ A2 @ B ) )
% 0.31/0.49 = ( ( ( A2 = bot_bot_set_nat )
% 0.31/0.49 & ( B
% 0.31/0.49 = ( insert_nat @ X3 @ bot_bot_set_nat ) ) )
% 0.31/0.49 | ( ( A2
% 0.31/0.49 = ( insert_nat @ X3 @ bot_bot_set_nat ) )
% 0.31/0.49 & ( B = bot_bot_set_nat ) )
% 0.31/0.49 | ( ( A2
% 0.31/0.49 = ( insert_nat @ X3 @ bot_bot_set_nat ) )
% 0.31/0.49 & ( B
% 0.31/0.49 = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % singleton_Un_iff
% 0.31/0.49 thf(fact_274_Un__singleton__iff,axiom,
% 0.31/0.49 ! [A2: set_nat,B: set_nat,X3: nat] :
% 0.31/0.49 ( ( ( sup_sup_set_nat @ A2 @ B )
% 0.31/0.49 = ( insert_nat @ X3 @ bot_bot_set_nat ) )
% 0.31/0.49 = ( ( ( A2 = bot_bot_set_nat )
% 0.31/0.49 & ( B
% 0.31/0.49 = ( insert_nat @ X3 @ bot_bot_set_nat ) ) )
% 0.31/0.49 | ( ( A2
% 0.31/0.49 = ( insert_nat @ X3 @ bot_bot_set_nat ) )
% 0.31/0.49 & ( B = bot_bot_set_nat ) )
% 0.31/0.49 | ( ( A2
% 0.31/0.49 = ( insert_nat @ X3 @ bot_bot_set_nat ) )
% 0.31/0.49 & ( B
% 0.31/0.49 = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % Un_singleton_iff
% 0.31/0.49 thf(fact_275_insert__is__Un,axiom,
% 0.31/0.49 ( insert_nat
% 0.31/0.49 = ( ^ [A3: nat] : ( sup_sup_set_nat @ ( insert_nat @ A3 @ bot_bot_set_nat ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % insert_is_Un
% 0.31/0.49 thf(fact_276_bound__tv__list_Osimps_I2_J,axiom,
% 0.31/0.49 ! [X3: type_Mirabelle_typ,L: list_T1103309005le_typ] :
% 0.31/0.49 ( ( type_M1539052445le_typ @ ( cons_T363929085le_typ @ X3 @ L ) )
% 0.31/0.49 = ( sup_sup_set_nat @ ( type_M801073677le_typ @ X3 ) @ ( type_M1539052445le_typ @ L ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % bound_tv_list.simps(2)
% 0.31/0.49 thf(fact_277_bound__tv__list_Osimps_I2_J,axiom,
% 0.31/0.49 ! [X3: nat > type_Mirabelle_typ,L: list_n396811828le_typ] :
% 0.31/0.49 ( ( type_M513401740le_typ @ ( cons_n499085924le_typ @ X3 @ L ) )
% 0.31/0.49 = ( sup_sup_set_nat @ ( type_M772783356le_typ @ X3 ) @ ( type_M513401740le_typ @ L ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % bound_tv_list.simps(2)
% 0.31/0.49 thf(fact_278_bound__tv__list_Osimps_I2_J,axiom,
% 0.31/0.49 ! [X3: list_T247403987scheme,L: list_l1334080099scheme] :
% 0.31/0.49 ( ( type_M1496178953scheme @ ( cons_l1910959773scheme @ X3 @ L ) )
% 0.31/0.49 = ( sup_sup_set_nat @ ( type_M961603331scheme @ X3 ) @ ( type_M1496178953scheme @ L ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % bound_tv_list.simps(2)
% 0.31/0.49 thf(fact_279_bound__tv__list_Osimps_I2_J,axiom,
% 0.31/0.49 ! [X3: type_M1694694083scheme,L: list_T247403987scheme] :
% 0.31/0.49 ( ( type_M961603331scheme @ ( cons_T633159821scheme @ X3 @ L ) )
% 0.31/0.49 = ( sup_sup_set_nat @ ( type_M326705277scheme @ X3 ) @ ( type_M961603331scheme @ L ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % bound_tv_list.simps(2)
% 0.31/0.49 thf(fact_280_free__tv__Fun,axiom,
% 0.31/0.49 ! [T1: type_Mirabelle_typ,T2: type_Mirabelle_typ] :
% 0.31/0.49 ( ( type_M49385309le_typ @ ( type_Mirabelle_Fun @ T1 @ T2 ) )
% 0.31/0.49 = ( sup_sup_set_nat @ ( type_M49385309le_typ @ T1 ) @ ( type_M49385309le_typ @ T2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % free_tv_Fun
% 0.31/0.49 thf(fact_281_free__tv__type__scheme_Osimps_I3_J,axiom,
% 0.31/0.49 ! [S1: type_M1694694083scheme,S2: type_M1694694083scheme] :
% 0.31/0.49 ( ( type_M1050318637scheme @ ( type_M155660035e_SFun @ S1 @ S2 ) )
% 0.31/0.49 = ( sup_sup_set_nat @ ( type_M1050318637scheme @ S1 ) @ ( type_M1050318637scheme @ S2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % free_tv_type_scheme.simps(3)
% 0.31/0.49 thf(fact_282_bound__tv__type__scheme_Osimps_I3_J,axiom,
% 0.31/0.49 ! [S1: type_M1694694083scheme,S2: type_M1694694083scheme] :
% 0.31/0.49 ( ( type_M326705277scheme @ ( type_M155660035e_SFun @ S1 @ S2 ) )
% 0.31/0.49 = ( sup_sup_set_nat @ ( type_M326705277scheme @ S1 ) @ ( type_M326705277scheme @ S2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % bound_tv_type_scheme.simps(3)
% 0.31/0.49 thf(fact_283_free__tv__list_Osimps_I2_J,axiom,
% 0.31/0.49 ! [X3: list_n396811828le_typ,L: list_l865305402le_typ] :
% 0.31/0.49 ( ( type_M906078444le_typ @ ( cons_l1800589546le_typ @ X3 @ L ) )
% 0.31/0.49 = ( sup_sup_set_nat @ ( type_M1691543772le_typ @ X3 ) @ ( type_M906078444le_typ @ L ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % free_tv_list.simps(2)
% 0.31/0.49 thf(fact_284_free__tv__list_Osimps_I2_J,axiom,
% 0.31/0.49 ! [X3: list_l1334080099scheme,L: list_l1704431731scheme] :
% 0.31/0.49 ( ( type_M1926053183scheme @ ( cons_l531914285scheme @ X3 @ L ) )
% 0.31/0.49 = ( sup_sup_set_nat @ ( type_M1958029241scheme @ X3 ) @ ( type_M1926053183scheme @ L ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % free_tv_list.simps(2)
% 0.31/0.49 thf(fact_285_free__tv__list_Osimps_I2_J,axiom,
% 0.31/0.49 ! [X3: list_T1103309005le_typ,L: list_l1790670291le_typ] :
% 0.31/0.49 ( ( type_M1418941437le_typ @ ( cons_l392684675le_typ @ X3 @ L ) )
% 0.31/0.49 = ( sup_sup_set_nat @ ( type_M510873837le_typ @ X3 ) @ ( type_M1418941437le_typ @ L ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % free_tv_list.simps(2)
% 0.31/0.49 thf(fact_286_free__tv__list_Osimps_I2_J,axiom,
% 0.31/0.49 ! [X3: type_Mirabelle_typ,L: list_T1103309005le_typ] :
% 0.31/0.49 ( ( type_M510873837le_typ @ ( cons_T363929085le_typ @ X3 @ L ) )
% 0.31/0.49 = ( sup_sup_set_nat @ ( type_M49385309le_typ @ X3 ) @ ( type_M510873837le_typ @ L ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % free_tv_list.simps(2)
% 0.31/0.49 thf(fact_287_free__tv__list_Osimps_I2_J,axiom,
% 0.31/0.49 ! [X3: list_T247403987scheme,L: list_l1334080099scheme] :
% 0.31/0.49 ( ( type_M1958029241scheme @ ( cons_l1910959773scheme @ X3 @ L ) )
% 0.31/0.49 = ( sup_sup_set_nat @ ( type_M141510067scheme @ X3 ) @ ( type_M1958029241scheme @ L ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % free_tv_list.simps(2)
% 0.31/0.49 thf(fact_288_free__tv__list_Osimps_I2_J,axiom,
% 0.31/0.49 ! [X3: nat > type_Mirabelle_typ,L: list_n396811828le_typ] :
% 0.31/0.49 ( ( type_M1691543772le_typ @ ( cons_n499085924le_typ @ X3 @ L ) )
% 0.31/0.49 = ( sup_sup_set_nat @ ( type_M1715972684le_typ @ X3 ) @ ( type_M1691543772le_typ @ L ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % free_tv_list.simps(2)
% 0.31/0.49 thf(fact_289_free__tv__list_Osimps_I2_J,axiom,
% 0.31/0.49 ! [X3: type_M1694694083scheme,L: list_T247403987scheme] :
% 0.31/0.49 ( ( type_M141510067scheme @ ( cons_T633159821scheme @ X3 @ L ) )
% 0.31/0.49 = ( sup_sup_set_nat @ ( type_M1050318637scheme @ X3 ) @ ( type_M141510067scheme @ L ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % free_tv_list.simps(2)
% 0.31/0.49 thf(fact_290_free__tv__fun__def,axiom,
% 0.31/0.49 ( type_M1715972684le_typ
% 0.31/0.49 = ( ^ [F2: nat > type_Mirabelle_typ] :
% 0.31/0.49 ( sup_sup_set_nat
% 0.31/0.49 @ ( type_Mirabelle_dom
% 0.31/0.49 @ ^ [N3: nat] : ( type_M1743451154le_typ @ ( F2 @ ( type_M1898948661at_nat @ N3 ) ) ) )
% 0.31/0.49 @ ( type_Mirabelle_cod
% 0.31/0.49 @ ^ [N3: nat] : ( type_M1743451154le_typ @ ( F2 @ ( type_M1898948661at_nat @ N3 ) ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % free_tv_fun_def
% 0.31/0.49 thf(fact_291_sup__bot__left,axiom,
% 0.31/0.49 ! [X3: nat > $o] :
% 0.31/0.49 ( ( sup_sup_nat_o @ bot_bot_nat_o @ X3 )
% 0.31/0.49 = X3 ) ).
% 0.31/0.49
% 0.31/0.49 % sup_bot_left
% 0.31/0.49 thf(fact_292_sup__bot__left,axiom,
% 0.31/0.49 ! [X3: set_nat] :
% 0.31/0.49 ( ( sup_sup_set_nat @ bot_bot_set_nat @ X3 )
% 0.31/0.49 = X3 ) ).
% 0.31/0.49
% 0.31/0.49 % sup_bot_left
% 0.31/0.49 thf(fact_293_sup__bot__right,axiom,
% 0.31/0.49 ! [X3: nat > $o] :
% 0.31/0.49 ( ( sup_sup_nat_o @ X3 @ bot_bot_nat_o )
% 0.31/0.49 = X3 ) ).
% 0.31/0.49
% 0.31/0.49 % sup_bot_right
% 0.31/0.49 thf(fact_294_sup__bot__right,axiom,
% 0.31/0.49 ! [X3: set_nat] :
% 0.31/0.49 ( ( sup_sup_set_nat @ X3 @ bot_bot_set_nat )
% 0.31/0.49 = X3 ) ).
% 0.31/0.49
% 0.31/0.49 % sup_bot_right
% 0.31/0.49 thf(fact_295_sup__bot_Oright__neutral,axiom,
% 0.31/0.49 ! [A: nat > $o] :
% 0.31/0.49 ( ( sup_sup_nat_o @ A @ bot_bot_nat_o )
% 0.31/0.49 = A ) ).
% 0.31/0.49
% 0.31/0.49 % sup_bot.right_neutral
% 0.31/0.49 thf(fact_296_sup__bot_Oright__neutral,axiom,
% 0.31/0.49 ! [A: set_nat] :
% 0.31/0.49 ( ( sup_sup_set_nat @ A @ bot_bot_set_nat )
% 0.31/0.49 = A ) ).
% 0.31/0.49
% 0.31/0.49 % sup_bot.right_neutral
% 0.31/0.49 thf(fact_297_sup__bot_Oneutr__eq__iff,axiom,
% 0.31/0.49 ! [A: nat > $o,B2: nat > $o] :
% 0.31/0.49 ( ( bot_bot_nat_o
% 0.31/0.49 = ( sup_sup_nat_o @ A @ B2 ) )
% 0.31/0.49 = ( ( A = bot_bot_nat_o )
% 0.31/0.49 & ( B2 = bot_bot_nat_o ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sup_bot.neutr_eq_iff
% 0.31/0.49 thf(fact_298_sup__bot_Oneutr__eq__iff,axiom,
% 0.31/0.49 ! [A: set_nat,B2: set_nat] :
% 0.31/0.49 ( ( bot_bot_set_nat
% 0.31/0.49 = ( sup_sup_set_nat @ A @ B2 ) )
% 0.31/0.49 = ( ( A = bot_bot_set_nat )
% 0.31/0.49 & ( B2 = bot_bot_set_nat ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sup_bot.neutr_eq_iff
% 0.31/0.49 thf(fact_299_sup__bot_Oleft__neutral,axiom,
% 0.31/0.49 ! [A: nat > $o] :
% 0.31/0.49 ( ( sup_sup_nat_o @ bot_bot_nat_o @ A )
% 0.31/0.49 = A ) ).
% 0.31/0.49
% 0.31/0.49 % sup_bot.left_neutral
% 0.31/0.49 thf(fact_300_sup__bot_Oleft__neutral,axiom,
% 0.31/0.49 ! [A: set_nat] :
% 0.31/0.49 ( ( sup_sup_set_nat @ bot_bot_set_nat @ A )
% 0.31/0.49 = A ) ).
% 0.31/0.49
% 0.31/0.49 % sup_bot.left_neutral
% 0.31/0.49 thf(fact_301_sup__bot_Oeq__neutr__iff,axiom,
% 0.31/0.49 ! [A: nat > $o,B2: nat > $o] :
% 0.31/0.49 ( ( ( sup_sup_nat_o @ A @ B2 )
% 0.31/0.49 = bot_bot_nat_o )
% 0.31/0.49 = ( ( A = bot_bot_nat_o )
% 0.31/0.49 & ( B2 = bot_bot_nat_o ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sup_bot.eq_neutr_iff
% 0.31/0.49 thf(fact_302_sup__bot_Oeq__neutr__iff,axiom,
% 0.31/0.49 ! [A: set_nat,B2: set_nat] :
% 0.31/0.49 ( ( ( sup_sup_set_nat @ A @ B2 )
% 0.31/0.49 = bot_bot_set_nat )
% 0.31/0.49 = ( ( A = bot_bot_set_nat )
% 0.31/0.49 & ( B2 = bot_bot_set_nat ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sup_bot.eq_neutr_iff
% 0.31/0.49 thf(fact_303_sup__eq__bot__iff,axiom,
% 0.31/0.49 ! [X3: nat > $o,Y: nat > $o] :
% 0.31/0.49 ( ( ( sup_sup_nat_o @ X3 @ Y )
% 0.31/0.49 = bot_bot_nat_o )
% 0.31/0.49 = ( ( X3 = bot_bot_nat_o )
% 0.31/0.49 & ( Y = bot_bot_nat_o ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sup_eq_bot_iff
% 0.31/0.49 thf(fact_304_sup__eq__bot__iff,axiom,
% 0.31/0.49 ! [X3: set_nat,Y: set_nat] :
% 0.31/0.49 ( ( ( sup_sup_set_nat @ X3 @ Y )
% 0.31/0.49 = bot_bot_set_nat )
% 0.31/0.49 = ( ( X3 = bot_bot_set_nat )
% 0.31/0.49 & ( Y = bot_bot_set_nat ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sup_eq_bot_iff
% 0.31/0.49 thf(fact_305_bot__eq__sup__iff,axiom,
% 0.31/0.49 ! [X3: nat > $o,Y: nat > $o] :
% 0.31/0.49 ( ( bot_bot_nat_o
% 0.31/0.49 = ( sup_sup_nat_o @ X3 @ Y ) )
% 0.31/0.49 = ( ( X3 = bot_bot_nat_o )
% 0.31/0.49 & ( Y = bot_bot_nat_o ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % bot_eq_sup_iff
% 0.31/0.49 thf(fact_306_bot__eq__sup__iff,axiom,
% 0.31/0.49 ! [X3: set_nat,Y: set_nat] :
% 0.31/0.49 ( ( bot_bot_set_nat
% 0.31/0.49 = ( sup_sup_set_nat @ X3 @ Y ) )
% 0.31/0.49 = ( ( X3 = bot_bot_set_nat )
% 0.31/0.49 & ( Y = bot_bot_set_nat ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % bot_eq_sup_iff
% 0.31/0.49 thf(fact_307_sup__Un__eq,axiom,
% 0.31/0.49 ! [R: set_nat,S: set_nat] :
% 0.31/0.49 ( ( sup_sup_nat_o
% 0.31/0.49 @ ^ [X4: nat] : ( member_nat @ X4 @ R )
% 0.31/0.49 @ ^ [X4: nat] : ( member_nat @ X4 @ S ) )
% 0.31/0.49 = ( ^ [X4: nat] : ( member_nat @ X4 @ ( sup_sup_set_nat @ R @ S ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sup_Un_eq
% 0.31/0.49 thf(fact_308_sup__set__def,axiom,
% 0.31/0.49 ( sup_sup_set_nat
% 0.31/0.49 = ( ^ [A4: set_nat,B4: set_nat] :
% 0.31/0.49 ( collect_nat
% 0.31/0.49 @ ( sup_sup_nat_o
% 0.31/0.49 @ ^ [X4: nat] : ( member_nat @ X4 @ A4 )
% 0.31/0.49 @ ^ [X4: nat] : ( member_nat @ X4 @ B4 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sup_set_def
% 0.31/0.49 thf(fact_309_less__supI1,axiom,
% 0.31/0.49 ! [X3: nat > $o,A: nat > $o,B2: nat > $o] :
% 0.31/0.49 ( ( ord_less_nat_o @ X3 @ A )
% 0.31/0.49 => ( ord_less_nat_o @ X3 @ ( sup_sup_nat_o @ A @ B2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_supI1
% 0.31/0.49 thf(fact_310_less__supI1,axiom,
% 0.31/0.49 ! [X3: set_nat,A: set_nat,B2: set_nat] :
% 0.31/0.49 ( ( ord_less_set_nat @ X3 @ A )
% 0.31/0.49 => ( ord_less_set_nat @ X3 @ ( sup_sup_set_nat @ A @ B2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_supI1
% 0.31/0.49 thf(fact_311_less__supI1,axiom,
% 0.31/0.49 ! [X3: nat,A: nat,B2: nat] :
% 0.31/0.49 ( ( ord_less_nat @ X3 @ A )
% 0.31/0.49 => ( ord_less_nat @ X3 @ ( sup_sup_nat @ A @ B2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_supI1
% 0.31/0.49 thf(fact_312_less__supI2,axiom,
% 0.31/0.49 ! [X3: nat > $o,B2: nat > $o,A: nat > $o] :
% 0.31/0.49 ( ( ord_less_nat_o @ X3 @ B2 )
% 0.31/0.49 => ( ord_less_nat_o @ X3 @ ( sup_sup_nat_o @ A @ B2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_supI2
% 0.31/0.49 thf(fact_313_less__supI2,axiom,
% 0.31/0.49 ! [X3: set_nat,B2: set_nat,A: set_nat] :
% 0.31/0.49 ( ( ord_less_set_nat @ X3 @ B2 )
% 0.31/0.49 => ( ord_less_set_nat @ X3 @ ( sup_sup_set_nat @ A @ B2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_supI2
% 0.31/0.49 thf(fact_314_less__supI2,axiom,
% 0.31/0.49 ! [X3: nat,B2: nat,A: nat] :
% 0.31/0.49 ( ( ord_less_nat @ X3 @ B2 )
% 0.31/0.49 => ( ord_less_nat @ X3 @ ( sup_sup_nat @ A @ B2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % less_supI2
% 0.31/0.49 thf(fact_315_sup_Ostrict__boundedE,axiom,
% 0.31/0.49 ! [B2: nat > $o,C: nat > $o,A: nat > $o] :
% 0.31/0.49 ( ( ord_less_nat_o @ ( sup_sup_nat_o @ B2 @ C ) @ A )
% 0.31/0.49 => ~ ( ( ord_less_nat_o @ B2 @ A )
% 0.31/0.49 => ~ ( ord_less_nat_o @ C @ A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sup.strict_boundedE
% 0.31/0.49 thf(fact_316_sup_Ostrict__boundedE,axiom,
% 0.31/0.49 ! [B2: set_nat,C: set_nat,A: set_nat] :
% 0.31/0.49 ( ( ord_less_set_nat @ ( sup_sup_set_nat @ B2 @ C ) @ A )
% 0.31/0.49 => ~ ( ( ord_less_set_nat @ B2 @ A )
% 0.31/0.49 => ~ ( ord_less_set_nat @ C @ A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sup.strict_boundedE
% 0.31/0.49 thf(fact_317_sup_Ostrict__boundedE,axiom,
% 0.31/0.49 ! [B2: nat,C: nat,A: nat] :
% 0.31/0.49 ( ( ord_less_nat @ ( sup_sup_nat @ B2 @ C ) @ A )
% 0.31/0.49 => ~ ( ( ord_less_nat @ B2 @ A )
% 0.31/0.49 => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sup.strict_boundedE
% 0.31/0.49 thf(fact_318_sup_Ostrict__order__iff,axiom,
% 0.31/0.49 ( ord_less_nat_o
% 0.31/0.49 = ( ^ [B6: nat > $o,A3: nat > $o] :
% 0.31/0.49 ( ( A3
% 0.31/0.49 = ( sup_sup_nat_o @ A3 @ B6 ) )
% 0.31/0.49 & ( A3 != B6 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sup.strict_order_iff
% 0.31/0.49 thf(fact_319_sup_Ostrict__order__iff,axiom,
% 0.31/0.49 ( ord_less_set_nat
% 0.31/0.49 = ( ^ [B6: set_nat,A3: set_nat] :
% 0.31/0.49 ( ( A3
% 0.31/0.49 = ( sup_sup_set_nat @ A3 @ B6 ) )
% 0.31/0.49 & ( A3 != B6 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sup.strict_order_iff
% 0.31/0.49 thf(fact_320_sup_Ostrict__order__iff,axiom,
% 0.31/0.49 ( ord_less_nat
% 0.31/0.49 = ( ^ [B6: nat,A3: nat] :
% 0.31/0.49 ( ( A3
% 0.31/0.49 = ( sup_sup_nat @ A3 @ B6 ) )
% 0.31/0.49 & ( A3 != B6 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sup.strict_order_iff
% 0.31/0.49 thf(fact_321_sup_Ostrict__coboundedI1,axiom,
% 0.31/0.49 ! [C: nat > $o,A: nat > $o,B2: nat > $o] :
% 0.31/0.49 ( ( ord_less_nat_o @ C @ A )
% 0.31/0.49 => ( ord_less_nat_o @ C @ ( sup_sup_nat_o @ A @ B2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sup.strict_coboundedI1
% 0.31/0.49 thf(fact_322_sup_Ostrict__coboundedI1,axiom,
% 0.31/0.49 ! [C: set_nat,A: set_nat,B2: set_nat] :
% 0.31/0.49 ( ( ord_less_set_nat @ C @ A )
% 0.31/0.49 => ( ord_less_set_nat @ C @ ( sup_sup_set_nat @ A @ B2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sup.strict_coboundedI1
% 0.31/0.49 thf(fact_323_sup_Ostrict__coboundedI1,axiom,
% 0.31/0.49 ! [C: nat,A: nat,B2: nat] :
% 0.31/0.49 ( ( ord_less_nat @ C @ A )
% 0.31/0.49 => ( ord_less_nat @ C @ ( sup_sup_nat @ A @ B2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sup.strict_coboundedI1
% 0.31/0.49 thf(fact_324_sup_Ostrict__coboundedI2,axiom,
% 0.31/0.49 ! [C: nat > $o,B2: nat > $o,A: nat > $o] :
% 0.31/0.49 ( ( ord_less_nat_o @ C @ B2 )
% 0.31/0.49 => ( ord_less_nat_o @ C @ ( sup_sup_nat_o @ A @ B2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sup.strict_coboundedI2
% 0.31/0.49 thf(fact_325_sup_Ostrict__coboundedI2,axiom,
% 0.31/0.49 ! [C: set_nat,B2: set_nat,A: set_nat] :
% 0.31/0.49 ( ( ord_less_set_nat @ C @ B2 )
% 0.31/0.49 => ( ord_less_set_nat @ C @ ( sup_sup_set_nat @ A @ B2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sup.strict_coboundedI2
% 0.31/0.49 thf(fact_326_sup_Ostrict__coboundedI2,axiom,
% 0.31/0.49 ! [C: nat,B2: nat,A: nat] :
% 0.31/0.49 ( ( ord_less_nat @ C @ B2 )
% 0.31/0.49 => ( ord_less_nat @ C @ ( sup_sup_nat @ A @ B2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sup.strict_coboundedI2
% 0.31/0.49 thf(fact_327_Nitpick_OThe__psimp,axiom,
% 0.31/0.49 ! [P: nat > $o,X3: nat] :
% 0.31/0.49 ( ( P
% 0.31/0.49 = ( ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.31/0.49 @ X3 ) )
% 0.31/0.49 => ( ( the_nat @ P )
% 0.31/0.49 = X3 ) ) ).
% 0.31/0.49
% 0.31/0.49 % Nitpick.The_psimp
% 0.31/0.49 thf(fact_328_theI__unique,axiom,
% 0.31/0.49 ! [P: nat > $o,X3: nat] :
% 0.31/0.49 ( ? [X7: nat] :
% 0.31/0.49 ( ( P @ X7 )
% 0.31/0.49 & ! [Y4: nat] :
% 0.31/0.49 ( ( P @ Y4 )
% 0.31/0.49 => ( Y4 = X7 ) ) )
% 0.31/0.49 => ( ( P @ X3 )
% 0.31/0.49 = ( X3
% 0.31/0.49 = ( the_nat @ P ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % theI_unique
% 0.31/0.49 thf(fact_329_sup__bot_Osemilattice__neutr__axioms,axiom,
% 0.31/0.49 semila1414375521_nat_o @ sup_sup_nat_o @ bot_bot_nat_o ).
% 0.31/0.49
% 0.31/0.49 % sup_bot.semilattice_neutr_axioms
% 0.31/0.49 thf(fact_330_sup__bot_Osemilattice__neutr__axioms,axiom,
% 0.31/0.49 semila1369944356et_nat @ sup_sup_set_nat @ bot_bot_set_nat ).
% 0.31/0.49
% 0.31/0.49 % sup_bot.semilattice_neutr_axioms
% 0.31/0.49 thf(fact_331_lexordp__eq__simps_I4_J,axiom,
% 0.31/0.49 ! [X3: set_nat,Xs: list_set_nat,Y: set_nat,Ys: list_set_nat] :
% 0.31/0.49 ( ( ord_le727790544et_nat @ ( cons_set_nat @ X3 @ Xs ) @ ( cons_set_nat @ Y @ Ys ) )
% 0.31/0.49 = ( ( ord_less_set_nat @ X3 @ Y )
% 0.31/0.49 | ( ~ ( ord_less_set_nat @ Y @ X3 )
% 0.31/0.49 & ( ord_le727790544et_nat @ Xs @ Ys ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq_simps(4)
% 0.31/0.49 thf(fact_332_lexordp__eq__simps_I4_J,axiom,
% 0.31/0.49 ! [X3: nat > $o,Xs: list_nat_o,Y: nat > $o,Ys: list_nat_o] :
% 0.31/0.49 ( ( ord_lexordp_eq_nat_o @ ( cons_nat_o @ X3 @ Xs ) @ ( cons_nat_o @ Y @ Ys ) )
% 0.31/0.49 = ( ( ord_less_nat_o @ X3 @ Y )
% 0.31/0.49 | ( ~ ( ord_less_nat_o @ Y @ X3 )
% 0.31/0.49 & ( ord_lexordp_eq_nat_o @ Xs @ Ys ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq_simps(4)
% 0.31/0.49 thf(fact_333_lexordp__eq__simps_I4_J,axiom,
% 0.31/0.49 ! [X3: nat,Xs: list_nat,Y: nat,Ys: list_nat] :
% 0.31/0.49 ( ( ord_lexordp_eq_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys ) )
% 0.31/0.49 = ( ( ord_less_nat @ X3 @ Y )
% 0.31/0.49 | ( ~ ( ord_less_nat @ Y @ X3 )
% 0.31/0.49 & ( ord_lexordp_eq_nat @ Xs @ Ys ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq_simps(4)
% 0.31/0.49 thf(fact_334_lexordp__eq_OCons__eq,axiom,
% 0.31/0.49 ! [X3: set_nat,Y: set_nat,Xs: list_set_nat,Ys: list_set_nat] :
% 0.31/0.49 ( ~ ( ord_less_set_nat @ X3 @ Y )
% 0.31/0.49 => ( ~ ( ord_less_set_nat @ Y @ X3 )
% 0.31/0.49 => ( ( ord_le727790544et_nat @ Xs @ Ys )
% 0.31/0.49 => ( ord_le727790544et_nat @ ( cons_set_nat @ X3 @ Xs ) @ ( cons_set_nat @ Y @ Ys ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq.Cons_eq
% 0.31/0.49 thf(fact_335_lexordp__eq_OCons__eq,axiom,
% 0.31/0.49 ! [X3: nat > $o,Y: nat > $o,Xs: list_nat_o,Ys: list_nat_o] :
% 0.31/0.49 ( ~ ( ord_less_nat_o @ X3 @ Y )
% 0.31/0.49 => ( ~ ( ord_less_nat_o @ Y @ X3 )
% 0.31/0.49 => ( ( ord_lexordp_eq_nat_o @ Xs @ Ys )
% 0.31/0.49 => ( ord_lexordp_eq_nat_o @ ( cons_nat_o @ X3 @ Xs ) @ ( cons_nat_o @ Y @ Ys ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq.Cons_eq
% 0.31/0.49 thf(fact_336_lexordp__eq_OCons__eq,axiom,
% 0.31/0.49 ! [X3: nat,Y: nat,Xs: list_nat,Ys: list_nat] :
% 0.31/0.49 ( ~ ( ord_less_nat @ X3 @ Y )
% 0.31/0.49 => ( ~ ( ord_less_nat @ Y @ X3 )
% 0.31/0.49 => ( ( ord_lexordp_eq_nat @ Xs @ Ys )
% 0.31/0.49 => ( ord_lexordp_eq_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq.Cons_eq
% 0.31/0.49 thf(fact_337_lexordp__eq_OCons,axiom,
% 0.31/0.49 ! [X3: set_nat,Y: set_nat,Xs: list_set_nat,Ys: list_set_nat] :
% 0.31/0.49 ( ( ord_less_set_nat @ X3 @ Y )
% 0.31/0.49 => ( ord_le727790544et_nat @ ( cons_set_nat @ X3 @ Xs ) @ ( cons_set_nat @ Y @ Ys ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq.Cons
% 0.31/0.49 thf(fact_338_lexordp__eq_OCons,axiom,
% 0.31/0.49 ! [X3: nat > $o,Y: nat > $o,Xs: list_nat_o,Ys: list_nat_o] :
% 0.31/0.49 ( ( ord_less_nat_o @ X3 @ Y )
% 0.31/0.49 => ( ord_lexordp_eq_nat_o @ ( cons_nat_o @ X3 @ Xs ) @ ( cons_nat_o @ Y @ Ys ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq.Cons
% 0.31/0.49 thf(fact_339_lexordp__eq_OCons,axiom,
% 0.31/0.49 ! [X3: nat,Y: nat,Xs: list_nat,Ys: list_nat] :
% 0.31/0.49 ( ( ord_less_nat @ X3 @ Y )
% 0.31/0.49 => ( ord_lexordp_eq_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq.Cons
% 0.31/0.49 thf(fact_340_lexordp__eq__antisym,axiom,
% 0.31/0.49 ! [Xs: list_nat,Ys: list_nat] :
% 0.31/0.49 ( ( ord_lexordp_eq_nat @ Xs @ Ys )
% 0.31/0.49 => ( ( ord_lexordp_eq_nat @ Ys @ Xs )
% 0.31/0.49 => ( Xs = Ys ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq_antisym
% 0.31/0.49 thf(fact_341_lexordp__eq__linear,axiom,
% 0.31/0.49 ! [Xs: list_nat,Ys: list_nat] :
% 0.31/0.49 ( ( ord_lexordp_eq_nat @ Xs @ Ys )
% 0.31/0.49 | ( ord_lexordp_eq_nat @ Ys @ Xs ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq_linear
% 0.31/0.49 thf(fact_342_lexordp__eq__trans,axiom,
% 0.31/0.49 ! [Xs: list_nat,Ys: list_nat,Zs: list_nat] :
% 0.31/0.49 ( ( ord_lexordp_eq_nat @ Xs @ Ys )
% 0.31/0.49 => ( ( ord_lexordp_eq_nat @ Ys @ Zs )
% 0.31/0.49 => ( ord_lexordp_eq_nat @ Xs @ Zs ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq_trans
% 0.31/0.49 thf(fact_343_lexordp__eq__refl,axiom,
% 0.31/0.49 ! [Xs: list_nat] : ( ord_lexordp_eq_nat @ Xs @ Xs ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq_refl
% 0.31/0.49 thf(fact_344_lexordp__eq_Ocases,axiom,
% 0.31/0.49 ! [A1: list_set_nat,A22: list_set_nat] :
% 0.31/0.49 ( ( ord_le727790544et_nat @ A1 @ A22 )
% 0.31/0.49 => ( ( A1 != nil_set_nat )
% 0.31/0.49 => ( ! [X: set_nat] :
% 0.31/0.49 ( ? [Xs2: list_set_nat] :
% 0.31/0.49 ( A1
% 0.31/0.49 = ( cons_set_nat @ X @ Xs2 ) )
% 0.31/0.49 => ! [Y4: set_nat] :
% 0.31/0.49 ( ? [Ys2: list_set_nat] :
% 0.31/0.49 ( A22
% 0.31/0.49 = ( cons_set_nat @ Y4 @ Ys2 ) )
% 0.31/0.49 => ~ ( ord_less_set_nat @ X @ Y4 ) ) )
% 0.31/0.49 => ~ ! [X: set_nat,Y4: set_nat,Xs2: list_set_nat] :
% 0.31/0.49 ( ( A1
% 0.31/0.49 = ( cons_set_nat @ X @ Xs2 ) )
% 0.31/0.49 => ! [Ys2: list_set_nat] :
% 0.31/0.49 ( ( A22
% 0.31/0.49 = ( cons_set_nat @ Y4 @ Ys2 ) )
% 0.31/0.49 => ( ~ ( ord_less_set_nat @ X @ Y4 )
% 0.31/0.49 => ( ~ ( ord_less_set_nat @ Y4 @ X )
% 0.31/0.49 => ~ ( ord_le727790544et_nat @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq.cases
% 0.31/0.49 thf(fact_345_lexordp__eq_Ocases,axiom,
% 0.31/0.49 ! [A1: list_nat_o,A22: list_nat_o] :
% 0.31/0.49 ( ( ord_lexordp_eq_nat_o @ A1 @ A22 )
% 0.31/0.49 => ( ( A1 != nil_nat_o )
% 0.31/0.49 => ( ! [X: nat > $o] :
% 0.31/0.49 ( ? [Xs2: list_nat_o] :
% 0.31/0.49 ( A1
% 0.31/0.49 = ( cons_nat_o @ X @ Xs2 ) )
% 0.31/0.49 => ! [Y4: nat > $o] :
% 0.31/0.49 ( ? [Ys2: list_nat_o] :
% 0.31/0.49 ( A22
% 0.31/0.49 = ( cons_nat_o @ Y4 @ Ys2 ) )
% 0.31/0.49 => ~ ( ord_less_nat_o @ X @ Y4 ) ) )
% 0.31/0.49 => ~ ! [X: nat > $o,Y4: nat > $o,Xs2: list_nat_o] :
% 0.31/0.49 ( ( A1
% 0.31/0.49 = ( cons_nat_o @ X @ Xs2 ) )
% 0.31/0.49 => ! [Ys2: list_nat_o] :
% 0.31/0.49 ( ( A22
% 0.31/0.49 = ( cons_nat_o @ Y4 @ Ys2 ) )
% 0.31/0.49 => ( ~ ( ord_less_nat_o @ X @ Y4 )
% 0.31/0.49 => ( ~ ( ord_less_nat_o @ Y4 @ X )
% 0.31/0.49 => ~ ( ord_lexordp_eq_nat_o @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq.cases
% 0.31/0.49 thf(fact_346_lexordp__eq_Ocases,axiom,
% 0.31/0.49 ! [A1: list_nat,A22: list_nat] :
% 0.31/0.49 ( ( ord_lexordp_eq_nat @ A1 @ A22 )
% 0.31/0.49 => ( ( A1 != nil_nat )
% 0.31/0.49 => ( ! [X: nat] :
% 0.31/0.49 ( ? [Xs2: list_nat] :
% 0.31/0.49 ( A1
% 0.31/0.49 = ( cons_nat @ X @ Xs2 ) )
% 0.31/0.49 => ! [Y4: nat] :
% 0.31/0.49 ( ? [Ys2: list_nat] :
% 0.31/0.49 ( A22
% 0.31/0.49 = ( cons_nat @ Y4 @ Ys2 ) )
% 0.31/0.49 => ~ ( ord_less_nat @ X @ Y4 ) ) )
% 0.31/0.49 => ~ ! [X: nat,Y4: nat,Xs2: list_nat] :
% 0.31/0.49 ( ( A1
% 0.31/0.49 = ( cons_nat @ X @ Xs2 ) )
% 0.31/0.49 => ! [Ys2: list_nat] :
% 0.31/0.49 ( ( A22
% 0.31/0.49 = ( cons_nat @ Y4 @ Ys2 ) )
% 0.31/0.49 => ( ~ ( ord_less_nat @ X @ Y4 )
% 0.31/0.49 => ( ~ ( ord_less_nat @ Y4 @ X )
% 0.31/0.49 => ~ ( ord_lexordp_eq_nat @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq.cases
% 0.31/0.49 thf(fact_347_lexordp__eq_Osimps,axiom,
% 0.31/0.49 ( ord_le727790544et_nat
% 0.31/0.49 = ( ^ [A12: list_set_nat,A23: list_set_nat] :
% 0.31/0.49 ( ? [Ys3: list_set_nat] :
% 0.31/0.49 ( ( A12 = nil_set_nat )
% 0.31/0.49 & ( A23 = Ys3 ) )
% 0.31/0.49 | ? [X4: set_nat,Y6: set_nat,Xs3: list_set_nat,Ys3: list_set_nat] :
% 0.31/0.49 ( ( A12
% 0.31/0.49 = ( cons_set_nat @ X4 @ Xs3 ) )
% 0.31/0.49 & ( A23
% 0.31/0.49 = ( cons_set_nat @ Y6 @ Ys3 ) )
% 0.31/0.49 & ( ord_less_set_nat @ X4 @ Y6 ) )
% 0.31/0.49 | ? [X4: set_nat,Y6: set_nat,Xs3: list_set_nat,Ys3: list_set_nat] :
% 0.31/0.49 ( ( A12
% 0.31/0.49 = ( cons_set_nat @ X4 @ Xs3 ) )
% 0.31/0.49 & ( A23
% 0.31/0.49 = ( cons_set_nat @ Y6 @ Ys3 ) )
% 0.31/0.49 & ~ ( ord_less_set_nat @ X4 @ Y6 )
% 0.31/0.49 & ~ ( ord_less_set_nat @ Y6 @ X4 )
% 0.31/0.49 & ( ord_le727790544et_nat @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq.simps
% 0.31/0.49 thf(fact_348_lexordp__eq_Osimps,axiom,
% 0.31/0.49 ( ord_lexordp_eq_nat_o
% 0.31/0.49 = ( ^ [A12: list_nat_o,A23: list_nat_o] :
% 0.31/0.49 ( ? [Ys3: list_nat_o] :
% 0.31/0.49 ( ( A12 = nil_nat_o )
% 0.31/0.49 & ( A23 = Ys3 ) )
% 0.31/0.49 | ? [X4: nat > $o,Y6: nat > $o,Xs3: list_nat_o,Ys3: list_nat_o] :
% 0.31/0.49 ( ( A12
% 0.31/0.49 = ( cons_nat_o @ X4 @ Xs3 ) )
% 0.31/0.49 & ( A23
% 0.31/0.49 = ( cons_nat_o @ Y6 @ Ys3 ) )
% 0.31/0.49 & ( ord_less_nat_o @ X4 @ Y6 ) )
% 0.31/0.49 | ? [X4: nat > $o,Y6: nat > $o,Xs3: list_nat_o,Ys3: list_nat_o] :
% 0.31/0.49 ( ( A12
% 0.31/0.49 = ( cons_nat_o @ X4 @ Xs3 ) )
% 0.31/0.49 & ( A23
% 0.31/0.49 = ( cons_nat_o @ Y6 @ Ys3 ) )
% 0.31/0.49 & ~ ( ord_less_nat_o @ X4 @ Y6 )
% 0.31/0.49 & ~ ( ord_less_nat_o @ Y6 @ X4 )
% 0.31/0.49 & ( ord_lexordp_eq_nat_o @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq.simps
% 0.31/0.49 thf(fact_349_lexordp__eq_Osimps,axiom,
% 0.31/0.49 ( ord_lexordp_eq_nat
% 0.31/0.49 = ( ^ [A12: list_nat,A23: list_nat] :
% 0.31/0.49 ( ? [Ys3: list_nat] :
% 0.31/0.49 ( ( A12 = nil_nat )
% 0.31/0.49 & ( A23 = Ys3 ) )
% 0.31/0.49 | ? [X4: nat,Y6: nat,Xs3: list_nat,Ys3: list_nat] :
% 0.31/0.49 ( ( A12
% 0.31/0.49 = ( cons_nat @ X4 @ Xs3 ) )
% 0.31/0.49 & ( A23
% 0.31/0.49 = ( cons_nat @ Y6 @ Ys3 ) )
% 0.31/0.49 & ( ord_less_nat @ X4 @ Y6 ) )
% 0.31/0.49 | ? [X4: nat,Y6: nat,Xs3: list_nat,Ys3: list_nat] :
% 0.31/0.49 ( ( A12
% 0.31/0.49 = ( cons_nat @ X4 @ Xs3 ) )
% 0.31/0.49 & ( A23
% 0.31/0.49 = ( cons_nat @ Y6 @ Ys3 ) )
% 0.31/0.49 & ~ ( ord_less_nat @ X4 @ Y6 )
% 0.31/0.49 & ~ ( ord_less_nat @ Y6 @ X4 )
% 0.31/0.49 & ( ord_lexordp_eq_nat @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq.simps
% 0.31/0.49 thf(fact_350_app__subst__Nil,axiom,
% 0.31/0.49 ! [S: nat > type_Mirabelle_typ] :
% 0.31/0.49 ( ( type_M1944210753scheme @ S @ nil_Ty61485117scheme )
% 0.31/0.49 = nil_Ty61485117scheme ) ).
% 0.31/0.49
% 0.31/0.49 % app_subst_Nil
% 0.31/0.49 thf(fact_351_new__tv__Nil,axiom,
% 0.31/0.49 ! [N2: nat] : ( type_M2064939256scheme @ N2 @ nil_Ty61485117scheme ) ).
% 0.31/0.49
% 0.31/0.49 % new_tv_Nil
% 0.31/0.49 thf(fact_352_free__tv__list_Osimps_I1_J,axiom,
% 0.31/0.49 ( ( type_M141510067scheme @ nil_Ty61485117scheme )
% 0.31/0.49 = bot_bot_set_nat ) ).
% 0.31/0.49
% 0.31/0.49 % free_tv_list.simps(1)
% 0.31/0.49 thf(fact_353_lexordp__eq_Oinducts,axiom,
% 0.31/0.49 ! [X1: list_nat,X2: list_nat,P: list_nat > list_nat > $o] :
% 0.31/0.49 ( ( ord_lexordp_eq_nat @ X1 @ X2 )
% 0.31/0.49 => ( ! [X_1: list_nat] : ( P @ nil_nat @ X_1 )
% 0.31/0.49 => ( ! [X: nat,Y4: nat,Xs2: list_nat,Ys2: list_nat] :
% 0.31/0.49 ( ( ord_less_nat @ X @ Y4 )
% 0.31/0.49 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y4 @ Ys2 ) ) )
% 0.31/0.49 => ( ! [X: nat,Y4: nat,Xs2: list_nat,Ys2: list_nat] :
% 0.31/0.49 ( ~ ( ord_less_nat @ X @ Y4 )
% 0.31/0.49 => ( ~ ( ord_less_nat @ Y4 @ X )
% 0.31/0.49 => ( ( ord_lexordp_eq_nat @ Xs2 @ Ys2 )
% 0.31/0.49 => ( ( P @ Xs2 @ Ys2 )
% 0.31/0.49 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y4 @ Ys2 ) ) ) ) ) )
% 0.31/0.49 => ( P @ X1 @ X2 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq.inducts
% 0.31/0.49
% 0.31/0.49 % Helper facts (5)
% 0.31/0.49 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 0.31/0.49 ! [X3: nat,Y: nat] :
% 0.31/0.49 ( ( if_nat @ $false @ X3 @ Y )
% 0.31/0.49 = Y ) ).
% 0.31/0.49
% 0.31/0.49 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 0.31/0.49 ! [X3: nat,Y: nat] :
% 0.31/0.49 ( ( if_nat @ $true @ X3 @ Y )
% 0.31/0.49 = X3 ) ).
% 0.31/0.49
% 0.31/0.49 thf(help_If_3_1_If_001t__Type____Mirabelle____lczmhmumaa__Otyp_T,axiom,
% 0.31/0.49 ! [P: $o] :
% 0.31/0.49 ( ( P = $true )
% 0.31/0.49 | ( P = $false ) ) ).
% 0.31/0.49
% 0.31/0.49 thf(help_If_2_1_If_001t__Type____Mirabelle____lczmhmumaa__Otyp_T,axiom,
% 0.31/0.49 ! [X3: type_Mirabelle_typ,Y: type_Mirabelle_typ] :
% 0.31/0.49 ( ( if_Typ1169047309le_typ @ $false @ X3 @ Y )
% 0.31/0.49 = Y ) ).
% 0.31/0.49
% 0.31/0.49 thf(help_If_1_1_If_001t__Type____Mirabelle____lczmhmumaa__Otyp_T,axiom,
% 0.31/0.49 ! [X3: type_Mirabelle_typ,Y: type_Mirabelle_typ] :
% 0.31/0.49 ( ( if_Typ1169047309le_typ @ $true @ X3 @ Y )
% 0.31/0.49 = X3 ) ).
% 0.31/0.49
% 0.31/0.49 % Conjectures (1)
% 0.31/0.49 thf(conj_0,conjecture,
% 0.31/0.49 ( ( ( type_M1690910139scheme @ s1 @ ( type_M876316792e_FVar @ x ) )
% 0.31/0.49 != ( type_M1690910139scheme @ s2 @ ( type_M876316792e_FVar @ x ) ) )
% 0.31/0.49 | ~ ( member_nat @ n @ ( type_M1050318637scheme @ ( type_M876316792e_FVar @ x ) ) )
% 0.31/0.49 | ( ( s1 @ n )
% 0.31/0.49 = ( s2 @ n ) ) ) ).
% 0.31/0.49
% 0.31/0.49 %------------------------------------------------------------------------------
% 0.31/0.49 ------------------------
% 0.33/1.60 ---- Embedded in THF ---
% 0.33/1.60 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.33/1.60 %%% Generated on Tue Feb 24 08:30:28 EST 2026
% 0.33/1.60 %%% using '$$dhol' embedding, version 1.3.0.
% 0.33/1.60 %%% Logic specification used:
% 0.33/1.60 %%% thf(spec, logic, $$dhol).
% 0.33/1.60
% 0.33/1.60 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2DTF3895.p
% See solution above
% 0.33/1.60 ------------------------
% 0.33/1.65 ---- Cleaned THF ---
% 0.33/1.65 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J_J_J,type,
% 0.33/1.65 list_l1704431731scheme: $tType ).
% 0.33/1.65
% 0.33/1.65 thf(ty_n_t__List__Olist_It__List__Olist_I_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J_J_J,type,
% 0.33/1.65 list_l865305402le_typ: $tType ).
% 0.33/1.65
% 0.33/1.65 thf(ty_n_t__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J_J,type,
% 0.33/1.65 list_l1334080099scheme: $tType ).
% 0.33/1.65
% 0.33/1.65 thf(ty_n_t__List__Olist_I_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J_J,type,
% 0.33/1.65 list_n396811828le_typ: $tType ).
% 0.33/1.65
% 0.33/1.65 thf(ty_n_t__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otyp_J_J,type,
% 0.33/1.65 list_l1790670291le_typ: $tType ).
% 0.33/1.65
% 0.33/1.65 thf(ty_n_t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J,type,
% 0.33/1.65 list_T247403987scheme: $tType ).
% 0.33/1.65
% 0.33/1.65 thf(ty_n_t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otyp_J,type,
% 0.33/1.65 list_T1103309005le_typ: $tType ).
% 0.33/1.65
% 0.33/1.65 thf(ty_n_t__Type____Mirabelle____lczmhmumaa__Otype____scheme,type,
% 0.33/1.65 type_M1694694083scheme: $tType ).
% 0.33/1.65
% 0.33/1.65 thf(ty_n_t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.33/1.65 list_set_nat: $tType ).
% 0.33/1.65
% 0.33/1.65 thf(ty_n_t__List__Olist_I_062_It__Nat__Onat_M_Eo_J_J,type,
% 0.33/1.65 list_nat_o: $tType ).
% 0.33/1.65
% 0.33/1.65 thf(ty_n_t__Type____Mirabelle____lczmhmumaa__Otyp,type,
% 0.33/1.65 type_Mirabelle_typ: $tType ).
% 0.33/1.65
% 0.33/1.65 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 0.33/1.65 list_nat: $tType ).
% 0.33/1.65
% 0.33/1.65 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.33/1.65 set_nat: $tType ).
% 0.33/1.65
% 0.33/1.65 thf(ty_n_t__Nat__Onat,type,
% 0.33/1.65 nat: $tType ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_HOL_OThe_001t__Nat__Onat,type,
% 0.33/1.65 the_nat: ( nat > $o ) > nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_If_001t__Nat__Onat,type,
% 0.33/1.65 if_nat: $o > nat > nat > nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_If_001t__Type____Mirabelle____lczmhmumaa__Otyp,type,
% 0.33/1.65 if_Typ1169047309le_typ: $o > type_Mirabelle_typ > type_Mirabelle_typ > type_Mirabelle_typ ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Lattices_Osemilattice__neutr_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.33/1.65 semila1414375521_nat_o: ( ( nat > $o ) > ( nat > $o ) > nat > $o ) > ( nat > $o ) > $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Lattices_Osemilattice__neutr_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.33/1.65 semila1369944356et_nat: ( set_nat > set_nat > set_nat ) > set_nat > $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.33/1.65 sup_sup_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 0.33/1.65 sup_sup_nat: nat > nat > nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.33/1.65 sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_List_Olist_OCons_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.33/1.65 cons_nat_o: ( nat > $o ) > list_nat_o > list_nat_o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_List_Olist_OCons_001_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J,type,
% 0.33/1.65 cons_n499085924le_typ: ( nat > type_Mirabelle_typ ) > list_n396811828le_typ > list_n396811828le_typ ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_List_Olist_OCons_001t__List__Olist_I_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J_J,type,
% 0.33/1.65 cons_l1800589546le_typ: list_n396811828le_typ > list_l865305402le_typ > list_l865305402le_typ ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J_J,type,
% 0.33/1.65 cons_l531914285scheme: list_l1334080099scheme > list_l1704431731scheme > list_l1704431731scheme ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otyp_J,type,
% 0.33/1.65 cons_l392684675le_typ: list_T1103309005le_typ > list_l1790670291le_typ > list_l1790670291le_typ ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J,type,
% 0.33/1.65 cons_l1910959773scheme: list_T247403987scheme > list_l1334080099scheme > list_l1334080099scheme ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 0.33/1.65 cons_nat: nat > list_nat > list_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_List_Olist_OCons_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.33/1.65 cons_set_nat: set_nat > list_set_nat > list_set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_List_Olist_OCons_001t__Type____Mirabelle____lczmhmumaa__Otyp,type,
% 0.33/1.65 cons_T363929085le_typ: type_Mirabelle_typ > list_T1103309005le_typ > list_T1103309005le_typ ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_List_Olist_OCons_001t__Type____Mirabelle____lczmhmumaa__Otype____scheme,type,
% 0.33/1.65 cons_T633159821scheme: type_M1694694083scheme > list_T247403987scheme > list_T247403987scheme ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_List_Olist_ONil_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.33/1.65 nil_nat_o: list_nat_o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 0.33/1.65 nil_nat: list_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_List_Olist_ONil_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.33/1.65 nil_set_nat: list_set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_List_Olist_ONil_001t__Type____Mirabelle____lczmhmumaa__Otype____scheme,type,
% 0.33/1.65 nil_Ty61485117scheme: list_T247403987scheme ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_List_Oord__class_Olexordp__eq_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.33/1.65 ord_lexordp_eq_nat_o: list_nat_o > list_nat_o > $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_List_Oord__class_Olexordp__eq_001t__Nat__Onat,type,
% 0.33/1.65 ord_lexordp_eq_nat: list_nat > list_nat > $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_List_Oord__class_Olexordp__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.33/1.65 ord_le727790544et_nat: list_set_nat > list_set_nat > $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.33/1.65 bot_bot_nat_o: nat > $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Orderings_Obot__class_Obot_001_Eo,type,
% 0.33/1.65 bot_bot_o: $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Orderings_Obot__class_Obot_001t__Nat__Onat,type,
% 0.33/1.65 bot_bot_nat: nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.33/1.65 bot_bot_set_nat: set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Orderings_Oord__class_Oless_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.33/1.65 ord_less_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.33/1.65 ord_less_nat: nat > nat > $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.33/1.65 ord_less_set_nat: set_nat > set_nat > $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.33/1.65 collect_nat: ( nat > $o ) > set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 0.33/1.65 insert_nat: nat > set_nat > set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Set_Ois__empty_001t__Nat__Onat,type,
% 0.33/1.65 is_empty_nat: set_nat > $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Set_Ois__singleton_001t__Nat__Onat,type,
% 0.33/1.65 is_singleton_nat: set_nat > $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Set_Othe__elem_001t__Nat__Onat,type,
% 0.33/1.65 the_elem_nat: set_nat > nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Ocod,type,
% 0.33/1.65 type_Mirabelle_cod: ( nat > type_Mirabelle_typ ) > set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Odom,type,
% 0.33/1.65 type_Mirabelle_dom: ( nat > type_Mirabelle_typ ) > set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Oid__subst,type,
% 0.33/1.65 type_M405566558_subst: nat > type_Mirabelle_typ ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Omk__scheme,type,
% 0.33/1.65 type_M1006385707scheme: type_Mirabelle_typ > type_M1694694083scheme ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Onew__tv_001_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J,type,
% 0.33/1.65 type_M1734147655le_typ: nat > ( nat > type_Mirabelle_typ ) > $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Onew__tv_001t__List__Olist_I_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J_J,type,
% 0.33/1.65 type_M244876119le_typ: nat > list_n396811828le_typ > $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Onew__tv_001t__List__Olist_It__List__Olist_I_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J_J_J,type,
% 0.33/1.65 type_M2086816231le_typ: nat > list_l865305402le_typ > $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Onew__tv_001t__List__Olist_It__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J_J_J,type,
% 0.33/1.65 type_M1172169604scheme: nat > list_l1704431731scheme > $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Onew__tv_001t__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otyp_J_J,type,
% 0.33/1.65 type_M1826376056le_typ: nat > list_l1790670291le_typ > $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Onew__tv_001t__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J_J,type,
% 0.33/1.65 type_M1377662078scheme: nat > list_l1334080099scheme > $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Onew__tv_001t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otyp_J,type,
% 0.33/1.65 type_M263553000le_typ: nat > list_T1103309005le_typ > $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Onew__tv_001t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J,type,
% 0.33/1.65 type_M2064939256scheme: nat > list_T247403987scheme > $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Onew__tv_001t__Type____Mirabelle____lczmhmumaa__Otyp,type,
% 0.33/1.65 type_M1211611096le_typ: nat > type_Mirabelle_typ > $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Onew__tv_001t__Type____Mirabelle____lczmhmumaa__Otype____scheme,type,
% 0.33/1.65 type_M1963061490scheme: nat > type_M1694694083scheme > $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Oof__nat__class_Oof__nat_001t__Nat__Onat,type,
% 0.33/1.65 type_M1898948661at_nat: nat > nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otyp_OFun,type,
% 0.33/1.65 type_Mirabelle_Fun: type_Mirabelle_typ > type_Mirabelle_typ > type_Mirabelle_typ ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otyp_OTVar,type,
% 0.33/1.65 type_Mirabelle_TVar: nat > type_Mirabelle_typ ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otyp__of__class_Otyp__of_001t__Type____Mirabelle____lczmhmumaa__Otyp,type,
% 0.33/1.65 type_M1743451154le_typ: type_Mirabelle_typ > type_Mirabelle_typ ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__scheme_OBVar,type,
% 0.33/1.65 type_M2048935292e_BVar: nat > type_M1694694083scheme ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__scheme_OFVar,type,
% 0.33/1.65 type_M876316792e_FVar: nat > type_M1694694083scheme ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__scheme_OSFun,type,
% 0.33/1.65 type_M155660035e_SFun: type_M1694694083scheme > type_M1694694083scheme > type_M1694694083scheme ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Oapp__subst_001_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J,type,
% 0.33/1.65 type_M1158474302le_typ: ( nat > type_Mirabelle_typ ) > ( nat > type_Mirabelle_typ ) > nat > type_Mirabelle_typ ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Oapp__subst_001t__List__Olist_I_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J_J,type,
% 0.33/1.65 type_M737052622le_typ: ( nat > type_Mirabelle_typ ) > list_n396811828le_typ > list_n396811828le_typ ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Oapp__subst_001t__List__Olist_It__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J_J_J,type,
% 0.33/1.65 type_M1385924301scheme: ( nat > type_Mirabelle_typ ) > list_l1704431731scheme > list_l1704431731scheme ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Oapp__subst_001t__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otyp_J_J,type,
% 0.33/1.65 type_M1913464047le_typ: ( nat > type_Mirabelle_typ ) > list_l1790670291le_typ > list_l1790670291le_typ ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Oapp__subst_001t__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J_J,type,
% 0.33/1.65 type_M1061687367scheme: ( nat > type_Mirabelle_typ ) > list_l1334080099scheme > list_l1334080099scheme ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Oapp__subst_001t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otyp_J,type,
% 0.33/1.65 type_M1440203487le_typ: ( nat > type_Mirabelle_typ ) > list_T1103309005le_typ > list_T1103309005le_typ ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Oapp__subst_001t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J,type,
% 0.33/1.65 type_M1944210753scheme: ( nat > type_Mirabelle_typ ) > list_T247403987scheme > list_T247403987scheme ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Oapp__subst_001t__Type____Mirabelle____lczmhmumaa__Otyp,type,
% 0.33/1.65 type_M784671311le_typ: ( nat > type_Mirabelle_typ ) > type_Mirabelle_typ > type_Mirabelle_typ ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Oapp__subst_001t__Type____Mirabelle____lczmhmumaa__Otype____scheme,type,
% 0.33/1.65 type_M1690910139scheme: ( nat > type_Mirabelle_typ ) > type_M1694694083scheme > type_M1694694083scheme ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Obound__tv_001_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J,type,
% 0.33/1.65 type_M772783356le_typ: ( nat > type_Mirabelle_typ ) > set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Obound__tv_001t__List__Olist_I_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J_J,type,
% 0.33/1.65 type_M513401740le_typ: list_n396811828le_typ > set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Obound__tv_001t__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J_J,type,
% 0.33/1.65 type_M1496178953scheme: list_l1334080099scheme > set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Obound__tv_001t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otyp_J,type,
% 0.33/1.65 type_M1539052445le_typ: list_T1103309005le_typ > set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Obound__tv_001t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J,type,
% 0.33/1.65 type_M961603331scheme: list_T247403987scheme > set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Obound__tv_001t__Type____Mirabelle____lczmhmumaa__Otyp,type,
% 0.33/1.65 type_M801073677le_typ: type_Mirabelle_typ > set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Obound__tv_001t__Type____Mirabelle____lczmhmumaa__Otype____scheme,type,
% 0.33/1.65 type_M326705277scheme: type_M1694694083scheme > set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Ofree__tv_001_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J,type,
% 0.33/1.65 type_M1715972684le_typ: ( nat > type_Mirabelle_typ ) > set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Ofree__tv_001t__List__Olist_I_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J_J,type,
% 0.33/1.65 type_M1691543772le_typ: list_n396811828le_typ > set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Ofree__tv_001t__List__Olist_It__List__Olist_I_062_It__Nat__Onat_Mt__Type____Mirabelle____lczmhmumaa__Otyp_J_J_J,type,
% 0.33/1.65 type_M906078444le_typ: list_l865305402le_typ > set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Ofree__tv_001t__List__Olist_It__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J_J_J,type,
% 0.33/1.65 type_M1926053183scheme: list_l1704431731scheme > set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Ofree__tv_001t__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otyp_J_J,type,
% 0.33/1.65 type_M1418941437le_typ: list_l1790670291le_typ > set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Ofree__tv_001t__List__Olist_It__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J_J,type,
% 0.33/1.65 type_M1958029241scheme: list_l1334080099scheme > set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Ofree__tv_001t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otyp_J,type,
% 0.33/1.65 type_M510873837le_typ: list_T1103309005le_typ > set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Ofree__tv_001t__List__Olist_It__Type____Mirabelle____lczmhmumaa__Otype____scheme_J,type,
% 0.33/1.65 type_M141510067scheme: list_T247403987scheme > set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Ofree__tv_001t__Type____Mirabelle____lczmhmumaa__Otyp,type,
% 0.33/1.65 type_M49385309le_typ: type_Mirabelle_typ > set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_Type__Mirabelle__lczmhmumaa_Otype__struct__class_Ofree__tv_001t__Type____Mirabelle____lczmhmumaa__Otype____scheme,type,
% 0.33/1.65 type_M1050318637scheme: type_M1694694083scheme > set_nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_c_member_001t__Nat__Onat,type,
% 0.33/1.65 member_nat: nat > set_nat > $o ).
% 0.33/1.65
% 0.33/1.65 thf(sy_v_S1,type,
% 0.33/1.65 s1: nat > type_Mirabelle_typ ).
% 0.33/1.65
% 0.33/1.65 thf(sy_v_S2,type,
% 0.33/1.65 s2: nat > type_Mirabelle_typ ).
% 0.33/1.65
% 0.33/1.65 thf(sy_v_n,type,
% 0.33/1.65 n: nat ).
% 0.33/1.65
% 0.33/1.65 thf(sy_v_x,type,
% 0.33/1.65 x: nat ).
% 0.33/1.65
% 0.33/1.65 thf(fact_0_type__scheme_Oinject_I1_J,axiom,
% 0.33/1.65 ! [X1: nat,Y1: nat] :
% 0.33/1.65 ( ( ( type_M876316792e_FVar @ X1 )
% 0.33/1.65 = ( type_M876316792e_FVar @ Y1 ) )
% 0.33/1.65 = ( X1 = Y1 ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_1_eq__free__eq__subst__type__scheme,axiom,
% 0.33/1.65 ! [Sch: type_M1694694083scheme,S1: nat > type_Mirabelle_typ,S2: nat > type_Mirabelle_typ] :
% 0.33/1.65 ( ! [N: nat] :
% 0.33/1.65 ( ( member_nat @ N @ ( type_M1050318637scheme @ Sch ) )
% 0.33/1.65 => ( ( S1 @ N )
% 0.33/1.65 = ( S2 @ N ) ) )
% 0.33/1.65 => ( ( type_M1690910139scheme @ S1 @ Sch )
% 0.33/1.65 = ( type_M1690910139scheme @ S2 @ Sch ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_2_scheme__substitutions__only__on__free__variables,axiom,
% 0.33/1.65 ! [Sch: type_M1694694083scheme,S: nat > type_Mirabelle_typ,S3: nat > type_Mirabelle_typ] :
% 0.33/1.65 ( ! [X: nat] :
% 0.33/1.65 ( ( member_nat @ X @ ( type_M1050318637scheme @ Sch ) )
% 0.33/1.65 => ( ( S @ X )
% 0.33/1.65 = ( S3 @ X ) ) )
% 0.33/1.65 => ( ( type_M1690910139scheme @ S @ Sch )
% 0.33/1.65 = ( type_M1690910139scheme @ S3 @ Sch ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_3_app__subst__type__scheme_Osimps_I1_J,axiom,
% 0.33/1.65 ! [S: nat > type_Mirabelle_typ,N2: nat] :
% 0.33/1.65 ( ( type_M1690910139scheme @ S @ ( type_M876316792e_FVar @ N2 ) )
% 0.33/1.65 = ( type_M1006385707scheme @ ( S @ N2 ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_4_app__subst__type__scheme_Osimps_I2_J,axiom,
% 0.33/1.65 ! [S: nat > type_Mirabelle_typ,N2: nat] :
% 0.33/1.65 ( ( type_M1690910139scheme @ S @ ( type_M2048935292e_BVar @ N2 ) )
% 0.33/1.65 = ( type_M2048935292e_BVar @ N2 ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_5_app__subst__type__scheme_Osimps_I3_J,axiom,
% 0.33/1.65 ! [S: nat > type_Mirabelle_typ,Sch1: type_M1694694083scheme,Sch2: type_M1694694083scheme] :
% 0.33/1.65 ( ( type_M1690910139scheme @ S @ ( type_M155660035e_SFun @ Sch1 @ Sch2 ) )
% 0.33/1.65 = ( type_M155660035e_SFun @ ( type_M1690910139scheme @ S @ Sch1 ) @ ( type_M1690910139scheme @ S @ Sch2 ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_6_type__scheme_Odistinct_I1_J,axiom,
% 0.33/1.65 ! [X1: nat,X2: nat] :
% 0.33/1.65 ( ( type_M876316792e_FVar @ X1 )
% 0.33/1.65 != ( type_M2048935292e_BVar @ X2 ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_7_type__scheme_Odistinct_I3_J,axiom,
% 0.33/1.65 ! [X1: nat,X31: type_M1694694083scheme,X32: type_M1694694083scheme] :
% 0.33/1.65 ( ( type_M876316792e_FVar @ X1 )
% 0.33/1.65 != ( type_M155660035e_SFun @ X31 @ X32 ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_8_app__subst__Cons,axiom,
% 0.33/1.65 ! [S: nat > type_Mirabelle_typ,X3: nat > type_Mirabelle_typ,L: list_n396811828le_typ] :
% 0.33/1.65 ( ( type_M737052622le_typ @ S @ ( cons_n499085924le_typ @ X3 @ L ) )
% 0.33/1.65 = ( cons_n499085924le_typ @ ( type_M1158474302le_typ @ S @ X3 ) @ ( type_M737052622le_typ @ S @ L ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_9_app__subst__Cons,axiom,
% 0.33/1.65 ! [S: nat > type_Mirabelle_typ,X3: list_l1334080099scheme,L: list_l1704431731scheme] :
% 0.33/1.65 ( ( type_M1385924301scheme @ S @ ( cons_l531914285scheme @ X3 @ L ) )
% 0.33/1.65 = ( cons_l531914285scheme @ ( type_M1061687367scheme @ S @ X3 ) @ ( type_M1385924301scheme @ S @ L ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_10_app__subst__Cons,axiom,
% 0.33/1.65 ! [S: nat > type_Mirabelle_typ,X3: list_T1103309005le_typ,L: list_l1790670291le_typ] :
% 0.33/1.65 ( ( type_M1913464047le_typ @ S @ ( cons_l392684675le_typ @ X3 @ L ) )
% 0.33/1.65 = ( cons_l392684675le_typ @ ( type_M1440203487le_typ @ S @ X3 ) @ ( type_M1913464047le_typ @ S @ L ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_11_app__subst__Cons,axiom,
% 0.33/1.65 ! [S: nat > type_Mirabelle_typ,X3: type_Mirabelle_typ,L: list_T1103309005le_typ] :
% 0.33/1.65 ( ( type_M1440203487le_typ @ S @ ( cons_T363929085le_typ @ X3 @ L ) )
% 0.33/1.65 = ( cons_T363929085le_typ @ ( type_M784671311le_typ @ S @ X3 ) @ ( type_M1440203487le_typ @ S @ L ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_12_app__subst__Cons,axiom,
% 0.33/1.65 ! [S: nat > type_Mirabelle_typ,X3: list_T247403987scheme,L: list_l1334080099scheme] :
% 0.33/1.65 ( ( type_M1061687367scheme @ S @ ( cons_l1910959773scheme @ X3 @ L ) )
% 0.33/1.65 = ( cons_l1910959773scheme @ ( type_M1944210753scheme @ S @ X3 ) @ ( type_M1061687367scheme @ S @ L ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_13_app__subst__Cons,axiom,
% 0.33/1.65 ! [S: nat > type_Mirabelle_typ,X3: type_M1694694083scheme,L: list_T247403987scheme] :
% 0.33/1.65 ( ( type_M1944210753scheme @ S @ ( cons_T633159821scheme @ X3 @ L ) )
% 0.33/1.65 = ( cons_T633159821scheme @ ( type_M1690910139scheme @ S @ X3 ) @ ( type_M1944210753scheme @ S @ L ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_14_free__tv__mk__scheme,axiom,
% 0.33/1.65 ! [T: type_Mirabelle_typ] :
% 0.33/1.65 ( ( type_M1050318637scheme @ ( type_M1006385707scheme @ T ) )
% 0.33/1.65 = ( type_M49385309le_typ @ T ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_15_free__tv__type__scheme_Osimps_I1_J,axiom,
% 0.33/1.65 ! [M: nat] :
% 0.33/1.65 ( ( type_M1050318637scheme @ ( type_M876316792e_FVar @ M ) )
% 0.33/1.65 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_16_new__if__subst__type__scheme,axiom,
% 0.33/1.65 ! [N2: nat,Sch: type_M1694694083scheme,S: nat > type_Mirabelle_typ,S3: nat > type_Mirabelle_typ] :
% 0.33/1.65 ( ( type_M1963061490scheme @ N2 @ Sch )
% 0.33/1.65 => ( ( type_M1690910139scheme
% 0.33/1.65 @ ^ [K: nat] : ( if_Typ1169047309le_typ @ ( ord_less_nat @ K @ N2 ) @ ( S @ K ) @ ( S3 @ K ) )
% 0.33/1.65 @ Sch )
% 0.33/1.65 = ( type_M1690910139scheme @ S @ Sch ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_17_type__scheme_Oinject_I3_J,axiom,
% 0.33/1.65 ! [X31: type_M1694694083scheme,X32: type_M1694694083scheme,Y31: type_M1694694083scheme,Y32: type_M1694694083scheme] :
% 0.33/1.65 ( ( ( type_M155660035e_SFun @ X31 @ X32 )
% 0.33/1.65 = ( type_M155660035e_SFun @ Y31 @ Y32 ) )
% 0.33/1.65 = ( ( X31 = Y31 )
% 0.33/1.65 & ( X32 = Y32 ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_18_type__scheme_Oinject_I2_J,axiom,
% 0.33/1.65 ! [X2: nat,Y2: nat] :
% 0.33/1.65 ( ( ( type_M2048935292e_BVar @ X2 )
% 0.33/1.65 = ( type_M2048935292e_BVar @ Y2 ) )
% 0.33/1.65 = ( X2 = Y2 ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_19_new__tv__Cons,axiom,
% 0.33/1.65 ! [N2: nat,X3: list_n396811828le_typ,L: list_l865305402le_typ] :
% 0.33/1.65 ( ( type_M2086816231le_typ @ N2 @ ( cons_l1800589546le_typ @ X3 @ L ) )
% 0.33/1.65 = ( ( type_M244876119le_typ @ N2 @ X3 )
% 0.33/1.65 & ( type_M2086816231le_typ @ N2 @ L ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_20_new__tv__Cons,axiom,
% 0.33/1.65 ! [N2: nat,X3: list_T1103309005le_typ,L: list_l1790670291le_typ] :
% 0.33/1.65 ( ( type_M1826376056le_typ @ N2 @ ( cons_l392684675le_typ @ X3 @ L ) )
% 0.33/1.65 = ( ( type_M263553000le_typ @ N2 @ X3 )
% 0.33/1.65 & ( type_M1826376056le_typ @ N2 @ L ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_21_new__tv__Cons,axiom,
% 0.33/1.65 ! [N2: nat,X3: list_l1334080099scheme,L: list_l1704431731scheme] :
% 0.33/1.65 ( ( type_M1172169604scheme @ N2 @ ( cons_l531914285scheme @ X3 @ L ) )
% 0.33/1.65 = ( ( type_M1377662078scheme @ N2 @ X3 )
% 0.33/1.65 & ( type_M1172169604scheme @ N2 @ L ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_22_new__tv__Cons,axiom,
% 0.33/1.65 ! [N2: nat,X3: list_T247403987scheme,L: list_l1334080099scheme] :
% 0.33/1.65 ( ( type_M1377662078scheme @ N2 @ ( cons_l1910959773scheme @ X3 @ L ) )
% 0.33/1.65 = ( ( type_M2064939256scheme @ N2 @ X3 )
% 0.33/1.65 & ( type_M1377662078scheme @ N2 @ L ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_23_new__tv__Cons,axiom,
% 0.33/1.65 ! [N2: nat,X3: type_Mirabelle_typ,L: list_T1103309005le_typ] :
% 0.33/1.65 ( ( type_M263553000le_typ @ N2 @ ( cons_T363929085le_typ @ X3 @ L ) )
% 0.33/1.65 = ( ( type_M1211611096le_typ @ N2 @ X3 )
% 0.33/1.65 & ( type_M263553000le_typ @ N2 @ L ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_24_new__tv__Cons,axiom,
% 0.33/1.65 ! [N2: nat,X3: nat > type_Mirabelle_typ,L: list_n396811828le_typ] :
% 0.33/1.65 ( ( type_M244876119le_typ @ N2 @ ( cons_n499085924le_typ @ X3 @ L ) )
% 0.33/1.65 = ( ( type_M1734147655le_typ @ N2 @ X3 )
% 0.33/1.65 & ( type_M244876119le_typ @ N2 @ L ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_25_new__tv__Cons,axiom,
% 0.33/1.65 ! [N2: nat,X3: type_M1694694083scheme,L: list_T247403987scheme] :
% 0.33/1.65 ( ( type_M2064939256scheme @ N2 @ ( cons_T633159821scheme @ X3 @ L ) )
% 0.33/1.65 = ( ( type_M1963061490scheme @ N2 @ X3 )
% 0.33/1.65 & ( type_M2064939256scheme @ N2 @ L ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_26_subst__mk__scheme,axiom,
% 0.33/1.65 ! [S: nat > type_Mirabelle_typ,T: type_Mirabelle_typ] :
% 0.33/1.65 ( ( type_M1690910139scheme @ S @ ( type_M1006385707scheme @ T ) )
% 0.33/1.65 = ( type_M1006385707scheme @ ( type_M784671311le_typ @ S @ T ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_27_new__tv__Fun2,axiom,
% 0.33/1.65 ! [N2: nat,T1: type_M1694694083scheme,T2: type_M1694694083scheme] :
% 0.33/1.65 ( ( type_M1963061490scheme @ N2 @ ( type_M155660035e_SFun @ T1 @ T2 ) )
% 0.33/1.65 = ( ( type_M1963061490scheme @ N2 @ T1 )
% 0.33/1.65 & ( type_M1963061490scheme @ N2 @ T2 ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_28_new__tv__BVar,axiom,
% 0.33/1.65 ! [N2: nat,M: nat] : ( type_M1963061490scheme @ N2 @ ( type_M2048935292e_BVar @ M ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_29_new__tv__FVar,axiom,
% 0.33/1.65 ! [N2: nat,M: nat] :
% 0.33/1.65 ( ( type_M1963061490scheme @ N2 @ ( type_M876316792e_FVar @ M ) )
% 0.33/1.65 = ( ord_less_nat @ M @ N2 ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_30_type__scheme_Odistinct_I5_J,axiom,
% 0.33/1.65 ! [X2: nat,X31: type_M1694694083scheme,X32: type_M1694694083scheme] :
% 0.33/1.65 ( ( type_M2048935292e_BVar @ X2 )
% 0.33/1.65 != ( type_M155660035e_SFun @ X31 @ X32 ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_31_mk__scheme__Fun,axiom,
% 0.33/1.65 ! [T: type_Mirabelle_typ,Sch1: type_M1694694083scheme,Sch2: type_M1694694083scheme] :
% 0.33/1.65 ( ( ( type_M1006385707scheme @ T )
% 0.33/1.65 = ( type_M155660035e_SFun @ Sch1 @ Sch2 ) )
% 0.33/1.65 => ? [T12: type_Mirabelle_typ,T22: type_Mirabelle_typ] :
% 0.33/1.65 ( ( Sch1
% 0.33/1.65 = ( type_M1006385707scheme @ T12 ) )
% 0.33/1.65 & ( Sch2
% 0.33/1.65 = ( type_M1006385707scheme @ T22 ) ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_32_eq__free__eq__subst__te,axiom,
% 0.33/1.65 ! [T: type_Mirabelle_typ,S1: nat > type_Mirabelle_typ,S2: nat > type_Mirabelle_typ] :
% 0.33/1.65 ( ! [N: nat] :
% 0.33/1.65 ( ( member_nat @ N @ ( type_M49385309le_typ @ T ) )
% 0.33/1.65 => ( ( S1 @ N )
% 0.33/1.65 = ( S2 @ N ) ) )
% 0.33/1.65 => ( ( type_M784671311le_typ @ S1 @ T )
% 0.33/1.65 = ( type_M784671311le_typ @ S2 @ T ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_33_eq__subst__te__eq__free,axiom,
% 0.33/1.65 ! [S1: nat > type_Mirabelle_typ,T: type_Mirabelle_typ,S2: nat > type_Mirabelle_typ,N2: nat] :
% 0.33/1.65 ( ( ( type_M784671311le_typ @ S1 @ T )
% 0.33/1.65 = ( type_M784671311le_typ @ S2 @ T ) )
% 0.33/1.65 => ( ( member_nat @ N2 @ ( type_M49385309le_typ @ T ) )
% 0.33/1.65 => ( ( S1 @ N2 )
% 0.33/1.65 = ( S2 @ N2 ) ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_34_typ__substitutions__only__on__free__variables,axiom,
% 0.33/1.65 ! [T: type_Mirabelle_typ,S: nat > type_Mirabelle_typ,S3: nat > type_Mirabelle_typ] :
% 0.33/1.65 ( ! [X: nat] :
% 0.33/1.65 ( ( member_nat @ X @ ( type_M49385309le_typ @ T ) )
% 0.33/1.65 => ( ( S @ X )
% 0.33/1.65 = ( S3 @ X ) ) )
% 0.33/1.65 => ( ( type_M784671311le_typ @ S @ T )
% 0.33/1.65 = ( type_M784671311le_typ @ S3 @ T ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_35_mk__scheme__injective,axiom,
% 0.33/1.65 ! [T: type_Mirabelle_typ,T3: type_Mirabelle_typ] :
% 0.33/1.65 ( ( ( type_M1006385707scheme @ T )
% 0.33/1.65 = ( type_M1006385707scheme @ T3 ) )
% 0.33/1.65 => ( T = T3 ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_36_free__tv__type__scheme_Osimps_I2_J,axiom,
% 0.33/1.65 ! [M: nat] :
% 0.33/1.65 ( ( type_M1050318637scheme @ ( type_M2048935292e_BVar @ M ) )
% 0.33/1.65 = bot_bot_set_nat ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_37_type__scheme_Oexhaust,axiom,
% 0.33/1.65 ! [Y: type_M1694694083scheme] :
% 0.33/1.65 ( ! [X12: nat] :
% 0.33/1.65 ( Y
% 0.33/1.65 != ( type_M876316792e_FVar @ X12 ) )
% 0.33/1.65 => ( ! [X22: nat] :
% 0.33/1.65 ( Y
% 0.33/1.65 != ( type_M2048935292e_BVar @ X22 ) )
% 0.33/1.65 => ~ ! [X312: type_M1694694083scheme,X322: type_M1694694083scheme] :
% 0.33/1.65 ( Y
% 0.33/1.65 != ( type_M155660035e_SFun @ X312 @ X322 ) ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_38_type__scheme_Oinduct,axiom,
% 0.33/1.65 ! [P: type_M1694694083scheme > $o,Type_scheme: type_M1694694083scheme] :
% 0.33/1.65 ( ! [X: nat] : ( P @ ( type_M876316792e_FVar @ X ) )
% 0.33/1.65 => ( ! [X: nat] : ( P @ ( type_M2048935292e_BVar @ X ) )
% 0.33/1.65 => ( ! [X1a: type_M1694694083scheme,X2a: type_M1694694083scheme] :
% 0.33/1.65 ( ( P @ X1a )
% 0.33/1.65 => ( ( P @ X2a )
% 0.33/1.65 => ( P @ ( type_M155660035e_SFun @ X1a @ X2a ) ) ) )
% 0.33/1.65 => ( P @ Type_scheme ) ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_39_new__tv__def,axiom,
% 0.33/1.65 ( type_M244876119le_typ
% 0.33/1.65 = ( ^ [N3: nat,Ts: list_n396811828le_typ] :
% 0.33/1.65 ! [M2: nat] :
% 0.33/1.65 ( ( member_nat @ M2 @ ( type_M1691543772le_typ @ Ts ) )
% 0.33/1.65 => ( ord_less_nat @ M2 @ N3 ) ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_40_new__tv__def,axiom,
% 0.33/1.65 ( type_M1377662078scheme
% 0.33/1.65 = ( ^ [N3: nat,Ts: list_l1334080099scheme] :
% 0.33/1.65 ! [M2: nat] :
% 0.33/1.65 ( ( member_nat @ M2 @ ( type_M1958029241scheme @ Ts ) )
% 0.33/1.65 => ( ord_less_nat @ M2 @ N3 ) ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_41_new__tv__def,axiom,
% 0.33/1.65 ( type_M263553000le_typ
% 0.33/1.65 = ( ^ [N3: nat,Ts: list_T1103309005le_typ] :
% 0.33/1.65 ! [M2: nat] :
% 0.33/1.65 ( ( member_nat @ M2 @ ( type_M510873837le_typ @ Ts ) )
% 0.33/1.65 => ( ord_less_nat @ M2 @ N3 ) ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_42_new__tv__def,axiom,
% 0.33/1.65 ( type_M1963061490scheme
% 0.33/1.65 = ( ^ [N3: nat,Ts: type_M1694694083scheme] :
% 0.33/1.65 ! [M2: nat] :
% 0.33/1.65 ( ( member_nat @ M2 @ ( type_M1050318637scheme @ Ts ) )
% 0.33/1.65 => ( ord_less_nat @ M2 @ N3 ) ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_43_new__tv__def,axiom,
% 0.33/1.65 ( type_M1211611096le_typ
% 0.33/1.65 = ( ^ [N3: nat,Ts: type_Mirabelle_typ] :
% 0.33/1.65 ! [M2: nat] :
% 0.33/1.65 ( ( member_nat @ M2 @ ( type_M49385309le_typ @ Ts ) )
% 0.33/1.65 => ( ord_less_nat @ M2 @ N3 ) ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_44_new__tv__def,axiom,
% 0.33/1.65 ( type_M2064939256scheme
% 0.33/1.65 = ( ^ [N3: nat,Ts: list_T247403987scheme] :
% 0.33/1.65 ! [M2: nat] :
% 0.33/1.65 ( ( member_nat @ M2 @ ( type_M141510067scheme @ Ts ) )
% 0.33/1.65 => ( ord_less_nat @ M2 @ N3 ) ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_45_new__tv__def,axiom,
% 0.33/1.65 ( type_M1734147655le_typ
% 0.33/1.65 = ( ^ [N3: nat,Ts: nat > type_Mirabelle_typ] :
% 0.33/1.65 ! [M2: nat] :
% 0.33/1.65 ( ( member_nat @ M2 @ ( type_M1715972684le_typ @ Ts ) )
% 0.33/1.65 => ( ord_less_nat @ M2 @ N3 ) ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_46_singleton__conv,axiom,
% 0.33/1.65 ! [A: nat] :
% 0.33/1.65 ( ( collect_nat
% 0.33/1.65 @ ^ [X4: nat] : ( X4 = A ) )
% 0.33/1.65 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_47_singleton__conv2,axiom,
% 0.33/1.65 ! [A: nat] :
% 0.33/1.65 ( ( collect_nat
% 0.33/1.65 @ ( ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/1.65 @ A ) )
% 0.33/1.65 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_48_singletonI,axiom,
% 0.33/1.65 ! [A: nat] : ( member_nat @ A @ ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_49_insertCI,axiom,
% 0.33/1.65 ! [A: nat,B: set_nat,B2: nat] :
% 0.33/1.65 ( ( ~ ( member_nat @ A @ B )
% 0.33/1.65 => ( A = B2 ) )
% 0.33/1.65 => ( member_nat @ A @ ( insert_nat @ B2 @ B ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_50_insert__iff,axiom,
% 0.33/1.65 ! [A: nat,B2: nat,A2: set_nat] :
% 0.33/1.65 ( ( member_nat @ A @ ( insert_nat @ B2 @ A2 ) )
% 0.33/1.65 = ( ( A = B2 )
% 0.33/1.65 | ( member_nat @ A @ A2 ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_51_insert__absorb2,axiom,
% 0.33/1.65 ! [X3: nat,A2: set_nat] :
% 0.33/1.65 ( ( insert_nat @ X3 @ ( insert_nat @ X3 @ A2 ) )
% 0.33/1.65 = ( insert_nat @ X3 @ A2 ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_52_list_Oinject,axiom,
% 0.33/1.65 ! [X21: type_M1694694083scheme,X222: list_T247403987scheme,Y21: type_M1694694083scheme,Y22: list_T247403987scheme] :
% 0.33/1.65 ( ( ( cons_T633159821scheme @ X21 @ X222 )
% 0.33/1.65 = ( cons_T633159821scheme @ Y21 @ Y22 ) )
% 0.33/1.65 = ( ( X21 = Y21 )
% 0.33/1.65 & ( X222 = Y22 ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_53_list_Oinject,axiom,
% 0.33/1.65 ! [X21: list_T247403987scheme,X222: list_l1334080099scheme,Y21: list_T247403987scheme,Y22: list_l1334080099scheme] :
% 0.33/1.65 ( ( ( cons_l1910959773scheme @ X21 @ X222 )
% 0.33/1.65 = ( cons_l1910959773scheme @ Y21 @ Y22 ) )
% 0.33/1.65 = ( ( X21 = Y21 )
% 0.33/1.65 & ( X222 = Y22 ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_54_list_Oinject,axiom,
% 0.33/1.65 ! [X21: type_Mirabelle_typ,X222: list_T1103309005le_typ,Y21: type_Mirabelle_typ,Y22: list_T1103309005le_typ] :
% 0.33/1.65 ( ( ( cons_T363929085le_typ @ X21 @ X222 )
% 0.33/1.65 = ( cons_T363929085le_typ @ Y21 @ Y22 ) )
% 0.33/1.65 = ( ( X21 = Y21 )
% 0.33/1.65 & ( X222 = Y22 ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_55_list_Oinject,axiom,
% 0.33/1.65 ! [X21: nat > type_Mirabelle_typ,X222: list_n396811828le_typ,Y21: nat > type_Mirabelle_typ,Y22: list_n396811828le_typ] :
% 0.33/1.65 ( ( ( cons_n499085924le_typ @ X21 @ X222 )
% 0.33/1.65 = ( cons_n499085924le_typ @ Y21 @ Y22 ) )
% 0.33/1.65 = ( ( X21 = Y21 )
% 0.33/1.65 & ( X222 = Y22 ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_56_list_Oinject,axiom,
% 0.33/1.65 ! [X21: nat,X222: list_nat,Y21: nat,Y22: list_nat] :
% 0.33/1.65 ( ( ( cons_nat @ X21 @ X222 )
% 0.33/1.65 = ( cons_nat @ Y21 @ Y22 ) )
% 0.33/1.65 = ( ( X21 = Y21 )
% 0.33/1.65 & ( X222 = Y22 ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_57_empty__iff,axiom,
% 0.33/1.65 ! [C: nat] :
% 0.33/1.65 ~ ( member_nat @ C @ bot_bot_set_nat ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_58_mem__Collect__eq,axiom,
% 0.33/1.65 ! [A: nat,P: nat > $o] :
% 0.33/1.65 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 0.33/1.65 = ( P @ A ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_59_Collect__mem__eq,axiom,
% 0.33/1.65 ! [A2: set_nat] :
% 0.33/1.65 ( ( collect_nat
% 0.33/1.65 @ ^ [X4: nat] : ( member_nat @ X4 @ A2 ) )
% 0.33/1.65 = A2 ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_60_Collect__cong,axiom,
% 0.33/1.65 ! [P: nat > $o,Q: nat > $o] :
% 0.33/1.65 ( ! [X: nat] :
% 0.33/1.65 ( ( P @ X )
% 0.33/1.65 = ( Q @ X ) )
% 0.33/1.65 => ( ( collect_nat @ P )
% 0.33/1.65 = ( collect_nat @ Q ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_61_all__not__in__conv,axiom,
% 0.33/1.65 ! [A2: set_nat] :
% 0.33/1.65 ( ( ! [X4: nat] :
% 0.33/1.65 ~ ( member_nat @ X4 @ A2 ) )
% 0.33/1.65 = ( A2 = bot_bot_set_nat ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_62_Collect__empty__eq,axiom,
% 0.33/1.65 ! [P: nat > $o] :
% 0.33/1.65 ( ( ( collect_nat @ P )
% 0.33/1.65 = bot_bot_set_nat )
% 0.33/1.65 = ( ! [X4: nat] :
% 0.33/1.65 ~ ( P @ X4 ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_63_empty__Collect__eq,axiom,
% 0.33/1.65 ! [P: nat > $o] :
% 0.33/1.65 ( ( bot_bot_set_nat
% 0.33/1.65 = ( collect_nat @ P ) )
% 0.33/1.65 = ( ! [X4: nat] :
% 0.33/1.65 ~ ( P @ X4 ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_64_new__if__subst__type__scheme__list,axiom,
% 0.33/1.65 ! [N2: nat,A2: list_T247403987scheme,S: nat > type_Mirabelle_typ,S3: nat > type_Mirabelle_typ] :
% 0.33/1.65 ( ( type_M2064939256scheme @ N2 @ A2 )
% 0.33/1.65 => ( ( type_M1944210753scheme
% 0.33/1.65 @ ^ [K: nat] : ( if_Typ1169047309le_typ @ ( ord_less_nat @ K @ N2 ) @ ( S @ K ) @ ( S3 @ K ) )
% 0.33/1.65 @ A2 )
% 0.33/1.65 = ( type_M1944210753scheme @ S @ A2 ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_65_ex__in__conv,axiom,
% 0.33/1.65 ! [A2: set_nat] :
% 0.33/1.65 ( ( ? [X4: nat] : ( member_nat @ X4 @ A2 ) )
% 0.33/1.65 = ( A2 != bot_bot_set_nat ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_66_equals0I,axiom,
% 0.33/1.65 ! [A2: set_nat] :
% 0.33/1.65 ( ! [Y4: nat] :
% 0.33/1.65 ~ ( member_nat @ Y4 @ A2 )
% 0.33/1.65 => ( A2 = bot_bot_set_nat ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_67_equals0D,axiom,
% 0.33/1.65 ! [A2: set_nat,A: nat] :
% 0.33/1.65 ( ( A2 = bot_bot_set_nat )
% 0.33/1.65 => ~ ( member_nat @ A @ A2 ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_68_emptyE,axiom,
% 0.33/1.65 ! [A: nat] :
% 0.33/1.65 ~ ( member_nat @ A @ bot_bot_set_nat ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_69_not__Cons__self2,axiom,
% 0.33/1.65 ! [X3: type_M1694694083scheme,Xs: list_T247403987scheme] :
% 0.33/1.65 ( ( cons_T633159821scheme @ X3 @ Xs )
% 0.33/1.65 != Xs ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_70_not__Cons__self2,axiom,
% 0.33/1.65 ! [X3: list_T247403987scheme,Xs: list_l1334080099scheme] :
% 0.33/1.65 ( ( cons_l1910959773scheme @ X3 @ Xs )
% 0.33/1.65 != Xs ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_71_not__Cons__self2,axiom,
% 0.33/1.65 ! [X3: type_Mirabelle_typ,Xs: list_T1103309005le_typ] :
% 0.33/1.65 ( ( cons_T363929085le_typ @ X3 @ Xs )
% 0.33/1.65 != Xs ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_72_not__Cons__self2,axiom,
% 0.33/1.65 ! [X3: nat > type_Mirabelle_typ,Xs: list_n396811828le_typ] :
% 0.33/1.65 ( ( cons_n499085924le_typ @ X3 @ Xs )
% 0.33/1.65 != Xs ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_73_not__Cons__self2,axiom,
% 0.33/1.65 ! [X3: nat,Xs: list_nat] :
% 0.33/1.65 ( ( cons_nat @ X3 @ Xs )
% 0.33/1.65 != Xs ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_74_mk__disjoint__insert,axiom,
% 0.33/1.65 ! [A: nat,A2: set_nat] :
% 0.33/1.65 ( ( member_nat @ A @ A2 )
% 0.33/1.65 => ? [B3: set_nat] :
% 0.33/1.65 ( ( A2
% 0.33/1.65 = ( insert_nat @ A @ B3 ) )
% 0.33/1.65 & ~ ( member_nat @ A @ B3 ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_75_insert__commute,axiom,
% 0.33/1.65 ! [X3: nat,Y: nat,A2: set_nat] :
% 0.33/1.65 ( ( insert_nat @ X3 @ ( insert_nat @ Y @ A2 ) )
% 0.33/1.65 = ( insert_nat @ Y @ ( insert_nat @ X3 @ A2 ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_76_insert__eq__iff,axiom,
% 0.33/1.65 ! [A: nat,A2: set_nat,B2: nat,B: set_nat] :
% 0.33/1.65 ( ~ ( member_nat @ A @ A2 )
% 0.33/1.65 => ( ~ ( member_nat @ B2 @ B )
% 0.33/1.65 => ( ( ( insert_nat @ A @ A2 )
% 0.33/1.65 = ( insert_nat @ B2 @ B ) )
% 0.33/1.65 = ( ( ( A = B2 )
% 0.33/1.65 => ( A2 = B ) )
% 0.33/1.65 & ( ( A != B2 )
% 0.33/1.65 => ? [C2: set_nat] :
% 0.33/1.65 ( ( A2
% 0.33/1.65 = ( insert_nat @ B2 @ C2 ) )
% 0.33/1.65 & ~ ( member_nat @ B2 @ C2 )
% 0.33/1.65 & ( B
% 0.33/1.65 = ( insert_nat @ A @ C2 ) )
% 0.33/1.65 & ~ ( member_nat @ A @ C2 ) ) ) ) ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_77_insert__absorb,axiom,
% 0.33/1.65 ! [A: nat,A2: set_nat] :
% 0.33/1.65 ( ( member_nat @ A @ A2 )
% 0.33/1.65 => ( ( insert_nat @ A @ A2 )
% 0.33/1.65 = A2 ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_78_insert__ident,axiom,
% 0.33/1.65 ! [X3: nat,A2: set_nat,B: set_nat] :
% 0.33/1.65 ( ~ ( member_nat @ X3 @ A2 )
% 0.33/1.65 => ( ~ ( member_nat @ X3 @ B )
% 0.33/1.65 => ( ( ( insert_nat @ X3 @ A2 )
% 0.33/1.65 = ( insert_nat @ X3 @ B ) )
% 0.33/1.65 = ( A2 = B ) ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_79_Set_Oset__insert,axiom,
% 0.33/1.65 ! [X3: nat,A2: set_nat] :
% 0.33/1.65 ( ( member_nat @ X3 @ A2 )
% 0.33/1.65 => ~ ! [B3: set_nat] :
% 0.33/1.65 ( ( A2
% 0.33/1.65 = ( insert_nat @ X3 @ B3 ) )
% 0.33/1.65 => ( member_nat @ X3 @ B3 ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_80_insertI2,axiom,
% 0.33/1.65 ! [A: nat,B: set_nat,B2: nat] :
% 0.33/1.65 ( ( member_nat @ A @ B )
% 0.33/1.65 => ( member_nat @ A @ ( insert_nat @ B2 @ B ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_81_insertI1,axiom,
% 0.33/1.65 ! [A: nat,B: set_nat] : ( member_nat @ A @ ( insert_nat @ A @ B ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_82_insertE,axiom,
% 0.33/1.65 ! [A: nat,B2: nat,A2: set_nat] :
% 0.33/1.65 ( ( member_nat @ A @ ( insert_nat @ B2 @ A2 ) )
% 0.33/1.65 => ( ( A != B2 )
% 0.33/1.65 => ( member_nat @ A @ A2 ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_83_empty__def,axiom,
% 0.33/1.65 ( bot_bot_set_nat
% 0.33/1.65 = ( collect_nat
% 0.33/1.65 @ ^ [X4: nat] : $false ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_84_insert__Collect,axiom,
% 0.33/1.65 ! [A: nat,P: nat > $o] :
% 0.33/1.65 ( ( insert_nat @ A @ ( collect_nat @ P ) )
% 0.33/1.65 = ( collect_nat
% 0.33/1.65 @ ^ [U: nat] :
% 0.33/1.65 ( ( U != A )
% 0.33/1.65 => ( P @ U ) ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_85_insert__compr,axiom,
% 0.33/1.65 ( insert_nat
% 0.33/1.65 = ( ^ [A3: nat,B4: set_nat] :
% 0.33/1.65 ( collect_nat
% 0.33/1.65 @ ^ [X4: nat] :
% 0.33/1.65 ( ( X4 = A3 )
% 0.33/1.65 | ( member_nat @ X4 @ B4 ) ) ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_86_singleton__inject,axiom,
% 0.33/1.65 ! [A: nat,B2: nat] :
% 0.33/1.65 ( ( ( insert_nat @ A @ bot_bot_set_nat )
% 0.33/1.65 = ( insert_nat @ B2 @ bot_bot_set_nat ) )
% 0.33/1.65 => ( A = B2 ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_87_insert__not__empty,axiom,
% 0.33/1.65 ! [A: nat,A2: set_nat] :
% 0.33/1.65 ( ( insert_nat @ A @ A2 )
% 0.33/1.65 != bot_bot_set_nat ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_88_doubleton__eq__iff,axiom,
% 0.33/1.65 ! [A: nat,B2: nat,C: nat,D: nat] :
% 0.33/1.65 ( ( ( insert_nat @ A @ ( insert_nat @ B2 @ bot_bot_set_nat ) )
% 0.33/1.65 = ( insert_nat @ C @ ( insert_nat @ D @ bot_bot_set_nat ) ) )
% 0.33/1.65 = ( ( ( A = C )
% 0.33/1.65 & ( B2 = D ) )
% 0.33/1.65 | ( ( A = D )
% 0.33/1.65 & ( B2 = C ) ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_89_singleton__iff,axiom,
% 0.33/1.65 ! [B2: nat,A: nat] :
% 0.33/1.65 ( ( member_nat @ B2 @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 0.33/1.65 = ( B2 = A ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_90_singletonD,axiom,
% 0.33/1.65 ! [B2: nat,A: nat] :
% 0.33/1.65 ( ( member_nat @ B2 @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 0.33/1.65 => ( B2 = A ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_91_Collect__conv__if2,axiom,
% 0.33/1.65 ! [P: nat > $o,A: nat] :
% 0.33/1.65 ( ( ( P @ A )
% 0.33/1.65 => ( ( collect_nat
% 0.33/1.65 @ ^ [X4: nat] :
% 0.33/1.65 ( ( A = X4 )
% 0.33/1.65 & ( P @ X4 ) ) )
% 0.33/1.65 = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.33/1.65 & ( ~ ( P @ A )
% 0.33/1.65 => ( ( collect_nat
% 0.33/1.65 @ ^ [X4: nat] :
% 0.33/1.65 ( ( A = X4 )
% 0.33/1.65 & ( P @ X4 ) ) )
% 0.33/1.65 = bot_bot_set_nat ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_92_Collect__conv__if,axiom,
% 0.33/1.65 ! [P: nat > $o,A: nat] :
% 0.33/1.65 ( ( ( P @ A )
% 0.33/1.65 => ( ( collect_nat
% 0.33/1.65 @ ^ [X4: nat] :
% 0.33/1.65 ( ( X4 = A )
% 0.33/1.65 & ( P @ X4 ) ) )
% 0.33/1.65 = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.33/1.65 & ( ~ ( P @ A )
% 0.33/1.65 => ( ( collect_nat
% 0.33/1.65 @ ^ [X4: nat] :
% 0.33/1.65 ( ( X4 = A )
% 0.33/1.65 & ( P @ X4 ) ) )
% 0.33/1.65 = bot_bot_set_nat ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_93_the__elem__eq,axiom,
% 0.33/1.65 ! [X3: nat] :
% 0.33/1.65 ( ( the_elem_nat @ ( insert_nat @ X3 @ bot_bot_set_nat ) )
% 0.33/1.65 = X3 ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_94_bot__apply,axiom,
% 0.33/1.65 ( bot_bot_nat_o
% 0.33/1.65 = ( ^ [X4: nat] : bot_bot_o ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_95_bound__tv__type__scheme_Osimps_I2_J,axiom,
% 0.33/1.65 ! [M: nat] :
% 0.33/1.65 ( ( type_M326705277scheme @ ( type_M2048935292e_BVar @ M ) )
% 0.33/1.65 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_96_is__singletonI,axiom,
% 0.33/1.65 ! [X3: nat] : ( is_singleton_nat @ ( insert_nat @ X3 @ bot_bot_set_nat ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_97_bot_Onot__eq__extremum,axiom,
% 0.33/1.65 ! [A: nat > $o] :
% 0.33/1.65 ( ( A != bot_bot_nat_o )
% 0.33/1.65 = ( ord_less_nat_o @ bot_bot_nat_o @ A ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_98_bot_Onot__eq__extremum,axiom,
% 0.33/1.65 ! [A: set_nat] :
% 0.33/1.65 ( ( A != bot_bot_set_nat )
% 0.33/1.65 = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_99_bot_Onot__eq__extremum,axiom,
% 0.33/1.65 ! [A: nat] :
% 0.33/1.65 ( ( A != bot_bot_nat )
% 0.33/1.65 = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_100_bot_Oextremum__strict,axiom,
% 0.33/1.65 ! [A: nat > $o] :
% 0.33/1.65 ~ ( ord_less_nat_o @ A @ bot_bot_nat_o ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_101_bot_Oextremum__strict,axiom,
% 0.33/1.65 ! [A: set_nat] :
% 0.33/1.65 ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_102_bot_Oextremum__strict,axiom,
% 0.33/1.65 ! [A: nat] :
% 0.33/1.65 ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_103_free__tv__TVar,axiom,
% 0.33/1.65 ! [M: nat] :
% 0.33/1.65 ( ( type_M49385309le_typ @ ( type_Mirabelle_TVar @ M ) )
% 0.33/1.65 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_104_bound__tv__type__scheme_Osimps_I1_J,axiom,
% 0.33/1.65 ! [M: nat] :
% 0.33/1.65 ( ( type_M326705277scheme @ ( type_M876316792e_FVar @ M ) )
% 0.33/1.65 = bot_bot_set_nat ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_105_typ_Oinject_I1_J,axiom,
% 0.33/1.65 ! [X1: nat,Y1: nat] :
% 0.33/1.65 ( ( ( type_Mirabelle_TVar @ X1 )
% 0.33/1.65 = ( type_Mirabelle_TVar @ Y1 ) )
% 0.33/1.65 = ( X1 = Y1 ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_106_new__tv__TVar,axiom,
% 0.33/1.65 ! [N2: nat,M: nat] :
% 0.33/1.65 ( ( type_M1211611096le_typ @ N2 @ ( type_Mirabelle_TVar @ M ) )
% 0.33/1.65 = ( ord_less_nat @ M @ N2 ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_107_new__tv__TVar__subst,axiom,
% 0.33/1.65 ! [N2: nat] : ( type_M1734147655le_typ @ N2 @ type_Mirabelle_TVar ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_108_eq__free__eq__subst__scheme__list,axiom,
% 0.33/1.65 ! [A2: list_T247403987scheme,S1: nat > type_Mirabelle_typ,S2: nat > type_Mirabelle_typ] :
% 0.33/1.65 ( ! [N: nat] :
% 0.33/1.65 ( ( member_nat @ N @ ( type_M141510067scheme @ A2 ) )
% 0.33/1.65 => ( ( S1 @ N )
% 0.33/1.65 = ( S2 @ N ) ) )
% 0.33/1.65 => ( ( type_M1944210753scheme @ S1 @ A2 )
% 0.33/1.65 = ( type_M1944210753scheme @ S2 @ A2 ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_109_scheme__list__substitutions__only__on__free__variables,axiom,
% 0.33/1.65 ! [A2: list_T247403987scheme,S: nat > type_Mirabelle_typ,S3: nat > type_Mirabelle_typ] :
% 0.33/1.65 ( ! [X: nat] :
% 0.33/1.65 ( ( member_nat @ X @ ( type_M141510067scheme @ A2 ) )
% 0.33/1.65 => ( ( S @ X )
% 0.33/1.65 = ( S3 @ X ) ) )
% 0.33/1.65 => ( ( type_M1944210753scheme @ S @ A2 )
% 0.33/1.65 = ( type_M1944210753scheme @ S3 @ A2 ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_110_bot__set__def,axiom,
% 0.33/1.65 ( bot_bot_set_nat
% 0.33/1.65 = ( collect_nat @ bot_bot_nat_o ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_111_not__psubset__empty,axiom,
% 0.33/1.65 ! [A2: set_nat] :
% 0.33/1.65 ~ ( ord_less_set_nat @ A2 @ bot_bot_set_nat ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_112_app__subst__TVar,axiom,
% 0.33/1.65 ! [S: nat > type_Mirabelle_typ,N2: nat] :
% 0.33/1.65 ( ( type_M784671311le_typ @ S @ ( type_Mirabelle_TVar @ N2 ) )
% 0.33/1.65 = ( S @ N2 ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_113_is__singleton__the__elem,axiom,
% 0.33/1.65 ( is_singleton_nat
% 0.33/1.65 = ( ^ [A4: set_nat] :
% 0.33/1.65 ( A4
% 0.33/1.65 = ( insert_nat @ ( the_elem_nat @ A4 ) @ bot_bot_set_nat ) ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_114_is__singletonI_H,axiom,
% 0.33/1.65 ! [A2: set_nat] :
% 0.33/1.65 ( ( A2 != bot_bot_set_nat )
% 0.33/1.65 => ( ! [X: nat,Y4: nat] :
% 0.33/1.65 ( ( member_nat @ X @ A2 )
% 0.33/1.65 => ( ( member_nat @ Y4 @ A2 )
% 0.33/1.65 => ( X = Y4 ) ) )
% 0.33/1.65 => ( is_singleton_nat @ A2 ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_115_ord__eq__less__subst,axiom,
% 0.33/1.65 ! [A: set_nat,F: nat > set_nat,B2: nat,C: nat] :
% 0.33/1.65 ( ( A
% 0.33/1.65 = ( F @ B2 ) )
% 0.33/1.65 => ( ( ord_less_nat @ B2 @ C )
% 0.33/1.65 => ( ! [X: nat,Y4: nat] :
% 0.33/1.65 ( ( ord_less_nat @ X @ Y4 )
% 0.33/1.65 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.65 => ( ord_less_set_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_116_ord__eq__less__subst,axiom,
% 0.33/1.65 ! [A: nat > $o,F: nat > nat > $o,B2: nat,C: nat] :
% 0.33/1.65 ( ( A
% 0.33/1.65 = ( F @ B2 ) )
% 0.33/1.65 => ( ( ord_less_nat @ B2 @ C )
% 0.33/1.65 => ( ! [X: nat,Y4: nat] :
% 0.33/1.65 ( ( ord_less_nat @ X @ Y4 )
% 0.33/1.65 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.65 => ( ord_less_nat_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.33/1.65
% 0.33/1.65 thf(fact_117_ord__eq__less__subst,axiom,
% 0.33/1.65 ! [A: nat,F: set_nat > nat,B2: set_nat,C: set_nat] :
% 0.33/1.65 ( ( A
% 0.33/1.65 = ( F @ B2 ) )
% 0.33/1.65 => ( ( ord_less_set_nat @ B2 @ C )
% 0.33/1.65 => ( ! [X: set_nat,Y4: set_nat] :
% 0.33/1.65 ( ( ord_less_set_nat @ X @ Y4 )
% 0.33/1.65 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_118_ord__eq__less__subst,axiom,
% 0.33/1.66 ! [A: set_nat,F: set_nat > set_nat,B2: set_nat,C: set_nat] :
% 0.33/1.66 ( ( A
% 0.33/1.66 = ( F @ B2 ) )
% 0.33/1.66 => ( ( ord_less_set_nat @ B2 @ C )
% 0.33/1.66 => ( ! [X: set_nat,Y4: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ X @ Y4 )
% 0.33/1.66 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_set_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_119_ord__eq__less__subst,axiom,
% 0.33/1.66 ! [A: nat > $o,F: set_nat > nat > $o,B2: set_nat,C: set_nat] :
% 0.33/1.66 ( ( A
% 0.33/1.66 = ( F @ B2 ) )
% 0.33/1.66 => ( ( ord_less_set_nat @ B2 @ C )
% 0.33/1.66 => ( ! [X: set_nat,Y4: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ X @ Y4 )
% 0.33/1.66 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_nat_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_120_ord__eq__less__subst,axiom,
% 0.33/1.66 ! [A: nat,F: ( nat > $o ) > nat,B2: nat > $o,C: nat > $o] :
% 0.33/1.66 ( ( A
% 0.33/1.66 = ( F @ B2 ) )
% 0.33/1.66 => ( ( ord_less_nat_o @ B2 @ C )
% 0.33/1.66 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ X @ Y4 )
% 0.33/1.66 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_121_ord__eq__less__subst,axiom,
% 0.33/1.66 ! [A: set_nat,F: ( nat > $o ) > set_nat,B2: nat > $o,C: nat > $o] :
% 0.33/1.66 ( ( A
% 0.33/1.66 = ( F @ B2 ) )
% 0.33/1.66 => ( ( ord_less_nat_o @ B2 @ C )
% 0.33/1.66 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ X @ Y4 )
% 0.33/1.66 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_set_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_122_ord__eq__less__subst,axiom,
% 0.33/1.66 ! [A: nat > $o,F: ( nat > $o ) > nat > $o,B2: nat > $o,C: nat > $o] :
% 0.33/1.66 ( ( A
% 0.33/1.66 = ( F @ B2 ) )
% 0.33/1.66 => ( ( ord_less_nat_o @ B2 @ C )
% 0.33/1.66 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ X @ Y4 )
% 0.33/1.66 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_nat_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_123_ord__eq__less__subst,axiom,
% 0.33/1.66 ! [A: nat,F: nat > nat,B2: nat,C: nat] :
% 0.33/1.66 ( ( A
% 0.33/1.66 = ( F @ B2 ) )
% 0.33/1.66 => ( ( ord_less_nat @ B2 @ C )
% 0.33/1.66 => ( ! [X: nat,Y4: nat] :
% 0.33/1.66 ( ( ord_less_nat @ X @ Y4 )
% 0.33/1.66 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_124_ord__less__eq__subst,axiom,
% 0.33/1.66 ! [A: nat,B2: nat,F: nat > set_nat,C: set_nat] :
% 0.33/1.66 ( ( ord_less_nat @ A @ B2 )
% 0.33/1.66 => ( ( ( F @ B2 )
% 0.33/1.66 = C )
% 0.33/1.66 => ( ! [X: nat,Y4: nat] :
% 0.33/1.66 ( ( ord_less_nat @ X @ Y4 )
% 0.33/1.66 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_set_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_125_ord__less__eq__subst,axiom,
% 0.33/1.66 ! [A: nat,B2: nat,F: nat > nat > $o,C: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat @ A @ B2 )
% 0.33/1.66 => ( ( ( F @ B2 )
% 0.33/1.66 = C )
% 0.33/1.66 => ( ! [X: nat,Y4: nat] :
% 0.33/1.66 ( ( ord_less_nat @ X @ Y4 )
% 0.33/1.66 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_nat_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_126_ord__less__eq__subst,axiom,
% 0.33/1.66 ! [A: set_nat,B2: set_nat,F: set_nat > nat,C: nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ A @ B2 )
% 0.33/1.66 => ( ( ( F @ B2 )
% 0.33/1.66 = C )
% 0.33/1.66 => ( ! [X: set_nat,Y4: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ X @ Y4 )
% 0.33/1.66 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_127_ord__less__eq__subst,axiom,
% 0.33/1.66 ! [A: set_nat,B2: set_nat,F: set_nat > set_nat,C: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ A @ B2 )
% 0.33/1.66 => ( ( ( F @ B2 )
% 0.33/1.66 = C )
% 0.33/1.66 => ( ! [X: set_nat,Y4: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ X @ Y4 )
% 0.33/1.66 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_set_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_128_ord__less__eq__subst,axiom,
% 0.33/1.66 ! [A: set_nat,B2: set_nat,F: set_nat > nat > $o,C: nat > $o] :
% 0.33/1.66 ( ( ord_less_set_nat @ A @ B2 )
% 0.33/1.66 => ( ( ( F @ B2 )
% 0.33/1.66 = C )
% 0.33/1.66 => ( ! [X: set_nat,Y4: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ X @ Y4 )
% 0.33/1.66 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_nat_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_129_ord__less__eq__subst,axiom,
% 0.33/1.66 ! [A: nat > $o,B2: nat > $o,F: ( nat > $o ) > nat,C: nat] :
% 0.33/1.66 ( ( ord_less_nat_o @ A @ B2 )
% 0.33/1.66 => ( ( ( F @ B2 )
% 0.33/1.66 = C )
% 0.33/1.66 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ X @ Y4 )
% 0.33/1.66 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_130_ord__less__eq__subst,axiom,
% 0.33/1.66 ! [A: nat > $o,B2: nat > $o,F: ( nat > $o ) > set_nat,C: set_nat] :
% 0.33/1.66 ( ( ord_less_nat_o @ A @ B2 )
% 0.33/1.66 => ( ( ( F @ B2 )
% 0.33/1.66 = C )
% 0.33/1.66 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ X @ Y4 )
% 0.33/1.66 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_set_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_131_ord__less__eq__subst,axiom,
% 0.33/1.66 ! [A: nat > $o,B2: nat > $o,F: ( nat > $o ) > nat > $o,C: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ A @ B2 )
% 0.33/1.66 => ( ( ( F @ B2 )
% 0.33/1.66 = C )
% 0.33/1.66 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ X @ Y4 )
% 0.33/1.66 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_nat_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_132_ord__less__eq__subst,axiom,
% 0.33/1.66 ! [A: nat,B2: nat,F: nat > nat,C: nat] :
% 0.33/1.66 ( ( ord_less_nat @ A @ B2 )
% 0.33/1.66 => ( ( ( F @ B2 )
% 0.33/1.66 = C )
% 0.33/1.66 => ( ! [X: nat,Y4: nat] :
% 0.33/1.66 ( ( ord_less_nat @ X @ Y4 )
% 0.33/1.66 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_133_order__less__subst1,axiom,
% 0.33/1.66 ! [A: nat,F: set_nat > nat,B2: set_nat,C: set_nat] :
% 0.33/1.66 ( ( ord_less_nat @ A @ ( F @ B2 ) )
% 0.33/1.66 => ( ( ord_less_set_nat @ B2 @ C )
% 0.33/1.66 => ( ! [X: set_nat,Y4: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ X @ Y4 )
% 0.33/1.66 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_134_order__less__subst1,axiom,
% 0.33/1.66 ! [A: nat,F: ( nat > $o ) > nat,B2: nat > $o,C: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat @ A @ ( F @ B2 ) )
% 0.33/1.66 => ( ( ord_less_nat_o @ B2 @ C )
% 0.33/1.66 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ X @ Y4 )
% 0.33/1.66 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_135_order__less__subst1,axiom,
% 0.33/1.66 ! [A: set_nat,F: nat > set_nat,B2: nat,C: nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ A @ ( F @ B2 ) )
% 0.33/1.66 => ( ( ord_less_nat @ B2 @ C )
% 0.33/1.66 => ( ! [X: nat,Y4: nat] :
% 0.33/1.66 ( ( ord_less_nat @ X @ Y4 )
% 0.33/1.66 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_set_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_136_order__less__subst1,axiom,
% 0.33/1.66 ! [A: set_nat,F: set_nat > set_nat,B2: set_nat,C: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ A @ ( F @ B2 ) )
% 0.33/1.66 => ( ( ord_less_set_nat @ B2 @ C )
% 0.33/1.66 => ( ! [X: set_nat,Y4: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ X @ Y4 )
% 0.33/1.66 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_set_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_137_order__less__subst1,axiom,
% 0.33/1.66 ! [A: set_nat,F: ( nat > $o ) > set_nat,B2: nat > $o,C: nat > $o] :
% 0.33/1.66 ( ( ord_less_set_nat @ A @ ( F @ B2 ) )
% 0.33/1.66 => ( ( ord_less_nat_o @ B2 @ C )
% 0.33/1.66 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ X @ Y4 )
% 0.33/1.66 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_set_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_138_order__less__subst1,axiom,
% 0.33/1.66 ! [A: nat > $o,F: nat > nat > $o,B2: nat,C: nat] :
% 0.33/1.66 ( ( ord_less_nat_o @ A @ ( F @ B2 ) )
% 0.33/1.66 => ( ( ord_less_nat @ B2 @ C )
% 0.33/1.66 => ( ! [X: nat,Y4: nat] :
% 0.33/1.66 ( ( ord_less_nat @ X @ Y4 )
% 0.33/1.66 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_nat_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_139_order__less__subst1,axiom,
% 0.33/1.66 ! [A: nat > $o,F: set_nat > nat > $o,B2: set_nat,C: set_nat] :
% 0.33/1.66 ( ( ord_less_nat_o @ A @ ( F @ B2 ) )
% 0.33/1.66 => ( ( ord_less_set_nat @ B2 @ C )
% 0.33/1.66 => ( ! [X: set_nat,Y4: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ X @ Y4 )
% 0.33/1.66 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_nat_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_140_order__less__subst1,axiom,
% 0.33/1.66 ! [A: nat > $o,F: ( nat > $o ) > nat > $o,B2: nat > $o,C: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ A @ ( F @ B2 ) )
% 0.33/1.66 => ( ( ord_less_nat_o @ B2 @ C )
% 0.33/1.66 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ X @ Y4 )
% 0.33/1.66 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_nat_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_141_order__less__subst1,axiom,
% 0.33/1.66 ! [A: nat,F: nat > nat,B2: nat,C: nat] :
% 0.33/1.66 ( ( ord_less_nat @ A @ ( F @ B2 ) )
% 0.33/1.66 => ( ( ord_less_nat @ B2 @ C )
% 0.33/1.66 => ( ! [X: nat,Y4: nat] :
% 0.33/1.66 ( ( ord_less_nat @ X @ Y4 )
% 0.33/1.66 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_142_order__less__subst2,axiom,
% 0.33/1.66 ! [A: nat,B2: nat,F: nat > set_nat,C: set_nat] :
% 0.33/1.66 ( ( ord_less_nat @ A @ B2 )
% 0.33/1.66 => ( ( ord_less_set_nat @ ( F @ B2 ) @ C )
% 0.33/1.66 => ( ! [X: nat,Y4: nat] :
% 0.33/1.66 ( ( ord_less_nat @ X @ Y4 )
% 0.33/1.66 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_set_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_143_order__less__subst2,axiom,
% 0.33/1.66 ! [A: nat,B2: nat,F: nat > nat > $o,C: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat @ A @ B2 )
% 0.33/1.66 => ( ( ord_less_nat_o @ ( F @ B2 ) @ C )
% 0.33/1.66 => ( ! [X: nat,Y4: nat] :
% 0.33/1.66 ( ( ord_less_nat @ X @ Y4 )
% 0.33/1.66 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_nat_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_144_order__less__subst2,axiom,
% 0.33/1.66 ! [A: set_nat,B2: set_nat,F: set_nat > nat,C: nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ A @ B2 )
% 0.33/1.66 => ( ( ord_less_nat @ ( F @ B2 ) @ C )
% 0.33/1.66 => ( ! [X: set_nat,Y4: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ X @ Y4 )
% 0.33/1.66 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_145_order__less__subst2,axiom,
% 0.33/1.66 ! [A: set_nat,B2: set_nat,F: set_nat > set_nat,C: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ A @ B2 )
% 0.33/1.66 => ( ( ord_less_set_nat @ ( F @ B2 ) @ C )
% 0.33/1.66 => ( ! [X: set_nat,Y4: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ X @ Y4 )
% 0.33/1.66 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_set_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_146_order__less__subst2,axiom,
% 0.33/1.66 ! [A: set_nat,B2: set_nat,F: set_nat > nat > $o,C: nat > $o] :
% 0.33/1.66 ( ( ord_less_set_nat @ A @ B2 )
% 0.33/1.66 => ( ( ord_less_nat_o @ ( F @ B2 ) @ C )
% 0.33/1.66 => ( ! [X: set_nat,Y4: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ X @ Y4 )
% 0.33/1.66 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_nat_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_147_order__less__subst2,axiom,
% 0.33/1.66 ! [A: nat > $o,B2: nat > $o,F: ( nat > $o ) > nat,C: nat] :
% 0.33/1.66 ( ( ord_less_nat_o @ A @ B2 )
% 0.33/1.66 => ( ( ord_less_nat @ ( F @ B2 ) @ C )
% 0.33/1.66 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ X @ Y4 )
% 0.33/1.66 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_148_order__less__subst2,axiom,
% 0.33/1.66 ! [A: nat > $o,B2: nat > $o,F: ( nat > $o ) > set_nat,C: set_nat] :
% 0.33/1.66 ( ( ord_less_nat_o @ A @ B2 )
% 0.33/1.66 => ( ( ord_less_set_nat @ ( F @ B2 ) @ C )
% 0.33/1.66 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ X @ Y4 )
% 0.33/1.66 => ( ord_less_set_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_set_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_149_order__less__subst2,axiom,
% 0.33/1.66 ! [A: nat > $o,B2: nat > $o,F: ( nat > $o ) > nat > $o,C: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ A @ B2 )
% 0.33/1.66 => ( ( ord_less_nat_o @ ( F @ B2 ) @ C )
% 0.33/1.66 => ( ! [X: nat > $o,Y4: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ X @ Y4 )
% 0.33/1.66 => ( ord_less_nat_o @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_nat_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_150_order__less__subst2,axiom,
% 0.33/1.66 ! [A: nat,B2: nat,F: nat > nat,C: nat] :
% 0.33/1.66 ( ( ord_less_nat @ A @ B2 )
% 0.33/1.66 => ( ( ord_less_nat @ ( F @ B2 ) @ C )
% 0.33/1.66 => ( ! [X: nat,Y4: nat] :
% 0.33/1.66 ( ( ord_less_nat @ X @ Y4 )
% 0.33/1.66 => ( ord_less_nat @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.33/1.66 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_151_gt__ex,axiom,
% 0.33/1.66 ! [X3: nat] :
% 0.33/1.66 ? [X_1: nat] : ( ord_less_nat @ X3 @ X_1 ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_152_neqE,axiom,
% 0.33/1.66 ! [X3: nat,Y: nat] :
% 0.33/1.66 ( ( X3 != Y )
% 0.33/1.66 => ( ~ ( ord_less_nat @ X3 @ Y )
% 0.33/1.66 => ( ord_less_nat @ Y @ X3 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_153_neq__iff,axiom,
% 0.33/1.66 ! [X3: nat,Y: nat] :
% 0.33/1.66 ( ( X3 != Y )
% 0.33/1.66 = ( ( ord_less_nat @ X3 @ Y )
% 0.33/1.66 | ( ord_less_nat @ Y @ X3 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_154_order_Oasym,axiom,
% 0.33/1.66 ! [A: set_nat,B2: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ A @ B2 )
% 0.33/1.66 => ~ ( ord_less_set_nat @ B2 @ A ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_155_order_Oasym,axiom,
% 0.33/1.66 ! [A: nat > $o,B2: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ A @ B2 )
% 0.33/1.66 => ~ ( ord_less_nat_o @ B2 @ A ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_156_order_Oasym,axiom,
% 0.33/1.66 ! [A: nat,B2: nat] :
% 0.33/1.66 ( ( ord_less_nat @ A @ B2 )
% 0.33/1.66 => ~ ( ord_less_nat @ B2 @ A ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_157_less__imp__neq,axiom,
% 0.33/1.66 ! [X3: set_nat,Y: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ X3 @ Y )
% 0.33/1.66 => ( X3 != Y ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_158_less__imp__neq,axiom,
% 0.33/1.66 ! [X3: nat > $o,Y: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ X3 @ Y )
% 0.33/1.66 => ( X3 != Y ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_159_less__imp__neq,axiom,
% 0.33/1.66 ! [X3: nat,Y: nat] :
% 0.33/1.66 ( ( ord_less_nat @ X3 @ Y )
% 0.33/1.66 => ( X3 != Y ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_160_less__asym,axiom,
% 0.33/1.66 ! [X3: set_nat,Y: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ X3 @ Y )
% 0.33/1.66 => ~ ( ord_less_set_nat @ Y @ X3 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_161_less__asym,axiom,
% 0.33/1.66 ! [X3: nat > $o,Y: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ X3 @ Y )
% 0.33/1.66 => ~ ( ord_less_nat_o @ Y @ X3 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_162_less__asym,axiom,
% 0.33/1.66 ! [X3: nat,Y: nat] :
% 0.33/1.66 ( ( ord_less_nat @ X3 @ Y )
% 0.33/1.66 => ~ ( ord_less_nat @ Y @ X3 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_163_less__asym_H,axiom,
% 0.33/1.66 ! [A: set_nat,B2: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ A @ B2 )
% 0.33/1.66 => ~ ( ord_less_set_nat @ B2 @ A ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_164_less__asym_H,axiom,
% 0.33/1.66 ! [A: nat > $o,B2: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ A @ B2 )
% 0.33/1.66 => ~ ( ord_less_nat_o @ B2 @ A ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_165_less__asym_H,axiom,
% 0.33/1.66 ! [A: nat,B2: nat] :
% 0.33/1.66 ( ( ord_less_nat @ A @ B2 )
% 0.33/1.66 => ~ ( ord_less_nat @ B2 @ A ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_166_less__trans,axiom,
% 0.33/1.66 ! [X3: set_nat,Y: set_nat,Z2: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ X3 @ Y )
% 0.33/1.66 => ( ( ord_less_set_nat @ Y @ Z2 )
% 0.33/1.66 => ( ord_less_set_nat @ X3 @ Z2 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_167_less__trans,axiom,
% 0.33/1.66 ! [X3: nat > $o,Y: nat > $o,Z2: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ X3 @ Y )
% 0.33/1.66 => ( ( ord_less_nat_o @ Y @ Z2 )
% 0.33/1.66 => ( ord_less_nat_o @ X3 @ Z2 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_168_less__trans,axiom,
% 0.33/1.66 ! [X3: nat,Y: nat,Z2: nat] :
% 0.33/1.66 ( ( ord_less_nat @ X3 @ Y )
% 0.33/1.66 => ( ( ord_less_nat @ Y @ Z2 )
% 0.33/1.66 => ( ord_less_nat @ X3 @ Z2 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_169_less__linear,axiom,
% 0.33/1.66 ! [X3: nat,Y: nat] :
% 0.33/1.66 ( ( ord_less_nat @ X3 @ Y )
% 0.33/1.66 | ( X3 = Y )
% 0.33/1.66 | ( ord_less_nat @ Y @ X3 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_170_less__irrefl,axiom,
% 0.33/1.66 ! [X3: set_nat] :
% 0.33/1.66 ~ ( ord_less_set_nat @ X3 @ X3 ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_171_less__irrefl,axiom,
% 0.33/1.66 ! [X3: nat > $o] :
% 0.33/1.66 ~ ( ord_less_nat_o @ X3 @ X3 ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_172_less__irrefl,axiom,
% 0.33/1.66 ! [X3: nat] :
% 0.33/1.66 ~ ( ord_less_nat @ X3 @ X3 ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_173_ord__eq__less__trans,axiom,
% 0.33/1.66 ! [A: set_nat,B2: set_nat,C: set_nat] :
% 0.33/1.66 ( ( A = B2 )
% 0.33/1.66 => ( ( ord_less_set_nat @ B2 @ C )
% 0.33/1.66 => ( ord_less_set_nat @ A @ C ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_174_ord__eq__less__trans,axiom,
% 0.33/1.66 ! [A: nat > $o,B2: nat > $o,C: nat > $o] :
% 0.33/1.66 ( ( A = B2 )
% 0.33/1.66 => ( ( ord_less_nat_o @ B2 @ C )
% 0.33/1.66 => ( ord_less_nat_o @ A @ C ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_175_ord__eq__less__trans,axiom,
% 0.33/1.66 ! [A: nat,B2: nat,C: nat] :
% 0.33/1.66 ( ( A = B2 )
% 0.33/1.66 => ( ( ord_less_nat @ B2 @ C )
% 0.33/1.66 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_176_ord__less__eq__trans,axiom,
% 0.33/1.66 ! [A: set_nat,B2: set_nat,C: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ A @ B2 )
% 0.33/1.66 => ( ( B2 = C )
% 0.33/1.66 => ( ord_less_set_nat @ A @ C ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_177_ord__less__eq__trans,axiom,
% 0.33/1.66 ! [A: nat > $o,B2: nat > $o,C: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ A @ B2 )
% 0.33/1.66 => ( ( B2 = C )
% 0.33/1.66 => ( ord_less_nat_o @ A @ C ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_178_ord__less__eq__trans,axiom,
% 0.33/1.66 ! [A: nat,B2: nat,C: nat] :
% 0.33/1.66 ( ( ord_less_nat @ A @ B2 )
% 0.33/1.66 => ( ( B2 = C )
% 0.33/1.66 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_179_dual__order_Oasym,axiom,
% 0.33/1.66 ! [B2: set_nat,A: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ B2 @ A )
% 0.33/1.66 => ~ ( ord_less_set_nat @ A @ B2 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_180_dual__order_Oasym,axiom,
% 0.33/1.66 ! [B2: nat > $o,A: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ B2 @ A )
% 0.33/1.66 => ~ ( ord_less_nat_o @ A @ B2 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_181_dual__order_Oasym,axiom,
% 0.33/1.66 ! [B2: nat,A: nat] :
% 0.33/1.66 ( ( ord_less_nat @ B2 @ A )
% 0.33/1.66 => ~ ( ord_less_nat @ A @ B2 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_182_less__imp__not__eq,axiom,
% 0.33/1.66 ! [X3: set_nat,Y: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ X3 @ Y )
% 0.33/1.66 => ( X3 != Y ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_183_less__imp__not__eq,axiom,
% 0.33/1.66 ! [X3: nat > $o,Y: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ X3 @ Y )
% 0.33/1.66 => ( X3 != Y ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_184_less__imp__not__eq,axiom,
% 0.33/1.66 ! [X3: nat,Y: nat] :
% 0.33/1.66 ( ( ord_less_nat @ X3 @ Y )
% 0.33/1.66 => ( X3 != Y ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_185_less__not__sym,axiom,
% 0.33/1.66 ! [X3: set_nat,Y: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ X3 @ Y )
% 0.33/1.66 => ~ ( ord_less_set_nat @ Y @ X3 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_186_less__not__sym,axiom,
% 0.33/1.66 ! [X3: nat > $o,Y: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ X3 @ Y )
% 0.33/1.66 => ~ ( ord_less_nat_o @ Y @ X3 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_187_less__not__sym,axiom,
% 0.33/1.66 ! [X3: nat,Y: nat] :
% 0.33/1.66 ( ( ord_less_nat @ X3 @ Y )
% 0.33/1.66 => ~ ( ord_less_nat @ Y @ X3 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_188_less__induct,axiom,
% 0.33/1.66 ! [P: nat > $o,A: nat] :
% 0.33/1.66 ( ! [X: nat] :
% 0.33/1.66 ( ! [Y5: nat] :
% 0.33/1.66 ( ( ord_less_nat @ Y5 @ X )
% 0.33/1.66 => ( P @ Y5 ) )
% 0.33/1.66 => ( P @ X ) )
% 0.33/1.66 => ( P @ A ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_189_antisym__conv3,axiom,
% 0.33/1.66 ! [Y: nat,X3: nat] :
% 0.33/1.66 ( ~ ( ord_less_nat @ Y @ X3 )
% 0.33/1.66 => ( ( ~ ( ord_less_nat @ X3 @ Y ) )
% 0.33/1.66 = ( X3 = Y ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_190_less__imp__not__eq2,axiom,
% 0.33/1.66 ! [X3: set_nat,Y: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ X3 @ Y )
% 0.33/1.66 => ( Y != X3 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_191_less__imp__not__eq2,axiom,
% 0.33/1.66 ! [X3: nat > $o,Y: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ X3 @ Y )
% 0.33/1.66 => ( Y != X3 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_192_less__imp__not__eq2,axiom,
% 0.33/1.66 ! [X3: nat,Y: nat] :
% 0.33/1.66 ( ( ord_less_nat @ X3 @ Y )
% 0.33/1.66 => ( Y != X3 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_193_less__imp__triv,axiom,
% 0.33/1.66 ! [X3: set_nat,Y: set_nat,P: $o] :
% 0.33/1.66 ( ( ord_less_set_nat @ X3 @ Y )
% 0.33/1.66 => ( ( ord_less_set_nat @ Y @ X3 )
% 0.33/1.66 => P ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_194_less__imp__triv,axiom,
% 0.33/1.66 ! [X3: nat > $o,Y: nat > $o,P: $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ X3 @ Y )
% 0.33/1.66 => ( ( ord_less_nat_o @ Y @ X3 )
% 0.33/1.66 => P ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_195_less__imp__triv,axiom,
% 0.33/1.66 ! [X3: nat,Y: nat,P: $o] :
% 0.33/1.66 ( ( ord_less_nat @ X3 @ Y )
% 0.33/1.66 => ( ( ord_less_nat @ Y @ X3 )
% 0.33/1.66 => P ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_196_linorder__cases,axiom,
% 0.33/1.66 ! [X3: nat,Y: nat] :
% 0.33/1.66 ( ~ ( ord_less_nat @ X3 @ Y )
% 0.33/1.66 => ( ( X3 != Y )
% 0.33/1.66 => ( ord_less_nat @ Y @ X3 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_197_dual__order_Oirrefl,axiom,
% 0.33/1.66 ! [A: set_nat] :
% 0.33/1.66 ~ ( ord_less_set_nat @ A @ A ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_198_dual__order_Oirrefl,axiom,
% 0.33/1.66 ! [A: nat > $o] :
% 0.33/1.66 ~ ( ord_less_nat_o @ A @ A ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_199_dual__order_Oirrefl,axiom,
% 0.33/1.66 ! [A: nat] :
% 0.33/1.66 ~ ( ord_less_nat @ A @ A ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_200_order_Ostrict__trans,axiom,
% 0.33/1.66 ! [A: set_nat,B2: set_nat,C: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ A @ B2 )
% 0.33/1.66 => ( ( ord_less_set_nat @ B2 @ C )
% 0.33/1.66 => ( ord_less_set_nat @ A @ C ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_201_order_Ostrict__trans,axiom,
% 0.33/1.66 ! [A: nat > $o,B2: nat > $o,C: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ A @ B2 )
% 0.33/1.66 => ( ( ord_less_nat_o @ B2 @ C )
% 0.33/1.66 => ( ord_less_nat_o @ A @ C ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_202_order_Ostrict__trans,axiom,
% 0.33/1.66 ! [A: nat,B2: nat,C: nat] :
% 0.33/1.66 ( ( ord_less_nat @ A @ B2 )
% 0.33/1.66 => ( ( ord_less_nat @ B2 @ C )
% 0.33/1.66 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_203_less__imp__not__less,axiom,
% 0.33/1.66 ! [X3: set_nat,Y: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ X3 @ Y )
% 0.33/1.66 => ~ ( ord_less_set_nat @ Y @ X3 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_204_less__imp__not__less,axiom,
% 0.33/1.66 ! [X3: nat > $o,Y: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ X3 @ Y )
% 0.33/1.66 => ~ ( ord_less_nat_o @ Y @ X3 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_205_less__imp__not__less,axiom,
% 0.33/1.66 ! [X3: nat,Y: nat] :
% 0.33/1.66 ( ( ord_less_nat @ X3 @ Y )
% 0.33/1.66 => ~ ( ord_less_nat @ Y @ X3 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_206_exists__least__iff,axiom,
% 0.33/1.66 ( ( ^ [P2: nat > $o] :
% 0.33/1.66 ? [X5: nat] : ( P2 @ X5 ) )
% 0.33/1.66 = ( ^ [P3: nat > $o] :
% 0.33/1.66 ? [N3: nat] :
% 0.33/1.66 ( ( P3 @ N3 )
% 0.33/1.66 & ! [M2: nat] :
% 0.33/1.66 ( ( ord_less_nat @ M2 @ N3 )
% 0.33/1.66 => ~ ( P3 @ M2 ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_207_linorder__less__wlog,axiom,
% 0.33/1.66 ! [P: nat > nat > $o,A: nat,B2: nat] :
% 0.33/1.66 ( ! [A5: nat,B5: nat] :
% 0.33/1.66 ( ( ord_less_nat @ A5 @ B5 )
% 0.33/1.66 => ( P @ A5 @ B5 ) )
% 0.33/1.66 => ( ! [A5: nat] : ( P @ A5 @ A5 )
% 0.33/1.66 => ( ! [A5: nat,B5: nat] :
% 0.33/1.66 ( ( P @ B5 @ A5 )
% 0.33/1.66 => ( P @ A5 @ B5 ) )
% 0.33/1.66 => ( P @ A @ B2 ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_208_dual__order_Ostrict__trans,axiom,
% 0.33/1.66 ! [B2: set_nat,A: set_nat,C: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ B2 @ A )
% 0.33/1.66 => ( ( ord_less_set_nat @ C @ B2 )
% 0.33/1.66 => ( ord_less_set_nat @ C @ A ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_209_dual__order_Ostrict__trans,axiom,
% 0.33/1.66 ! [B2: nat > $o,A: nat > $o,C: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ B2 @ A )
% 0.33/1.66 => ( ( ord_less_nat_o @ C @ B2 )
% 0.33/1.66 => ( ord_less_nat_o @ C @ A ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_210_dual__order_Ostrict__trans,axiom,
% 0.33/1.66 ! [B2: nat,A: nat,C: nat] :
% 0.33/1.66 ( ( ord_less_nat @ B2 @ A )
% 0.33/1.66 => ( ( ord_less_nat @ C @ B2 )
% 0.33/1.66 => ( ord_less_nat @ C @ A ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_211_not__less__iff__gr__or__eq,axiom,
% 0.33/1.66 ! [X3: nat,Y: nat] :
% 0.33/1.66 ( ( ~ ( ord_less_nat @ X3 @ Y ) )
% 0.33/1.66 = ( ( ord_less_nat @ Y @ X3 )
% 0.33/1.66 | ( X3 = Y ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_212_order_Ostrict__implies__not__eq,axiom,
% 0.33/1.66 ! [A: set_nat,B2: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ A @ B2 )
% 0.33/1.66 => ( A != B2 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_213_order_Ostrict__implies__not__eq,axiom,
% 0.33/1.66 ! [A: nat > $o,B2: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ A @ B2 )
% 0.33/1.66 => ( A != B2 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_214_order_Ostrict__implies__not__eq,axiom,
% 0.33/1.66 ! [A: nat,B2: nat] :
% 0.33/1.66 ( ( ord_less_nat @ A @ B2 )
% 0.33/1.66 => ( A != B2 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_215_dual__order_Ostrict__implies__not__eq,axiom,
% 0.33/1.66 ! [B2: set_nat,A: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ B2 @ A )
% 0.33/1.66 => ( A != B2 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_216_dual__order_Ostrict__implies__not__eq,axiom,
% 0.33/1.66 ! [B2: nat > $o,A: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ B2 @ A )
% 0.33/1.66 => ( A != B2 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_217_dual__order_Ostrict__implies__not__eq,axiom,
% 0.33/1.66 ! [B2: nat,A: nat] :
% 0.33/1.66 ( ( ord_less_nat @ B2 @ A )
% 0.33/1.66 => ( A != B2 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_218_bot__fun__def,axiom,
% 0.33/1.66 ( bot_bot_nat_o
% 0.33/1.66 = ( ^ [X4: nat] : bot_bot_o ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_219_mk__scheme_Osimps_I1_J,axiom,
% 0.33/1.66 ! [N2: nat] :
% 0.33/1.66 ( ( type_M1006385707scheme @ ( type_Mirabelle_TVar @ N2 ) )
% 0.33/1.66 = ( type_M876316792e_FVar @ N2 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_220_is__singletonE,axiom,
% 0.33/1.66 ! [A2: set_nat] :
% 0.33/1.66 ( ( is_singleton_nat @ A2 )
% 0.33/1.66 => ~ ! [X: nat] :
% 0.33/1.66 ( A2
% 0.33/1.66 != ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_221_is__singleton__def,axiom,
% 0.33/1.66 ( is_singleton_nat
% 0.33/1.66 = ( ^ [A4: set_nat] :
% 0.33/1.66 ? [X4: nat] :
% 0.33/1.66 ( A4
% 0.33/1.66 = ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_222_free__tv__id__subst,axiom,
% 0.33/1.66 ( ( type_M1715972684le_typ @ type_M405566558_subst )
% 0.33/1.66 = bot_bot_set_nat ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_223_Set_Ois__empty__def,axiom,
% 0.33/1.66 ( is_empty_nat
% 0.33/1.66 = ( ^ [A4: set_nat] : ( A4 = bot_bot_set_nat ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_224_the__elem__def,axiom,
% 0.33/1.66 ( the_elem_nat
% 0.33/1.66 = ( ^ [X6: set_nat] :
% 0.33/1.66 ( the_nat
% 0.33/1.66 @ ^ [X4: nat] :
% 0.33/1.66 ( X6
% 0.33/1.66 = ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_225_mk__scheme_Osimps_I2_J,axiom,
% 0.33/1.66 ! [T1: type_Mirabelle_typ,T2: type_Mirabelle_typ] :
% 0.33/1.66 ( ( type_M1006385707scheme @ ( type_Mirabelle_Fun @ T1 @ T2 ) )
% 0.33/1.66 = ( type_M155660035e_SFun @ ( type_M1006385707scheme @ T1 ) @ ( type_M1006385707scheme @ T2 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_226_Type__Mirabelle__lczmhmumaa_Odom__def,axiom,
% 0.33/1.66 ( type_Mirabelle_dom
% 0.33/1.66 = ( ^ [S4: nat > type_Mirabelle_typ] :
% 0.33/1.66 ( collect_nat
% 0.33/1.66 @ ^ [N3: nat] :
% 0.33/1.66 ( ( S4 @ N3 )
% 0.33/1.66 != ( type_Mirabelle_TVar @ N3 ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_227_id__subst__def,axiom,
% 0.33/1.66 type_M405566558_subst = type_Mirabelle_TVar ).
% 0.33/1.66
% 0.33/1.66 thf(fact_228_typ_Oinject_I2_J,axiom,
% 0.33/1.66 ! [X21: type_Mirabelle_typ,X222: type_Mirabelle_typ,Y21: type_Mirabelle_typ,Y22: type_Mirabelle_typ] :
% 0.33/1.66 ( ( ( type_Mirabelle_Fun @ X21 @ X222 )
% 0.33/1.66 = ( type_Mirabelle_Fun @ Y21 @ Y22 ) )
% 0.33/1.66 = ( ( X21 = Y21 )
% 0.33/1.66 & ( X222 = Y22 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_229_new__tv__Fun,axiom,
% 0.33/1.66 ! [N2: nat,T1: type_Mirabelle_typ,T2: type_Mirabelle_typ] :
% 0.33/1.66 ( ( type_M1211611096le_typ @ N2 @ ( type_Mirabelle_Fun @ T1 @ T2 ) )
% 0.33/1.66 = ( ( type_M1211611096le_typ @ N2 @ T1 )
% 0.33/1.66 & ( type_M1211611096le_typ @ N2 @ T2 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_230_dom__id__subst,axiom,
% 0.33/1.66 ( ( type_Mirabelle_dom @ type_M405566558_subst )
% 0.33/1.66 = bot_bot_set_nat ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_231_psubsetD,axiom,
% 0.33/1.66 ! [A2: set_nat,B: set_nat,C: nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ A2 @ B )
% 0.33/1.66 => ( ( member_nat @ C @ A2 )
% 0.33/1.66 => ( member_nat @ C @ B ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_232_less__set__def,axiom,
% 0.33/1.66 ( ord_less_set_nat
% 0.33/1.66 = ( ^ [A4: set_nat,B4: set_nat] :
% 0.33/1.66 ( ord_less_nat_o
% 0.33/1.66 @ ^ [X4: nat] : ( member_nat @ X4 @ A4 )
% 0.33/1.66 @ ^ [X4: nat] : ( member_nat @ X4 @ B4 ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_233_psubset__trans,axiom,
% 0.33/1.66 ! [A2: set_nat,B: set_nat,C3: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ A2 @ B )
% 0.33/1.66 => ( ( ord_less_set_nat @ B @ C3 )
% 0.33/1.66 => ( ord_less_set_nat @ A2 @ C3 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_234_new__tv__id__subst,axiom,
% 0.33/1.66 ! [N2: nat] : ( type_M1734147655le_typ @ N2 @ type_M405566558_subst ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_235_app__subst__Fun,axiom,
% 0.33/1.66 ! [S: nat > type_Mirabelle_typ,T1: type_Mirabelle_typ,T2: type_Mirabelle_typ] :
% 0.33/1.66 ( ( type_M784671311le_typ @ S @ ( type_Mirabelle_Fun @ T1 @ T2 ) )
% 0.33/1.66 = ( type_Mirabelle_Fun @ ( type_M784671311le_typ @ S @ T1 ) @ ( type_M784671311le_typ @ S @ T2 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_236_typ_Oexhaust,axiom,
% 0.33/1.66 ! [Y: type_Mirabelle_typ] :
% 0.33/1.66 ( ! [X12: nat] :
% 0.33/1.66 ( Y
% 0.33/1.66 != ( type_Mirabelle_TVar @ X12 ) )
% 0.33/1.66 => ~ ! [X212: type_Mirabelle_typ,X223: type_Mirabelle_typ] :
% 0.33/1.66 ( Y
% 0.33/1.66 != ( type_Mirabelle_Fun @ X212 @ X223 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_237_typ_Oinduct,axiom,
% 0.33/1.66 ! [P: type_Mirabelle_typ > $o,Typ: type_Mirabelle_typ] :
% 0.33/1.66 ( ! [X: nat] : ( P @ ( type_Mirabelle_TVar @ X ) )
% 0.33/1.66 => ( ! [X1a: type_Mirabelle_typ,X22: type_Mirabelle_typ] :
% 0.33/1.66 ( ( P @ X1a )
% 0.33/1.66 => ( ( P @ X22 )
% 0.33/1.66 => ( P @ ( type_Mirabelle_Fun @ X1a @ X22 ) ) ) )
% 0.33/1.66 => ( P @ Typ ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_238_typ_Odistinct_I1_J,axiom,
% 0.33/1.66 ! [X1: nat,X21: type_Mirabelle_typ,X222: type_Mirabelle_typ] :
% 0.33/1.66 ( ( type_Mirabelle_TVar @ X1 )
% 0.33/1.66 != ( type_Mirabelle_Fun @ X21 @ X222 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_239_the__sym__eq__trivial,axiom,
% 0.33/1.66 ! [X3: nat] :
% 0.33/1.66 ( ( the_nat
% 0.33/1.66 @ ( ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/1.66 @ X3 ) )
% 0.33/1.66 = X3 ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_240_the__eq__trivial,axiom,
% 0.33/1.66 ! [A: nat] :
% 0.33/1.66 ( ( the_nat
% 0.33/1.66 @ ^ [X4: nat] : ( X4 = A ) )
% 0.33/1.66 = A ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_241_the__equality,axiom,
% 0.33/1.66 ! [P: nat > $o,A: nat] :
% 0.33/1.66 ( ( P @ A )
% 0.33/1.66 => ( ! [X: nat] :
% 0.33/1.66 ( ( P @ X )
% 0.33/1.66 => ( X = A ) )
% 0.33/1.66 => ( ( the_nat @ P )
% 0.33/1.66 = A ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_242_cod__id__subst,axiom,
% 0.33/1.66 ( ( type_Mirabelle_cod @ type_M405566558_subst )
% 0.33/1.66 = bot_bot_set_nat ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_243_theI,axiom,
% 0.33/1.66 ! [P: nat > $o,A: nat] :
% 0.33/1.66 ( ( P @ A )
% 0.33/1.66 => ( ! [X: nat] :
% 0.33/1.66 ( ( P @ X )
% 0.33/1.66 => ( X = A ) )
% 0.33/1.66 => ( P @ ( the_nat @ P ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_244_theI_H,axiom,
% 0.33/1.66 ! [P: nat > $o] :
% 0.33/1.66 ( ? [X7: nat] :
% 0.33/1.66 ( ( P @ X7 )
% 0.33/1.66 & ! [Y4: nat] :
% 0.33/1.66 ( ( P @ Y4 )
% 0.33/1.66 => ( Y4 = X7 ) ) )
% 0.33/1.66 => ( P @ ( the_nat @ P ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_245_theI2,axiom,
% 0.33/1.66 ! [P: nat > $o,A: nat,Q: nat > $o] :
% 0.33/1.66 ( ( P @ A )
% 0.33/1.66 => ( ! [X: nat] :
% 0.33/1.66 ( ( P @ X )
% 0.33/1.66 => ( X = A ) )
% 0.33/1.66 => ( ! [X: nat] :
% 0.33/1.66 ( ( P @ X )
% 0.33/1.66 => ( Q @ X ) )
% 0.33/1.66 => ( Q @ ( the_nat @ P ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_246_If__def,axiom,
% 0.33/1.66 ( if_nat
% 0.33/1.66 = ( ^ [P3: $o,X4: nat,Y6: nat] :
% 0.33/1.66 ( the_nat
% 0.33/1.66 @ ^ [Z3: nat] :
% 0.33/1.66 ( ( P3
% 0.33/1.66 => ( Z3 = X4 ) )
% 0.33/1.66 & ( ~ P3
% 0.33/1.66 => ( Z3 = Y6 ) ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_247_the1I2,axiom,
% 0.33/1.66 ! [P: nat > $o,Q: nat > $o] :
% 0.33/1.66 ( ? [X7: nat] :
% 0.33/1.66 ( ( P @ X7 )
% 0.33/1.66 & ! [Y4: nat] :
% 0.33/1.66 ( ( P @ Y4 )
% 0.33/1.66 => ( Y4 = X7 ) ) )
% 0.33/1.66 => ( ! [X: nat] :
% 0.33/1.66 ( ( P @ X )
% 0.33/1.66 => ( Q @ X ) )
% 0.33/1.66 => ( Q @ ( the_nat @ P ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_248_the1__equality,axiom,
% 0.33/1.66 ! [P: nat > $o,A: nat] :
% 0.33/1.66 ( ? [X7: nat] :
% 0.33/1.66 ( ( P @ X7 )
% 0.33/1.66 & ! [Y4: nat] :
% 0.33/1.66 ( ( P @ Y4 )
% 0.33/1.66 => ( Y4 = X7 ) ) )
% 0.33/1.66 => ( ( P @ A )
% 0.33/1.66 => ( ( the_nat @ P )
% 0.33/1.66 = A ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_249_Collect__empty__eq__bot,axiom,
% 0.33/1.66 ! [P: nat > $o] :
% 0.33/1.66 ( ( ( collect_nat @ P )
% 0.33/1.66 = bot_bot_set_nat )
% 0.33/1.66 = ( P = bot_bot_nat_o ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_250_bot__empty__eq,axiom,
% 0.33/1.66 ( bot_bot_nat_o
% 0.33/1.66 = ( ^ [X4: nat] : ( member_nat @ X4 @ bot_bot_set_nat ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_251_free__tv__subst,axiom,
% 0.33/1.66 ( type_M1715972684le_typ
% 0.33/1.66 = ( ^ [S4: nat > type_Mirabelle_typ] : ( sup_sup_set_nat @ ( type_Mirabelle_dom @ S4 ) @ ( type_Mirabelle_cod @ S4 ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_252_UnCI,axiom,
% 0.33/1.66 ! [C: nat,B: set_nat,A2: set_nat] :
% 0.33/1.66 ( ( ~ ( member_nat @ C @ B )
% 0.33/1.66 => ( member_nat @ C @ A2 ) )
% 0.33/1.66 => ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_253_Un__iff,axiom,
% 0.33/1.66 ! [C: nat,A2: set_nat,B: set_nat] :
% 0.33/1.66 ( ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B ) )
% 0.33/1.66 = ( ( member_nat @ C @ A2 )
% 0.33/1.66 | ( member_nat @ C @ B ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_254_Un__empty,axiom,
% 0.33/1.66 ! [A2: set_nat,B: set_nat] :
% 0.33/1.66 ( ( ( sup_sup_set_nat @ A2 @ B )
% 0.33/1.66 = bot_bot_set_nat )
% 0.33/1.66 = ( ( A2 = bot_bot_set_nat )
% 0.33/1.66 & ( B = bot_bot_set_nat ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_255_Un__insert__left,axiom,
% 0.33/1.66 ! [A: nat,B: set_nat,C3: set_nat] :
% 0.33/1.66 ( ( sup_sup_set_nat @ ( insert_nat @ A @ B ) @ C3 )
% 0.33/1.66 = ( insert_nat @ A @ ( sup_sup_set_nat @ B @ C3 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_256_Un__insert__right,axiom,
% 0.33/1.66 ! [A2: set_nat,A: nat,B: set_nat] :
% 0.33/1.66 ( ( sup_sup_set_nat @ A2 @ ( insert_nat @ A @ B ) )
% 0.33/1.66 = ( insert_nat @ A @ ( sup_sup_set_nat @ A2 @ B ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_257_weaken__asm__Un,axiom,
% 0.33/1.66 ! [A2: set_nat,P: nat > $o,Q: $o,B: set_nat] :
% 0.33/1.66 ( ( ! [X7: nat] :
% 0.33/1.66 ( ( member_nat @ X7 @ A2 )
% 0.33/1.66 => ( P @ X7 ) )
% 0.33/1.66 => Q )
% 0.33/1.66 => ( ! [X: nat] :
% 0.33/1.66 ( ( member_nat @ X @ ( sup_sup_set_nat @ A2 @ B ) )
% 0.33/1.66 => ( P @ X ) )
% 0.33/1.66 => Q ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_258_UnE,axiom,
% 0.33/1.66 ! [C: nat,A2: set_nat,B: set_nat] :
% 0.33/1.66 ( ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B ) )
% 0.33/1.66 => ( ~ ( member_nat @ C @ A2 )
% 0.33/1.66 => ( member_nat @ C @ B ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_259_UnI1,axiom,
% 0.33/1.66 ! [C: nat,A2: set_nat,B: set_nat] :
% 0.33/1.66 ( ( member_nat @ C @ A2 )
% 0.33/1.66 => ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_260_UnI2,axiom,
% 0.33/1.66 ! [C: nat,B: set_nat,A2: set_nat] :
% 0.33/1.66 ( ( member_nat @ C @ B )
% 0.33/1.66 => ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_261_Un__def,axiom,
% 0.33/1.66 ( sup_sup_set_nat
% 0.33/1.66 = ( ^ [A4: set_nat,B4: set_nat] :
% 0.33/1.66 ( collect_nat
% 0.33/1.66 @ ^ [X4: nat] :
% 0.33/1.66 ( ( member_nat @ X4 @ A4 )
% 0.33/1.66 | ( member_nat @ X4 @ B4 ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_262_bex__Un,axiom,
% 0.33/1.66 ! [A2: set_nat,B: set_nat,P: nat > $o] :
% 0.33/1.66 ( ( ? [X4: nat] :
% 0.33/1.66 ( ( member_nat @ X4 @ ( sup_sup_set_nat @ A2 @ B ) )
% 0.33/1.66 & ( P @ X4 ) ) )
% 0.33/1.66 = ( ? [X4: nat] :
% 0.33/1.66 ( ( member_nat @ X4 @ A2 )
% 0.33/1.66 & ( P @ X4 ) )
% 0.33/1.66 | ? [X4: nat] :
% 0.33/1.66 ( ( member_nat @ X4 @ B )
% 0.33/1.66 & ( P @ X4 ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_263_ball__Un,axiom,
% 0.33/1.66 ! [A2: set_nat,B: set_nat,P: nat > $o] :
% 0.33/1.66 ( ( ! [X4: nat] :
% 0.33/1.66 ( ( member_nat @ X4 @ ( sup_sup_set_nat @ A2 @ B ) )
% 0.33/1.66 => ( P @ X4 ) ) )
% 0.33/1.66 = ( ! [X4: nat] :
% 0.33/1.66 ( ( member_nat @ X4 @ A2 )
% 0.33/1.66 => ( P @ X4 ) )
% 0.33/1.66 & ! [X4: nat] :
% 0.33/1.66 ( ( member_nat @ X4 @ B )
% 0.33/1.66 => ( P @ X4 ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_264_Un__assoc,axiom,
% 0.33/1.66 ! [A2: set_nat,B: set_nat,C3: set_nat] :
% 0.33/1.66 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A2 @ B ) @ C3 )
% 0.33/1.66 = ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ B @ C3 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_265_Un__absorb,axiom,
% 0.33/1.66 ! [A2: set_nat] :
% 0.33/1.66 ( ( sup_sup_set_nat @ A2 @ A2 )
% 0.33/1.66 = A2 ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_266_Un__commute,axiom,
% 0.33/1.66 ( sup_sup_set_nat
% 0.33/1.66 = ( ^ [A4: set_nat,B4: set_nat] : ( sup_sup_set_nat @ B4 @ A4 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_267_Un__left__absorb,axiom,
% 0.33/1.66 ! [A2: set_nat,B: set_nat] :
% 0.33/1.66 ( ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ A2 @ B ) )
% 0.33/1.66 = ( sup_sup_set_nat @ A2 @ B ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_268_Collect__disj__eq,axiom,
% 0.33/1.66 ! [P: nat > $o,Q: nat > $o] :
% 0.33/1.66 ( ( collect_nat
% 0.33/1.66 @ ^ [X4: nat] :
% 0.33/1.66 ( ( P @ X4 )
% 0.33/1.66 | ( Q @ X4 ) ) )
% 0.33/1.66 = ( sup_sup_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_269_Un__left__commute,axiom,
% 0.33/1.66 ! [A2: set_nat,B: set_nat,C3: set_nat] :
% 0.33/1.66 ( ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ B @ C3 ) )
% 0.33/1.66 = ( sup_sup_set_nat @ B @ ( sup_sup_set_nat @ A2 @ C3 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_270_insert__def,axiom,
% 0.33/1.66 ( insert_nat
% 0.33/1.66 = ( ^ [A3: nat] :
% 0.33/1.66 ( sup_sup_set_nat
% 0.33/1.66 @ ( collect_nat
% 0.33/1.66 @ ^ [X4: nat] : ( X4 = A3 ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_271_Un__empty__left,axiom,
% 0.33/1.66 ! [B: set_nat] :
% 0.33/1.66 ( ( sup_sup_set_nat @ bot_bot_set_nat @ B )
% 0.33/1.66 = B ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_272_Un__empty__right,axiom,
% 0.33/1.66 ! [A2: set_nat] :
% 0.33/1.66 ( ( sup_sup_set_nat @ A2 @ bot_bot_set_nat )
% 0.33/1.66 = A2 ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_273_singleton__Un__iff,axiom,
% 0.33/1.66 ! [X3: nat,A2: set_nat,B: set_nat] :
% 0.33/1.66 ( ( ( insert_nat @ X3 @ bot_bot_set_nat )
% 0.33/1.66 = ( sup_sup_set_nat @ A2 @ B ) )
% 0.33/1.66 = ( ( ( A2 = bot_bot_set_nat )
% 0.33/1.66 & ( B
% 0.33/1.66 = ( insert_nat @ X3 @ bot_bot_set_nat ) ) )
% 0.33/1.66 | ( ( A2
% 0.33/1.66 = ( insert_nat @ X3 @ bot_bot_set_nat ) )
% 0.33/1.66 & ( B = bot_bot_set_nat ) )
% 0.33/1.66 | ( ( A2
% 0.33/1.66 = ( insert_nat @ X3 @ bot_bot_set_nat ) )
% 0.33/1.66 & ( B
% 0.33/1.66 = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_274_Un__singleton__iff,axiom,
% 0.33/1.66 ! [A2: set_nat,B: set_nat,X3: nat] :
% 0.33/1.66 ( ( ( sup_sup_set_nat @ A2 @ B )
% 0.33/1.66 = ( insert_nat @ X3 @ bot_bot_set_nat ) )
% 0.33/1.66 = ( ( ( A2 = bot_bot_set_nat )
% 0.33/1.66 & ( B
% 0.33/1.66 = ( insert_nat @ X3 @ bot_bot_set_nat ) ) )
% 0.33/1.66 | ( ( A2
% 0.33/1.66 = ( insert_nat @ X3 @ bot_bot_set_nat ) )
% 0.33/1.66 & ( B = bot_bot_set_nat ) )
% 0.33/1.66 | ( ( A2
% 0.33/1.66 = ( insert_nat @ X3 @ bot_bot_set_nat ) )
% 0.33/1.66 & ( B
% 0.33/1.66 = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_275_insert__is__Un,axiom,
% 0.33/1.66 ( insert_nat
% 0.33/1.66 = ( ^ [A3: nat] : ( sup_sup_set_nat @ ( insert_nat @ A3 @ bot_bot_set_nat ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_276_bound__tv__list_Osimps_I2_J,axiom,
% 0.33/1.66 ! [X3: type_Mirabelle_typ,L: list_T1103309005le_typ] :
% 0.33/1.66 ( ( type_M1539052445le_typ @ ( cons_T363929085le_typ @ X3 @ L ) )
% 0.33/1.66 = ( sup_sup_set_nat @ ( type_M801073677le_typ @ X3 ) @ ( type_M1539052445le_typ @ L ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_277_bound__tv__list_Osimps_I2_J,axiom,
% 0.33/1.66 ! [X3: nat > type_Mirabelle_typ,L: list_n396811828le_typ] :
% 0.33/1.66 ( ( type_M513401740le_typ @ ( cons_n499085924le_typ @ X3 @ L ) )
% 0.33/1.66 = ( sup_sup_set_nat @ ( type_M772783356le_typ @ X3 ) @ ( type_M513401740le_typ @ L ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_278_bound__tv__list_Osimps_I2_J,axiom,
% 0.33/1.66 ! [X3: list_T247403987scheme,L: list_l1334080099scheme] :
% 0.33/1.66 ( ( type_M1496178953scheme @ ( cons_l1910959773scheme @ X3 @ L ) )
% 0.33/1.66 = ( sup_sup_set_nat @ ( type_M961603331scheme @ X3 ) @ ( type_M1496178953scheme @ L ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_279_bound__tv__list_Osimps_I2_J,axiom,
% 0.33/1.66 ! [X3: type_M1694694083scheme,L: list_T247403987scheme] :
% 0.33/1.66 ( ( type_M961603331scheme @ ( cons_T633159821scheme @ X3 @ L ) )
% 0.33/1.66 = ( sup_sup_set_nat @ ( type_M326705277scheme @ X3 ) @ ( type_M961603331scheme @ L ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_280_free__tv__Fun,axiom,
% 0.33/1.66 ! [T1: type_Mirabelle_typ,T2: type_Mirabelle_typ] :
% 0.33/1.66 ( ( type_M49385309le_typ @ ( type_Mirabelle_Fun @ T1 @ T2 ) )
% 0.33/1.66 = ( sup_sup_set_nat @ ( type_M49385309le_typ @ T1 ) @ ( type_M49385309le_typ @ T2 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_281_free__tv__type__scheme_Osimps_I3_J,axiom,
% 0.33/1.66 ! [S1: type_M1694694083scheme,S2: type_M1694694083scheme] :
% 0.33/1.66 ( ( type_M1050318637scheme @ ( type_M155660035e_SFun @ S1 @ S2 ) )
% 0.33/1.66 = ( sup_sup_set_nat @ ( type_M1050318637scheme @ S1 ) @ ( type_M1050318637scheme @ S2 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_282_bound__tv__type__scheme_Osimps_I3_J,axiom,
% 0.33/1.66 ! [S1: type_M1694694083scheme,S2: type_M1694694083scheme] :
% 0.33/1.66 ( ( type_M326705277scheme @ ( type_M155660035e_SFun @ S1 @ S2 ) )
% 0.33/1.66 = ( sup_sup_set_nat @ ( type_M326705277scheme @ S1 ) @ ( type_M326705277scheme @ S2 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_283_free__tv__list_Osimps_I2_J,axiom,
% 0.33/1.66 ! [X3: list_n396811828le_typ,L: list_l865305402le_typ] :
% 0.33/1.66 ( ( type_M906078444le_typ @ ( cons_l1800589546le_typ @ X3 @ L ) )
% 0.33/1.66 = ( sup_sup_set_nat @ ( type_M1691543772le_typ @ X3 ) @ ( type_M906078444le_typ @ L ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_284_free__tv__list_Osimps_I2_J,axiom,
% 0.33/1.66 ! [X3: list_l1334080099scheme,L: list_l1704431731scheme] :
% 0.33/1.66 ( ( type_M1926053183scheme @ ( cons_l531914285scheme @ X3 @ L ) )
% 0.33/1.66 = ( sup_sup_set_nat @ ( type_M1958029241scheme @ X3 ) @ ( type_M1926053183scheme @ L ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_285_free__tv__list_Osimps_I2_J,axiom,
% 0.33/1.66 ! [X3: list_T1103309005le_typ,L: list_l1790670291le_typ] :
% 0.33/1.66 ( ( type_M1418941437le_typ @ ( cons_l392684675le_typ @ X3 @ L ) )
% 0.33/1.66 = ( sup_sup_set_nat @ ( type_M510873837le_typ @ X3 ) @ ( type_M1418941437le_typ @ L ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_286_free__tv__list_Osimps_I2_J,axiom,
% 0.33/1.66 ! [X3: type_Mirabelle_typ,L: list_T1103309005le_typ] :
% 0.33/1.66 ( ( type_M510873837le_typ @ ( cons_T363929085le_typ @ X3 @ L ) )
% 0.33/1.66 = ( sup_sup_set_nat @ ( type_M49385309le_typ @ X3 ) @ ( type_M510873837le_typ @ L ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_287_free__tv__list_Osimps_I2_J,axiom,
% 0.33/1.66 ! [X3: list_T247403987scheme,L: list_l1334080099scheme] :
% 0.33/1.66 ( ( type_M1958029241scheme @ ( cons_l1910959773scheme @ X3 @ L ) )
% 0.33/1.66 = ( sup_sup_set_nat @ ( type_M141510067scheme @ X3 ) @ ( type_M1958029241scheme @ L ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_288_free__tv__list_Osimps_I2_J,axiom,
% 0.33/1.66 ! [X3: nat > type_Mirabelle_typ,L: list_n396811828le_typ] :
% 0.33/1.66 ( ( type_M1691543772le_typ @ ( cons_n499085924le_typ @ X3 @ L ) )
% 0.33/1.66 = ( sup_sup_set_nat @ ( type_M1715972684le_typ @ X3 ) @ ( type_M1691543772le_typ @ L ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_289_free__tv__list_Osimps_I2_J,axiom,
% 0.33/1.66 ! [X3: type_M1694694083scheme,L: list_T247403987scheme] :
% 0.33/1.66 ( ( type_M141510067scheme @ ( cons_T633159821scheme @ X3 @ L ) )
% 0.33/1.66 = ( sup_sup_set_nat @ ( type_M1050318637scheme @ X3 ) @ ( type_M141510067scheme @ L ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_290_free__tv__fun__def,axiom,
% 0.33/1.66 ( type_M1715972684le_typ
% 0.33/1.66 = ( ^ [F2: nat > type_Mirabelle_typ] :
% 0.33/1.66 ( sup_sup_set_nat
% 0.33/1.66 @ ( type_Mirabelle_dom
% 0.33/1.66 @ ^ [N3: nat] : ( type_M1743451154le_typ @ ( F2 @ ( type_M1898948661at_nat @ N3 ) ) ) )
% 0.33/1.66 @ ( type_Mirabelle_cod
% 0.33/1.66 @ ^ [N3: nat] : ( type_M1743451154le_typ @ ( F2 @ ( type_M1898948661at_nat @ N3 ) ) ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_291_sup__bot__left,axiom,
% 0.33/1.66 ! [X3: nat > $o] :
% 0.33/1.66 ( ( sup_sup_nat_o @ bot_bot_nat_o @ X3 )
% 0.33/1.66 = X3 ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_292_sup__bot__left,axiom,
% 0.33/1.66 ! [X3: set_nat] :
% 0.33/1.66 ( ( sup_sup_set_nat @ bot_bot_set_nat @ X3 )
% 0.33/1.66 = X3 ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_293_sup__bot__right,axiom,
% 0.33/1.66 ! [X3: nat > $o] :
% 0.33/1.66 ( ( sup_sup_nat_o @ X3 @ bot_bot_nat_o )
% 0.33/1.66 = X3 ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_294_sup__bot__right,axiom,
% 0.33/1.66 ! [X3: set_nat] :
% 0.33/1.66 ( ( sup_sup_set_nat @ X3 @ bot_bot_set_nat )
% 0.33/1.66 = X3 ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_295_sup__bot_Oright__neutral,axiom,
% 0.33/1.66 ! [A: nat > $o] :
% 0.33/1.66 ( ( sup_sup_nat_o @ A @ bot_bot_nat_o )
% 0.33/1.66 = A ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_296_sup__bot_Oright__neutral,axiom,
% 0.33/1.66 ! [A: set_nat] :
% 0.33/1.66 ( ( sup_sup_set_nat @ A @ bot_bot_set_nat )
% 0.33/1.66 = A ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_297_sup__bot_Oneutr__eq__iff,axiom,
% 0.33/1.66 ! [A: nat > $o,B2: nat > $o] :
% 0.33/1.66 ( ( bot_bot_nat_o
% 0.33/1.66 = ( sup_sup_nat_o @ A @ B2 ) )
% 0.33/1.66 = ( ( A = bot_bot_nat_o )
% 0.33/1.66 & ( B2 = bot_bot_nat_o ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_298_sup__bot_Oneutr__eq__iff,axiom,
% 0.33/1.66 ! [A: set_nat,B2: set_nat] :
% 0.33/1.66 ( ( bot_bot_set_nat
% 0.33/1.66 = ( sup_sup_set_nat @ A @ B2 ) )
% 0.33/1.66 = ( ( A = bot_bot_set_nat )
% 0.33/1.66 & ( B2 = bot_bot_set_nat ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_299_sup__bot_Oleft__neutral,axiom,
% 0.33/1.66 ! [A: nat > $o] :
% 0.33/1.66 ( ( sup_sup_nat_o @ bot_bot_nat_o @ A )
% 0.33/1.66 = A ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_300_sup__bot_Oleft__neutral,axiom,
% 0.33/1.66 ! [A: set_nat] :
% 0.33/1.66 ( ( sup_sup_set_nat @ bot_bot_set_nat @ A )
% 0.33/1.66 = A ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_301_sup__bot_Oeq__neutr__iff,axiom,
% 0.33/1.66 ! [A: nat > $o,B2: nat > $o] :
% 0.33/1.66 ( ( ( sup_sup_nat_o @ A @ B2 )
% 0.33/1.66 = bot_bot_nat_o )
% 0.33/1.66 = ( ( A = bot_bot_nat_o )
% 0.33/1.66 & ( B2 = bot_bot_nat_o ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_302_sup__bot_Oeq__neutr__iff,axiom,
% 0.33/1.66 ! [A: set_nat,B2: set_nat] :
% 0.33/1.66 ( ( ( sup_sup_set_nat @ A @ B2 )
% 0.33/1.66 = bot_bot_set_nat )
% 0.33/1.66 = ( ( A = bot_bot_set_nat )
% 0.33/1.66 & ( B2 = bot_bot_set_nat ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_303_sup__eq__bot__iff,axiom,
% 0.33/1.66 ! [X3: nat > $o,Y: nat > $o] :
% 0.33/1.66 ( ( ( sup_sup_nat_o @ X3 @ Y )
% 0.33/1.66 = bot_bot_nat_o )
% 0.33/1.66 = ( ( X3 = bot_bot_nat_o )
% 0.33/1.66 & ( Y = bot_bot_nat_o ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_304_sup__eq__bot__iff,axiom,
% 0.33/1.66 ! [X3: set_nat,Y: set_nat] :
% 0.33/1.66 ( ( ( sup_sup_set_nat @ X3 @ Y )
% 0.33/1.66 = bot_bot_set_nat )
% 0.33/1.66 = ( ( X3 = bot_bot_set_nat )
% 0.33/1.66 & ( Y = bot_bot_set_nat ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_305_bot__eq__sup__iff,axiom,
% 0.33/1.66 ! [X3: nat > $o,Y: nat > $o] :
% 0.33/1.66 ( ( bot_bot_nat_o
% 0.33/1.66 = ( sup_sup_nat_o @ X3 @ Y ) )
% 0.33/1.66 = ( ( X3 = bot_bot_nat_o )
% 0.33/1.66 & ( Y = bot_bot_nat_o ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_306_bot__eq__sup__iff,axiom,
% 0.33/1.66 ! [X3: set_nat,Y: set_nat] :
% 0.33/1.66 ( ( bot_bot_set_nat
% 0.33/1.66 = ( sup_sup_set_nat @ X3 @ Y ) )
% 0.33/1.66 = ( ( X3 = bot_bot_set_nat )
% 0.33/1.66 & ( Y = bot_bot_set_nat ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_307_sup__Un__eq,axiom,
% 0.33/1.66 ! [R: set_nat,S: set_nat] :
% 0.33/1.66 ( ( sup_sup_nat_o
% 0.33/1.66 @ ^ [X4: nat] : ( member_nat @ X4 @ R )
% 0.33/1.66 @ ^ [X4: nat] : ( member_nat @ X4 @ S ) )
% 0.33/1.66 = ( ^ [X4: nat] : ( member_nat @ X4 @ ( sup_sup_set_nat @ R @ S ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_308_sup__set__def,axiom,
% 0.33/1.66 ( sup_sup_set_nat
% 0.33/1.66 = ( ^ [A4: set_nat,B4: set_nat] :
% 0.33/1.66 ( collect_nat
% 0.33/1.66 @ ( sup_sup_nat_o
% 0.33/1.66 @ ^ [X4: nat] : ( member_nat @ X4 @ A4 )
% 0.33/1.66 @ ^ [X4: nat] : ( member_nat @ X4 @ B4 ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_309_less__supI1,axiom,
% 0.33/1.66 ! [X3: nat > $o,A: nat > $o,B2: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ X3 @ A )
% 0.33/1.66 => ( ord_less_nat_o @ X3 @ ( sup_sup_nat_o @ A @ B2 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_310_less__supI1,axiom,
% 0.33/1.66 ! [X3: set_nat,A: set_nat,B2: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ X3 @ A )
% 0.33/1.66 => ( ord_less_set_nat @ X3 @ ( sup_sup_set_nat @ A @ B2 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_311_less__supI1,axiom,
% 0.33/1.66 ! [X3: nat,A: nat,B2: nat] :
% 0.33/1.66 ( ( ord_less_nat @ X3 @ A )
% 0.33/1.66 => ( ord_less_nat @ X3 @ ( sup_sup_nat @ A @ B2 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_312_less__supI2,axiom,
% 0.33/1.66 ! [X3: nat > $o,B2: nat > $o,A: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ X3 @ B2 )
% 0.33/1.66 => ( ord_less_nat_o @ X3 @ ( sup_sup_nat_o @ A @ B2 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_313_less__supI2,axiom,
% 0.33/1.66 ! [X3: set_nat,B2: set_nat,A: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ X3 @ B2 )
% 0.33/1.66 => ( ord_less_set_nat @ X3 @ ( sup_sup_set_nat @ A @ B2 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_314_less__supI2,axiom,
% 0.33/1.66 ! [X3: nat,B2: nat,A: nat] :
% 0.33/1.66 ( ( ord_less_nat @ X3 @ B2 )
% 0.33/1.66 => ( ord_less_nat @ X3 @ ( sup_sup_nat @ A @ B2 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_315_sup_Ostrict__boundedE,axiom,
% 0.33/1.66 ! [B2: nat > $o,C: nat > $o,A: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ ( sup_sup_nat_o @ B2 @ C ) @ A )
% 0.33/1.66 => ~ ( ( ord_less_nat_o @ B2 @ A )
% 0.33/1.66 => ~ ( ord_less_nat_o @ C @ A ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_316_sup_Ostrict__boundedE,axiom,
% 0.33/1.66 ! [B2: set_nat,C: set_nat,A: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ ( sup_sup_set_nat @ B2 @ C ) @ A )
% 0.33/1.66 => ~ ( ( ord_less_set_nat @ B2 @ A )
% 0.33/1.66 => ~ ( ord_less_set_nat @ C @ A ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_317_sup_Ostrict__boundedE,axiom,
% 0.33/1.66 ! [B2: nat,C: nat,A: nat] :
% 0.33/1.66 ( ( ord_less_nat @ ( sup_sup_nat @ B2 @ C ) @ A )
% 0.33/1.66 => ~ ( ( ord_less_nat @ B2 @ A )
% 0.33/1.66 => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_318_sup_Ostrict__order__iff,axiom,
% 0.33/1.66 ( ord_less_nat_o
% 0.33/1.66 = ( ^ [B6: nat > $o,A3: nat > $o] :
% 0.33/1.66 ( ( A3
% 0.33/1.66 = ( sup_sup_nat_o @ A3 @ B6 ) )
% 0.33/1.66 & ( A3 != B6 ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_319_sup_Ostrict__order__iff,axiom,
% 0.33/1.66 ( ord_less_set_nat
% 0.33/1.66 = ( ^ [B6: set_nat,A3: set_nat] :
% 0.33/1.66 ( ( A3
% 0.33/1.66 = ( sup_sup_set_nat @ A3 @ B6 ) )
% 0.33/1.66 & ( A3 != B6 ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_320_sup_Ostrict__order__iff,axiom,
% 0.33/1.66 ( ord_less_nat
% 0.33/1.66 = ( ^ [B6: nat,A3: nat] :
% 0.33/1.66 ( ( A3
% 0.33/1.66 = ( sup_sup_nat @ A3 @ B6 ) )
% 0.33/1.66 & ( A3 != B6 ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_321_sup_Ostrict__coboundedI1,axiom,
% 0.33/1.66 ! [C: nat > $o,A: nat > $o,B2: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ C @ A )
% 0.33/1.66 => ( ord_less_nat_o @ C @ ( sup_sup_nat_o @ A @ B2 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_322_sup_Ostrict__coboundedI1,axiom,
% 0.33/1.66 ! [C: set_nat,A: set_nat,B2: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ C @ A )
% 0.33/1.66 => ( ord_less_set_nat @ C @ ( sup_sup_set_nat @ A @ B2 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_323_sup_Ostrict__coboundedI1,axiom,
% 0.33/1.66 ! [C: nat,A: nat,B2: nat] :
% 0.33/1.66 ( ( ord_less_nat @ C @ A )
% 0.33/1.66 => ( ord_less_nat @ C @ ( sup_sup_nat @ A @ B2 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_324_sup_Ostrict__coboundedI2,axiom,
% 0.33/1.66 ! [C: nat > $o,B2: nat > $o,A: nat > $o] :
% 0.33/1.66 ( ( ord_less_nat_o @ C @ B2 )
% 0.33/1.66 => ( ord_less_nat_o @ C @ ( sup_sup_nat_o @ A @ B2 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_325_sup_Ostrict__coboundedI2,axiom,
% 0.33/1.66 ! [C: set_nat,B2: set_nat,A: set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ C @ B2 )
% 0.33/1.66 => ( ord_less_set_nat @ C @ ( sup_sup_set_nat @ A @ B2 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_326_sup_Ostrict__coboundedI2,axiom,
% 0.33/1.66 ! [C: nat,B2: nat,A: nat] :
% 0.33/1.66 ( ( ord_less_nat @ C @ B2 )
% 0.33/1.66 => ( ord_less_nat @ C @ ( sup_sup_nat @ A @ B2 ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_327_Nitpick_OThe__psimp,axiom,
% 0.33/1.66 ! [P: nat > $o,X3: nat] :
% 0.33/1.66 ( ( P
% 0.33/1.66 = ( ^ [Y3: nat,Z: nat] : ( Y3 = Z )
% 0.33/1.66 @ X3 ) )
% 0.33/1.66 => ( ( the_nat @ P )
% 0.33/1.66 = X3 ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_328_theI__unique,axiom,
% 0.33/1.66 ! [P: nat > $o,X3: nat] :
% 0.33/1.66 ( ? [X7: nat] :
% 0.33/1.66 ( ( P @ X7 )
% 0.33/1.66 & ! [Y4: nat] :
% 0.33/1.66 ( ( P @ Y4 )
% 0.33/1.66 => ( Y4 = X7 ) ) )
% 0.33/1.66 => ( ( P @ X3 )
% 0.33/1.66 = ( X3
% 0.33/1.66 = ( the_nat @ P ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_329_sup__bot_Osemilattice__neutr__axioms,axiom,
% 0.33/1.66 semila1414375521_nat_o @ sup_sup_nat_o @ bot_bot_nat_o ).
% 0.33/1.66
% 0.33/1.66 thf(fact_330_sup__bot_Osemilattice__neutr__axioms,axiom,
% 0.33/1.66 semila1369944356et_nat @ sup_sup_set_nat @ bot_bot_set_nat ).
% 0.33/1.66
% 0.33/1.66 thf(fact_331_lexordp__eq__simps_I4_J,axiom,
% 0.33/1.66 ! [X3: set_nat,Xs: list_set_nat,Y: set_nat,Ys: list_set_nat] :
% 0.33/1.66 ( ( ord_le727790544et_nat @ ( cons_set_nat @ X3 @ Xs ) @ ( cons_set_nat @ Y @ Ys ) )
% 0.33/1.66 = ( ( ord_less_set_nat @ X3 @ Y )
% 0.33/1.66 | ( ~ ( ord_less_set_nat @ Y @ X3 )
% 0.33/1.66 & ( ord_le727790544et_nat @ Xs @ Ys ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_332_lexordp__eq__simps_I4_J,axiom,
% 0.33/1.66 ! [X3: nat > $o,Xs: list_nat_o,Y: nat > $o,Ys: list_nat_o] :
% 0.33/1.66 ( ( ord_lexordp_eq_nat_o @ ( cons_nat_o @ X3 @ Xs ) @ ( cons_nat_o @ Y @ Ys ) )
% 0.33/1.66 = ( ( ord_less_nat_o @ X3 @ Y )
% 0.33/1.66 | ( ~ ( ord_less_nat_o @ Y @ X3 )
% 0.33/1.66 & ( ord_lexordp_eq_nat_o @ Xs @ Ys ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_333_lexordp__eq__simps_I4_J,axiom,
% 0.33/1.66 ! [X3: nat,Xs: list_nat,Y: nat,Ys: list_nat] :
% 0.33/1.66 ( ( ord_lexordp_eq_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys ) )
% 0.33/1.66 = ( ( ord_less_nat @ X3 @ Y )
% 0.33/1.66 | ( ~ ( ord_less_nat @ Y @ X3 )
% 0.33/1.66 & ( ord_lexordp_eq_nat @ Xs @ Ys ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_334_lexordp__eq_OCons__eq,axiom,
% 0.33/1.66 ! [X3: set_nat,Y: set_nat,Xs: list_set_nat,Ys: list_set_nat] :
% 0.33/1.66 ( ~ ( ord_less_set_nat @ X3 @ Y )
% 0.33/1.66 => ( ~ ( ord_less_set_nat @ Y @ X3 )
% 0.33/1.66 => ( ( ord_le727790544et_nat @ Xs @ Ys )
% 0.33/1.66 => ( ord_le727790544et_nat @ ( cons_set_nat @ X3 @ Xs ) @ ( cons_set_nat @ Y @ Ys ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_335_lexordp__eq_OCons__eq,axiom,
% 0.33/1.66 ! [X3: nat > $o,Y: nat > $o,Xs: list_nat_o,Ys: list_nat_o] :
% 0.33/1.66 ( ~ ( ord_less_nat_o @ X3 @ Y )
% 0.33/1.66 => ( ~ ( ord_less_nat_o @ Y @ X3 )
% 0.33/1.66 => ( ( ord_lexordp_eq_nat_o @ Xs @ Ys )
% 0.33/1.66 => ( ord_lexordp_eq_nat_o @ ( cons_nat_o @ X3 @ Xs ) @ ( cons_nat_o @ Y @ Ys ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_336_lexordp__eq_OCons__eq,axiom,
% 0.33/1.66 ! [X3: nat,Y: nat,Xs: list_nat,Ys: list_nat] :
% 0.33/1.66 ( ~ ( ord_less_nat @ X3 @ Y )
% 0.33/1.66 => ( ~ ( ord_less_nat @ Y @ X3 )
% 0.33/1.66 => ( ( ord_lexordp_eq_nat @ Xs @ Ys )
% 0.33/1.66 => ( ord_lexordp_eq_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_337_lexordp__eq_OCons,axiom,
% 0.33/1.66 ! [X3: set_nat,Y: set_nat,Xs: list_set_nat,Ys: list_set_nat] :
% 0.33/1.66 ( ( ord_less_set_nat @ X3 @ Y )
% 0.33/1.66 => ( ord_le727790544et_nat @ ( cons_set_nat @ X3 @ Xs ) @ ( cons_set_nat @ Y @ Ys ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_338_lexordp__eq_OCons,axiom,
% 0.33/1.66 ! [X3: nat > $o,Y: nat > $o,Xs: list_nat_o,Ys: list_nat_o] :
% 0.33/1.66 ( ( ord_less_nat_o @ X3 @ Y )
% 0.33/1.66 => ( ord_lexordp_eq_nat_o @ ( cons_nat_o @ X3 @ Xs ) @ ( cons_nat_o @ Y @ Ys ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_339_lexordp__eq_OCons,axiom,
% 0.33/1.66 ! [X3: nat,Y: nat,Xs: list_nat,Ys: list_nat] :
% 0.33/1.66 ( ( ord_less_nat @ X3 @ Y )
% 0.33/1.66 => ( ord_lexordp_eq_nat @ ( cons_nat @ X3 @ Xs ) @ ( cons_nat @ Y @ Ys ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_340_lexordp__eq__antisym,axiom,
% 0.33/1.66 ! [Xs: list_nat,Ys: list_nat] :
% 0.33/1.66 ( ( ord_lexordp_eq_nat @ Xs @ Ys )
% 0.33/1.66 => ( ( ord_lexordp_eq_nat @ Ys @ Xs )
% 0.33/1.66 => ( Xs = Ys ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_341_lexordp__eq__linear,axiom,
% 0.33/1.66 ! [Xs: list_nat,Ys: list_nat] :
% 0.33/1.66 ( ( ord_lexordp_eq_nat @ Xs @ Ys )
% 0.33/1.66 | ( ord_lexordp_eq_nat @ Ys @ Xs ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_342_lexordp__eq__trans,axiom,
% 0.33/1.66 ! [Xs: list_nat,Ys: list_nat,Zs: list_nat] :
% 0.33/1.66 ( ( ord_lexordp_eq_nat @ Xs @ Ys )
% 0.33/1.66 => ( ( ord_lexordp_eq_nat @ Ys @ Zs )
% 0.33/1.66 => ( ord_lexordp_eq_nat @ Xs @ Zs ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_343_lexordp__eq__refl,axiom,
% 0.33/1.66 ! [Xs: list_nat] : ( ord_lexordp_eq_nat @ Xs @ Xs ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_344_lexordp__eq_Ocases,axiom,
% 0.33/1.66 ! [A1: list_set_nat,A22: list_set_nat] :
% 0.33/1.66 ( ( ord_le727790544et_nat @ A1 @ A22 )
% 0.33/1.66 => ( ( A1 != nil_set_nat )
% 0.33/1.66 => ( ! [X: set_nat] :
% 0.33/1.66 ( ? [Xs2: list_set_nat] :
% 0.33/1.66 ( A1
% 0.33/1.66 = ( cons_set_nat @ X @ Xs2 ) )
% 0.33/1.66 => ! [Y4: set_nat] :
% 0.33/1.66 ( ? [Ys2: list_set_nat] :
% 0.33/1.66 ( A22
% 0.33/1.66 = ( cons_set_nat @ Y4 @ Ys2 ) )
% 0.33/1.66 => ~ ( ord_less_set_nat @ X @ Y4 ) ) )
% 0.33/1.66 => ~ ! [X: set_nat,Y4: set_nat,Xs2: list_set_nat] :
% 0.33/1.66 ( ( A1
% 0.33/1.66 = ( cons_set_nat @ X @ Xs2 ) )
% 0.33/1.66 => ! [Ys2: list_set_nat] :
% 0.33/1.66 ( ( A22
% 0.33/1.66 = ( cons_set_nat @ Y4 @ Ys2 ) )
% 0.33/1.66 => ( ~ ( ord_less_set_nat @ X @ Y4 )
% 0.33/1.66 => ( ~ ( ord_less_set_nat @ Y4 @ X )
% 0.33/1.66 => ~ ( ord_le727790544et_nat @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_345_lexordp__eq_Ocases,axiom,
% 0.33/1.66 ! [A1: list_nat_o,A22: list_nat_o] :
% 0.33/1.66 ( ( ord_lexordp_eq_nat_o @ A1 @ A22 )
% 0.33/1.66 => ( ( A1 != nil_nat_o )
% 0.33/1.66 => ( ! [X: nat > $o] :
% 0.33/1.66 ( ? [Xs2: list_nat_o] :
% 0.33/1.66 ( A1
% 0.33/1.66 = ( cons_nat_o @ X @ Xs2 ) )
% 0.33/1.66 => ! [Y4: nat > $o] :
% 0.33/1.66 ( ? [Ys2: list_nat_o] :
% 0.33/1.66 ( A22
% 0.33/1.66 = ( cons_nat_o @ Y4 @ Ys2 ) )
% 0.33/1.66 => ~ ( ord_less_nat_o @ X @ Y4 ) ) )
% 0.33/1.66 => ~ ! [X: nat > $o,Y4: nat > $o,Xs2: list_nat_o] :
% 0.33/1.66 ( ( A1
% 0.33/1.66 = ( cons_nat_o @ X @ Xs2 ) )
% 0.33/1.66 => ! [Ys2: list_nat_o] :
% 0.33/1.66 ( ( A22
% 0.33/1.66 = ( cons_nat_o @ Y4 @ Ys2 ) )
% 0.33/1.66 => ( ~ ( ord_less_nat_o @ X @ Y4 )
% 0.33/1.66 => ( ~ ( ord_less_nat_o @ Y4 @ X )
% 0.33/1.66 => ~ ( ord_lexordp_eq_nat_o @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_346_lexordp__eq_Ocases,axiom,
% 0.33/1.66 ! [A1: list_nat,A22: list_nat] :
% 0.33/1.66 ( ( ord_lexordp_eq_nat @ A1 @ A22 )
% 0.33/1.66 => ( ( A1 != nil_nat )
% 0.33/1.66 => ( ! [X: nat] :
% 0.33/1.66 ( ? [Xs2: list_nat] :
% 0.33/1.66 ( A1
% 0.33/1.66 = ( cons_nat @ X @ Xs2 ) )
% 0.33/1.66 => ! [Y4: nat] :
% 0.33/1.66 ( ? [Ys2: list_nat] :
% 0.33/1.66 ( A22
% 0.33/1.66 = ( cons_nat @ Y4 @ Ys2 ) )
% 0.33/1.66 => ~ ( ord_less_nat @ X @ Y4 ) ) )
% 0.33/1.66 => ~ ! [X: nat,Y4: nat,Xs2: list_nat] :
% 0.33/1.66 ( ( A1
% 0.33/1.66 = ( cons_nat @ X @ Xs2 ) )
% 0.33/1.66 => ! [Ys2: list_nat] :
% 0.33/1.66 ( ( A22
% 0.33/1.66 = ( cons_nat @ Y4 @ Ys2 ) )
% 0.33/1.66 => ( ~ ( ord_less_nat @ X @ Y4 )
% 0.33/1.66 => ( ~ ( ord_less_nat @ Y4 @ X )
% 0.33/1.66 => ~ ( ord_lexordp_eq_nat @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_347_lexordp__eq_Osimps,axiom,
% 0.33/1.66 ( ord_le727790544et_nat
% 0.33/1.66 = ( ^ [A12: list_set_nat,A23: list_set_nat] :
% 0.33/1.66 ( ? [Ys3: list_set_nat] :
% 0.33/1.66 ( ( A12 = nil_set_nat )
% 0.33/1.66 & ( A23 = Ys3 ) )
% 0.33/1.66 | ? [X4: set_nat,Y6: set_nat,Xs3: list_set_nat,Ys3: list_set_nat] :
% 0.33/1.66 ( ( A12
% 0.33/1.66 = ( cons_set_nat @ X4 @ Xs3 ) )
% 0.33/1.66 & ( A23
% 0.33/1.66 = ( cons_set_nat @ Y6 @ Ys3 ) )
% 0.33/1.66 & ( ord_less_set_nat @ X4 @ Y6 ) )
% 0.33/1.66 | ? [X4: set_nat,Y6: set_nat,Xs3: list_set_nat,Ys3: list_set_nat] :
% 0.33/1.66 ( ( A12
% 0.33/1.66 = ( cons_set_nat @ X4 @ Xs3 ) )
% 0.33/1.66 & ( A23
% 0.33/1.66 = ( cons_set_nat @ Y6 @ Ys3 ) )
% 0.33/1.66 & ~ ( ord_less_set_nat @ X4 @ Y6 )
% 0.33/1.66 & ~ ( ord_less_set_nat @ Y6 @ X4 )
% 0.33/1.66 & ( ord_le727790544et_nat @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_348_lexordp__eq_Osimps,axiom,
% 0.33/1.66 ( ord_lexordp_eq_nat_o
% 0.33/1.66 = ( ^ [A12: list_nat_o,A23: list_nat_o] :
% 0.33/1.66 ( ? [Ys3: list_nat_o] :
% 0.33/1.66 ( ( A12 = nil_nat_o )
% 0.33/1.66 & ( A23 = Ys3 ) )
% 0.33/1.66 | ? [X4: nat > $o,Y6: nat > $o,Xs3: list_nat_o,Ys3: list_nat_o] :
% 0.33/1.66 ( ( A12
% 0.33/1.66 = ( cons_nat_o @ X4 @ Xs3 ) )
% 0.33/1.66 & ( A23
% 0.33/1.66 = ( cons_nat_o @ Y6 @ Ys3 ) )
% 0.33/1.66 & ( ord_less_nat_o @ X4 @ Y6 ) )
% 0.33/1.66 | ? [X4: nat > $o,Y6: nat > $o,Xs3: list_nat_o,Ys3: list_nat_o] :
% 0.33/1.66 ( ( A12
% 0.33/1.66 = ( cons_nat_o @ X4 @ Xs3 ) )
% 0.33/1.66 & ( A23
% 0.33/1.66 = ( cons_nat_o @ Y6 @ Ys3 ) )
% 0.33/1.66 & ~ ( ord_less_nat_o @ X4 @ Y6 )
% 0.33/1.66 & ~ ( ord_less_nat_o @ Y6 @ X4 )
% 0.33/1.66 & ( ord_lexordp_eq_nat_o @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_349_lexordp__eq_Osimps,axiom,
% 0.33/1.66 ( ord_lexordp_eq_nat
% 0.33/1.66 = ( ^ [A12: list_nat,A23: list_nat] :
% 0.33/1.66 ( ? [Ys3: list_nat] :
% 0.33/1.66 ( ( A12 = nil_nat )
% 0.33/1.66 & ( A23 = Ys3 ) )
% 0.33/1.66 | ? [X4: nat,Y6: nat,Xs3: list_nat,Ys3: list_nat] :
% 0.33/1.66 ( ( A12
% 0.33/1.66 = ( cons_nat @ X4 @ Xs3 ) )
% 0.33/1.66 & ( A23
% 0.33/1.66 = ( cons_nat @ Y6 @ Ys3 ) )
% 0.33/1.66 & ( ord_less_nat @ X4 @ Y6 ) )
% 0.33/1.66 | ? [X4: nat,Y6: nat,Xs3: list_nat,Ys3: list_nat] :
% 0.33/1.66 ( ( A12
% 0.33/1.66 = ( cons_nat @ X4 @ Xs3 ) )
% 0.33/1.66 & ( A23
% 0.33/1.66 = ( cons_nat @ Y6 @ Ys3 ) )
% 0.33/1.66 & ~ ( ord_less_nat @ X4 @ Y6 )
% 0.33/1.66 & ~ ( ord_less_nat @ Y6 @ X4 )
% 0.33/1.66 & ( ord_lexordp_eq_nat @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_350_app__subst__Nil,axiom,
% 0.33/1.66 ! [S: nat > type_Mirabelle_typ] :
% 0.33/1.66 ( ( type_M1944210753scheme @ S @ nil_Ty61485117scheme )
% 0.33/1.66 = nil_Ty61485117scheme ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_351_new__tv__Nil,axiom,
% 0.33/1.66 ! [N2: nat] : ( type_M2064939256scheme @ N2 @ nil_Ty61485117scheme ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_352_free__tv__list_Osimps_I1_J,axiom,
% 0.33/1.66 ( ( type_M141510067scheme @ nil_Ty61485117scheme )
% 0.33/1.66 = bot_bot_set_nat ) ).
% 0.33/1.66
% 0.33/1.66 thf(fact_353_lexordp__eq_Oinducts,axiom,
% 0.33/1.66 ! [X1: list_nat,X2: list_nat,P: list_nat > list_nat > $o] :
% 0.33/1.66 ( ( ord_lexordp_eq_nat @ X1 @ X2 )
% 0.33/1.66 => ( ! [X_1: list_nat] : ( P @ nil_nat @ X_1 )
% 0.33/1.66 => ( ! [X: nat,Y4: nat,Xs2: list_nat,Ys2: list_nat] :
% 0.33/1.66 ( ( ord_less_nat @ X @ Y4 )
% 0.33/1.66 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y4 @ Ys2 ) ) )
% 0.33/1.66 => ( ! [X: nat,Y4: nat,Xs2: list_nat,Ys2: list_nat] :
% 0.33/1.66 ( ~ ( ord_less_nat @ X @ Y4 )
% 0.33/1.66 => ( ~ ( ord_less_nat @ Y4 @ X )
% 0.33/1.66 => ( ( ord_lexordp_eq_nat @ Xs2 @ Ys2 )
% 0.33/1.66 => ( ( P @ Xs2 @ Ys2 )
% 0.33/1.66 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y4 @ Ys2 ) ) ) ) ) )
% 0.33/1.66 => ( P @ X1 @ X2 ) ) ) ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 0.33/1.66 ! [X3: nat,Y: nat] :
% 0.33/1.66 ( ( if_nat @ $false @ X3 @ Y )
% 0.33/1.66 = Y ) ).
% 0.33/1.66
% 0.33/1.66 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 0.33/1.66 ! [X3: nat,Y: nat] :
% 0.33/1.66 ( ( if_nat @ $true @ X3 @ Y )
% 0.33/1.66 = X3 ) ).
% 0.33/1.66
% 0.33/1.66 thf(help_If_3_1_If_001t__Type____Mirabelle____lczmhmumaa__Otyp_T,axiom,
% 0.33/1.66 ! [P: $o] :
% 0.33/1.66 ( ( P = $true )
% 0.33/1.66 | ( P = $false ) ) ).
% 0.33/1.66
% 0.33/1.66 thf(help_If_2_1_If_001t__Type____Mirabelle____lczmhmumaa__Otyp_T,axiom,
% 0.33/1.66 ! [X3: type_Mirabelle_typ,Y: type_Mirabelle_typ] :
% 0.33/1.66 ( ( if_Typ1169047309le_typ @ $false @ X3 @ Y )
% 0.33/1.66 = Y ) ).
% 0.33/1.66
% 0.33/1.66 thf(help_If_1_1_If_001t__Type____Mirabelle____lczmhmumaa__Otyp_T,axiom,
% 0.33/1.66 ! [X3: type_Mirabelle_typ,Y: type_Mirabelle_typ] :
% 0.33/1.66 ( ( if_Typ1169047309le_typ @ $true @ X3 @ Y )
% 0.33/1.66 = X3 ) ).
% 0.33/1.66
% 0.33/1.66 thf(conj_0,conjecture,
% 0.33/1.66 ( ( ( type_M1690910139scheme @ s1 @ ( type_M876316792e_FVar @ x ) )
% 0.33/1.66 != ( type_M1690910139scheme @ s2 @ ( type_M876316792e_FVar @ x ) ) )
% 0.33/1.66 | ~ ( member_nat @ n @ ( type_M1050318637scheme @ ( type_M876316792e_FVar @ x ) ) )
% 0.33/1.66 | ( ( s1 @ n )
% 0.33/1.66 = ( s2 @ n ) ) ) ).
% 0.33/1.66 ------------------------
% 0.33/1.69 % (4010)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_3895 for (2999ds/2Mi)
% 0.33/1.69 % (4009)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3895 for (2999ds/2Mi)
% 0.33/1.69 % (4012)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3895 for (2999ds/18Mi)
% 0.33/1.69 % (4009)Instruction limit reached!
% 0.33/1.69 % (4009)------------------------------
% 0.33/1.69 % (4009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.69 % (4009)Termination reason: Unknown
% 0.33/1.69 % (4009)Termination phase: shuffling
% 0.33/1.69
% 0.33/1.69 % (4009)Memory used [KB]: 1535
% 0.33/1.69 % (4009)Time elapsed: 0.002 s
% 0.33/1.69 % (4009)Instructions burned: 2 (million)
% 0.33/1.69 % (4010)Instruction limit reached!
% 0.33/1.69 % (4010)------------------------------
% 0.33/1.69 % (4010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.69 % (4009)------------------------------
% 0.33/1.69 % (4009)------------------------------
% 0.33/1.69 % (4010)Termination reason: Unknown
% 0.33/1.69 % (4010)Termination phase: shuffling
% 0.33/1.69
% 0.33/1.69 % (4010)Memory used [KB]: 1535
% 0.33/1.69 % (4010)Time elapsed: 0.003 s
% 0.33/1.69 % (4010)Instructions burned: 5 (million)
% 0.33/1.69 % (4010)------------------------------
% 0.33/1.69 % (4010)------------------------------
% 0.33/1.69 % (4006)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3895 for (2999ds/183Mi)
% 3.12/1.70 % (4012)Instruction limit reached!
% 3.12/1.70 % (4012)------------------------------
% 3.12/1.70 % (4012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.70 % (4012)Termination reason: Unknown
% 3.12/1.70 % (4012)Termination phase: shuffling
% 3.12/1.70
% 3.12/1.70 % (4012)Memory used [KB]: 1918
% 3.12/1.70 % (4012)Time elapsed: 0.007 s
% 3.12/1.70 % (4012)Instructions burned: 18 (million)
% 3.12/1.70 % (4012)------------------------------
% 3.12/1.70 % (4012)------------------------------
% 3.12/1.70 % (4008)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_3895 for (2999ds/27Mi)
% 3.12/1.70 % (4007)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_3895 for (2999ds/4Mi)
% 3.12/1.70 % (4011)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_3895 for (2999ds/275Mi)
% 3.12/1.70 % (4007)Instruction limit reached!
% 3.12/1.70 % (4007)------------------------------
% 3.12/1.70 % (4007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.70 % (4007)Termination reason: Unknown
% 3.12/1.70 % (4007)Termination phase: shuffling
% 3.12/1.70
% 3.12/1.70 % (4007)Memory used [KB]: 1535
% 3.12/1.70 % (4007)Time elapsed: 0.005 s
% 3.12/1.70 % (4007)Instructions burned: 5 (million)
% 3.12/1.70 % (4007)------------------------------
% 3.12/1.70 % (4007)------------------------------
% 3.12/1.70 % (4014)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_3895 for (2999ds/37Mi)
% 3.12/1.70 % (4013)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3895 for (2999ds/3Mi)
% 3.12/1.70 % (4013)Instruction limit reached!
% 3.12/1.70 % (4013)------------------------------
% 3.12/1.70 % (4013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.70 % (4013)Termination reason: Unknown
% 3.12/1.70 % (4013)Termination phase: shuffling
% 3.12/1.70
% 3.12/1.70 % (4013)Memory used [KB]: 1535
% 3.12/1.70 % (4013)Time elapsed: 0.003 s
% 3.12/1.70 % (4013)Instructions burned: 3 (million)
% 3.12/1.70 % (4013)------------------------------
% 3.12/1.70 % (4013)------------------------------
% 3.12/1.71 % (4015)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_3895 for (2999ds/15Mi)
% 3.12/1.71 % (4014)Instruction limit reached!
% 3.12/1.71 % (4014)------------------------------
% 3.12/1.71 % (4014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.71 % (4014)Termination reason: Unknown
% 3.12/1.71 % (4014)Termination phase: shuffling
% 3.12/1.71
% 3.12/1.71 % (4014)Memory used [KB]: 2302
% 3.12/1.71 % (4014)Time elapsed: 0.011 s
% 3.12/1.71 % (4014)Instructions burned: 37 (million)
% 3.12/1.71 % (4014)------------------------------
% 3.12/1.71 % (4014)------------------------------
% 3.12/1.71 % (4015)Instruction limit reached!
% 3.12/1.71 % (4015)------------------------------
% 3.12/1.71 % (4015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.71 % (4015)Termination reason: Unknown
% 3.12/1.71 % (4015)Termination phase: shuffling
% 3.12/1.71
% 3.12/1.71 % (4015)Memory used [KB]: 1791
% 3.12/1.71 % (4015)Time elapsed: 0.006 s
% 3.12/1.71 % (4015)Instructions burned: 15 (million)
% 3.12/1.71 % (4015)------------------------------
% 3.12/1.71 % (4015)------------------------------
% 3.12/1.71 % (4008)Instruction limit reached!
% 3.12/1.71 % (4008)------------------------------
% 3.12/1.71 % (4008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.71 % (4008)Termination reason: Unknown
% 3.12/1.71 % (4008)Termination phase: Property scanning
% 3.12/1.71
% 3.12/1.71 % (4008)Memory used [KB]: 2046
% 3.12/1.71 % (4008)Time elapsed: 0.018 s
% 3.12/1.71 % (4008)Instructions burned: 28 (million)
% 3.12/1.71 % (4008)------------------------------
% 3.12/1.71 % (4008)------------------------------
% 3.12/1.71 % (4017)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_3895 for (2999ds/1041Mi)
% 3.12/1.72 % (4016)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_3895 for (2999ds/3Mi)
% 3.12/1.72 % (4016)Instruction limit reached!
% 3.12/1.72 % (4016)------------------------------
% 3.12/1.72 % (4016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.72 % (4016)Termination reason: Unknown
% 3.12/1.72 % (4016)Termination phase: shuffling
% 3.12/1.72
% 3.12/1.72 % (4016)Memory used [KB]: 1535
% 3.12/1.72 % (4016)Time elapsed: 0.004 s
% 3.12/1.72 % (4016)Instructions burned: 3 (million)
% 3.12/1.72 % (4016)------------------------------
% 3.12/1.72 % (4016)------------------------------
% 3.12/1.72 % (4018)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3895 for (2999ds/7Mi)
% 3.12/1.72 % (4019)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3895 for (2999ds/16Mi)
% 3.12/1.72 % (4018)Instruction limit reached!
% 3.12/1.72 % (4018)------------------------------
% 3.12/1.72 % (4018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.72 % (4018)Termination reason: Unknown
% 3.12/1.72 % (4018)Termination phase: shuffling
% 3.12/1.72
% 3.12/1.72 % (4018)Memory used [KB]: 1663
% 3.12/1.72 % (4018)Time elapsed: 0.004 s
% 3.12/1.72 % (4018)Instructions burned: 10 (million)
% 3.12/1.72 % (4018)------------------------------
% 3.12/1.72 % (4018)------------------------------
% 3.12/1.73 % (4020)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_3895 for (2999ds/3Mi)
% 3.12/1.73 % (4019)Instruction limit reached!
% 3.12/1.73 % (4019)------------------------------
% 3.12/1.73 % (4019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.73 % (4019)Termination reason: Unknown
% 3.12/1.73 % (4019)Termination phase: shuffling
% 3.12/1.73
% 3.12/1.73 % (4019)Memory used [KB]: 1918
% 3.12/1.73 % (4019)Time elapsed: 0.006 s
% 3.12/1.73 % (4019)Instructions burned: 16 (million)
% 3.12/1.73 % (4019)------------------------------
% 3.12/1.73 % (4019)------------------------------
% 3.12/1.73 % (4020)Instruction limit reached!
% 3.12/1.73 % (4020)------------------------------
% 3.12/1.73 % (4020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.73 % (4020)Termination reason: Unknown
% 3.12/1.73 % (4020)Termination phase: shuffling
% 3.12/1.73
% 3.12/1.73 % (4020)Memory used [KB]: 1535
% 3.12/1.73 % (4020)Time elapsed: 0.003 s
% 3.12/1.73 % (4020)Instructions burned: 4 (million)
% 3.12/1.73 % (4020)------------------------------
% 3.12/1.73 % (4020)------------------------------
% 3.12/1.73 % (4022)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3895 for (2999ds/7Mi)
% 3.12/1.74 % (4023)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3895 for (2999ds/3Mi)
% 3.12/1.74 % (4022)Instruction limit reached!
% 3.12/1.74 % (4022)------------------------------
% 3.12/1.74 % (4022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.74 % (4022)Termination reason: Unknown
% 3.12/1.74 % (4022)Termination phase: shuffling
% 3.12/1.74
% 3.12/1.74 % (4022)Memory used [KB]: 1663
% 3.12/1.74 % (4022)Time elapsed: 0.004 s
% 3.12/1.74 % (4022)Instructions burned: 10 (million)
% 3.12/1.74 % (4022)------------------------------
% 3.12/1.74 % (4022)------------------------------
% 3.12/1.74 % (4023)Instruction limit reached!
% 3.12/1.74 % (4023)------------------------------
% 3.12/1.74 % (4023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.74 % (4024)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3895 for (2999ds/4Mi)
% 3.12/1.74 % (4023)Termination reason: Unknown
% 3.12/1.74 % (4023)Termination phase: shuffling
% 3.12/1.74
% 3.12/1.74 % (4023)Memory used [KB]: 1535
% 3.12/1.74 % (4023)Time elapsed: 0.002 s
% 3.12/1.74 % (4023)Instructions burned: 3 (million)
% 3.12/1.74 % (4023)------------------------------
% 3.12/1.74 % (4023)------------------------------
% 3.12/1.74 % (4024)Instruction limit reached!
% 3.12/1.74 % (4024)------------------------------
% 3.12/1.74 % (4024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.74 % (4024)Termination reason: Unknown
% 3.12/1.74 % (4024)Termination phase: shuffling
% 3.12/1.74
% 3.12/1.74 % (4024)Memory used [KB]: 1535
% 3.12/1.74 % (4024)Time elapsed: 0.003 s
% 3.12/1.74 % (4024)Instructions burned: 4 (million)
% 3.12/1.74 % (4024)------------------------------
% 3.12/1.74 % (4024)------------------------------
% 3.12/1.74 % (4021)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_3895 for (2999ds/3Mi)
% 3.12/1.74 % (4021)Instruction limit reached!
% 3.12/1.74 % (4021)------------------------------
% 3.12/1.74 % (4021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.74 % (4021)Termination reason: Unknown
% 3.12/1.74 % (4021)Termination phase: shuffling
% 3.12/1.74
% 3.12/1.74 % (4021)Memory used [KB]: 1535
% 3.12/1.74 % (4021)Time elapsed: 0.004 s
% 3.12/1.74 % (4021)Instructions burned: 3 (million)
% 3.12/1.74 % (4021)------------------------------
% 3.12/1.74 % (4021)------------------------------
% 3.12/1.75 % (4025)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3895 for (2999ds/18Mi)
% 3.12/1.75 % (4026)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3895 for (2999ds/710Mi)
% 3.12/1.75 % (4006)Instruction limit reached!
% 3.12/1.75 % (4006)------------------------------
% 3.12/1.75 % (4006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.75 % (4006)Termination reason: Unknown
% 3.12/1.75 % (4006)Termination phase: Saturation
% 3.12/1.75
% 3.12/1.75 % (4006)Memory used [KB]: 7291
% 3.12/1.75 % (4006)Time elapsed: 0.057 s
% 3.12/1.75 % (4006)Instructions burned: 186 (million)
% 3.12/1.75 % (4006)------------------------------
% 3.12/1.75 % (4006)------------------------------
% 3.12/1.75 % (4027)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3895 for (2999ds/6Mi)
% 3.12/1.75 % (4027)Instruction limit reached!
% 3.12/1.75 % (4027)------------------------------
% 3.12/1.75 % (4027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.75 % (4027)Termination reason: Unknown
% 3.12/1.75 % (4027)Termination phase: shuffling
% 3.12/1.75
% 3.12/1.75 % (4027)Memory used [KB]: 1535
% 3.12/1.75 % (4027)Time elapsed: 0.004 s
% 3.12/1.75 % (4027)Instructions burned: 6 (million)
% 3.12/1.75 % (4027)------------------------------
% 3.12/1.75 % (4027)------------------------------
% 3.12/1.75 % (4025)Instruction limit reached!
% 3.12/1.75 % (4025)------------------------------
% 3.12/1.75 % (4025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.75 % (4025)Termination reason: Unknown
% 3.12/1.75 % (4025)Termination phase: shuffling
% 3.12/1.75
% 3.12/1.75 % (4025)Memory used [KB]: 1918
% 3.12/1.75 % (4025)Time elapsed: 0.007 s
% 3.12/1.75 % (4025)Instructions burned: 19 (million)
% 3.12/1.75 % (4025)------------------------------
% 3.12/1.75 % (4025)------------------------------
% 3.12/1.76 % (4028)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_3895 for (2999ds/902Mi)
% 3.12/1.76 % (4029)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_3895 for (2999ds/21Mi)
% 3.12/1.76 % (4030)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3895 for (2999ds/5Mi)
% 3.12/1.76 % (4031)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_3895 for (2999ds/6Mi)
% 3.12/1.76 % (4030)Instruction limit reached!
% 3.12/1.76 % (4030)------------------------------
% 3.12/1.76 % (4030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.76 % (4030)Termination reason: Unknown
% 3.12/1.76 % (4030)Termination phase: shuffling
% 3.12/1.76
% 3.12/1.76 % (4030)Memory used [KB]: 1663
% 3.12/1.76 % (4030)Time elapsed: 0.004 s
% 3.12/1.76 % (4030)Instructions burned: 7 (million)
% 3.12/1.76 % (4030)------------------------------
% 3.12/1.76 % (4030)------------------------------
% 3.12/1.76 % (4031)Instruction limit reached!
% 3.12/1.76 % (4031)------------------------------
% 3.12/1.76 % (4031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.76 % (4031)Termination reason: Unknown
% 3.12/1.76 % (4031)Termination phase: shuffling
% 3.12/1.76
% 3.12/1.76 % (4031)Memory used [KB]: 1663
% 3.12/1.76 % (4031)Time elapsed: 0.003 s
% 3.12/1.76 % (4031)Instructions burned: 7 (million)
% 3.12/1.76 % (4031)------------------------------
% 3.12/1.76 % (4031)------------------------------
% 3.12/1.77 % (4029)Instruction limit reached!
% 3.12/1.77 % (4029)------------------------------
% 3.12/1.77 % (4029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.77 % (4029)Termination reason: Unknown
% 3.12/1.77 % (4029)Termination phase: shuffling
% 3.12/1.77
% 3.12/1.77 % (4029)Memory used [KB]: 1918
% 3.12/1.77 % (4029)Time elapsed: 0.009 s
% 3.12/1.77 % (4029)Instructions burned: 21 (million)
% 3.12/1.77 % (4029)------------------------------
% 3.12/1.77 % (4029)------------------------------
% 3.12/1.77 % (4033)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_3895 for (2999ds/779Mi)
% 3.12/1.77 % (4032)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3895 for (2999ds/377Mi)
% 3.12/1.78 % (4034)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_3895 for (2999ds/19Mi)
% 3.12/1.78 % (4034)Instruction limit reached!
% 3.12/1.78 % (4034)------------------------------
% 3.12/1.78 % (4034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.78 % (4034)Termination reason: Unknown
% 3.12/1.78 % (4034)Termination phase: shuffling
% 3.12/1.78
% 3.12/1.78 % (4034)Memory used [KB]: 1918
% 3.12/1.78 % (4034)Time elapsed: 0.008 s
% 3.12/1.78 % (4034)Instructions burned: 21 (million)
% 3.12/1.78 % (4034)------------------------------
% 3.12/1.78 % (4034)------------------------------
% 3.12/1.79 % (4035)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3895 for (2998ds/879Mi)
% 3.12/1.80 % (4011)Instruction limit reached!
% 3.12/1.80 % (4011)------------------------------
% 3.12/1.80 % (4011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.80 % (4011)Termination reason: Unknown
% 3.12/1.80 % (4011)Termination phase: Saturation
% 3.12/1.80
% 3.12/1.80 % (4011)Memory used [KB]: 7291
% 3.12/1.80 % (4011)Time elapsed: 0.102 s
% 3.12/1.80 % (4011)Instructions burned: 277 (million)
% 3.12/1.80 % (4011)------------------------------
% 3.12/1.80 % (4011)------------------------------
% 3.12/1.81 % (4036)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_3895 for (2998ds/17Mi)
% 3.12/1.81 % (4036)Instruction limit reached!
% 3.12/1.81 % (4036)------------------------------
% 3.12/1.81 % (4036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.81 % (4036)Termination reason: Unknown
% 3.12/1.81 % (4036)Termination phase: shuffling
% 3.12/1.81
% 3.12/1.81 % (4036)Memory used [KB]: 1918
% 3.12/1.81 % (4036)Time elapsed: 0.007 s
% 3.12/1.81 % (4036)Instructions burned: 19 (million)
% 3.12/1.81 % (4036)------------------------------
% 3.12/1.81 % (4036)------------------------------
% 3.12/1.82 % (4037)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3895 for (2998ds/3Mi)
% 3.12/1.82 % (4037)Instruction limit reached!
% 3.12/1.82 % (4037)------------------------------
% 3.12/1.82 % (4037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.82 % (4037)Termination reason: Unknown
% 3.12/1.82 % (4037)Termination phase: shuffling
% 3.12/1.82
% 3.12/1.82 % (4037)Memory used [KB]: 1535
% 3.12/1.82 % (4037)Time elapsed: 0.002 s
% 3.12/1.82 % (4037)Instructions burned: 3 (million)
% 3.12/1.82 % (4037)------------------------------
% 3.12/1.82 % (4037)------------------------------
% 3.12/1.83 % (4038)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_3895 for (2998ds/30Mi)
% 3.12/1.84 % (4038)Instruction limit reached!
% 3.12/1.84 % (4038)------------------------------
% 3.12/1.84 % (4038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.84 % (4038)Termination reason: Unknown
% 3.12/1.84 % (4038)Termination phase: Property scanning
% 3.12/1.84
% 3.12/1.84 % (4038)Memory used [KB]: 2046
% 3.12/1.84 % (4038)Time elapsed: 0.011 s
% 3.12/1.84 % (4038)Instructions burned: 33 (million)
% 3.12/1.84 % (4038)------------------------------
% 3.12/1.84 % (4038)------------------------------
% 3.12/1.85 % (4039)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_3895 for (2998ds/127Mi)
% 3.12/1.88 % (4032)Instruction limit reached!
% 3.12/1.88 % (4032)------------------------------
% 3.12/1.88 % (4032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.88 % (4032)Termination reason: Unknown
% 3.12/1.88 % (4032)Termination phase: Saturation
% 3.12/1.88
% 3.12/1.88 % (4032)Memory used [KB]: 7931
% 3.12/1.88 % (4032)Time elapsed: 0.112 s
% 3.12/1.88 % (4032)Instructions burned: 379 (million)
% 3.12/1.88 % (4032)------------------------------
% 3.12/1.88 % (4032)------------------------------
% 3.12/1.89 % (4039)Instruction limit reached!
% 3.12/1.89 % (4039)------------------------------
% 3.12/1.89 % (4039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.89 % (4039)Termination reason: Unknown
% 3.12/1.89 % (4039)Termination phase: Property scanning
% 3.12/1.89
% 3.12/1.89 % (4039)Memory used [KB]: 2814
% 3.12/1.89 % (4039)Time elapsed: 0.036 s
% 3.12/1.89 % (4039)Instructions burned: 131 (million)
% 3.12/1.89 % (4039)------------------------------
% 3.12/1.89 % (4039)------------------------------
% 3.12/1.89 % (4040)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_3895 for (2997ds/100Mi)
% 3.12/1.90 % (4041)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_3895 for (2997ds/3Mi)
% 3.12/1.90 % (4041)Instruction limit reached!
% 3.12/1.90 % (4041)------------------------------
% 3.12/1.90 % (4041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.90 % (4041)Termination reason: Unknown
% 3.12/1.90 % (4041)Termination phase: shuffling
% 3.12/1.90
% 3.12/1.90 % (4041)Memory used [KB]: 1535
% 3.12/1.90 % (4041)Time elapsed: 0.002 s
% 3.12/1.90 % (4041)Instructions burned: 3 (million)
% 3.12/1.90 % (4041)------------------------------
% 3.12/1.90 % (4041)------------------------------
% 3.12/1.91 % (4042)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_3895 for (2997ds/20Mi)
% 3.12/1.92 % (4042)Instruction limit reached!
% 3.12/1.92 % (4042)------------------------------
% 3.12/1.92 % (4042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.92 % (4042)Termination reason: Unknown
% 3.12/1.92 % (4042)Termination phase: shuffling
% 3.12/1.92
% 3.12/1.92 % (4042)Memory used [KB]: 1918
% 3.12/1.92 % (4042)Time elapsed: 0.008 s
% 3.12/1.92 % (4042)Instructions burned: 22 (million)
% 3.12/1.92 % (4042)------------------------------
% 3.12/1.92 % (4042)------------------------------
% 3.12/1.92 % (4040)Instruction limit reached!
% 3.12/1.92 % (4040)------------------------------
% 3.12/1.92 % (4040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.92 % (4040)Termination reason: Unknown
% 3.12/1.92 % (4040)Termination phase: Property scanning
% 3.12/1.92
% 3.12/1.92 % (4040)Memory used [KB]: 2686
% 3.12/1.92 % (4040)Time elapsed: 0.031 s
% 3.12/1.92 % (4040)Instructions burned: 102 (million)
% 3.12/1.92 % (4040)------------------------------
% 3.12/1.92 % (4040)------------------------------
% 3.12/1.92 % (4043)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_3895 for (2997ds/86Mi)
% 3.12/1.93 % (4044)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_3895 for (2997ds/107Mi)
% 3.12/1.95 % (4043)Instruction limit reached!
% 3.12/1.95 % (4043)------------------------------
% 3.12/1.95 % (4043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.95 % (4043)Termination reason: Unknown
% 3.12/1.95 % (4043)Termination phase: Function definition elimination
% 3.12/1.95
% 3.12/1.95 % (4043)Memory used [KB]: 2686
% 3.12/1.95 % (4043)Time elapsed: 0.025 s
% 3.12/1.95 % (4043)Instructions burned: 87 (million)
% 3.12/1.95 % (4043)------------------------------
% 3.12/1.95 % (4043)------------------------------
% 3.12/1.96 % (4045)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_3895 for (2997ds/39Mi)
% 3.12/1.96 % (4026)Instruction limit reached!
% 3.12/1.96 % (4026)------------------------------
% 3.12/1.96 % (4026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.96 % (4026)Termination reason: Unknown
% 3.12/1.96 % (4026)Termination phase: Saturation
% 3.12/1.96
% 3.12/1.96 % (4026)Memory used [KB]: 8187
% 3.12/1.96 % (4026)Time elapsed: 0.217 s
% 3.12/1.96 % (4026)Instructions burned: 712 (million)
% 3.12/1.96 % (4026)------------------------------
% 3.12/1.96 % (4026)------------------------------
% 3.12/1.97 % (4044)Instruction limit reached!
% 3.12/1.97 % (4044)------------------------------
% 3.12/1.97 % (4044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.97 % (4044)Termination reason: Unknown
% 3.12/1.97 % (4044)Termination phase: Property scanning
% 3.12/1.97
% 3.12/1.97 % (4044)Memory used [KB]: 2558
% 3.12/1.97 % (4044)Time elapsed: 0.034 s
% 3.12/1.97 % (4044)Instructions burned: 109 (million)
% 3.12/1.97 % (4044)------------------------------
% 3.12/1.97 % (4044)------------------------------
% 3.12/1.97 % (4045)Instruction limit reached!
% 3.12/1.97 % (4045)------------------------------
% 3.12/1.97 % (4045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.97 % (4045)Termination reason: Unknown
% 3.12/1.97 % (4045)Termination phase: shuffling
% 3.12/1.97
% 3.12/1.97 % (4045)Memory used [KB]: 2302
% 3.12/1.97 % (4045)Time elapsed: 0.012 s
% 3.12/1.97 % (4045)Instructions burned: 41 (million)
% 3.12/1.97 % (4045)------------------------------
% 3.12/1.97 % (4045)------------------------------
% 3.12/1.97 % (4017)First to succeed.
% 3.12/1.97 % (4046)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_3895 for (2997ds/448Mi)
% 3.12/1.98 % (4017)Refutation found. Thanks to Tanya!
% 3.12/1.98 % SZS status Theorem for DTF2THF_3895
% 3.12/1.98 % SZS output start Proof for DTF2THF_3895
% 3.12/1.98 thf(type_def_5, type, nat: $tType).
% 3.12/1.98 thf(type_def_7, type, type_Mirabelle_typ: $tType).
% 3.12/1.98 thf(type_def_8, type, set_nat: $tType).
% 3.12/1.98 thf(type_def_9, type, list_nat_o: $tType).
% 3.12/1.98 thf(type_def_10, type, list_n396811828le_typ: $tType).
% 3.12/1.98 thf(type_def_11, type, list_l865305402le_typ: $tType).
% 3.12/1.98 thf(type_def_12, type, list_l1334080099scheme: $tType).
% 3.12/1.98 thf(type_def_13, type, list_l1704431731scheme: $tType).
% 3.12/1.98 thf(type_def_14, type, list_T1103309005le_typ: $tType).
% 3.12/1.98 thf(type_def_15, type, list_l1790670291le_typ: $tType).
% 3.12/1.98 thf(type_def_16, type, list_T247403987scheme: $tType).
% 3.12/1.98 thf(type_def_17, type, list_nat: $tType).
% 3.12/1.98 thf(type_def_18, type, list_set_nat: $tType).
% 3.12/1.98 thf(type_def_19, type, type_M1694694083scheme: $tType).
% 3.12/1.98 thf(func_def_0, type, list_l1704431731scheme: $tType).
% 3.12/1.98 thf(func_def_1, type, list_l865305402le_typ: $tType).
% 3.12/1.98 thf(func_def_2, type, list_l1334080099scheme: $tType).
% 3.12/1.98 thf(func_def_3, type, list_n396811828le_typ: $tType).
% 3.12/1.98 thf(func_def_4, type, list_l1790670291le_typ: $tType).
% 3.12/1.98 thf(func_def_5, type, list_T247403987scheme: $tType).
% 3.12/1.98 thf(func_def_6, type, list_T1103309005le_typ: $tType).
% 3.12/1.98 thf(func_def_7, type, type_M1694694083scheme: $tType).
% 3.12/1.98 thf(func_def_8, type, list_set_nat: $tType).
% 3.12/1.98 thf(func_def_9, type, list_nat_o: $tType).
% 3.12/1.98 thf(func_def_10, type, type_Mirabelle_typ: $tType).
% 3.12/1.98 thf(func_def_11, type, list_nat: $tType).
% 3.12/1.98 thf(func_def_12, type, set_nat: $tType).
% 3.12/1.98 thf(func_def_13, type, nat: $tType).
% 3.12/1.98 thf(func_def_14, type, the_nat: (nat > $o) > nat).
% 3.12/1.98 thf(func_def_15, type, if_nat: $o > nat > nat > nat).
% 3.12/1.98 thf(func_def_16, type, if_Typ1169047309le_typ: $o > type_Mirabelle_typ > type_Mirabelle_typ > type_Mirabelle_typ).
% 3.12/1.98 thf(func_def_17, type, semila1414375521_nat_o: ((nat > $o) > (nat > $o) > nat > $o) > (nat > $o) > $o).
% 3.12/1.98 thf(func_def_18, type, semila1369944356et_nat: (set_nat > set_nat > set_nat) > set_nat > $o).
% 3.12/1.98 thf(func_def_19, type, sup_sup_nat_o: (nat > $o) > (nat > $o) > nat > $o).
% 3.12/1.98 thf(func_def_20, type, sup_sup_nat: nat > nat > nat).
% 3.12/1.98 thf(func_def_21, type, sup_sup_set_nat: set_nat > set_nat > set_nat).
% 3.12/1.98 thf(func_def_22, type, cons_nat_o: (nat > $o) > list_nat_o > list_nat_o).
% 3.12/1.98 thf(func_def_23, type, cons_n499085924le_typ: (nat > type_Mirabelle_typ) > list_n396811828le_typ > list_n396811828le_typ).
% 3.12/1.98 thf(func_def_24, type, cons_l1800589546le_typ: list_n396811828le_typ > list_l865305402le_typ > list_l865305402le_typ).
% 3.12/1.98 thf(func_def_25, type, cons_l531914285scheme: list_l1334080099scheme > list_l1704431731scheme > list_l1704431731scheme).
% 3.12/1.98 thf(func_def_26, type, cons_l392684675le_typ: list_T1103309005le_typ > list_l1790670291le_typ > list_l1790670291le_typ).
% 3.12/1.98 thf(func_def_27, type, cons_l1910959773scheme: list_T247403987scheme > list_l1334080099scheme > list_l1334080099scheme).
% 3.12/1.98 thf(func_def_28, type, cons_nat: nat > list_nat > list_nat).
% 3.12/1.98 thf(func_def_29, type, cons_set_nat: set_nat > list_set_nat > list_set_nat).
% 3.12/1.98 thf(func_def_30, type, cons_T363929085le_typ: type_Mirabelle_typ > list_T1103309005le_typ > list_T1103309005le_typ).
% 3.12/1.98 thf(func_def_31, type, cons_T633159821scheme: type_M1694694083scheme > list_T247403987scheme > list_T247403987scheme).
% 3.12/1.98 thf(func_def_32, type, nil_nat_o: list_nat_o).
% 3.12/1.98 thf(func_def_33, type, nil_nat: list_nat).
% 3.12/1.98 thf(func_def_34, type, nil_set_nat: list_set_nat).
% 3.12/1.98 thf(func_def_35, type, nil_Ty61485117scheme: list_T247403987scheme).
% 3.12/1.98 thf(func_def_36, type, ord_lexordp_eq_nat_o: list_nat_o > list_nat_o > $o).
% 3.12/1.98 thf(func_def_37, type, ord_lexordp_eq_nat: list_nat > list_nat > $o).
% 3.12/1.98 thf(func_def_38, type, ord_le727790544et_nat: list_set_nat > list_set_nat > $o).
% 3.12/1.98 thf(func_def_39, type, bot_bot_nat_o: nat > $o).
% 3.12/1.98 thf(func_def_41, type, bot_bot_nat: nat).
% 3.12/1.98 thf(func_def_42, type, bot_bot_set_nat: set_nat).
% 3.12/1.98 thf(func_def_43, type, ord_less_nat_o: (nat > $o) > (nat > $o) > $o).
% 3.12/1.98 thf(func_def_44, type, ord_less_nat: nat > nat > $o).
% 3.12/1.98 thf(func_def_45, type, ord_less_set_nat: set_nat > set_nat > $o).
% 3.12/1.98 thf(func_def_46, type, collect_nat: (nat > $o) > set_nat).
% 3.12/1.98 thf(func_def_47, type, insert_nat: nat > set_nat > set_nat).
% 3.12/1.98 thf(func_def_48, type, is_empty_nat: set_nat > $o).
% 3.12/1.98 thf(func_def_49, type, is_singleton_nat: set_nat > $o).
% 3.12/1.98 thf(func_def_50, type, the_elem_nat: set_nat > nat).
% 3.12/1.98 thf(func_def_51, type, type_Mirabelle_cod: (nat > type_Mirabelle_typ) > set_nat).
% 3.12/1.98 thf(func_def_52, type, type_Mirabelle_dom: (nat > type_Mirabelle_typ) > set_nat).
% 3.12/1.98 thf(func_def_53, type, type_M405566558_subst: nat > type_Mirabelle_typ).
% 3.12/1.98 thf(func_def_54, type, type_M1006385707scheme: type_Mirabelle_typ > type_M1694694083scheme).
% 3.12/1.98 thf(func_def_55, type, type_M1734147655le_typ: nat > (nat > type_Mirabelle_typ) > $o).
% 3.12/1.98 thf(func_def_56, type, type_M244876119le_typ: nat > list_n396811828le_typ > $o).
% 3.12/1.98 thf(func_def_57, type, type_M2086816231le_typ: nat > list_l865305402le_typ > $o).
% 3.12/1.98 thf(func_def_58, type, type_M1172169604scheme: nat > list_l1704431731scheme > $o).
% 3.12/1.98 thf(func_def_59, type, type_M1826376056le_typ: nat > list_l1790670291le_typ > $o).
% 3.12/1.98 thf(func_def_60, type, type_M1377662078scheme: nat > list_l1334080099scheme > $o).
% 3.12/1.98 thf(func_def_61, type, type_M263553000le_typ: nat > list_T1103309005le_typ > $o).
% 3.12/1.98 thf(func_def_62, type, type_M2064939256scheme: nat > list_T247403987scheme > $o).
% 3.12/1.98 thf(func_def_63, type, type_M1211611096le_typ: nat > type_Mirabelle_typ > $o).
% 3.12/1.98 thf(func_def_64, type, type_M1963061490scheme: nat > type_M1694694083scheme > $o).
% 3.12/1.98 thf(func_def_65, type, type_M1898948661at_nat: nat > nat).
% 3.12/1.98 thf(func_def_66, type, type_Mirabelle_Fun: type_Mirabelle_typ > type_Mirabelle_typ > type_Mirabelle_typ).
% 3.12/1.98 thf(func_def_67, type, type_Mirabelle_TVar: nat > type_Mirabelle_typ).
% 3.12/1.98 thf(func_def_68, type, type_M1743451154le_typ: type_Mirabelle_typ > type_Mirabelle_typ).
% 3.12/1.98 thf(func_def_69, type, type_M2048935292e_BVar: nat > type_M1694694083scheme).
% 3.12/1.98 thf(func_def_70, type, type_M876316792e_FVar: nat > type_M1694694083scheme).
% 3.12/1.98 thf(func_def_71, type, type_M155660035e_SFun: type_M1694694083scheme > type_M1694694083scheme > type_M1694694083scheme).
% 3.12/1.98 thf(func_def_72, type, type_M1158474302le_typ: (nat > type_Mirabelle_typ) > (nat > type_Mirabelle_typ) > nat > type_Mirabelle_typ).
% 3.12/1.98 thf(func_def_73, type, type_M737052622le_typ: (nat > type_Mirabelle_typ) > list_n396811828le_typ > list_n396811828le_typ).
% 3.12/1.98 thf(func_def_74, type, type_M1385924301scheme: (nat > type_Mirabelle_typ) > list_l1704431731scheme > list_l1704431731scheme).
% 3.12/1.98 thf(func_def_75, type, type_M1913464047le_typ: (nat > type_Mirabelle_typ) > list_l1790670291le_typ > list_l1790670291le_typ).
% 3.12/1.98 thf(func_def_76, type, type_M1061687367scheme: (nat > type_Mirabelle_typ) > list_l1334080099scheme > list_l1334080099scheme).
% 3.12/1.98 thf(func_def_77, type, type_M1440203487le_typ: (nat > type_Mirabelle_typ) > list_T1103309005le_typ > list_T1103309005le_typ).
% 3.12/1.98 thf(func_def_78, type, type_M1944210753scheme: (nat > type_Mirabelle_typ) > list_T247403987scheme > list_T247403987scheme).
% 3.12/1.98 thf(func_def_79, type, type_M784671311le_typ: (nat > type_Mirabelle_typ) > type_Mirabelle_typ > type_Mirabelle_typ).
% 3.12/1.98 thf(func_def_80, type, type_M1690910139scheme: (nat > type_Mirabelle_typ) > type_M1694694083scheme > type_M1694694083scheme).
% 3.12/1.98 thf(func_def_81, type, type_M772783356le_typ: (nat > type_Mirabelle_typ) > set_nat).
% 3.12/1.98 thf(func_def_82, type, type_M513401740le_typ: list_n396811828le_typ > set_nat).
% 3.12/1.98 thf(func_def_83, type, type_M1496178953scheme: list_l1334080099scheme > set_nat).
% 3.12/1.98 thf(func_def_84, type, type_M1539052445le_typ: list_T1103309005le_typ > set_nat).
% 3.12/1.98 thf(func_def_85, type, type_M961603331scheme: list_T247403987scheme > set_nat).
% 3.12/1.98 thf(func_def_86, type, type_M801073677le_typ: type_Mirabelle_typ > set_nat).
% 3.12/1.98 thf(func_def_87, type, type_M326705277scheme: type_M1694694083scheme > set_nat).
% 3.12/1.98 thf(func_def_88, type, type_M1715972684le_typ: (nat > type_Mirabelle_typ) > set_nat).
% 3.12/1.98 thf(func_def_89, type, type_M1691543772le_typ: list_n396811828le_typ > set_nat).
% 3.12/1.98 thf(func_def_90, type, type_M906078444le_typ: list_l865305402le_typ > set_nat).
% 3.12/1.98 thf(func_def_91, type, type_M1926053183scheme: list_l1704431731scheme > set_nat).
% 3.12/1.98 thf(func_def_92, type, type_M1418941437le_typ: list_l1790670291le_typ > set_nat).
% 3.12/1.98 thf(func_def_93, type, type_M1958029241scheme: list_l1334080099scheme > set_nat).
% 3.12/1.98 thf(func_def_94, type, type_M510873837le_typ: list_T1103309005le_typ > set_nat).
% 3.12/1.98 thf(func_def_95, type, type_M141510067scheme: list_T247403987scheme > set_nat).
% 3.12/1.98 thf(func_def_96, type, type_M49385309le_typ: type_Mirabelle_typ > set_nat).
% 3.12/1.98 thf(func_def_97, type, type_M1050318637scheme: type_M1694694083scheme > set_nat).
% 3.12/1.98 thf(func_def_98, type, member_nat: nat > set_nat > $o).
% 3.12/1.98 thf(func_def_99, type, s1: nat > type_Mirabelle_typ).
% 3.12/1.98 thf(func_def_100, type, s2: nat > type_Mirabelle_typ).
% 3.12/1.98 thf(func_def_101, type, n: nat).
% 3.12/1.98 thf(func_def_102, type, x: nat).
% 3.12/1.98 thf(func_def_123, type, ph1: !>[X0: $tType]:(X0)).
% 3.12/1.98 thf(func_def_124, type, sK2: nat > nat).
% 3.12/1.98 thf(func_def_125, type, sK3: nat).
% 3.12/1.98 thf(func_def_126, type, sK4: nat > nat).
% 3.12/1.98 thf(func_def_127, type, sK5: nat > nat).
% 3.12/1.98 thf(func_def_128, type, sK6: nat).
% 3.12/1.98 thf(func_def_129, type, sK7: nat).
% 3.12/1.98 thf(func_def_130, type, sK8: nat > nat).
% 3.12/1.98 thf(f3967,plain,(
% 3.12/1.98 $false),
% 3.12/1.98 inference(subsumption_resolution,[status(thm)],[f3964,f3284])).
% 3.12/1.98 thf(f3284,plain,(
% 3.12/1.98 ((s1 @ n) != (s2 @ n))),
% 3.12/1.98 inference(equality_proxy_clausification,[status(thm)],[f3269])).
% 3.12/1.98 thf(f3269,plain,(
% 3.12/1.98 ($false = ((s1 @ n) = (s2 @ n)))),
% 3.12/1.98 inference(trivial_inequality_removal,[status(thm)],[f3268])).
% 3.12/1.98 thf(f3268,plain,(
% 3.12/1.98 ($false = ((s1 @ n) = (s2 @ n))) | ($false = $true)),
% 3.12/1.98 inference(boolean_simplification,[status(thm)],[f3267])).
% 3.12/1.98 thf(f3267,plain,(
% 3.12/1.98 ($false = ((s1 @ n) = (s2 @ n))) | ($true = (~ $true))),
% 3.12/1.98 inference(boolean_simplification,[status(thm)],[f3266])).
% 3.12/1.98 thf(f3266,plain,(
% 3.12/1.98 ($true = (~ ($true | (~ (member_nat @ n @ (type_M49385309le_typ @ (type_M405566558_subst @ x))))))) | ($false = ((s1 @ n) = (s2 @ n)))),
% 3.12/1.98 inference(boolean_simplification,[status(thm)],[f3245])).
% 3.12/1.98 thf(f3245,plain,(
% 3.12/1.98 ($false = ((s1 @ n) = (s2 @ n))) | ($true = (~ (((~ ((type_M1006385707scheme @ (s1 @ x)) = (type_M1006385707scheme @ (s2 @ x)))) | $true) | (~ (member_nat @ n @ (type_M49385309le_typ @ (type_M405566558_subst @ x)))))))),
% 3.12/1.98 inference(superposition,[status(thm)],[f2534,f2294])).
% 3.12/1.98 thf(f2294,plain,(
% 3.12/1.98 ( ! [X1 : $o] : (($true = X1) | ($false = X1)) )),
% 3.12/1.98 inference(equality_proxy_clausification,[status(thm)],[f2141])).
% 3.12/1.98 thf(f2141,plain,(
% 3.12/1.98 ( ! [X1 : $o] : (($true = ($false = X1)) | ($true = X1)) )),
% 3.12/1.98 inference(equality_proxy_clausification,[status(thm)],[f2091])).
% 3.12/1.98 thf(f2091,plain,(
% 3.12/1.98 ( ! [X1 : $o] : (($true = ($true = X1)) | ($true = ($false = X1))) )),
% 3.12/1.98 inference(binary_proxy_clausification,[status(thm)],[f2090])).
% 3.12/1.98 thf(f2090,plain,(
% 3.12/1.98 ( ! [X1 : $o] : (((($false = X1) | ($true = X1)) = $true)) )),
% 3.12/1.98 inference(beta_eta_normalization,[status(thm)],[f2089])).
% 3.12/1.98 thf(f2089,plain,(
% 3.12/1.98 ( ! [X1 : $o] : ((((^[Y0 : $o]: (($false = Y0) | ($true = Y0))) @ X1) = $true)) )),
% 3.12/1.98 inference(pi_clausification,[status(thm)],[f1273])).
% 3.12/1.98 thf(f1273,plain,(
% 3.12/1.98 ($true = (!! @ $o @ (^[Y0 : $o]: (($false = Y0) | ($true = Y0)))))),
% 3.12/1.98 inference(cnf_transformation,[status(thm)],[f781])).
% 3.12/1.98 thf(f781,plain,(
% 3.12/1.98 ($true = (!! @ $o @ (^[Y0 : $o]: (($false = Y0) | ($true = Y0)))))),
% 3.12/1.98 inference(fool_elimination,[status(thm)],[f780])).
% 3.12/1.98 thf(f780,plain,(
% 3.12/1.98 ! [X0 : $o] : (($true = X0) | ($false = X0))),
% 3.12/1.98 inference(rectify,[status(thm)],[f357])).
% 3.12/1.98 thf(f357,axiom,(
% 3.12/1.98 ! [X33 : $o] : (($true = X33) | ($false = X33))),
% 3.12/1.98 file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',help_If_3_1_If_001t__Type____Mirabelle____lczmhmumaa__Otyp_T)).
% 3.12/1.98 thf(f2534,plain,(
% 3.12/1.98 ((~ (((~ ((type_M1006385707scheme @ (s1 @ x)) = (type_M1006385707scheme @ (s2 @ x)))) | ((s1 @ n) = (s2 @ n))) | (~ (member_nat @ n @ (type_M49385309le_typ @ (type_M405566558_subst @ x)))))) = $true)),
% 3.12/1.98 inference(forward_demodulation,[status(thm)],[f2531,f2529])).
% 3.12/1.98 thf(f2529,plain,(
% 3.12/1.98 ( ! [X2 : nat > type_Mirabelle_typ,X1 : nat] : (((type_M1690910139scheme @ X2 @ (type_M876316792e_FVar @ X1)) = (type_M1006385707scheme @ (X2 @ X1)))) )),
% 3.12/1.98 inference(equality_proxy_clausification,[status(thm)],[f2527])).
% 3.12/1.98 thf(f2527,plain,(
% 3.12/1.98 ( ! [X2 : nat > type_Mirabelle_typ,X1 : nat] : ((((type_M1006385707scheme @ (X2 @ X1)) = (type_M1690910139scheme @ X2 @ (type_M876316792e_FVar @ X1))) = $true)) )),
% 3.12/1.98 inference(beta_eta_normalization,[status(thm)],[f2526])).
% 3.12/1.98 thf(f2526,plain,(
% 3.12/1.98 ( ! [X2 : nat > type_Mirabelle_typ,X1 : nat] : ((((^[Y0 : nat > type_Mirabelle_typ]: ((type_M1006385707scheme @ (Y0 @ X1)) = (type_M1690910139scheme @ Y0 @ (type_M876316792e_FVar @ X1)))) @ X2) = $true)) )),
% 3.12/1.98 inference(pi_clausification,[status(thm)],[f2522])).
% 3.12/1.98 thf(f2522,plain,(
% 3.12/1.98 ( ! [X1 : nat] : (((!! @ (nat > type_Mirabelle_typ) @ (^[Y0 : nat > type_Mirabelle_typ]: ((type_M1006385707scheme @ (Y0 @ X1)) = (type_M1690910139scheme @ Y0 @ (type_M876316792e_FVar @ X1))))) = $true)) )),
% 3.12/1.98 inference(beta_eta_normalization,[status(thm)],[f2521])).
% 3.12/1.98 thf(f2521,plain,(
% 3.12/1.98 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: (!! @ (nat > type_Mirabelle_typ) @ (^[Y1 : nat > type_Mirabelle_typ]: ((type_M1006385707scheme @ (Y1 @ Y0)) = (type_M1690910139scheme @ Y1 @ (type_M876316792e_FVar @ Y0)))))) @ X1))) )),
% 3.12/1.98 inference(pi_clausification,[status(thm)],[f1373])).
% 3.12/1.98 thf(f1373,plain,(
% 3.12/1.98 ((!! @ nat @ (^[Y0 : nat]: (!! @ (nat > type_Mirabelle_typ) @ (^[Y1 : nat > type_Mirabelle_typ]: ((type_M1006385707scheme @ (Y1 @ Y0)) = (type_M1690910139scheme @ Y1 @ (type_M876316792e_FVar @ Y0))))))) = $true)),
% 3.12/1.98 inference(cnf_transformation,[status(thm)],[f1066])).
% 3.12/1.98 thf(f1066,plain,(
% 3.12/1.98 ((!! @ nat @ (^[Y0 : nat]: (!! @ (nat > type_Mirabelle_typ) @ (^[Y1 : nat > type_Mirabelle_typ]: ((type_M1006385707scheme @ (Y1 @ Y0)) = (type_M1690910139scheme @ Y1 @ (type_M876316792e_FVar @ Y0))))))) = $true)),
% 3.12/1.98 inference(fool_elimination,[status(thm)],[f1065])).
% 3.12/1.98 thf(f1065,plain,(
% 3.12/1.98 ! [X0 : nat > type_Mirabelle_typ,X1 : nat] : ((type_M1006385707scheme @ (X0 @ X1)) = (type_M1690910139scheme @ X0 @ (type_M876316792e_FVar @ X1)))),
% 3.12/1.98 inference(rectify,[status(thm)],[f4])).
% 3.12/1.98 thf(f4,axiom,(
% 3.12/1.98 ! [X6 : nat > type_Mirabelle_typ,X9 : nat] : ((type_M1690910139scheme @ X6 @ (type_M876316792e_FVar @ X9)) = (type_M1006385707scheme @ (X6 @ X9)))),
% 3.12/1.98 file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_3_app__subst__type__scheme_Osimps_I1_J)).
% 3.12/1.98 thf(f2531,plain,(
% 3.12/1.98 ((~ (((~ ((type_M1006385707scheme @ (s1 @ x)) = (type_M1690910139scheme @ s2 @ (type_M876316792e_FVar @ x)))) | ((s1 @ n) = (s2 @ n))) | (~ (member_nat @ n @ (type_M49385309le_typ @ (type_M405566558_subst @ x)))))) = $true)),
% 3.12/1.98 inference(backward_demodulation,[status(thm)],[f2069,f2529])).
% 3.12/1.98 thf(f2069,plain,(
% 3.12/1.98 ($true = (~ (((~ ((type_M1690910139scheme @ s1 @ (type_M876316792e_FVar @ x)) = (type_M1690910139scheme @ s2 @ (type_M876316792e_FVar @ x)))) | ((s1 @ n) = (s2 @ n))) | (~ (member_nat @ n @ (type_M49385309le_typ @ (type_M405566558_subst @ x)))))))),
% 3.12/1.98 inference(backward_demodulation,[status(thm)],[f1375,f2068])).
% 3.12/1.98 thf(f2068,plain,(
% 3.12/1.98 ( ! [X0 : nat] : (((type_M1050318637scheme @ (type_M876316792e_FVar @ X0)) = (type_M49385309le_typ @ (type_M405566558_subst @ X0)))) )),
% 3.12/1.98 inference(superposition,[status(thm)],[f2060,f2065])).
% 3.12/1.98 thf(f2065,plain,(
% 3.12/1.98 ( ! [X1 : nat] : (((type_M876316792e_FVar @ X1) = (type_M1006385707scheme @ (type_M405566558_subst @ X1)))) )),
% 3.12/1.98 inference(equality_proxy_clausification,[status(thm)],[f2064])).
% 3.12/1.98 thf(f2064,plain,(
% 3.12/1.98 ( ! [X1 : nat] : (($true = ((type_M876316792e_FVar @ X1) = (type_M1006385707scheme @ (type_M405566558_subst @ X1))))) )),
% 3.12/1.98 inference(beta_eta_normalization,[status(thm)],[f2063])).
% 3.12/1.98 thf(f2063,plain,(
% 3.12/1.98 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: ((type_M876316792e_FVar @ Y0) = (type_M1006385707scheme @ (type_M405566558_subst @ Y0)))) @ X1))) )),
% 3.12/1.98 inference(pi_clausification,[status(thm)],[f1470])).
% 3.12/1.98 thf(f1470,plain,(
% 3.12/1.98 ((!! @ nat @ (^[Y0 : nat]: ((type_M876316792e_FVar @ Y0) = (type_M1006385707scheme @ (type_M405566558_subst @ Y0))))) = $true)),
% 3.12/1.98 inference(definition_unfolding,[status(thm)],[f1101,f1324])).
% 3.12/1.98 thf(f1324,plain,(
% 3.12/1.98 (type_Mirabelle_TVar = type_M405566558_subst)),
% 3.12/1.98 inference(cnf_transformation,[status(thm)],[f1055])).
% 3.12/1.98 thf(f1055,plain,(
% 3.12/1.98 (type_Mirabelle_TVar = type_M405566558_subst)),
% 3.12/1.98 inference(fool_elimination,[status(thm)],[f228])).
% 3.12/1.98 thf(f228,axiom,(
% 3.12/1.98 (type_Mirabelle_TVar = type_M405566558_subst)),
% 3.12/1.98 file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_227_id__subst__def)).
% 3.12/1.98 thf(f1101,plain,(
% 3.12/1.98 ((!! @ nat @ (^[Y0 : nat]: ((type_M876316792e_FVar @ Y0) = (type_M1006385707scheme @ (type_Mirabelle_TVar @ Y0))))) = $true)),
% 3.12/1.98 inference(cnf_transformation,[status(thm)],[f1017])).
% 3.12/1.98 thf(f1017,plain,(
% 3.12/1.98 ((!! @ nat @ (^[Y0 : nat]: ((type_M876316792e_FVar @ Y0) = (type_M1006385707scheme @ (type_Mirabelle_TVar @ Y0))))) = $true)),
% 3.12/1.98 inference(fool_elimination,[status(thm)],[f1016])).
% 3.12/1.98 thf(f1016,plain,(
% 3.12/1.98 ! [X0 : nat] : ((type_M876316792e_FVar @ X0) = (type_M1006385707scheme @ (type_Mirabelle_TVar @ X0)))),
% 3.12/1.98 inference(rectify,[status(thm)],[f220])).
% 3.12/1.98 thf(f220,axiom,(
% 3.12/1.98 ! [X9 : nat] : ((type_M876316792e_FVar @ X9) = (type_M1006385707scheme @ (type_Mirabelle_TVar @ X9)))),
% 3.12/1.98 file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_219_mk__scheme_Osimps_I1_J)).
% 3.12/1.98 thf(f2060,plain,(
% 3.12/1.98 ( ! [X1 : type_Mirabelle_typ] : (((type_M1050318637scheme @ (type_M1006385707scheme @ X1)) = (type_M49385309le_typ @ X1))) )),
% 3.12/1.98 inference(equality_proxy_clausification,[status(thm)],[f2059])).
% 3.12/1.98 thf(f2059,plain,(
% 3.12/1.98 ( ! [X1 : type_Mirabelle_typ] : ((((type_M49385309le_typ @ X1) = (type_M1050318637scheme @ (type_M1006385707scheme @ X1))) = $true)) )),
% 3.12/1.98 inference(beta_eta_normalization,[status(thm)],[f2058])).
% 3.12/1.98 thf(f2058,plain,(
% 3.12/1.98 ( ! [X1 : type_Mirabelle_typ] : (($true = ((^[Y0 : type_Mirabelle_typ]: ((type_M49385309le_typ @ Y0) = (type_M1050318637scheme @ (type_M1006385707scheme @ Y0)))) @ X1))) )),
% 3.12/1.98 inference(pi_clausification,[status(thm)],[f1166])).
% 3.12/1.98 thf(f1166,plain,(
% 3.12/1.98 ((!! @ type_Mirabelle_typ @ (^[Y0 : type_Mirabelle_typ]: ((type_M49385309le_typ @ Y0) = (type_M1050318637scheme @ (type_M1006385707scheme @ Y0))))) = $true)),
% 3.12/1.98 inference(cnf_transformation,[status(thm)],[f918])).
% 3.12/1.98 thf(f918,plain,(
% 3.12/1.98 ((!! @ type_Mirabelle_typ @ (^[Y0 : type_Mirabelle_typ]: ((type_M49385309le_typ @ Y0) = (type_M1050318637scheme @ (type_M1006385707scheme @ Y0))))) = $true)),
% 3.12/1.98 inference(fool_elimination,[status(thm)],[f917])).
% 3.12/1.98 thf(f917,plain,(
% 3.12/1.98 ! [X0 : type_Mirabelle_typ] : ((type_M49385309le_typ @ X0) = (type_M1050318637scheme @ (type_M1006385707scheme @ X0)))),
% 3.12/1.98 inference(rectify,[status(thm)],[f15])).
% 3.12/1.98 thf(f15,axiom,(
% 3.12/1.98 ! [X17 : type_Mirabelle_typ] : ((type_M1050318637scheme @ (type_M1006385707scheme @ X17)) = (type_M49385309le_typ @ X17))),
% 3.12/1.98 file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_14_free__tv__mk__scheme)).
% 3.12/1.98 thf(f1375,plain,(
% 3.12/1.98 ($true = (~ (((~ ((type_M1690910139scheme @ s1 @ (type_M876316792e_FVar @ x)) = (type_M1690910139scheme @ s2 @ (type_M876316792e_FVar @ x)))) | ((s1 @ n) = (s2 @ n))) | (~ (member_nat @ n @ (type_M1050318637scheme @ (type_M876316792e_FVar @ x)))))))),
% 3.12/1.98 inference(cnf_transformation,[status(thm)],[f982])).
% 3.12/1.98 thf(f982,plain,(
% 3.12/1.98 ($true = (~ (((~ ((type_M1690910139scheme @ s1 @ (type_M876316792e_FVar @ x)) = (type_M1690910139scheme @ s2 @ (type_M876316792e_FVar @ x)))) | ((s1 @ n) = (s2 @ n))) | (~ (member_nat @ n @ (type_M1050318637scheme @ (type_M876316792e_FVar @ x)))))))),
% 3.12/1.98 inference(fool_elimination,[status(thm)],[f981])).
% 3.12/1.98 thf(f981,plain,(
% 3.12/1.98 ~(~(member_nat @ n @ (type_M1050318637scheme @ (type_M876316792e_FVar @ x))) | ((s1 @ n) = (s2 @ n)) | ((type_M1690910139scheme @ s1 @ (type_M876316792e_FVar @ x)) != (type_M1690910139scheme @ s2 @ (type_M876316792e_FVar @ x))))),
% 3.12/1.98 inference(rectify,[status(thm)],[f361])).
% 3.12/1.98 thf(f361,negated_conjecture,(
% 3.12/1.98 ~(~(member_nat @ n @ (type_M1050318637scheme @ (type_M876316792e_FVar @ x))) | ((s1 @ n) = (s2 @ n)) | ((type_M1690910139scheme @ s1 @ (type_M876316792e_FVar @ x)) != (type_M1690910139scheme @ s2 @ (type_M876316792e_FVar @ x))))),
% 3.12/1.98 inference(negated_conjecture,[status(cth)],[f360])).
% 3.12/1.98 thf(f360,conjecture,(
% 3.12/1.98 ~(member_nat @ n @ (type_M1050318637scheme @ (type_M876316792e_FVar @ x))) | ((s1 @ n) = (s2 @ n)) | ((type_M1690910139scheme @ s1 @ (type_M876316792e_FVar @ x)) != (type_M1690910139scheme @ s2 @ (type_M876316792e_FVar @ x)))),
% 3.12/1.98 file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',conj_0)).
% 3.12/1.98 thf(f3964,plain,(
% 3.12/1.98 ((s1 @ n) = (s2 @ n))),
% 3.12/1.98 inference(backward_demodulation,[status(thm)],[f3821,f3941])).
% 3.12/1.98 thf(f3941,plain,(
% 3.12/1.98 (x = n)),
% 3.12/1.98 inference(equality_proxy_clausification,[status(thm)],[f3930])).
% 3.12/1.98 thf(f3930,plain,(
% 3.12/1.98 ((x = n) = $true)),
% 3.12/1.98 inference(superposition,[status(thm)],[f3299,f3896])).
% 3.12/1.98 thf(f3896,plain,(
% 3.12/1.98 ( ! [X0 : nat,X1 : nat] : (((member_nat @ X1 @ (type_M49385309le_typ @ (type_M405566558_subst @ X0))) = (X0 = X1))) )),
% 3.12/1.98 inference(superposition,[status(thm)],[f2317,f3866])).
% 3.12/1.98 thf(f3866,plain,(
% 3.12/1.98 ( ! [X0 : nat] : (((type_M49385309le_typ @ (type_M405566558_subst @ X0)) = (collect_nat @ (= @ X0)))) )),
% 3.12/1.98 inference(equality_proxy_clausification,[status(thm)],[f3548])).
% 3.12/1.98 thf(f3548,plain,(
% 3.12/1.98 ( ! [X0 : nat] : ((((type_M49385309le_typ @ (type_M405566558_subst @ X0)) = (collect_nat @ (= @ X0))) = $true)) )),
% 3.12/1.98 inference(forward_demodulation,[status(thm)],[f3547,f2082])).
% 3.12/1.98 thf(f2082,plain,(
% 3.12/1.98 ( ! [X1 : set_nat] : (((collect_nat @ (^[Y0 : nat]: (member_nat @ Y0 @ X1))) = X1)) )),
% 3.12/1.98 inference(equality_proxy_clausification,[status(thm)],[f2081])).
% 3.12/1.98 thf(f2081,plain,(
% 3.12/1.98 ( ! [X1 : set_nat] : (((X1 = (collect_nat @ (^[Y0 : nat]: (member_nat @ Y0 @ X1)))) = $true)) )),
% 3.12/1.98 inference(beta_eta_normalization,[status(thm)],[f2080])).
% 3.12/1.98 thf(f2080,plain,(
% 3.12/1.98 ( ! [X1 : set_nat] : ((((^[Y0 : set_nat]: (Y0 = (collect_nat @ (^[Y1 : nat]: (member_nat @ Y1 @ Y0))))) @ X1) = $true)) )),
% 3.12/1.98 inference(pi_clausification,[status(thm)],[f1370])).
% 3.12/1.98 thf(f1370,plain,(
% 3.12/1.98 ($true = (!! @ set_nat @ (^[Y0 : set_nat]: (Y0 = (collect_nat @ (^[Y1 : nat]: (member_nat @ Y1 @ Y0)))))))),
% 3.12/1.98 inference(cnf_transformation,[status(thm)],[f366])).
% 3.12/1.98 thf(f366,plain,(
% 3.12/1.98 ($true = (!! @ set_nat @ (^[Y0 : set_nat]: (Y0 = (collect_nat @ (^[Y1 : nat]: (member_nat @ Y1 @ Y0)))))))),
% 3.12/1.98 inference(fool_elimination,[status(thm)],[f365])).
% 3.12/1.98 thf(f365,plain,(
% 3.12/1.98 ! [X0 : set_nat] : (X0 = (collect_nat @ (^[X1 : nat] : (member_nat @ X1 @ X0))))),
% 3.12/1.98 inference(rectify,[status(thm)],[f60])).
% 3.12/1.98 thf(f60,axiom,(
% 3.12/1.98 ! [X46 : set_nat] : (X46 = (collect_nat @ (^[X41 : nat] : (member_nat @ X41 @ X46))))),
% 3.12/1.98 file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_59_Collect__mem__eq)).
% 3.12/1.98 thf(f3547,plain,(
% 3.12/1.98 ( ! [X0 : nat] : ((((type_M49385309le_typ @ (type_M405566558_subst @ X0)) = (collect_nat @ (^[Y0 : nat]: (member_nat @ Y0 @ (collect_nat @ (= @ X0)))))) = $true)) )),
% 3.12/1.98 inference(forward_demodulation,[status(thm)],[f3546,f2282])).
% 3.12/1.98 thf(f2282,plain,(
% 3.12/1.98 ( ! [X1 : nat > $o] : (((sup_sup_nat_o @ X1 @ (^[Y0 : nat]: (bot_bot_o))) = X1)) )),
% 3.12/1.98 inference(equality_proxy_clausification,[status(thm)],[f2280])).
% 3.12/1.98 thf(f2280,plain,(
% 3.12/1.98 ( ! [X1 : nat > $o] : ((((sup_sup_nat_o @ X1 @ (^[Y0 : nat]: (bot_bot_o))) = X1) = $true)) )),
% 3.12/1.98 inference(beta_eta_normalization,[status(thm)],[f2279])).
% 3.12/1.98 thf(f2279,plain,(
% 3.12/1.98 ( ! [X1 : nat > $o] : ((((^[Y0 : nat > $o]: ((sup_sup_nat_o @ Y0 @ (^[Y1 : nat]: (bot_bot_o))) = Y0)) @ X1) = $true)) )),
% 3.12/1.98 inference(pi_clausification,[status(thm)],[f1616])).
% 3.12/1.98 thf(f1616,plain,(
% 3.12/1.98 ($true = (!! @ (nat > $o) @ (^[Y0 : nat > $o]: ((sup_sup_nat_o @ Y0 @ (^[Y1 : nat]: (bot_bot_o))) = Y0))))),
% 3.12/1.98 inference(definition_unfolding,[status(thm)],[f1296,f1284])).
% 3.12/1.98 thf(f1284,plain,(
% 3.12/1.98 (bot_bot_nat_o = (^[Y0 : nat]: (bot_bot_o)))),
% 3.12/1.98 inference(cnf_transformation,[status(thm)],[f573])).
% 3.12/1.98 thf(f573,plain,(
% 3.12/1.98 (bot_bot_nat_o = (^[Y0 : nat]: (bot_bot_o)))),
% 3.12/1.98 inference(fool_elimination,[status(thm)],[f572])).
% 3.12/1.98 thf(f572,plain,(
% 3.12/1.98 ((^[X0 : nat] : (bot_bot_o)) = bot_bot_nat_o)),
% 3.12/1.98 inference(rectify,[status(thm)],[f219])).
% 3.12/1.98 thf(f219,axiom,(
% 3.12/1.98 ((^[X41 : nat] : (bot_bot_o)) = bot_bot_nat_o)),
% 3.12/1.98 file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_218_bot__fun__def)).
% 3.12/1.98 thf(f1296,plain,(
% 3.12/1.98 ($true = (!! @ (nat > $o) @ (^[Y0 : nat > $o]: ((sup_sup_nat_o @ Y0 @ bot_bot_nat_o) = Y0))))),
% 3.12/1.98 inference(cnf_transformation,[status(thm)],[f960])).
% 3.12/1.98 thf(f960,plain,(
% 3.12/1.98 ($true = (!! @ (nat > $o) @ (^[Y0 : nat > $o]: ((sup_sup_nat_o @ Y0 @ bot_bot_nat_o) = Y0))))),
% 3.12/1.98 inference(fool_elimination,[status(thm)],[f959])).
% 3.12/1.98 thf(f959,plain,(
% 3.12/1.98 ! [X0 : nat > $o] : ((sup_sup_nat_o @ X0 @ bot_bot_nat_o) = X0)),
% 3.12/1.98 inference(rectify,[status(thm)],[f294])).
% 3.12/1.98 thf(f294,axiom,(
% 3.12/1.98 ! [X15 : nat > $o] : ((sup_sup_nat_o @ X15 @ bot_bot_nat_o) = X15)),
% 3.12/1.98 file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_293_sup__bot__right)).
% 3.12/1.98 thf(f3546,plain,(
% 3.12/1.98 ( ! [X0 : nat] : ((((type_M49385309le_typ @ (type_M405566558_subst @ X0)) = (collect_nat @ (sup_sup_nat_o @ (^[Y0 : nat]: (member_nat @ Y0 @ (collect_nat @ (= @ X0)))) @ (^[Y0 : nat]: (bot_bot_o))))) = $true)) )),
% 3.12/1.98 inference(forward_demodulation,[status(thm)],[f3545,f1712])).
% 3.12/1.98 thf(f1712,plain,(
% 3.12/1.98 ((^[Y0 : nat]: (member_nat @ Y0 @ (type_M141510067scheme @ nil_Ty61485117scheme))) = (^[Y0 : nat]: (bot_bot_o)))),
% 3.12/1.98 inference(definition_unfolding,[status(thm)],[f1420,f1284,f1124])).
% 3.12/1.98 thf(f1124,plain,(
% 3.12/1.98 (bot_bot_set_nat = (type_M141510067scheme @ nil_Ty61485117scheme))),
% 3.12/1.98 inference(cnf_transformation,[status(thm)],[f745])).
% 3.12/1.98 thf(f745,plain,(
% 3.12/1.98 (bot_bot_set_nat = (type_M141510067scheme @ nil_Ty61485117scheme))),
% 3.12/1.98 inference(fool_elimination,[status(thm)],[f353])).
% 3.12/1.98 thf(f353,axiom,(
% 3.12/1.98 (bot_bot_set_nat = (type_M141510067scheme @ nil_Ty61485117scheme))),
% 3.12/1.98 file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_352_free__tv__list_Osimps_I1_J)).
% 3.12/1.98 thf(f1420,plain,(
% 3.12/1.98 (bot_bot_nat_o = (^[Y0 : nat]: (member_nat @ Y0 @ bot_bot_set_nat)))),
% 3.12/1.98 inference(cnf_transformation,[status(thm)],[f698])).
% 3.12/1.98 thf(f698,plain,(
% 3.12/1.98 (bot_bot_nat_o = (^[Y0 : nat]: (member_nat @ Y0 @ bot_bot_set_nat)))),
% 3.12/1.98 inference(fool_elimination,[status(thm)],[f697])).
% 3.12/1.98 thf(f697,plain,(
% 3.12/1.98 (bot_bot_nat_o = (^[X0 : nat] : (member_nat @ X0 @ bot_bot_set_nat)))),
% 3.12/1.98 inference(rectify,[status(thm)],[f251])).
% 3.12/1.98 thf(f251,axiom,(
% 3.12/1.98 (bot_bot_nat_o = (^[X41 : nat] : (member_nat @ X41 @ bot_bot_set_nat)))),
% 3.12/1.98 file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_250_bot__empty__eq)).
% 3.12/1.98 thf(f3545,plain,(
% 3.12/1.98 ( ! [X0 : nat] : ((((type_M49385309le_typ @ (type_M405566558_subst @ X0)) = (collect_nat @ (sup_sup_nat_o @ (^[Y0 : nat]: (member_nat @ Y0 @ (collect_nat @ (= @ X0)))) @ (^[Y0 : nat]: (member_nat @ Y0 @ (type_M141510067scheme @ nil_Ty61485117scheme)))))) = $true)) )),
% 3.12/1.98 inference(forward_demodulation,[status(thm)],[f3544,f2068])).
% 3.12/1.98 thf(f3544,plain,(
% 3.12/1.98 ( ! [X0 : nat] : (($true = ((type_M1050318637scheme @ (type_M876316792e_FVar @ X0)) = (collect_nat @ (sup_sup_nat_o @ (^[Y0 : nat]: (member_nat @ Y0 @ (collect_nat @ (= @ X0)))) @ (^[Y0 : nat]: (member_nat @ Y0 @ (type_M141510067scheme @ nil_Ty61485117scheme)))))))) )),
% 3.12/1.98 inference(boolean_simplification,[status(thm)],[f3543])).
% 3.12/1.98 thf(f3543,plain,(
% 3.12/1.98 ( ! [X0 : nat] : (($true = ($true => ((type_M1050318637scheme @ (type_M876316792e_FVar @ X0)) = (collect_nat @ (sup_sup_nat_o @ (^[Y0 : nat]: (member_nat @ Y0 @ (collect_nat @ (= @ X0)))) @ (^[Y0 : nat]: (member_nat @ Y0 @ (type_M141510067scheme @ nil_Ty61485117scheme))))))))) )),
% 3.12/1.98 inference(beta_eta_normalization,[status(thm)],[f3541])).
% 3.12/1.98 thf(f3541,plain,(
% 3.12/1.98 ( ! [X0 : nat] : (($true = ($true => ((^[Y0 : nat]: ((type_M1050318637scheme @ (type_M876316792e_FVar @ Y0)) = (collect_nat @ (sup_sup_nat_o @ (^[Y1 : nat]: (member_nat @ Y1 @ (collect_nat @ (= @ Y0)))) @ (^[Y1 : nat]: (member_nat @ Y1 @ (type_M141510067scheme @ nil_Ty61485117scheme))))))) @ X0)))) )),
% 3.12/1.98 inference(superposition,[status(thm)],[f2618,f1779])).
% 3.12/1.98 thf(f1779,plain,(
% 3.12/1.98 ((!! @ nat @ (^[Y0 : nat]: ((type_M1050318637scheme @ (type_M876316792e_FVar @ Y0)) = (collect_nat @ (sup_sup_nat_o @ (^[Y1 : nat]: (member_nat @ Y1 @ (collect_nat @ (= @ Y0)))) @ (^[Y1 : nat]: (member_nat @ Y1 @ (type_M141510067scheme @ nil_Ty61485117scheme)))))))) = $true)),
% 3.12/1.98 inference(beta_eta_normalization,[status(thm)],[f1557])).
% 3.12/1.98 thf(f1557,plain,(
% 3.12/1.98 ($true = (!! @ nat @ (^[Y0 : nat]: ((type_M1050318637scheme @ (type_M876316792e_FVar @ Y0)) = ((^[Y1 : nat]: ((^[Y2 : set_nat]: ((^[Y3 : set_nat]: (collect_nat @ (sup_sup_nat_o @ (^[Y4 : nat]: (member_nat @ Y4 @ Y2)) @ (^[Y4 : nat]: (member_nat @ Y4 @ Y3))))))) @ (collect_nat @ (^[Y2 : nat]: (Y1 = Y2))))) @ Y0 @ (type_M141510067scheme @ nil_Ty61485117scheme))))))),
% 3.12/1.98 inference(definition_unfolding,[status(thm)],[f1214,f1442,f1124])).
% 3.12/1.98 thf(f1442,plain,(
% 3.12/1.98 (insert_nat = (^[Y0 : nat]: ((^[Y1 : set_nat]: ((^[Y2 : set_nat]: (collect_nat @ (sup_sup_nat_o @ (^[Y3 : nat]: (member_nat @ Y3 @ Y1)) @ (^[Y3 : nat]: (member_nat @ Y3 @ Y2))))))) @ (collect_nat @ (^[Y1 : nat]: (Y0 = Y1))))))),
% 3.12/1.98 inference(definition_unfolding,[status(thm)],[f1281,f1344])).
% 3.12/1.98 thf(f1344,plain,(
% 3.12/1.98 (sup_sup_set_nat = (^[Y0 : set_nat]: ((^[Y1 : set_nat]: (collect_nat @ (sup_sup_nat_o @ (^[Y2 : nat]: (member_nat @ Y2 @ Y0)) @ (^[Y2 : nat]: (member_nat @ Y2 @ Y1))))))))),
% 3.12/1.98 inference(cnf_transformation,[status(thm)],[f749])).
% 3.12/1.98 thf(f749,plain,(
% 3.12/1.98 (sup_sup_set_nat = (^[Y0 : set_nat]: ((^[Y1 : set_nat]: (collect_nat @ (sup_sup_nat_o @ (^[Y2 : nat]: (member_nat @ Y2 @ Y0)) @ (^[Y2 : nat]: (member_nat @ Y2 @ Y1))))))))),
% 3.12/1.98 inference(fool_elimination,[status(thm)],[f748])).
% 3.12/1.98 thf(f748,plain,(
% 3.12/1.98 (sup_sup_set_nat = (^[X0 : set_nat, X1 : set_nat] : (collect_nat @ (sup_sup_nat_o @ (^[X2 : nat] : (member_nat @ X2 @ X0)) @ (^[X3 : nat] : (member_nat @ X3 @ X1))))))),
% 3.12/1.98 inference(rectify,[status(thm)],[f309])).
% 3.12/1.98 thf(f309,axiom,(
% 3.12/1.98 (sup_sup_set_nat = (^[X61 : set_nat, X59 : set_nat] : (collect_nat @ (sup_sup_nat_o @ (^[X41 : nat] : (member_nat @ X41 @ X61)) @ (^[X41 : nat] : (member_nat @ X41 @ X59))))))),
% 3.12/1.98 file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_308_sup__set__def)).
% 3.12/1.98 thf(f1281,plain,(
% 3.12/1.98 (insert_nat = (^[Y0 : nat]: (sup_sup_set_nat @ (collect_nat @ (^[Y1 : nat]: (Y0 = Y1))))))),
% 3.12/1.98 inference(cnf_transformation,[status(thm)],[f655])).
% 3.12/1.98 thf(f655,plain,(
% 3.12/1.98 (insert_nat = (^[Y0 : nat]: (sup_sup_set_nat @ (collect_nat @ (^[Y1 : nat]: (Y0 = Y1))))))),
% 3.12/1.98 inference(fool_elimination,[status(thm)],[f654])).
% 3.12/1.98 thf(f654,plain,(
% 3.12/1.98 (insert_nat = (^[X0 : nat] : (sup_sup_set_nat @ (collect_nat @ (^[X1 : nat] : ((X0 = X1)))))))),
% 3.12/1.98 inference(rectify,[status(thm)],[f271])).
% 3.12/1.98 thf(f271,axiom,(
% 3.12/1.98 (insert_nat = (^[X58 : nat] : (sup_sup_set_nat @ (collect_nat @ (^[X41 : nat] : ((X41 = X58)))))))),
% 3.12/1.98 file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_270_insert__def)).
% 3.12/1.98 thf(f1214,plain,(
% 3.12/1.98 ((!! @ nat @ (^[Y0 : nat]: ((type_M1050318637scheme @ (type_M876316792e_FVar @ Y0)) = (insert_nat @ Y0 @ bot_bot_set_nat)))) = $true)),
% 3.12/1.98 inference(cnf_transformation,[status(thm)],[f659])).
% 3.12/1.98 thf(f659,plain,(
% 3.12/1.98 ((!! @ nat @ (^[Y0 : nat]: ((type_M1050318637scheme @ (type_M876316792e_FVar @ Y0)) = (insert_nat @ Y0 @ bot_bot_set_nat)))) = $true)),
% 3.12/1.98 inference(fool_elimination,[status(thm)],[f658])).
% 3.12/1.98 thf(f658,plain,(
% 3.12/1.98 ! [X0 : nat] : ((type_M1050318637scheme @ (type_M876316792e_FVar @ X0)) = (insert_nat @ X0 @ bot_bot_set_nat))),
% 3.12/1.98 inference(rectify,[status(thm)],[f16])).
% 3.12/1.98 thf(f16,axiom,(
% 3.12/1.98 ! [X18 : nat] : ((type_M1050318637scheme @ (type_M876316792e_FVar @ X18)) = (insert_nat @ X18 @ bot_bot_set_nat))),
% 3.12/1.98 file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_15_free__tv__type__scheme_Osimps_I1_J)).
% 3.12/1.98 thf(f2618,plain,(
% 3.12/1.98 ( ! [X0 : nat,X1 : nat > $o] : (($true = ((!! @ nat @ X1) => (X1 @ X0)))) )),
% 3.12/1.98 inference(beta_eta_normalization,[status(thm)],[f2617])).
% 3.12/1.98 thf(f2617,plain,(
% 3.12/1.98 ( ! [X0 : nat,X1 : nat > $o] : ((((!! @ nat @ (^[Y0 : nat]: (X1 @ Y0))) => (X1 @ X0)) = $true)) )),
% 3.12/1.98 inference(boolean_simplification,[status(thm)],[f2616])).
% 3.12/1.98 thf(f2616,plain,(
% 3.12/1.98 ( ! [X0 : nat,X1 : nat > $o] : ((((!! @ nat @ (^[Y0 : nat]: (~ (~ (X1 @ Y0))))) => (X1 @ X0)) = $true)) )),
% 3.12/1.98 inference(beta_eta_normalization,[status(thm)],[f2614])).
% 3.12/1.98 thf(f2614,plain,(
% 3.12/1.98 ( ! [X0 : nat,X1 : nat > $o] : (($true = ((!! @ nat @ (^[Y0 : nat]: (~ ((^[Y1 : nat]: (~ (X1 @ Y1))) @ Y0)))) => (X1 @ X0)))) )),
% 3.12/1.98 inference(backward_demodulation,[status(thm)],[f2415,f2593])).
% 3.12/1.98 thf(f2593,plain,(
% 3.12/1.98 ( ! [X1 : nat > $o] : ((((type_M141510067scheme @ nil_Ty61485117scheme) = (collect_nat @ X1)) = (!! @ nat @ (^[Y0 : nat]: (~ (X1 @ Y0)))))) )),
% 3.12/1.98 inference(equality_proxy_clausification,[status(thm)],[f2591])).
% 3.12/1.98 thf(f2591,plain,(
% 3.12/1.98 ( ! [X1 : nat > $o] : (($true = ((!! @ nat @ (^[Y0 : nat]: (~ (X1 @ Y0)))) = ((type_M141510067scheme @ nil_Ty61485117scheme) = (collect_nat @ X1))))) )),
% 3.12/1.98 inference(beta_eta_normalization,[status(thm)],[f2590])).
% 3.12/1.98 thf(f2590,plain,(
% 3.12/1.98 ( ! [X1 : nat > $o] : ((((^[Y0 : nat > $o]: ((!! @ nat @ (^[Y1 : nat]: (~ (Y0 @ Y1)))) = ((type_M141510067scheme @ nil_Ty61485117scheme) = (collect_nat @ Y0)))) @ X1) = $true)) )),
% 3.12/1.98 inference(pi_clausification,[status(thm)],[f1594])).
% 3.12/1.98 thf(f1594,plain,(
% 3.12/1.98 ($true = (!! @ (nat > $o) @ (^[Y0 : nat > $o]: ((!! @ nat @ (^[Y1 : nat]: (~ (Y0 @ Y1)))) = ((type_M141510067scheme @ nil_Ty61485117scheme) = (collect_nat @ Y0))))))),
% 3.12/1.98 inference(definition_unfolding,[status(thm)],[f1265,f1124])).
% 3.12/1.98 thf(f1265,plain,(
% 3.12/1.98 ($true = (!! @ (nat > $o) @ (^[Y0 : nat > $o]: ((!! @ nat @ (^[Y1 : nat]: (~ (Y0 @ Y1)))) = (bot_bot_set_nat = (collect_nat @ Y0))))))),
% 3.12/1.98 inference(cnf_transformation,[status(thm)],[f775])).
% 3.12/1.98 thf(f775,plain,(
% 3.12/1.98 ($true = (!! @ (nat > $o) @ (^[Y0 : nat > $o]: ((!! @ nat @ (^[Y1 : nat]: (~ (Y0 @ Y1)))) = (bot_bot_set_nat = (collect_nat @ Y0))))))),
% 3.12/1.98 inference(fool_elimination,[status(thm)],[f774])).
% 3.12/1.98 thf(f774,plain,(
% 3.12/1.98 ! [X0 : nat > $o] : (! [X1 : nat] : ~(X0 @ X1) = (bot_bot_set_nat = (collect_nat @ X0)))),
% 3.12/1.98 inference(rectify,[status(thm)],[f64])).
% 3.12/1.98 thf(f64,axiom,(
% 3.12/1.98 ! [X33 : nat > $o] : (! [X41 : nat] : ~(X33 @ X41) = (bot_bot_set_nat = (collect_nat @ X33)))),
% 3.12/1.98 file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_63_empty__Collect__eq)).
% 3.12/1.98 thf(f2415,plain,(
% 3.12/1.98 ( ! [X0 : nat,X1 : nat > $o] : (((((type_M141510067scheme @ nil_Ty61485117scheme) = (collect_nat @ (^[Y0 : nat]: (~ (X1 @ Y0))))) => (X1 @ X0)) = $true)) )),
% 3.12/1.98 inference(boolean_simplification,[status(thm)],[f2414])).
% 3.12/1.98 thf(f2414,plain,(
% 3.12/1.98 ( ! [X0 : nat,X1 : nat > $o] : (((((type_M141510067scheme @ nil_Ty61485117scheme) = (collect_nat @ (^[Y0 : nat]: (~ (X1 @ Y0))))) => (~ (~ (X1 @ X0)))) = $true)) )),
% 3.12/1.98 inference(superposition,[status(thm)],[f2206,f2354])).
% 3.12/1.98 thf(f2354,plain,(
% 3.12/1.98 ( ! [X1 : nat,X5 : nat > $o] : (((member_nat @ X1 @ (collect_nat @ (^[Y0 : nat]: (~ (X5 @ Y0))))) = (~ (X5 @ X1)))) )),
% 3.12/1.98 inference(beta_eta_normalization,[status(thm)],[f2348])).
% 3.12/1.98 thf(f2348,plain,(
% 3.12/1.98 ( ! [X1 : nat,X5 : nat > $o] : (((member_nat @ X1 @ (collect_nat @ (^[Y0 : nat]: (~ (X5 @ Y0))))) = ((^[Y0 : nat]: (~ (X5 @ Y0))) @ X1))) )),
% 3.12/1.98 inference(primitive_instantiation,[status(thm)],[f2317])).
% 3.12/1.98 thf(f2206,plain,(
% 3.12/1.98 ( ! [X2 : set_nat,X1 : nat] : (((((type_M141510067scheme @ nil_Ty61485117scheme) = X2) => (~ (member_nat @ X1 @ X2))) = $true)) )),
% 3.12/1.98 inference(beta_eta_normalization,[status(thm)],[f2205])).
% 3.12/1.98 thf(f2205,plain,(
% 3.12/1.98 ( ! [X2 : set_nat,X1 : nat] : (($true = ((^[Y0 : set_nat]: (((type_M141510067scheme @ nil_Ty61485117scheme) = Y0) => (~ (member_nat @ X1 @ Y0)))) @ X2))) )),
% 3.12/1.98 inference(pi_clausification,[status(thm)],[f2204])).
% 3.12/1.98 thf(f2204,plain,(
% 3.12/1.98 ( ! [X1 : nat] : (($true = (!! @ set_nat @ (^[Y0 : set_nat]: (((type_M141510067scheme @ nil_Ty61485117scheme) = Y0) => (~ (member_nat @ X1 @ Y0))))))) )),
% 3.12/1.98 inference(beta_eta_normalization,[status(thm)],[f2203])).
% 3.12/1.98 thf(f2203,plain,(
% 3.12/1.98 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: (!! @ set_nat @ (^[Y1 : set_nat]: (((type_M141510067scheme @ nil_Ty61485117scheme) = Y1) => (~ (member_nat @ Y0 @ Y1)))))) @ X1))) )),
% 3.12/1.98 inference(pi_clausification,[status(thm)],[f1505])).
% 3.12/1.98 thf(f1505,plain,(
% 3.12/1.98 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ set_nat @ (^[Y1 : set_nat]: (((type_M141510067scheme @ nil_Ty61485117scheme) = Y1) => (~ (member_nat @ Y0 @ Y1))))))))),
% 3.12/1.98 inference(definition_unfolding,[status(thm)],[f1148,f1124])).
% 3.12/1.98 thf(f1148,plain,(
% 3.12/1.98 ((!! @ nat @ (^[Y0 : nat]: (!! @ set_nat @ (^[Y1 : set_nat]: ((bot_bot_set_nat = Y1) => (~ (member_nat @ Y0 @ Y1))))))) = $true)),
% 3.12/1.98 inference(cnf_transformation,[status(thm)],[f686])).
% 3.12/1.98 thf(f686,plain,(
% 3.12/1.98 ((!! @ nat @ (^[Y0 : nat]: (!! @ set_nat @ (^[Y1 : set_nat]: ((bot_bot_set_nat = Y1) => (~ (member_nat @ Y0 @ Y1))))))) = $true)),
% 3.12/1.98 inference(fool_elimination,[status(thm)],[f685])).
% 3.12/1.98 thf(f685,plain,(
% 3.12/1.98 ! [X0 : set_nat,X1 : nat] : ((bot_bot_set_nat = X0) => ~(member_nat @ X1 @ X0))),
% 3.12/1.98 inference(rectify,[status(thm)],[f68])).
% 3.12/1.98 thf(f68,axiom,(
% 3.12/1.98 ! [X46 : set_nat,X40 : nat] : ((bot_bot_set_nat = X46) => ~(member_nat @ X40 @ X46))),
% 3.12/1.98 file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_67_equals0D)).
% 3.12/1.98 thf(f2317,plain,(
% 3.12/1.98 ( ! [X2 : nat > $o,X1 : nat] : (((X2 @ X1) = (member_nat @ X1 @ (collect_nat @ X2)))) )),
% 3.12/1.98 inference(equality_proxy_clausification,[status(thm)],[f2316])).
% 3.12/1.98 thf(f2316,plain,(
% 3.12/1.98 ( ! [X2 : nat > $o,X1 : nat] : ((((member_nat @ X1 @ (collect_nat @ X2)) = (X2 @ X1)) = $true)) )),
% 3.12/1.98 inference(beta_eta_normalization,[status(thm)],[f2315])).
% 3.12/1.98 thf(f2315,plain,(
% 3.12/1.98 ( ! [X2 : nat > $o,X1 : nat] : (($true = ((^[Y0 : nat > $o]: ((member_nat @ X1 @ (collect_nat @ Y0)) = (Y0 @ X1))) @ X2))) )),
% 3.12/1.98 inference(pi_clausification,[status(thm)],[f2310])).
% 3.12/1.98 thf(f2310,plain,(
% 3.12/1.98 ( ! [X1 : nat] : (($true = (!! @ (nat > $o) @ (^[Y0 : nat > $o]: ((member_nat @ X1 @ (collect_nat @ Y0)) = (Y0 @ X1)))))) )),
% 3.12/1.98 inference(beta_eta_normalization,[status(thm)],[f2309])).
% 3.12/1.98 thf(f2309,plain,(
% 3.12/1.98 ( ! [X1 : nat] : ((((^[Y0 : nat]: (!! @ (nat > $o) @ (^[Y1 : nat > $o]: ((member_nat @ Y0 @ (collect_nat @ Y1)) = (Y1 @ Y0))))) @ X1) = $true)) )),
% 3.12/1.98 inference(pi_clausification,[status(thm)],[f1161])).
% 3.12/1.98 thf(f1161,plain,(
% 3.12/1.98 ((!! @ nat @ (^[Y0 : nat]: (!! @ (nat > $o) @ (^[Y1 : nat > $o]: ((member_nat @ Y0 @ (collect_nat @ Y1)) = (Y1 @ Y0)))))) = $true)),
% 3.12/1.98 inference(cnf_transformation,[status(thm)],[f515])).
% 3.12/1.98 thf(f515,plain,(
% 3.12/1.98 ((!! @ nat @ (^[Y0 : nat]: (!! @ (nat > $o) @ (^[Y1 : nat > $o]: ((member_nat @ Y0 @ (collect_nat @ Y1)) = (Y1 @ Y0)))))) = $true)),
% 3.12/1.98 inference(fool_elimination,[status(thm)],[f514])).
% 3.12/1.98 thf(f514,plain,(
% 3.12/1.98 ! [X0 : nat > $o,X1 : nat] : ((member_nat @ X1 @ (collect_nat @ X0)) = (X0 @ X1))),
% 3.12/1.98 inference(rectify,[status(thm)],[f59])).
% 3.12/1.98 thf(f59,axiom,(
% 3.12/1.98 ! [X33 : nat > $o,X40 : nat] : ((member_nat @ X40 @ (collect_nat @ X33)) = (X33 @ X40))),
% 3.12/1.98 file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_58_mem__Collect__eq)).
% 3.12/1.98 thf(f3299,plain,(
% 3.12/1.98 ((member_nat @ n @ (type_M49385309le_typ @ (type_M405566558_subst @ x))) = $true)),
% 3.12/1.98 inference(not_proxy_clausification,[status(thm)],[f3263])).
% 3.12/1.98 thf(f3263,plain,(
% 3.12/1.98 ($false = (~ (member_nat @ n @ (type_M49385309le_typ @ (type_M405566558_subst @ x)))))),
% 3.12/1.98 inference(trivial_inequality_removal,[status(thm)],[f3262])).
% 3.12/1.98 thf(f3262,plain,(
% 3.12/1.98 ($false = (~ (member_nat @ n @ (type_M49385309le_typ @ (type_M405566558_subst @ x))))) | ($false = $true)),
% 3.12/1.98 inference(boolean_simplification,[status(thm)],[f3261])).
% 3.12/1.98 thf(f3261,plain,(
% 3.12/1.98 ($false = (~ (member_nat @ n @ (type_M49385309le_typ @ (type_M405566558_subst @ x))))) | ($true = (~ $true))),
% 3.12/1.98 inference(boolean_simplification,[status(thm)],[f3244])).
% 3.12/1.98 thf(f3244,plain,(
% 3.12/1.98 ($false = (~ (member_nat @ n @ (type_M49385309le_typ @ (type_M405566558_subst @ x))))) | ($true = (~ (((~ ((type_M1006385707scheme @ (s1 @ x)) = (type_M1006385707scheme @ (s2 @ x)))) | ((s1 @ n) = (s2 @ n))) | $true)))),
% 3.12/1.98 inference(superposition,[status(thm)],[f2534,f2294])).
% 3.12/1.98 thf(f3821,plain,(
% 3.12/1.98 ((s2 @ x) = (s1 @ x))),
% 3.12/1.98 inference(equality_proxy_clausification,[status(thm)],[f3790])).
% 3.12/1.98 thf(f3790,plain,(
% 3.12/1.98 (((s1 @ x) = (s2 @ x)) = $true)),
% 3.12/1.98 inference(boolean_simplification,[status(thm)],[f3789])).
% 3.12/1.98 thf(f3789,plain,(
% 3.12/1.98 (($true => ((s1 @ x) = (s2 @ x))) = $true)),
% 3.12/1.98 inference(superposition,[status(thm)],[f2269,f3758])).
% 3.12/1.98 thf(f3758,plain,(
% 3.12/1.98 (((type_M1006385707scheme @ (s1 @ x)) = (type_M1006385707scheme @ (s2 @ x))) = $true)),
% 3.12/1.98 inference(not_proxy_clausification,[status(thm)],[f3277])).
% 3.12/1.98 thf(f3277,plain,(
% 3.12/1.98 ((~ ((type_M1006385707scheme @ (s1 @ x)) = (type_M1006385707scheme @ (s2 @ x)))) = $false)),
% 3.12/1.98 inference(boolean_simplification,[status(thm)],[f3276])).
% 3.12/1.98 thf(f3276,plain,(
% 3.12/1.98 ($false = ((~ ((type_M1006385707scheme @ (s1 @ x)) = (type_M1006385707scheme @ (s2 @ x)))) | $false))),
% 3.12/1.98 inference(backward_demodulation,[status(thm)],[f3273,f3263])).
% 3.12/1.98 thf(f3273,plain,(
% 3.12/1.98 ($false = ((~ ((type_M1006385707scheme @ (s1 @ x)) = (type_M1006385707scheme @ (s2 @ x)))) | (~ (member_nat @ n @ (type_M49385309le_typ @ (type_M405566558_subst @ x))))))),
% 3.12/1.98 inference(boolean_simplification,[status(thm)],[f3272])).
% 3.12/1.98 thf(f3272,plain,(
% 3.12/1.98 ($false = (((~ ((type_M1006385707scheme @ (s1 @ x)) = (type_M1006385707scheme @ (s2 @ x)))) | $false) | (~ (member_nat @ n @ (type_M49385309le_typ @ (type_M405566558_subst @ x))))))),
% 3.12/1.98 inference(forward_demodulation,[status(thm)],[f3265,f3269])).
% 3.12/1.98 thf(f3265,plain,(
% 3.12/1.98 ($false = (((~ ((type_M1006385707scheme @ (s1 @ x)) = (type_M1006385707scheme @ (s2 @ x)))) | ((s1 @ n) = (s2 @ n))) | (~ (member_nat @ n @ (type_M49385309le_typ @ (type_M405566558_subst @ x))))))),
% 3.12/1.98 inference(trivial_inequality_removal,[status(thm)],[f3264])).
% 3.12/1.98 thf(f3264,plain,(
% 3.12/1.98 ($false = $true) | ($false = (((~ ((type_M1006385707scheme @ (s1 @ x)) = (type_M1006385707scheme @ (s2 @ x)))) | ((s1 @ n) = (s2 @ n))) | (~ (member_nat @ n @ (type_M49385309le_typ @ (type_M405566558_subst @ x))))))),
% 3.12/1.98 inference(boolean_simplification,[status(thm)],[f3249])).
% 3.12/1.98 thf(f3249,plain,(
% 3.12/1.98 ($false = (((~ ((type_M1006385707scheme @ (s1 @ x)) = (type_M1006385707scheme @ (s2 @ x)))) | ((s1 @ n) = (s2 @ n))) | (~ (member_nat @ n @ (type_M49385309le_typ @ (type_M405566558_subst @ x)))))) | ($true = (~ $true))),
% 3.12/1.98 inference(superposition,[status(thm)],[f2534,f2294])).
% 3.12/1.98 thf(f2269,plain,(
% 3.12/1.98 ( ! [X2 : type_Mirabelle_typ,X1 : type_Mirabelle_typ] : (($true = (((type_M1006385707scheme @ X2) = (type_M1006385707scheme @ X1)) => (X2 = X1)))) )),
% 3.12/1.98 inference(beta_eta_normalization,[status(thm)],[f2268])).
% 3.12/1.98 thf(f2268,plain,(
% 3.12/1.98 ( ! [X2 : type_Mirabelle_typ,X1 : type_Mirabelle_typ] : ((((^[Y0 : type_Mirabelle_typ]: (((type_M1006385707scheme @ Y0) = (type_M1006385707scheme @ X1)) => (Y0 = X1))) @ X2) = $true)) )),
% 3.12/1.98 inference(pi_clausification,[status(thm)],[f2267])).
% 3.12/1.98 thf(f2267,plain,(
% 3.12/1.98 ( ! [X1 : type_Mirabelle_typ] : (($true = (!! @ type_Mirabelle_typ @ (^[Y0 : type_Mirabelle_typ]: (((type_M1006385707scheme @ Y0) = (type_M1006385707scheme @ X1)) => (Y0 = X1)))))) )),
% 3.12/1.98 inference(beta_eta_normalization,[status(thm)],[f2266])).
% 3.12/1.98 thf(f2266,plain,(
% 3.12/1.98 ( ! [X1 : type_Mirabelle_typ] : ((((^[Y0 : type_Mirabelle_typ]: (!! @ type_Mirabelle_typ @ (^[Y1 : type_Mirabelle_typ]: (((type_M1006385707scheme @ Y1) = (type_M1006385707scheme @ Y0)) => (Y1 = Y0))))) @ X1) = $true)) )),
% 3.12/1.98 inference(pi_clausification,[status(thm)],[f1396])).
% 3.12/1.98 thf(f1396,plain,(
% 3.12/1.98 ($true = (!! @ type_Mirabelle_typ @ (^[Y0 : type_Mirabelle_typ]: (!! @ type_Mirabelle_typ @ (^[Y1 : type_Mirabelle_typ]: (((type_M1006385707scheme @ Y1) = (type_M1006385707scheme @ Y0)) => (Y1 = Y0)))))))),
% 3.12/1.98 inference(cnf_transformation,[status(thm)],[f998])).
% 3.12/1.98 thf(f998,plain,(
% 3.12/1.98 ($true = (!! @ type_Mirabelle_typ @ (^[Y0 : type_Mirabelle_typ]: (!! @ type_Mirabelle_typ @ (^[Y1 : type_Mirabelle_typ]: (((type_M1006385707scheme @ Y1) = (type_M1006385707scheme @ Y0)) => (Y1 = Y0)))))))),
% 3.12/1.98 inference(fool_elimination,[status(thm)],[f997])).
% 3.12/1.98 thf(f997,plain,(
% 3.12/1.98 ! [X0 : type_Mirabelle_typ,X1 : type_Mirabelle_typ] : (((type_M1006385707scheme @ X0) = (type_M1006385707scheme @ X1)) => (X0 = X1))),
% 3.12/1.98 inference(rectify,[status(thm)],[f36])).
% 3.12/1.98 thf(f36,axiom,(
% 3.12/1.98 ! [X17 : type_Mirabelle_typ,X27 : type_Mirabelle_typ] : (((type_M1006385707scheme @ X17) = (type_M1006385707scheme @ X27)) => (X17 = X27))),
% 3.12/1.98 file('/export/starexec/sandbox/tmp/tmp.tyzLXAuVr7/DTF2THF_3895.p',fact_35_mk__scheme__injective)).
% 3.12/1.98 % SZS output end Proof for DTF2THF_3895
% 3.12/1.98 % (4017)------------------------------
% 3.12/1.98 % (4017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.12/1.98 % (4017)Termination reason: Refutation
% 3.12/1.98
% 3.12/1.98 % (4017)Memory used [KB]: 10106
% 3.12/1.98 % (4017)Time elapsed: 0.261 s
% 3.12/1.98 % (4017)Instructions burned: 875 (million)
% 3.12/1.98 % (4017)------------------------------
% 3.12/1.98 % (4017)------------------------------
% 3.12/1.98 % (4005)Success in time 0.298 s
%------------------------------------------------------------------------------