TPTP Problem File: SLH0518^1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SLH0000^1 : TPTP v8.2.0. Released v8.2.0.
% Domain : Archive of Formal Proofs
% Problem :
% Version : Especial.
% English :
% Refs : [Des23] Desharnais (2023), Email to Geoff Sutcliffe
% Source : [Des23]
% Names : Knights_Tour/0000_KnightsTour/prob_00447_018193__5722284_1 [Des23]
% Status : Theorem
% Rating : ? v8.2.0
% Syntax : Number of formulae : 1435 ( 748 unt; 154 typ; 0 def)
% Number of atoms : 3174 (1836 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 10060 ( 522 ~; 89 |; 322 &;8045 @)
% ( 0 <=>;1082 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 17 ( 16 usr)
% Number of type conns : 411 ( 411 >; 0 *; 0 +; 0 <<)
% Number of symbols : 141 ( 138 usr; 18 con; 0-3 aty)
% Number of variables : 3279 ( 122 ^;3017 !; 140 ?;3279 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2023-01-19 09:00:29.654
%------------------------------------------------------------------------------
% Could-be-implicit typings (16)
thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
list_P2336717926344734829nt_int: $tType ).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
set_Pr2560585780119916871nt_int: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
produc1219242969750017639nt_int: $tType ).
thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
list_l2734933928136073931nt_int: $tType ).
thf(ty_n_t__List__Olist_It__List__Olist_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J_J,type,
list_l2036039776804522917nt_int: $tType ).
thf(ty_n_t__List__Olist_It__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
list_l1670014477004246597nt_int: $tType ).
thf(ty_n_t__Set__Oset_It__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
set_li3855193629254082847nt_int: $tType ).
thf(ty_n_t__List__Olist_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
list_s8839374986383574687nt_int: $tType ).
thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
set_se6260736226359567993nt_int: $tType ).
thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
list_P5707943133018811711nt_int: $tType ).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
set_Pr958786334691620121nt_int: $tType ).
thf(ty_n_t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
product_prod_int_int: $tType ).
thf(ty_n_t__List__Olist_It__List__Olist_It__Int__Oint_J_J,type,
list_list_int: $tType ).
thf(ty_n_t__List__Olist_It__Int__Oint_J,type,
list_int: $tType ).
thf(ty_n_t__Set__Oset_It__Int__Oint_J,type,
set_int: $tType ).
thf(ty_n_t__Int__Oint,type,
int: $tType ).
% Explicit typings (138)
thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
bNF_Gr9175161896313899224nt_int: set_li3855193629254082847nt_int > product_prod_int_int > set_li3855193629254082847nt_int ).
thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
bNF_Gr2185362013987207252nt_int: set_li3855193629254082847nt_int > list_P5707943133018811711nt_int > set_Pr958786334691620121nt_int ).
thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
finite2998713641127702882nt_int: set_Pr958786334691620121nt_int > $o ).
thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
finite8744585540193469122nt_int: set_se6260736226359567993nt_int > $o ).
thf(sy_c_Finite__Set_Ofold_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
finite21431522256130664nt_int: ( product_prod_int_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ) > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
thf(sy_c_Finite__Set_Ofold_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
finite7977572941483360520nt_int: ( set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ) > set_Pr958786334691620121nt_int > set_se6260736226359567993nt_int > set_Pr958786334691620121nt_int ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Int__Oint_J,type,
minus_minus_set_int: set_int > set_int > set_int ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
minus_456201022768243590nt_int: set_li3855193629254082847nt_int > set_li3855193629254082847nt_int > set_li3855193629254082847nt_int ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
minus_1052850069191792384nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
minus_2188297577953631406nt_int: set_Pr2560585780119916871nt_int > set_Pr2560585780119916871nt_int > set_Pr2560585780119916871nt_int ).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
minus_2612819937483484256nt_int: set_se6260736226359567993nt_int > set_se6260736226359567993nt_int > set_se6260736226359567993nt_int ).
thf(sy_c_If_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
if_lis8883190402267401221nt_int: $o > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
thf(sy_c_If_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
if_set4441254072200386271nt_int: $o > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
thf(sy_c_KnightsTour_Ocircuit__checker,type,
circuit_checker: set_Pr958786334691620121nt_int > list_P5707943133018811711nt_int > $o ).
thf(sy_c_KnightsTour_Oknights__circuit,type,
knights_circuit: set_Pr958786334691620121nt_int > list_P5707943133018811711nt_int > $o ).
thf(sy_c_KnightsTour_Oknights__path,type,
knights_path: set_Pr958786334691620121nt_int > list_P5707943133018811711nt_int > $o ).
thf(sy_c_KnightsTour_Opath__checker,type,
path_checker: set_Pr958786334691620121nt_int > list_P5707943133018811711nt_int > $o ).
thf(sy_c_KnightsTour_Ostep__checker,type,
step_checker: product_prod_int_int > product_prod_int_int > $o ).
thf(sy_c_KnightsTour_Ovalid__step,type,
valid_step: product_prod_int_int > product_prod_int_int > $o ).
thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Int__Oint_J,type,
inf_inf_set_int: set_int > set_int > set_int ).
thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
inf_in8463092517017915661nt_int: set_li3855193629254082847nt_int > set_li3855193629254082847nt_int > set_li3855193629254082847nt_int ).
thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
inf_in2269163501485487111nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
inf_in7392334082413294389nt_int: set_Pr2560585780119916871nt_int > set_Pr2560585780119916871nt_int > set_Pr2560585780119916871nt_int ).
thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
inf_in8396524679539076455nt_int: set_se6260736226359567993nt_int > set_se6260736226359567993nt_int > set_se6260736226359567993nt_int ).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Int__Oint_J,type,
sup_sup_set_int: set_int > set_int > set_int ).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
sup_su3633867531522857715nt_int: set_li3855193629254082847nt_int > set_li3855193629254082847nt_int > set_li3855193629254082847nt_int ).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
sup_su6024340866399070445nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
sup_su3808334714663352091nt_int: set_Pr2560585780119916871nt_int > set_Pr2560585780119916871nt_int > set_Pr2560585780119916871nt_int ).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
sup_su2047564715030645325nt_int: set_se6260736226359567993nt_int > set_se6260736226359567993nt_int > set_se6260736226359567993nt_int ).
thf(sy_c_Lattices__Big_Osemilattice__inf__class_OInf__fin_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
lattic8951152183982934710nt_int: set_se6260736226359567993nt_int > set_Pr958786334691620121nt_int ).
thf(sy_c_Lattices__Big_Osemilattice__sup__class_OSup__fin_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
lattic1237861848008701264nt_int: set_se6260736226359567993nt_int > set_Pr958786334691620121nt_int ).
thf(sy_c_List_Oappend_001t__Int__Oint,type,
append_int: list_int > list_int > list_int ).
thf(sy_c_List_Oappend_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
append1237393811882493146nt_int: list_l1670014477004246597nt_int > list_l1670014477004246597nt_int > list_l1670014477004246597nt_int ).
thf(sy_c_List_Oappend_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
append7030698103840186580nt_int: list_P5707943133018811711nt_int > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
thf(sy_c_List_Oappend_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
append3889155854801840692nt_int: list_s8839374986383574687nt_int > list_s8839374986383574687nt_int > list_s8839374986383574687nt_int ).
thf(sy_c_List_Obind_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
bind_P8056059132564497095nt_int: list_P5707943133018811711nt_int > ( product_prod_int_int > list_P5707943133018811711nt_int ) > list_P5707943133018811711nt_int ).
thf(sy_c_List_Obutlast_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
butlas2390654596765537291nt_int: list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
thf(sy_c_List_Ocan__select_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
can_se1576335439491303350nt_int: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int > $o ).
thf(sy_c_List_Oconcat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
concat4512918505337516154nt_int: list_l1670014477004246597nt_int > list_P5707943133018811711nt_int ).
thf(sy_c_List_Ocoset_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
coset_3631019413092825772nt_int: list_P5707943133018811711nt_int > set_Pr958786334691620121nt_int ).
thf(sy_c_List_Odistinct_001t__Int__Oint,type,
distinct_int: list_int > $o ).
thf(sy_c_List_Odistinct_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
distin8114605256187547832nt_int: list_l1670014477004246597nt_int > $o ).
thf(sy_c_List_Odistinct_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
distin3744728255968310194nt_int: list_P5707943133018811711nt_int > $o ).
thf(sy_c_List_Odistinct_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
distin7265875916114366688nt_int: list_P2336717926344734829nt_int > $o ).
thf(sy_c_List_Odistinct__adj_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
distin7999467515711547031nt_int: list_P5707943133018811711nt_int > $o ).
thf(sy_c_List_Ofold_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
fold_P6555583138535618987nt_int: ( product_prod_int_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ) > list_P5707943133018811711nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
thf(sy_c_List_Ofold_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
fold_s6119275068807568459nt_int: ( set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ) > list_s8839374986383574687nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
thf(sy_c_List_Ofoldr_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
foldr_8633130848730196071nt_int: ( list_P5707943133018811711nt_int > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ) > list_l1670014477004246597nt_int > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
thf(sy_c_List_Oinsert_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
insert5765537519290168021nt_int: product_prod_int_int > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
thf(sy_c_List_Olast_001t__Int__Oint,type,
last_int: list_int > int ).
thf(sy_c_List_Olast_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
last_l5818330359162608606nt_int: list_l1670014477004246597nt_int > list_P5707943133018811711nt_int ).
thf(sy_c_List_Olast_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
last_P3305686521732843992nt_int: list_P5707943133018811711nt_int > product_prod_int_int ).
thf(sy_c_List_Olast_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
last_s3107260788710622008nt_int: list_s8839374986383574687nt_int > set_Pr958786334691620121nt_int ).
thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
cons_int: int > list_int > list_int ).
thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Int__Oint_J,type,
cons_list_int: list_int > list_list_int > list_list_int ).
thf(sy_c_List_Olist_OCons_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
cons_l4848925899132326139nt_int: list_l1670014477004246597nt_int > list_l2734933928136073931nt_int > list_l2734933928136073931nt_int ).
thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
cons_l7309679040211256053nt_int: list_P5707943133018811711nt_int > list_l1670014477004246597nt_int > list_l1670014477004246597nt_int ).
thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
cons_l2735253805790495829nt_int: list_s8839374986383574687nt_int > list_l2036039776804522917nt_int > list_l2036039776804522917nt_int ).
thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
cons_P3334398858971670639nt_int: product_prod_int_int > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
thf(sy_c_List_Olist_OCons_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
cons_s6578334183908017615nt_int: set_Pr958786334691620121nt_int > list_s8839374986383574687nt_int > list_s8839374986383574687nt_int ).
thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
nil_int: list_int ).
thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Int__Oint_J,type,
nil_list_int: list_list_int ).
thf(sy_c_List_Olist_ONil_001t__List__Olist_It__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
nil_li8254795547437800779nt_int: list_l2734933928136073931nt_int ).
thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
nil_li8670148097206105925nt_int: list_l1670014477004246597nt_int ).
thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
nil_li5787722104129124517nt_int: list_l2036039776804522917nt_int ).
thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
nil_Pr2300489316682597567nt_int: list_P5707943133018811711nt_int ).
thf(sy_c_List_Olist_ONil_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
nil_se54404438492013087nt_int: list_s8839374986383574687nt_int ).
thf(sy_c_List_Olist_Ohd_001t__Int__Oint,type,
hd_int: list_int > int ).
thf(sy_c_List_Olist_Ohd_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
hd_lis8550591025403828010nt_int: list_l1670014477004246597nt_int > list_P5707943133018811711nt_int ).
thf(sy_c_List_Olist_Ohd_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
hd_Pro282112905867057956nt_int: list_P5707943133018811711nt_int > product_prod_int_int ).
thf(sy_c_List_Olist_Ohd_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
hd_set5458074601020007556nt_int: list_s8839374986383574687nt_int > set_Pr958786334691620121nt_int ).
thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
set_li2659200638379878868nt_int: list_l1670014477004246597nt_int > set_li3855193629254082847nt_int ).
thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
set_Pr2470121279949933262nt_int: list_P5707943133018811711nt_int > set_Pr958786334691620121nt_int ).
thf(sy_c_List_Olist_Oset_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
set_se4746441305218329646nt_int: list_s8839374986383574687nt_int > set_se6260736226359567993nt_int ).
thf(sy_c_List_Olist_Otl_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
tl_Pro1049539609081552168nt_int: list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
thf(sy_c_List_Olist__ex1_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
list_e5465588451548443778nt_int: ( product_prod_int_int > $o ) > list_P5707943133018811711nt_int > $o ).
thf(sy_c_List_Olists_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
lists_9111190511995884973nt_int: set_Pr958786334691620121nt_int > set_li3855193629254082847nt_int ).
thf(sy_c_List_Olistset_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
listse7073127531753840414nt_int: list_s8839374986383574687nt_int > set_li3855193629254082847nt_int ).
thf(sy_c_List_Omap__tailrec__rev_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
map_ta5484600921387902261nt_int: ( product_prod_int_int > product_prod_int_int ) > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
thf(sy_c_List_Omaps_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
maps_P133354487822995585nt_int: ( product_prod_int_int > list_P5707943133018811711nt_int ) > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
thf(sy_c_List_Onull_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
null_P4123483736518020807nt_int: list_P5707943133018811711nt_int > $o ).
thf(sy_c_List_Oproduct_001t__Int__Oint_001t__Int__Oint,type,
product_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
thf(sy_c_List_Oproduct_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
produc1028813369992947845nt_int: list_P5707943133018811711nt_int > list_P5707943133018811711nt_int > list_P2336717926344734829nt_int ).
thf(sy_c_List_Oproduct__lists_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
produc5568053154996169768nt_int: list_l1670014477004246597nt_int > list_l1670014477004246597nt_int ).
thf(sy_c_List_Oremdups_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
remdup3392976464123081940nt_int: list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
thf(sy_c_List_Oremdups__adj_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
remdup6889124116291670005nt_int: list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
thf(sy_c_List_Oremove1_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
remove2588356790385189205nt_int: product_prod_int_int > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
thf(sy_c_List_OremoveAll_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
remove8754733362737398603nt_int: list_P5707943133018811711nt_int > list_l1670014477004246597nt_int > list_l1670014477004246597nt_int ).
thf(sy_c_List_OremoveAll_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
remove494893200766290885nt_int: product_prod_int_int > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
thf(sy_c_List_Orotate1_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
rotate9137591727117064716nt_int: list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
thf(sy_c_List_Oshuffles_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
shuffl1909956583008895700nt_int: list_P5707943133018811711nt_int > list_P5707943133018811711nt_int > set_li3855193629254082847nt_int ).
thf(sy_c_List_Osubseqs_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
subseq1357044202310323342nt_int: list_P5707943133018811711nt_int > list_l1670014477004246597nt_int ).
thf(sy_c_List_Osuccessively_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
succes497254780304326540nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > list_P5707943133018811711nt_int > $o ).
thf(sy_c_List_Otranspose_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
transp5579559677893564233nt_int: list_l1670014477004246597nt_int > list_l1670014477004246597nt_int ).
thf(sy_c_List_Ounion_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
union_56799373549498035nt_int: list_P5707943133018811711nt_int > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
bot_bo8147686125503663512_int_o: product_prod_int_int > $o ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Int__Oint_J,type,
bot_bot_set_int: set_int ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
bot_bo3809061186584590219nt_int: set_li3855193629254082847nt_int ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
bot_bo1796632182523588997nt_int: set_Pr958786334691620121nt_int ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
bot_bo8417956007504411571nt_int: set_Pr2560585780119916871nt_int ).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
bot_bo1488462491386950373nt_int: set_se6260736226359567993nt_int ).
thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
ord_le7563427860532173253nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
ord_le6386220896155801791nt_int: set_li3855193629254082847nt_int > set_li3855193629254082847nt_int > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
ord_le2843351958646193337nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o ).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
ord_le483042692224249369nt_int: set_se6260736226359567993nt_int > set_se6260736226359567993nt_int > $o ).
thf(sy_c_Orderings_Oord__class_Omin_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
ord_mi3891036259616950784nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
top_to4366644338036079209nt_int: set_Pr958786334691620121nt_int ).
thf(sy_c_Relation_OId__on_001t__Int__Oint,type,
id_on_int: set_int > set_Pr958786334691620121nt_int ).
thf(sy_c_Relation_OId__on_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
id_on_8598933527810153430nt_int: set_Pr958786334691620121nt_int > set_Pr2560585780119916871nt_int ).
thf(sy_c_Set_OCollect_001t__Int__Oint,type,
collect_int: ( int > $o ) > set_int ).
thf(sy_c_Set_OCollect_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
collec3040439045487124906nt_int: ( list_P5707943133018811711nt_int > $o ) > set_li3855193629254082847nt_int ).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
collec213857154873943460nt_int: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
collec7447955092554649554nt_int: ( produc1219242969750017639nt_int > $o ) > set_Pr2560585780119916871nt_int ).
thf(sy_c_Set_OCollect_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
collec5210948495886036740nt_int: ( set_Pr958786334691620121nt_int > $o ) > set_se6260736226359567993nt_int ).
thf(sy_c_Set_OPow_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
pow_Pr288375884809803734nt_int: set_Pr958786334691620121nt_int > set_se6260736226359567993nt_int ).
thf(sy_c_Set_Oimage_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
image_689455831346312645nt_int: ( list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ) > set_li3855193629254082847nt_int > set_li3855193629254082847nt_int ).
thf(sy_c_Set_Oimage_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
image_689400715899363487nt_int: ( list_P5707943133018811711nt_int > set_Pr958786334691620121nt_int ) > set_li3855193629254082847nt_int > set_se6260736226359567993nt_int ).
thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
image_2653370878348428101nt_int: ( product_prod_int_int > product_prod_int_int ) > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
thf(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
image_1544889507766666053nt_int: ( set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ) > set_se6260736226359567993nt_int > set_se6260736226359567993nt_int ).
thf(sy_c_Set_Oinsert_001t__Int__Oint,type,
insert_int: int > set_int > set_int ).
thf(sy_c_Set_Oinsert_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
insert393344137582914319nt_int: list_P5707943133018811711nt_int > set_li3855193629254082847nt_int > set_li3855193629254082847nt_int ).
thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
insert5033312907999012233nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
insert5410160437170799671nt_int: produc1219242969750017639nt_int > set_Pr2560585780119916871nt_int > set_Pr2560585780119916871nt_int ).
thf(sy_c_Set_Oinsert_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
insert8897473484851387113nt_int: set_Pr958786334691620121nt_int > set_se6260736226359567993nt_int > set_se6260736226359567993nt_int ).
thf(sy_c_Set_Ois__empty_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
is_emp7707449487952173963nt_int: set_Pr958786334691620121nt_int > $o ).
thf(sy_c_Set_Ois__singleton_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
is_sin8895854488172861613nt_int: set_Pr958786334691620121nt_int > $o ).
thf(sy_c_Set_Opairwise_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
pairwi3178678004212613796nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > set_Pr958786334691620121nt_int > $o ).
thf(sy_c_Set_Oremove_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
remove3288057706648593438nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
thf(sy_c_Set_Othe__elem_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
the_el8326832613380209454nt_int: set_Pr958786334691620121nt_int > product_prod_int_int ).
thf(sy_c_Set_Ovimage_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
vimage9157098373889594107nt_int: ( product_prod_int_int > product_prod_int_int ) > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
thf(sy_c_member_001t__Int__Oint,type,
member_int: int > set_int > $o ).
thf(sy_c_member_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
member2764346250752101224nt_int: list_P5707943133018811711nt_int > set_li3855193629254082847nt_int > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
member8566619992076573584nt_int: produc1219242969750017639nt_int > set_Pr2560585780119916871nt_int > $o ).
thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
member2340774599025711042nt_int: set_Pr958786334691620121nt_int > set_se6260736226359567993nt_int > $o ).
thf(sy_v_b,type,
b: set_Pr958786334691620121nt_int ).
thf(sy_v_ps,type,
ps: list_P5707943133018811711nt_int ).
thf(sy_v_s_092_060_094sub_062i,type,
s_i: product_prod_int_int ).
% Relevant facts (1275)
thf(fact_0_False,axiom,
ps != nil_Pr2300489316682597567nt_int ).
% False
thf(fact_1__092_060open_062b_A_N_A_123s_092_060_094sub_062i_125_A_092_060union_062_A_123s_092_060_094sub_062i_125_A_061_Ab_092_060close_062,axiom,
( ( sup_su6024340866399070445nt_int @ ( minus_1052850069191792384nt_int @ b @ ( insert5033312907999012233nt_int @ s_i @ bot_bo1796632182523588997nt_int ) ) @ ( insert5033312907999012233nt_int @ s_i @ bot_bo1796632182523588997nt_int ) )
= b ) ).
% \<open>b - {s\<^sub>i} \<union> {s\<^sub>i} = b\<close>
thf(fact_2_assms,axiom,
knights_circuit @ b @ ( cons_P3334398858971670639nt_int @ s_i @ ps ) ).
% assms
thf(fact_3_kp__elim_I2_J,axiom,
valid_step @ s_i @ ( hd_Pro282112905867057956nt_int @ ps ) ).
% kp_elim(2)
thf(fact_4_kp1_I1_J,axiom,
knights_path @ b @ ( cons_P3334398858971670639nt_int @ s_i @ ps ) ).
% kp1(1)
thf(fact_5_kp1_I2_J,axiom,
valid_step @ ( last_P3305686521732843992nt_int @ ( cons_P3334398858971670639nt_int @ s_i @ ps ) ) @ ( hd_Pro282112905867057956nt_int @ ( cons_P3334398858971670639nt_int @ s_i @ ps ) ) ).
% kp1(2)
thf(fact_6_vs,axiom,
valid_step @ ( last_P3305686521732843992nt_int @ ps ) @ ( hd_Pro282112905867057956nt_int @ ( cons_P3334398858971670639nt_int @ s_i @ nil_Pr2300489316682597567nt_int ) ) ).
% vs
thf(fact_7_vs_H,axiom,
valid_step @ ( last_P3305686521732843992nt_int @ ( append7030698103840186580nt_int @ ps @ ( cons_P3334398858971670639nt_int @ s_i @ nil_Pr2300489316682597567nt_int ) ) ) @ ( hd_Pro282112905867057956nt_int @ ( append7030698103840186580nt_int @ ps @ ( cons_P3334398858971670639nt_int @ s_i @ nil_Pr2300489316682597567nt_int ) ) ) ).
% vs'
thf(fact_8_kp2_I1_J,axiom,
knights_path @ ( insert5033312907999012233nt_int @ s_i @ bot_bo1796632182523588997nt_int ) @ ( cons_P3334398858971670639nt_int @ s_i @ nil_Pr2300489316682597567nt_int ) ).
% kp2(1)
thf(fact_9_valid__step__neq,axiom,
! [S_i: product_prod_int_int,S_j: product_prod_int_int] :
( ( valid_step @ S_i @ S_j )
=> ( S_i != S_j ) ) ).
% valid_step_neq
thf(fact_10_valid__step__rev,axiom,
! [S_i: product_prod_int_int,S_j: product_prod_int_int] :
( ( valid_step @ S_i @ S_j )
=> ( valid_step @ S_j @ S_i ) ) ).
% valid_step_rev
thf(fact_11_knights__path__non__nil,axiom,
! [B: set_Pr958786334691620121nt_int,Ps: list_P5707943133018811711nt_int] :
( ( knights_path @ B @ Ps )
=> ( Ps != nil_Pr2300489316682597567nt_int ) ) ).
% knights_path_non_nil
thf(fact_12_knights__path__board__unique,axiom,
! [B_1: set_Pr958786334691620121nt_int,Ps: list_P5707943133018811711nt_int,B_2: set_Pr958786334691620121nt_int] :
( ( knights_path @ B_1 @ Ps )
=> ( ( knights_path @ B_2 @ Ps )
=> ( B_1 = B_2 ) ) ) ).
% knights_path_board_unique
thf(fact_13_valid__step__non__transitive,axiom,
! [S_i: product_prod_int_int,S_j: product_prod_int_int,S_k: product_prod_int_int] :
( ( valid_step @ S_i @ S_j )
=> ( ( valid_step @ S_j @ S_k )
=> ~ ( valid_step @ S_i @ S_k ) ) ) ).
% valid_step_non_transitive
thf(fact_14_kp__elim_I3_J,axiom,
knights_path @ ( minus_1052850069191792384nt_int @ b @ ( insert5033312907999012233nt_int @ s_i @ bot_bo1796632182523588997nt_int ) ) @ ps ).
% kp_elim(3)
thf(fact_15_last__snoc,axiom,
! [Xs: list_int,X: int] :
( ( last_int @ ( append_int @ Xs @ ( cons_int @ X @ nil_int ) ) )
= X ) ).
% last_snoc
thf(fact_16_last__snoc,axiom,
! [Xs: list_l1670014477004246597nt_int,X: list_P5707943133018811711nt_int] :
( ( last_l5818330359162608606nt_int @ ( append1237393811882493146nt_int @ Xs @ ( cons_l7309679040211256053nt_int @ X @ nil_li8670148097206105925nt_int ) ) )
= X ) ).
% last_snoc
thf(fact_17_last__snoc,axiom,
! [Xs: list_s8839374986383574687nt_int,X: set_Pr958786334691620121nt_int] :
( ( last_s3107260788710622008nt_int @ ( append3889155854801840692nt_int @ Xs @ ( cons_s6578334183908017615nt_int @ X @ nil_se54404438492013087nt_int ) ) )
= X ) ).
% last_snoc
thf(fact_18_last__snoc,axiom,
! [Xs: list_P5707943133018811711nt_int,X: product_prod_int_int] :
( ( last_P3305686521732843992nt_int @ ( append7030698103840186580nt_int @ Xs @ ( cons_P3334398858971670639nt_int @ X @ nil_Pr2300489316682597567nt_int ) ) )
= X ) ).
% last_snoc
thf(fact_19_kp__elim_I1_J,axiom,
~ ( member5262025264175285858nt_int @ s_i @ ( minus_1052850069191792384nt_int @ b @ ( insert5033312907999012233nt_int @ s_i @ bot_bo1796632182523588997nt_int ) ) ) ).
% kp_elim(1)
thf(fact_20_last__appendL,axiom,
! [Ys: list_l1670014477004246597nt_int,Xs: list_l1670014477004246597nt_int] :
( ( Ys = nil_li8670148097206105925nt_int )
=> ( ( last_l5818330359162608606nt_int @ ( append1237393811882493146nt_int @ Xs @ Ys ) )
= ( last_l5818330359162608606nt_int @ Xs ) ) ) ).
% last_appendL
thf(fact_21_last__appendL,axiom,
! [Ys: list_int,Xs: list_int] :
( ( Ys = nil_int )
=> ( ( last_int @ ( append_int @ Xs @ Ys ) )
= ( last_int @ Xs ) ) ) ).
% last_appendL
thf(fact_22_last__appendL,axiom,
! [Ys: list_s8839374986383574687nt_int,Xs: list_s8839374986383574687nt_int] :
( ( Ys = nil_se54404438492013087nt_int )
=> ( ( last_s3107260788710622008nt_int @ ( append3889155854801840692nt_int @ Xs @ Ys ) )
= ( last_s3107260788710622008nt_int @ Xs ) ) ) ).
% last_appendL
thf(fact_23_last__appendL,axiom,
! [Ys: list_P5707943133018811711nt_int,Xs: list_P5707943133018811711nt_int] :
( ( Ys = nil_Pr2300489316682597567nt_int )
=> ( ( last_P3305686521732843992nt_int @ ( append7030698103840186580nt_int @ Xs @ Ys ) )
= ( last_P3305686521732843992nt_int @ Xs ) ) ) ).
% last_appendL
thf(fact_24_last__appendR,axiom,
! [Ys: list_l1670014477004246597nt_int,Xs: list_l1670014477004246597nt_int] :
( ( Ys != nil_li8670148097206105925nt_int )
=> ( ( last_l5818330359162608606nt_int @ ( append1237393811882493146nt_int @ Xs @ Ys ) )
= ( last_l5818330359162608606nt_int @ Ys ) ) ) ).
% last_appendR
thf(fact_25_last__appendR,axiom,
! [Ys: list_int,Xs: list_int] :
( ( Ys != nil_int )
=> ( ( last_int @ ( append_int @ Xs @ Ys ) )
= ( last_int @ Ys ) ) ) ).
% last_appendR
thf(fact_26_last__appendR,axiom,
! [Ys: list_s8839374986383574687nt_int,Xs: list_s8839374986383574687nt_int] :
( ( Ys != nil_se54404438492013087nt_int )
=> ( ( last_s3107260788710622008nt_int @ ( append3889155854801840692nt_int @ Xs @ Ys ) )
= ( last_s3107260788710622008nt_int @ Ys ) ) ) ).
% last_appendR
thf(fact_27_last__appendR,axiom,
! [Ys: list_P5707943133018811711nt_int,Xs: list_P5707943133018811711nt_int] :
( ( Ys != nil_Pr2300489316682597567nt_int )
=> ( ( last_P3305686521732843992nt_int @ ( append7030698103840186580nt_int @ Xs @ Ys ) )
= ( last_P3305686521732843992nt_int @ Ys ) ) ) ).
% last_appendR
thf(fact_28_hd__append2,axiom,
! [Xs: list_l1670014477004246597nt_int,Ys: list_l1670014477004246597nt_int] :
( ( Xs != nil_li8670148097206105925nt_int )
=> ( ( hd_lis8550591025403828010nt_int @ ( append1237393811882493146nt_int @ Xs @ Ys ) )
= ( hd_lis8550591025403828010nt_int @ Xs ) ) ) ).
% hd_append2
thf(fact_29_hd__append2,axiom,
! [Xs: list_int,Ys: list_int] :
( ( Xs != nil_int )
=> ( ( hd_int @ ( append_int @ Xs @ Ys ) )
= ( hd_int @ Xs ) ) ) ).
% hd_append2
thf(fact_30_hd__append2,axiom,
! [Xs: list_s8839374986383574687nt_int,Ys: list_s8839374986383574687nt_int] :
( ( Xs != nil_se54404438492013087nt_int )
=> ( ( hd_set5458074601020007556nt_int @ ( append3889155854801840692nt_int @ Xs @ Ys ) )
= ( hd_set5458074601020007556nt_int @ Xs ) ) ) ).
% hd_append2
thf(fact_31_hd__append2,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( Xs != nil_Pr2300489316682597567nt_int )
=> ( ( hd_Pro282112905867057956nt_int @ ( append7030698103840186580nt_int @ Xs @ Ys ) )
= ( hd_Pro282112905867057956nt_int @ Xs ) ) ) ).
% hd_append2
thf(fact_32_append1__eq__conv,axiom,
! [Xs: list_int,X: int,Ys: list_int,Y: int] :
( ( ( append_int @ Xs @ ( cons_int @ X @ nil_int ) )
= ( append_int @ Ys @ ( cons_int @ Y @ nil_int ) ) )
= ( ( Xs = Ys )
& ( X = Y ) ) ) ).
% append1_eq_conv
thf(fact_33_append1__eq__conv,axiom,
! [Xs: list_l1670014477004246597nt_int,X: list_P5707943133018811711nt_int,Ys: list_l1670014477004246597nt_int,Y: list_P5707943133018811711nt_int] :
( ( ( append1237393811882493146nt_int @ Xs @ ( cons_l7309679040211256053nt_int @ X @ nil_li8670148097206105925nt_int ) )
= ( append1237393811882493146nt_int @ Ys @ ( cons_l7309679040211256053nt_int @ Y @ nil_li8670148097206105925nt_int ) ) )
= ( ( Xs = Ys )
& ( X = Y ) ) ) ).
% append1_eq_conv
thf(fact_34_append1__eq__conv,axiom,
! [Xs: list_s8839374986383574687nt_int,X: set_Pr958786334691620121nt_int,Ys: list_s8839374986383574687nt_int,Y: set_Pr958786334691620121nt_int] :
( ( ( append3889155854801840692nt_int @ Xs @ ( cons_s6578334183908017615nt_int @ X @ nil_se54404438492013087nt_int ) )
= ( append3889155854801840692nt_int @ Ys @ ( cons_s6578334183908017615nt_int @ Y @ nil_se54404438492013087nt_int ) ) )
= ( ( Xs = Ys )
& ( X = Y ) ) ) ).
% append1_eq_conv
thf(fact_35_append1__eq__conv,axiom,
! [Xs: list_P5707943133018811711nt_int,X: product_prod_int_int,Ys: list_P5707943133018811711nt_int,Y: product_prod_int_int] :
( ( ( append7030698103840186580nt_int @ Xs @ ( cons_P3334398858971670639nt_int @ X @ nil_Pr2300489316682597567nt_int ) )
= ( append7030698103840186580nt_int @ Ys @ ( cons_P3334398858971670639nt_int @ Y @ nil_Pr2300489316682597567nt_int ) ) )
= ( ( Xs = Ys )
& ( X = Y ) ) ) ).
% append1_eq_conv
thf(fact_36_append_Oright__neutral,axiom,
! [A: list_l1670014477004246597nt_int] :
( ( append1237393811882493146nt_int @ A @ nil_li8670148097206105925nt_int )
= A ) ).
% append.right_neutral
thf(fact_37_append_Oright__neutral,axiom,
! [A: list_int] :
( ( append_int @ A @ nil_int )
= A ) ).
% append.right_neutral
thf(fact_38_append_Oright__neutral,axiom,
! [A: list_s8839374986383574687nt_int] :
( ( append3889155854801840692nt_int @ A @ nil_se54404438492013087nt_int )
= A ) ).
% append.right_neutral
thf(fact_39_append_Oright__neutral,axiom,
! [A: list_P5707943133018811711nt_int] :
( ( append7030698103840186580nt_int @ A @ nil_Pr2300489316682597567nt_int )
= A ) ).
% append.right_neutral
thf(fact_40_append__Nil2,axiom,
! [Xs: list_l1670014477004246597nt_int] :
( ( append1237393811882493146nt_int @ Xs @ nil_li8670148097206105925nt_int )
= Xs ) ).
% append_Nil2
thf(fact_41_append__Nil2,axiom,
! [Xs: list_int] :
( ( append_int @ Xs @ nil_int )
= Xs ) ).
% append_Nil2
thf(fact_42_append__Nil2,axiom,
! [Xs: list_s8839374986383574687nt_int] :
( ( append3889155854801840692nt_int @ Xs @ nil_se54404438492013087nt_int )
= Xs ) ).
% append_Nil2
thf(fact_43_append__Nil2,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( append7030698103840186580nt_int @ Xs @ nil_Pr2300489316682597567nt_int )
= Xs ) ).
% append_Nil2
thf(fact_44_append__self__conv,axiom,
! [Xs: list_l1670014477004246597nt_int,Ys: list_l1670014477004246597nt_int] :
( ( ( append1237393811882493146nt_int @ Xs @ Ys )
= Xs )
= ( Ys = nil_li8670148097206105925nt_int ) ) ).
% append_self_conv
thf(fact_45_append__self__conv,axiom,
! [Xs: list_int,Ys: list_int] :
( ( ( append_int @ Xs @ Ys )
= Xs )
= ( Ys = nil_int ) ) ).
% append_self_conv
thf(fact_46_append__self__conv,axiom,
! [Xs: list_s8839374986383574687nt_int,Ys: list_s8839374986383574687nt_int] :
( ( ( append3889155854801840692nt_int @ Xs @ Ys )
= Xs )
= ( Ys = nil_se54404438492013087nt_int ) ) ).
% append_self_conv
thf(fact_47_append__self__conv,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( ( append7030698103840186580nt_int @ Xs @ Ys )
= Xs )
= ( Ys = nil_Pr2300489316682597567nt_int ) ) ).
% append_self_conv
thf(fact_48_self__append__conv,axiom,
! [Y: list_l1670014477004246597nt_int,Ys: list_l1670014477004246597nt_int] :
( ( Y
= ( append1237393811882493146nt_int @ Y @ Ys ) )
= ( Ys = nil_li8670148097206105925nt_int ) ) ).
% self_append_conv
thf(fact_49_self__append__conv,axiom,
! [Y: list_int,Ys: list_int] :
( ( Y
= ( append_int @ Y @ Ys ) )
= ( Ys = nil_int ) ) ).
% self_append_conv
thf(fact_50_self__append__conv,axiom,
! [Y: list_s8839374986383574687nt_int,Ys: list_s8839374986383574687nt_int] :
( ( Y
= ( append3889155854801840692nt_int @ Y @ Ys ) )
= ( Ys = nil_se54404438492013087nt_int ) ) ).
% self_append_conv
thf(fact_51_self__append__conv,axiom,
! [Y: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( Y
= ( append7030698103840186580nt_int @ Y @ Ys ) )
= ( Ys = nil_Pr2300489316682597567nt_int ) ) ).
% self_append_conv
thf(fact_52_append__self__conv2,axiom,
! [Xs: list_l1670014477004246597nt_int,Ys: list_l1670014477004246597nt_int] :
( ( ( append1237393811882493146nt_int @ Xs @ Ys )
= Ys )
= ( Xs = nil_li8670148097206105925nt_int ) ) ).
% append_self_conv2
thf(fact_53_append__self__conv2,axiom,
! [Xs: list_int,Ys: list_int] :
( ( ( append_int @ Xs @ Ys )
= Ys )
= ( Xs = nil_int ) ) ).
% append_self_conv2
thf(fact_54_append__self__conv2,axiom,
! [Xs: list_s8839374986383574687nt_int,Ys: list_s8839374986383574687nt_int] :
( ( ( append3889155854801840692nt_int @ Xs @ Ys )
= Ys )
= ( Xs = nil_se54404438492013087nt_int ) ) ).
% append_self_conv2
thf(fact_55_append__self__conv2,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( ( append7030698103840186580nt_int @ Xs @ Ys )
= Ys )
= ( Xs = nil_Pr2300489316682597567nt_int ) ) ).
% append_self_conv2
thf(fact_56_list_Oinject,axiom,
! [X21: list_P5707943133018811711nt_int,X22: list_l1670014477004246597nt_int,Y21: list_P5707943133018811711nt_int,Y22: list_l1670014477004246597nt_int] :
( ( ( cons_l7309679040211256053nt_int @ X21 @ X22 )
= ( cons_l7309679040211256053nt_int @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X22 = Y22 ) ) ) ).
% list.inject
thf(fact_57_list_Oinject,axiom,
! [X21: set_Pr958786334691620121nt_int,X22: list_s8839374986383574687nt_int,Y21: set_Pr958786334691620121nt_int,Y22: list_s8839374986383574687nt_int] :
( ( ( cons_s6578334183908017615nt_int @ X21 @ X22 )
= ( cons_s6578334183908017615nt_int @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X22 = Y22 ) ) ) ).
% list.inject
thf(fact_58_list_Oinject,axiom,
! [X21: product_prod_int_int,X22: list_P5707943133018811711nt_int,Y21: product_prod_int_int,Y22: list_P5707943133018811711nt_int] :
( ( ( cons_P3334398858971670639nt_int @ X21 @ X22 )
= ( cons_P3334398858971670639nt_int @ Y21 @ Y22 ) )
= ( ( X21 = Y21 )
& ( X22 = Y22 ) ) ) ).
% list.inject
thf(fact_59_same__append__eq,axiom,
! [Xs: list_l1670014477004246597nt_int,Ys: list_l1670014477004246597nt_int,Zs: list_l1670014477004246597nt_int] :
( ( ( append1237393811882493146nt_int @ Xs @ Ys )
= ( append1237393811882493146nt_int @ Xs @ Zs ) )
= ( Ys = Zs ) ) ).
% same_append_eq
thf(fact_60_same__append__eq,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int,Zs: list_P5707943133018811711nt_int] :
( ( ( append7030698103840186580nt_int @ Xs @ Ys )
= ( append7030698103840186580nt_int @ Xs @ Zs ) )
= ( Ys = Zs ) ) ).
% same_append_eq
thf(fact_61_append__same__eq,axiom,
! [Ys: list_l1670014477004246597nt_int,Xs: list_l1670014477004246597nt_int,Zs: list_l1670014477004246597nt_int] :
( ( ( append1237393811882493146nt_int @ Ys @ Xs )
= ( append1237393811882493146nt_int @ Zs @ Xs ) )
= ( Ys = Zs ) ) ).
% append_same_eq
thf(fact_62_append__same__eq,axiom,
! [Ys: list_P5707943133018811711nt_int,Xs: list_P5707943133018811711nt_int,Zs: list_P5707943133018811711nt_int] :
( ( ( append7030698103840186580nt_int @ Ys @ Xs )
= ( append7030698103840186580nt_int @ Zs @ Xs ) )
= ( Ys = Zs ) ) ).
% append_same_eq
thf(fact_63_append__assoc,axiom,
! [Xs: list_l1670014477004246597nt_int,Ys: list_l1670014477004246597nt_int,Zs: list_l1670014477004246597nt_int] :
( ( append1237393811882493146nt_int @ ( append1237393811882493146nt_int @ Xs @ Ys ) @ Zs )
= ( append1237393811882493146nt_int @ Xs @ ( append1237393811882493146nt_int @ Ys @ Zs ) ) ) ).
% append_assoc
thf(fact_64_append__assoc,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int,Zs: list_P5707943133018811711nt_int] :
( ( append7030698103840186580nt_int @ ( append7030698103840186580nt_int @ Xs @ Ys ) @ Zs )
= ( append7030698103840186580nt_int @ Xs @ ( append7030698103840186580nt_int @ Ys @ Zs ) ) ) ).
% append_assoc
thf(fact_65_append_Oassoc,axiom,
! [A: list_l1670014477004246597nt_int,B: list_l1670014477004246597nt_int,C: list_l1670014477004246597nt_int] :
( ( append1237393811882493146nt_int @ ( append1237393811882493146nt_int @ A @ B ) @ C )
= ( append1237393811882493146nt_int @ A @ ( append1237393811882493146nt_int @ B @ C ) ) ) ).
% append.assoc
thf(fact_66_append_Oassoc,axiom,
! [A: list_P5707943133018811711nt_int,B: list_P5707943133018811711nt_int,C: list_P5707943133018811711nt_int] :
( ( append7030698103840186580nt_int @ ( append7030698103840186580nt_int @ A @ B ) @ C )
= ( append7030698103840186580nt_int @ A @ ( append7030698103840186580nt_int @ B @ C ) ) ) ).
% append.assoc
thf(fact_67_append__is__Nil__conv,axiom,
! [Xs: list_l1670014477004246597nt_int,Ys: list_l1670014477004246597nt_int] :
( ( ( append1237393811882493146nt_int @ Xs @ Ys )
= nil_li8670148097206105925nt_int )
= ( ( Xs = nil_li8670148097206105925nt_int )
& ( Ys = nil_li8670148097206105925nt_int ) ) ) ).
% append_is_Nil_conv
thf(fact_68_append__is__Nil__conv,axiom,
! [Xs: list_int,Ys: list_int] :
( ( ( append_int @ Xs @ Ys )
= nil_int )
= ( ( Xs = nil_int )
& ( Ys = nil_int ) ) ) ).
% append_is_Nil_conv
thf(fact_69_append__is__Nil__conv,axiom,
! [Xs: list_s8839374986383574687nt_int,Ys: list_s8839374986383574687nt_int] :
( ( ( append3889155854801840692nt_int @ Xs @ Ys )
= nil_se54404438492013087nt_int )
= ( ( Xs = nil_se54404438492013087nt_int )
& ( Ys = nil_se54404438492013087nt_int ) ) ) ).
% append_is_Nil_conv
thf(fact_70_append__is__Nil__conv,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( ( append7030698103840186580nt_int @ Xs @ Ys )
= nil_Pr2300489316682597567nt_int )
= ( ( Xs = nil_Pr2300489316682597567nt_int )
& ( Ys = nil_Pr2300489316682597567nt_int ) ) ) ).
% append_is_Nil_conv
thf(fact_71_Nil__is__append__conv,axiom,
! [Xs: list_l1670014477004246597nt_int,Ys: list_l1670014477004246597nt_int] :
( ( nil_li8670148097206105925nt_int
= ( append1237393811882493146nt_int @ Xs @ Ys ) )
= ( ( Xs = nil_li8670148097206105925nt_int )
& ( Ys = nil_li8670148097206105925nt_int ) ) ) ).
% Nil_is_append_conv
thf(fact_72_Nil__is__append__conv,axiom,
! [Xs: list_int,Ys: list_int] :
( ( nil_int
= ( append_int @ Xs @ Ys ) )
= ( ( Xs = nil_int )
& ( Ys = nil_int ) ) ) ).
% Nil_is_append_conv
thf(fact_73_Nil__is__append__conv,axiom,
! [Xs: list_s8839374986383574687nt_int,Ys: list_s8839374986383574687nt_int] :
( ( nil_se54404438492013087nt_int
= ( append3889155854801840692nt_int @ Xs @ Ys ) )
= ( ( Xs = nil_se54404438492013087nt_int )
& ( Ys = nil_se54404438492013087nt_int ) ) ) ).
% Nil_is_append_conv
thf(fact_74_Nil__is__append__conv,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( nil_Pr2300489316682597567nt_int
= ( append7030698103840186580nt_int @ Xs @ Ys ) )
= ( ( Xs = nil_Pr2300489316682597567nt_int )
& ( Ys = nil_Pr2300489316682597567nt_int ) ) ) ).
% Nil_is_append_conv
thf(fact_75_self__append__conv2,axiom,
! [Y: list_l1670014477004246597nt_int,Xs: list_l1670014477004246597nt_int] :
( ( Y
= ( append1237393811882493146nt_int @ Xs @ Y ) )
= ( Xs = nil_li8670148097206105925nt_int ) ) ).
% self_append_conv2
thf(fact_76_self__append__conv2,axiom,
! [Y: list_int,Xs: list_int] :
( ( Y
= ( append_int @ Xs @ Y ) )
= ( Xs = nil_int ) ) ).
% self_append_conv2
thf(fact_77_self__append__conv2,axiom,
! [Y: list_s8839374986383574687nt_int,Xs: list_s8839374986383574687nt_int] :
( ( Y
= ( append3889155854801840692nt_int @ Xs @ Y ) )
= ( Xs = nil_se54404438492013087nt_int ) ) ).
% self_append_conv2
thf(fact_78_self__append__conv2,axiom,
! [Y: list_P5707943133018811711nt_int,Xs: list_P5707943133018811711nt_int] :
( ( Y
= ( append7030698103840186580nt_int @ Xs @ Y ) )
= ( Xs = nil_Pr2300489316682597567nt_int ) ) ).
% self_append_conv2
thf(fact_79_not__Cons__self2,axiom,
! [X: list_P5707943133018811711nt_int,Xs: list_l1670014477004246597nt_int] :
( ( cons_l7309679040211256053nt_int @ X @ Xs )
!= Xs ) ).
% not_Cons_self2
thf(fact_80_not__Cons__self2,axiom,
! [X: set_Pr958786334691620121nt_int,Xs: list_s8839374986383574687nt_int] :
( ( cons_s6578334183908017615nt_int @ X @ Xs )
!= Xs ) ).
% not_Cons_self2
thf(fact_81_not__Cons__self2,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( cons_P3334398858971670639nt_int @ X @ Xs )
!= Xs ) ).
% not_Cons_self2
thf(fact_82_append__eq__append__conv2,axiom,
! [Xs: list_l1670014477004246597nt_int,Ys: list_l1670014477004246597nt_int,Zs: list_l1670014477004246597nt_int,Ts: list_l1670014477004246597nt_int] :
( ( ( append1237393811882493146nt_int @ Xs @ Ys )
= ( append1237393811882493146nt_int @ Zs @ Ts ) )
= ( ? [Us: list_l1670014477004246597nt_int] :
( ( ( Xs
= ( append1237393811882493146nt_int @ Zs @ Us ) )
& ( ( append1237393811882493146nt_int @ Us @ Ys )
= Ts ) )
| ( ( ( append1237393811882493146nt_int @ Xs @ Us )
= Zs )
& ( Ys
= ( append1237393811882493146nt_int @ Us @ Ts ) ) ) ) ) ) ).
% append_eq_append_conv2
thf(fact_83_append__eq__append__conv2,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int,Zs: list_P5707943133018811711nt_int,Ts: list_P5707943133018811711nt_int] :
( ( ( append7030698103840186580nt_int @ Xs @ Ys )
= ( append7030698103840186580nt_int @ Zs @ Ts ) )
= ( ? [Us: list_P5707943133018811711nt_int] :
( ( ( Xs
= ( append7030698103840186580nt_int @ Zs @ Us ) )
& ( ( append7030698103840186580nt_int @ Us @ Ys )
= Ts ) )
| ( ( ( append7030698103840186580nt_int @ Xs @ Us )
= Zs )
& ( Ys
= ( append7030698103840186580nt_int @ Us @ Ts ) ) ) ) ) ) ).
% append_eq_append_conv2
thf(fact_84_append__eq__appendI,axiom,
! [Xs: list_l1670014477004246597nt_int,Xs1: list_l1670014477004246597nt_int,Zs: list_l1670014477004246597nt_int,Ys: list_l1670014477004246597nt_int,Us2: list_l1670014477004246597nt_int] :
( ( ( append1237393811882493146nt_int @ Xs @ Xs1 )
= Zs )
=> ( ( Ys
= ( append1237393811882493146nt_int @ Xs1 @ Us2 ) )
=> ( ( append1237393811882493146nt_int @ Xs @ Ys )
= ( append1237393811882493146nt_int @ Zs @ Us2 ) ) ) ) ).
% append_eq_appendI
thf(fact_85_append__eq__appendI,axiom,
! [Xs: list_P5707943133018811711nt_int,Xs1: list_P5707943133018811711nt_int,Zs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int,Us2: list_P5707943133018811711nt_int] :
( ( ( append7030698103840186580nt_int @ Xs @ Xs1 )
= Zs )
=> ( ( Ys
= ( append7030698103840186580nt_int @ Xs1 @ Us2 ) )
=> ( ( append7030698103840186580nt_int @ Xs @ Ys )
= ( append7030698103840186580nt_int @ Zs @ Us2 ) ) ) ) ).
% append_eq_appendI
thf(fact_86_knights__path_Ointros_I2_J,axiom,
! [S_i: product_prod_int_int,B: set_Pr958786334691620121nt_int,S_j: product_prod_int_int,Ps: list_P5707943133018811711nt_int] :
( ~ ( member5262025264175285858nt_int @ S_i @ B )
=> ( ( valid_step @ S_i @ S_j )
=> ( ( knights_path @ B @ ( cons_P3334398858971670639nt_int @ S_j @ Ps ) )
=> ( knights_path @ ( sup_su6024340866399070445nt_int @ B @ ( insert5033312907999012233nt_int @ S_i @ bot_bo1796632182523588997nt_int ) ) @ ( cons_P3334398858971670639nt_int @ S_i @ ( cons_P3334398858971670639nt_int @ S_j @ Ps ) ) ) ) ) ) ).
% knights_path.intros(2)
thf(fact_87_knights__path__intro__rev,axiom,
! [S_i: product_prod_int_int,B: set_Pr958786334691620121nt_int,S_j: product_prod_int_int,Ps: list_P5707943133018811711nt_int] :
( ( member5262025264175285858nt_int @ S_i @ B )
=> ( ( valid_step @ S_i @ S_j )
=> ( ( knights_path @ ( minus_1052850069191792384nt_int @ B @ ( insert5033312907999012233nt_int @ S_i @ bot_bo1796632182523588997nt_int ) ) @ ( cons_P3334398858971670639nt_int @ S_j @ Ps ) )
=> ( knights_path @ B @ ( cons_P3334398858971670639nt_int @ S_i @ ( cons_P3334398858971670639nt_int @ S_j @ Ps ) ) ) ) ) ) ).
% knights_path_intro_rev
thf(fact_88_knights__path__board__non__empty,axiom,
! [B: set_Pr958786334691620121nt_int,Ps: list_P5707943133018811711nt_int] :
( ( knights_path @ B @ Ps )
=> ( B != bot_bo1796632182523588997nt_int ) ) ).
% knights_path_board_non_empty
thf(fact_89_knights__path_Osimps,axiom,
( knights_path
= ( ^ [A1: set_Pr958786334691620121nt_int,A2: list_P5707943133018811711nt_int] :
( ? [S_i2: product_prod_int_int] :
( ( A1
= ( insert5033312907999012233nt_int @ S_i2 @ bot_bo1796632182523588997nt_int ) )
& ( A2
= ( cons_P3334398858971670639nt_int @ S_i2 @ nil_Pr2300489316682597567nt_int ) ) )
| ? [S_i2: product_prod_int_int,B2: set_Pr958786334691620121nt_int,S_j2: product_prod_int_int,Ps2: list_P5707943133018811711nt_int] :
( ( A1
= ( sup_su6024340866399070445nt_int @ B2 @ ( insert5033312907999012233nt_int @ S_i2 @ bot_bo1796632182523588997nt_int ) ) )
& ( A2
= ( cons_P3334398858971670639nt_int @ S_i2 @ ( cons_P3334398858971670639nt_int @ S_j2 @ Ps2 ) ) )
& ~ ( member5262025264175285858nt_int @ S_i2 @ B2 )
& ( valid_step @ S_i2 @ S_j2 )
& ( knights_path @ B2 @ ( cons_P3334398858971670639nt_int @ S_j2 @ Ps2 ) ) ) ) ) ) ).
% knights_path.simps
thf(fact_90_knights__path_Ocases,axiom,
! [A12: set_Pr958786334691620121nt_int,A22: list_P5707943133018811711nt_int] :
( ( knights_path @ A12 @ A22 )
=> ( ! [S_i3: product_prod_int_int] :
( ( A12
= ( insert5033312907999012233nt_int @ S_i3 @ bot_bo1796632182523588997nt_int ) )
=> ( A22
!= ( cons_P3334398858971670639nt_int @ S_i3 @ nil_Pr2300489316682597567nt_int ) ) )
=> ~ ! [S_i3: product_prod_int_int,B3: set_Pr958786334691620121nt_int] :
( ( A12
= ( sup_su6024340866399070445nt_int @ B3 @ ( insert5033312907999012233nt_int @ S_i3 @ bot_bo1796632182523588997nt_int ) ) )
=> ! [S_j3: product_prod_int_int,Ps3: list_P5707943133018811711nt_int] :
( ( A22
= ( cons_P3334398858971670639nt_int @ S_i3 @ ( cons_P3334398858971670639nt_int @ S_j3 @ Ps3 ) ) )
=> ( ~ ( member5262025264175285858nt_int @ S_i3 @ B3 )
=> ( ( valid_step @ S_i3 @ S_j3 )
=> ~ ( knights_path @ B3 @ ( cons_P3334398858971670639nt_int @ S_j3 @ Ps3 ) ) ) ) ) ) ) ) ).
% knights_path.cases
thf(fact_91_mem__Collect__eq,axiom,
! [A: list_P5707943133018811711nt_int,P: list_P5707943133018811711nt_int > $o] :
( ( member2764346250752101224nt_int @ A @ ( collec3040439045487124906nt_int @ P ) )
= ( P @ A ) ) ).
% mem_Collect_eq
thf(fact_92_mem__Collect__eq,axiom,
! [A: set_Pr958786334691620121nt_int,P: set_Pr958786334691620121nt_int > $o] :
( ( member2340774599025711042nt_int @ A @ ( collec5210948495886036740nt_int @ P ) )
= ( P @ A ) ) ).
% mem_Collect_eq
thf(fact_93_mem__Collect__eq,axiom,
! [A: product_prod_int_int,P: product_prod_int_int > $o] :
( ( member5262025264175285858nt_int @ A @ ( collec213857154873943460nt_int @ P ) )
= ( P @ A ) ) ).
% mem_Collect_eq
thf(fact_94_Collect__mem__eq,axiom,
! [A3: set_li3855193629254082847nt_int] :
( ( collec3040439045487124906nt_int
@ ^ [X2: list_P5707943133018811711nt_int] : ( member2764346250752101224nt_int @ X2 @ A3 ) )
= A3 ) ).
% Collect_mem_eq
thf(fact_95_Collect__mem__eq,axiom,
! [A3: set_se6260736226359567993nt_int] :
( ( collec5210948495886036740nt_int
@ ^ [X2: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X2 @ A3 ) )
= A3 ) ).
% Collect_mem_eq
thf(fact_96_Collect__mem__eq,axiom,
! [A3: set_Pr958786334691620121nt_int] :
( ( collec213857154873943460nt_int
@ ^ [X2: product_prod_int_int] : ( member5262025264175285858nt_int @ X2 @ A3 ) )
= A3 ) ).
% Collect_mem_eq
thf(fact_97_Collect__cong,axiom,
! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
( ! [X3: product_prod_int_int] :
( ( P @ X3 )
= ( Q @ X3 ) )
=> ( ( collec213857154873943460nt_int @ P )
= ( collec213857154873943460nt_int @ Q ) ) ) ).
% Collect_cong
thf(fact_98_list__nonempty__induct,axiom,
! [Xs: list_int,P: list_int > $o] :
( ( Xs != nil_int )
=> ( ! [X3: int] : ( P @ ( cons_int @ X3 @ nil_int ) )
=> ( ! [X3: int,Xs2: list_int] :
( ( Xs2 != nil_int )
=> ( ( P @ Xs2 )
=> ( P @ ( cons_int @ X3 @ Xs2 ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_99_list__nonempty__induct,axiom,
! [Xs: list_l1670014477004246597nt_int,P: list_l1670014477004246597nt_int > $o] :
( ( Xs != nil_li8670148097206105925nt_int )
=> ( ! [X3: list_P5707943133018811711nt_int] : ( P @ ( cons_l7309679040211256053nt_int @ X3 @ nil_li8670148097206105925nt_int ) )
=> ( ! [X3: list_P5707943133018811711nt_int,Xs2: list_l1670014477004246597nt_int] :
( ( Xs2 != nil_li8670148097206105925nt_int )
=> ( ( P @ Xs2 )
=> ( P @ ( cons_l7309679040211256053nt_int @ X3 @ Xs2 ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_100_list__nonempty__induct,axiom,
! [Xs: list_s8839374986383574687nt_int,P: list_s8839374986383574687nt_int > $o] :
( ( Xs != nil_se54404438492013087nt_int )
=> ( ! [X3: set_Pr958786334691620121nt_int] : ( P @ ( cons_s6578334183908017615nt_int @ X3 @ nil_se54404438492013087nt_int ) )
=> ( ! [X3: set_Pr958786334691620121nt_int,Xs2: list_s8839374986383574687nt_int] :
( ( Xs2 != nil_se54404438492013087nt_int )
=> ( ( P @ Xs2 )
=> ( P @ ( cons_s6578334183908017615nt_int @ X3 @ Xs2 ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_101_list__nonempty__induct,axiom,
! [Xs: list_P5707943133018811711nt_int,P: list_P5707943133018811711nt_int > $o] :
( ( Xs != nil_Pr2300489316682597567nt_int )
=> ( ! [X3: product_prod_int_int] : ( P @ ( cons_P3334398858971670639nt_int @ X3 @ nil_Pr2300489316682597567nt_int ) )
=> ( ! [X3: product_prod_int_int,Xs2: list_P5707943133018811711nt_int] :
( ( Xs2 != nil_Pr2300489316682597567nt_int )
=> ( ( P @ Xs2 )
=> ( P @ ( cons_P3334398858971670639nt_int @ X3 @ Xs2 ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% list_nonempty_induct
thf(fact_102_list__induct2_H,axiom,
! [P: list_P5707943133018811711nt_int > list_P5707943133018811711nt_int > $o,Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( P @ nil_Pr2300489316682597567nt_int @ nil_Pr2300489316682597567nt_int )
=> ( ! [X3: product_prod_int_int,Xs2: list_P5707943133018811711nt_int] : ( P @ ( cons_P3334398858971670639nt_int @ X3 @ Xs2 ) @ nil_Pr2300489316682597567nt_int )
=> ( ! [Y2: product_prod_int_int,Ys2: list_P5707943133018811711nt_int] : ( P @ nil_Pr2300489316682597567nt_int @ ( cons_P3334398858971670639nt_int @ Y2 @ Ys2 ) )
=> ( ! [X3: product_prod_int_int,Xs2: list_P5707943133018811711nt_int,Y2: product_prod_int_int,Ys2: list_P5707943133018811711nt_int] :
( ( P @ Xs2 @ Ys2 )
=> ( P @ ( cons_P3334398858971670639nt_int @ X3 @ Xs2 ) @ ( cons_P3334398858971670639nt_int @ Y2 @ Ys2 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_103_list__induct2_H,axiom,
! [P: list_int > list_int > $o,Xs: list_int,Ys: list_int] :
( ( P @ nil_int @ nil_int )
=> ( ! [X3: int,Xs2: list_int] : ( P @ ( cons_int @ X3 @ Xs2 ) @ nil_int )
=> ( ! [Y2: int,Ys2: list_int] : ( P @ nil_int @ ( cons_int @ Y2 @ Ys2 ) )
=> ( ! [X3: int,Xs2: list_int,Y2: int,Ys2: list_int] :
( ( P @ Xs2 @ Ys2 )
=> ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys2 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_104_list__induct2_H,axiom,
! [P: list_int > list_P5707943133018811711nt_int > $o,Xs: list_int,Ys: list_P5707943133018811711nt_int] :
( ( P @ nil_int @ nil_Pr2300489316682597567nt_int )
=> ( ! [X3: int,Xs2: list_int] : ( P @ ( cons_int @ X3 @ Xs2 ) @ nil_Pr2300489316682597567nt_int )
=> ( ! [Y2: product_prod_int_int,Ys2: list_P5707943133018811711nt_int] : ( P @ nil_int @ ( cons_P3334398858971670639nt_int @ Y2 @ Ys2 ) )
=> ( ! [X3: int,Xs2: list_int,Y2: product_prod_int_int,Ys2: list_P5707943133018811711nt_int] :
( ( P @ Xs2 @ Ys2 )
=> ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_P3334398858971670639nt_int @ Y2 @ Ys2 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_105_list__induct2_H,axiom,
! [P: list_P5707943133018811711nt_int > list_int > $o,Xs: list_P5707943133018811711nt_int,Ys: list_int] :
( ( P @ nil_Pr2300489316682597567nt_int @ nil_int )
=> ( ! [X3: product_prod_int_int,Xs2: list_P5707943133018811711nt_int] : ( P @ ( cons_P3334398858971670639nt_int @ X3 @ Xs2 ) @ nil_int )
=> ( ! [Y2: int,Ys2: list_int] : ( P @ nil_Pr2300489316682597567nt_int @ ( cons_int @ Y2 @ Ys2 ) )
=> ( ! [X3: product_prod_int_int,Xs2: list_P5707943133018811711nt_int,Y2: int,Ys2: list_int] :
( ( P @ Xs2 @ Ys2 )
=> ( P @ ( cons_P3334398858971670639nt_int @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys2 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_106_list__induct2_H,axiom,
! [P: list_int > list_l1670014477004246597nt_int > $o,Xs: list_int,Ys: list_l1670014477004246597nt_int] :
( ( P @ nil_int @ nil_li8670148097206105925nt_int )
=> ( ! [X3: int,Xs2: list_int] : ( P @ ( cons_int @ X3 @ Xs2 ) @ nil_li8670148097206105925nt_int )
=> ( ! [Y2: list_P5707943133018811711nt_int,Ys2: list_l1670014477004246597nt_int] : ( P @ nil_int @ ( cons_l7309679040211256053nt_int @ Y2 @ Ys2 ) )
=> ( ! [X3: int,Xs2: list_int,Y2: list_P5707943133018811711nt_int,Ys2: list_l1670014477004246597nt_int] :
( ( P @ Xs2 @ Ys2 )
=> ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_l7309679040211256053nt_int @ Y2 @ Ys2 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_107_list__induct2_H,axiom,
! [P: list_int > list_s8839374986383574687nt_int > $o,Xs: list_int,Ys: list_s8839374986383574687nt_int] :
( ( P @ nil_int @ nil_se54404438492013087nt_int )
=> ( ! [X3: int,Xs2: list_int] : ( P @ ( cons_int @ X3 @ Xs2 ) @ nil_se54404438492013087nt_int )
=> ( ! [Y2: set_Pr958786334691620121nt_int,Ys2: list_s8839374986383574687nt_int] : ( P @ nil_int @ ( cons_s6578334183908017615nt_int @ Y2 @ Ys2 ) )
=> ( ! [X3: int,Xs2: list_int,Y2: set_Pr958786334691620121nt_int,Ys2: list_s8839374986383574687nt_int] :
( ( P @ Xs2 @ Ys2 )
=> ( P @ ( cons_int @ X3 @ Xs2 ) @ ( cons_s6578334183908017615nt_int @ Y2 @ Ys2 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_108_list__induct2_H,axiom,
! [P: list_l1670014477004246597nt_int > list_int > $o,Xs: list_l1670014477004246597nt_int,Ys: list_int] :
( ( P @ nil_li8670148097206105925nt_int @ nil_int )
=> ( ! [X3: list_P5707943133018811711nt_int,Xs2: list_l1670014477004246597nt_int] : ( P @ ( cons_l7309679040211256053nt_int @ X3 @ Xs2 ) @ nil_int )
=> ( ! [Y2: int,Ys2: list_int] : ( P @ nil_li8670148097206105925nt_int @ ( cons_int @ Y2 @ Ys2 ) )
=> ( ! [X3: list_P5707943133018811711nt_int,Xs2: list_l1670014477004246597nt_int,Y2: int,Ys2: list_int] :
( ( P @ Xs2 @ Ys2 )
=> ( P @ ( cons_l7309679040211256053nt_int @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys2 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_109_list__induct2_H,axiom,
! [P: list_s8839374986383574687nt_int > list_int > $o,Xs: list_s8839374986383574687nt_int,Ys: list_int] :
( ( P @ nil_se54404438492013087nt_int @ nil_int )
=> ( ! [X3: set_Pr958786334691620121nt_int,Xs2: list_s8839374986383574687nt_int] : ( P @ ( cons_s6578334183908017615nt_int @ X3 @ Xs2 ) @ nil_int )
=> ( ! [Y2: int,Ys2: list_int] : ( P @ nil_se54404438492013087nt_int @ ( cons_int @ Y2 @ Ys2 ) )
=> ( ! [X3: set_Pr958786334691620121nt_int,Xs2: list_s8839374986383574687nt_int,Y2: int,Ys2: list_int] :
( ( P @ Xs2 @ Ys2 )
=> ( P @ ( cons_s6578334183908017615nt_int @ X3 @ Xs2 ) @ ( cons_int @ Y2 @ Ys2 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_110_list__induct2_H,axiom,
! [P: list_P5707943133018811711nt_int > list_l1670014477004246597nt_int > $o,Xs: list_P5707943133018811711nt_int,Ys: list_l1670014477004246597nt_int] :
( ( P @ nil_Pr2300489316682597567nt_int @ nil_li8670148097206105925nt_int )
=> ( ! [X3: product_prod_int_int,Xs2: list_P5707943133018811711nt_int] : ( P @ ( cons_P3334398858971670639nt_int @ X3 @ Xs2 ) @ nil_li8670148097206105925nt_int )
=> ( ! [Y2: list_P5707943133018811711nt_int,Ys2: list_l1670014477004246597nt_int] : ( P @ nil_Pr2300489316682597567nt_int @ ( cons_l7309679040211256053nt_int @ Y2 @ Ys2 ) )
=> ( ! [X3: product_prod_int_int,Xs2: list_P5707943133018811711nt_int,Y2: list_P5707943133018811711nt_int,Ys2: list_l1670014477004246597nt_int] :
( ( P @ Xs2 @ Ys2 )
=> ( P @ ( cons_P3334398858971670639nt_int @ X3 @ Xs2 ) @ ( cons_l7309679040211256053nt_int @ Y2 @ Ys2 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_111_list__induct2_H,axiom,
! [P: list_P5707943133018811711nt_int > list_s8839374986383574687nt_int > $o,Xs: list_P5707943133018811711nt_int,Ys: list_s8839374986383574687nt_int] :
( ( P @ nil_Pr2300489316682597567nt_int @ nil_se54404438492013087nt_int )
=> ( ! [X3: product_prod_int_int,Xs2: list_P5707943133018811711nt_int] : ( P @ ( cons_P3334398858971670639nt_int @ X3 @ Xs2 ) @ nil_se54404438492013087nt_int )
=> ( ! [Y2: set_Pr958786334691620121nt_int,Ys2: list_s8839374986383574687nt_int] : ( P @ nil_Pr2300489316682597567nt_int @ ( cons_s6578334183908017615nt_int @ Y2 @ Ys2 ) )
=> ( ! [X3: product_prod_int_int,Xs2: list_P5707943133018811711nt_int,Y2: set_Pr958786334691620121nt_int,Ys2: list_s8839374986383574687nt_int] :
( ( P @ Xs2 @ Ys2 )
=> ( P @ ( cons_P3334398858971670639nt_int @ X3 @ Xs2 ) @ ( cons_s6578334183908017615nt_int @ Y2 @ Ys2 ) ) )
=> ( P @ Xs @ Ys ) ) ) ) ) ).
% list_induct2'
thf(fact_112_neq__Nil__conv,axiom,
! [Xs: list_int] :
( ( Xs != nil_int )
= ( ? [Y3: int,Ys3: list_int] :
( Xs
= ( cons_int @ Y3 @ Ys3 ) ) ) ) ).
% neq_Nil_conv
thf(fact_113_neq__Nil__conv,axiom,
! [Xs: list_l1670014477004246597nt_int] :
( ( Xs != nil_li8670148097206105925nt_int )
= ( ? [Y3: list_P5707943133018811711nt_int,Ys3: list_l1670014477004246597nt_int] :
( Xs
= ( cons_l7309679040211256053nt_int @ Y3 @ Ys3 ) ) ) ) ).
% neq_Nil_conv
thf(fact_114_neq__Nil__conv,axiom,
! [Xs: list_s8839374986383574687nt_int] :
( ( Xs != nil_se54404438492013087nt_int )
= ( ? [Y3: set_Pr958786334691620121nt_int,Ys3: list_s8839374986383574687nt_int] :
( Xs
= ( cons_s6578334183908017615nt_int @ Y3 @ Ys3 ) ) ) ) ).
% neq_Nil_conv
thf(fact_115_neq__Nil__conv,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( Xs != nil_Pr2300489316682597567nt_int )
= ( ? [Y3: product_prod_int_int,Ys3: list_P5707943133018811711nt_int] :
( Xs
= ( cons_P3334398858971670639nt_int @ Y3 @ Ys3 ) ) ) ) ).
% neq_Nil_conv
thf(fact_116_remdups__adj_Ocases,axiom,
! [X: list_int] :
( ( X != nil_int )
=> ( ! [X3: int] :
( X
!= ( cons_int @ X3 @ nil_int ) )
=> ~ ! [X3: int,Y2: int,Xs2: list_int] :
( X
!= ( cons_int @ X3 @ ( cons_int @ Y2 @ Xs2 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_117_remdups__adj_Ocases,axiom,
! [X: list_l1670014477004246597nt_int] :
( ( X != nil_li8670148097206105925nt_int )
=> ( ! [X3: list_P5707943133018811711nt_int] :
( X
!= ( cons_l7309679040211256053nt_int @ X3 @ nil_li8670148097206105925nt_int ) )
=> ~ ! [X3: list_P5707943133018811711nt_int,Y2: list_P5707943133018811711nt_int,Xs2: list_l1670014477004246597nt_int] :
( X
!= ( cons_l7309679040211256053nt_int @ X3 @ ( cons_l7309679040211256053nt_int @ Y2 @ Xs2 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_118_remdups__adj_Ocases,axiom,
! [X: list_s8839374986383574687nt_int] :
( ( X != nil_se54404438492013087nt_int )
=> ( ! [X3: set_Pr958786334691620121nt_int] :
( X
!= ( cons_s6578334183908017615nt_int @ X3 @ nil_se54404438492013087nt_int ) )
=> ~ ! [X3: set_Pr958786334691620121nt_int,Y2: set_Pr958786334691620121nt_int,Xs2: list_s8839374986383574687nt_int] :
( X
!= ( cons_s6578334183908017615nt_int @ X3 @ ( cons_s6578334183908017615nt_int @ Y2 @ Xs2 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_119_remdups__adj_Ocases,axiom,
! [X: list_P5707943133018811711nt_int] :
( ( X != nil_Pr2300489316682597567nt_int )
=> ( ! [X3: product_prod_int_int] :
( X
!= ( cons_P3334398858971670639nt_int @ X3 @ nil_Pr2300489316682597567nt_int ) )
=> ~ ! [X3: product_prod_int_int,Y2: product_prod_int_int,Xs2: list_P5707943133018811711nt_int] :
( X
!= ( cons_P3334398858971670639nt_int @ X3 @ ( cons_P3334398858971670639nt_int @ Y2 @ Xs2 ) ) ) ) ) ).
% remdups_adj.cases
thf(fact_120_transpose_Ocases,axiom,
! [X: list_list_int] :
( ( X != nil_list_int )
=> ( ! [Xss: list_list_int] :
( X
!= ( cons_list_int @ nil_int @ Xss ) )
=> ~ ! [X3: int,Xs2: list_int,Xss: list_list_int] :
( X
!= ( cons_list_int @ ( cons_int @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_121_transpose_Ocases,axiom,
! [X: list_l2734933928136073931nt_int] :
( ( X != nil_li8254795547437800779nt_int )
=> ( ! [Xss: list_l2734933928136073931nt_int] :
( X
!= ( cons_l4848925899132326139nt_int @ nil_li8670148097206105925nt_int @ Xss ) )
=> ~ ! [X3: list_P5707943133018811711nt_int,Xs2: list_l1670014477004246597nt_int,Xss: list_l2734933928136073931nt_int] :
( X
!= ( cons_l4848925899132326139nt_int @ ( cons_l7309679040211256053nt_int @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_122_transpose_Ocases,axiom,
! [X: list_l2036039776804522917nt_int] :
( ( X != nil_li5787722104129124517nt_int )
=> ( ! [Xss: list_l2036039776804522917nt_int] :
( X
!= ( cons_l2735253805790495829nt_int @ nil_se54404438492013087nt_int @ Xss ) )
=> ~ ! [X3: set_Pr958786334691620121nt_int,Xs2: list_s8839374986383574687nt_int,Xss: list_l2036039776804522917nt_int] :
( X
!= ( cons_l2735253805790495829nt_int @ ( cons_s6578334183908017615nt_int @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_123_transpose_Ocases,axiom,
! [X: list_l1670014477004246597nt_int] :
( ( X != nil_li8670148097206105925nt_int )
=> ( ! [Xss: list_l1670014477004246597nt_int] :
( X
!= ( cons_l7309679040211256053nt_int @ nil_Pr2300489316682597567nt_int @ Xss ) )
=> ~ ! [X3: product_prod_int_int,Xs2: list_P5707943133018811711nt_int,Xss: list_l1670014477004246597nt_int] :
( X
!= ( cons_l7309679040211256053nt_int @ ( cons_P3334398858971670639nt_int @ X3 @ Xs2 ) @ Xss ) ) ) ) ).
% transpose.cases
thf(fact_124_min__list_Ocases,axiom,
! [X: list_int] :
( ! [X3: int,Xs2: list_int] :
( X
!= ( cons_int @ X3 @ Xs2 ) )
=> ( X = nil_int ) ) ).
% min_list.cases
thf(fact_125_min__list_Ocases,axiom,
! [X: list_s8839374986383574687nt_int] :
( ! [X3: set_Pr958786334691620121nt_int,Xs2: list_s8839374986383574687nt_int] :
( X
!= ( cons_s6578334183908017615nt_int @ X3 @ Xs2 ) )
=> ( X = nil_se54404438492013087nt_int ) ) ).
% min_list.cases
thf(fact_126_list_Oexhaust,axiom,
! [Y: list_int] :
( ( Y != nil_int )
=> ~ ! [X212: int,X222: list_int] :
( Y
!= ( cons_int @ X212 @ X222 ) ) ) ).
% list.exhaust
thf(fact_127_list_Oexhaust,axiom,
! [Y: list_l1670014477004246597nt_int] :
( ( Y != nil_li8670148097206105925nt_int )
=> ~ ! [X212: list_P5707943133018811711nt_int,X222: list_l1670014477004246597nt_int] :
( Y
!= ( cons_l7309679040211256053nt_int @ X212 @ X222 ) ) ) ).
% list.exhaust
thf(fact_128_list_Oexhaust,axiom,
! [Y: list_s8839374986383574687nt_int] :
( ( Y != nil_se54404438492013087nt_int )
=> ~ ! [X212: set_Pr958786334691620121nt_int,X222: list_s8839374986383574687nt_int] :
( Y
!= ( cons_s6578334183908017615nt_int @ X212 @ X222 ) ) ) ).
% list.exhaust
thf(fact_129_list_Oexhaust,axiom,
! [Y: list_P5707943133018811711nt_int] :
( ( Y != nil_Pr2300489316682597567nt_int )
=> ~ ! [X212: product_prod_int_int,X222: list_P5707943133018811711nt_int] :
( Y
!= ( cons_P3334398858971670639nt_int @ X212 @ X222 ) ) ) ).
% list.exhaust
thf(fact_130_list_OdiscI,axiom,
! [List: list_int,X21: int,X22: list_int] :
( ( List
= ( cons_int @ X21 @ X22 ) )
=> ( List != nil_int ) ) ).
% list.discI
thf(fact_131_list_OdiscI,axiom,
! [List: list_l1670014477004246597nt_int,X21: list_P5707943133018811711nt_int,X22: list_l1670014477004246597nt_int] :
( ( List
= ( cons_l7309679040211256053nt_int @ X21 @ X22 ) )
=> ( List != nil_li8670148097206105925nt_int ) ) ).
% list.discI
thf(fact_132_list_OdiscI,axiom,
! [List: list_s8839374986383574687nt_int,X21: set_Pr958786334691620121nt_int,X22: list_s8839374986383574687nt_int] :
( ( List
= ( cons_s6578334183908017615nt_int @ X21 @ X22 ) )
=> ( List != nil_se54404438492013087nt_int ) ) ).
% list.discI
thf(fact_133_list_OdiscI,axiom,
! [List: list_P5707943133018811711nt_int,X21: product_prod_int_int,X22: list_P5707943133018811711nt_int] :
( ( List
= ( cons_P3334398858971670639nt_int @ X21 @ X22 ) )
=> ( List != nil_Pr2300489316682597567nt_int ) ) ).
% list.discI
thf(fact_134_list_Odistinct_I1_J,axiom,
! [X21: int,X22: list_int] :
( nil_int
!= ( cons_int @ X21 @ X22 ) ) ).
% list.distinct(1)
thf(fact_135_list_Odistinct_I1_J,axiom,
! [X21: list_P5707943133018811711nt_int,X22: list_l1670014477004246597nt_int] :
( nil_li8670148097206105925nt_int
!= ( cons_l7309679040211256053nt_int @ X21 @ X22 ) ) ).
% list.distinct(1)
thf(fact_136_list_Odistinct_I1_J,axiom,
! [X21: set_Pr958786334691620121nt_int,X22: list_s8839374986383574687nt_int] :
( nil_se54404438492013087nt_int
!= ( cons_s6578334183908017615nt_int @ X21 @ X22 ) ) ).
% list.distinct(1)
thf(fact_137_list_Odistinct_I1_J,axiom,
! [X21: product_prod_int_int,X22: list_P5707943133018811711nt_int] :
( nil_Pr2300489316682597567nt_int
!= ( cons_P3334398858971670639nt_int @ X21 @ X22 ) ) ).
% list.distinct(1)
thf(fact_138_Cons__eq__appendI,axiom,
! [X: list_P5707943133018811711nt_int,Xs1: list_l1670014477004246597nt_int,Ys: list_l1670014477004246597nt_int,Xs: list_l1670014477004246597nt_int,Zs: list_l1670014477004246597nt_int] :
( ( ( cons_l7309679040211256053nt_int @ X @ Xs1 )
= Ys )
=> ( ( Xs
= ( append1237393811882493146nt_int @ Xs1 @ Zs ) )
=> ( ( cons_l7309679040211256053nt_int @ X @ Xs )
= ( append1237393811882493146nt_int @ Ys @ Zs ) ) ) ) ).
% Cons_eq_appendI
thf(fact_139_Cons__eq__appendI,axiom,
! [X: set_Pr958786334691620121nt_int,Xs1: list_s8839374986383574687nt_int,Ys: list_s8839374986383574687nt_int,Xs: list_s8839374986383574687nt_int,Zs: list_s8839374986383574687nt_int] :
( ( ( cons_s6578334183908017615nt_int @ X @ Xs1 )
= Ys )
=> ( ( Xs
= ( append3889155854801840692nt_int @ Xs1 @ Zs ) )
=> ( ( cons_s6578334183908017615nt_int @ X @ Xs )
= ( append3889155854801840692nt_int @ Ys @ Zs ) ) ) ) ).
% Cons_eq_appendI
thf(fact_140_Cons__eq__appendI,axiom,
! [X: product_prod_int_int,Xs1: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int,Xs: list_P5707943133018811711nt_int,Zs: list_P5707943133018811711nt_int] :
( ( ( cons_P3334398858971670639nt_int @ X @ Xs1 )
= Ys )
=> ( ( Xs
= ( append7030698103840186580nt_int @ Xs1 @ Zs ) )
=> ( ( cons_P3334398858971670639nt_int @ X @ Xs )
= ( append7030698103840186580nt_int @ Ys @ Zs ) ) ) ) ).
% Cons_eq_appendI
thf(fact_141_append__Cons,axiom,
! [X: list_P5707943133018811711nt_int,Xs: list_l1670014477004246597nt_int,Ys: list_l1670014477004246597nt_int] :
( ( append1237393811882493146nt_int @ ( cons_l7309679040211256053nt_int @ X @ Xs ) @ Ys )
= ( cons_l7309679040211256053nt_int @ X @ ( append1237393811882493146nt_int @ Xs @ Ys ) ) ) ).
% append_Cons
thf(fact_142_append__Cons,axiom,
! [X: set_Pr958786334691620121nt_int,Xs: list_s8839374986383574687nt_int,Ys: list_s8839374986383574687nt_int] :
( ( append3889155854801840692nt_int @ ( cons_s6578334183908017615nt_int @ X @ Xs ) @ Ys )
= ( cons_s6578334183908017615nt_int @ X @ ( append3889155854801840692nt_int @ Xs @ Ys ) ) ) ).
% append_Cons
thf(fact_143_append__Cons,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( append7030698103840186580nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) @ Ys )
= ( cons_P3334398858971670639nt_int @ X @ ( append7030698103840186580nt_int @ Xs @ Ys ) ) ) ).
% append_Cons
thf(fact_144_eq__Nil__appendI,axiom,
! [Xs: list_l1670014477004246597nt_int,Ys: list_l1670014477004246597nt_int] :
( ( Xs = Ys )
=> ( Xs
= ( append1237393811882493146nt_int @ nil_li8670148097206105925nt_int @ Ys ) ) ) ).
% eq_Nil_appendI
thf(fact_145_eq__Nil__appendI,axiom,
! [Xs: list_int,Ys: list_int] :
( ( Xs = Ys )
=> ( Xs
= ( append_int @ nil_int @ Ys ) ) ) ).
% eq_Nil_appendI
thf(fact_146_eq__Nil__appendI,axiom,
! [Xs: list_s8839374986383574687nt_int,Ys: list_s8839374986383574687nt_int] :
( ( Xs = Ys )
=> ( Xs
= ( append3889155854801840692nt_int @ nil_se54404438492013087nt_int @ Ys ) ) ) ).
% eq_Nil_appendI
thf(fact_147_eq__Nil__appendI,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( Xs = Ys )
=> ( Xs
= ( append7030698103840186580nt_int @ nil_Pr2300489316682597567nt_int @ Ys ) ) ) ).
% eq_Nil_appendI
thf(fact_148_append_Oleft__neutral,axiom,
! [A: list_l1670014477004246597nt_int] :
( ( append1237393811882493146nt_int @ nil_li8670148097206105925nt_int @ A )
= A ) ).
% append.left_neutral
thf(fact_149_append_Oleft__neutral,axiom,
! [A: list_int] :
( ( append_int @ nil_int @ A )
= A ) ).
% append.left_neutral
thf(fact_150_append_Oleft__neutral,axiom,
! [A: list_s8839374986383574687nt_int] :
( ( append3889155854801840692nt_int @ nil_se54404438492013087nt_int @ A )
= A ) ).
% append.left_neutral
thf(fact_151_append_Oleft__neutral,axiom,
! [A: list_P5707943133018811711nt_int] :
( ( append7030698103840186580nt_int @ nil_Pr2300489316682597567nt_int @ A )
= A ) ).
% append.left_neutral
thf(fact_152_append__Nil,axiom,
! [Ys: list_l1670014477004246597nt_int] :
( ( append1237393811882493146nt_int @ nil_li8670148097206105925nt_int @ Ys )
= Ys ) ).
% append_Nil
thf(fact_153_append__Nil,axiom,
! [Ys: list_int] :
( ( append_int @ nil_int @ Ys )
= Ys ) ).
% append_Nil
thf(fact_154_append__Nil,axiom,
! [Ys: list_s8839374986383574687nt_int] :
( ( append3889155854801840692nt_int @ nil_se54404438492013087nt_int @ Ys )
= Ys ) ).
% append_Nil
thf(fact_155_append__Nil,axiom,
! [Ys: list_P5707943133018811711nt_int] :
( ( append7030698103840186580nt_int @ nil_Pr2300489316682597567nt_int @ Ys )
= Ys ) ).
% append_Nil
thf(fact_156_list_Osel_I1_J,axiom,
! [X21: list_P5707943133018811711nt_int,X22: list_l1670014477004246597nt_int] :
( ( hd_lis8550591025403828010nt_int @ ( cons_l7309679040211256053nt_int @ X21 @ X22 ) )
= X21 ) ).
% list.sel(1)
thf(fact_157_list_Osel_I1_J,axiom,
! [X21: set_Pr958786334691620121nt_int,X22: list_s8839374986383574687nt_int] :
( ( hd_set5458074601020007556nt_int @ ( cons_s6578334183908017615nt_int @ X21 @ X22 ) )
= X21 ) ).
% list.sel(1)
thf(fact_158_list_Osel_I1_J,axiom,
! [X21: product_prod_int_int,X22: list_P5707943133018811711nt_int] :
( ( hd_Pro282112905867057956nt_int @ ( cons_P3334398858971670639nt_int @ X21 @ X22 ) )
= X21 ) ).
% list.sel(1)
thf(fact_159_knights__path_Ointros_I1_J,axiom,
! [S_i: product_prod_int_int] : ( knights_path @ ( insert5033312907999012233nt_int @ S_i @ bot_bo1796632182523588997nt_int ) @ ( cons_P3334398858971670639nt_int @ S_i @ nil_Pr2300489316682597567nt_int ) ) ).
% knights_path.intros(1)
thf(fact_160_rev__nonempty__induct,axiom,
! [Xs: list_int,P: list_int > $o] :
( ( Xs != nil_int )
=> ( ! [X3: int] : ( P @ ( cons_int @ X3 @ nil_int ) )
=> ( ! [X3: int,Xs2: list_int] :
( ( Xs2 != nil_int )
=> ( ( P @ Xs2 )
=> ( P @ ( append_int @ Xs2 @ ( cons_int @ X3 @ nil_int ) ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% rev_nonempty_induct
thf(fact_161_rev__nonempty__induct,axiom,
! [Xs: list_l1670014477004246597nt_int,P: list_l1670014477004246597nt_int > $o] :
( ( Xs != nil_li8670148097206105925nt_int )
=> ( ! [X3: list_P5707943133018811711nt_int] : ( P @ ( cons_l7309679040211256053nt_int @ X3 @ nil_li8670148097206105925nt_int ) )
=> ( ! [X3: list_P5707943133018811711nt_int,Xs2: list_l1670014477004246597nt_int] :
( ( Xs2 != nil_li8670148097206105925nt_int )
=> ( ( P @ Xs2 )
=> ( P @ ( append1237393811882493146nt_int @ Xs2 @ ( cons_l7309679040211256053nt_int @ X3 @ nil_li8670148097206105925nt_int ) ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% rev_nonempty_induct
thf(fact_162_rev__nonempty__induct,axiom,
! [Xs: list_s8839374986383574687nt_int,P: list_s8839374986383574687nt_int > $o] :
( ( Xs != nil_se54404438492013087nt_int )
=> ( ! [X3: set_Pr958786334691620121nt_int] : ( P @ ( cons_s6578334183908017615nt_int @ X3 @ nil_se54404438492013087nt_int ) )
=> ( ! [X3: set_Pr958786334691620121nt_int,Xs2: list_s8839374986383574687nt_int] :
( ( Xs2 != nil_se54404438492013087nt_int )
=> ( ( P @ Xs2 )
=> ( P @ ( append3889155854801840692nt_int @ Xs2 @ ( cons_s6578334183908017615nt_int @ X3 @ nil_se54404438492013087nt_int ) ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% rev_nonempty_induct
thf(fact_163_rev__nonempty__induct,axiom,
! [Xs: list_P5707943133018811711nt_int,P: list_P5707943133018811711nt_int > $o] :
( ( Xs != nil_Pr2300489316682597567nt_int )
=> ( ! [X3: product_prod_int_int] : ( P @ ( cons_P3334398858971670639nt_int @ X3 @ nil_Pr2300489316682597567nt_int ) )
=> ( ! [X3: product_prod_int_int,Xs2: list_P5707943133018811711nt_int] :
( ( Xs2 != nil_Pr2300489316682597567nt_int )
=> ( ( P @ Xs2 )
=> ( P @ ( append7030698103840186580nt_int @ Xs2 @ ( cons_P3334398858971670639nt_int @ X3 @ nil_Pr2300489316682597567nt_int ) ) ) ) )
=> ( P @ Xs ) ) ) ) ).
% rev_nonempty_induct
thf(fact_164_append__eq__Cons__conv,axiom,
! [Ys: list_int,Zs: list_int,X: int,Xs: list_int] :
( ( ( append_int @ Ys @ Zs )
= ( cons_int @ X @ Xs ) )
= ( ( ( Ys = nil_int )
& ( Zs
= ( cons_int @ X @ Xs ) ) )
| ? [Ys4: list_int] :
( ( Ys
= ( cons_int @ X @ Ys4 ) )
& ( ( append_int @ Ys4 @ Zs )
= Xs ) ) ) ) ).
% append_eq_Cons_conv
thf(fact_165_append__eq__Cons__conv,axiom,
! [Ys: list_l1670014477004246597nt_int,Zs: list_l1670014477004246597nt_int,X: list_P5707943133018811711nt_int,Xs: list_l1670014477004246597nt_int] :
( ( ( append1237393811882493146nt_int @ Ys @ Zs )
= ( cons_l7309679040211256053nt_int @ X @ Xs ) )
= ( ( ( Ys = nil_li8670148097206105925nt_int )
& ( Zs
= ( cons_l7309679040211256053nt_int @ X @ Xs ) ) )
| ? [Ys4: list_l1670014477004246597nt_int] :
( ( Ys
= ( cons_l7309679040211256053nt_int @ X @ Ys4 ) )
& ( ( append1237393811882493146nt_int @ Ys4 @ Zs )
= Xs ) ) ) ) ).
% append_eq_Cons_conv
thf(fact_166_append__eq__Cons__conv,axiom,
! [Ys: list_s8839374986383574687nt_int,Zs: list_s8839374986383574687nt_int,X: set_Pr958786334691620121nt_int,Xs: list_s8839374986383574687nt_int] :
( ( ( append3889155854801840692nt_int @ Ys @ Zs )
= ( cons_s6578334183908017615nt_int @ X @ Xs ) )
= ( ( ( Ys = nil_se54404438492013087nt_int )
& ( Zs
= ( cons_s6578334183908017615nt_int @ X @ Xs ) ) )
| ? [Ys4: list_s8839374986383574687nt_int] :
( ( Ys
= ( cons_s6578334183908017615nt_int @ X @ Ys4 ) )
& ( ( append3889155854801840692nt_int @ Ys4 @ Zs )
= Xs ) ) ) ) ).
% append_eq_Cons_conv
thf(fact_167_append__eq__Cons__conv,axiom,
! [Ys: list_P5707943133018811711nt_int,Zs: list_P5707943133018811711nt_int,X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( ( append7030698103840186580nt_int @ Ys @ Zs )
= ( cons_P3334398858971670639nt_int @ X @ Xs ) )
= ( ( ( Ys = nil_Pr2300489316682597567nt_int )
& ( Zs
= ( cons_P3334398858971670639nt_int @ X @ Xs ) ) )
| ? [Ys4: list_P5707943133018811711nt_int] :
( ( Ys
= ( cons_P3334398858971670639nt_int @ X @ Ys4 ) )
& ( ( append7030698103840186580nt_int @ Ys4 @ Zs )
= Xs ) ) ) ) ).
% append_eq_Cons_conv
thf(fact_168_Cons__eq__append__conv,axiom,
! [X: int,Xs: list_int,Ys: list_int,Zs: list_int] :
( ( ( cons_int @ X @ Xs )
= ( append_int @ Ys @ Zs ) )
= ( ( ( Ys = nil_int )
& ( ( cons_int @ X @ Xs )
= Zs ) )
| ? [Ys4: list_int] :
( ( ( cons_int @ X @ Ys4 )
= Ys )
& ( Xs
= ( append_int @ Ys4 @ Zs ) ) ) ) ) ).
% Cons_eq_append_conv
thf(fact_169_Cons__eq__append__conv,axiom,
! [X: list_P5707943133018811711nt_int,Xs: list_l1670014477004246597nt_int,Ys: list_l1670014477004246597nt_int,Zs: list_l1670014477004246597nt_int] :
( ( ( cons_l7309679040211256053nt_int @ X @ Xs )
= ( append1237393811882493146nt_int @ Ys @ Zs ) )
= ( ( ( Ys = nil_li8670148097206105925nt_int )
& ( ( cons_l7309679040211256053nt_int @ X @ Xs )
= Zs ) )
| ? [Ys4: list_l1670014477004246597nt_int] :
( ( ( cons_l7309679040211256053nt_int @ X @ Ys4 )
= Ys )
& ( Xs
= ( append1237393811882493146nt_int @ Ys4 @ Zs ) ) ) ) ) ).
% Cons_eq_append_conv
thf(fact_170_Cons__eq__append__conv,axiom,
! [X: set_Pr958786334691620121nt_int,Xs: list_s8839374986383574687nt_int,Ys: list_s8839374986383574687nt_int,Zs: list_s8839374986383574687nt_int] :
( ( ( cons_s6578334183908017615nt_int @ X @ Xs )
= ( append3889155854801840692nt_int @ Ys @ Zs ) )
= ( ( ( Ys = nil_se54404438492013087nt_int )
& ( ( cons_s6578334183908017615nt_int @ X @ Xs )
= Zs ) )
| ? [Ys4: list_s8839374986383574687nt_int] :
( ( ( cons_s6578334183908017615nt_int @ X @ Ys4 )
= Ys )
& ( Xs
= ( append3889155854801840692nt_int @ Ys4 @ Zs ) ) ) ) ) ).
% Cons_eq_append_conv
thf(fact_171_Cons__eq__append__conv,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int,Zs: list_P5707943133018811711nt_int] :
( ( ( cons_P3334398858971670639nt_int @ X @ Xs )
= ( append7030698103840186580nt_int @ Ys @ Zs ) )
= ( ( ( Ys = nil_Pr2300489316682597567nt_int )
& ( ( cons_P3334398858971670639nt_int @ X @ Xs )
= Zs ) )
| ? [Ys4: list_P5707943133018811711nt_int] :
( ( ( cons_P3334398858971670639nt_int @ X @ Ys4 )
= Ys )
& ( Xs
= ( append7030698103840186580nt_int @ Ys4 @ Zs ) ) ) ) ) ).
% Cons_eq_append_conv
thf(fact_172_rev__exhaust,axiom,
! [Xs: list_int] :
( ( Xs != nil_int )
=> ~ ! [Ys2: list_int,Y2: int] :
( Xs
!= ( append_int @ Ys2 @ ( cons_int @ Y2 @ nil_int ) ) ) ) ).
% rev_exhaust
thf(fact_173_rev__exhaust,axiom,
! [Xs: list_l1670014477004246597nt_int] :
( ( Xs != nil_li8670148097206105925nt_int )
=> ~ ! [Ys2: list_l1670014477004246597nt_int,Y2: list_P5707943133018811711nt_int] :
( Xs
!= ( append1237393811882493146nt_int @ Ys2 @ ( cons_l7309679040211256053nt_int @ Y2 @ nil_li8670148097206105925nt_int ) ) ) ) ).
% rev_exhaust
thf(fact_174_rev__exhaust,axiom,
! [Xs: list_s8839374986383574687nt_int] :
( ( Xs != nil_se54404438492013087nt_int )
=> ~ ! [Ys2: list_s8839374986383574687nt_int,Y2: set_Pr958786334691620121nt_int] :
( Xs
!= ( append3889155854801840692nt_int @ Ys2 @ ( cons_s6578334183908017615nt_int @ Y2 @ nil_se54404438492013087nt_int ) ) ) ) ).
% rev_exhaust
thf(fact_175_rev__exhaust,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( Xs != nil_Pr2300489316682597567nt_int )
=> ~ ! [Ys2: list_P5707943133018811711nt_int,Y2: product_prod_int_int] :
( Xs
!= ( append7030698103840186580nt_int @ Ys2 @ ( cons_P3334398858971670639nt_int @ Y2 @ nil_Pr2300489316682597567nt_int ) ) ) ) ).
% rev_exhaust
thf(fact_176_rev__induct,axiom,
! [P: list_int > $o,Xs: list_int] :
( ( P @ nil_int )
=> ( ! [X3: int,Xs2: list_int] :
( ( P @ Xs2 )
=> ( P @ ( append_int @ Xs2 @ ( cons_int @ X3 @ nil_int ) ) ) )
=> ( P @ Xs ) ) ) ).
% rev_induct
thf(fact_177_rev__induct,axiom,
! [P: list_l1670014477004246597nt_int > $o,Xs: list_l1670014477004246597nt_int] :
( ( P @ nil_li8670148097206105925nt_int )
=> ( ! [X3: list_P5707943133018811711nt_int,Xs2: list_l1670014477004246597nt_int] :
( ( P @ Xs2 )
=> ( P @ ( append1237393811882493146nt_int @ Xs2 @ ( cons_l7309679040211256053nt_int @ X3 @ nil_li8670148097206105925nt_int ) ) ) )
=> ( P @ Xs ) ) ) ).
% rev_induct
thf(fact_178_rev__induct,axiom,
! [P: list_s8839374986383574687nt_int > $o,Xs: list_s8839374986383574687nt_int] :
( ( P @ nil_se54404438492013087nt_int )
=> ( ! [X3: set_Pr958786334691620121nt_int,Xs2: list_s8839374986383574687nt_int] :
( ( P @ Xs2 )
=> ( P @ ( append3889155854801840692nt_int @ Xs2 @ ( cons_s6578334183908017615nt_int @ X3 @ nil_se54404438492013087nt_int ) ) ) )
=> ( P @ Xs ) ) ) ).
% rev_induct
thf(fact_179_rev__induct,axiom,
! [P: list_P5707943133018811711nt_int > $o,Xs: list_P5707943133018811711nt_int] :
( ( P @ nil_Pr2300489316682597567nt_int )
=> ( ! [X3: product_prod_int_int,Xs2: list_P5707943133018811711nt_int] :
( ( P @ Xs2 )
=> ( P @ ( append7030698103840186580nt_int @ Xs2 @ ( cons_P3334398858971670639nt_int @ X3 @ nil_Pr2300489316682597567nt_int ) ) ) )
=> ( P @ Xs ) ) ) ).
% rev_induct
thf(fact_180_last__ConsR,axiom,
! [Xs: list_int,X: int] :
( ( Xs != nil_int )
=> ( ( last_int @ ( cons_int @ X @ Xs ) )
= ( last_int @ Xs ) ) ) ).
% last_ConsR
thf(fact_181_last__ConsR,axiom,
! [Xs: list_l1670014477004246597nt_int,X: list_P5707943133018811711nt_int] :
( ( Xs != nil_li8670148097206105925nt_int )
=> ( ( last_l5818330359162608606nt_int @ ( cons_l7309679040211256053nt_int @ X @ Xs ) )
= ( last_l5818330359162608606nt_int @ Xs ) ) ) ).
% last_ConsR
thf(fact_182_last__ConsR,axiom,
! [Xs: list_s8839374986383574687nt_int,X: set_Pr958786334691620121nt_int] :
( ( Xs != nil_se54404438492013087nt_int )
=> ( ( last_s3107260788710622008nt_int @ ( cons_s6578334183908017615nt_int @ X @ Xs ) )
= ( last_s3107260788710622008nt_int @ Xs ) ) ) ).
% last_ConsR
thf(fact_183_last__ConsR,axiom,
! [Xs: list_P5707943133018811711nt_int,X: product_prod_int_int] :
( ( Xs != nil_Pr2300489316682597567nt_int )
=> ( ( last_P3305686521732843992nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) )
= ( last_P3305686521732843992nt_int @ Xs ) ) ) ).
% last_ConsR
thf(fact_184_last__ConsL,axiom,
! [Xs: list_int,X: int] :
( ( Xs = nil_int )
=> ( ( last_int @ ( cons_int @ X @ Xs ) )
= X ) ) ).
% last_ConsL
thf(fact_185_last__ConsL,axiom,
! [Xs: list_l1670014477004246597nt_int,X: list_P5707943133018811711nt_int] :
( ( Xs = nil_li8670148097206105925nt_int )
=> ( ( last_l5818330359162608606nt_int @ ( cons_l7309679040211256053nt_int @ X @ Xs ) )
= X ) ) ).
% last_ConsL
thf(fact_186_last__ConsL,axiom,
! [Xs: list_s8839374986383574687nt_int,X: set_Pr958786334691620121nt_int] :
( ( Xs = nil_se54404438492013087nt_int )
=> ( ( last_s3107260788710622008nt_int @ ( cons_s6578334183908017615nt_int @ X @ Xs ) )
= X ) ) ).
% last_ConsL
thf(fact_187_last__ConsL,axiom,
! [Xs: list_P5707943133018811711nt_int,X: product_prod_int_int] :
( ( Xs = nil_Pr2300489316682597567nt_int )
=> ( ( last_P3305686521732843992nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) )
= X ) ) ).
% last_ConsL
thf(fact_188_last_Osimps,axiom,
! [Xs: list_int,X: int] :
( ( ( Xs = nil_int )
=> ( ( last_int @ ( cons_int @ X @ Xs ) )
= X ) )
& ( ( Xs != nil_int )
=> ( ( last_int @ ( cons_int @ X @ Xs ) )
= ( last_int @ Xs ) ) ) ) ).
% last.simps
thf(fact_189_last_Osimps,axiom,
! [Xs: list_l1670014477004246597nt_int,X: list_P5707943133018811711nt_int] :
( ( ( Xs = nil_li8670148097206105925nt_int )
=> ( ( last_l5818330359162608606nt_int @ ( cons_l7309679040211256053nt_int @ X @ Xs ) )
= X ) )
& ( ( Xs != nil_li8670148097206105925nt_int )
=> ( ( last_l5818330359162608606nt_int @ ( cons_l7309679040211256053nt_int @ X @ Xs ) )
= ( last_l5818330359162608606nt_int @ Xs ) ) ) ) ).
% last.simps
thf(fact_190_last_Osimps,axiom,
! [Xs: list_s8839374986383574687nt_int,X: set_Pr958786334691620121nt_int] :
( ( ( Xs = nil_se54404438492013087nt_int )
=> ( ( last_s3107260788710622008nt_int @ ( cons_s6578334183908017615nt_int @ X @ Xs ) )
= X ) )
& ( ( Xs != nil_se54404438492013087nt_int )
=> ( ( last_s3107260788710622008nt_int @ ( cons_s6578334183908017615nt_int @ X @ Xs ) )
= ( last_s3107260788710622008nt_int @ Xs ) ) ) ) ).
% last.simps
thf(fact_191_last_Osimps,axiom,
! [Xs: list_P5707943133018811711nt_int,X: product_prod_int_int] :
( ( ( Xs = nil_Pr2300489316682597567nt_int )
=> ( ( last_P3305686521732843992nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) )
= X ) )
& ( ( Xs != nil_Pr2300489316682597567nt_int )
=> ( ( last_P3305686521732843992nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) )
= ( last_P3305686521732843992nt_int @ Xs ) ) ) ) ).
% last.simps
thf(fact_192_longest__common__prefix,axiom,
! [Xs: list_l1670014477004246597nt_int,Ys: list_l1670014477004246597nt_int] :
? [Ps3: list_l1670014477004246597nt_int,Xs3: list_l1670014477004246597nt_int,Ys5: list_l1670014477004246597nt_int] :
( ( Xs
= ( append1237393811882493146nt_int @ Ps3 @ Xs3 ) )
& ( Ys
= ( append1237393811882493146nt_int @ Ps3 @ Ys5 ) )
& ( ( Xs3 = nil_li8670148097206105925nt_int )
| ( Ys5 = nil_li8670148097206105925nt_int )
| ( ( hd_lis8550591025403828010nt_int @ Xs3 )
!= ( hd_lis8550591025403828010nt_int @ Ys5 ) ) ) ) ).
% longest_common_prefix
thf(fact_193_longest__common__prefix,axiom,
! [Xs: list_int,Ys: list_int] :
? [Ps3: list_int,Xs3: list_int,Ys5: list_int] :
( ( Xs
= ( append_int @ Ps3 @ Xs3 ) )
& ( Ys
= ( append_int @ Ps3 @ Ys5 ) )
& ( ( Xs3 = nil_int )
| ( Ys5 = nil_int )
| ( ( hd_int @ Xs3 )
!= ( hd_int @ Ys5 ) ) ) ) ).
% longest_common_prefix
thf(fact_194_longest__common__prefix,axiom,
! [Xs: list_s8839374986383574687nt_int,Ys: list_s8839374986383574687nt_int] :
? [Ps3: list_s8839374986383574687nt_int,Xs3: list_s8839374986383574687nt_int,Ys5: list_s8839374986383574687nt_int] :
( ( Xs
= ( append3889155854801840692nt_int @ Ps3 @ Xs3 ) )
& ( Ys
= ( append3889155854801840692nt_int @ Ps3 @ Ys5 ) )
& ( ( Xs3 = nil_se54404438492013087nt_int )
| ( Ys5 = nil_se54404438492013087nt_int )
| ( ( hd_set5458074601020007556nt_int @ Xs3 )
!= ( hd_set5458074601020007556nt_int @ Ys5 ) ) ) ) ).
% longest_common_prefix
thf(fact_195_longest__common__prefix,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
? [Ps3: list_P5707943133018811711nt_int,Xs3: list_P5707943133018811711nt_int,Ys5: list_P5707943133018811711nt_int] :
( ( Xs
= ( append7030698103840186580nt_int @ Ps3 @ Xs3 ) )
& ( Ys
= ( append7030698103840186580nt_int @ Ps3 @ Ys5 ) )
& ( ( Xs3 = nil_Pr2300489316682597567nt_int )
| ( Ys5 = nil_Pr2300489316682597567nt_int )
| ( ( hd_Pro282112905867057956nt_int @ Xs3 )
!= ( hd_Pro282112905867057956nt_int @ Ys5 ) ) ) ) ).
% longest_common_prefix
thf(fact_196_hd__append,axiom,
! [Xs: list_l1670014477004246597nt_int,Ys: list_l1670014477004246597nt_int] :
( ( ( Xs = nil_li8670148097206105925nt_int )
=> ( ( hd_lis8550591025403828010nt_int @ ( append1237393811882493146nt_int @ Xs @ Ys ) )
= ( hd_lis8550591025403828010nt_int @ Ys ) ) )
& ( ( Xs != nil_li8670148097206105925nt_int )
=> ( ( hd_lis8550591025403828010nt_int @ ( append1237393811882493146nt_int @ Xs @ Ys ) )
= ( hd_lis8550591025403828010nt_int @ Xs ) ) ) ) ).
% hd_append
thf(fact_197_hd__append,axiom,
! [Xs: list_int,Ys: list_int] :
( ( ( Xs = nil_int )
=> ( ( hd_int @ ( append_int @ Xs @ Ys ) )
= ( hd_int @ Ys ) ) )
& ( ( Xs != nil_int )
=> ( ( hd_int @ ( append_int @ Xs @ Ys ) )
= ( hd_int @ Xs ) ) ) ) ).
% hd_append
thf(fact_198_hd__append,axiom,
! [Xs: list_s8839374986383574687nt_int,Ys: list_s8839374986383574687nt_int] :
( ( ( Xs = nil_se54404438492013087nt_int )
=> ( ( hd_set5458074601020007556nt_int @ ( append3889155854801840692nt_int @ Xs @ Ys ) )
= ( hd_set5458074601020007556nt_int @ Ys ) ) )
& ( ( Xs != nil_se54404438492013087nt_int )
=> ( ( hd_set5458074601020007556nt_int @ ( append3889155854801840692nt_int @ Xs @ Ys ) )
= ( hd_set5458074601020007556nt_int @ Xs ) ) ) ) ).
% hd_append
thf(fact_199_hd__append,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( ( Xs = nil_Pr2300489316682597567nt_int )
=> ( ( hd_Pro282112905867057956nt_int @ ( append7030698103840186580nt_int @ Xs @ Ys ) )
= ( hd_Pro282112905867057956nt_int @ Ys ) ) )
& ( ( Xs != nil_Pr2300489316682597567nt_int )
=> ( ( hd_Pro282112905867057956nt_int @ ( append7030698103840186580nt_int @ Xs @ Ys ) )
= ( hd_Pro282112905867057956nt_int @ Xs ) ) ) ) ).
% hd_append
thf(fact_200_longest__common__suffix,axiom,
! [Xs: list_l1670014477004246597nt_int,Ys: list_l1670014477004246597nt_int] :
? [Ss: list_l1670014477004246597nt_int,Xs3: list_l1670014477004246597nt_int,Ys5: list_l1670014477004246597nt_int] :
( ( Xs
= ( append1237393811882493146nt_int @ Xs3 @ Ss ) )
& ( Ys
= ( append1237393811882493146nt_int @ Ys5 @ Ss ) )
& ( ( Xs3 = nil_li8670148097206105925nt_int )
| ( Ys5 = nil_li8670148097206105925nt_int )
| ( ( last_l5818330359162608606nt_int @ Xs3 )
!= ( last_l5818330359162608606nt_int @ Ys5 ) ) ) ) ).
% longest_common_suffix
thf(fact_201_longest__common__suffix,axiom,
! [Xs: list_int,Ys: list_int] :
? [Ss: list_int,Xs3: list_int,Ys5: list_int] :
( ( Xs
= ( append_int @ Xs3 @ Ss ) )
& ( Ys
= ( append_int @ Ys5 @ Ss ) )
& ( ( Xs3 = nil_int )
| ( Ys5 = nil_int )
| ( ( last_int @ Xs3 )
!= ( last_int @ Ys5 ) ) ) ) ).
% longest_common_suffix
thf(fact_202_longest__common__suffix,axiom,
! [Xs: list_s8839374986383574687nt_int,Ys: list_s8839374986383574687nt_int] :
? [Ss: list_s8839374986383574687nt_int,Xs3: list_s8839374986383574687nt_int,Ys5: list_s8839374986383574687nt_int] :
( ( Xs
= ( append3889155854801840692nt_int @ Xs3 @ Ss ) )
& ( Ys
= ( append3889155854801840692nt_int @ Ys5 @ Ss ) )
& ( ( Xs3 = nil_se54404438492013087nt_int )
| ( Ys5 = nil_se54404438492013087nt_int )
| ( ( last_s3107260788710622008nt_int @ Xs3 )
!= ( last_s3107260788710622008nt_int @ Ys5 ) ) ) ) ).
% longest_common_suffix
thf(fact_203_longest__common__suffix,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
? [Ss: list_P5707943133018811711nt_int,Xs3: list_P5707943133018811711nt_int,Ys5: list_P5707943133018811711nt_int] :
( ( Xs
= ( append7030698103840186580nt_int @ Xs3 @ Ss ) )
& ( Ys
= ( append7030698103840186580nt_int @ Ys5 @ Ss ) )
& ( ( Xs3 = nil_Pr2300489316682597567nt_int )
| ( Ys5 = nil_Pr2300489316682597567nt_int )
| ( ( last_P3305686521732843992nt_int @ Xs3 )
!= ( last_P3305686521732843992nt_int @ Ys5 ) ) ) ) ).
% longest_common_suffix
thf(fact_204_last__append,axiom,
! [Ys: list_l1670014477004246597nt_int,Xs: list_l1670014477004246597nt_int] :
( ( ( Ys = nil_li8670148097206105925nt_int )
=> ( ( last_l5818330359162608606nt_int @ ( append1237393811882493146nt_int @ Xs @ Ys ) )
= ( last_l5818330359162608606nt_int @ Xs ) ) )
& ( ( Ys != nil_li8670148097206105925nt_int )
=> ( ( last_l5818330359162608606nt_int @ ( append1237393811882493146nt_int @ Xs @ Ys ) )
= ( last_l5818330359162608606nt_int @ Ys ) ) ) ) ).
% last_append
thf(fact_205_last__append,axiom,
! [Ys: list_int,Xs: list_int] :
( ( ( Ys = nil_int )
=> ( ( last_int @ ( append_int @ Xs @ Ys ) )
= ( last_int @ Xs ) ) )
& ( ( Ys != nil_int )
=> ( ( last_int @ ( append_int @ Xs @ Ys ) )
= ( last_int @ Ys ) ) ) ) ).
% last_append
thf(fact_206_last__append,axiom,
! [Ys: list_s8839374986383574687nt_int,Xs: list_s8839374986383574687nt_int] :
( ( ( Ys = nil_se54404438492013087nt_int )
=> ( ( last_s3107260788710622008nt_int @ ( append3889155854801840692nt_int @ Xs @ Ys ) )
= ( last_s3107260788710622008nt_int @ Xs ) ) )
& ( ( Ys != nil_se54404438492013087nt_int )
=> ( ( last_s3107260788710622008nt_int @ ( append3889155854801840692nt_int @ Xs @ Ys ) )
= ( last_s3107260788710622008nt_int @ Ys ) ) ) ) ).
% last_append
thf(fact_207_last__append,axiom,
! [Ys: list_P5707943133018811711nt_int,Xs: list_P5707943133018811711nt_int] :
( ( ( Ys = nil_Pr2300489316682597567nt_int )
=> ( ( last_P3305686521732843992nt_int @ ( append7030698103840186580nt_int @ Xs @ Ys ) )
= ( last_P3305686521732843992nt_int @ Xs ) ) )
& ( ( Ys != nil_Pr2300489316682597567nt_int )
=> ( ( last_P3305686521732843992nt_int @ ( append7030698103840186580nt_int @ Xs @ Ys ) )
= ( last_P3305686521732843992nt_int @ Ys ) ) ) ) ).
% last_append
thf(fact_208_hd__Nil__eq__last,axiom,
( ( hd_lis8550591025403828010nt_int @ nil_li8670148097206105925nt_int )
= ( last_l5818330359162608606nt_int @ nil_li8670148097206105925nt_int ) ) ).
% hd_Nil_eq_last
thf(fact_209_hd__Nil__eq__last,axiom,
( ( hd_int @ nil_int )
= ( last_int @ nil_int ) ) ).
% hd_Nil_eq_last
thf(fact_210_hd__Nil__eq__last,axiom,
( ( hd_set5458074601020007556nt_int @ nil_se54404438492013087nt_int )
= ( last_s3107260788710622008nt_int @ nil_se54404438492013087nt_int ) ) ).
% hd_Nil_eq_last
thf(fact_211_hd__Nil__eq__last,axiom,
( ( hd_Pro282112905867057956nt_int @ nil_Pr2300489316682597567nt_int )
= ( last_P3305686521732843992nt_int @ nil_Pr2300489316682597567nt_int ) ) ).
% hd_Nil_eq_last
thf(fact_212_knights__circuit__def,axiom,
( knights_circuit
= ( ^ [B2: set_Pr958786334691620121nt_int,Ps2: list_P5707943133018811711nt_int] :
( ( knights_path @ B2 @ Ps2 )
& ( valid_step @ ( last_P3305686521732843992nt_int @ Ps2 ) @ ( hd_Pro282112905867057956nt_int @ Ps2 ) ) ) ) ) ).
% knights_circuit_def
thf(fact_213_insert__Diff__single,axiom,
! [A: produc1219242969750017639nt_int,A3: set_Pr2560585780119916871nt_int] :
( ( insert5410160437170799671nt_int @ A @ ( minus_2188297577953631406nt_int @ A3 @ ( insert5410160437170799671nt_int @ A @ bot_bo8417956007504411571nt_int ) ) )
= ( insert5410160437170799671nt_int @ A @ A3 ) ) ).
% insert_Diff_single
thf(fact_214_insert__Diff__single,axiom,
! [A: int,A3: set_int] :
( ( insert_int @ A @ ( minus_minus_set_int @ A3 @ ( insert_int @ A @ bot_bot_set_int ) ) )
= ( insert_int @ A @ A3 ) ) ).
% insert_Diff_single
thf(fact_215_insert__Diff__single,axiom,
! [A: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int] :
( ( insert393344137582914319nt_int @ A @ ( minus_456201022768243590nt_int @ A3 @ ( insert393344137582914319nt_int @ A @ bot_bo3809061186584590219nt_int ) ) )
= ( insert393344137582914319nt_int @ A @ A3 ) ) ).
% insert_Diff_single
thf(fact_216_insert__Diff__single,axiom,
! [A: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int] :
( ( insert8897473484851387113nt_int @ A @ ( minus_2612819937483484256nt_int @ A3 @ ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) )
= ( insert8897473484851387113nt_int @ A @ A3 ) ) ).
% insert_Diff_single
thf(fact_217_insert__Diff__single,axiom,
! [A: product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( insert5033312907999012233nt_int @ A @ ( minus_1052850069191792384nt_int @ A3 @ ( insert5033312907999012233nt_int @ A @ bot_bo1796632182523588997nt_int ) ) )
= ( insert5033312907999012233nt_int @ A @ A3 ) ) ).
% insert_Diff_single
thf(fact_218_kp2_I2_J,axiom,
( ( inf_in2269163501485487111nt_int @ ( minus_1052850069191792384nt_int @ b @ ( insert5033312907999012233nt_int @ s_i @ bot_bo1796632182523588997nt_int ) ) @ ( insert5033312907999012233nt_int @ s_i @ bot_bo1796632182523588997nt_int ) )
= bot_bo1796632182523588997nt_int ) ).
% kp2(2)
thf(fact_219_Un__Diff__cancel,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( sup_su3633867531522857715nt_int @ A3 @ ( minus_456201022768243590nt_int @ B4 @ A3 ) )
= ( sup_su3633867531522857715nt_int @ A3 @ B4 ) ) ).
% Un_Diff_cancel
thf(fact_220_Un__Diff__cancel,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( sup_su2047564715030645325nt_int @ A3 @ ( minus_2612819937483484256nt_int @ B4 @ A3 ) )
= ( sup_su2047564715030645325nt_int @ A3 @ B4 ) ) ).
% Un_Diff_cancel
thf(fact_221_Un__Diff__cancel,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ A3 @ ( minus_1052850069191792384nt_int @ B4 @ A3 ) )
= ( sup_su6024340866399070445nt_int @ A3 @ B4 ) ) ).
% Un_Diff_cancel
thf(fact_222_Un__Diff__cancel2,axiom,
! [B4: set_li3855193629254082847nt_int,A3: set_li3855193629254082847nt_int] :
( ( sup_su3633867531522857715nt_int @ ( minus_456201022768243590nt_int @ B4 @ A3 ) @ A3 )
= ( sup_su3633867531522857715nt_int @ B4 @ A3 ) ) ).
% Un_Diff_cancel2
thf(fact_223_Un__Diff__cancel2,axiom,
! [B4: set_se6260736226359567993nt_int,A3: set_se6260736226359567993nt_int] :
( ( sup_su2047564715030645325nt_int @ ( minus_2612819937483484256nt_int @ B4 @ A3 ) @ A3 )
= ( sup_su2047564715030645325nt_int @ B4 @ A3 ) ) ).
% Un_Diff_cancel2
thf(fact_224_Un__Diff__cancel2,axiom,
! [B4: set_Pr958786334691620121nt_int,A3: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ ( minus_1052850069191792384nt_int @ B4 @ A3 ) @ A3 )
= ( sup_su6024340866399070445nt_int @ B4 @ A3 ) ) ).
% Un_Diff_cancel2
thf(fact_225_Diff__insert0,axiom,
! [X: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ~ ( member2764346250752101224nt_int @ X @ A3 )
=> ( ( minus_456201022768243590nt_int @ A3 @ ( insert393344137582914319nt_int @ X @ B4 ) )
= ( minus_456201022768243590nt_int @ A3 @ B4 ) ) ) ).
% Diff_insert0
thf(fact_226_Diff__insert0,axiom,
! [X: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ~ ( member2340774599025711042nt_int @ X @ A3 )
=> ( ( minus_2612819937483484256nt_int @ A3 @ ( insert8897473484851387113nt_int @ X @ B4 ) )
= ( minus_2612819937483484256nt_int @ A3 @ B4 ) ) ) ).
% Diff_insert0
thf(fact_227_Diff__insert0,axiom,
! [X: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ~ ( member5262025264175285858nt_int @ X @ A3 )
=> ( ( minus_1052850069191792384nt_int @ A3 @ ( insert5033312907999012233nt_int @ X @ B4 ) )
= ( minus_1052850069191792384nt_int @ A3 @ B4 ) ) ) ).
% Diff_insert0
thf(fact_228_insert__Diff1,axiom,
! [X: list_P5707943133018811711nt_int,B4: set_li3855193629254082847nt_int,A3: set_li3855193629254082847nt_int] :
( ( member2764346250752101224nt_int @ X @ B4 )
=> ( ( minus_456201022768243590nt_int @ ( insert393344137582914319nt_int @ X @ A3 ) @ B4 )
= ( minus_456201022768243590nt_int @ A3 @ B4 ) ) ) ).
% insert_Diff1
thf(fact_229_insert__Diff1,axiom,
! [X: set_Pr958786334691620121nt_int,B4: set_se6260736226359567993nt_int,A3: set_se6260736226359567993nt_int] :
( ( member2340774599025711042nt_int @ X @ B4 )
=> ( ( minus_2612819937483484256nt_int @ ( insert8897473484851387113nt_int @ X @ A3 ) @ B4 )
= ( minus_2612819937483484256nt_int @ A3 @ B4 ) ) ) ).
% insert_Diff1
thf(fact_230_insert__Diff1,axiom,
! [X: product_prod_int_int,B4: set_Pr958786334691620121nt_int,A3: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ X @ B4 )
=> ( ( minus_1052850069191792384nt_int @ ( insert5033312907999012233nt_int @ X @ A3 ) @ B4 )
= ( minus_1052850069191792384nt_int @ A3 @ B4 ) ) ) ).
% insert_Diff1
thf(fact_231_Un__insert__left,axiom,
! [A: list_P5707943133018811711nt_int,B4: set_li3855193629254082847nt_int,C2: set_li3855193629254082847nt_int] :
( ( sup_su3633867531522857715nt_int @ ( insert393344137582914319nt_int @ A @ B4 ) @ C2 )
= ( insert393344137582914319nt_int @ A @ ( sup_su3633867531522857715nt_int @ B4 @ C2 ) ) ) ).
% Un_insert_left
thf(fact_232_Un__insert__left,axiom,
! [A: set_Pr958786334691620121nt_int,B4: set_se6260736226359567993nt_int,C2: set_se6260736226359567993nt_int] :
( ( sup_su2047564715030645325nt_int @ ( insert8897473484851387113nt_int @ A @ B4 ) @ C2 )
= ( insert8897473484851387113nt_int @ A @ ( sup_su2047564715030645325nt_int @ B4 @ C2 ) ) ) ).
% Un_insert_left
thf(fact_233_Un__insert__left,axiom,
! [A: product_prod_int_int,B4: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ ( insert5033312907999012233nt_int @ A @ B4 ) @ C2 )
= ( insert5033312907999012233nt_int @ A @ ( sup_su6024340866399070445nt_int @ B4 @ C2 ) ) ) ).
% Un_insert_left
thf(fact_234_Un__insert__right,axiom,
! [A3: set_li3855193629254082847nt_int,A: list_P5707943133018811711nt_int,B4: set_li3855193629254082847nt_int] :
( ( sup_su3633867531522857715nt_int @ A3 @ ( insert393344137582914319nt_int @ A @ B4 ) )
= ( insert393344137582914319nt_int @ A @ ( sup_su3633867531522857715nt_int @ A3 @ B4 ) ) ) ).
% Un_insert_right
thf(fact_235_Un__insert__right,axiom,
! [A3: set_se6260736226359567993nt_int,A: set_Pr958786334691620121nt_int,B4: set_se6260736226359567993nt_int] :
( ( sup_su2047564715030645325nt_int @ A3 @ ( insert8897473484851387113nt_int @ A @ B4 ) )
= ( insert8897473484851387113nt_int @ A @ ( sup_su2047564715030645325nt_int @ A3 @ B4 ) ) ) ).
% Un_insert_right
thf(fact_236_Un__insert__right,axiom,
! [A3: set_Pr958786334691620121nt_int,A: product_prod_int_int,B4: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ A3 @ ( insert5033312907999012233nt_int @ A @ B4 ) )
= ( insert5033312907999012233nt_int @ A @ ( sup_su6024340866399070445nt_int @ A3 @ B4 ) ) ) ).
% Un_insert_right
thf(fact_237_Diff__empty,axiom,
! [A3: set_Pr2560585780119916871nt_int] :
( ( minus_2188297577953631406nt_int @ A3 @ bot_bo8417956007504411571nt_int )
= A3 ) ).
% Diff_empty
thf(fact_238_Diff__empty,axiom,
! [A3: set_int] :
( ( minus_minus_set_int @ A3 @ bot_bot_set_int )
= A3 ) ).
% Diff_empty
thf(fact_239_Diff__empty,axiom,
! [A3: set_li3855193629254082847nt_int] :
( ( minus_456201022768243590nt_int @ A3 @ bot_bo3809061186584590219nt_int )
= A3 ) ).
% Diff_empty
thf(fact_240_Diff__empty,axiom,
! [A3: set_se6260736226359567993nt_int] :
( ( minus_2612819937483484256nt_int @ A3 @ bot_bo1488462491386950373nt_int )
= A3 ) ).
% Diff_empty
thf(fact_241_Diff__empty,axiom,
! [A3: set_Pr958786334691620121nt_int] :
( ( minus_1052850069191792384nt_int @ A3 @ bot_bo1796632182523588997nt_int )
= A3 ) ).
% Diff_empty
thf(fact_242_empty__Diff,axiom,
! [A3: set_Pr2560585780119916871nt_int] :
( ( minus_2188297577953631406nt_int @ bot_bo8417956007504411571nt_int @ A3 )
= bot_bo8417956007504411571nt_int ) ).
% empty_Diff
thf(fact_243_empty__Diff,axiom,
! [A3: set_int] :
( ( minus_minus_set_int @ bot_bot_set_int @ A3 )
= bot_bot_set_int ) ).
% empty_Diff
thf(fact_244_empty__Diff,axiom,
! [A3: set_li3855193629254082847nt_int] :
( ( minus_456201022768243590nt_int @ bot_bo3809061186584590219nt_int @ A3 )
= bot_bo3809061186584590219nt_int ) ).
% empty_Diff
thf(fact_245_empty__Diff,axiom,
! [A3: set_se6260736226359567993nt_int] :
( ( minus_2612819937483484256nt_int @ bot_bo1488462491386950373nt_int @ A3 )
= bot_bo1488462491386950373nt_int ) ).
% empty_Diff
thf(fact_246_empty__Diff,axiom,
! [A3: set_Pr958786334691620121nt_int] :
( ( minus_1052850069191792384nt_int @ bot_bo1796632182523588997nt_int @ A3 )
= bot_bo1796632182523588997nt_int ) ).
% empty_Diff
thf(fact_247_Diff__cancel,axiom,
! [A3: set_Pr2560585780119916871nt_int] :
( ( minus_2188297577953631406nt_int @ A3 @ A3 )
= bot_bo8417956007504411571nt_int ) ).
% Diff_cancel
thf(fact_248_Diff__cancel,axiom,
! [A3: set_int] :
( ( minus_minus_set_int @ A3 @ A3 )
= bot_bot_set_int ) ).
% Diff_cancel
thf(fact_249_Diff__cancel,axiom,
! [A3: set_li3855193629254082847nt_int] :
( ( minus_456201022768243590nt_int @ A3 @ A3 )
= bot_bo3809061186584590219nt_int ) ).
% Diff_cancel
thf(fact_250_Diff__cancel,axiom,
! [A3: set_se6260736226359567993nt_int] :
( ( minus_2612819937483484256nt_int @ A3 @ A3 )
= bot_bo1488462491386950373nt_int ) ).
% Diff_cancel
thf(fact_251_Diff__cancel,axiom,
! [A3: set_Pr958786334691620121nt_int] :
( ( minus_1052850069191792384nt_int @ A3 @ A3 )
= bot_bo1796632182523588997nt_int ) ).
% Diff_cancel
thf(fact_252_empty__Collect__eq,axiom,
! [P: produc1219242969750017639nt_int > $o] :
( ( bot_bo8417956007504411571nt_int
= ( collec7447955092554649554nt_int @ P ) )
= ( ! [X2: produc1219242969750017639nt_int] :
~ ( P @ X2 ) ) ) ).
% empty_Collect_eq
thf(fact_253_empty__Collect__eq,axiom,
! [P: int > $o] :
( ( bot_bot_set_int
= ( collect_int @ P ) )
= ( ! [X2: int] :
~ ( P @ X2 ) ) ) ).
% empty_Collect_eq
thf(fact_254_empty__Collect__eq,axiom,
! [P: list_P5707943133018811711nt_int > $o] :
( ( bot_bo3809061186584590219nt_int
= ( collec3040439045487124906nt_int @ P ) )
= ( ! [X2: list_P5707943133018811711nt_int] :
~ ( P @ X2 ) ) ) ).
% empty_Collect_eq
thf(fact_255_empty__Collect__eq,axiom,
! [P: set_Pr958786334691620121nt_int > $o] :
( ( bot_bo1488462491386950373nt_int
= ( collec5210948495886036740nt_int @ P ) )
= ( ! [X2: set_Pr958786334691620121nt_int] :
~ ( P @ X2 ) ) ) ).
% empty_Collect_eq
thf(fact_256_empty__Collect__eq,axiom,
! [P: product_prod_int_int > $o] :
( ( bot_bo1796632182523588997nt_int
= ( collec213857154873943460nt_int @ P ) )
= ( ! [X2: product_prod_int_int] :
~ ( P @ X2 ) ) ) ).
% empty_Collect_eq
thf(fact_257_Collect__empty__eq,axiom,
! [P: produc1219242969750017639nt_int > $o] :
( ( ( collec7447955092554649554nt_int @ P )
= bot_bo8417956007504411571nt_int )
= ( ! [X2: produc1219242969750017639nt_int] :
~ ( P @ X2 ) ) ) ).
% Collect_empty_eq
thf(fact_258_Collect__empty__eq,axiom,
! [P: int > $o] :
( ( ( collect_int @ P )
= bot_bot_set_int )
= ( ! [X2: int] :
~ ( P @ X2 ) ) ) ).
% Collect_empty_eq
thf(fact_259_Collect__empty__eq,axiom,
! [P: list_P5707943133018811711nt_int > $o] :
( ( ( collec3040439045487124906nt_int @ P )
= bot_bo3809061186584590219nt_int )
= ( ! [X2: list_P5707943133018811711nt_int] :
~ ( P @ X2 ) ) ) ).
% Collect_empty_eq
thf(fact_260_Collect__empty__eq,axiom,
! [P: set_Pr958786334691620121nt_int > $o] :
( ( ( collec5210948495886036740nt_int @ P )
= bot_bo1488462491386950373nt_int )
= ( ! [X2: set_Pr958786334691620121nt_int] :
~ ( P @ X2 ) ) ) ).
% Collect_empty_eq
thf(fact_261_Collect__empty__eq,axiom,
! [P: product_prod_int_int > $o] :
( ( ( collec213857154873943460nt_int @ P )
= bot_bo1796632182523588997nt_int )
= ( ! [X2: product_prod_int_int] :
~ ( P @ X2 ) ) ) ).
% Collect_empty_eq
thf(fact_262_all__not__in__conv,axiom,
! [A3: set_Pr2560585780119916871nt_int] :
( ( ! [X2: produc1219242969750017639nt_int] :
~ ( member8566619992076573584nt_int @ X2 @ A3 ) )
= ( A3 = bot_bo8417956007504411571nt_int ) ) ).
% all_not_in_conv
thf(fact_263_all__not__in__conv,axiom,
! [A3: set_int] :
( ( ! [X2: int] :
~ ( member_int @ X2 @ A3 ) )
= ( A3 = bot_bot_set_int ) ) ).
% all_not_in_conv
thf(fact_264_all__not__in__conv,axiom,
! [A3: set_li3855193629254082847nt_int] :
( ( ! [X2: list_P5707943133018811711nt_int] :
~ ( member2764346250752101224nt_int @ X2 @ A3 ) )
= ( A3 = bot_bo3809061186584590219nt_int ) ) ).
% all_not_in_conv
thf(fact_265_all__not__in__conv,axiom,
! [A3: set_se6260736226359567993nt_int] :
( ( ! [X2: set_Pr958786334691620121nt_int] :
~ ( member2340774599025711042nt_int @ X2 @ A3 ) )
= ( A3 = bot_bo1488462491386950373nt_int ) ) ).
% all_not_in_conv
thf(fact_266_all__not__in__conv,axiom,
! [A3: set_Pr958786334691620121nt_int] :
( ( ! [X2: product_prod_int_int] :
~ ( member5262025264175285858nt_int @ X2 @ A3 ) )
= ( A3 = bot_bo1796632182523588997nt_int ) ) ).
% all_not_in_conv
thf(fact_267_empty__iff,axiom,
! [C: produc1219242969750017639nt_int] :
~ ( member8566619992076573584nt_int @ C @ bot_bo8417956007504411571nt_int ) ).
% empty_iff
thf(fact_268_empty__iff,axiom,
! [C: int] :
~ ( member_int @ C @ bot_bot_set_int ) ).
% empty_iff
thf(fact_269_empty__iff,axiom,
! [C: list_P5707943133018811711nt_int] :
~ ( member2764346250752101224nt_int @ C @ bot_bo3809061186584590219nt_int ) ).
% empty_iff
thf(fact_270_empty__iff,axiom,
! [C: set_Pr958786334691620121nt_int] :
~ ( member2340774599025711042nt_int @ C @ bot_bo1488462491386950373nt_int ) ).
% empty_iff
thf(fact_271_empty__iff,axiom,
! [C: product_prod_int_int] :
~ ( member5262025264175285858nt_int @ C @ bot_bo1796632182523588997nt_int ) ).
% empty_iff
thf(fact_272_insert__absorb2,axiom,
! [X: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int] :
( ( insert393344137582914319nt_int @ X @ ( insert393344137582914319nt_int @ X @ A3 ) )
= ( insert393344137582914319nt_int @ X @ A3 ) ) ).
% insert_absorb2
thf(fact_273_insert__absorb2,axiom,
! [X: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int] :
( ( insert8897473484851387113nt_int @ X @ ( insert8897473484851387113nt_int @ X @ A3 ) )
= ( insert8897473484851387113nt_int @ X @ A3 ) ) ).
% insert_absorb2
thf(fact_274_insert__absorb2,axiom,
! [X: product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( insert5033312907999012233nt_int @ X @ ( insert5033312907999012233nt_int @ X @ A3 ) )
= ( insert5033312907999012233nt_int @ X @ A3 ) ) ).
% insert_absorb2
thf(fact_275_insert__iff,axiom,
! [A: list_P5707943133018811711nt_int,B: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int] :
( ( member2764346250752101224nt_int @ A @ ( insert393344137582914319nt_int @ B @ A3 ) )
= ( ( A = B )
| ( member2764346250752101224nt_int @ A @ A3 ) ) ) ).
% insert_iff
thf(fact_276_insert__iff,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int] :
( ( member2340774599025711042nt_int @ A @ ( insert8897473484851387113nt_int @ B @ A3 ) )
= ( ( A = B )
| ( member2340774599025711042nt_int @ A @ A3 ) ) ) ).
% insert_iff
thf(fact_277_insert__iff,axiom,
! [A: product_prod_int_int,B: product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ A @ ( insert5033312907999012233nt_int @ B @ A3 ) )
= ( ( A = B )
| ( member5262025264175285858nt_int @ A @ A3 ) ) ) ).
% insert_iff
thf(fact_278_insertCI,axiom,
! [A: list_P5707943133018811711nt_int,B4: set_li3855193629254082847nt_int,B: list_P5707943133018811711nt_int] :
( ( ~ ( member2764346250752101224nt_int @ A @ B4 )
=> ( A = B ) )
=> ( member2764346250752101224nt_int @ A @ ( insert393344137582914319nt_int @ B @ B4 ) ) ) ).
% insertCI
thf(fact_279_insertCI,axiom,
! [A: set_Pr958786334691620121nt_int,B4: set_se6260736226359567993nt_int,B: set_Pr958786334691620121nt_int] :
( ( ~ ( member2340774599025711042nt_int @ A @ B4 )
=> ( A = B ) )
=> ( member2340774599025711042nt_int @ A @ ( insert8897473484851387113nt_int @ B @ B4 ) ) ) ).
% insertCI
thf(fact_280_insertCI,axiom,
! [A: product_prod_int_int,B4: set_Pr958786334691620121nt_int,B: product_prod_int_int] :
( ( ~ ( member5262025264175285858nt_int @ A @ B4 )
=> ( A = B ) )
=> ( member5262025264175285858nt_int @ A @ ( insert5033312907999012233nt_int @ B @ B4 ) ) ) ).
% insertCI
thf(fact_281_Int__iff,axiom,
! [C: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( member2764346250752101224nt_int @ C @ ( inf_in8463092517017915661nt_int @ A3 @ B4 ) )
= ( ( member2764346250752101224nt_int @ C @ A3 )
& ( member2764346250752101224nt_int @ C @ B4 ) ) ) ).
% Int_iff
thf(fact_282_Int__iff,axiom,
! [C: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( member2340774599025711042nt_int @ C @ ( inf_in8396524679539076455nt_int @ A3 @ B4 ) )
= ( ( member2340774599025711042nt_int @ C @ A3 )
& ( member2340774599025711042nt_int @ C @ B4 ) ) ) ).
% Int_iff
thf(fact_283_Int__iff,axiom,
! [C: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ C @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) )
= ( ( member5262025264175285858nt_int @ C @ A3 )
& ( member5262025264175285858nt_int @ C @ B4 ) ) ) ).
% Int_iff
thf(fact_284_IntI,axiom,
! [C: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( member2764346250752101224nt_int @ C @ A3 )
=> ( ( member2764346250752101224nt_int @ C @ B4 )
=> ( member2764346250752101224nt_int @ C @ ( inf_in8463092517017915661nt_int @ A3 @ B4 ) ) ) ) ).
% IntI
thf(fact_285_IntI,axiom,
! [C: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( member2340774599025711042nt_int @ C @ A3 )
=> ( ( member2340774599025711042nt_int @ C @ B4 )
=> ( member2340774599025711042nt_int @ C @ ( inf_in8396524679539076455nt_int @ A3 @ B4 ) ) ) ) ).
% IntI
thf(fact_286_IntI,axiom,
! [C: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ C @ A3 )
=> ( ( member5262025264175285858nt_int @ C @ B4 )
=> ( member5262025264175285858nt_int @ C @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) ) ) ) ).
% IntI
thf(fact_287_Un__iff,axiom,
! [C: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( member2764346250752101224nt_int @ C @ ( sup_su3633867531522857715nt_int @ A3 @ B4 ) )
= ( ( member2764346250752101224nt_int @ C @ A3 )
| ( member2764346250752101224nt_int @ C @ B4 ) ) ) ).
% Un_iff
thf(fact_288_Un__iff,axiom,
! [C: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( member2340774599025711042nt_int @ C @ ( sup_su2047564715030645325nt_int @ A3 @ B4 ) )
= ( ( member2340774599025711042nt_int @ C @ A3 )
| ( member2340774599025711042nt_int @ C @ B4 ) ) ) ).
% Un_iff
thf(fact_289_Un__iff,axiom,
! [C: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ C @ ( sup_su6024340866399070445nt_int @ A3 @ B4 ) )
= ( ( member5262025264175285858nt_int @ C @ A3 )
| ( member5262025264175285858nt_int @ C @ B4 ) ) ) ).
% Un_iff
thf(fact_290_UnCI,axiom,
! [C: list_P5707943133018811711nt_int,B4: set_li3855193629254082847nt_int,A3: set_li3855193629254082847nt_int] :
( ( ~ ( member2764346250752101224nt_int @ C @ B4 )
=> ( member2764346250752101224nt_int @ C @ A3 ) )
=> ( member2764346250752101224nt_int @ C @ ( sup_su3633867531522857715nt_int @ A3 @ B4 ) ) ) ).
% UnCI
thf(fact_291_UnCI,axiom,
! [C: set_Pr958786334691620121nt_int,B4: set_se6260736226359567993nt_int,A3: set_se6260736226359567993nt_int] :
( ( ~ ( member2340774599025711042nt_int @ C @ B4 )
=> ( member2340774599025711042nt_int @ C @ A3 ) )
=> ( member2340774599025711042nt_int @ C @ ( sup_su2047564715030645325nt_int @ A3 @ B4 ) ) ) ).
% UnCI
thf(fact_292_UnCI,axiom,
! [C: product_prod_int_int,B4: set_Pr958786334691620121nt_int,A3: set_Pr958786334691620121nt_int] :
( ( ~ ( member5262025264175285858nt_int @ C @ B4 )
=> ( member5262025264175285858nt_int @ C @ A3 ) )
=> ( member5262025264175285858nt_int @ C @ ( sup_su6024340866399070445nt_int @ A3 @ B4 ) ) ) ).
% UnCI
thf(fact_293_Diff__idemp,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( minus_2612819937483484256nt_int @ ( minus_2612819937483484256nt_int @ A3 @ B4 ) @ B4 )
= ( minus_2612819937483484256nt_int @ A3 @ B4 ) ) ).
% Diff_idemp
thf(fact_294_Diff__idemp,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( minus_1052850069191792384nt_int @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) @ B4 )
= ( minus_1052850069191792384nt_int @ A3 @ B4 ) ) ).
% Diff_idemp
thf(fact_295_Diff__iff,axiom,
! [C: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( member2764346250752101224nt_int @ C @ ( minus_456201022768243590nt_int @ A3 @ B4 ) )
= ( ( member2764346250752101224nt_int @ C @ A3 )
& ~ ( member2764346250752101224nt_int @ C @ B4 ) ) ) ).
% Diff_iff
thf(fact_296_Diff__iff,axiom,
! [C: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( member2340774599025711042nt_int @ C @ ( minus_2612819937483484256nt_int @ A3 @ B4 ) )
= ( ( member2340774599025711042nt_int @ C @ A3 )
& ~ ( member2340774599025711042nt_int @ C @ B4 ) ) ) ).
% Diff_iff
thf(fact_297_Diff__iff,axiom,
! [C: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ C @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) )
= ( ( member5262025264175285858nt_int @ C @ A3 )
& ~ ( member5262025264175285858nt_int @ C @ B4 ) ) ) ).
% Diff_iff
thf(fact_298_DiffI,axiom,
! [C: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( member2764346250752101224nt_int @ C @ A3 )
=> ( ~ ( member2764346250752101224nt_int @ C @ B4 )
=> ( member2764346250752101224nt_int @ C @ ( minus_456201022768243590nt_int @ A3 @ B4 ) ) ) ) ).
% DiffI
thf(fact_299_DiffI,axiom,
! [C: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( member2340774599025711042nt_int @ C @ A3 )
=> ( ~ ( member2340774599025711042nt_int @ C @ B4 )
=> ( member2340774599025711042nt_int @ C @ ( minus_2612819937483484256nt_int @ A3 @ B4 ) ) ) ) ).
% DiffI
thf(fact_300_DiffI,axiom,
! [C: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ C @ A3 )
=> ( ~ ( member5262025264175285858nt_int @ C @ B4 )
=> ( member5262025264175285858nt_int @ C @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) ) ) ) ).
% DiffI
thf(fact_301_singletonI,axiom,
! [A: produc1219242969750017639nt_int] : ( member8566619992076573584nt_int @ A @ ( insert5410160437170799671nt_int @ A @ bot_bo8417956007504411571nt_int ) ) ).
% singletonI
thf(fact_302_singletonI,axiom,
! [A: int] : ( member_int @ A @ ( insert_int @ A @ bot_bot_set_int ) ) ).
% singletonI
thf(fact_303_singletonI,axiom,
! [A: list_P5707943133018811711nt_int] : ( member2764346250752101224nt_int @ A @ ( insert393344137582914319nt_int @ A @ bot_bo3809061186584590219nt_int ) ) ).
% singletonI
thf(fact_304_singletonI,axiom,
! [A: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ A @ ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) ).
% singletonI
thf(fact_305_singletonI,axiom,
! [A: product_prod_int_int] : ( member5262025264175285858nt_int @ A @ ( insert5033312907999012233nt_int @ A @ bot_bo1796632182523588997nt_int ) ) ).
% singletonI
thf(fact_306_Un__empty,axiom,
! [A3: set_Pr2560585780119916871nt_int,B4: set_Pr2560585780119916871nt_int] :
( ( ( sup_su3808334714663352091nt_int @ A3 @ B4 )
= bot_bo8417956007504411571nt_int )
= ( ( A3 = bot_bo8417956007504411571nt_int )
& ( B4 = bot_bo8417956007504411571nt_int ) ) ) ).
% Un_empty
thf(fact_307_Un__empty,axiom,
! [A3: set_int,B4: set_int] :
( ( ( sup_sup_set_int @ A3 @ B4 )
= bot_bot_set_int )
= ( ( A3 = bot_bot_set_int )
& ( B4 = bot_bot_set_int ) ) ) ).
% Un_empty
thf(fact_308_Un__empty,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( ( sup_su3633867531522857715nt_int @ A3 @ B4 )
= bot_bo3809061186584590219nt_int )
= ( ( A3 = bot_bo3809061186584590219nt_int )
& ( B4 = bot_bo3809061186584590219nt_int ) ) ) ).
% Un_empty
thf(fact_309_Un__empty,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( ( sup_su2047564715030645325nt_int @ A3 @ B4 )
= bot_bo1488462491386950373nt_int )
= ( ( A3 = bot_bo1488462491386950373nt_int )
& ( B4 = bot_bo1488462491386950373nt_int ) ) ) ).
% Un_empty
thf(fact_310_Un__empty,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ( sup_su6024340866399070445nt_int @ A3 @ B4 )
= bot_bo1796632182523588997nt_int )
= ( ( A3 = bot_bo1796632182523588997nt_int )
& ( B4 = bot_bo1796632182523588997nt_int ) ) ) ).
% Un_empty
thf(fact_311_Int__insert__right__if1,axiom,
! [A: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( member2764346250752101224nt_int @ A @ A3 )
=> ( ( inf_in8463092517017915661nt_int @ A3 @ ( insert393344137582914319nt_int @ A @ B4 ) )
= ( insert393344137582914319nt_int @ A @ ( inf_in8463092517017915661nt_int @ A3 @ B4 ) ) ) ) ).
% Int_insert_right_if1
thf(fact_312_Int__insert__right__if1,axiom,
! [A: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( member2340774599025711042nt_int @ A @ A3 )
=> ( ( inf_in8396524679539076455nt_int @ A3 @ ( insert8897473484851387113nt_int @ A @ B4 ) )
= ( insert8897473484851387113nt_int @ A @ ( inf_in8396524679539076455nt_int @ A3 @ B4 ) ) ) ) ).
% Int_insert_right_if1
thf(fact_313_Int__insert__right__if1,axiom,
! [A: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ A @ A3 )
=> ( ( inf_in2269163501485487111nt_int @ A3 @ ( insert5033312907999012233nt_int @ A @ B4 ) )
= ( insert5033312907999012233nt_int @ A @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) ) ) ) ).
% Int_insert_right_if1
thf(fact_314_Int__insert__right__if0,axiom,
! [A: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ~ ( member2764346250752101224nt_int @ A @ A3 )
=> ( ( inf_in8463092517017915661nt_int @ A3 @ ( insert393344137582914319nt_int @ A @ B4 ) )
= ( inf_in8463092517017915661nt_int @ A3 @ B4 ) ) ) ).
% Int_insert_right_if0
thf(fact_315_Int__insert__right__if0,axiom,
! [A: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ~ ( member2340774599025711042nt_int @ A @ A3 )
=> ( ( inf_in8396524679539076455nt_int @ A3 @ ( insert8897473484851387113nt_int @ A @ B4 ) )
= ( inf_in8396524679539076455nt_int @ A3 @ B4 ) ) ) ).
% Int_insert_right_if0
thf(fact_316_Int__insert__right__if0,axiom,
! [A: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ~ ( member5262025264175285858nt_int @ A @ A3 )
=> ( ( inf_in2269163501485487111nt_int @ A3 @ ( insert5033312907999012233nt_int @ A @ B4 ) )
= ( inf_in2269163501485487111nt_int @ A3 @ B4 ) ) ) ).
% Int_insert_right_if0
thf(fact_317_insert__inter__insert,axiom,
! [A: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( inf_in8463092517017915661nt_int @ ( insert393344137582914319nt_int @ A @ A3 ) @ ( insert393344137582914319nt_int @ A @ B4 ) )
= ( insert393344137582914319nt_int @ A @ ( inf_in8463092517017915661nt_int @ A3 @ B4 ) ) ) ).
% insert_inter_insert
thf(fact_318_insert__inter__insert,axiom,
! [A: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ A3 ) @ ( insert8897473484851387113nt_int @ A @ B4 ) )
= ( insert8897473484851387113nt_int @ A @ ( inf_in8396524679539076455nt_int @ A3 @ B4 ) ) ) ).
% insert_inter_insert
thf(fact_319_insert__inter__insert,axiom,
! [A: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ ( insert5033312907999012233nt_int @ A @ A3 ) @ ( insert5033312907999012233nt_int @ A @ B4 ) )
= ( insert5033312907999012233nt_int @ A @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) ) ) ).
% insert_inter_insert
thf(fact_320_Int__insert__left__if1,axiom,
! [A: list_P5707943133018811711nt_int,C2: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( member2764346250752101224nt_int @ A @ C2 )
=> ( ( inf_in8463092517017915661nt_int @ ( insert393344137582914319nt_int @ A @ B4 ) @ C2 )
= ( insert393344137582914319nt_int @ A @ ( inf_in8463092517017915661nt_int @ B4 @ C2 ) ) ) ) ).
% Int_insert_left_if1
thf(fact_321_Int__insert__left__if1,axiom,
! [A: set_Pr958786334691620121nt_int,C2: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( member2340774599025711042nt_int @ A @ C2 )
=> ( ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ B4 ) @ C2 )
= ( insert8897473484851387113nt_int @ A @ ( inf_in8396524679539076455nt_int @ B4 @ C2 ) ) ) ) ).
% Int_insert_left_if1
thf(fact_322_Int__insert__left__if1,axiom,
! [A: product_prod_int_int,C2: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ A @ C2 )
=> ( ( inf_in2269163501485487111nt_int @ ( insert5033312907999012233nt_int @ A @ B4 ) @ C2 )
= ( insert5033312907999012233nt_int @ A @ ( inf_in2269163501485487111nt_int @ B4 @ C2 ) ) ) ) ).
% Int_insert_left_if1
thf(fact_323_Int__insert__left__if0,axiom,
! [A: list_P5707943133018811711nt_int,C2: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ~ ( member2764346250752101224nt_int @ A @ C2 )
=> ( ( inf_in8463092517017915661nt_int @ ( insert393344137582914319nt_int @ A @ B4 ) @ C2 )
= ( inf_in8463092517017915661nt_int @ B4 @ C2 ) ) ) ).
% Int_insert_left_if0
thf(fact_324_Int__insert__left__if0,axiom,
! [A: set_Pr958786334691620121nt_int,C2: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ~ ( member2340774599025711042nt_int @ A @ C2 )
=> ( ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ B4 ) @ C2 )
= ( inf_in8396524679539076455nt_int @ B4 @ C2 ) ) ) ).
% Int_insert_left_if0
thf(fact_325_Int__insert__left__if0,axiom,
! [A: product_prod_int_int,C2: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ~ ( member5262025264175285858nt_int @ A @ C2 )
=> ( ( inf_in2269163501485487111nt_int @ ( insert5033312907999012233nt_int @ A @ B4 ) @ C2 )
= ( inf_in2269163501485487111nt_int @ B4 @ C2 ) ) ) ).
% Int_insert_left_if0
thf(fact_326_Un__Int__eq_I1_J,axiom,
! [S: set_li3855193629254082847nt_int,T: set_li3855193629254082847nt_int] :
( ( inf_in8463092517017915661nt_int @ ( sup_su3633867531522857715nt_int @ S @ T ) @ S )
= S ) ).
% Un_Int_eq(1)
thf(fact_327_Un__Int__eq_I1_J,axiom,
! [S: set_se6260736226359567993nt_int,T: set_se6260736226359567993nt_int] :
( ( inf_in8396524679539076455nt_int @ ( sup_su2047564715030645325nt_int @ S @ T ) @ S )
= S ) ).
% Un_Int_eq(1)
thf(fact_328_Un__Int__eq_I1_J,axiom,
! [S: set_Pr958786334691620121nt_int,T: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ ( sup_su6024340866399070445nt_int @ S @ T ) @ S )
= S ) ).
% Un_Int_eq(1)
thf(fact_329_Un__Int__eq_I2_J,axiom,
! [S: set_li3855193629254082847nt_int,T: set_li3855193629254082847nt_int] :
( ( inf_in8463092517017915661nt_int @ ( sup_su3633867531522857715nt_int @ S @ T ) @ T )
= T ) ).
% Un_Int_eq(2)
thf(fact_330_Un__Int__eq_I2_J,axiom,
! [S: set_se6260736226359567993nt_int,T: set_se6260736226359567993nt_int] :
( ( inf_in8396524679539076455nt_int @ ( sup_su2047564715030645325nt_int @ S @ T ) @ T )
= T ) ).
% Un_Int_eq(2)
thf(fact_331_Un__Int__eq_I2_J,axiom,
! [S: set_Pr958786334691620121nt_int,T: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ ( sup_su6024340866399070445nt_int @ S @ T ) @ T )
= T ) ).
% Un_Int_eq(2)
thf(fact_332_Un__Int__eq_I3_J,axiom,
! [S: set_li3855193629254082847nt_int,T: set_li3855193629254082847nt_int] :
( ( inf_in8463092517017915661nt_int @ S @ ( sup_su3633867531522857715nt_int @ S @ T ) )
= S ) ).
% Un_Int_eq(3)
thf(fact_333_Un__Int__eq_I3_J,axiom,
! [S: set_se6260736226359567993nt_int,T: set_se6260736226359567993nt_int] :
( ( inf_in8396524679539076455nt_int @ S @ ( sup_su2047564715030645325nt_int @ S @ T ) )
= S ) ).
% Un_Int_eq(3)
thf(fact_334_Un__Int__eq_I3_J,axiom,
! [S: set_Pr958786334691620121nt_int,T: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ S @ ( sup_su6024340866399070445nt_int @ S @ T ) )
= S ) ).
% Un_Int_eq(3)
thf(fact_335_Un__Int__eq_I4_J,axiom,
! [T: set_li3855193629254082847nt_int,S: set_li3855193629254082847nt_int] :
( ( inf_in8463092517017915661nt_int @ T @ ( sup_su3633867531522857715nt_int @ S @ T ) )
= T ) ).
% Un_Int_eq(4)
thf(fact_336_Un__Int__eq_I4_J,axiom,
! [T: set_se6260736226359567993nt_int,S: set_se6260736226359567993nt_int] :
( ( inf_in8396524679539076455nt_int @ T @ ( sup_su2047564715030645325nt_int @ S @ T ) )
= T ) ).
% Un_Int_eq(4)
thf(fact_337_Un__Int__eq_I4_J,axiom,
! [T: set_Pr958786334691620121nt_int,S: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ T @ ( sup_su6024340866399070445nt_int @ S @ T ) )
= T ) ).
% Un_Int_eq(4)
thf(fact_338_Int__Un__eq_I1_J,axiom,
! [S: set_li3855193629254082847nt_int,T: set_li3855193629254082847nt_int] :
( ( sup_su3633867531522857715nt_int @ ( inf_in8463092517017915661nt_int @ S @ T ) @ S )
= S ) ).
% Int_Un_eq(1)
thf(fact_339_Int__Un__eq_I1_J,axiom,
! [S: set_se6260736226359567993nt_int,T: set_se6260736226359567993nt_int] :
( ( sup_su2047564715030645325nt_int @ ( inf_in8396524679539076455nt_int @ S @ T ) @ S )
= S ) ).
% Int_Un_eq(1)
thf(fact_340_Int__Un__eq_I1_J,axiom,
! [S: set_Pr958786334691620121nt_int,T: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ ( inf_in2269163501485487111nt_int @ S @ T ) @ S )
= S ) ).
% Int_Un_eq(1)
thf(fact_341_Int__Un__eq_I2_J,axiom,
! [S: set_li3855193629254082847nt_int,T: set_li3855193629254082847nt_int] :
( ( sup_su3633867531522857715nt_int @ ( inf_in8463092517017915661nt_int @ S @ T ) @ T )
= T ) ).
% Int_Un_eq(2)
thf(fact_342_Int__Un__eq_I2_J,axiom,
! [S: set_se6260736226359567993nt_int,T: set_se6260736226359567993nt_int] :
( ( sup_su2047564715030645325nt_int @ ( inf_in8396524679539076455nt_int @ S @ T ) @ T )
= T ) ).
% Int_Un_eq(2)
thf(fact_343_Int__Un__eq_I2_J,axiom,
! [S: set_Pr958786334691620121nt_int,T: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ ( inf_in2269163501485487111nt_int @ S @ T ) @ T )
= T ) ).
% Int_Un_eq(2)
thf(fact_344_Int__Un__eq_I3_J,axiom,
! [S: set_li3855193629254082847nt_int,T: set_li3855193629254082847nt_int] :
( ( sup_su3633867531522857715nt_int @ S @ ( inf_in8463092517017915661nt_int @ S @ T ) )
= S ) ).
% Int_Un_eq(3)
thf(fact_345_Int__Un__eq_I3_J,axiom,
! [S: set_se6260736226359567993nt_int,T: set_se6260736226359567993nt_int] :
( ( sup_su2047564715030645325nt_int @ S @ ( inf_in8396524679539076455nt_int @ S @ T ) )
= S ) ).
% Int_Un_eq(3)
thf(fact_346_Int__Un__eq_I3_J,axiom,
! [S: set_Pr958786334691620121nt_int,T: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ S @ ( inf_in2269163501485487111nt_int @ S @ T ) )
= S ) ).
% Int_Un_eq(3)
thf(fact_347_Int__Un__eq_I4_J,axiom,
! [T: set_li3855193629254082847nt_int,S: set_li3855193629254082847nt_int] :
( ( sup_su3633867531522857715nt_int @ T @ ( inf_in8463092517017915661nt_int @ S @ T ) )
= T ) ).
% Int_Un_eq(4)
thf(fact_348_Int__Un__eq_I4_J,axiom,
! [T: set_se6260736226359567993nt_int,S: set_se6260736226359567993nt_int] :
( ( sup_su2047564715030645325nt_int @ T @ ( inf_in8396524679539076455nt_int @ S @ T ) )
= T ) ).
% Int_Un_eq(4)
thf(fact_349_Int__Un__eq_I4_J,axiom,
! [T: set_Pr958786334691620121nt_int,S: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ T @ ( inf_in2269163501485487111nt_int @ S @ T ) )
= T ) ).
% Int_Un_eq(4)
thf(fact_350_insert__disjoint_I1_J,axiom,
! [A: produc1219242969750017639nt_int,A3: set_Pr2560585780119916871nt_int,B4: set_Pr2560585780119916871nt_int] :
( ( ( inf_in7392334082413294389nt_int @ ( insert5410160437170799671nt_int @ A @ A3 ) @ B4 )
= bot_bo8417956007504411571nt_int )
= ( ~ ( member8566619992076573584nt_int @ A @ B4 )
& ( ( inf_in7392334082413294389nt_int @ A3 @ B4 )
= bot_bo8417956007504411571nt_int ) ) ) ).
% insert_disjoint(1)
thf(fact_351_insert__disjoint_I1_J,axiom,
! [A: int,A3: set_int,B4: set_int] :
( ( ( inf_inf_set_int @ ( insert_int @ A @ A3 ) @ B4 )
= bot_bot_set_int )
= ( ~ ( member_int @ A @ B4 )
& ( ( inf_inf_set_int @ A3 @ B4 )
= bot_bot_set_int ) ) ) ).
% insert_disjoint(1)
thf(fact_352_insert__disjoint_I1_J,axiom,
! [A: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( ( inf_in8463092517017915661nt_int @ ( insert393344137582914319nt_int @ A @ A3 ) @ B4 )
= bot_bo3809061186584590219nt_int )
= ( ~ ( member2764346250752101224nt_int @ A @ B4 )
& ( ( inf_in8463092517017915661nt_int @ A3 @ B4 )
= bot_bo3809061186584590219nt_int ) ) ) ).
% insert_disjoint(1)
thf(fact_353_insert__disjoint_I1_J,axiom,
! [A: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ A3 ) @ B4 )
= bot_bo1488462491386950373nt_int )
= ( ~ ( member2340774599025711042nt_int @ A @ B4 )
& ( ( inf_in8396524679539076455nt_int @ A3 @ B4 )
= bot_bo1488462491386950373nt_int ) ) ) ).
% insert_disjoint(1)
thf(fact_354_insert__disjoint_I1_J,axiom,
! [A: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ( inf_in2269163501485487111nt_int @ ( insert5033312907999012233nt_int @ A @ A3 ) @ B4 )
= bot_bo1796632182523588997nt_int )
= ( ~ ( member5262025264175285858nt_int @ A @ B4 )
& ( ( inf_in2269163501485487111nt_int @ A3 @ B4 )
= bot_bo1796632182523588997nt_int ) ) ) ).
% insert_disjoint(1)
thf(fact_355_insert__disjoint_I2_J,axiom,
! [A: produc1219242969750017639nt_int,A3: set_Pr2560585780119916871nt_int,B4: set_Pr2560585780119916871nt_int] :
( ( bot_bo8417956007504411571nt_int
= ( inf_in7392334082413294389nt_int @ ( insert5410160437170799671nt_int @ A @ A3 ) @ B4 ) )
= ( ~ ( member8566619992076573584nt_int @ A @ B4 )
& ( bot_bo8417956007504411571nt_int
= ( inf_in7392334082413294389nt_int @ A3 @ B4 ) ) ) ) ).
% insert_disjoint(2)
thf(fact_356_insert__disjoint_I2_J,axiom,
! [A: int,A3: set_int,B4: set_int] :
( ( bot_bot_set_int
= ( inf_inf_set_int @ ( insert_int @ A @ A3 ) @ B4 ) )
= ( ~ ( member_int @ A @ B4 )
& ( bot_bot_set_int
= ( inf_inf_set_int @ A3 @ B4 ) ) ) ) ).
% insert_disjoint(2)
thf(fact_357_insert__disjoint_I2_J,axiom,
! [A: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( bot_bo3809061186584590219nt_int
= ( inf_in8463092517017915661nt_int @ ( insert393344137582914319nt_int @ A @ A3 ) @ B4 ) )
= ( ~ ( member2764346250752101224nt_int @ A @ B4 )
& ( bot_bo3809061186584590219nt_int
= ( inf_in8463092517017915661nt_int @ A3 @ B4 ) ) ) ) ).
% insert_disjoint(2)
thf(fact_358_insert__disjoint_I2_J,axiom,
! [A: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( bot_bo1488462491386950373nt_int
= ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ A3 ) @ B4 ) )
= ( ~ ( member2340774599025711042nt_int @ A @ B4 )
& ( bot_bo1488462491386950373nt_int
= ( inf_in8396524679539076455nt_int @ A3 @ B4 ) ) ) ) ).
% insert_disjoint(2)
thf(fact_359_insert__disjoint_I2_J,axiom,
! [A: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( bot_bo1796632182523588997nt_int
= ( inf_in2269163501485487111nt_int @ ( insert5033312907999012233nt_int @ A @ A3 ) @ B4 ) )
= ( ~ ( member5262025264175285858nt_int @ A @ B4 )
& ( bot_bo1796632182523588997nt_int
= ( inf_in2269163501485487111nt_int @ A3 @ B4 ) ) ) ) ).
% insert_disjoint(2)
thf(fact_360_disjoint__insert_I1_J,axiom,
! [B4: set_Pr2560585780119916871nt_int,A: produc1219242969750017639nt_int,A3: set_Pr2560585780119916871nt_int] :
( ( ( inf_in7392334082413294389nt_int @ B4 @ ( insert5410160437170799671nt_int @ A @ A3 ) )
= bot_bo8417956007504411571nt_int )
= ( ~ ( member8566619992076573584nt_int @ A @ B4 )
& ( ( inf_in7392334082413294389nt_int @ B4 @ A3 )
= bot_bo8417956007504411571nt_int ) ) ) ).
% disjoint_insert(1)
thf(fact_361_disjoint__insert_I1_J,axiom,
! [B4: set_int,A: int,A3: set_int] :
( ( ( inf_inf_set_int @ B4 @ ( insert_int @ A @ A3 ) )
= bot_bot_set_int )
= ( ~ ( member_int @ A @ B4 )
& ( ( inf_inf_set_int @ B4 @ A3 )
= bot_bot_set_int ) ) ) ).
% disjoint_insert(1)
thf(fact_362_disjoint__insert_I1_J,axiom,
! [B4: set_li3855193629254082847nt_int,A: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int] :
( ( ( inf_in8463092517017915661nt_int @ B4 @ ( insert393344137582914319nt_int @ A @ A3 ) )
= bot_bo3809061186584590219nt_int )
= ( ~ ( member2764346250752101224nt_int @ A @ B4 )
& ( ( inf_in8463092517017915661nt_int @ B4 @ A3 )
= bot_bo3809061186584590219nt_int ) ) ) ).
% disjoint_insert(1)
thf(fact_363_disjoint__insert_I1_J,axiom,
! [B4: set_se6260736226359567993nt_int,A: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int] :
( ( ( inf_in8396524679539076455nt_int @ B4 @ ( insert8897473484851387113nt_int @ A @ A3 ) )
= bot_bo1488462491386950373nt_int )
= ( ~ ( member2340774599025711042nt_int @ A @ B4 )
& ( ( inf_in8396524679539076455nt_int @ B4 @ A3 )
= bot_bo1488462491386950373nt_int ) ) ) ).
% disjoint_insert(1)
thf(fact_364_disjoint__insert_I1_J,axiom,
! [B4: set_Pr958786334691620121nt_int,A: product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( ( inf_in2269163501485487111nt_int @ B4 @ ( insert5033312907999012233nt_int @ A @ A3 ) )
= bot_bo1796632182523588997nt_int )
= ( ~ ( member5262025264175285858nt_int @ A @ B4 )
& ( ( inf_in2269163501485487111nt_int @ B4 @ A3 )
= bot_bo1796632182523588997nt_int ) ) ) ).
% disjoint_insert(1)
thf(fact_365_disjoint__insert_I2_J,axiom,
! [A3: set_Pr2560585780119916871nt_int,B: produc1219242969750017639nt_int,B4: set_Pr2560585780119916871nt_int] :
( ( bot_bo8417956007504411571nt_int
= ( inf_in7392334082413294389nt_int @ A3 @ ( insert5410160437170799671nt_int @ B @ B4 ) ) )
= ( ~ ( member8566619992076573584nt_int @ B @ A3 )
& ( bot_bo8417956007504411571nt_int
= ( inf_in7392334082413294389nt_int @ A3 @ B4 ) ) ) ) ).
% disjoint_insert(2)
thf(fact_366_disjoint__insert_I2_J,axiom,
! [A3: set_int,B: int,B4: set_int] :
( ( bot_bot_set_int
= ( inf_inf_set_int @ A3 @ ( insert_int @ B @ B4 ) ) )
= ( ~ ( member_int @ B @ A3 )
& ( bot_bot_set_int
= ( inf_inf_set_int @ A3 @ B4 ) ) ) ) ).
% disjoint_insert(2)
thf(fact_367_disjoint__insert_I2_J,axiom,
! [A3: set_li3855193629254082847nt_int,B: list_P5707943133018811711nt_int,B4: set_li3855193629254082847nt_int] :
( ( bot_bo3809061186584590219nt_int
= ( inf_in8463092517017915661nt_int @ A3 @ ( insert393344137582914319nt_int @ B @ B4 ) ) )
= ( ~ ( member2764346250752101224nt_int @ B @ A3 )
& ( bot_bo3809061186584590219nt_int
= ( inf_in8463092517017915661nt_int @ A3 @ B4 ) ) ) ) ).
% disjoint_insert(2)
thf(fact_368_disjoint__insert_I2_J,axiom,
! [A3: set_se6260736226359567993nt_int,B: set_Pr958786334691620121nt_int,B4: set_se6260736226359567993nt_int] :
( ( bot_bo1488462491386950373nt_int
= ( inf_in8396524679539076455nt_int @ A3 @ ( insert8897473484851387113nt_int @ B @ B4 ) ) )
= ( ~ ( member2340774599025711042nt_int @ B @ A3 )
& ( bot_bo1488462491386950373nt_int
= ( inf_in8396524679539076455nt_int @ A3 @ B4 ) ) ) ) ).
% disjoint_insert(2)
thf(fact_369_disjoint__insert_I2_J,axiom,
! [A3: set_Pr958786334691620121nt_int,B: product_prod_int_int,B4: set_Pr958786334691620121nt_int] :
( ( bot_bo1796632182523588997nt_int
= ( inf_in2269163501485487111nt_int @ A3 @ ( insert5033312907999012233nt_int @ B @ B4 ) ) )
= ( ~ ( member5262025264175285858nt_int @ B @ A3 )
& ( bot_bo1796632182523588997nt_int
= ( inf_in2269163501485487111nt_int @ A3 @ B4 ) ) ) ) ).
% disjoint_insert(2)
thf(fact_370_Diff__disjoint,axiom,
! [A3: set_Pr2560585780119916871nt_int,B4: set_Pr2560585780119916871nt_int] :
( ( inf_in7392334082413294389nt_int @ A3 @ ( minus_2188297577953631406nt_int @ B4 @ A3 ) )
= bot_bo8417956007504411571nt_int ) ).
% Diff_disjoint
thf(fact_371_Diff__disjoint,axiom,
! [A3: set_int,B4: set_int] :
( ( inf_inf_set_int @ A3 @ ( minus_minus_set_int @ B4 @ A3 ) )
= bot_bot_set_int ) ).
% Diff_disjoint
thf(fact_372_Diff__disjoint,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( inf_in8463092517017915661nt_int @ A3 @ ( minus_456201022768243590nt_int @ B4 @ A3 ) )
= bot_bo3809061186584590219nt_int ) ).
% Diff_disjoint
thf(fact_373_Diff__disjoint,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( inf_in8396524679539076455nt_int @ A3 @ ( minus_2612819937483484256nt_int @ B4 @ A3 ) )
= bot_bo1488462491386950373nt_int ) ).
% Diff_disjoint
thf(fact_374_Diff__disjoint,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ A3 @ ( minus_1052850069191792384nt_int @ B4 @ A3 ) )
= bot_bo1796632182523588997nt_int ) ).
% Diff_disjoint
thf(fact_375_Int__left__commute,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int,C2: set_li3855193629254082847nt_int] :
( ( inf_in8463092517017915661nt_int @ A3 @ ( inf_in8463092517017915661nt_int @ B4 @ C2 ) )
= ( inf_in8463092517017915661nt_int @ B4 @ ( inf_in8463092517017915661nt_int @ A3 @ C2 ) ) ) ).
% Int_left_commute
thf(fact_376_Int__left__commute,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int,C2: set_se6260736226359567993nt_int] :
( ( inf_in8396524679539076455nt_int @ A3 @ ( inf_in8396524679539076455nt_int @ B4 @ C2 ) )
= ( inf_in8396524679539076455nt_int @ B4 @ ( inf_in8396524679539076455nt_int @ A3 @ C2 ) ) ) ).
% Int_left_commute
thf(fact_377_Int__left__commute,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ A3 @ ( inf_in2269163501485487111nt_int @ B4 @ C2 ) )
= ( inf_in2269163501485487111nt_int @ B4 @ ( inf_in2269163501485487111nt_int @ A3 @ C2 ) ) ) ).
% Int_left_commute
thf(fact_378_Int__left__absorb,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( inf_in8463092517017915661nt_int @ A3 @ ( inf_in8463092517017915661nt_int @ A3 @ B4 ) )
= ( inf_in8463092517017915661nt_int @ A3 @ B4 ) ) ).
% Int_left_absorb
thf(fact_379_Int__left__absorb,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( inf_in8396524679539076455nt_int @ A3 @ ( inf_in8396524679539076455nt_int @ A3 @ B4 ) )
= ( inf_in8396524679539076455nt_int @ A3 @ B4 ) ) ).
% Int_left_absorb
thf(fact_380_Int__left__absorb,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ A3 @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) )
= ( inf_in2269163501485487111nt_int @ A3 @ B4 ) ) ).
% Int_left_absorb
thf(fact_381_Int__commute,axiom,
( inf_in8463092517017915661nt_int
= ( ^ [A4: set_li3855193629254082847nt_int,B5: set_li3855193629254082847nt_int] : ( inf_in8463092517017915661nt_int @ B5 @ A4 ) ) ) ).
% Int_commute
thf(fact_382_Int__commute,axiom,
( inf_in8396524679539076455nt_int
= ( ^ [A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] : ( inf_in8396524679539076455nt_int @ B5 @ A4 ) ) ) ).
% Int_commute
thf(fact_383_Int__commute,axiom,
( inf_in2269163501485487111nt_int
= ( ^ [A4: set_Pr958786334691620121nt_int,B5: set_Pr958786334691620121nt_int] : ( inf_in2269163501485487111nt_int @ B5 @ A4 ) ) ) ).
% Int_commute
thf(fact_384_Int__absorb,axiom,
! [A3: set_li3855193629254082847nt_int] :
( ( inf_in8463092517017915661nt_int @ A3 @ A3 )
= A3 ) ).
% Int_absorb
thf(fact_385_Int__absorb,axiom,
! [A3: set_se6260736226359567993nt_int] :
( ( inf_in8396524679539076455nt_int @ A3 @ A3 )
= A3 ) ).
% Int_absorb
thf(fact_386_Int__absorb,axiom,
! [A3: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ A3 @ A3 )
= A3 ) ).
% Int_absorb
thf(fact_387_Int__assoc,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int,C2: set_li3855193629254082847nt_int] :
( ( inf_in8463092517017915661nt_int @ ( inf_in8463092517017915661nt_int @ A3 @ B4 ) @ C2 )
= ( inf_in8463092517017915661nt_int @ A3 @ ( inf_in8463092517017915661nt_int @ B4 @ C2 ) ) ) ).
% Int_assoc
thf(fact_388_Int__assoc,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int,C2: set_se6260736226359567993nt_int] :
( ( inf_in8396524679539076455nt_int @ ( inf_in8396524679539076455nt_int @ A3 @ B4 ) @ C2 )
= ( inf_in8396524679539076455nt_int @ A3 @ ( inf_in8396524679539076455nt_int @ B4 @ C2 ) ) ) ).
% Int_assoc
thf(fact_389_Int__assoc,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) @ C2 )
= ( inf_in2269163501485487111nt_int @ A3 @ ( inf_in2269163501485487111nt_int @ B4 @ C2 ) ) ) ).
% Int_assoc
thf(fact_390_IntD2,axiom,
! [C: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( member2764346250752101224nt_int @ C @ ( inf_in8463092517017915661nt_int @ A3 @ B4 ) )
=> ( member2764346250752101224nt_int @ C @ B4 ) ) ).
% IntD2
thf(fact_391_IntD2,axiom,
! [C: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( member2340774599025711042nt_int @ C @ ( inf_in8396524679539076455nt_int @ A3 @ B4 ) )
=> ( member2340774599025711042nt_int @ C @ B4 ) ) ).
% IntD2
thf(fact_392_IntD2,axiom,
! [C: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ C @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) )
=> ( member5262025264175285858nt_int @ C @ B4 ) ) ).
% IntD2
thf(fact_393_IntD1,axiom,
! [C: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( member2764346250752101224nt_int @ C @ ( inf_in8463092517017915661nt_int @ A3 @ B4 ) )
=> ( member2764346250752101224nt_int @ C @ A3 ) ) ).
% IntD1
thf(fact_394_IntD1,axiom,
! [C: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( member2340774599025711042nt_int @ C @ ( inf_in8396524679539076455nt_int @ A3 @ B4 ) )
=> ( member2340774599025711042nt_int @ C @ A3 ) ) ).
% IntD1
thf(fact_395_IntD1,axiom,
! [C: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ C @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) )
=> ( member5262025264175285858nt_int @ C @ A3 ) ) ).
% IntD1
thf(fact_396_IntE,axiom,
! [C: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( member2764346250752101224nt_int @ C @ ( inf_in8463092517017915661nt_int @ A3 @ B4 ) )
=> ~ ( ( member2764346250752101224nt_int @ C @ A3 )
=> ~ ( member2764346250752101224nt_int @ C @ B4 ) ) ) ).
% IntE
thf(fact_397_IntE,axiom,
! [C: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( member2340774599025711042nt_int @ C @ ( inf_in8396524679539076455nt_int @ A3 @ B4 ) )
=> ~ ( ( member2340774599025711042nt_int @ C @ A3 )
=> ~ ( member2340774599025711042nt_int @ C @ B4 ) ) ) ).
% IntE
thf(fact_398_IntE,axiom,
! [C: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ C @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) )
=> ~ ( ( member5262025264175285858nt_int @ C @ A3 )
=> ~ ( member5262025264175285858nt_int @ C @ B4 ) ) ) ).
% IntE
thf(fact_399_disjoint__iff__not__equal,axiom,
! [A3: set_Pr2560585780119916871nt_int,B4: set_Pr2560585780119916871nt_int] :
( ( ( inf_in7392334082413294389nt_int @ A3 @ B4 )
= bot_bo8417956007504411571nt_int )
= ( ! [X2: produc1219242969750017639nt_int] :
( ( member8566619992076573584nt_int @ X2 @ A3 )
=> ! [Y3: produc1219242969750017639nt_int] :
( ( member8566619992076573584nt_int @ Y3 @ B4 )
=> ( X2 != Y3 ) ) ) ) ) ).
% disjoint_iff_not_equal
thf(fact_400_disjoint__iff__not__equal,axiom,
! [A3: set_int,B4: set_int] :
( ( ( inf_inf_set_int @ A3 @ B4 )
= bot_bot_set_int )
= ( ! [X2: int] :
( ( member_int @ X2 @ A3 )
=> ! [Y3: int] :
( ( member_int @ Y3 @ B4 )
=> ( X2 != Y3 ) ) ) ) ) ).
% disjoint_iff_not_equal
thf(fact_401_disjoint__iff__not__equal,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( ( inf_in8463092517017915661nt_int @ A3 @ B4 )
= bot_bo3809061186584590219nt_int )
= ( ! [X2: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ X2 @ A3 )
=> ! [Y3: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ Y3 @ B4 )
=> ( X2 != Y3 ) ) ) ) ) ).
% disjoint_iff_not_equal
thf(fact_402_disjoint__iff__not__equal,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( ( inf_in8396524679539076455nt_int @ A3 @ B4 )
= bot_bo1488462491386950373nt_int )
= ( ! [X2: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ X2 @ A3 )
=> ! [Y3: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ Y3 @ B4 )
=> ( X2 != Y3 ) ) ) ) ) ).
% disjoint_iff_not_equal
thf(fact_403_disjoint__iff__not__equal,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ( inf_in2269163501485487111nt_int @ A3 @ B4 )
= bot_bo1796632182523588997nt_int )
= ( ! [X2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X2 @ A3 )
=> ! [Y3: product_prod_int_int] :
( ( member5262025264175285858nt_int @ Y3 @ B4 )
=> ( X2 != Y3 ) ) ) ) ) ).
% disjoint_iff_not_equal
thf(fact_404_Int__empty__right,axiom,
! [A3: set_Pr2560585780119916871nt_int] :
( ( inf_in7392334082413294389nt_int @ A3 @ bot_bo8417956007504411571nt_int )
= bot_bo8417956007504411571nt_int ) ).
% Int_empty_right
thf(fact_405_Int__empty__right,axiom,
! [A3: set_int] :
( ( inf_inf_set_int @ A3 @ bot_bot_set_int )
= bot_bot_set_int ) ).
% Int_empty_right
thf(fact_406_Int__empty__right,axiom,
! [A3: set_li3855193629254082847nt_int] :
( ( inf_in8463092517017915661nt_int @ A3 @ bot_bo3809061186584590219nt_int )
= bot_bo3809061186584590219nt_int ) ).
% Int_empty_right
thf(fact_407_Int__empty__right,axiom,
! [A3: set_se6260736226359567993nt_int] :
( ( inf_in8396524679539076455nt_int @ A3 @ bot_bo1488462491386950373nt_int )
= bot_bo1488462491386950373nt_int ) ).
% Int_empty_right
thf(fact_408_Int__empty__right,axiom,
! [A3: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ A3 @ bot_bo1796632182523588997nt_int )
= bot_bo1796632182523588997nt_int ) ).
% Int_empty_right
thf(fact_409_Int__empty__left,axiom,
! [B4: set_Pr2560585780119916871nt_int] :
( ( inf_in7392334082413294389nt_int @ bot_bo8417956007504411571nt_int @ B4 )
= bot_bo8417956007504411571nt_int ) ).
% Int_empty_left
thf(fact_410_Int__empty__left,axiom,
! [B4: set_int] :
( ( inf_inf_set_int @ bot_bot_set_int @ B4 )
= bot_bot_set_int ) ).
% Int_empty_left
thf(fact_411_Int__empty__left,axiom,
! [B4: set_li3855193629254082847nt_int] :
( ( inf_in8463092517017915661nt_int @ bot_bo3809061186584590219nt_int @ B4 )
= bot_bo3809061186584590219nt_int ) ).
% Int_empty_left
thf(fact_412_Int__empty__left,axiom,
! [B4: set_se6260736226359567993nt_int] :
( ( inf_in8396524679539076455nt_int @ bot_bo1488462491386950373nt_int @ B4 )
= bot_bo1488462491386950373nt_int ) ).
% Int_empty_left
thf(fact_413_Int__empty__left,axiom,
! [B4: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ bot_bo1796632182523588997nt_int @ B4 )
= bot_bo1796632182523588997nt_int ) ).
% Int_empty_left
thf(fact_414_disjoint__iff,axiom,
! [A3: set_Pr2560585780119916871nt_int,B4: set_Pr2560585780119916871nt_int] :
( ( ( inf_in7392334082413294389nt_int @ A3 @ B4 )
= bot_bo8417956007504411571nt_int )
= ( ! [X2: produc1219242969750017639nt_int] :
( ( member8566619992076573584nt_int @ X2 @ A3 )
=> ~ ( member8566619992076573584nt_int @ X2 @ B4 ) ) ) ) ).
% disjoint_iff
thf(fact_415_disjoint__iff,axiom,
! [A3: set_int,B4: set_int] :
( ( ( inf_inf_set_int @ A3 @ B4 )
= bot_bot_set_int )
= ( ! [X2: int] :
( ( member_int @ X2 @ A3 )
=> ~ ( member_int @ X2 @ B4 ) ) ) ) ).
% disjoint_iff
thf(fact_416_disjoint__iff,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( ( inf_in8463092517017915661nt_int @ A3 @ B4 )
= bot_bo3809061186584590219nt_int )
= ( ! [X2: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ X2 @ A3 )
=> ~ ( member2764346250752101224nt_int @ X2 @ B4 ) ) ) ) ).
% disjoint_iff
thf(fact_417_disjoint__iff,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( ( inf_in8396524679539076455nt_int @ A3 @ B4 )
= bot_bo1488462491386950373nt_int )
= ( ! [X2: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ X2 @ A3 )
=> ~ ( member2340774599025711042nt_int @ X2 @ B4 ) ) ) ) ).
% disjoint_iff
thf(fact_418_disjoint__iff,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ( inf_in2269163501485487111nt_int @ A3 @ B4 )
= bot_bo1796632182523588997nt_int )
= ( ! [X2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X2 @ A3 )
=> ~ ( member5262025264175285858nt_int @ X2 @ B4 ) ) ) ) ).
% disjoint_iff
thf(fact_419_Int__emptyI,axiom,
! [A3: set_Pr2560585780119916871nt_int,B4: set_Pr2560585780119916871nt_int] :
( ! [X3: produc1219242969750017639nt_int] :
( ( member8566619992076573584nt_int @ X3 @ A3 )
=> ~ ( member8566619992076573584nt_int @ X3 @ B4 ) )
=> ( ( inf_in7392334082413294389nt_int @ A3 @ B4 )
= bot_bo8417956007504411571nt_int ) ) ).
% Int_emptyI
thf(fact_420_Int__emptyI,axiom,
! [A3: set_int,B4: set_int] :
( ! [X3: int] :
( ( member_int @ X3 @ A3 )
=> ~ ( member_int @ X3 @ B4 ) )
=> ( ( inf_inf_set_int @ A3 @ B4 )
= bot_bot_set_int ) ) ).
% Int_emptyI
thf(fact_421_Int__emptyI,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ! [X3: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ X3 @ A3 )
=> ~ ( member2764346250752101224nt_int @ X3 @ B4 ) )
=> ( ( inf_in8463092517017915661nt_int @ A3 @ B4 )
= bot_bo3809061186584590219nt_int ) ) ).
% Int_emptyI
thf(fact_422_Int__emptyI,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ! [X3: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ X3 @ A3 )
=> ~ ( member2340774599025711042nt_int @ X3 @ B4 ) )
=> ( ( inf_in8396524679539076455nt_int @ A3 @ B4 )
= bot_bo1488462491386950373nt_int ) ) ).
% Int_emptyI
thf(fact_423_Int__emptyI,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ! [X3: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X3 @ A3 )
=> ~ ( member5262025264175285858nt_int @ X3 @ B4 ) )
=> ( ( inf_in2269163501485487111nt_int @ A3 @ B4 )
= bot_bo1796632182523588997nt_int ) ) ).
% Int_emptyI
thf(fact_424_Int__insert__right,axiom,
! [A: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( ( member2764346250752101224nt_int @ A @ A3 )
=> ( ( inf_in8463092517017915661nt_int @ A3 @ ( insert393344137582914319nt_int @ A @ B4 ) )
= ( insert393344137582914319nt_int @ A @ ( inf_in8463092517017915661nt_int @ A3 @ B4 ) ) ) )
& ( ~ ( member2764346250752101224nt_int @ A @ A3 )
=> ( ( inf_in8463092517017915661nt_int @ A3 @ ( insert393344137582914319nt_int @ A @ B4 ) )
= ( inf_in8463092517017915661nt_int @ A3 @ B4 ) ) ) ) ).
% Int_insert_right
thf(fact_425_Int__insert__right,axiom,
! [A: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( ( member2340774599025711042nt_int @ A @ A3 )
=> ( ( inf_in8396524679539076455nt_int @ A3 @ ( insert8897473484851387113nt_int @ A @ B4 ) )
= ( insert8897473484851387113nt_int @ A @ ( inf_in8396524679539076455nt_int @ A3 @ B4 ) ) ) )
& ( ~ ( member2340774599025711042nt_int @ A @ A3 )
=> ( ( inf_in8396524679539076455nt_int @ A3 @ ( insert8897473484851387113nt_int @ A @ B4 ) )
= ( inf_in8396524679539076455nt_int @ A3 @ B4 ) ) ) ) ).
% Int_insert_right
thf(fact_426_Int__insert__right,axiom,
! [A: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ( member5262025264175285858nt_int @ A @ A3 )
=> ( ( inf_in2269163501485487111nt_int @ A3 @ ( insert5033312907999012233nt_int @ A @ B4 ) )
= ( insert5033312907999012233nt_int @ A @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) ) ) )
& ( ~ ( member5262025264175285858nt_int @ A @ A3 )
=> ( ( inf_in2269163501485487111nt_int @ A3 @ ( insert5033312907999012233nt_int @ A @ B4 ) )
= ( inf_in2269163501485487111nt_int @ A3 @ B4 ) ) ) ) ).
% Int_insert_right
thf(fact_427_Int__insert__left,axiom,
! [A: list_P5707943133018811711nt_int,C2: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( ( member2764346250752101224nt_int @ A @ C2 )
=> ( ( inf_in8463092517017915661nt_int @ ( insert393344137582914319nt_int @ A @ B4 ) @ C2 )
= ( insert393344137582914319nt_int @ A @ ( inf_in8463092517017915661nt_int @ B4 @ C2 ) ) ) )
& ( ~ ( member2764346250752101224nt_int @ A @ C2 )
=> ( ( inf_in8463092517017915661nt_int @ ( insert393344137582914319nt_int @ A @ B4 ) @ C2 )
= ( inf_in8463092517017915661nt_int @ B4 @ C2 ) ) ) ) ).
% Int_insert_left
thf(fact_428_Int__insert__left,axiom,
! [A: set_Pr958786334691620121nt_int,C2: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( ( member2340774599025711042nt_int @ A @ C2 )
=> ( ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ B4 ) @ C2 )
= ( insert8897473484851387113nt_int @ A @ ( inf_in8396524679539076455nt_int @ B4 @ C2 ) ) ) )
& ( ~ ( member2340774599025711042nt_int @ A @ C2 )
=> ( ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ B4 ) @ C2 )
= ( inf_in8396524679539076455nt_int @ B4 @ C2 ) ) ) ) ).
% Int_insert_left
thf(fact_429_Int__insert__left,axiom,
! [A: product_prod_int_int,C2: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ( member5262025264175285858nt_int @ A @ C2 )
=> ( ( inf_in2269163501485487111nt_int @ ( insert5033312907999012233nt_int @ A @ B4 ) @ C2 )
= ( insert5033312907999012233nt_int @ A @ ( inf_in2269163501485487111nt_int @ B4 @ C2 ) ) ) )
& ( ~ ( member5262025264175285858nt_int @ A @ C2 )
=> ( ( inf_in2269163501485487111nt_int @ ( insert5033312907999012233nt_int @ A @ B4 ) @ C2 )
= ( inf_in2269163501485487111nt_int @ B4 @ C2 ) ) ) ) ).
% Int_insert_left
thf(fact_430_Un__Int__distrib2,axiom,
! [B4: set_li3855193629254082847nt_int,C2: set_li3855193629254082847nt_int,A3: set_li3855193629254082847nt_int] :
( ( sup_su3633867531522857715nt_int @ ( inf_in8463092517017915661nt_int @ B4 @ C2 ) @ A3 )
= ( inf_in8463092517017915661nt_int @ ( sup_su3633867531522857715nt_int @ B4 @ A3 ) @ ( sup_su3633867531522857715nt_int @ C2 @ A3 ) ) ) ).
% Un_Int_distrib2
thf(fact_431_Un__Int__distrib2,axiom,
! [B4: set_se6260736226359567993nt_int,C2: set_se6260736226359567993nt_int,A3: set_se6260736226359567993nt_int] :
( ( sup_su2047564715030645325nt_int @ ( inf_in8396524679539076455nt_int @ B4 @ C2 ) @ A3 )
= ( inf_in8396524679539076455nt_int @ ( sup_su2047564715030645325nt_int @ B4 @ A3 ) @ ( sup_su2047564715030645325nt_int @ C2 @ A3 ) ) ) ).
% Un_Int_distrib2
thf(fact_432_Un__Int__distrib2,axiom,
! [B4: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int,A3: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ ( inf_in2269163501485487111nt_int @ B4 @ C2 ) @ A3 )
= ( inf_in2269163501485487111nt_int @ ( sup_su6024340866399070445nt_int @ B4 @ A3 ) @ ( sup_su6024340866399070445nt_int @ C2 @ A3 ) ) ) ).
% Un_Int_distrib2
thf(fact_433_Int__Un__distrib2,axiom,
! [B4: set_li3855193629254082847nt_int,C2: set_li3855193629254082847nt_int,A3: set_li3855193629254082847nt_int] :
( ( inf_in8463092517017915661nt_int @ ( sup_su3633867531522857715nt_int @ B4 @ C2 ) @ A3 )
= ( sup_su3633867531522857715nt_int @ ( inf_in8463092517017915661nt_int @ B4 @ A3 ) @ ( inf_in8463092517017915661nt_int @ C2 @ A3 ) ) ) ).
% Int_Un_distrib2
thf(fact_434_Int__Un__distrib2,axiom,
! [B4: set_se6260736226359567993nt_int,C2: set_se6260736226359567993nt_int,A3: set_se6260736226359567993nt_int] :
( ( inf_in8396524679539076455nt_int @ ( sup_su2047564715030645325nt_int @ B4 @ C2 ) @ A3 )
= ( sup_su2047564715030645325nt_int @ ( inf_in8396524679539076455nt_int @ B4 @ A3 ) @ ( inf_in8396524679539076455nt_int @ C2 @ A3 ) ) ) ).
% Int_Un_distrib2
thf(fact_435_Int__Un__distrib2,axiom,
! [B4: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int,A3: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ ( sup_su6024340866399070445nt_int @ B4 @ C2 ) @ A3 )
= ( sup_su6024340866399070445nt_int @ ( inf_in2269163501485487111nt_int @ B4 @ A3 ) @ ( inf_in2269163501485487111nt_int @ C2 @ A3 ) ) ) ).
% Int_Un_distrib2
thf(fact_436_Un__Int__distrib,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int,C2: set_li3855193629254082847nt_int] :
( ( sup_su3633867531522857715nt_int @ A3 @ ( inf_in8463092517017915661nt_int @ B4 @ C2 ) )
= ( inf_in8463092517017915661nt_int @ ( sup_su3633867531522857715nt_int @ A3 @ B4 ) @ ( sup_su3633867531522857715nt_int @ A3 @ C2 ) ) ) ).
% Un_Int_distrib
thf(fact_437_Un__Int__distrib,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int,C2: set_se6260736226359567993nt_int] :
( ( sup_su2047564715030645325nt_int @ A3 @ ( inf_in8396524679539076455nt_int @ B4 @ C2 ) )
= ( inf_in8396524679539076455nt_int @ ( sup_su2047564715030645325nt_int @ A3 @ B4 ) @ ( sup_su2047564715030645325nt_int @ A3 @ C2 ) ) ) ).
% Un_Int_distrib
thf(fact_438_Un__Int__distrib,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ A3 @ ( inf_in2269163501485487111nt_int @ B4 @ C2 ) )
= ( inf_in2269163501485487111nt_int @ ( sup_su6024340866399070445nt_int @ A3 @ B4 ) @ ( sup_su6024340866399070445nt_int @ A3 @ C2 ) ) ) ).
% Un_Int_distrib
thf(fact_439_Int__Un__distrib,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int,C2: set_li3855193629254082847nt_int] :
( ( inf_in8463092517017915661nt_int @ A3 @ ( sup_su3633867531522857715nt_int @ B4 @ C2 ) )
= ( sup_su3633867531522857715nt_int @ ( inf_in8463092517017915661nt_int @ A3 @ B4 ) @ ( inf_in8463092517017915661nt_int @ A3 @ C2 ) ) ) ).
% Int_Un_distrib
thf(fact_440_Int__Un__distrib,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int,C2: set_se6260736226359567993nt_int] :
( ( inf_in8396524679539076455nt_int @ A3 @ ( sup_su2047564715030645325nt_int @ B4 @ C2 ) )
= ( sup_su2047564715030645325nt_int @ ( inf_in8396524679539076455nt_int @ A3 @ B4 ) @ ( inf_in8396524679539076455nt_int @ A3 @ C2 ) ) ) ).
% Int_Un_distrib
thf(fact_441_Int__Un__distrib,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ A3 @ ( sup_su6024340866399070445nt_int @ B4 @ C2 ) )
= ( sup_su6024340866399070445nt_int @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) @ ( inf_in2269163501485487111nt_int @ A3 @ C2 ) ) ) ).
% Int_Un_distrib
thf(fact_442_Un__Int__crazy,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int,C2: set_li3855193629254082847nt_int] :
( ( sup_su3633867531522857715nt_int @ ( sup_su3633867531522857715nt_int @ ( inf_in8463092517017915661nt_int @ A3 @ B4 ) @ ( inf_in8463092517017915661nt_int @ B4 @ C2 ) ) @ ( inf_in8463092517017915661nt_int @ C2 @ A3 ) )
= ( inf_in8463092517017915661nt_int @ ( inf_in8463092517017915661nt_int @ ( sup_su3633867531522857715nt_int @ A3 @ B4 ) @ ( sup_su3633867531522857715nt_int @ B4 @ C2 ) ) @ ( sup_su3633867531522857715nt_int @ C2 @ A3 ) ) ) ).
% Un_Int_crazy
thf(fact_443_Un__Int__crazy,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int,C2: set_se6260736226359567993nt_int] :
( ( sup_su2047564715030645325nt_int @ ( sup_su2047564715030645325nt_int @ ( inf_in8396524679539076455nt_int @ A3 @ B4 ) @ ( inf_in8396524679539076455nt_int @ B4 @ C2 ) ) @ ( inf_in8396524679539076455nt_int @ C2 @ A3 ) )
= ( inf_in8396524679539076455nt_int @ ( inf_in8396524679539076455nt_int @ ( sup_su2047564715030645325nt_int @ A3 @ B4 ) @ ( sup_su2047564715030645325nt_int @ B4 @ C2 ) ) @ ( sup_su2047564715030645325nt_int @ C2 @ A3 ) ) ) ).
% Un_Int_crazy
thf(fact_444_Un__Int__crazy,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ ( sup_su6024340866399070445nt_int @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) @ ( inf_in2269163501485487111nt_int @ B4 @ C2 ) ) @ ( inf_in2269163501485487111nt_int @ C2 @ A3 ) )
= ( inf_in2269163501485487111nt_int @ ( inf_in2269163501485487111nt_int @ ( sup_su6024340866399070445nt_int @ A3 @ B4 ) @ ( sup_su6024340866399070445nt_int @ B4 @ C2 ) ) @ ( sup_su6024340866399070445nt_int @ C2 @ A3 ) ) ) ).
% Un_Int_crazy
thf(fact_445_Diff__Int__distrib2,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int,C2: set_li3855193629254082847nt_int] :
( ( inf_in8463092517017915661nt_int @ ( minus_456201022768243590nt_int @ A3 @ B4 ) @ C2 )
= ( minus_456201022768243590nt_int @ ( inf_in8463092517017915661nt_int @ A3 @ C2 ) @ ( inf_in8463092517017915661nt_int @ B4 @ C2 ) ) ) ).
% Diff_Int_distrib2
thf(fact_446_Diff__Int__distrib2,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int,C2: set_se6260736226359567993nt_int] :
( ( inf_in8396524679539076455nt_int @ ( minus_2612819937483484256nt_int @ A3 @ B4 ) @ C2 )
= ( minus_2612819937483484256nt_int @ ( inf_in8396524679539076455nt_int @ A3 @ C2 ) @ ( inf_in8396524679539076455nt_int @ B4 @ C2 ) ) ) ).
% Diff_Int_distrib2
thf(fact_447_Diff__Int__distrib2,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) @ C2 )
= ( minus_1052850069191792384nt_int @ ( inf_in2269163501485487111nt_int @ A3 @ C2 ) @ ( inf_in2269163501485487111nt_int @ B4 @ C2 ) ) ) ).
% Diff_Int_distrib2
thf(fact_448_Diff__Int__distrib,axiom,
! [C2: set_li3855193629254082847nt_int,A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( inf_in8463092517017915661nt_int @ C2 @ ( minus_456201022768243590nt_int @ A3 @ B4 ) )
= ( minus_456201022768243590nt_int @ ( inf_in8463092517017915661nt_int @ C2 @ A3 ) @ ( inf_in8463092517017915661nt_int @ C2 @ B4 ) ) ) ).
% Diff_Int_distrib
thf(fact_449_Diff__Int__distrib,axiom,
! [C2: set_se6260736226359567993nt_int,A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( inf_in8396524679539076455nt_int @ C2 @ ( minus_2612819937483484256nt_int @ A3 @ B4 ) )
= ( minus_2612819937483484256nt_int @ ( inf_in8396524679539076455nt_int @ C2 @ A3 ) @ ( inf_in8396524679539076455nt_int @ C2 @ B4 ) ) ) ).
% Diff_Int_distrib
thf(fact_450_Diff__Int__distrib,axiom,
! [C2: set_Pr958786334691620121nt_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ C2 @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) )
= ( minus_1052850069191792384nt_int @ ( inf_in2269163501485487111nt_int @ C2 @ A3 ) @ ( inf_in2269163501485487111nt_int @ C2 @ B4 ) ) ) ).
% Diff_Int_distrib
thf(fact_451_Diff__Diff__Int,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( minus_456201022768243590nt_int @ A3 @ ( minus_456201022768243590nt_int @ A3 @ B4 ) )
= ( inf_in8463092517017915661nt_int @ A3 @ B4 ) ) ).
% Diff_Diff_Int
thf(fact_452_Diff__Diff__Int,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( minus_2612819937483484256nt_int @ A3 @ ( minus_2612819937483484256nt_int @ A3 @ B4 ) )
= ( inf_in8396524679539076455nt_int @ A3 @ B4 ) ) ).
% Diff_Diff_Int
thf(fact_453_Diff__Diff__Int,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( minus_1052850069191792384nt_int @ A3 @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) )
= ( inf_in2269163501485487111nt_int @ A3 @ B4 ) ) ).
% Diff_Diff_Int
thf(fact_454_Diff__Int2,axiom,
! [A3: set_li3855193629254082847nt_int,C2: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( minus_456201022768243590nt_int @ ( inf_in8463092517017915661nt_int @ A3 @ C2 ) @ ( inf_in8463092517017915661nt_int @ B4 @ C2 ) )
= ( minus_456201022768243590nt_int @ ( inf_in8463092517017915661nt_int @ A3 @ C2 ) @ B4 ) ) ).
% Diff_Int2
thf(fact_455_Diff__Int2,axiom,
! [A3: set_se6260736226359567993nt_int,C2: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( minus_2612819937483484256nt_int @ ( inf_in8396524679539076455nt_int @ A3 @ C2 ) @ ( inf_in8396524679539076455nt_int @ B4 @ C2 ) )
= ( minus_2612819937483484256nt_int @ ( inf_in8396524679539076455nt_int @ A3 @ C2 ) @ B4 ) ) ).
% Diff_Int2
thf(fact_456_Diff__Int2,axiom,
! [A3: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( minus_1052850069191792384nt_int @ ( inf_in2269163501485487111nt_int @ A3 @ C2 ) @ ( inf_in2269163501485487111nt_int @ B4 @ C2 ) )
= ( minus_1052850069191792384nt_int @ ( inf_in2269163501485487111nt_int @ A3 @ C2 ) @ B4 ) ) ).
% Diff_Int2
thf(fact_457_Int__Diff,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int,C2: set_li3855193629254082847nt_int] :
( ( minus_456201022768243590nt_int @ ( inf_in8463092517017915661nt_int @ A3 @ B4 ) @ C2 )
= ( inf_in8463092517017915661nt_int @ A3 @ ( minus_456201022768243590nt_int @ B4 @ C2 ) ) ) ).
% Int_Diff
thf(fact_458_Int__Diff,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int,C2: set_se6260736226359567993nt_int] :
( ( minus_2612819937483484256nt_int @ ( inf_in8396524679539076455nt_int @ A3 @ B4 ) @ C2 )
= ( inf_in8396524679539076455nt_int @ A3 @ ( minus_2612819937483484256nt_int @ B4 @ C2 ) ) ) ).
% Int_Diff
thf(fact_459_Int__Diff,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int] :
( ( minus_1052850069191792384nt_int @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) @ C2 )
= ( inf_in2269163501485487111nt_int @ A3 @ ( minus_1052850069191792384nt_int @ B4 @ C2 ) ) ) ).
% Int_Diff
thf(fact_460_Int__Diff__disjoint,axiom,
! [A3: set_Pr2560585780119916871nt_int,B4: set_Pr2560585780119916871nt_int] :
( ( inf_in7392334082413294389nt_int @ ( inf_in7392334082413294389nt_int @ A3 @ B4 ) @ ( minus_2188297577953631406nt_int @ A3 @ B4 ) )
= bot_bo8417956007504411571nt_int ) ).
% Int_Diff_disjoint
thf(fact_461_Int__Diff__disjoint,axiom,
! [A3: set_int,B4: set_int] :
( ( inf_inf_set_int @ ( inf_inf_set_int @ A3 @ B4 ) @ ( minus_minus_set_int @ A3 @ B4 ) )
= bot_bot_set_int ) ).
% Int_Diff_disjoint
thf(fact_462_Int__Diff__disjoint,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( inf_in8463092517017915661nt_int @ ( inf_in8463092517017915661nt_int @ A3 @ B4 ) @ ( minus_456201022768243590nt_int @ A3 @ B4 ) )
= bot_bo3809061186584590219nt_int ) ).
% Int_Diff_disjoint
thf(fact_463_Int__Diff__disjoint,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( inf_in8396524679539076455nt_int @ ( inf_in8396524679539076455nt_int @ A3 @ B4 ) @ ( minus_2612819937483484256nt_int @ A3 @ B4 ) )
= bot_bo1488462491386950373nt_int ) ).
% Int_Diff_disjoint
thf(fact_464_Int__Diff__disjoint,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) )
= bot_bo1796632182523588997nt_int ) ).
% Int_Diff_disjoint
thf(fact_465_Diff__triv,axiom,
! [A3: set_Pr2560585780119916871nt_int,B4: set_Pr2560585780119916871nt_int] :
( ( ( inf_in7392334082413294389nt_int @ A3 @ B4 )
= bot_bo8417956007504411571nt_int )
=> ( ( minus_2188297577953631406nt_int @ A3 @ B4 )
= A3 ) ) ).
% Diff_triv
thf(fact_466_Diff__triv,axiom,
! [A3: set_int,B4: set_int] :
( ( ( inf_inf_set_int @ A3 @ B4 )
= bot_bot_set_int )
=> ( ( minus_minus_set_int @ A3 @ B4 )
= A3 ) ) ).
% Diff_triv
thf(fact_467_Diff__triv,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( ( inf_in8463092517017915661nt_int @ A3 @ B4 )
= bot_bo3809061186584590219nt_int )
=> ( ( minus_456201022768243590nt_int @ A3 @ B4 )
= A3 ) ) ).
% Diff_triv
thf(fact_468_Diff__triv,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( ( inf_in8396524679539076455nt_int @ A3 @ B4 )
= bot_bo1488462491386950373nt_int )
=> ( ( minus_2612819937483484256nt_int @ A3 @ B4 )
= A3 ) ) ).
% Diff_triv
thf(fact_469_Diff__triv,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ( inf_in2269163501485487111nt_int @ A3 @ B4 )
= bot_bo1796632182523588997nt_int )
=> ( ( minus_1052850069191792384nt_int @ A3 @ B4 )
= A3 ) ) ).
% Diff_triv
thf(fact_470_Un__Diff__Int,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( sup_su3633867531522857715nt_int @ ( minus_456201022768243590nt_int @ A3 @ B4 ) @ ( inf_in8463092517017915661nt_int @ A3 @ B4 ) )
= A3 ) ).
% Un_Diff_Int
thf(fact_471_Un__Diff__Int,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( sup_su2047564715030645325nt_int @ ( minus_2612819937483484256nt_int @ A3 @ B4 ) @ ( inf_in8396524679539076455nt_int @ A3 @ B4 ) )
= A3 ) ).
% Un_Diff_Int
thf(fact_472_Un__Diff__Int,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) )
= A3 ) ).
% Un_Diff_Int
thf(fact_473_Int__Diff__Un,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( sup_su3633867531522857715nt_int @ ( inf_in8463092517017915661nt_int @ A3 @ B4 ) @ ( minus_456201022768243590nt_int @ A3 @ B4 ) )
= A3 ) ).
% Int_Diff_Un
thf(fact_474_Int__Diff__Un,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( sup_su2047564715030645325nt_int @ ( inf_in8396524679539076455nt_int @ A3 @ B4 ) @ ( minus_2612819937483484256nt_int @ A3 @ B4 ) )
= A3 ) ).
% Int_Diff_Un
thf(fact_475_Int__Diff__Un,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) )
= A3 ) ).
% Int_Diff_Un
thf(fact_476_Diff__Int,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int,C2: set_li3855193629254082847nt_int] :
( ( minus_456201022768243590nt_int @ A3 @ ( inf_in8463092517017915661nt_int @ B4 @ C2 ) )
= ( sup_su3633867531522857715nt_int @ ( minus_456201022768243590nt_int @ A3 @ B4 ) @ ( minus_456201022768243590nt_int @ A3 @ C2 ) ) ) ).
% Diff_Int
thf(fact_477_Diff__Int,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int,C2: set_se6260736226359567993nt_int] :
( ( minus_2612819937483484256nt_int @ A3 @ ( inf_in8396524679539076455nt_int @ B4 @ C2 ) )
= ( sup_su2047564715030645325nt_int @ ( minus_2612819937483484256nt_int @ A3 @ B4 ) @ ( minus_2612819937483484256nt_int @ A3 @ C2 ) ) ) ).
% Diff_Int
thf(fact_478_Diff__Int,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int] :
( ( minus_1052850069191792384nt_int @ A3 @ ( inf_in2269163501485487111nt_int @ B4 @ C2 ) )
= ( sup_su6024340866399070445nt_int @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) @ ( minus_1052850069191792384nt_int @ A3 @ C2 ) ) ) ).
% Diff_Int
thf(fact_479_Diff__Un,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int,C2: set_li3855193629254082847nt_int] :
( ( minus_456201022768243590nt_int @ A3 @ ( sup_su3633867531522857715nt_int @ B4 @ C2 ) )
= ( inf_in8463092517017915661nt_int @ ( minus_456201022768243590nt_int @ A3 @ B4 ) @ ( minus_456201022768243590nt_int @ A3 @ C2 ) ) ) ).
% Diff_Un
thf(fact_480_Diff__Un,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int,C2: set_se6260736226359567993nt_int] :
( ( minus_2612819937483484256nt_int @ A3 @ ( sup_su2047564715030645325nt_int @ B4 @ C2 ) )
= ( inf_in8396524679539076455nt_int @ ( minus_2612819937483484256nt_int @ A3 @ B4 ) @ ( minus_2612819937483484256nt_int @ A3 @ C2 ) ) ) ).
% Diff_Un
thf(fact_481_Diff__Un,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int] :
( ( minus_1052850069191792384nt_int @ A3 @ ( sup_su6024340866399070445nt_int @ B4 @ C2 ) )
= ( inf_in2269163501485487111nt_int @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) @ ( minus_1052850069191792384nt_int @ A3 @ C2 ) ) ) ).
% Diff_Un
thf(fact_482_ex__in__conv,axiom,
! [A3: set_Pr2560585780119916871nt_int] :
( ( ? [X2: produc1219242969750017639nt_int] : ( member8566619992076573584nt_int @ X2 @ A3 ) )
= ( A3 != bot_bo8417956007504411571nt_int ) ) ).
% ex_in_conv
thf(fact_483_ex__in__conv,axiom,
! [A3: set_int] :
( ( ? [X2: int] : ( member_int @ X2 @ A3 ) )
= ( A3 != bot_bot_set_int ) ) ).
% ex_in_conv
thf(fact_484_ex__in__conv,axiom,
! [A3: set_li3855193629254082847nt_int] :
( ( ? [X2: list_P5707943133018811711nt_int] : ( member2764346250752101224nt_int @ X2 @ A3 ) )
= ( A3 != bot_bo3809061186584590219nt_int ) ) ).
% ex_in_conv
thf(fact_485_ex__in__conv,axiom,
! [A3: set_se6260736226359567993nt_int] :
( ( ? [X2: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X2 @ A3 ) )
= ( A3 != bot_bo1488462491386950373nt_int ) ) ).
% ex_in_conv
thf(fact_486_ex__in__conv,axiom,
! [A3: set_Pr958786334691620121nt_int] :
( ( ? [X2: product_prod_int_int] : ( member5262025264175285858nt_int @ X2 @ A3 ) )
= ( A3 != bot_bo1796632182523588997nt_int ) ) ).
% ex_in_conv
thf(fact_487_equals0I,axiom,
! [A3: set_Pr2560585780119916871nt_int] :
( ! [Y2: produc1219242969750017639nt_int] :
~ ( member8566619992076573584nt_int @ Y2 @ A3 )
=> ( A3 = bot_bo8417956007504411571nt_int ) ) ).
% equals0I
thf(fact_488_equals0I,axiom,
! [A3: set_int] :
( ! [Y2: int] :
~ ( member_int @ Y2 @ A3 )
=> ( A3 = bot_bot_set_int ) ) ).
% equals0I
thf(fact_489_equals0I,axiom,
! [A3: set_li3855193629254082847nt_int] :
( ! [Y2: list_P5707943133018811711nt_int] :
~ ( member2764346250752101224nt_int @ Y2 @ A3 )
=> ( A3 = bot_bo3809061186584590219nt_int ) ) ).
% equals0I
thf(fact_490_equals0I,axiom,
! [A3: set_se6260736226359567993nt_int] :
( ! [Y2: set_Pr958786334691620121nt_int] :
~ ( member2340774599025711042nt_int @ Y2 @ A3 )
=> ( A3 = bot_bo1488462491386950373nt_int ) ) ).
% equals0I
thf(fact_491_equals0I,axiom,
! [A3: set_Pr958786334691620121nt_int] :
( ! [Y2: product_prod_int_int] :
~ ( member5262025264175285858nt_int @ Y2 @ A3 )
=> ( A3 = bot_bo1796632182523588997nt_int ) ) ).
% equals0I
thf(fact_492_equals0D,axiom,
! [A3: set_Pr2560585780119916871nt_int,A: produc1219242969750017639nt_int] :
( ( A3 = bot_bo8417956007504411571nt_int )
=> ~ ( member8566619992076573584nt_int @ A @ A3 ) ) ).
% equals0D
thf(fact_493_equals0D,axiom,
! [A3: set_int,A: int] :
( ( A3 = bot_bot_set_int )
=> ~ ( member_int @ A @ A3 ) ) ).
% equals0D
thf(fact_494_equals0D,axiom,
! [A3: set_li3855193629254082847nt_int,A: list_P5707943133018811711nt_int] :
( ( A3 = bot_bo3809061186584590219nt_int )
=> ~ ( member2764346250752101224nt_int @ A @ A3 ) ) ).
% equals0D
thf(fact_495_equals0D,axiom,
! [A3: set_se6260736226359567993nt_int,A: set_Pr958786334691620121nt_int] :
( ( A3 = bot_bo1488462491386950373nt_int )
=> ~ ( member2340774599025711042nt_int @ A @ A3 ) ) ).
% equals0D
thf(fact_496_equals0D,axiom,
! [A3: set_Pr958786334691620121nt_int,A: product_prod_int_int] :
( ( A3 = bot_bo1796632182523588997nt_int )
=> ~ ( member5262025264175285858nt_int @ A @ A3 ) ) ).
% equals0D
thf(fact_497_emptyE,axiom,
! [A: produc1219242969750017639nt_int] :
~ ( member8566619992076573584nt_int @ A @ bot_bo8417956007504411571nt_int ) ).
% emptyE
thf(fact_498_emptyE,axiom,
! [A: int] :
~ ( member_int @ A @ bot_bot_set_int ) ).
% emptyE
thf(fact_499_emptyE,axiom,
! [A: list_P5707943133018811711nt_int] :
~ ( member2764346250752101224nt_int @ A @ bot_bo3809061186584590219nt_int ) ).
% emptyE
thf(fact_500_emptyE,axiom,
! [A: set_Pr958786334691620121nt_int] :
~ ( member2340774599025711042nt_int @ A @ bot_bo1488462491386950373nt_int ) ).
% emptyE
thf(fact_501_emptyE,axiom,
! [A: product_prod_int_int] :
~ ( member5262025264175285858nt_int @ A @ bot_bo1796632182523588997nt_int ) ).
% emptyE
thf(fact_502_mk__disjoint__insert,axiom,
! [A: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int] :
( ( member2764346250752101224nt_int @ A @ A3 )
=> ? [B6: set_li3855193629254082847nt_int] :
( ( A3
= ( insert393344137582914319nt_int @ A @ B6 ) )
& ~ ( member2764346250752101224nt_int @ A @ B6 ) ) ) ).
% mk_disjoint_insert
thf(fact_503_mk__disjoint__insert,axiom,
! [A: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int] :
( ( member2340774599025711042nt_int @ A @ A3 )
=> ? [B6: set_se6260736226359567993nt_int] :
( ( A3
= ( insert8897473484851387113nt_int @ A @ B6 ) )
& ~ ( member2340774599025711042nt_int @ A @ B6 ) ) ) ).
% mk_disjoint_insert
thf(fact_504_mk__disjoint__insert,axiom,
! [A: product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ A @ A3 )
=> ? [B6: set_Pr958786334691620121nt_int] :
( ( A3
= ( insert5033312907999012233nt_int @ A @ B6 ) )
& ~ ( member5262025264175285858nt_int @ A @ B6 ) ) ) ).
% mk_disjoint_insert
thf(fact_505_insert__commute,axiom,
! [X: list_P5707943133018811711nt_int,Y: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int] :
( ( insert393344137582914319nt_int @ X @ ( insert393344137582914319nt_int @ Y @ A3 ) )
= ( insert393344137582914319nt_int @ Y @ ( insert393344137582914319nt_int @ X @ A3 ) ) ) ).
% insert_commute
thf(fact_506_insert__commute,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int] :
( ( insert8897473484851387113nt_int @ X @ ( insert8897473484851387113nt_int @ Y @ A3 ) )
= ( insert8897473484851387113nt_int @ Y @ ( insert8897473484851387113nt_int @ X @ A3 ) ) ) ).
% insert_commute
thf(fact_507_insert__commute,axiom,
! [X: product_prod_int_int,Y: product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( insert5033312907999012233nt_int @ X @ ( insert5033312907999012233nt_int @ Y @ A3 ) )
= ( insert5033312907999012233nt_int @ Y @ ( insert5033312907999012233nt_int @ X @ A3 ) ) ) ).
% insert_commute
thf(fact_508_insert__eq__iff,axiom,
! [A: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int,B: list_P5707943133018811711nt_int,B4: set_li3855193629254082847nt_int] :
( ~ ( member2764346250752101224nt_int @ A @ A3 )
=> ( ~ ( member2764346250752101224nt_int @ B @ B4 )
=> ( ( ( insert393344137582914319nt_int @ A @ A3 )
= ( insert393344137582914319nt_int @ B @ B4 ) )
= ( ( ( A = B )
=> ( A3 = B4 ) )
& ( ( A != B )
=> ? [C3: set_li3855193629254082847nt_int] :
( ( A3
= ( insert393344137582914319nt_int @ B @ C3 ) )
& ~ ( member2764346250752101224nt_int @ B @ C3 )
& ( B4
= ( insert393344137582914319nt_int @ A @ C3 ) )
& ~ ( member2764346250752101224nt_int @ A @ C3 ) ) ) ) ) ) ) ).
% insert_eq_iff
thf(fact_509_insert__eq__iff,axiom,
! [A: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int,B: set_Pr958786334691620121nt_int,B4: set_se6260736226359567993nt_int] :
( ~ ( member2340774599025711042nt_int @ A @ A3 )
=> ( ~ ( member2340774599025711042nt_int @ B @ B4 )
=> ( ( ( insert8897473484851387113nt_int @ A @ A3 )
= ( insert8897473484851387113nt_int @ B @ B4 ) )
= ( ( ( A = B )
=> ( A3 = B4 ) )
& ( ( A != B )
=> ? [C3: set_se6260736226359567993nt_int] :
( ( A3
= ( insert8897473484851387113nt_int @ B @ C3 ) )
& ~ ( member2340774599025711042nt_int @ B @ C3 )
& ( B4
= ( insert8897473484851387113nt_int @ A @ C3 ) )
& ~ ( member2340774599025711042nt_int @ A @ C3 ) ) ) ) ) ) ) ).
% insert_eq_iff
thf(fact_510_insert__eq__iff,axiom,
! [A: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B: product_prod_int_int,B4: set_Pr958786334691620121nt_int] :
( ~ ( member5262025264175285858nt_int @ A @ A3 )
=> ( ~ ( member5262025264175285858nt_int @ B @ B4 )
=> ( ( ( insert5033312907999012233nt_int @ A @ A3 )
= ( insert5033312907999012233nt_int @ B @ B4 ) )
= ( ( ( A = B )
=> ( A3 = B4 ) )
& ( ( A != B )
=> ? [C3: set_Pr958786334691620121nt_int] :
( ( A3
= ( insert5033312907999012233nt_int @ B @ C3 ) )
& ~ ( member5262025264175285858nt_int @ B @ C3 )
& ( B4
= ( insert5033312907999012233nt_int @ A @ C3 ) )
& ~ ( member5262025264175285858nt_int @ A @ C3 ) ) ) ) ) ) ) ).
% insert_eq_iff
thf(fact_511_insert__absorb,axiom,
! [A: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int] :
( ( member2764346250752101224nt_int @ A @ A3 )
=> ( ( insert393344137582914319nt_int @ A @ A3 )
= A3 ) ) ).
% insert_absorb
thf(fact_512_insert__absorb,axiom,
! [A: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int] :
( ( member2340774599025711042nt_int @ A @ A3 )
=> ( ( insert8897473484851387113nt_int @ A @ A3 )
= A3 ) ) ).
% insert_absorb
thf(fact_513_insert__absorb,axiom,
! [A: product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ A @ A3 )
=> ( ( insert5033312907999012233nt_int @ A @ A3 )
= A3 ) ) ).
% insert_absorb
thf(fact_514_insert__ident,axiom,
! [X: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ~ ( member2764346250752101224nt_int @ X @ A3 )
=> ( ~ ( member2764346250752101224nt_int @ X @ B4 )
=> ( ( ( insert393344137582914319nt_int @ X @ A3 )
= ( insert393344137582914319nt_int @ X @ B4 ) )
= ( A3 = B4 ) ) ) ) ).
% insert_ident
thf(fact_515_insert__ident,axiom,
! [X: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ~ ( member2340774599025711042nt_int @ X @ A3 )
=> ( ~ ( member2340774599025711042nt_int @ X @ B4 )
=> ( ( ( insert8897473484851387113nt_int @ X @ A3 )
= ( insert8897473484851387113nt_int @ X @ B4 ) )
= ( A3 = B4 ) ) ) ) ).
% insert_ident
thf(fact_516_insert__ident,axiom,
! [X: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ~ ( member5262025264175285858nt_int @ X @ A3 )
=> ( ~ ( member5262025264175285858nt_int @ X @ B4 )
=> ( ( ( insert5033312907999012233nt_int @ X @ A3 )
= ( insert5033312907999012233nt_int @ X @ B4 ) )
= ( A3 = B4 ) ) ) ) ).
% insert_ident
thf(fact_517_Set_Oset__insert,axiom,
! [X: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int] :
( ( member2764346250752101224nt_int @ X @ A3 )
=> ~ ! [B6: set_li3855193629254082847nt_int] :
( ( A3
= ( insert393344137582914319nt_int @ X @ B6 ) )
=> ( member2764346250752101224nt_int @ X @ B6 ) ) ) ).
% Set.set_insert
thf(fact_518_Set_Oset__insert,axiom,
! [X: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int] :
( ( member2340774599025711042nt_int @ X @ A3 )
=> ~ ! [B6: set_se6260736226359567993nt_int] :
( ( A3
= ( insert8897473484851387113nt_int @ X @ B6 ) )
=> ( member2340774599025711042nt_int @ X @ B6 ) ) ) ).
% Set.set_insert
thf(fact_519_Set_Oset__insert,axiom,
! [X: product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ X @ A3 )
=> ~ ! [B6: set_Pr958786334691620121nt_int] :
( ( A3
= ( insert5033312907999012233nt_int @ X @ B6 ) )
=> ( member5262025264175285858nt_int @ X @ B6 ) ) ) ).
% Set.set_insert
thf(fact_520_insertI2,axiom,
! [A: list_P5707943133018811711nt_int,B4: set_li3855193629254082847nt_int,B: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ A @ B4 )
=> ( member2764346250752101224nt_int @ A @ ( insert393344137582914319nt_int @ B @ B4 ) ) ) ).
% insertI2
thf(fact_521_insertI2,axiom,
! [A: set_Pr958786334691620121nt_int,B4: set_se6260736226359567993nt_int,B: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ A @ B4 )
=> ( member2340774599025711042nt_int @ A @ ( insert8897473484851387113nt_int @ B @ B4 ) ) ) ).
% insertI2
thf(fact_522_insertI2,axiom,
! [A: product_prod_int_int,B4: set_Pr958786334691620121nt_int,B: product_prod_int_int] :
( ( member5262025264175285858nt_int @ A @ B4 )
=> ( member5262025264175285858nt_int @ A @ ( insert5033312907999012233nt_int @ B @ B4 ) ) ) ).
% insertI2
thf(fact_523_insertI1,axiom,
! [A: list_P5707943133018811711nt_int,B4: set_li3855193629254082847nt_int] : ( member2764346250752101224nt_int @ A @ ( insert393344137582914319nt_int @ A @ B4 ) ) ).
% insertI1
thf(fact_524_insertI1,axiom,
! [A: set_Pr958786334691620121nt_int,B4: set_se6260736226359567993nt_int] : ( member2340774599025711042nt_int @ A @ ( insert8897473484851387113nt_int @ A @ B4 ) ) ).
% insertI1
thf(fact_525_insertI1,axiom,
! [A: product_prod_int_int,B4: set_Pr958786334691620121nt_int] : ( member5262025264175285858nt_int @ A @ ( insert5033312907999012233nt_int @ A @ B4 ) ) ).
% insertI1
thf(fact_526_insertE,axiom,
! [A: list_P5707943133018811711nt_int,B: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int] :
( ( member2764346250752101224nt_int @ A @ ( insert393344137582914319nt_int @ B @ A3 ) )
=> ( ( A != B )
=> ( member2764346250752101224nt_int @ A @ A3 ) ) ) ).
% insertE
thf(fact_527_insertE,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int] :
( ( member2340774599025711042nt_int @ A @ ( insert8897473484851387113nt_int @ B @ A3 ) )
=> ( ( A != B )
=> ( member2340774599025711042nt_int @ A @ A3 ) ) ) ).
% insertE
thf(fact_528_insertE,axiom,
! [A: product_prod_int_int,B: product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ A @ ( insert5033312907999012233nt_int @ B @ A3 ) )
=> ( ( A != B )
=> ( member5262025264175285858nt_int @ A @ A3 ) ) ) ).
% insertE
thf(fact_529_Un__left__commute,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int,C2: set_li3855193629254082847nt_int] :
( ( sup_su3633867531522857715nt_int @ A3 @ ( sup_su3633867531522857715nt_int @ B4 @ C2 ) )
= ( sup_su3633867531522857715nt_int @ B4 @ ( sup_su3633867531522857715nt_int @ A3 @ C2 ) ) ) ).
% Un_left_commute
thf(fact_530_Un__left__commute,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int,C2: set_se6260736226359567993nt_int] :
( ( sup_su2047564715030645325nt_int @ A3 @ ( sup_su2047564715030645325nt_int @ B4 @ C2 ) )
= ( sup_su2047564715030645325nt_int @ B4 @ ( sup_su2047564715030645325nt_int @ A3 @ C2 ) ) ) ).
% Un_left_commute
thf(fact_531_Un__left__commute,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ A3 @ ( sup_su6024340866399070445nt_int @ B4 @ C2 ) )
= ( sup_su6024340866399070445nt_int @ B4 @ ( sup_su6024340866399070445nt_int @ A3 @ C2 ) ) ) ).
% Un_left_commute
thf(fact_532_Un__left__absorb,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( sup_su3633867531522857715nt_int @ A3 @ ( sup_su3633867531522857715nt_int @ A3 @ B4 ) )
= ( sup_su3633867531522857715nt_int @ A3 @ B4 ) ) ).
% Un_left_absorb
thf(fact_533_Un__left__absorb,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( sup_su2047564715030645325nt_int @ A3 @ ( sup_su2047564715030645325nt_int @ A3 @ B4 ) )
= ( sup_su2047564715030645325nt_int @ A3 @ B4 ) ) ).
% Un_left_absorb
thf(fact_534_Un__left__absorb,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ A3 @ ( sup_su6024340866399070445nt_int @ A3 @ B4 ) )
= ( sup_su6024340866399070445nt_int @ A3 @ B4 ) ) ).
% Un_left_absorb
thf(fact_535_Un__commute,axiom,
( sup_su3633867531522857715nt_int
= ( ^ [A4: set_li3855193629254082847nt_int,B5: set_li3855193629254082847nt_int] : ( sup_su3633867531522857715nt_int @ B5 @ A4 ) ) ) ).
% Un_commute
thf(fact_536_Un__commute,axiom,
( sup_su2047564715030645325nt_int
= ( ^ [A4: set_se6260736226359567993nt_int,B5: set_se6260736226359567993nt_int] : ( sup_su2047564715030645325nt_int @ B5 @ A4 ) ) ) ).
% Un_commute
thf(fact_537_Un__commute,axiom,
( sup_su6024340866399070445nt_int
= ( ^ [A4: set_Pr958786334691620121nt_int,B5: set_Pr958786334691620121nt_int] : ( sup_su6024340866399070445nt_int @ B5 @ A4 ) ) ) ).
% Un_commute
thf(fact_538_Un__absorb,axiom,
! [A3: set_li3855193629254082847nt_int] :
( ( sup_su3633867531522857715nt_int @ A3 @ A3 )
= A3 ) ).
% Un_absorb
thf(fact_539_Un__absorb,axiom,
! [A3: set_se6260736226359567993nt_int] :
( ( sup_su2047564715030645325nt_int @ A3 @ A3 )
= A3 ) ).
% Un_absorb
thf(fact_540_Un__absorb,axiom,
! [A3: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ A3 @ A3 )
= A3 ) ).
% Un_absorb
thf(fact_541_Un__assoc,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int,C2: set_li3855193629254082847nt_int] :
( ( sup_su3633867531522857715nt_int @ ( sup_su3633867531522857715nt_int @ A3 @ B4 ) @ C2 )
= ( sup_su3633867531522857715nt_int @ A3 @ ( sup_su3633867531522857715nt_int @ B4 @ C2 ) ) ) ).
% Un_assoc
thf(fact_542_Un__assoc,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int,C2: set_se6260736226359567993nt_int] :
( ( sup_su2047564715030645325nt_int @ ( sup_su2047564715030645325nt_int @ A3 @ B4 ) @ C2 )
= ( sup_su2047564715030645325nt_int @ A3 @ ( sup_su2047564715030645325nt_int @ B4 @ C2 ) ) ) ).
% Un_assoc
thf(fact_543_Un__assoc,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ ( sup_su6024340866399070445nt_int @ A3 @ B4 ) @ C2 )
= ( sup_su6024340866399070445nt_int @ A3 @ ( sup_su6024340866399070445nt_int @ B4 @ C2 ) ) ) ).
% Un_assoc
thf(fact_544_ball__Un,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int,P: list_P5707943133018811711nt_int > $o] :
( ( ! [X2: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ X2 @ ( sup_su3633867531522857715nt_int @ A3 @ B4 ) )
=> ( P @ X2 ) ) )
= ( ! [X2: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ X2 @ A3 )
=> ( P @ X2 ) )
& ! [X2: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ X2 @ B4 )
=> ( P @ X2 ) ) ) ) ).
% ball_Un
thf(fact_545_ball__Un,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int,P: set_Pr958786334691620121nt_int > $o] :
( ( ! [X2: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ X2 @ ( sup_su2047564715030645325nt_int @ A3 @ B4 ) )
=> ( P @ X2 ) ) )
= ( ! [X2: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ X2 @ A3 )
=> ( P @ X2 ) )
& ! [X2: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ X2 @ B4 )
=> ( P @ X2 ) ) ) ) ).
% ball_Un
thf(fact_546_ball__Un,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,P: product_prod_int_int > $o] :
( ( ! [X2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X2 @ ( sup_su6024340866399070445nt_int @ A3 @ B4 ) )
=> ( P @ X2 ) ) )
= ( ! [X2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X2 @ A3 )
=> ( P @ X2 ) )
& ! [X2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X2 @ B4 )
=> ( P @ X2 ) ) ) ) ).
% ball_Un
thf(fact_547_bex__Un,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int,P: list_P5707943133018811711nt_int > $o] :
( ( ? [X2: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ X2 @ ( sup_su3633867531522857715nt_int @ A3 @ B4 ) )
& ( P @ X2 ) ) )
= ( ? [X2: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ X2 @ A3 )
& ( P @ X2 ) )
| ? [X2: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ X2 @ B4 )
& ( P @ X2 ) ) ) ) ).
% bex_Un
thf(fact_548_bex__Un,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int,P: set_Pr958786334691620121nt_int > $o] :
( ( ? [X2: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ X2 @ ( sup_su2047564715030645325nt_int @ A3 @ B4 ) )
& ( P @ X2 ) ) )
= ( ? [X2: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ X2 @ A3 )
& ( P @ X2 ) )
| ? [X2: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ X2 @ B4 )
& ( P @ X2 ) ) ) ) ).
% bex_Un
thf(fact_549_bex__Un,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,P: product_prod_int_int > $o] :
( ( ? [X2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X2 @ ( sup_su6024340866399070445nt_int @ A3 @ B4 ) )
& ( P @ X2 ) ) )
= ( ? [X2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X2 @ A3 )
& ( P @ X2 ) )
| ? [X2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X2 @ B4 )
& ( P @ X2 ) ) ) ) ).
% bex_Un
thf(fact_550_UnI2,axiom,
! [C: list_P5707943133018811711nt_int,B4: set_li3855193629254082847nt_int,A3: set_li3855193629254082847nt_int] :
( ( member2764346250752101224nt_int @ C @ B4 )
=> ( member2764346250752101224nt_int @ C @ ( sup_su3633867531522857715nt_int @ A3 @ B4 ) ) ) ).
% UnI2
thf(fact_551_UnI2,axiom,
! [C: set_Pr958786334691620121nt_int,B4: set_se6260736226359567993nt_int,A3: set_se6260736226359567993nt_int] :
( ( member2340774599025711042nt_int @ C @ B4 )
=> ( member2340774599025711042nt_int @ C @ ( sup_su2047564715030645325nt_int @ A3 @ B4 ) ) ) ).
% UnI2
thf(fact_552_UnI2,axiom,
! [C: product_prod_int_int,B4: set_Pr958786334691620121nt_int,A3: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ C @ B4 )
=> ( member5262025264175285858nt_int @ C @ ( sup_su6024340866399070445nt_int @ A3 @ B4 ) ) ) ).
% UnI2
thf(fact_553_UnI1,axiom,
! [C: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( member2764346250752101224nt_int @ C @ A3 )
=> ( member2764346250752101224nt_int @ C @ ( sup_su3633867531522857715nt_int @ A3 @ B4 ) ) ) ).
% UnI1
thf(fact_554_UnI1,axiom,
! [C: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( member2340774599025711042nt_int @ C @ A3 )
=> ( member2340774599025711042nt_int @ C @ ( sup_su2047564715030645325nt_int @ A3 @ B4 ) ) ) ).
% UnI1
thf(fact_555_UnI1,axiom,
! [C: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ C @ A3 )
=> ( member5262025264175285858nt_int @ C @ ( sup_su6024340866399070445nt_int @ A3 @ B4 ) ) ) ).
% UnI1
thf(fact_556_UnE,axiom,
! [C: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( member2764346250752101224nt_int @ C @ ( sup_su3633867531522857715nt_int @ A3 @ B4 ) )
=> ( ~ ( member2764346250752101224nt_int @ C @ A3 )
=> ( member2764346250752101224nt_int @ C @ B4 ) ) ) ).
% UnE
thf(fact_557_UnE,axiom,
! [C: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( member2340774599025711042nt_int @ C @ ( sup_su2047564715030645325nt_int @ A3 @ B4 ) )
=> ( ~ ( member2340774599025711042nt_int @ C @ A3 )
=> ( member2340774599025711042nt_int @ C @ B4 ) ) ) ).
% UnE
thf(fact_558_UnE,axiom,
! [C: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ C @ ( sup_su6024340866399070445nt_int @ A3 @ B4 ) )
=> ( ~ ( member5262025264175285858nt_int @ C @ A3 )
=> ( member5262025264175285858nt_int @ C @ B4 ) ) ) ).
% UnE
thf(fact_559_DiffD2,axiom,
! [C: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( member2764346250752101224nt_int @ C @ ( minus_456201022768243590nt_int @ A3 @ B4 ) )
=> ~ ( member2764346250752101224nt_int @ C @ B4 ) ) ).
% DiffD2
thf(fact_560_DiffD2,axiom,
! [C: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( member2340774599025711042nt_int @ C @ ( minus_2612819937483484256nt_int @ A3 @ B4 ) )
=> ~ ( member2340774599025711042nt_int @ C @ B4 ) ) ).
% DiffD2
thf(fact_561_DiffD2,axiom,
! [C: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ C @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) )
=> ~ ( member5262025264175285858nt_int @ C @ B4 ) ) ).
% DiffD2
thf(fact_562_DiffD1,axiom,
! [C: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( member2764346250752101224nt_int @ C @ ( minus_456201022768243590nt_int @ A3 @ B4 ) )
=> ( member2764346250752101224nt_int @ C @ A3 ) ) ).
% DiffD1
thf(fact_563_DiffD1,axiom,
! [C: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( member2340774599025711042nt_int @ C @ ( minus_2612819937483484256nt_int @ A3 @ B4 ) )
=> ( member2340774599025711042nt_int @ C @ A3 ) ) ).
% DiffD1
thf(fact_564_DiffD1,axiom,
! [C: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ C @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) )
=> ( member5262025264175285858nt_int @ C @ A3 ) ) ).
% DiffD1
thf(fact_565_DiffE,axiom,
! [C: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( member2764346250752101224nt_int @ C @ ( minus_456201022768243590nt_int @ A3 @ B4 ) )
=> ~ ( ( member2764346250752101224nt_int @ C @ A3 )
=> ( member2764346250752101224nt_int @ C @ B4 ) ) ) ).
% DiffE
thf(fact_566_DiffE,axiom,
! [C: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( member2340774599025711042nt_int @ C @ ( minus_2612819937483484256nt_int @ A3 @ B4 ) )
=> ~ ( ( member2340774599025711042nt_int @ C @ A3 )
=> ( member2340774599025711042nt_int @ C @ B4 ) ) ) ).
% DiffE
thf(fact_567_DiffE,axiom,
! [C: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ C @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) )
=> ~ ( ( member5262025264175285858nt_int @ C @ A3 )
=> ( member5262025264175285858nt_int @ C @ B4 ) ) ) ).
% DiffE
thf(fact_568_singleton__inject,axiom,
! [A: produc1219242969750017639nt_int,B: produc1219242969750017639nt_int] :
( ( ( insert5410160437170799671nt_int @ A @ bot_bo8417956007504411571nt_int )
= ( insert5410160437170799671nt_int @ B @ bot_bo8417956007504411571nt_int ) )
=> ( A = B ) ) ).
% singleton_inject
thf(fact_569_singleton__inject,axiom,
! [A: int,B: int] :
( ( ( insert_int @ A @ bot_bot_set_int )
= ( insert_int @ B @ bot_bot_set_int ) )
=> ( A = B ) ) ).
% singleton_inject
thf(fact_570_singleton__inject,axiom,
! [A: list_P5707943133018811711nt_int,B: list_P5707943133018811711nt_int] :
( ( ( insert393344137582914319nt_int @ A @ bot_bo3809061186584590219nt_int )
= ( insert393344137582914319nt_int @ B @ bot_bo3809061186584590219nt_int ) )
=> ( A = B ) ) ).
% singleton_inject
thf(fact_571_singleton__inject,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int )
= ( insert8897473484851387113nt_int @ B @ bot_bo1488462491386950373nt_int ) )
=> ( A = B ) ) ).
% singleton_inject
thf(fact_572_singleton__inject,axiom,
! [A: product_prod_int_int,B: product_prod_int_int] :
( ( ( insert5033312907999012233nt_int @ A @ bot_bo1796632182523588997nt_int )
= ( insert5033312907999012233nt_int @ B @ bot_bo1796632182523588997nt_int ) )
=> ( A = B ) ) ).
% singleton_inject
thf(fact_573_insert__not__empty,axiom,
! [A: produc1219242969750017639nt_int,A3: set_Pr2560585780119916871nt_int] :
( ( insert5410160437170799671nt_int @ A @ A3 )
!= bot_bo8417956007504411571nt_int ) ).
% insert_not_empty
thf(fact_574_insert__not__empty,axiom,
! [A: int,A3: set_int] :
( ( insert_int @ A @ A3 )
!= bot_bot_set_int ) ).
% insert_not_empty
thf(fact_575_insert__not__empty,axiom,
! [A: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int] :
( ( insert393344137582914319nt_int @ A @ A3 )
!= bot_bo3809061186584590219nt_int ) ).
% insert_not_empty
thf(fact_576_insert__not__empty,axiom,
! [A: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int] :
( ( insert8897473484851387113nt_int @ A @ A3 )
!= bot_bo1488462491386950373nt_int ) ).
% insert_not_empty
thf(fact_577_insert__not__empty,axiom,
! [A: product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( insert5033312907999012233nt_int @ A @ A3 )
!= bot_bo1796632182523588997nt_int ) ).
% insert_not_empty
thf(fact_578_doubleton__eq__iff,axiom,
! [A: produc1219242969750017639nt_int,B: produc1219242969750017639nt_int,C: produc1219242969750017639nt_int,D: produc1219242969750017639nt_int] :
( ( ( insert5410160437170799671nt_int @ A @ ( insert5410160437170799671nt_int @ B @ bot_bo8417956007504411571nt_int ) )
= ( insert5410160437170799671nt_int @ C @ ( insert5410160437170799671nt_int @ D @ bot_bo8417956007504411571nt_int ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ) ).
% doubleton_eq_iff
thf(fact_579_doubleton__eq__iff,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( insert_int @ A @ ( insert_int @ B @ bot_bot_set_int ) )
= ( insert_int @ C @ ( insert_int @ D @ bot_bot_set_int ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ) ).
% doubleton_eq_iff
thf(fact_580_doubleton__eq__iff,axiom,
! [A: list_P5707943133018811711nt_int,B: list_P5707943133018811711nt_int,C: list_P5707943133018811711nt_int,D: list_P5707943133018811711nt_int] :
( ( ( insert393344137582914319nt_int @ A @ ( insert393344137582914319nt_int @ B @ bot_bo3809061186584590219nt_int ) )
= ( insert393344137582914319nt_int @ C @ ( insert393344137582914319nt_int @ D @ bot_bo3809061186584590219nt_int ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ) ).
% doubleton_eq_iff
thf(fact_581_doubleton__eq__iff,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int,D: set_Pr958786334691620121nt_int] :
( ( ( insert8897473484851387113nt_int @ A @ ( insert8897473484851387113nt_int @ B @ bot_bo1488462491386950373nt_int ) )
= ( insert8897473484851387113nt_int @ C @ ( insert8897473484851387113nt_int @ D @ bot_bo1488462491386950373nt_int ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ) ).
% doubleton_eq_iff
thf(fact_582_doubleton__eq__iff,axiom,
! [A: product_prod_int_int,B: product_prod_int_int,C: product_prod_int_int,D: product_prod_int_int] :
( ( ( insert5033312907999012233nt_int @ A @ ( insert5033312907999012233nt_int @ B @ bot_bo1796632182523588997nt_int ) )
= ( insert5033312907999012233nt_int @ C @ ( insert5033312907999012233nt_int @ D @ bot_bo1796632182523588997nt_int ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ) ).
% doubleton_eq_iff
thf(fact_583_singleton__iff,axiom,
! [B: produc1219242969750017639nt_int,A: produc1219242969750017639nt_int] :
( ( member8566619992076573584nt_int @ B @ ( insert5410160437170799671nt_int @ A @ bot_bo8417956007504411571nt_int ) )
= ( B = A ) ) ).
% singleton_iff
thf(fact_584_singleton__iff,axiom,
! [B: int,A: int] :
( ( member_int @ B @ ( insert_int @ A @ bot_bot_set_int ) )
= ( B = A ) ) ).
% singleton_iff
thf(fact_585_singleton__iff,axiom,
! [B: list_P5707943133018811711nt_int,A: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ B @ ( insert393344137582914319nt_int @ A @ bot_bo3809061186584590219nt_int ) )
= ( B = A ) ) ).
% singleton_iff
thf(fact_586_singleton__iff,axiom,
! [B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ B @ ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) )
= ( B = A ) ) ).
% singleton_iff
thf(fact_587_singleton__iff,axiom,
! [B: product_prod_int_int,A: product_prod_int_int] :
( ( member5262025264175285858nt_int @ B @ ( insert5033312907999012233nt_int @ A @ bot_bo1796632182523588997nt_int ) )
= ( B = A ) ) ).
% singleton_iff
thf(fact_588_singletonD,axiom,
! [B: produc1219242969750017639nt_int,A: produc1219242969750017639nt_int] :
( ( member8566619992076573584nt_int @ B @ ( insert5410160437170799671nt_int @ A @ bot_bo8417956007504411571nt_int ) )
=> ( B = A ) ) ).
% singletonD
thf(fact_589_singletonD,axiom,
! [B: int,A: int] :
( ( member_int @ B @ ( insert_int @ A @ bot_bot_set_int ) )
=> ( B = A ) ) ).
% singletonD
thf(fact_590_singletonD,axiom,
! [B: list_P5707943133018811711nt_int,A: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ B @ ( insert393344137582914319nt_int @ A @ bot_bo3809061186584590219nt_int ) )
=> ( B = A ) ) ).
% singletonD
thf(fact_591_singletonD,axiom,
! [B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ B @ ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) )
=> ( B = A ) ) ).
% singletonD
thf(fact_592_singletonD,axiom,
! [B: product_prod_int_int,A: product_prod_int_int] :
( ( member5262025264175285858nt_int @ B @ ( insert5033312907999012233nt_int @ A @ bot_bo1796632182523588997nt_int ) )
=> ( B = A ) ) ).
% singletonD
thf(fact_593_Un__empty__right,axiom,
! [A3: set_Pr2560585780119916871nt_int] :
( ( sup_su3808334714663352091nt_int @ A3 @ bot_bo8417956007504411571nt_int )
= A3 ) ).
% Un_empty_right
thf(fact_594_Un__empty__right,axiom,
! [A3: set_int] :
( ( sup_sup_set_int @ A3 @ bot_bot_set_int )
= A3 ) ).
% Un_empty_right
thf(fact_595_Un__empty__right,axiom,
! [A3: set_li3855193629254082847nt_int] :
( ( sup_su3633867531522857715nt_int @ A3 @ bot_bo3809061186584590219nt_int )
= A3 ) ).
% Un_empty_right
thf(fact_596_Un__empty__right,axiom,
! [A3: set_se6260736226359567993nt_int] :
( ( sup_su2047564715030645325nt_int @ A3 @ bot_bo1488462491386950373nt_int )
= A3 ) ).
% Un_empty_right
thf(fact_597_Un__empty__right,axiom,
! [A3: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ A3 @ bot_bo1796632182523588997nt_int )
= A3 ) ).
% Un_empty_right
thf(fact_598_Un__empty__left,axiom,
! [B4: set_Pr2560585780119916871nt_int] :
( ( sup_su3808334714663352091nt_int @ bot_bo8417956007504411571nt_int @ B4 )
= B4 ) ).
% Un_empty_left
thf(fact_599_Un__empty__left,axiom,
! [B4: set_int] :
( ( sup_sup_set_int @ bot_bot_set_int @ B4 )
= B4 ) ).
% Un_empty_left
thf(fact_600_Un__empty__left,axiom,
! [B4: set_li3855193629254082847nt_int] :
( ( sup_su3633867531522857715nt_int @ bot_bo3809061186584590219nt_int @ B4 )
= B4 ) ).
% Un_empty_left
thf(fact_601_Un__empty__left,axiom,
! [B4: set_se6260736226359567993nt_int] :
( ( sup_su2047564715030645325nt_int @ bot_bo1488462491386950373nt_int @ B4 )
= B4 ) ).
% Un_empty_left
thf(fact_602_Un__empty__left,axiom,
! [B4: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ bot_bo1796632182523588997nt_int @ B4 )
= B4 ) ).
% Un_empty_left
thf(fact_603_insert__Diff__if,axiom,
! [X: list_P5707943133018811711nt_int,B4: set_li3855193629254082847nt_int,A3: set_li3855193629254082847nt_int] :
( ( ( member2764346250752101224nt_int @ X @ B4 )
=> ( ( minus_456201022768243590nt_int @ ( insert393344137582914319nt_int @ X @ A3 ) @ B4 )
= ( minus_456201022768243590nt_int @ A3 @ B4 ) ) )
& ( ~ ( member2764346250752101224nt_int @ X @ B4 )
=> ( ( minus_456201022768243590nt_int @ ( insert393344137582914319nt_int @ X @ A3 ) @ B4 )
= ( insert393344137582914319nt_int @ X @ ( minus_456201022768243590nt_int @ A3 @ B4 ) ) ) ) ) ).
% insert_Diff_if
thf(fact_604_insert__Diff__if,axiom,
! [X: set_Pr958786334691620121nt_int,B4: set_se6260736226359567993nt_int,A3: set_se6260736226359567993nt_int] :
( ( ( member2340774599025711042nt_int @ X @ B4 )
=> ( ( minus_2612819937483484256nt_int @ ( insert8897473484851387113nt_int @ X @ A3 ) @ B4 )
= ( minus_2612819937483484256nt_int @ A3 @ B4 ) ) )
& ( ~ ( member2340774599025711042nt_int @ X @ B4 )
=> ( ( minus_2612819937483484256nt_int @ ( insert8897473484851387113nt_int @ X @ A3 ) @ B4 )
= ( insert8897473484851387113nt_int @ X @ ( minus_2612819937483484256nt_int @ A3 @ B4 ) ) ) ) ) ).
% insert_Diff_if
thf(fact_605_insert__Diff__if,axiom,
! [X: product_prod_int_int,B4: set_Pr958786334691620121nt_int,A3: set_Pr958786334691620121nt_int] :
( ( ( member5262025264175285858nt_int @ X @ B4 )
=> ( ( minus_1052850069191792384nt_int @ ( insert5033312907999012233nt_int @ X @ A3 ) @ B4 )
= ( minus_1052850069191792384nt_int @ A3 @ B4 ) ) )
& ( ~ ( member5262025264175285858nt_int @ X @ B4 )
=> ( ( minus_1052850069191792384nt_int @ ( insert5033312907999012233nt_int @ X @ A3 ) @ B4 )
= ( insert5033312907999012233nt_int @ X @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) ) ) ) ) ).
% insert_Diff_if
thf(fact_606_Un__Diff,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int,C2: set_li3855193629254082847nt_int] :
( ( minus_456201022768243590nt_int @ ( sup_su3633867531522857715nt_int @ A3 @ B4 ) @ C2 )
= ( sup_su3633867531522857715nt_int @ ( minus_456201022768243590nt_int @ A3 @ C2 ) @ ( minus_456201022768243590nt_int @ B4 @ C2 ) ) ) ).
% Un_Diff
thf(fact_607_Un__Diff,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int,C2: set_se6260736226359567993nt_int] :
( ( minus_2612819937483484256nt_int @ ( sup_su2047564715030645325nt_int @ A3 @ B4 ) @ C2 )
= ( sup_su2047564715030645325nt_int @ ( minus_2612819937483484256nt_int @ A3 @ C2 ) @ ( minus_2612819937483484256nt_int @ B4 @ C2 ) ) ) ).
% Un_Diff
thf(fact_608_Un__Diff,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int] :
( ( minus_1052850069191792384nt_int @ ( sup_su6024340866399070445nt_int @ A3 @ B4 ) @ C2 )
= ( sup_su6024340866399070445nt_int @ ( minus_1052850069191792384nt_int @ A3 @ C2 ) @ ( minus_1052850069191792384nt_int @ B4 @ C2 ) ) ) ).
% Un_Diff
thf(fact_609_knights__path__append,axiom,
! [B_1: set_Pr958786334691620121nt_int,Ps_1: list_P5707943133018811711nt_int,B_2: set_Pr958786334691620121nt_int,Ps_2: list_P5707943133018811711nt_int] :
( ( knights_path @ B_1 @ Ps_1 )
=> ( ( knights_path @ B_2 @ Ps_2 )
=> ( ( ( inf_in2269163501485487111nt_int @ B_1 @ B_2 )
= bot_bo1796632182523588997nt_int )
=> ( ( valid_step @ ( last_P3305686521732843992nt_int @ Ps_1 ) @ ( hd_Pro282112905867057956nt_int @ Ps_2 ) )
=> ( knights_path @ ( sup_su6024340866399070445nt_int @ B_1 @ B_2 ) @ ( append7030698103840186580nt_int @ Ps_1 @ Ps_2 ) ) ) ) ) ) ).
% knights_path_append
thf(fact_610_singleton__Un__iff,axiom,
! [X: produc1219242969750017639nt_int,A3: set_Pr2560585780119916871nt_int,B4: set_Pr2560585780119916871nt_int] :
( ( ( insert5410160437170799671nt_int @ X @ bot_bo8417956007504411571nt_int )
= ( sup_su3808334714663352091nt_int @ A3 @ B4 ) )
= ( ( ( A3 = bot_bo8417956007504411571nt_int )
& ( B4
= ( insert5410160437170799671nt_int @ X @ bot_bo8417956007504411571nt_int ) ) )
| ( ( A3
= ( insert5410160437170799671nt_int @ X @ bot_bo8417956007504411571nt_int ) )
& ( B4 = bot_bo8417956007504411571nt_int ) )
| ( ( A3
= ( insert5410160437170799671nt_int @ X @ bot_bo8417956007504411571nt_int ) )
& ( B4
= ( insert5410160437170799671nt_int @ X @ bot_bo8417956007504411571nt_int ) ) ) ) ) ).
% singleton_Un_iff
thf(fact_611_singleton__Un__iff,axiom,
! [X: int,A3: set_int,B4: set_int] :
( ( ( insert_int @ X @ bot_bot_set_int )
= ( sup_sup_set_int @ A3 @ B4 ) )
= ( ( ( A3 = bot_bot_set_int )
& ( B4
= ( insert_int @ X @ bot_bot_set_int ) ) )
| ( ( A3
= ( insert_int @ X @ bot_bot_set_int ) )
& ( B4 = bot_bot_set_int ) )
| ( ( A3
= ( insert_int @ X @ bot_bot_set_int ) )
& ( B4
= ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ).
% singleton_Un_iff
thf(fact_612_singleton__Un__iff,axiom,
! [X: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int] :
( ( ( insert393344137582914319nt_int @ X @ bot_bo3809061186584590219nt_int )
= ( sup_su3633867531522857715nt_int @ A3 @ B4 ) )
= ( ( ( A3 = bot_bo3809061186584590219nt_int )
& ( B4
= ( insert393344137582914319nt_int @ X @ bot_bo3809061186584590219nt_int ) ) )
| ( ( A3
= ( insert393344137582914319nt_int @ X @ bot_bo3809061186584590219nt_int ) )
& ( B4 = bot_bo3809061186584590219nt_int ) )
| ( ( A3
= ( insert393344137582914319nt_int @ X @ bot_bo3809061186584590219nt_int ) )
& ( B4
= ( insert393344137582914319nt_int @ X @ bot_bo3809061186584590219nt_int ) ) ) ) ) ).
% singleton_Un_iff
thf(fact_613_singleton__Un__iff,axiom,
! [X: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int )
= ( sup_su2047564715030645325nt_int @ A3 @ B4 ) )
= ( ( ( A3 = bot_bo1488462491386950373nt_int )
& ( B4
= ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) ) )
| ( ( A3
= ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
& ( B4 = bot_bo1488462491386950373nt_int ) )
| ( ( A3
= ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
& ( B4
= ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) ) ) ) ) ).
% singleton_Un_iff
thf(fact_614_singleton__Un__iff,axiom,
! [X: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ( insert5033312907999012233nt_int @ X @ bot_bo1796632182523588997nt_int )
= ( sup_su6024340866399070445nt_int @ A3 @ B4 ) )
= ( ( ( A3 = bot_bo1796632182523588997nt_int )
& ( B4
= ( insert5033312907999012233nt_int @ X @ bot_bo1796632182523588997nt_int ) ) )
| ( ( A3
= ( insert5033312907999012233nt_int @ X @ bot_bo1796632182523588997nt_int ) )
& ( B4 = bot_bo1796632182523588997nt_int ) )
| ( ( A3
= ( insert5033312907999012233nt_int @ X @ bot_bo1796632182523588997nt_int ) )
& ( B4
= ( insert5033312907999012233nt_int @ X @ bot_bo1796632182523588997nt_int ) ) ) ) ) ).
% singleton_Un_iff
thf(fact_615_Un__singleton__iff,axiom,
! [A3: set_Pr2560585780119916871nt_int,B4: set_Pr2560585780119916871nt_int,X: produc1219242969750017639nt_int] :
( ( ( sup_su3808334714663352091nt_int @ A3 @ B4 )
= ( insert5410160437170799671nt_int @ X @ bot_bo8417956007504411571nt_int ) )
= ( ( ( A3 = bot_bo8417956007504411571nt_int )
& ( B4
= ( insert5410160437170799671nt_int @ X @ bot_bo8417956007504411571nt_int ) ) )
| ( ( A3
= ( insert5410160437170799671nt_int @ X @ bot_bo8417956007504411571nt_int ) )
& ( B4 = bot_bo8417956007504411571nt_int ) )
| ( ( A3
= ( insert5410160437170799671nt_int @ X @ bot_bo8417956007504411571nt_int ) )
& ( B4
= ( insert5410160437170799671nt_int @ X @ bot_bo8417956007504411571nt_int ) ) ) ) ) ).
% Un_singleton_iff
thf(fact_616_Un__singleton__iff,axiom,
! [A3: set_int,B4: set_int,X: int] :
( ( ( sup_sup_set_int @ A3 @ B4 )
= ( insert_int @ X @ bot_bot_set_int ) )
= ( ( ( A3 = bot_bot_set_int )
& ( B4
= ( insert_int @ X @ bot_bot_set_int ) ) )
| ( ( A3
= ( insert_int @ X @ bot_bot_set_int ) )
& ( B4 = bot_bot_set_int ) )
| ( ( A3
= ( insert_int @ X @ bot_bot_set_int ) )
& ( B4
= ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ).
% Un_singleton_iff
thf(fact_617_Un__singleton__iff,axiom,
! [A3: set_li3855193629254082847nt_int,B4: set_li3855193629254082847nt_int,X: list_P5707943133018811711nt_int] :
( ( ( sup_su3633867531522857715nt_int @ A3 @ B4 )
= ( insert393344137582914319nt_int @ X @ bot_bo3809061186584590219nt_int ) )
= ( ( ( A3 = bot_bo3809061186584590219nt_int )
& ( B4
= ( insert393344137582914319nt_int @ X @ bot_bo3809061186584590219nt_int ) ) )
| ( ( A3
= ( insert393344137582914319nt_int @ X @ bot_bo3809061186584590219nt_int ) )
& ( B4 = bot_bo3809061186584590219nt_int ) )
| ( ( A3
= ( insert393344137582914319nt_int @ X @ bot_bo3809061186584590219nt_int ) )
& ( B4
= ( insert393344137582914319nt_int @ X @ bot_bo3809061186584590219nt_int ) ) ) ) ) ).
% Un_singleton_iff
thf(fact_618_Un__singleton__iff,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int] :
( ( ( sup_su2047564715030645325nt_int @ A3 @ B4 )
= ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
= ( ( ( A3 = bot_bo1488462491386950373nt_int )
& ( B4
= ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) ) )
| ( ( A3
= ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
& ( B4 = bot_bo1488462491386950373nt_int ) )
| ( ( A3
= ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
& ( B4
= ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) ) ) ) ) ).
% Un_singleton_iff
thf(fact_619_Un__singleton__iff,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,X: product_prod_int_int] :
( ( ( sup_su6024340866399070445nt_int @ A3 @ B4 )
= ( insert5033312907999012233nt_int @ X @ bot_bo1796632182523588997nt_int ) )
= ( ( ( A3 = bot_bo1796632182523588997nt_int )
& ( B4
= ( insert5033312907999012233nt_int @ X @ bot_bo1796632182523588997nt_int ) ) )
| ( ( A3
= ( insert5033312907999012233nt_int @ X @ bot_bo1796632182523588997nt_int ) )
& ( B4 = bot_bo1796632182523588997nt_int ) )
| ( ( A3
= ( insert5033312907999012233nt_int @ X @ bot_bo1796632182523588997nt_int ) )
& ( B4
= ( insert5033312907999012233nt_int @ X @ bot_bo1796632182523588997nt_int ) ) ) ) ) ).
% Un_singleton_iff
thf(fact_620_insert__is__Un,axiom,
( insert5410160437170799671nt_int
= ( ^ [A5: produc1219242969750017639nt_int] : ( sup_su3808334714663352091nt_int @ ( insert5410160437170799671nt_int @ A5 @ bot_bo8417956007504411571nt_int ) ) ) ) ).
% insert_is_Un
thf(fact_621_insert__is__Un,axiom,
( insert_int
= ( ^ [A5: int] : ( sup_sup_set_int @ ( insert_int @ A5 @ bot_bot_set_int ) ) ) ) ).
% insert_is_Un
thf(fact_622_insert__is__Un,axiom,
( insert393344137582914319nt_int
= ( ^ [A5: list_P5707943133018811711nt_int] : ( sup_su3633867531522857715nt_int @ ( insert393344137582914319nt_int @ A5 @ bot_bo3809061186584590219nt_int ) ) ) ) ).
% insert_is_Un
thf(fact_623_insert__is__Un,axiom,
( insert8897473484851387113nt_int
= ( ^ [A5: set_Pr958786334691620121nt_int] : ( sup_su2047564715030645325nt_int @ ( insert8897473484851387113nt_int @ A5 @ bot_bo1488462491386950373nt_int ) ) ) ) ).
% insert_is_Un
thf(fact_624_insert__is__Un,axiom,
( insert5033312907999012233nt_int
= ( ^ [A5: product_prod_int_int] : ( sup_su6024340866399070445nt_int @ ( insert5033312907999012233nt_int @ A5 @ bot_bo1796632182523588997nt_int ) ) ) ) ).
% insert_is_Un
thf(fact_625_Diff__insert__absorb,axiom,
! [X: list_P5707943133018811711nt_int,A3: set_li3855193629254082847nt_int] :
( ~ ( member2764346250752101224nt_int @ X @ A3 )
=> ( ( minus_456201022768243590nt_int @ ( insert393344137582914319nt_int @ X @ A3 ) @ ( insert393344137582914319nt_int @ X @ bot_bo3809061186584590219nt_int ) )
= A3 ) ) ).
% Diff_insert_absorb
thf(fact_626_Diff__insert__absorb,axiom,
! [X: set_Pr958786334691620121nt_int,A3: set_se6260736226359567993nt_int] :
( ~ ( member2340774599025711042nt_int @ X @ A3 )
=> ( ( minus_2612819937483484256nt_int @ ( insert8897473484851387113nt_int @ X @ A3 ) @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
= A3 ) ) ).
% Diff_insert_absorb
thf(fact_627_Diff__insert__absorb,axiom,
! [X: product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ~ ( member5262025264175285858nt_int @ X @ A3 )
=> ( ( minus_1052850069191792384nt_int @ ( insert5033312907999012233nt_int @ X @ A3 ) @ ( insert5033312907999012233nt_int @ X @ bot_bo1796632182523588997nt_int ) )
= A3 ) ) ).
% Diff_insert_absorb
thf(fact_628_Diff__insert2,axiom,
! [A3: set_Pr958786334691620121nt_int,A: product_prod_int_int,B4: set_Pr958786334691620121nt_int] :
( ( minus_1052850069191792384nt_int @ A3 @ ( insert5033312907999012233nt_int @ A @ B4 ) )
= ( minus_1052850069191792384nt_int @ ( minus_1052850069191792384nt_int @ A3 @ ( insert5033312907999012233nt_int @ A @ bot_bo1796632182523588997nt_int ) ) @ B4 ) ) ).
% Diff_insert2
thf(fact_629_insert__Diff,axiom,
! [A: product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ A @ A3 )
=> ( ( insert5033312907999012233nt_int @ A @ ( minus_1052850069191792384nt_int @ A3 @ ( insert5033312907999012233nt_int @ A @ bot_bo1796632182523588997nt_int ) ) )
= A3 ) ) ).
% insert_Diff
thf(fact_630_Diff__insert,axiom,
! [A3: set_Pr958786334691620121nt_int,A: product_prod_int_int,B4: set_Pr958786334691620121nt_int] :
( ( minus_1052850069191792384nt_int @ A3 @ ( insert5033312907999012233nt_int @ A @ B4 ) )
= ( minus_1052850069191792384nt_int @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) @ ( insert5033312907999012233nt_int @ A @ bot_bo1796632182523588997nt_int ) ) ) ).
% Diff_insert
thf(fact_631_sup__inf__absorb,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ X @ ( inf_in2269163501485487111nt_int @ X @ Y ) )
= X ) ).
% sup_inf_absorb
thf(fact_632_inf__sup__absorb,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ X @ ( sup_su6024340866399070445nt_int @ X @ Y ) )
= X ) ).
% inf_sup_absorb
thf(fact_633_sup__bot_Oright__neutral,axiom,
! [A: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ A @ bot_bo1796632182523588997nt_int )
= A ) ).
% sup_bot.right_neutral
thf(fact_634_sup__bot_Oneutr__eq__iff,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( bot_bo1796632182523588997nt_int
= ( sup_su6024340866399070445nt_int @ A @ B ) )
= ( ( A = bot_bo1796632182523588997nt_int )
& ( B = bot_bo1796632182523588997nt_int ) ) ) ).
% sup_bot.neutr_eq_iff
thf(fact_635_sup__bot_Oleft__neutral,axiom,
! [A: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ bot_bo1796632182523588997nt_int @ A )
= A ) ).
% sup_bot.left_neutral
thf(fact_636_sup__bot_Oeq__neutr__iff,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ( sup_su6024340866399070445nt_int @ A @ B )
= bot_bo1796632182523588997nt_int )
= ( ( A = bot_bo1796632182523588997nt_int )
& ( B = bot_bo1796632182523588997nt_int ) ) ) ).
% sup_bot.eq_neutr_iff
thf(fact_637_sup__eq__bot__iff,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ( ( sup_su6024340866399070445nt_int @ X @ Y )
= bot_bo1796632182523588997nt_int )
= ( ( X = bot_bo1796632182523588997nt_int )
& ( Y = bot_bo1796632182523588997nt_int ) ) ) ).
% sup_eq_bot_iff
thf(fact_638_bot__eq__sup__iff,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ( bot_bo1796632182523588997nt_int
= ( sup_su6024340866399070445nt_int @ X @ Y ) )
= ( ( X = bot_bo1796632182523588997nt_int )
& ( Y = bot_bo1796632182523588997nt_int ) ) ) ).
% bot_eq_sup_iff
thf(fact_639_sup__bot__right,axiom,
! [X: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ X @ bot_bo1796632182523588997nt_int )
= X ) ).
% sup_bot_right
thf(fact_640_sup__bot__left,axiom,
! [X: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ bot_bo1796632182523588997nt_int @ X )
= X ) ).
% sup_bot_left
thf(fact_641_inf_Oidem,axiom,
! [A: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ A @ A )
= A ) ).
% inf.idem
thf(fact_642_inf__idem,axiom,
! [X: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ X @ X )
= X ) ).
% inf_idem
thf(fact_643_inf_Oleft__idem,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ A @ ( inf_in2269163501485487111nt_int @ A @ B ) )
= ( inf_in2269163501485487111nt_int @ A @ B ) ) ).
% inf.left_idem
thf(fact_644_inf__left__idem,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ X @ ( inf_in2269163501485487111nt_int @ X @ Y ) )
= ( inf_in2269163501485487111nt_int @ X @ Y ) ) ).
% inf_left_idem
thf(fact_645_inf_Oright__idem,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ ( inf_in2269163501485487111nt_int @ A @ B ) @ B )
= ( inf_in2269163501485487111nt_int @ A @ B ) ) ).
% inf.right_idem
thf(fact_646_inf__right__idem,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ ( inf_in2269163501485487111nt_int @ X @ Y ) @ Y )
= ( inf_in2269163501485487111nt_int @ X @ Y ) ) ).
% inf_right_idem
thf(fact_647_sup_Oidem,axiom,
! [A: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ A @ A )
= A ) ).
% sup.idem
thf(fact_648_sup__idem,axiom,
! [X: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ X @ X )
= X ) ).
% sup_idem
thf(fact_649_sup_Oleft__idem,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ A @ ( sup_su6024340866399070445nt_int @ A @ B ) )
= ( sup_su6024340866399070445nt_int @ A @ B ) ) ).
% sup.left_idem
thf(fact_650_sup__left__idem,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ X @ ( sup_su6024340866399070445nt_int @ X @ Y ) )
= ( sup_su6024340866399070445nt_int @ X @ Y ) ) ).
% sup_left_idem
thf(fact_651_sup_Oright__idem,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ ( sup_su6024340866399070445nt_int @ A @ B ) @ B )
= ( sup_su6024340866399070445nt_int @ A @ B ) ) ).
% sup.right_idem
thf(fact_652_inf__bot__left,axiom,
! [X: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ bot_bo1796632182523588997nt_int @ X )
= bot_bo1796632182523588997nt_int ) ).
% inf_bot_left
thf(fact_653_inf__bot__right,axiom,
! [X: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ X @ bot_bo1796632182523588997nt_int )
= bot_bo1796632182523588997nt_int ) ).
% inf_bot_right
thf(fact_654_bot__set__def,axiom,
( bot_bo1796632182523588997nt_int
= ( collec213857154873943460nt_int @ bot_bo8147686125503663512_int_o ) ) ).
% bot_set_def
thf(fact_655_inf__sup__aci_I4_J,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ X @ ( inf_in2269163501485487111nt_int @ X @ Y ) )
= ( inf_in2269163501485487111nt_int @ X @ Y ) ) ).
% inf_sup_aci(4)
thf(fact_656_inf__sup__aci_I3_J,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ X @ ( inf_in2269163501485487111nt_int @ Y @ Z ) )
= ( inf_in2269163501485487111nt_int @ Y @ ( inf_in2269163501485487111nt_int @ X @ Z ) ) ) ).
% inf_sup_aci(3)
thf(fact_657_inf__sup__aci_I2_J,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ ( inf_in2269163501485487111nt_int @ X @ Y ) @ Z )
= ( inf_in2269163501485487111nt_int @ X @ ( inf_in2269163501485487111nt_int @ Y @ Z ) ) ) ).
% inf_sup_aci(2)
thf(fact_658_inf__sup__aci_I1_J,axiom,
( inf_in2269163501485487111nt_int
= ( ^ [X2: set_Pr958786334691620121nt_int,Y3: set_Pr958786334691620121nt_int] : ( inf_in2269163501485487111nt_int @ Y3 @ X2 ) ) ) ).
% inf_sup_aci(1)
thf(fact_659_inf_Oassoc,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ ( inf_in2269163501485487111nt_int @ A @ B ) @ C )
= ( inf_in2269163501485487111nt_int @ A @ ( inf_in2269163501485487111nt_int @ B @ C ) ) ) ).
% inf.assoc
thf(fact_660_inf__assoc,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ ( inf_in2269163501485487111nt_int @ X @ Y ) @ Z )
= ( inf_in2269163501485487111nt_int @ X @ ( inf_in2269163501485487111nt_int @ Y @ Z ) ) ) ).
% inf_assoc
thf(fact_661_inf_Ocommute,axiom,
( inf_in2269163501485487111nt_int
= ( ^ [A5: set_Pr958786334691620121nt_int,B2: set_Pr958786334691620121nt_int] : ( inf_in2269163501485487111nt_int @ B2 @ A5 ) ) ) ).
% inf.commute
thf(fact_662_inf__commute,axiom,
( inf_in2269163501485487111nt_int
= ( ^ [X2: set_Pr958786334691620121nt_int,Y3: set_Pr958786334691620121nt_int] : ( inf_in2269163501485487111nt_int @ Y3 @ X2 ) ) ) ).
% inf_commute
thf(fact_663_inf_Oleft__commute,axiom,
! [B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ B @ ( inf_in2269163501485487111nt_int @ A @ C ) )
= ( inf_in2269163501485487111nt_int @ A @ ( inf_in2269163501485487111nt_int @ B @ C ) ) ) ).
% inf.left_commute
thf(fact_664_inf__left__commute,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ X @ ( inf_in2269163501485487111nt_int @ Y @ Z ) )
= ( inf_in2269163501485487111nt_int @ Y @ ( inf_in2269163501485487111nt_int @ X @ Z ) ) ) ).
% inf_left_commute
thf(fact_665_inf__sup__aci_I8_J,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ X @ ( sup_su6024340866399070445nt_int @ X @ Y ) )
= ( sup_su6024340866399070445nt_int @ X @ Y ) ) ).
% inf_sup_aci(8)
thf(fact_666_inf__sup__aci_I7_J,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ X @ ( sup_su6024340866399070445nt_int @ Y @ Z ) )
= ( sup_su6024340866399070445nt_int @ Y @ ( sup_su6024340866399070445nt_int @ X @ Z ) ) ) ).
% inf_sup_aci(7)
thf(fact_667_inf__sup__aci_I6_J,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ ( sup_su6024340866399070445nt_int @ X @ Y ) @ Z )
= ( sup_su6024340866399070445nt_int @ X @ ( sup_su6024340866399070445nt_int @ Y @ Z ) ) ) ).
% inf_sup_aci(6)
thf(fact_668_inf__sup__aci_I5_J,axiom,
( sup_su6024340866399070445nt_int
= ( ^ [X2: set_Pr958786334691620121nt_int,Y3: set_Pr958786334691620121nt_int] : ( sup_su6024340866399070445nt_int @ Y3 @ X2 ) ) ) ).
% inf_sup_aci(5)
thf(fact_669_sup_Oassoc,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ ( sup_su6024340866399070445nt_int @ A @ B ) @ C )
= ( sup_su6024340866399070445nt_int @ A @ ( sup_su6024340866399070445nt_int @ B @ C ) ) ) ).
% sup.assoc
thf(fact_670_sup__assoc,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ ( sup_su6024340866399070445nt_int @ X @ Y ) @ Z )
= ( sup_su6024340866399070445nt_int @ X @ ( sup_su6024340866399070445nt_int @ Y @ Z ) ) ) ).
% sup_assoc
thf(fact_671_sup_Ocommute,axiom,
( sup_su6024340866399070445nt_int
= ( ^ [A5: set_Pr958786334691620121nt_int,B2: set_Pr958786334691620121nt_int] : ( sup_su6024340866399070445nt_int @ B2 @ A5 ) ) ) ).
% sup.commute
thf(fact_672_sup__commute,axiom,
( sup_su6024340866399070445nt_int
= ( ^ [X2: set_Pr958786334691620121nt_int,Y3: set_Pr958786334691620121nt_int] : ( sup_su6024340866399070445nt_int @ Y3 @ X2 ) ) ) ).
% sup_commute
thf(fact_673_sup_Oleft__commute,axiom,
! [B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ B @ ( sup_su6024340866399070445nt_int @ A @ C ) )
= ( sup_su6024340866399070445nt_int @ A @ ( sup_su6024340866399070445nt_int @ B @ C ) ) ) ).
% sup.left_commute
thf(fact_674_sup__left__commute,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ X @ ( sup_su6024340866399070445nt_int @ Y @ Z ) )
= ( sup_su6024340866399070445nt_int @ Y @ ( sup_su6024340866399070445nt_int @ X @ Z ) ) ) ).
% sup_left_commute
thf(fact_675_distrib__imp1,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int] :
( ! [X3: set_Pr958786334691620121nt_int,Y2: set_Pr958786334691620121nt_int,Z2: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ X3 @ ( sup_su6024340866399070445nt_int @ Y2 @ Z2 ) )
= ( sup_su6024340866399070445nt_int @ ( inf_in2269163501485487111nt_int @ X3 @ Y2 ) @ ( inf_in2269163501485487111nt_int @ X3 @ Z2 ) ) )
=> ( ( sup_su6024340866399070445nt_int @ X @ ( inf_in2269163501485487111nt_int @ Y @ Z ) )
= ( inf_in2269163501485487111nt_int @ ( sup_su6024340866399070445nt_int @ X @ Y ) @ ( sup_su6024340866399070445nt_int @ X @ Z ) ) ) ) ).
% distrib_imp1
thf(fact_676_distrib__imp2,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int] :
( ! [X3: set_Pr958786334691620121nt_int,Y2: set_Pr958786334691620121nt_int,Z2: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ X3 @ ( inf_in2269163501485487111nt_int @ Y2 @ Z2 ) )
= ( inf_in2269163501485487111nt_int @ ( sup_su6024340866399070445nt_int @ X3 @ Y2 ) @ ( sup_su6024340866399070445nt_int @ X3 @ Z2 ) ) )
=> ( ( inf_in2269163501485487111nt_int @ X @ ( sup_su6024340866399070445nt_int @ Y @ Z ) )
= ( sup_su6024340866399070445nt_int @ ( inf_in2269163501485487111nt_int @ X @ Y ) @ ( inf_in2269163501485487111nt_int @ X @ Z ) ) ) ) ).
% distrib_imp2
thf(fact_677_inf__sup__distrib1,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ X @ ( sup_su6024340866399070445nt_int @ Y @ Z ) )
= ( sup_su6024340866399070445nt_int @ ( inf_in2269163501485487111nt_int @ X @ Y ) @ ( inf_in2269163501485487111nt_int @ X @ Z ) ) ) ).
% inf_sup_distrib1
thf(fact_678_inf__sup__distrib2,axiom,
! [Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int,X: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ ( sup_su6024340866399070445nt_int @ Y @ Z ) @ X )
= ( sup_su6024340866399070445nt_int @ ( inf_in2269163501485487111nt_int @ Y @ X ) @ ( inf_in2269163501485487111nt_int @ Z @ X ) ) ) ).
% inf_sup_distrib2
thf(fact_679_sup__inf__distrib1,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ X @ ( inf_in2269163501485487111nt_int @ Y @ Z ) )
= ( inf_in2269163501485487111nt_int @ ( sup_su6024340866399070445nt_int @ X @ Y ) @ ( sup_su6024340866399070445nt_int @ X @ Z ) ) ) ).
% sup_inf_distrib1
thf(fact_680_sup__inf__distrib2,axiom,
! [Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int,X: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ ( inf_in2269163501485487111nt_int @ Y @ Z ) @ X )
= ( inf_in2269163501485487111nt_int @ ( sup_su6024340866399070445nt_int @ Y @ X ) @ ( sup_su6024340866399070445nt_int @ Z @ X ) ) ) ).
% sup_inf_distrib2
thf(fact_681_boolean__algebra_Oconj__zero__left,axiom,
! [X: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ bot_bo1796632182523588997nt_int @ X )
= bot_bo1796632182523588997nt_int ) ).
% boolean_algebra.conj_zero_left
thf(fact_682_boolean__algebra_Oconj__zero__right,axiom,
! [X: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ X @ bot_bo1796632182523588997nt_int )
= bot_bo1796632182523588997nt_int ) ).
% boolean_algebra.conj_zero_right
thf(fact_683_the__elem__eq,axiom,
! [X: product_prod_int_int] :
( ( the_el8326832613380209454nt_int @ ( insert5033312907999012233nt_int @ X @ bot_bo1796632182523588997nt_int ) )
= X ) ).
% the_elem_eq
thf(fact_684_is__singletonI,axiom,
! [X: product_prod_int_int] : ( is_sin8895854488172861613nt_int @ ( insert5033312907999012233nt_int @ X @ bot_bo1796632182523588997nt_int ) ) ).
% is_singletonI
thf(fact_685_boolean__algebra_Oconj__disj__distrib,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ X @ ( sup_su6024340866399070445nt_int @ Y @ Z ) )
= ( sup_su6024340866399070445nt_int @ ( inf_in2269163501485487111nt_int @ X @ Y ) @ ( inf_in2269163501485487111nt_int @ X @ Z ) ) ) ).
% boolean_algebra.conj_disj_distrib
thf(fact_686_boolean__algebra_Odisj__conj__distrib,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ X @ ( inf_in2269163501485487111nt_int @ Y @ Z ) )
= ( inf_in2269163501485487111nt_int @ ( sup_su6024340866399070445nt_int @ X @ Y ) @ ( sup_su6024340866399070445nt_int @ X @ Z ) ) ) ).
% boolean_algebra.disj_conj_distrib
thf(fact_687_is__singleton__the__elem,axiom,
( is_sin8895854488172861613nt_int
= ( ^ [A4: set_Pr958786334691620121nt_int] :
( A4
= ( insert5033312907999012233nt_int @ ( the_el8326832613380209454nt_int @ A4 ) @ bot_bo1796632182523588997nt_int ) ) ) ) ).
% is_singleton_the_elem
thf(fact_688_is__singletonI_H,axiom,
! [A3: set_Pr958786334691620121nt_int] :
( ( A3 != bot_bo1796632182523588997nt_int )
=> ( ! [X3: product_prod_int_int,Y2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X3 @ A3 )
=> ( ( member5262025264175285858nt_int @ Y2 @ A3 )
=> ( X3 = Y2 ) ) )
=> ( is_sin8895854488172861613nt_int @ A3 ) ) ) ).
% is_singletonI'
thf(fact_689_boolean__algebra__cancel_Oinf2,axiom,
! [B4: set_Pr958786334691620121nt_int,K: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
( ( B4
= ( inf_in2269163501485487111nt_int @ K @ B ) )
=> ( ( inf_in2269163501485487111nt_int @ A @ B4 )
= ( inf_in2269163501485487111nt_int @ K @ ( inf_in2269163501485487111nt_int @ A @ B ) ) ) ) ).
% boolean_algebra_cancel.inf2
thf(fact_690_boolean__algebra__cancel_Oinf1,axiom,
! [A3: set_Pr958786334691620121nt_int,K: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( A3
= ( inf_in2269163501485487111nt_int @ K @ A ) )
=> ( ( inf_in2269163501485487111nt_int @ A3 @ B )
= ( inf_in2269163501485487111nt_int @ K @ ( inf_in2269163501485487111nt_int @ A @ B ) ) ) ) ).
% boolean_algebra_cancel.inf1
thf(fact_691_boolean__algebra__cancel_Osup2,axiom,
! [B4: set_Pr958786334691620121nt_int,K: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
( ( B4
= ( sup_su6024340866399070445nt_int @ K @ B ) )
=> ( ( sup_su6024340866399070445nt_int @ A @ B4 )
= ( sup_su6024340866399070445nt_int @ K @ ( sup_su6024340866399070445nt_int @ A @ B ) ) ) ) ).
% boolean_algebra_cancel.sup2
thf(fact_692_boolean__algebra__cancel_Osup1,axiom,
! [A3: set_Pr958786334691620121nt_int,K: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( A3
= ( sup_su6024340866399070445nt_int @ K @ A ) )
=> ( ( sup_su6024340866399070445nt_int @ A3 @ B )
= ( sup_su6024340866399070445nt_int @ K @ ( sup_su6024340866399070445nt_int @ A @ B ) ) ) ) ).
% boolean_algebra_cancel.sup1
thf(fact_693_is__singleton__def,axiom,
( is_sin8895854488172861613nt_int
= ( ^ [A4: set_Pr958786334691620121nt_int] :
? [X2: product_prod_int_int] :
( A4
= ( insert5033312907999012233nt_int @ X2 @ bot_bo1796632182523588997nt_int ) ) ) ) ).
% is_singleton_def
thf(fact_694_is__singletonE,axiom,
! [A3: set_Pr958786334691620121nt_int] :
( ( is_sin8895854488172861613nt_int @ A3 )
=> ~ ! [X3: product_prod_int_int] :
( A3
!= ( insert5033312907999012233nt_int @ X3 @ bot_bo1796632182523588997nt_int ) ) ) ).
% is_singletonE
thf(fact_695_boolean__algebra_Odisj__zero__right,axiom,
! [X: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ X @ bot_bo1796632182523588997nt_int )
= X ) ).
% boolean_algebra.disj_zero_right
thf(fact_696_boolean__algebra_Odisj__conj__distrib2,axiom,
! [Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int,X: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ ( inf_in2269163501485487111nt_int @ Y @ Z ) @ X )
= ( inf_in2269163501485487111nt_int @ ( sup_su6024340866399070445nt_int @ Y @ X ) @ ( sup_su6024340866399070445nt_int @ Z @ X ) ) ) ).
% boolean_algebra.disj_conj_distrib2
thf(fact_697_boolean__algebra_Oconj__disj__distrib2,axiom,
! [Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int,X: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ ( sup_su6024340866399070445nt_int @ Y @ Z ) @ X )
= ( sup_su6024340866399070445nt_int @ ( inf_in2269163501485487111nt_int @ Y @ X ) @ ( inf_in2269163501485487111nt_int @ Z @ X ) ) ) ).
% boolean_algebra.conj_disj_distrib2
thf(fact_698_bot__empty__eq,axiom,
( bot_bo8147686125503663512_int_o
= ( ^ [X2: product_prod_int_int] : ( member5262025264175285858nt_int @ X2 @ bot_bo1796632182523588997nt_int ) ) ) ).
% bot_empty_eq
thf(fact_699_Collect__empty__eq__bot,axiom,
! [P: product_prod_int_int > $o] :
( ( ( collec213857154873943460nt_int @ P )
= bot_bo1796632182523588997nt_int )
= ( P = bot_bo8147686125503663512_int_o ) ) ).
% Collect_empty_eq_bot
thf(fact_700_path__checker_Osimps_I2_J,axiom,
! [B: set_Pr958786334691620121nt_int,S_i: product_prod_int_int] :
( ( path_checker @ B @ ( cons_P3334398858971670639nt_int @ S_i @ nil_Pr2300489316682597567nt_int ) )
= ( ( insert5033312907999012233nt_int @ S_i @ bot_bo1796632182523588997nt_int )
= B ) ) ).
% path_checker.simps(2)
thf(fact_701_product__lists_Osimps_I1_J,axiom,
( ( produc5568053154996169768nt_int @ nil_li8670148097206105925nt_int )
= ( cons_l7309679040211256053nt_int @ nil_Pr2300489316682597567nt_int @ nil_li8670148097206105925nt_int ) ) ).
% product_lists.simps(1)
thf(fact_702_bind__simps_I2_J,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int,F: product_prod_int_int > list_P5707943133018811711nt_int] :
( ( bind_P8056059132564497095nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) @ F )
= ( append7030698103840186580nt_int @ ( F @ X ) @ ( bind_P8056059132564497095nt_int @ Xs @ F ) ) ) ).
% bind_simps(2)
thf(fact_703_append__butlast__last__id,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( Xs != nil_Pr2300489316682597567nt_int )
=> ( ( append7030698103840186580nt_int @ ( butlas2390654596765537291nt_int @ Xs ) @ ( cons_P3334398858971670639nt_int @ ( last_P3305686521732843992nt_int @ Xs ) @ nil_Pr2300489316682597567nt_int ) )
= Xs ) ) ).
% append_butlast_last_id
thf(fact_704_remove__def,axiom,
( remove3288057706648593438nt_int
= ( ^ [X2: product_prod_int_int,A4: set_Pr958786334691620121nt_int] : ( minus_1052850069191792384nt_int @ A4 @ ( insert5033312907999012233nt_int @ X2 @ bot_bo1796632182523588997nt_int ) ) ) ) ).
% remove_def
thf(fact_705_member__remove,axiom,
! [X: product_prod_int_int,Y: product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ X @ ( remove3288057706648593438nt_int @ Y @ A3 ) )
= ( ( member5262025264175285858nt_int @ X @ A3 )
& ( X != Y ) ) ) ).
% member_remove
thf(fact_706_bind__simps_I1_J,axiom,
! [F: product_prod_int_int > list_P5707943133018811711nt_int] :
( ( bind_P8056059132564497095nt_int @ nil_Pr2300489316682597567nt_int @ F )
= nil_Pr2300489316682597567nt_int ) ).
% bind_simps(1)
thf(fact_707_butlast__snoc,axiom,
! [Xs: list_P5707943133018811711nt_int,X: product_prod_int_int] :
( ( butlas2390654596765537291nt_int @ ( append7030698103840186580nt_int @ Xs @ ( cons_P3334398858971670639nt_int @ X @ nil_Pr2300489316682597567nt_int ) ) )
= Xs ) ).
% butlast_snoc
thf(fact_708_butlast_Osimps_I1_J,axiom,
( ( butlas2390654596765537291nt_int @ nil_Pr2300489316682597567nt_int )
= nil_Pr2300489316682597567nt_int ) ).
% butlast.simps(1)
thf(fact_709_path__checker__correct,axiom,
path_checker = knights_path ).
% path_checker_correct
thf(fact_710_path__checker_Osimps_I1_J,axiom,
! [B: set_Pr958786334691620121nt_int] :
~ ( path_checker @ B @ nil_Pr2300489316682597567nt_int ) ).
% path_checker.simps(1)
thf(fact_711_butlast_Osimps_I2_J,axiom,
! [Xs: list_P5707943133018811711nt_int,X: product_prod_int_int] :
( ( ( Xs = nil_Pr2300489316682597567nt_int )
=> ( ( butlas2390654596765537291nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) )
= nil_Pr2300489316682597567nt_int ) )
& ( ( Xs != nil_Pr2300489316682597567nt_int )
=> ( ( butlas2390654596765537291nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) )
= ( cons_P3334398858971670639nt_int @ X @ ( butlas2390654596765537291nt_int @ Xs ) ) ) ) ) ).
% butlast.simps(2)
thf(fact_712_butlast__append,axiom,
! [Ys: list_P5707943133018811711nt_int,Xs: list_P5707943133018811711nt_int] :
( ( ( Ys = nil_Pr2300489316682597567nt_int )
=> ( ( butlas2390654596765537291nt_int @ ( append7030698103840186580nt_int @ Xs @ Ys ) )
= ( butlas2390654596765537291nt_int @ Xs ) ) )
& ( ( Ys != nil_Pr2300489316682597567nt_int )
=> ( ( butlas2390654596765537291nt_int @ ( append7030698103840186580nt_int @ Xs @ Ys ) )
= ( append7030698103840186580nt_int @ Xs @ ( butlas2390654596765537291nt_int @ Ys ) ) ) ) ) ).
% butlast_append
thf(fact_713_snoc__eq__iff__butlast,axiom,
! [Xs: list_P5707943133018811711nt_int,X: product_prod_int_int,Ys: list_P5707943133018811711nt_int] :
( ( ( append7030698103840186580nt_int @ Xs @ ( cons_P3334398858971670639nt_int @ X @ nil_Pr2300489316682597567nt_int ) )
= Ys )
= ( ( Ys != nil_Pr2300489316682597567nt_int )
& ( ( butlas2390654596765537291nt_int @ Ys )
= Xs )
& ( ( last_P3305686521732843992nt_int @ Ys )
= X ) ) ) ).
% snoc_eq_iff_butlast
thf(fact_714_path__checker_Oelims_I1_J,axiom,
! [X: set_Pr958786334691620121nt_int,Xa: list_P5707943133018811711nt_int,Y: $o] :
( ( ( path_checker @ X @ Xa )
= Y )
=> ( ( ( Xa = nil_Pr2300489316682597567nt_int )
=> Y )
=> ( ! [S_i3: product_prod_int_int] :
( ( Xa
= ( cons_P3334398858971670639nt_int @ S_i3 @ nil_Pr2300489316682597567nt_int ) )
=> ( Y
= ( ( insert5033312907999012233nt_int @ S_i3 @ bot_bo1796632182523588997nt_int )
!= X ) ) )
=> ~ ! [S_i3: product_prod_int_int,S_j3: product_prod_int_int,Ps3: list_P5707943133018811711nt_int] :
( ( Xa
= ( cons_P3334398858971670639nt_int @ S_i3 @ ( cons_P3334398858971670639nt_int @ S_j3 @ Ps3 ) ) )
=> ( Y
= ( ~ ( ( member5262025264175285858nt_int @ S_i3 @ X )
& ( step_checker @ S_i3 @ S_j3 )
& ( path_checker @ ( minus_1052850069191792384nt_int @ X @ ( insert5033312907999012233nt_int @ S_i3 @ bot_bo1796632182523588997nt_int ) ) @ ( cons_P3334398858971670639nt_int @ S_j3 @ Ps3 ) ) ) ) ) ) ) ) ) ).
% path_checker.elims(1)
thf(fact_715_path__checker_Oelims_I2_J,axiom,
! [X: set_Pr958786334691620121nt_int,Xa: list_P5707943133018811711nt_int] :
( ( path_checker @ X @ Xa )
=> ( ! [S_i3: product_prod_int_int] :
( ( Xa
= ( cons_P3334398858971670639nt_int @ S_i3 @ nil_Pr2300489316682597567nt_int ) )
=> ( ( insert5033312907999012233nt_int @ S_i3 @ bot_bo1796632182523588997nt_int )
!= X ) )
=> ~ ! [S_i3: product_prod_int_int,S_j3: product_prod_int_int,Ps3: list_P5707943133018811711nt_int] :
( ( Xa
= ( cons_P3334398858971670639nt_int @ S_i3 @ ( cons_P3334398858971670639nt_int @ S_j3 @ Ps3 ) ) )
=> ~ ( ( member5262025264175285858nt_int @ S_i3 @ X )
& ( step_checker @ S_i3 @ S_j3 )
& ( path_checker @ ( minus_1052850069191792384nt_int @ X @ ( insert5033312907999012233nt_int @ S_i3 @ bot_bo1796632182523588997nt_int ) ) @ ( cons_P3334398858971670639nt_int @ S_j3 @ Ps3 ) ) ) ) ) ) ).
% path_checker.elims(2)
thf(fact_716_path__checker_Oelims_I3_J,axiom,
! [X: set_Pr958786334691620121nt_int,Xa: list_P5707943133018811711nt_int] :
( ~ ( path_checker @ X @ Xa )
=> ( ( Xa != nil_Pr2300489316682597567nt_int )
=> ( ! [S_i3: product_prod_int_int] :
( ( Xa
= ( cons_P3334398858971670639nt_int @ S_i3 @ nil_Pr2300489316682597567nt_int ) )
=> ( ( insert5033312907999012233nt_int @ S_i3 @ bot_bo1796632182523588997nt_int )
= X ) )
=> ~ ! [S_i3: product_prod_int_int,S_j3: product_prod_int_int,Ps3: list_P5707943133018811711nt_int] :
( ( Xa
= ( cons_P3334398858971670639nt_int @ S_i3 @ ( cons_P3334398858971670639nt_int @ S_j3 @ Ps3 ) ) )
=> ( ( member5262025264175285858nt_int @ S_i3 @ X )
& ( step_checker @ S_i3 @ S_j3 )
& ( path_checker @ ( minus_1052850069191792384nt_int @ X @ ( insert5033312907999012233nt_int @ S_i3 @ bot_bo1796632182523588997nt_int ) ) @ ( cons_P3334398858971670639nt_int @ S_j3 @ Ps3 ) ) ) ) ) ) ) ).
% path_checker.elims(3)
thf(fact_717_path__checker_Osimps_I3_J,axiom,
! [B: set_Pr958786334691620121nt_int,S_i: product_prod_int_int,S_j: product_prod_int_int,Ps: list_P5707943133018811711nt_int] :
( ( path_checker @ B @ ( cons_P3334398858971670639nt_int @ S_i @ ( cons_P3334398858971670639nt_int @ S_j @ Ps ) ) )
= ( ( member5262025264175285858nt_int @ S_i @ B )
& ( step_checker @ S_i @ S_j )
& ( path_checker @ ( minus_1052850069191792384nt_int @ B @ ( insert5033312907999012233nt_int @ S_i @ bot_bo1796632182523588997nt_int ) ) @ ( cons_P3334398858971670639nt_int @ S_j @ Ps ) ) ) ) ).
% path_checker.simps(3)
thf(fact_718_subseqs_Osimps_I1_J,axiom,
( ( subseq1357044202310323342nt_int @ nil_Pr2300489316682597567nt_int )
= ( cons_l7309679040211256053nt_int @ nil_Pr2300489316682597567nt_int @ nil_li8670148097206105925nt_int ) ) ).
% subseqs.simps(1)
thf(fact_719_distinct__adj__append__iff,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( distin7999467515711547031nt_int @ ( append7030698103840186580nt_int @ Xs @ Ys ) )
= ( ( distin7999467515711547031nt_int @ Xs )
& ( distin7999467515711547031nt_int @ Ys )
& ( ( Xs = nil_Pr2300489316682597567nt_int )
| ( Ys = nil_Pr2300489316682597567nt_int )
| ( ( last_P3305686521732843992nt_int @ Xs )
!= ( hd_Pro282112905867057956nt_int @ Ys ) ) ) ) ) ).
% distinct_adj_append_iff
thf(fact_720_distinct__adj__Cons__Cons,axiom,
! [X: product_prod_int_int,Y: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( distin7999467515711547031nt_int @ ( cons_P3334398858971670639nt_int @ X @ ( cons_P3334398858971670639nt_int @ Y @ Xs ) ) )
= ( ( X != Y )
& ( distin7999467515711547031nt_int @ ( cons_P3334398858971670639nt_int @ Y @ Xs ) ) ) ) ).
% distinct_adj_Cons_Cons
thf(fact_721_distinct__adj__ConsD,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( distin7999467515711547031nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) )
=> ( distin7999467515711547031nt_int @ Xs ) ) ).
% distinct_adj_ConsD
thf(fact_722_distinct__adj__Nil,axiom,
distin7999467515711547031nt_int @ nil_Pr2300489316682597567nt_int ).
% distinct_adj_Nil
thf(fact_723_distinct__adj__appendD1,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( distin7999467515711547031nt_int @ ( append7030698103840186580nt_int @ Xs @ Ys ) )
=> ( distin7999467515711547031nt_int @ Xs ) ) ).
% distinct_adj_appendD1
thf(fact_724_distinct__adj__appendD2,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( distin7999467515711547031nt_int @ ( append7030698103840186580nt_int @ Xs @ Ys ) )
=> ( distin7999467515711547031nt_int @ Ys ) ) ).
% distinct_adj_appendD2
thf(fact_725_step__checker__correct,axiom,
step_checker = valid_step ).
% step_checker_correct
thf(fact_726_distinct__adj__singleton,axiom,
! [X: product_prod_int_int] : ( distin7999467515711547031nt_int @ ( cons_P3334398858971670639nt_int @ X @ nil_Pr2300489316682597567nt_int ) ) ).
% distinct_adj_singleton
thf(fact_727_distinct__adj__Cons,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( distin7999467515711547031nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) )
= ( ( Xs = nil_Pr2300489316682597567nt_int )
| ( ( X
!= ( hd_Pro282112905867057956nt_int @ Xs ) )
& ( distin7999467515711547031nt_int @ Xs ) ) ) ) ).
% distinct_adj_Cons
thf(fact_728_circuit__checker_Oelims_I3_J,axiom,
! [X: set_Pr958786334691620121nt_int,Xa: list_P5707943133018811711nt_int] :
( ~ ( circuit_checker @ X @ Xa )
=> ~ ( ( path_checker @ X @ Xa )
& ( step_checker @ ( last_P3305686521732843992nt_int @ Xa ) @ ( hd_Pro282112905867057956nt_int @ Xa ) ) ) ) ).
% circuit_checker.elims(3)
thf(fact_729_circuit__checker_Oelims_I2_J,axiom,
! [X: set_Pr958786334691620121nt_int,Xa: list_P5707943133018811711nt_int] :
( ( circuit_checker @ X @ Xa )
=> ( ( path_checker @ X @ Xa )
& ( step_checker @ ( last_P3305686521732843992nt_int @ Xa ) @ ( hd_Pro282112905867057956nt_int @ Xa ) ) ) ) ).
% circuit_checker.elims(2)
thf(fact_730_circuit__checker_Oelims_I1_J,axiom,
! [X: set_Pr958786334691620121nt_int,Xa: list_P5707943133018811711nt_int,Y: $o] :
( ( ( circuit_checker @ X @ Xa )
= Y )
=> ( Y
= ( ( path_checker @ X @ Xa )
& ( step_checker @ ( last_P3305686521732843992nt_int @ Xa ) @ ( hd_Pro282112905867057956nt_int @ Xa ) ) ) ) ) ).
% circuit_checker.elims(1)
thf(fact_731_circuit__checker_Osimps,axiom,
( circuit_checker
= ( ^ [B2: set_Pr958786334691620121nt_int,Ps2: list_P5707943133018811711nt_int] :
( ( path_checker @ B2 @ Ps2 )
& ( step_checker @ ( last_P3305686521732843992nt_int @ Ps2 ) @ ( hd_Pro282112905867057956nt_int @ Ps2 ) ) ) ) ) ).
% circuit_checker.simps
thf(fact_732_maps__simps_I1_J,axiom,
! [F: product_prod_int_int > list_P5707943133018811711nt_int,X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( maps_P133354487822995585nt_int @ F @ ( cons_P3334398858971670639nt_int @ X @ Xs ) )
= ( append7030698103840186580nt_int @ ( F @ X ) @ ( maps_P133354487822995585nt_int @ F @ Xs ) ) ) ).
% maps_simps(1)
thf(fact_733_insert__Nil,axiom,
! [X: product_prod_int_int] :
( ( insert5765537519290168021nt_int @ X @ nil_Pr2300489316682597567nt_int )
= ( cons_P3334398858971670639nt_int @ X @ nil_Pr2300489316682597567nt_int ) ) ).
% insert_Nil
thf(fact_734_maps__simps_I2_J,axiom,
! [F: product_prod_int_int > list_P5707943133018811711nt_int] :
( ( maps_P133354487822995585nt_int @ F @ nil_Pr2300489316682597567nt_int )
= nil_Pr2300489316682597567nt_int ) ).
% maps_simps(2)
thf(fact_735_circuit__checker__correct,axiom,
circuit_checker = knights_circuit ).
% circuit_checker_correct
thf(fact_736_Set_Ois__empty__def,axiom,
( is_emp7707449487952173963nt_int
= ( ^ [A4: set_Pr958786334691620121nt_int] : ( A4 = bot_bo1796632182523588997nt_int ) ) ) ).
% Set.is_empty_def
thf(fact_737_concat__eq__append__conv,axiom,
! [Xss2: list_l1670014477004246597nt_int,Ys: list_P5707943133018811711nt_int,Zs: list_P5707943133018811711nt_int] :
( ( ( concat4512918505337516154nt_int @ Xss2 )
= ( append7030698103840186580nt_int @ Ys @ Zs ) )
= ( ( ( Xss2 = nil_li8670148097206105925nt_int )
=> ( ( Ys = nil_Pr2300489316682597567nt_int )
& ( Zs = nil_Pr2300489316682597567nt_int ) ) )
& ( ( Xss2 != nil_li8670148097206105925nt_int )
=> ? [Xss1: list_l1670014477004246597nt_int,Xs4: list_P5707943133018811711nt_int,Xs5: list_P5707943133018811711nt_int,Xss22: list_l1670014477004246597nt_int] :
( ( Xss2
= ( append1237393811882493146nt_int @ Xss1 @ ( cons_l7309679040211256053nt_int @ ( append7030698103840186580nt_int @ Xs4 @ Xs5 ) @ Xss22 ) ) )
& ( Ys
= ( append7030698103840186580nt_int @ ( concat4512918505337516154nt_int @ Xss1 ) @ Xs4 ) )
& ( Zs
= ( append7030698103840186580nt_int @ Xs5 @ ( concat4512918505337516154nt_int @ Xss22 ) ) ) ) ) ) ) ).
% concat_eq_append_conv
thf(fact_738_successively__append__iff,axiom,
! [P: product_prod_int_int > product_prod_int_int > $o,Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( succes497254780304326540nt_int @ P @ ( append7030698103840186580nt_int @ Xs @ Ys ) )
= ( ( succes497254780304326540nt_int @ P @ Xs )
& ( succes497254780304326540nt_int @ P @ Ys )
& ( ( Xs = nil_Pr2300489316682597567nt_int )
| ( Ys = nil_Pr2300489316682597567nt_int )
| ( P @ ( last_P3305686521732843992nt_int @ Xs ) @ ( hd_Pro282112905867057956nt_int @ Ys ) ) ) ) ) ).
% successively_append_iff
thf(fact_739_list__ex1__simps_I1_J,axiom,
! [P: product_prod_int_int > $o] :
~ ( list_e5465588451548443778nt_int @ P @ nil_Pr2300489316682597567nt_int ) ).
% list_ex1_simps(1)
thf(fact_740_remdups__adj__append_H,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( ( Xs = nil_Pr2300489316682597567nt_int )
| ( Ys = nil_Pr2300489316682597567nt_int )
| ( ( last_P3305686521732843992nt_int @ Xs )
!= ( hd_Pro282112905867057956nt_int @ Ys ) ) )
=> ( ( remdup6889124116291670005nt_int @ ( append7030698103840186580nt_int @ Xs @ Ys ) )
= ( append7030698103840186580nt_int @ ( remdup6889124116291670005nt_int @ Xs ) @ ( remdup6889124116291670005nt_int @ Ys ) ) ) ) ).
% remdups_adj_append'
thf(fact_741_remdups__adj__Nil__iff,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( ( remdup6889124116291670005nt_int @ Xs )
= nil_Pr2300489316682597567nt_int )
= ( Xs = nil_Pr2300489316682597567nt_int ) ) ).
% remdups_adj_Nil_iff
thf(fact_742_hd__remdups__adj,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( hd_Pro282112905867057956nt_int @ ( remdup6889124116291670005nt_int @ Xs ) )
= ( hd_Pro282112905867057956nt_int @ Xs ) ) ).
% hd_remdups_adj
thf(fact_743_last__remdups__adj,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( last_P3305686521732843992nt_int @ ( remdup6889124116291670005nt_int @ Xs ) )
= ( last_P3305686521732843992nt_int @ Xs ) ) ).
% last_remdups_adj
thf(fact_744_concat__append,axiom,
! [Xs: list_l1670014477004246597nt_int,Ys: list_l1670014477004246597nt_int] :
( ( concat4512918505337516154nt_int @ ( append1237393811882493146nt_int @ Xs @ Ys ) )
= ( append7030698103840186580nt_int @ ( concat4512918505337516154nt_int @ Xs ) @ ( concat4512918505337516154nt_int @ Ys ) ) ) ).
% concat_append
thf(fact_745_remdups__adj_Osimps_I3_J,axiom,
! [X: product_prod_int_int,Y: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( ( X = Y )
=> ( ( remdup6889124116291670005nt_int @ ( cons_P3334398858971670639nt_int @ X @ ( cons_P3334398858971670639nt_int @ Y @ Xs ) ) )
= ( remdup6889124116291670005nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) ) ) )
& ( ( X != Y )
=> ( ( remdup6889124116291670005nt_int @ ( cons_P3334398858971670639nt_int @ X @ ( cons_P3334398858971670639nt_int @ Y @ Xs ) ) )
= ( cons_P3334398858971670639nt_int @ X @ ( remdup6889124116291670005nt_int @ ( cons_P3334398858971670639nt_int @ Y @ Xs ) ) ) ) ) ) ).
% remdups_adj.simps(3)
thf(fact_746_remdups__adj_Osimps_I1_J,axiom,
( ( remdup6889124116291670005nt_int @ nil_Pr2300489316682597567nt_int )
= nil_Pr2300489316682597567nt_int ) ).
% remdups_adj.simps(1)
thf(fact_747_successively_Oelims_I3_J,axiom,
! [X: product_prod_int_int > product_prod_int_int > $o,Xa: list_P5707943133018811711nt_int] :
( ~ ( succes497254780304326540nt_int @ X @ Xa )
=> ~ ! [X3: product_prod_int_int,Y2: product_prod_int_int,Xs2: list_P5707943133018811711nt_int] :
( ( Xa
= ( cons_P3334398858971670639nt_int @ X3 @ ( cons_P3334398858971670639nt_int @ Y2 @ Xs2 ) ) )
=> ( ( X @ X3 @ Y2 )
& ( succes497254780304326540nt_int @ X @ ( cons_P3334398858971670639nt_int @ Y2 @ Xs2 ) ) ) ) ) ).
% successively.elims(3)
thf(fact_748_successively_Osimps_I3_J,axiom,
! [P: product_prod_int_int > product_prod_int_int > $o,X: product_prod_int_int,Y: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( succes497254780304326540nt_int @ P @ ( cons_P3334398858971670639nt_int @ X @ ( cons_P3334398858971670639nt_int @ Y @ Xs ) ) )
= ( ( P @ X @ Y )
& ( succes497254780304326540nt_int @ P @ ( cons_P3334398858971670639nt_int @ Y @ Xs ) ) ) ) ).
% successively.simps(3)
thf(fact_749_successively_Osimps_I1_J,axiom,
! [P: product_prod_int_int > product_prod_int_int > $o] : ( succes497254780304326540nt_int @ P @ nil_Pr2300489316682597567nt_int ) ).
% successively.simps(1)
thf(fact_750_remdups__adj_Osimps_I2_J,axiom,
! [X: product_prod_int_int] :
( ( remdup6889124116291670005nt_int @ ( cons_P3334398858971670639nt_int @ X @ nil_Pr2300489316682597567nt_int ) )
= ( cons_P3334398858971670639nt_int @ X @ nil_Pr2300489316682597567nt_int ) ) ).
% remdups_adj.simps(2)
thf(fact_751_remdups__adj_Oelims,axiom,
! [X: list_P5707943133018811711nt_int,Y: list_P5707943133018811711nt_int] :
( ( ( remdup6889124116291670005nt_int @ X )
= Y )
=> ( ( ( X = nil_Pr2300489316682597567nt_int )
=> ( Y != nil_Pr2300489316682597567nt_int ) )
=> ( ! [X3: product_prod_int_int] :
( ( X
= ( cons_P3334398858971670639nt_int @ X3 @ nil_Pr2300489316682597567nt_int ) )
=> ( Y
!= ( cons_P3334398858971670639nt_int @ X3 @ nil_Pr2300489316682597567nt_int ) ) )
=> ~ ! [X3: product_prod_int_int,Y2: product_prod_int_int,Xs2: list_P5707943133018811711nt_int] :
( ( X
= ( cons_P3334398858971670639nt_int @ X3 @ ( cons_P3334398858971670639nt_int @ Y2 @ Xs2 ) ) )
=> ~ ( ( ( X3 = Y2 )
=> ( Y
= ( remdup6889124116291670005nt_int @ ( cons_P3334398858971670639nt_int @ X3 @ Xs2 ) ) ) )
& ( ( X3 != Y2 )
=> ( Y
= ( cons_P3334398858971670639nt_int @ X3 @ ( remdup6889124116291670005nt_int @ ( cons_P3334398858971670639nt_int @ Y2 @ Xs2 ) ) ) ) ) ) ) ) ) ) ).
% remdups_adj.elims
thf(fact_752_successively_Oelims_I2_J,axiom,
! [X: product_prod_int_int > product_prod_int_int > $o,Xa: list_P5707943133018811711nt_int] :
( ( succes497254780304326540nt_int @ X @ Xa )
=> ( ( Xa != nil_Pr2300489316682597567nt_int )
=> ( ! [X3: product_prod_int_int] :
( Xa
!= ( cons_P3334398858971670639nt_int @ X3 @ nil_Pr2300489316682597567nt_int ) )
=> ~ ! [X3: product_prod_int_int,Y2: product_prod_int_int,Xs2: list_P5707943133018811711nt_int] :
( ( Xa
= ( cons_P3334398858971670639nt_int @ X3 @ ( cons_P3334398858971670639nt_int @ Y2 @ Xs2 ) ) )
=> ~ ( ( X @ X3 @ Y2 )
& ( succes497254780304326540nt_int @ X @ ( cons_P3334398858971670639nt_int @ Y2 @ Xs2 ) ) ) ) ) ) ) ).
% successively.elims(2)
thf(fact_753_successively_Oelims_I1_J,axiom,
! [X: product_prod_int_int > product_prod_int_int > $o,Xa: list_P5707943133018811711nt_int,Y: $o] :
( ( ( succes497254780304326540nt_int @ X @ Xa )
= Y )
=> ( ( ( Xa = nil_Pr2300489316682597567nt_int )
=> ~ Y )
=> ( ( ? [X3: product_prod_int_int] :
( Xa
= ( cons_P3334398858971670639nt_int @ X3 @ nil_Pr2300489316682597567nt_int ) )
=> ~ Y )
=> ~ ! [X3: product_prod_int_int,Y2: product_prod_int_int,Xs2: list_P5707943133018811711nt_int] :
( ( Xa
= ( cons_P3334398858971670639nt_int @ X3 @ ( cons_P3334398858971670639nt_int @ Y2 @ Xs2 ) ) )
=> ( Y
= ( ~ ( ( X @ X3 @ Y2 )
& ( succes497254780304326540nt_int @ X @ ( cons_P3334398858971670639nt_int @ Y2 @ Xs2 ) ) ) ) ) ) ) ) ) ).
% successively.elims(1)
thf(fact_754_successively_Osimps_I2_J,axiom,
! [P: product_prod_int_int > product_prod_int_int > $o,X: product_prod_int_int] : ( succes497254780304326540nt_int @ P @ ( cons_P3334398858971670639nt_int @ X @ nil_Pr2300489316682597567nt_int ) ) ).
% successively.simps(2)
thf(fact_755_concat_Osimps_I1_J,axiom,
( ( concat4512918505337516154nt_int @ nil_li8670148097206105925nt_int )
= nil_Pr2300489316682597567nt_int ) ).
% concat.simps(1)
thf(fact_756_concat_Osimps_I2_J,axiom,
! [X: list_P5707943133018811711nt_int,Xs: list_l1670014477004246597nt_int] :
( ( concat4512918505337516154nt_int @ ( cons_l7309679040211256053nt_int @ X @ Xs ) )
= ( append7030698103840186580nt_int @ X @ ( concat4512918505337516154nt_int @ Xs ) ) ) ).
% concat.simps(2)
thf(fact_757_remdups__adj__append__two,axiom,
! [Xs: list_P5707943133018811711nt_int,X: product_prod_int_int,Y: product_prod_int_int] :
( ( remdup6889124116291670005nt_int @ ( append7030698103840186580nt_int @ Xs @ ( cons_P3334398858971670639nt_int @ X @ ( cons_P3334398858971670639nt_int @ Y @ nil_Pr2300489316682597567nt_int ) ) ) )
= ( append7030698103840186580nt_int @ ( remdup6889124116291670005nt_int @ ( append7030698103840186580nt_int @ Xs @ ( cons_P3334398858971670639nt_int @ X @ nil_Pr2300489316682597567nt_int ) ) ) @ ( if_lis8883190402267401221nt_int @ ( X = Y ) @ nil_Pr2300489316682597567nt_int @ ( cons_P3334398858971670639nt_int @ Y @ nil_Pr2300489316682597567nt_int ) ) ) ) ).
% remdups_adj_append_two
thf(fact_758_successively__Cons,axiom,
! [P: product_prod_int_int > product_prod_int_int > $o,X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( succes497254780304326540nt_int @ P @ ( cons_P3334398858971670639nt_int @ X @ Xs ) )
= ( ( Xs = nil_Pr2300489316682597567nt_int )
| ( ( P @ X @ ( hd_Pro282112905867057956nt_int @ Xs ) )
& ( succes497254780304326540nt_int @ P @ Xs ) ) ) ) ).
% successively_Cons
thf(fact_759_hd__concat,axiom,
! [Xs: list_l1670014477004246597nt_int] :
( ( Xs != nil_li8670148097206105925nt_int )
=> ( ( ( hd_lis8550591025403828010nt_int @ Xs )
!= nil_Pr2300489316682597567nt_int )
=> ( ( hd_Pro282112905867057956nt_int @ ( concat4512918505337516154nt_int @ Xs ) )
= ( hd_Pro282112905867057956nt_int @ ( hd_lis8550591025403828010nt_int @ Xs ) ) ) ) ) ).
% hd_concat
thf(fact_760_concat__eq__appendD,axiom,
! [Xss2: list_l1670014477004246597nt_int,Ys: list_P5707943133018811711nt_int,Zs: list_P5707943133018811711nt_int] :
( ( ( concat4512918505337516154nt_int @ Xss2 )
= ( append7030698103840186580nt_int @ Ys @ Zs ) )
=> ( ( Xss2 != nil_li8670148097206105925nt_int )
=> ? [Xss12: list_l1670014477004246597nt_int,Xs2: list_P5707943133018811711nt_int,Xs3: list_P5707943133018811711nt_int,Xss23: list_l1670014477004246597nt_int] :
( ( Xss2
= ( append1237393811882493146nt_int @ Xss12 @ ( cons_l7309679040211256053nt_int @ ( append7030698103840186580nt_int @ Xs2 @ Xs3 ) @ Xss23 ) ) )
& ( Ys
= ( append7030698103840186580nt_int @ ( concat4512918505337516154nt_int @ Xss12 ) @ Xs2 ) )
& ( Zs
= ( append7030698103840186580nt_int @ Xs3 @ ( concat4512918505337516154nt_int @ Xss23 ) ) ) ) ) ) ).
% concat_eq_appendD
thf(fact_761_remdups__adj__append,axiom,
! [Xs_1: list_P5707943133018811711nt_int,X: product_prod_int_int,Xs_2: list_P5707943133018811711nt_int] :
( ( remdup6889124116291670005nt_int @ ( append7030698103840186580nt_int @ Xs_1 @ ( cons_P3334398858971670639nt_int @ X @ Xs_2 ) ) )
= ( append7030698103840186580nt_int @ ( remdup6889124116291670005nt_int @ ( append7030698103840186580nt_int @ Xs_1 @ ( cons_P3334398858971670639nt_int @ X @ nil_Pr2300489316682597567nt_int ) ) ) @ ( tl_Pro1049539609081552168nt_int @ ( remdup6889124116291670005nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs_2 ) ) ) ) ) ).
% remdups_adj_append
thf(fact_762_rotate1_Osimps_I2_J,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( rotate9137591727117064716nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) )
= ( append7030698103840186580nt_int @ Xs @ ( cons_P3334398858971670639nt_int @ X @ nil_Pr2300489316682597567nt_int ) ) ) ).
% rotate1.simps(2)
thf(fact_763_pairwise__alt,axiom,
( pairwi3178678004212613796nt_int
= ( ^ [R: product_prod_int_int > product_prod_int_int > $o,S2: set_Pr958786334691620121nt_int] :
! [X2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X2 @ S2 )
=> ! [Y3: product_prod_int_int] :
( ( member5262025264175285858nt_int @ Y3 @ ( minus_1052850069191792384nt_int @ S2 @ ( insert5033312907999012233nt_int @ X2 @ bot_bo1796632182523588997nt_int ) ) )
=> ( R @ X2 @ Y3 ) ) ) ) ) ).
% pairwise_alt
thf(fact_764_product_Osimps_I1_J,axiom,
! [Uu: list_int] :
( ( product_int_int @ nil_int @ Uu )
= nil_Pr2300489316682597567nt_int ) ).
% product.simps(1)
thf(fact_765_concat__conv__foldr,axiom,
( concat4512918505337516154nt_int
= ( ^ [Xss3: list_l1670014477004246597nt_int] : ( foldr_8633130848730196071nt_int @ append7030698103840186580nt_int @ Xss3 @ nil_Pr2300489316682597567nt_int ) ) ) ).
% concat_conv_foldr
thf(fact_766_list_Ocollapse,axiom,
! [List: list_P5707943133018811711nt_int] :
( ( List != nil_Pr2300489316682597567nt_int )
=> ( ( cons_P3334398858971670639nt_int @ ( hd_Pro282112905867057956nt_int @ List ) @ ( tl_Pro1049539609081552168nt_int @ List ) )
= List ) ) ).
% list.collapse
thf(fact_767_rotate1__is__Nil__conv,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( ( rotate9137591727117064716nt_int @ Xs )
= nil_Pr2300489316682597567nt_int )
= ( Xs = nil_Pr2300489316682597567nt_int ) ) ).
% rotate1_is_Nil_conv
thf(fact_768_tl__append2,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( Xs != nil_Pr2300489316682597567nt_int )
=> ( ( tl_Pro1049539609081552168nt_int @ ( append7030698103840186580nt_int @ Xs @ Ys ) )
= ( append7030698103840186580nt_int @ ( tl_Pro1049539609081552168nt_int @ Xs ) @ Ys ) ) ) ).
% tl_append2
thf(fact_769_remdups__adj__Cons__alt,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( cons_P3334398858971670639nt_int @ X @ ( tl_Pro1049539609081552168nt_int @ ( remdup6889124116291670005nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) ) ) )
= ( remdup6889124116291670005nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) ) ) ).
% remdups_adj_Cons_alt
thf(fact_770_hd__Cons__tl,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( Xs != nil_Pr2300489316682597567nt_int )
=> ( ( cons_P3334398858971670639nt_int @ ( hd_Pro282112905867057956nt_int @ Xs ) @ ( tl_Pro1049539609081552168nt_int @ Xs ) )
= Xs ) ) ).
% hd_Cons_tl
thf(fact_771_pairwiseI,axiom,
! [S: set_Pr958786334691620121nt_int,R2: product_prod_int_int > product_prod_int_int > $o] :
( ! [X3: product_prod_int_int,Y2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X3 @ S )
=> ( ( member5262025264175285858nt_int @ Y2 @ S )
=> ( ( X3 != Y2 )
=> ( R2 @ X3 @ Y2 ) ) ) )
=> ( pairwi3178678004212613796nt_int @ R2 @ S ) ) ).
% pairwiseI
thf(fact_772_pairwiseD,axiom,
! [R2: product_prod_int_int > product_prod_int_int > $o,S: set_Pr958786334691620121nt_int,X: product_prod_int_int,Y: product_prod_int_int] :
( ( pairwi3178678004212613796nt_int @ R2 @ S )
=> ( ( member5262025264175285858nt_int @ X @ S )
=> ( ( member5262025264175285858nt_int @ Y @ S )
=> ( ( X != Y )
=> ( R2 @ X @ Y ) ) ) ) ) ).
% pairwiseD
thf(fact_773_list_Osel_I3_J,axiom,
! [X21: product_prod_int_int,X22: list_P5707943133018811711nt_int] :
( ( tl_Pro1049539609081552168nt_int @ ( cons_P3334398858971670639nt_int @ X21 @ X22 ) )
= X22 ) ).
% list.sel(3)
thf(fact_774_list_Osel_I2_J,axiom,
( ( tl_Pro1049539609081552168nt_int @ nil_Pr2300489316682597567nt_int )
= nil_Pr2300489316682597567nt_int ) ).
% list.sel(2)
thf(fact_775_pairwise__empty,axiom,
! [P: product_prod_int_int > product_prod_int_int > $o] : ( pairwi3178678004212613796nt_int @ P @ bot_bo1796632182523588997nt_int ) ).
% pairwise_empty
thf(fact_776_pairwise__insert,axiom,
! [R3: product_prod_int_int > product_prod_int_int > $o,X: product_prod_int_int,S3: set_Pr958786334691620121nt_int] :
( ( pairwi3178678004212613796nt_int @ R3 @ ( insert5033312907999012233nt_int @ X @ S3 ) )
= ( ! [Y3: product_prod_int_int] :
( ( ( member5262025264175285858nt_int @ Y3 @ S3 )
& ( Y3 != X ) )
=> ( ( R3 @ X @ Y3 )
& ( R3 @ Y3 @ X ) ) )
& ( pairwi3178678004212613796nt_int @ R3 @ S3 ) ) ) ).
% pairwise_insert
thf(fact_777_rotate1_Osimps_I1_J,axiom,
( ( rotate9137591727117064716nt_int @ nil_Pr2300489316682597567nt_int )
= nil_Pr2300489316682597567nt_int ) ).
% rotate1.simps(1)
thf(fact_778_tl__Nil,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( ( tl_Pro1049539609081552168nt_int @ Xs )
= nil_Pr2300489316682597567nt_int )
= ( ( Xs = nil_Pr2300489316682597567nt_int )
| ? [X2: product_prod_int_int] :
( Xs
= ( cons_P3334398858971670639nt_int @ X2 @ nil_Pr2300489316682597567nt_int ) ) ) ) ).
% tl_Nil
thf(fact_779_Nil__tl,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( nil_Pr2300489316682597567nt_int
= ( tl_Pro1049539609081552168nt_int @ Xs ) )
= ( ( Xs = nil_Pr2300489316682597567nt_int )
| ? [X2: product_prod_int_int] :
( Xs
= ( cons_P3334398858971670639nt_int @ X2 @ nil_Pr2300489316682597567nt_int ) ) ) ) ).
% Nil_tl
thf(fact_780_tl__append__if,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( ( Xs = nil_Pr2300489316682597567nt_int )
=> ( ( tl_Pro1049539609081552168nt_int @ ( append7030698103840186580nt_int @ Xs @ Ys ) )
= ( tl_Pro1049539609081552168nt_int @ Ys ) ) )
& ( ( Xs != nil_Pr2300489316682597567nt_int )
=> ( ( tl_Pro1049539609081552168nt_int @ ( append7030698103840186580nt_int @ Xs @ Ys ) )
= ( append7030698103840186580nt_int @ ( tl_Pro1049539609081552168nt_int @ Xs ) @ Ys ) ) ) ) ).
% tl_append_if
thf(fact_781_list_Oexpand,axiom,
! [List: list_P5707943133018811711nt_int,List2: list_P5707943133018811711nt_int] :
( ( ( List = nil_Pr2300489316682597567nt_int )
= ( List2 = nil_Pr2300489316682597567nt_int ) )
=> ( ( ( List != nil_Pr2300489316682597567nt_int )
=> ( ( List2 != nil_Pr2300489316682597567nt_int )
=> ( ( ( hd_Pro282112905867057956nt_int @ List )
= ( hd_Pro282112905867057956nt_int @ List2 ) )
& ( ( tl_Pro1049539609081552168nt_int @ List )
= ( tl_Pro1049539609081552168nt_int @ List2 ) ) ) ) )
=> ( List = List2 ) ) ) ).
% list.expand
thf(fact_782_last__tl,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( ( Xs = nil_Pr2300489316682597567nt_int )
| ( ( tl_Pro1049539609081552168nt_int @ Xs )
!= nil_Pr2300489316682597567nt_int ) )
=> ( ( last_P3305686521732843992nt_int @ ( tl_Pro1049539609081552168nt_int @ Xs ) )
= ( last_P3305686521732843992nt_int @ Xs ) ) ) ).
% last_tl
thf(fact_783_rotate1__hd__tl,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( Xs != nil_Pr2300489316682597567nt_int )
=> ( ( rotate9137591727117064716nt_int @ Xs )
= ( append7030698103840186580nt_int @ ( tl_Pro1049539609081552168nt_int @ Xs ) @ ( cons_P3334398858971670639nt_int @ ( hd_Pro282112905867057956nt_int @ Xs ) @ nil_Pr2300489316682597567nt_int ) ) ) ) ).
% rotate1_hd_tl
thf(fact_784_pairwise__singleton,axiom,
! [P: product_prod_int_int > product_prod_int_int > $o,A3: product_prod_int_int] : ( pairwi3178678004212613796nt_int @ P @ ( insert5033312907999012233nt_int @ A3 @ bot_bo1796632182523588997nt_int ) ) ).
% pairwise_singleton
thf(fact_785_list_Oexhaust__sel,axiom,
! [List: list_P5707943133018811711nt_int] :
( ( List != nil_Pr2300489316682597567nt_int )
=> ( List
= ( cons_P3334398858971670639nt_int @ ( hd_Pro282112905867057956nt_int @ List ) @ ( tl_Pro1049539609081552168nt_int @ List ) ) ) ) ).
% list.exhaust_sel
thf(fact_786_Cons__in__shuffles__iff,axiom,
! [Z: product_prod_int_int,Zs: list_P5707943133018811711nt_int,Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ ( cons_P3334398858971670639nt_int @ Z @ Zs ) @ ( shuffl1909956583008895700nt_int @ Xs @ Ys ) )
= ( ( ( Xs != nil_Pr2300489316682597567nt_int )
& ( ( hd_Pro282112905867057956nt_int @ Xs )
= Z )
& ( member2764346250752101224nt_int @ Zs @ ( shuffl1909956583008895700nt_int @ ( tl_Pro1049539609081552168nt_int @ Xs ) @ Ys ) ) )
| ( ( Ys != nil_Pr2300489316682597567nt_int )
& ( ( hd_Pro282112905867057956nt_int @ Ys )
= Z )
& ( member2764346250752101224nt_int @ Zs @ ( shuffl1909956583008895700nt_int @ Xs @ ( tl_Pro1049539609081552168nt_int @ Ys ) ) ) ) ) ) ).
% Cons_in_shuffles_iff
thf(fact_787_inter__coset__fold,axiom,
! [A3: set_Pr958786334691620121nt_int,Xs: list_P5707943133018811711nt_int] :
( ( inf_in2269163501485487111nt_int @ A3 @ ( coset_3631019413092825772nt_int @ Xs ) )
= ( fold_P6555583138535618987nt_int @ remove3288057706648593438nt_int @ Xs @ A3 ) ) ).
% inter_coset_fold
thf(fact_788_Id__on__empty,axiom,
( ( id_on_int @ bot_bot_set_int )
= bot_bo1796632182523588997nt_int ) ).
% Id_on_empty
thf(fact_789_Id__on__empty,axiom,
( ( id_on_8598933527810153430nt_int @ bot_bo1796632182523588997nt_int )
= bot_bo8417956007504411571nt_int ) ).
% Id_on_empty
thf(fact_790_Nil__in__shuffles,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ nil_Pr2300489316682597567nt_int @ ( shuffl1909956583008895700nt_int @ Xs @ Ys ) )
= ( ( Xs = nil_Pr2300489316682597567nt_int )
& ( Ys = nil_Pr2300489316682597567nt_int ) ) ) ).
% Nil_in_shuffles
thf(fact_791_Cons__in__shuffles__leftI,axiom,
! [Zs: list_P5707943133018811711nt_int,Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int,Z: product_prod_int_int] :
( ( member2764346250752101224nt_int @ Zs @ ( shuffl1909956583008895700nt_int @ Xs @ Ys ) )
=> ( member2764346250752101224nt_int @ ( cons_P3334398858971670639nt_int @ Z @ Zs ) @ ( shuffl1909956583008895700nt_int @ ( cons_P3334398858971670639nt_int @ Z @ Xs ) @ Ys ) ) ) ).
% Cons_in_shuffles_leftI
thf(fact_792_Cons__in__shuffles__rightI,axiom,
! [Zs: list_P5707943133018811711nt_int,Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int,Z: product_prod_int_int] :
( ( member2764346250752101224nt_int @ Zs @ ( shuffl1909956583008895700nt_int @ Xs @ Ys ) )
=> ( member2764346250752101224nt_int @ ( cons_P3334398858971670639nt_int @ Z @ Zs ) @ ( shuffl1909956583008895700nt_int @ Xs @ ( cons_P3334398858971670639nt_int @ Z @ Ys ) ) ) ) ).
% Cons_in_shuffles_rightI
thf(fact_793_shuffles_Osimps_I2_J,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( shuffl1909956583008895700nt_int @ Xs @ nil_Pr2300489316682597567nt_int )
= ( insert393344137582914319nt_int @ Xs @ bot_bo3809061186584590219nt_int ) ) ).
% shuffles.simps(2)
thf(fact_794_shuffles_Osimps_I1_J,axiom,
! [Ys: list_P5707943133018811711nt_int] :
( ( shuffl1909956583008895700nt_int @ nil_Pr2300489316682597567nt_int @ Ys )
= ( insert393344137582914319nt_int @ Ys @ bot_bo3809061186584590219nt_int ) ) ).
% shuffles.simps(1)
thf(fact_795_Nil__in__shufflesI,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( Xs = nil_Pr2300489316682597567nt_int )
=> ( ( Ys = nil_Pr2300489316682597567nt_int )
=> ( member2764346250752101224nt_int @ nil_Pr2300489316682597567nt_int @ ( shuffl1909956583008895700nt_int @ Xs @ Ys ) ) ) ) ).
% Nil_in_shufflesI
thf(fact_796_shufflesE,axiom,
! [Zs: list_P5707943133018811711nt_int,Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ Zs @ ( shuffl1909956583008895700nt_int @ Xs @ Ys ) )
=> ( ( ( Zs = Xs )
=> ( Ys != nil_Pr2300489316682597567nt_int ) )
=> ( ( ( Zs = Ys )
=> ( Xs != nil_Pr2300489316682597567nt_int ) )
=> ( ! [X3: product_prod_int_int,Xs3: list_P5707943133018811711nt_int] :
( ( Xs
= ( cons_P3334398858971670639nt_int @ X3 @ Xs3 ) )
=> ! [Z2: product_prod_int_int,Zs2: list_P5707943133018811711nt_int] :
( ( Zs
= ( cons_P3334398858971670639nt_int @ Z2 @ Zs2 ) )
=> ( ( X3 = Z2 )
=> ~ ( member2764346250752101224nt_int @ Zs2 @ ( shuffl1909956583008895700nt_int @ Xs3 @ Ys ) ) ) ) )
=> ~ ! [Y2: product_prod_int_int,Ys5: list_P5707943133018811711nt_int] :
( ( Ys
= ( cons_P3334398858971670639nt_int @ Y2 @ Ys5 ) )
=> ! [Z2: product_prod_int_int,Zs2: list_P5707943133018811711nt_int] :
( ( Zs
= ( cons_P3334398858971670639nt_int @ Z2 @ Zs2 ) )
=> ( ( Y2 = Z2 )
=> ~ ( member2764346250752101224nt_int @ Zs2 @ ( shuffl1909956583008895700nt_int @ Xs @ Ys5 ) ) ) ) ) ) ) ) ) ).
% shufflesE
thf(fact_797_minus__set__fold,axiom,
! [A3: set_Pr958786334691620121nt_int,Xs: list_P5707943133018811711nt_int] :
( ( minus_1052850069191792384nt_int @ A3 @ ( set_Pr2470121279949933262nt_int @ Xs ) )
= ( fold_P6555583138535618987nt_int @ remove3288057706648593438nt_int @ Xs @ A3 ) ) ).
% minus_set_fold
thf(fact_798_union__set__fold,axiom,
! [Xs: list_P5707943133018811711nt_int,A3: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ ( set_Pr2470121279949933262nt_int @ Xs ) @ A3 )
= ( fold_P6555583138535618987nt_int @ insert5033312907999012233nt_int @ Xs @ A3 ) ) ).
% union_set_fold
thf(fact_799_map__tailrec__rev_Oelims,axiom,
! [X: product_prod_int_int > product_prod_int_int,Xa: list_P5707943133018811711nt_int,Xb: list_P5707943133018811711nt_int,Y: list_P5707943133018811711nt_int] :
( ( ( map_ta5484600921387902261nt_int @ X @ Xa @ Xb )
= Y )
=> ( ( ( Xa = nil_Pr2300489316682597567nt_int )
=> ( Y != Xb ) )
=> ~ ! [A6: product_prod_int_int,As: list_P5707943133018811711nt_int] :
( ( Xa
= ( cons_P3334398858971670639nt_int @ A6 @ As ) )
=> ( Y
!= ( map_ta5484600921387902261nt_int @ X @ As @ ( cons_P3334398858971670639nt_int @ ( X @ A6 ) @ Xb ) ) ) ) ) ) ).
% map_tailrec_rev.elims
thf(fact_800_SuccD,axiom,
! [K: product_prod_int_int,Kl: set_li3855193629254082847nt_int,Kl2: list_P5707943133018811711nt_int] :
( ( member5262025264175285858nt_int @ K @ ( bNF_Gr2185362013987207252nt_int @ Kl @ Kl2 ) )
=> ( member2764346250752101224nt_int @ ( append7030698103840186580nt_int @ Kl2 @ ( cons_P3334398858971670639nt_int @ K @ nil_Pr2300489316682597567nt_int ) ) @ Kl ) ) ).
% SuccD
thf(fact_801_concat__eq__Nil__conv,axiom,
! [Xss2: list_l1670014477004246597nt_int] :
( ( ( concat4512918505337516154nt_int @ Xss2 )
= nil_Pr2300489316682597567nt_int )
= ( ! [X2: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ X2 @ ( set_li2659200638379878868nt_int @ Xss2 ) )
=> ( X2 = nil_Pr2300489316682597567nt_int ) ) ) ) ).
% concat_eq_Nil_conv
thf(fact_802_Nil__eq__concat__conv,axiom,
! [Xss2: list_l1670014477004246597nt_int] :
( ( nil_Pr2300489316682597567nt_int
= ( concat4512918505337516154nt_int @ Xss2 ) )
= ( ! [X2: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ X2 @ ( set_li2659200638379878868nt_int @ Xss2 ) )
=> ( X2 = nil_Pr2300489316682597567nt_int ) ) ) ) ).
% Nil_eq_concat_conv
thf(fact_803_remdups__adj__set,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( set_Pr2470121279949933262nt_int @ ( remdup6889124116291670005nt_int @ Xs ) )
= ( set_Pr2470121279949933262nt_int @ Xs ) ) ).
% remdups_adj_set
thf(fact_804_set__rotate1,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( set_Pr2470121279949933262nt_int @ ( rotate9137591727117064716nt_int @ Xs ) )
= ( set_Pr2470121279949933262nt_int @ Xs ) ) ).
% set_rotate1
thf(fact_805_in__set__insert,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ( ( insert5765537519290168021nt_int @ X @ Xs )
= Xs ) ) ).
% in_set_insert
thf(fact_806_set__empty2,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( bot_bo1796632182523588997nt_int
= ( set_Pr2470121279949933262nt_int @ Xs ) )
= ( Xs = nil_Pr2300489316682597567nt_int ) ) ).
% set_empty2
thf(fact_807_set__empty,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( ( set_Pr2470121279949933262nt_int @ Xs )
= bot_bo1796632182523588997nt_int )
= ( Xs = nil_Pr2300489316682597567nt_int ) ) ).
% set_empty
thf(fact_808_list_Osimps_I15_J,axiom,
! [X21: product_prod_int_int,X22: list_P5707943133018811711nt_int] :
( ( set_Pr2470121279949933262nt_int @ ( cons_P3334398858971670639nt_int @ X21 @ X22 ) )
= ( insert5033312907999012233nt_int @ X21 @ ( set_Pr2470121279949933262nt_int @ X22 ) ) ) ).
% list.simps(15)
thf(fact_809_set__append,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( set_Pr2470121279949933262nt_int @ ( append7030698103840186580nt_int @ Xs @ Ys ) )
= ( sup_su6024340866399070445nt_int @ ( set_Pr2470121279949933262nt_int @ Xs ) @ ( set_Pr2470121279949933262nt_int @ Ys ) ) ) ).
% set_append
thf(fact_810_not__in__set__insert,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ~ ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ( ( insert5765537519290168021nt_int @ X @ Xs )
= ( cons_P3334398858971670639nt_int @ X @ Xs ) ) ) ).
% not_in_set_insert
thf(fact_811_List_Oset__insert,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( set_Pr2470121279949933262nt_int @ ( insert5765537519290168021nt_int @ X @ Xs ) )
= ( insert5033312907999012233nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Xs ) ) ) ).
% List.set_insert
thf(fact_812_set__ConsD,axiom,
! [Y: product_prod_int_int,X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( member5262025264175285858nt_int @ Y @ ( set_Pr2470121279949933262nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) ) )
=> ( ( Y = X )
| ( member5262025264175285858nt_int @ Y @ ( set_Pr2470121279949933262nt_int @ Xs ) ) ) ) ).
% set_ConsD
thf(fact_813_list_Oset__cases,axiom,
! [E: product_prod_int_int,A: list_P5707943133018811711nt_int] :
( ( member5262025264175285858nt_int @ E @ ( set_Pr2470121279949933262nt_int @ A ) )
=> ( ! [Z22: list_P5707943133018811711nt_int] :
( A
!= ( cons_P3334398858971670639nt_int @ E @ Z22 ) )
=> ~ ! [Z1: product_prod_int_int,Z22: list_P5707943133018811711nt_int] :
( ( A
= ( cons_P3334398858971670639nt_int @ Z1 @ Z22 ) )
=> ~ ( member5262025264175285858nt_int @ E @ ( set_Pr2470121279949933262nt_int @ Z22 ) ) ) ) ) ).
% list.set_cases
thf(fact_814_list_Oset__intros_I1_J,axiom,
! [X21: product_prod_int_int,X22: list_P5707943133018811711nt_int] : ( member5262025264175285858nt_int @ X21 @ ( set_Pr2470121279949933262nt_int @ ( cons_P3334398858971670639nt_int @ X21 @ X22 ) ) ) ).
% list.set_intros(1)
thf(fact_815_list_Oset__intros_I2_J,axiom,
! [Y: product_prod_int_int,X22: list_P5707943133018811711nt_int,X21: product_prod_int_int] :
( ( member5262025264175285858nt_int @ Y @ ( set_Pr2470121279949933262nt_int @ X22 ) )
=> ( member5262025264175285858nt_int @ Y @ ( set_Pr2470121279949933262nt_int @ ( cons_P3334398858971670639nt_int @ X21 @ X22 ) ) ) ) ).
% list.set_intros(2)
thf(fact_816_knights__path__set__eq,axiom,
! [B: set_Pr958786334691620121nt_int,Ps: list_P5707943133018811711nt_int] :
( ( knights_path @ B @ Ps )
=> ( ( set_Pr2470121279949933262nt_int @ Ps )
= B ) ) ).
% knights_path_set_eq
thf(fact_817_successively__mono,axiom,
! [P: product_prod_int_int > product_prod_int_int > $o,Xs: list_P5707943133018811711nt_int,Q: product_prod_int_int > product_prod_int_int > $o] :
( ( succes497254780304326540nt_int @ P @ Xs )
=> ( ! [X3: product_prod_int_int,Y2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X3 @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ( ( member5262025264175285858nt_int @ Y2 @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ( ( P @ X3 @ Y2 )
=> ( Q @ X3 @ Y2 ) ) ) )
=> ( succes497254780304326540nt_int @ Q @ Xs ) ) ) ).
% successively_mono
thf(fact_818_successively__cong,axiom,
! [Xs: list_P5707943133018811711nt_int,P: product_prod_int_int > product_prod_int_int > $o,Q: product_prod_int_int > product_prod_int_int > $o,Ys: list_P5707943133018811711nt_int] :
( ! [X3: product_prod_int_int,Y2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X3 @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ( ( member5262025264175285858nt_int @ Y2 @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ( ( P @ X3 @ Y2 )
= ( Q @ X3 @ Y2 ) ) ) )
=> ( ( Xs = Ys )
=> ( ( succes497254780304326540nt_int @ P @ Xs )
= ( succes497254780304326540nt_int @ Q @ Ys ) ) ) ) ).
% successively_cong
thf(fact_819_in__set__butlastD,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ ( butlas2390654596765537291nt_int @ Xs ) ) )
=> ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Xs ) ) ) ).
% in_set_butlastD
thf(fact_820_list__ex1__iff,axiom,
( list_e5465588451548443778nt_int
= ( ^ [P2: product_prod_int_int > $o,Xs4: list_P5707943133018811711nt_int] :
? [X2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X2 @ ( set_Pr2470121279949933262nt_int @ Xs4 ) )
& ( P2 @ X2 )
& ! [Y3: product_prod_int_int] :
( ( ( member5262025264175285858nt_int @ Y3 @ ( set_Pr2470121279949933262nt_int @ Xs4 ) )
& ( P2 @ Y3 ) )
=> ( Y3 = X2 ) ) ) ) ) ).
% list_ex1_iff
thf(fact_821_empty__set,axiom,
( bot_bo1796632182523588997nt_int
= ( set_Pr2470121279949933262nt_int @ nil_Pr2300489316682597567nt_int ) ) ).
% empty_set
thf(fact_822_split__list__first__prop__iff,axiom,
! [Xs: list_P5707943133018811711nt_int,P: product_prod_int_int > $o] :
( ( ? [X2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X2 @ ( set_Pr2470121279949933262nt_int @ Xs ) )
& ( P @ X2 ) ) )
= ( ? [Ys3: list_P5707943133018811711nt_int,X2: product_prod_int_int] :
( ? [Zs3: list_P5707943133018811711nt_int] :
( Xs
= ( append7030698103840186580nt_int @ Ys3 @ ( cons_P3334398858971670639nt_int @ X2 @ Zs3 ) ) )
& ( P @ X2 )
& ! [Y3: product_prod_int_int] :
( ( member5262025264175285858nt_int @ Y3 @ ( set_Pr2470121279949933262nt_int @ Ys3 ) )
=> ~ ( P @ Y3 ) ) ) ) ) ).
% split_list_first_prop_iff
thf(fact_823_split__list__last__prop__iff,axiom,
! [Xs: list_P5707943133018811711nt_int,P: product_prod_int_int > $o] :
( ( ? [X2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X2 @ ( set_Pr2470121279949933262nt_int @ Xs ) )
& ( P @ X2 ) ) )
= ( ? [Ys3: list_P5707943133018811711nt_int,X2: product_prod_int_int,Zs3: list_P5707943133018811711nt_int] :
( ( Xs
= ( append7030698103840186580nt_int @ Ys3 @ ( cons_P3334398858971670639nt_int @ X2 @ Zs3 ) ) )
& ( P @ X2 )
& ! [Y3: product_prod_int_int] :
( ( member5262025264175285858nt_int @ Y3 @ ( set_Pr2470121279949933262nt_int @ Zs3 ) )
=> ~ ( P @ Y3 ) ) ) ) ) ).
% split_list_last_prop_iff
thf(fact_824_in__set__conv__decomp__first,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Xs ) )
= ( ? [Ys3: list_P5707943133018811711nt_int,Zs3: list_P5707943133018811711nt_int] :
( ( Xs
= ( append7030698103840186580nt_int @ Ys3 @ ( cons_P3334398858971670639nt_int @ X @ Zs3 ) ) )
& ~ ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Ys3 ) ) ) ) ) ).
% in_set_conv_decomp_first
thf(fact_825_in__set__conv__decomp__last,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Xs ) )
= ( ? [Ys3: list_P5707943133018811711nt_int,Zs3: list_P5707943133018811711nt_int] :
( ( Xs
= ( append7030698103840186580nt_int @ Ys3 @ ( cons_P3334398858971670639nt_int @ X @ Zs3 ) ) )
& ~ ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Zs3 ) ) ) ) ) ).
% in_set_conv_decomp_last
thf(fact_826_split__list__first__propE,axiom,
! [Xs: list_P5707943133018811711nt_int,P: product_prod_int_int > $o] :
( ? [X4: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X4 @ ( set_Pr2470121279949933262nt_int @ Xs ) )
& ( P @ X4 ) )
=> ~ ! [Ys2: list_P5707943133018811711nt_int,X3: product_prod_int_int] :
( ? [Zs4: list_P5707943133018811711nt_int] :
( Xs
= ( append7030698103840186580nt_int @ Ys2 @ ( cons_P3334398858971670639nt_int @ X3 @ Zs4 ) ) )
=> ( ( P @ X3 )
=> ~ ! [Xa2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ Xa2 @ ( set_Pr2470121279949933262nt_int @ Ys2 ) )
=> ~ ( P @ Xa2 ) ) ) ) ) ).
% split_list_first_propE
thf(fact_827_split__list__last__propE,axiom,
! [Xs: list_P5707943133018811711nt_int,P: product_prod_int_int > $o] :
( ? [X4: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X4 @ ( set_Pr2470121279949933262nt_int @ Xs ) )
& ( P @ X4 ) )
=> ~ ! [Ys2: list_P5707943133018811711nt_int,X3: product_prod_int_int,Zs4: list_P5707943133018811711nt_int] :
( ( Xs
= ( append7030698103840186580nt_int @ Ys2 @ ( cons_P3334398858971670639nt_int @ X3 @ Zs4 ) ) )
=> ( ( P @ X3 )
=> ~ ! [Xa2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ Xa2 @ ( set_Pr2470121279949933262nt_int @ Zs4 ) )
=> ~ ( P @ Xa2 ) ) ) ) ) ).
% split_list_last_propE
thf(fact_828_split__list__first__prop,axiom,
! [Xs: list_P5707943133018811711nt_int,P: product_prod_int_int > $o] :
( ? [X4: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X4 @ ( set_Pr2470121279949933262nt_int @ Xs ) )
& ( P @ X4 ) )
=> ? [Ys2: list_P5707943133018811711nt_int,X3: product_prod_int_int] :
( ? [Zs4: list_P5707943133018811711nt_int] :
( Xs
= ( append7030698103840186580nt_int @ Ys2 @ ( cons_P3334398858971670639nt_int @ X3 @ Zs4 ) ) )
& ( P @ X3 )
& ! [Xa2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ Xa2 @ ( set_Pr2470121279949933262nt_int @ Ys2 ) )
=> ~ ( P @ Xa2 ) ) ) ) ).
% split_list_first_prop
thf(fact_829_split__list__last__prop,axiom,
! [Xs: list_P5707943133018811711nt_int,P: product_prod_int_int > $o] :
( ? [X4: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X4 @ ( set_Pr2470121279949933262nt_int @ Xs ) )
& ( P @ X4 ) )
=> ? [Ys2: list_P5707943133018811711nt_int,X3: product_prod_int_int,Zs4: list_P5707943133018811711nt_int] :
( ( Xs
= ( append7030698103840186580nt_int @ Ys2 @ ( cons_P3334398858971670639nt_int @ X3 @ Zs4 ) ) )
& ( P @ X3 )
& ! [Xa2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ Xa2 @ ( set_Pr2470121279949933262nt_int @ Zs4 ) )
=> ~ ( P @ Xa2 ) ) ) ) ).
% split_list_last_prop
thf(fact_830_in__set__conv__decomp,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Xs ) )
= ( ? [Ys3: list_P5707943133018811711nt_int,Zs3: list_P5707943133018811711nt_int] :
( Xs
= ( append7030698103840186580nt_int @ Ys3 @ ( cons_P3334398858971670639nt_int @ X @ Zs3 ) ) ) ) ) ).
% in_set_conv_decomp
thf(fact_831_append__Cons__eq__iff,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int,Xs6: list_P5707943133018811711nt_int,Ys6: list_P5707943133018811711nt_int] :
( ~ ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ( ~ ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Ys ) )
=> ( ( ( append7030698103840186580nt_int @ Xs @ ( cons_P3334398858971670639nt_int @ X @ Ys ) )
= ( append7030698103840186580nt_int @ Xs6 @ ( cons_P3334398858971670639nt_int @ X @ Ys6 ) ) )
= ( ( Xs = Xs6 )
& ( Ys = Ys6 ) ) ) ) ) ).
% append_Cons_eq_iff
thf(fact_832_split__list__propE,axiom,
! [Xs: list_P5707943133018811711nt_int,P: product_prod_int_int > $o] :
( ? [X4: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X4 @ ( set_Pr2470121279949933262nt_int @ Xs ) )
& ( P @ X4 ) )
=> ~ ! [Ys2: list_P5707943133018811711nt_int,X3: product_prod_int_int] :
( ? [Zs4: list_P5707943133018811711nt_int] :
( Xs
= ( append7030698103840186580nt_int @ Ys2 @ ( cons_P3334398858971670639nt_int @ X3 @ Zs4 ) ) )
=> ~ ( P @ X3 ) ) ) ).
% split_list_propE
thf(fact_833_split__list__first,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ? [Ys2: list_P5707943133018811711nt_int,Zs4: list_P5707943133018811711nt_int] :
( ( Xs
= ( append7030698103840186580nt_int @ Ys2 @ ( cons_P3334398858971670639nt_int @ X @ Zs4 ) ) )
& ~ ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Ys2 ) ) ) ) ).
% split_list_first
thf(fact_834_split__list__prop,axiom,
! [Xs: list_P5707943133018811711nt_int,P: product_prod_int_int > $o] :
( ? [X4: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X4 @ ( set_Pr2470121279949933262nt_int @ Xs ) )
& ( P @ X4 ) )
=> ? [Ys2: list_P5707943133018811711nt_int,X3: product_prod_int_int] :
( ? [Zs4: list_P5707943133018811711nt_int] :
( Xs
= ( append7030698103840186580nt_int @ Ys2 @ ( cons_P3334398858971670639nt_int @ X3 @ Zs4 ) ) )
& ( P @ X3 ) ) ) ).
% split_list_prop
thf(fact_835_split__list__last,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ? [Ys2: list_P5707943133018811711nt_int,Zs4: list_P5707943133018811711nt_int] :
( ( Xs
= ( append7030698103840186580nt_int @ Ys2 @ ( cons_P3334398858971670639nt_int @ X @ Zs4 ) ) )
& ~ ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Zs4 ) ) ) ) ).
% split_list_last
thf(fact_836_split__list,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ? [Ys2: list_P5707943133018811711nt_int,Zs4: list_P5707943133018811711nt_int] :
( Xs
= ( append7030698103840186580nt_int @ Ys2 @ ( cons_P3334398858971670639nt_int @ X @ Zs4 ) ) ) ) ).
% split_list
thf(fact_837_map__tailrec__rev_Osimps_I2_J,axiom,
! [F: product_prod_int_int > product_prod_int_int,A: product_prod_int_int,As2: list_P5707943133018811711nt_int,Bs: list_P5707943133018811711nt_int] :
( ( map_ta5484600921387902261nt_int @ F @ ( cons_P3334398858971670639nt_int @ A @ As2 ) @ Bs )
= ( map_ta5484600921387902261nt_int @ F @ As2 @ ( cons_P3334398858971670639nt_int @ ( F @ A ) @ Bs ) ) ) ).
% map_tailrec_rev.simps(2)
thf(fact_838_hd__in__set,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( Xs != nil_Pr2300489316682597567nt_int )
=> ( member5262025264175285858nt_int @ ( hd_Pro282112905867057956nt_int @ Xs ) @ ( set_Pr2470121279949933262nt_int @ Xs ) ) ) ).
% hd_in_set
thf(fact_839_list_Oset__sel_I1_J,axiom,
! [A: list_P5707943133018811711nt_int] :
( ( A != nil_Pr2300489316682597567nt_int )
=> ( member5262025264175285858nt_int @ ( hd_Pro282112905867057956nt_int @ A ) @ ( set_Pr2470121279949933262nt_int @ A ) ) ) ).
% list.set_sel(1)
thf(fact_840_list_Oset__sel_I2_J,axiom,
! [A: list_P5707943133018811711nt_int,X: product_prod_int_int] :
( ( A != nil_Pr2300489316682597567nt_int )
=> ( ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ ( tl_Pro1049539609081552168nt_int @ A ) ) )
=> ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ A ) ) ) ) ).
% list.set_sel(2)
thf(fact_841_last__in__set,axiom,
! [As2: list_P5707943133018811711nt_int] :
( ( As2 != nil_Pr2300489316682597567nt_int )
=> ( member5262025264175285858nt_int @ ( last_P3305686521732843992nt_int @ As2 ) @ ( set_Pr2470121279949933262nt_int @ As2 ) ) ) ).
% last_in_set
thf(fact_842_set__shuffles,axiom,
! [Zs: list_P5707943133018811711nt_int,Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ Zs @ ( shuffl1909956583008895700nt_int @ Xs @ Ys ) )
=> ( ( set_Pr2470121279949933262nt_int @ Zs )
= ( sup_su6024340866399070445nt_int @ ( set_Pr2470121279949933262nt_int @ Xs ) @ ( set_Pr2470121279949933262nt_int @ Ys ) ) ) ) ).
% set_shuffles
thf(fact_843_in__set__butlast__appendI,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ ( butlas2390654596765537291nt_int @ Xs ) ) )
| ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ ( butlas2390654596765537291nt_int @ Ys ) ) ) )
=> ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ ( butlas2390654596765537291nt_int @ ( append7030698103840186580nt_int @ Xs @ Ys ) ) ) ) ) ).
% in_set_butlast_appendI
thf(fact_844_successively__remdups__adj__iff,axiom,
! [Xs: list_P5707943133018811711nt_int,P: product_prod_int_int > product_prod_int_int > $o] :
( ! [X3: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X3 @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ( P @ X3 @ X3 ) )
=> ( ( succes497254780304326540nt_int @ P @ ( remdup6889124116291670005nt_int @ Xs ) )
= ( succes497254780304326540nt_int @ P @ Xs ) ) ) ).
% successively_remdups_adj_iff
thf(fact_845_Cons__in__subseqsD,axiom,
! [Y: product_prod_int_int,Ys: list_P5707943133018811711nt_int,Xs: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ ( cons_P3334398858971670639nt_int @ Y @ Ys ) @ ( set_li2659200638379878868nt_int @ ( subseq1357044202310323342nt_int @ Xs ) ) )
=> ( member2764346250752101224nt_int @ Ys @ ( set_li2659200638379878868nt_int @ ( subseq1357044202310323342nt_int @ Xs ) ) ) ) ).
% Cons_in_subseqsD
thf(fact_846_List_Oinsert__def,axiom,
( insert5765537519290168021nt_int
= ( ^ [X2: product_prod_int_int,Xs4: list_P5707943133018811711nt_int] : ( if_lis8883190402267401221nt_int @ ( member5262025264175285858nt_int @ X2 @ ( set_Pr2470121279949933262nt_int @ Xs4 ) ) @ Xs4 @ ( cons_P3334398858971670639nt_int @ X2 @ Xs4 ) ) ) ) ).
% List.insert_def
thf(fact_847_the__elem__set,axiom,
! [X: product_prod_int_int] :
( ( the_el8326832613380209454nt_int @ ( set_Pr2470121279949933262nt_int @ ( cons_P3334398858971670639nt_int @ X @ nil_Pr2300489316682597567nt_int ) ) )
= X ) ).
% the_elem_set
thf(fact_848_SuccI,axiom,
! [Kl2: list_P5707943133018811711nt_int,K: product_prod_int_int,Kl: set_li3855193629254082847nt_int] :
( ( member2764346250752101224nt_int @ ( append7030698103840186580nt_int @ Kl2 @ ( cons_P3334398858971670639nt_int @ K @ nil_Pr2300489316682597567nt_int ) ) @ Kl )
=> ( member5262025264175285858nt_int @ K @ ( bNF_Gr2185362013987207252nt_int @ Kl @ Kl2 ) ) ) ).
% SuccI
thf(fact_849_set__union,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( set_Pr2470121279949933262nt_int @ ( union_56799373549498035nt_int @ Xs @ Ys ) )
= ( sup_su6024340866399070445nt_int @ ( set_Pr2470121279949933262nt_int @ Xs ) @ ( set_Pr2470121279949933262nt_int @ Ys ) ) ) ).
% set_union
thf(fact_850_can__select__set__list__ex1,axiom,
! [P: product_prod_int_int > $o,A3: list_P5707943133018811711nt_int] :
( ( can_se1576335439491303350nt_int @ P @ ( set_Pr2470121279949933262nt_int @ A3 ) )
= ( list_e5465588451548443778nt_int @ P @ A3 ) ) ).
% can_select_set_list_ex1
thf(fact_851_listset_Osimps_I1_J,axiom,
( ( listse7073127531753840414nt_int @ nil_se54404438492013087nt_int )
= ( insert393344137582914319nt_int @ nil_Pr2300489316682597567nt_int @ bot_bo3809061186584590219nt_int ) ) ).
% listset.simps(1)
thf(fact_852_empty__Shift,axiom,
! [Kl: set_li3855193629254082847nt_int,K: product_prod_int_int] :
( ( member2764346250752101224nt_int @ nil_Pr2300489316682597567nt_int @ Kl )
=> ( ( member5262025264175285858nt_int @ K @ ( bNF_Gr2185362013987207252nt_int @ Kl @ nil_Pr2300489316682597567nt_int ) )
=> ( member2764346250752101224nt_int @ nil_Pr2300489316682597567nt_int @ ( bNF_Gr9175161896313899224nt_int @ Kl @ K ) ) ) ) ).
% empty_Shift
thf(fact_853_can__select__def,axiom,
( can_se1576335439491303350nt_int
= ( ^ [P2: product_prod_int_int > $o,A4: set_Pr958786334691620121nt_int] :
? [X2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X2 @ A4 )
& ( P2 @ X2 )
& ! [Y3: product_prod_int_int] :
( ( ( member5262025264175285858nt_int @ Y3 @ A4 )
& ( P2 @ Y3 ) )
=> ( Y3 = X2 ) ) ) ) ) ).
% can_select_def
thf(fact_854_ShiftD,axiom,
! [Kl2: list_P5707943133018811711nt_int,Kl: set_li3855193629254082847nt_int,K: product_prod_int_int] :
( ( member2764346250752101224nt_int @ Kl2 @ ( bNF_Gr9175161896313899224nt_int @ Kl @ K ) )
=> ( member2764346250752101224nt_int @ ( cons_P3334398858971670639nt_int @ K @ Kl2 ) @ Kl ) ) ).
% ShiftD
thf(fact_855_Succ__Shift,axiom,
! [Kl: set_li3855193629254082847nt_int,K: product_prod_int_int,Kl2: list_P5707943133018811711nt_int] :
( ( bNF_Gr2185362013987207252nt_int @ ( bNF_Gr9175161896313899224nt_int @ Kl @ K ) @ Kl2 )
= ( bNF_Gr2185362013987207252nt_int @ Kl @ ( cons_P3334398858971670639nt_int @ K @ Kl2 ) ) ) ).
% Succ_Shift
thf(fact_856_is__empty__set,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( is_emp7707449487952173963nt_int @ ( set_Pr2470121279949933262nt_int @ Xs ) )
= ( null_P4123483736518020807nt_int @ Xs ) ) ).
% is_empty_set
thf(fact_857_set__removeAll,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( set_Pr2470121279949933262nt_int @ ( remove494893200766290885nt_int @ X @ Xs ) )
= ( minus_1052850069191792384nt_int @ ( set_Pr2470121279949933262nt_int @ Xs ) @ ( insert5033312907999012233nt_int @ X @ bot_bo1796632182523588997nt_int ) ) ) ).
% set_removeAll
thf(fact_858_lists__empty,axiom,
( ( lists_9111190511995884973nt_int @ bot_bo1796632182523588997nt_int )
= ( insert393344137582914319nt_int @ nil_Pr2300489316682597567nt_int @ bot_bo3809061186584590219nt_int ) ) ).
% lists_empty
thf(fact_859_shuffles_Oelims,axiom,
! [X: list_P5707943133018811711nt_int,Xa: list_P5707943133018811711nt_int,Y: set_li3855193629254082847nt_int] :
( ( ( shuffl1909956583008895700nt_int @ X @ Xa )
= Y )
=> ( ( ( X = nil_Pr2300489316682597567nt_int )
=> ( Y
!= ( insert393344137582914319nt_int @ Xa @ bot_bo3809061186584590219nt_int ) ) )
=> ( ( ( Xa = nil_Pr2300489316682597567nt_int )
=> ( Y
!= ( insert393344137582914319nt_int @ X @ bot_bo3809061186584590219nt_int ) ) )
=> ~ ! [X3: product_prod_int_int,Xs2: list_P5707943133018811711nt_int] :
( ( X
= ( cons_P3334398858971670639nt_int @ X3 @ Xs2 ) )
=> ! [Y2: product_prod_int_int,Ys2: list_P5707943133018811711nt_int] :
( ( Xa
= ( cons_P3334398858971670639nt_int @ Y2 @ Ys2 ) )
=> ( Y
!= ( sup_su3633867531522857715nt_int @ ( image_689455831346312645nt_int @ ( cons_P3334398858971670639nt_int @ X3 ) @ ( shuffl1909956583008895700nt_int @ Xs2 @ ( cons_P3334398858971670639nt_int @ Y2 @ Ys2 ) ) ) @ ( image_689455831346312645nt_int @ ( cons_P3334398858971670639nt_int @ Y2 ) @ ( shuffl1909956583008895700nt_int @ ( cons_P3334398858971670639nt_int @ X3 @ Xs2 ) @ Ys2 ) ) ) ) ) ) ) ) ) ).
% shuffles.elims
thf(fact_860_image__eqI,axiom,
! [B: product_prod_int_int,F: product_prod_int_int > product_prod_int_int,X: product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( B
= ( F @ X ) )
=> ( ( member5262025264175285858nt_int @ X @ A3 )
=> ( member5262025264175285858nt_int @ B @ ( image_2653370878348428101nt_int @ F @ A3 ) ) ) ) ).
% image_eqI
thf(fact_861_image__empty,axiom,
! [F: product_prod_int_int > product_prod_int_int] :
( ( image_2653370878348428101nt_int @ F @ bot_bo1796632182523588997nt_int )
= bot_bo1796632182523588997nt_int ) ).
% image_empty
thf(fact_862_empty__is__image,axiom,
! [F: product_prod_int_int > product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( bot_bo1796632182523588997nt_int
= ( image_2653370878348428101nt_int @ F @ A3 ) )
= ( A3 = bot_bo1796632182523588997nt_int ) ) ).
% empty_is_image
thf(fact_863_image__is__empty,axiom,
! [F: product_prod_int_int > product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( ( image_2653370878348428101nt_int @ F @ A3 )
= bot_bo1796632182523588997nt_int )
= ( A3 = bot_bo1796632182523588997nt_int ) ) ).
% image_is_empty
thf(fact_864_image__insert,axiom,
! [F: product_prod_int_int > product_prod_int_int,A: product_prod_int_int,B4: set_Pr958786334691620121nt_int] :
( ( image_2653370878348428101nt_int @ F @ ( insert5033312907999012233nt_int @ A @ B4 ) )
= ( insert5033312907999012233nt_int @ ( F @ A ) @ ( image_2653370878348428101nt_int @ F @ B4 ) ) ) ).
% image_insert
thf(fact_865_insert__image,axiom,
! [X: product_prod_int_int,A3: set_Pr958786334691620121nt_int,F: product_prod_int_int > product_prod_int_int] :
( ( member5262025264175285858nt_int @ X @ A3 )
=> ( ( insert5033312907999012233nt_int @ ( F @ X ) @ ( image_2653370878348428101nt_int @ F @ A3 ) )
= ( image_2653370878348428101nt_int @ F @ A3 ) ) ) ).
% insert_image
thf(fact_866_Cons__in__lists__iff,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int,A3: set_Pr958786334691620121nt_int] :
( ( member2764346250752101224nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) @ ( lists_9111190511995884973nt_int @ A3 ) )
= ( ( member5262025264175285858nt_int @ X @ A3 )
& ( member2764346250752101224nt_int @ Xs @ ( lists_9111190511995884973nt_int @ A3 ) ) ) ) ).
% Cons_in_lists_iff
thf(fact_867_in__listsI,axiom,
! [Xs: list_P5707943133018811711nt_int,A3: set_Pr958786334691620121nt_int] :
( ! [X3: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X3 @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ( member5262025264175285858nt_int @ X3 @ A3 ) )
=> ( member2764346250752101224nt_int @ Xs @ ( lists_9111190511995884973nt_int @ A3 ) ) ) ).
% in_listsI
thf(fact_868_lists__Int__eq,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( lists_9111190511995884973nt_int @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) )
= ( inf_in8463092517017915661nt_int @ ( lists_9111190511995884973nt_int @ A3 ) @ ( lists_9111190511995884973nt_int @ B4 ) ) ) ).
% lists_Int_eq
thf(fact_869_append__in__lists__conv,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int,A3: set_Pr958786334691620121nt_int] :
( ( member2764346250752101224nt_int @ ( append7030698103840186580nt_int @ Xs @ Ys ) @ ( lists_9111190511995884973nt_int @ A3 ) )
= ( ( member2764346250752101224nt_int @ Xs @ ( lists_9111190511995884973nt_int @ A3 ) )
& ( member2764346250752101224nt_int @ Ys @ ( lists_9111190511995884973nt_int @ A3 ) ) ) ) ).
% append_in_lists_conv
thf(fact_870_removeAll__id,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ~ ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ( ( remove494893200766290885nt_int @ X @ Xs )
= Xs ) ) ).
% removeAll_id
thf(fact_871_removeAll__append,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( remove494893200766290885nt_int @ X @ ( append7030698103840186580nt_int @ Xs @ Ys ) )
= ( append7030698103840186580nt_int @ ( remove494893200766290885nt_int @ X @ Xs ) @ ( remove494893200766290885nt_int @ X @ Ys ) ) ) ).
% removeAll_append
thf(fact_872_lists_OCons,axiom,
! [A: product_prod_int_int,A3: set_Pr958786334691620121nt_int,L: list_P5707943133018811711nt_int] :
( ( member5262025264175285858nt_int @ A @ A3 )
=> ( ( member2764346250752101224nt_int @ L @ ( lists_9111190511995884973nt_int @ A3 ) )
=> ( member2764346250752101224nt_int @ ( cons_P3334398858971670639nt_int @ A @ L ) @ ( lists_9111190511995884973nt_int @ A3 ) ) ) ) ).
% lists.Cons
thf(fact_873_listsE,axiom,
! [X: product_prod_int_int,L: list_P5707943133018811711nt_int,A3: set_Pr958786334691620121nt_int] :
( ( member2764346250752101224nt_int @ ( cons_P3334398858971670639nt_int @ X @ L ) @ ( lists_9111190511995884973nt_int @ A3 ) )
=> ~ ( ( member5262025264175285858nt_int @ X @ A3 )
=> ~ ( member2764346250752101224nt_int @ L @ ( lists_9111190511995884973nt_int @ A3 ) ) ) ) ).
% listsE
thf(fact_874_lists_ONil,axiom,
! [A3: set_Pr958786334691620121nt_int] : ( member2764346250752101224nt_int @ nil_Pr2300489316682597567nt_int @ ( lists_9111190511995884973nt_int @ A3 ) ) ).
% lists.Nil
thf(fact_875_rev__image__eqI,axiom,
! [X: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B: product_prod_int_int,F: product_prod_int_int > product_prod_int_int] :
( ( member5262025264175285858nt_int @ X @ A3 )
=> ( ( B
= ( F @ X ) )
=> ( member5262025264175285858nt_int @ B @ ( image_2653370878348428101nt_int @ F @ A3 ) ) ) ) ).
% rev_image_eqI
thf(fact_876_imageI,axiom,
! [X: product_prod_int_int,A3: set_Pr958786334691620121nt_int,F: product_prod_int_int > product_prod_int_int] :
( ( member5262025264175285858nt_int @ X @ A3 )
=> ( member5262025264175285858nt_int @ ( F @ X ) @ ( image_2653370878348428101nt_int @ F @ A3 ) ) ) ).
% imageI
thf(fact_877_image__Un,axiom,
! [F: product_prod_int_int > product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( image_2653370878348428101nt_int @ F @ ( sup_su6024340866399070445nt_int @ A3 @ B4 ) )
= ( sup_su6024340866399070445nt_int @ ( image_2653370878348428101nt_int @ F @ A3 ) @ ( image_2653370878348428101nt_int @ F @ B4 ) ) ) ).
% image_Un
thf(fact_878_in__lists__conv__set,axiom,
! [Xs: list_P5707943133018811711nt_int,A3: set_Pr958786334691620121nt_int] :
( ( member2764346250752101224nt_int @ Xs @ ( lists_9111190511995884973nt_int @ A3 ) )
= ( ! [X2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X2 @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ( member5262025264175285858nt_int @ X2 @ A3 ) ) ) ) ).
% in_lists_conv_set
thf(fact_879_in__listsD,axiom,
! [Xs: list_P5707943133018811711nt_int,A3: set_Pr958786334691620121nt_int] :
( ( member2764346250752101224nt_int @ Xs @ ( lists_9111190511995884973nt_int @ A3 ) )
=> ! [X4: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X4 @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ( member5262025264175285858nt_int @ X4 @ A3 ) ) ) ).
% in_listsD
thf(fact_880_lists__IntI,axiom,
! [L: list_P5707943133018811711nt_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( member2764346250752101224nt_int @ L @ ( lists_9111190511995884973nt_int @ A3 ) )
=> ( ( member2764346250752101224nt_int @ L @ ( lists_9111190511995884973nt_int @ B4 ) )
=> ( member2764346250752101224nt_int @ L @ ( lists_9111190511995884973nt_int @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) ) ) ) ) ).
% lists_IntI
thf(fact_881_removeAll_Osimps_I2_J,axiom,
! [X: product_prod_int_int,Y: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( ( X = Y )
=> ( ( remove494893200766290885nt_int @ X @ ( cons_P3334398858971670639nt_int @ Y @ Xs ) )
= ( remove494893200766290885nt_int @ X @ Xs ) ) )
& ( ( X != Y )
=> ( ( remove494893200766290885nt_int @ X @ ( cons_P3334398858971670639nt_int @ Y @ Xs ) )
= ( cons_P3334398858971670639nt_int @ Y @ ( remove494893200766290885nt_int @ X @ Xs ) ) ) ) ) ).
% removeAll.simps(2)
thf(fact_882_removeAll_Osimps_I1_J,axiom,
! [X: product_prod_int_int] :
( ( remove494893200766290885nt_int @ X @ nil_Pr2300489316682597567nt_int )
= nil_Pr2300489316682597567nt_int ) ).
% removeAll.simps(1)
thf(fact_883_shuffles_Osimps_I3_J,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int,Y: product_prod_int_int,Ys: list_P5707943133018811711nt_int] :
( ( shuffl1909956583008895700nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) @ ( cons_P3334398858971670639nt_int @ Y @ Ys ) )
= ( sup_su3633867531522857715nt_int @ ( image_689455831346312645nt_int @ ( cons_P3334398858971670639nt_int @ X ) @ ( shuffl1909956583008895700nt_int @ Xs @ ( cons_P3334398858971670639nt_int @ Y @ Ys ) ) ) @ ( image_689455831346312645nt_int @ ( cons_P3334398858971670639nt_int @ Y ) @ ( shuffl1909956583008895700nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) @ Ys ) ) ) ) ).
% shuffles.simps(3)
thf(fact_884_lists_Osimps,axiom,
! [A: list_P5707943133018811711nt_int,A3: set_Pr958786334691620121nt_int] :
( ( member2764346250752101224nt_int @ A @ ( lists_9111190511995884973nt_int @ A3 ) )
= ( ( A = nil_Pr2300489316682597567nt_int )
| ? [A5: product_prod_int_int,L2: list_P5707943133018811711nt_int] :
( ( A
= ( cons_P3334398858971670639nt_int @ A5 @ L2 ) )
& ( member5262025264175285858nt_int @ A5 @ A3 )
& ( member2764346250752101224nt_int @ L2 @ ( lists_9111190511995884973nt_int @ A3 ) ) ) ) ) ).
% lists.simps
thf(fact_885_lists_Ocases,axiom,
! [A: list_P5707943133018811711nt_int,A3: set_Pr958786334691620121nt_int] :
( ( member2764346250752101224nt_int @ A @ ( lists_9111190511995884973nt_int @ A3 ) )
=> ( ( A != nil_Pr2300489316682597567nt_int )
=> ~ ! [A6: product_prod_int_int,L3: list_P5707943133018811711nt_int] :
( ( A
= ( cons_P3334398858971670639nt_int @ A6 @ L3 ) )
=> ( ( member5262025264175285858nt_int @ A6 @ A3 )
=> ~ ( member2764346250752101224nt_int @ L3 @ ( lists_9111190511995884973nt_int @ A3 ) ) ) ) ) ) ).
% lists.cases
thf(fact_886_null__rec_I1_J,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
~ ( null_P4123483736518020807nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) ) ).
% null_rec(1)
thf(fact_887_eq__Nil__null,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( Xs = nil_Pr2300489316682597567nt_int )
= ( null_P4123483736518020807nt_int @ Xs ) ) ).
% eq_Nil_null
thf(fact_888_null__rec_I2_J,axiom,
null_P4123483736518020807nt_int @ nil_Pr2300489316682597567nt_int ).
% null_rec(2)
thf(fact_889_insert__code_I2_J,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( insert5033312907999012233nt_int @ X @ ( coset_3631019413092825772nt_int @ Xs ) )
= ( coset_3631019413092825772nt_int @ ( remove494893200766290885nt_int @ X @ Xs ) ) ) ).
% insert_code(2)
thf(fact_890_remove__code_I1_J,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( remove3288057706648593438nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Xs ) )
= ( set_Pr2470121279949933262nt_int @ ( remove494893200766290885nt_int @ X @ Xs ) ) ) ).
% remove_code(1)
thf(fact_891_Sup__fin_Oset__eq__fold,axiom,
! [X: set_Pr958786334691620121nt_int,Xs: list_s8839374986383574687nt_int] :
( ( lattic1237861848008701264nt_int @ ( set_se4746441305218329646nt_int @ ( cons_s6578334183908017615nt_int @ X @ Xs ) ) )
= ( fold_s6119275068807568459nt_int @ sup_su6024340866399070445nt_int @ Xs @ X ) ) ).
% Sup_fin.set_eq_fold
thf(fact_892_Inf__fin_Oset__eq__fold,axiom,
! [X: set_Pr958786334691620121nt_int,Xs: list_s8839374986383574687nt_int] :
( ( lattic8951152183982934710nt_int @ ( set_se4746441305218329646nt_int @ ( cons_s6578334183908017615nt_int @ X @ Xs ) ) )
= ( fold_s6119275068807568459nt_int @ inf_in2269163501485487111nt_int @ Xs @ X ) ) ).
% Inf_fin.set_eq_fold
thf(fact_893_distinct__append,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( distin3744728255968310194nt_int @ ( append7030698103840186580nt_int @ Xs @ Ys ) )
= ( ( distin3744728255968310194nt_int @ Xs )
& ( distin3744728255968310194nt_int @ Ys )
& ( ( inf_in2269163501485487111nt_int @ ( set_Pr2470121279949933262nt_int @ Xs ) @ ( set_Pr2470121279949933262nt_int @ Ys ) )
= bot_bo1796632182523588997nt_int ) ) ) ).
% distinct_append
thf(fact_894_distinct1__rotate,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( distin3744728255968310194nt_int @ ( rotate9137591727117064716nt_int @ Xs ) )
= ( distin3744728255968310194nt_int @ Xs ) ) ).
% distinct1_rotate
thf(fact_895_distinct__insert,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( distin3744728255968310194nt_int @ ( insert5765537519290168021nt_int @ X @ Xs ) )
= ( distin3744728255968310194nt_int @ Xs ) ) ).
% distinct_insert
thf(fact_896_distinct__union,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( distin3744728255968310194nt_int @ ( union_56799373549498035nt_int @ Xs @ Ys ) )
= ( distin3744728255968310194nt_int @ Ys ) ) ).
% distinct_union
thf(fact_897_distinct__removeAll,axiom,
! [Xs: list_P5707943133018811711nt_int,X: product_prod_int_int] :
( ( distin3744728255968310194nt_int @ Xs )
=> ( distin3744728255968310194nt_int @ ( remove494893200766290885nt_int @ X @ Xs ) ) ) ).
% distinct_removeAll
thf(fact_898_distinct__product,axiom,
! [Xs: list_int,Ys: list_int] :
( ( distinct_int @ Xs )
=> ( ( distinct_int @ Ys )
=> ( distin3744728255968310194nt_int @ ( product_int_int @ Xs @ Ys ) ) ) ) ).
% distinct_product
thf(fact_899_distinct__product,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( distin3744728255968310194nt_int @ Xs )
=> ( ( distin3744728255968310194nt_int @ Ys )
=> ( distin7265875916114366688nt_int @ ( produc1028813369992947845nt_int @ Xs @ Ys ) ) ) ) ).
% distinct_product
thf(fact_900_distinct__length__2__or__more,axiom,
! [A: product_prod_int_int,B: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( distin3744728255968310194nt_int @ ( cons_P3334398858971670639nt_int @ A @ ( cons_P3334398858971670639nt_int @ B @ Xs ) ) )
= ( ( A != B )
& ( distin3744728255968310194nt_int @ ( cons_P3334398858971670639nt_int @ A @ Xs ) )
& ( distin3744728255968310194nt_int @ ( cons_P3334398858971670639nt_int @ B @ Xs ) ) ) ) ).
% distinct_length_2_or_more
thf(fact_901_distinct__butlast,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( distin3744728255968310194nt_int @ Xs )
=> ( distin3744728255968310194nt_int @ ( butlas2390654596765537291nt_int @ Xs ) ) ) ).
% distinct_butlast
thf(fact_902_knights__path__distinct,axiom,
! [B: set_Pr958786334691620121nt_int,Ps: list_P5707943133018811711nt_int] :
( ( knights_path @ B @ Ps )
=> ( distin3744728255968310194nt_int @ Ps ) ) ).
% knights_path_distinct
thf(fact_903_remdups__adj__distinct,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( distin3744728255968310194nt_int @ Xs )
=> ( ( remdup6889124116291670005nt_int @ Xs )
= Xs ) ) ).
% remdups_adj_distinct
thf(fact_904_distinct__tl,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( distin3744728255968310194nt_int @ Xs )
=> ( distin3744728255968310194nt_int @ ( tl_Pro1049539609081552168nt_int @ Xs ) ) ) ).
% distinct_tl
thf(fact_905_distinct_Osimps_I1_J,axiom,
distin3744728255968310194nt_int @ nil_Pr2300489316682597567nt_int ).
% distinct.simps(1)
thf(fact_906_distinct__product__lists,axiom,
! [Xss2: list_l1670014477004246597nt_int] :
( ! [X3: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ X3 @ ( set_li2659200638379878868nt_int @ Xss2 ) )
=> ( distin3744728255968310194nt_int @ X3 ) )
=> ( distin8114605256187547832nt_int @ ( produc5568053154996169768nt_int @ Xss2 ) ) ) ).
% distinct_product_lists
thf(fact_907_distinct__singleton,axiom,
! [X: product_prod_int_int] : ( distin3744728255968310194nt_int @ ( cons_P3334398858971670639nt_int @ X @ nil_Pr2300489316682597567nt_int ) ) ).
% distinct_singleton
thf(fact_908_distinct_Osimps_I2_J,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( distin3744728255968310194nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) )
= ( ~ ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Xs ) )
& ( distin3744728255968310194nt_int @ Xs ) ) ) ).
% distinct.simps(2)
thf(fact_909_distinct__concat,axiom,
! [Xs: list_l1670014477004246597nt_int] :
( ( distin8114605256187547832nt_int @ Xs )
=> ( ! [Ys2: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ Ys2 @ ( set_li2659200638379878868nt_int @ Xs ) )
=> ( distin3744728255968310194nt_int @ Ys2 ) )
=> ( ! [Ys2: list_P5707943133018811711nt_int,Zs4: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ Ys2 @ ( set_li2659200638379878868nt_int @ Xs ) )
=> ( ( member2764346250752101224nt_int @ Zs4 @ ( set_li2659200638379878868nt_int @ Xs ) )
=> ( ( Ys2 != Zs4 )
=> ( ( inf_in2269163501485487111nt_int @ ( set_Pr2470121279949933262nt_int @ Ys2 ) @ ( set_Pr2470121279949933262nt_int @ Zs4 ) )
= bot_bo1796632182523588997nt_int ) ) ) )
=> ( distin3744728255968310194nt_int @ ( concat4512918505337516154nt_int @ Xs ) ) ) ) ) ).
% distinct_concat
thf(fact_910_subseqs__distinctD,axiom,
! [Ys: list_P5707943133018811711nt_int,Xs: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ Ys @ ( set_li2659200638379878868nt_int @ ( subseq1357044202310323342nt_int @ Xs ) ) )
=> ( ( distin3744728255968310194nt_int @ Xs )
=> ( distin3744728255968310194nt_int @ Ys ) ) ) ).
% subseqs_distinctD
thf(fact_911_distinct__concat__iff,axiom,
! [Xs: list_l1670014477004246597nt_int] :
( ( distin3744728255968310194nt_int @ ( concat4512918505337516154nt_int @ Xs ) )
= ( ( distin8114605256187547832nt_int @ ( remove8754733362737398603nt_int @ nil_Pr2300489316682597567nt_int @ Xs ) )
& ! [Ys3: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ Ys3 @ ( set_li2659200638379878868nt_int @ Xs ) )
=> ( distin3744728255968310194nt_int @ Ys3 ) )
& ! [Ys3: list_P5707943133018811711nt_int,Zs3: list_P5707943133018811711nt_int] :
( ( ( member2764346250752101224nt_int @ Ys3 @ ( set_li2659200638379878868nt_int @ Xs ) )
& ( member2764346250752101224nt_int @ Zs3 @ ( set_li2659200638379878868nt_int @ Xs ) )
& ( Ys3 != Zs3 ) )
=> ( ( inf_in2269163501485487111nt_int @ ( set_Pr2470121279949933262nt_int @ Ys3 ) @ ( set_Pr2470121279949933262nt_int @ Zs3 ) )
= bot_bo1796632182523588997nt_int ) ) ) ) ).
% distinct_concat_iff
thf(fact_912_not__distinct__decomp,axiom,
! [Ws: list_P5707943133018811711nt_int] :
( ~ ( distin3744728255968310194nt_int @ Ws )
=> ? [Xs2: list_P5707943133018811711nt_int,Ys2: list_P5707943133018811711nt_int,Zs4: list_P5707943133018811711nt_int,Y2: product_prod_int_int] :
( Ws
= ( append7030698103840186580nt_int @ Xs2 @ ( append7030698103840186580nt_int @ ( cons_P3334398858971670639nt_int @ Y2 @ nil_Pr2300489316682597567nt_int ) @ ( append7030698103840186580nt_int @ Ys2 @ ( append7030698103840186580nt_int @ ( cons_P3334398858971670639nt_int @ Y2 @ nil_Pr2300489316682597567nt_int ) @ Zs4 ) ) ) ) ) ) ).
% not_distinct_decomp
thf(fact_913_not__distinct__conv__prefix,axiom,
! [As2: list_P5707943133018811711nt_int] :
( ( ~ ( distin3744728255968310194nt_int @ As2 ) )
= ( ? [Xs4: list_P5707943133018811711nt_int,Y3: product_prod_int_int,Ys3: list_P5707943133018811711nt_int] :
( ( member5262025264175285858nt_int @ Y3 @ ( set_Pr2470121279949933262nt_int @ Xs4 ) )
& ( distin3744728255968310194nt_int @ Xs4 )
& ( As2
= ( append7030698103840186580nt_int @ Xs4 @ ( cons_P3334398858971670639nt_int @ Y3 @ Ys3 ) ) ) ) ) ) ).
% not_distinct_conv_prefix
thf(fact_914_in__image__insert__iff,axiom,
! [B4: set_se6260736226359567993nt_int,X: product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ! [C4: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ C4 @ B4 )
=> ~ ( member5262025264175285858nt_int @ X @ C4 ) )
=> ( ( member2340774599025711042nt_int @ A3 @ ( image_1544889507766666053nt_int @ ( insert5033312907999012233nt_int @ X ) @ B4 ) )
= ( ( member5262025264175285858nt_int @ X @ A3 )
& ( member2340774599025711042nt_int @ ( minus_1052850069191792384nt_int @ A3 @ ( insert5033312907999012233nt_int @ X @ bot_bo1796632182523588997nt_int ) ) @ B4 ) ) ) ) ).
% in_image_insert_iff
thf(fact_915_distinct__disjoint__shuffles,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int,Zs: list_P5707943133018811711nt_int] :
( ( distin3744728255968310194nt_int @ Xs )
=> ( ( distin3744728255968310194nt_int @ Ys )
=> ( ( ( inf_in2269163501485487111nt_int @ ( set_Pr2470121279949933262nt_int @ Xs ) @ ( set_Pr2470121279949933262nt_int @ Ys ) )
= bot_bo1796632182523588997nt_int )
=> ( ( member2764346250752101224nt_int @ Zs @ ( shuffl1909956583008895700nt_int @ Xs @ Ys ) )
=> ( distin3744728255968310194nt_int @ Zs ) ) ) ) ) ).
% distinct_disjoint_shuffles
thf(fact_916_set__remove1__eq,axiom,
! [Xs: list_P5707943133018811711nt_int,X: product_prod_int_int] :
( ( distin3744728255968310194nt_int @ Xs )
=> ( ( set_Pr2470121279949933262nt_int @ ( remove2588356790385189205nt_int @ X @ Xs ) )
= ( minus_1052850069191792384nt_int @ ( set_Pr2470121279949933262nt_int @ Xs ) @ ( insert5033312907999012233nt_int @ X @ bot_bo1796632182523588997nt_int ) ) ) ) ).
% set_remove1_eq
thf(fact_917_in__set__remove1,axiom,
! [A: product_prod_int_int,B: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( A != B )
=> ( ( member5262025264175285858nt_int @ A @ ( set_Pr2470121279949933262nt_int @ ( remove2588356790385189205nt_int @ B @ Xs ) ) )
= ( member5262025264175285858nt_int @ A @ ( set_Pr2470121279949933262nt_int @ Xs ) ) ) ) ).
% in_set_remove1
thf(fact_918_remove1_Osimps_I2_J,axiom,
! [X: product_prod_int_int,Y: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( ( X = Y )
=> ( ( remove2588356790385189205nt_int @ X @ ( cons_P3334398858971670639nt_int @ Y @ Xs ) )
= Xs ) )
& ( ( X != Y )
=> ( ( remove2588356790385189205nt_int @ X @ ( cons_P3334398858971670639nt_int @ Y @ Xs ) )
= ( cons_P3334398858971670639nt_int @ Y @ ( remove2588356790385189205nt_int @ X @ Xs ) ) ) ) ) ).
% remove1.simps(2)
thf(fact_919_remove1_Osimps_I1_J,axiom,
! [X: product_prod_int_int] :
( ( remove2588356790385189205nt_int @ X @ nil_Pr2300489316682597567nt_int )
= nil_Pr2300489316682597567nt_int ) ).
% remove1.simps(1)
thf(fact_920_remove1__idem,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ~ ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ( ( remove2588356790385189205nt_int @ X @ Xs )
= Xs ) ) ).
% remove1_idem
thf(fact_921_notin__set__remove1,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int,Y: product_prod_int_int] :
( ~ ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ~ ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ ( remove2588356790385189205nt_int @ Y @ Xs ) ) ) ) ).
% notin_set_remove1
thf(fact_922_distinct__remove1,axiom,
! [Xs: list_P5707943133018811711nt_int,X: product_prod_int_int] :
( ( distin3744728255968310194nt_int @ Xs )
=> ( distin3744728255968310194nt_int @ ( remove2588356790385189205nt_int @ X @ Xs ) ) ) ).
% distinct_remove1
thf(fact_923_remove1__append,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ( ( remove2588356790385189205nt_int @ X @ ( append7030698103840186580nt_int @ Xs @ Ys ) )
= ( append7030698103840186580nt_int @ ( remove2588356790385189205nt_int @ X @ Xs ) @ Ys ) ) )
& ( ~ ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ( ( remove2588356790385189205nt_int @ X @ ( append7030698103840186580nt_int @ Xs @ Ys ) )
= ( append7030698103840186580nt_int @ Xs @ ( remove2588356790385189205nt_int @ X @ Ys ) ) ) ) ) ).
% remove1_append
thf(fact_924_distinct__remove1__removeAll,axiom,
! [Xs: list_P5707943133018811711nt_int,X: product_prod_int_int] :
( ( distin3744728255968310194nt_int @ Xs )
=> ( ( remove2588356790385189205nt_int @ X @ Xs )
= ( remove494893200766290885nt_int @ X @ Xs ) ) ) ).
% distinct_remove1_removeAll
thf(fact_925_remove1__split,axiom,
! [A: product_prod_int_int,Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( member5262025264175285858nt_int @ A @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ( ( ( remove2588356790385189205nt_int @ A @ Xs )
= Ys )
= ( ? [Ls: list_P5707943133018811711nt_int,Rs: list_P5707943133018811711nt_int] :
( ( Xs
= ( append7030698103840186580nt_int @ Ls @ ( cons_P3334398858971670639nt_int @ A @ Rs ) ) )
& ~ ( member5262025264175285858nt_int @ A @ ( set_Pr2470121279949933262nt_int @ Ls ) )
& ( Ys
= ( append7030698103840186580nt_int @ Ls @ Rs ) ) ) ) ) ) ).
% remove1_split
thf(fact_926_Sup__fin_Oremove,axiom,
! [A3: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( member2340774599025711042nt_int @ X @ A3 )
=> ( ( ( ( minus_2612819937483484256nt_int @ A3 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
= bot_bo1488462491386950373nt_int )
=> ( ( lattic1237861848008701264nt_int @ A3 )
= X ) )
& ( ( ( minus_2612819937483484256nt_int @ A3 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
!= bot_bo1488462491386950373nt_int )
=> ( ( lattic1237861848008701264nt_int @ A3 )
= ( sup_su6024340866399070445nt_int @ X @ ( lattic1237861848008701264nt_int @ ( minus_2612819937483484256nt_int @ A3 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) ) ) ) ) ) ) ) ) ).
% Sup_fin.remove
thf(fact_927_Sup__fin_Oinsert__remove,axiom,
! [A3: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( ( ( minus_2612819937483484256nt_int @ A3 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
= bot_bo1488462491386950373nt_int )
=> ( ( lattic1237861848008701264nt_int @ ( insert8897473484851387113nt_int @ X @ A3 ) )
= X ) )
& ( ( ( minus_2612819937483484256nt_int @ A3 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
!= bot_bo1488462491386950373nt_int )
=> ( ( lattic1237861848008701264nt_int @ ( insert8897473484851387113nt_int @ X @ A3 ) )
= ( sup_su6024340866399070445nt_int @ X @ ( lattic1237861848008701264nt_int @ ( minus_2612819937483484256nt_int @ A3 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) ) ) ) ) ) ) ) ).
% Sup_fin.insert_remove
thf(fact_928_Inf__fin_Oremove,axiom,
! [A3: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( member2340774599025711042nt_int @ X @ A3 )
=> ( ( ( ( minus_2612819937483484256nt_int @ A3 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
= bot_bo1488462491386950373nt_int )
=> ( ( lattic8951152183982934710nt_int @ A3 )
= X ) )
& ( ( ( minus_2612819937483484256nt_int @ A3 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
!= bot_bo1488462491386950373nt_int )
=> ( ( lattic8951152183982934710nt_int @ A3 )
= ( inf_in2269163501485487111nt_int @ X @ ( lattic8951152183982934710nt_int @ ( minus_2612819937483484256nt_int @ A3 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) ) ) ) ) ) ) ) ) ).
% Inf_fin.remove
thf(fact_929_List_Ofinite__set,axiom,
! [Xs: list_P5707943133018811711nt_int] : ( finite2998713641127702882nt_int @ ( set_Pr2470121279949933262nt_int @ Xs ) ) ).
% List.finite_set
thf(fact_930_inf__Sup__absorb,axiom,
! [A3: set_se6260736226359567993nt_int,A: set_Pr958786334691620121nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( member2340774599025711042nt_int @ A @ A3 )
=> ( ( inf_in2269163501485487111nt_int @ A @ ( lattic1237861848008701264nt_int @ A3 ) )
= A ) ) ) ).
% inf_Sup_absorb
thf(fact_931_sup__Inf__absorb,axiom,
! [A3: set_se6260736226359567993nt_int,A: set_Pr958786334691620121nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( member2340774599025711042nt_int @ A @ A3 )
=> ( ( sup_su6024340866399070445nt_int @ ( lattic8951152183982934710nt_int @ A3 ) @ A )
= A ) ) ) ).
% sup_Inf_absorb
thf(fact_932_Inf__fin_Oinsert,axiom,
! [A3: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( A3 != bot_bo1488462491386950373nt_int )
=> ( ( lattic8951152183982934710nt_int @ ( insert8897473484851387113nt_int @ X @ A3 ) )
= ( inf_in2269163501485487111nt_int @ X @ ( lattic8951152183982934710nt_int @ A3 ) ) ) ) ) ).
% Inf_fin.insert
thf(fact_933_Sup__fin_Oinsert,axiom,
! [A3: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( A3 != bot_bo1488462491386950373nt_int )
=> ( ( lattic1237861848008701264nt_int @ ( insert8897473484851387113nt_int @ X @ A3 ) )
= ( sup_su6024340866399070445nt_int @ X @ ( lattic1237861848008701264nt_int @ A3 ) ) ) ) ) ).
% Sup_fin.insert
thf(fact_934_finite__list,axiom,
! [A3: set_Pr958786334691620121nt_int] :
( ( finite2998713641127702882nt_int @ A3 )
=> ? [Xs2: list_P5707943133018811711nt_int] :
( ( set_Pr2470121279949933262nt_int @ Xs2 )
= A3 ) ) ).
% finite_list
thf(fact_935_finite__distinct__list,axiom,
! [A3: set_Pr958786334691620121nt_int] :
( ( finite2998713641127702882nt_int @ A3 )
=> ? [Xs2: list_P5707943133018811711nt_int] :
( ( ( set_Pr2470121279949933262nt_int @ Xs2 )
= A3 )
& ( distin3744728255968310194nt_int @ Xs2 ) ) ) ).
% finite_distinct_list
thf(fact_936_Inf__fin_Oin__idem,axiom,
! [A3: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( member2340774599025711042nt_int @ X @ A3 )
=> ( ( inf_in2269163501485487111nt_int @ X @ ( lattic8951152183982934710nt_int @ A3 ) )
= ( lattic8951152183982934710nt_int @ A3 ) ) ) ) ).
% Inf_fin.in_idem
thf(fact_937_Sup__fin_Oin__idem,axiom,
! [A3: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( member2340774599025711042nt_int @ X @ A3 )
=> ( ( sup_su6024340866399070445nt_int @ X @ ( lattic1237861848008701264nt_int @ A3 ) )
= ( lattic1237861848008701264nt_int @ A3 ) ) ) ) ).
% Sup_fin.in_idem
thf(fact_938_Inf__fin_Ohom__commute,axiom,
! [H: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int,N: set_se6260736226359567993nt_int] :
( ! [X3: set_Pr958786334691620121nt_int,Y2: set_Pr958786334691620121nt_int] :
( ( H @ ( inf_in2269163501485487111nt_int @ X3 @ Y2 ) )
= ( inf_in2269163501485487111nt_int @ ( H @ X3 ) @ ( H @ Y2 ) ) )
=> ( ( finite8744585540193469122nt_int @ N )
=> ( ( N != bot_bo1488462491386950373nt_int )
=> ( ( H @ ( lattic8951152183982934710nt_int @ N ) )
= ( lattic8951152183982934710nt_int @ ( image_1544889507766666053nt_int @ H @ N ) ) ) ) ) ) ).
% Inf_fin.hom_commute
thf(fact_939_Sup__fin_Ohom__commute,axiom,
! [H: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int,N: set_se6260736226359567993nt_int] :
( ! [X3: set_Pr958786334691620121nt_int,Y2: set_Pr958786334691620121nt_int] :
( ( H @ ( sup_su6024340866399070445nt_int @ X3 @ Y2 ) )
= ( sup_su6024340866399070445nt_int @ ( H @ X3 ) @ ( H @ Y2 ) ) )
=> ( ( finite8744585540193469122nt_int @ N )
=> ( ( N != bot_bo1488462491386950373nt_int )
=> ( ( H @ ( lattic1237861848008701264nt_int @ N ) )
= ( lattic1237861848008701264nt_int @ ( image_1544889507766666053nt_int @ H @ N ) ) ) ) ) ) ).
% Sup_fin.hom_commute
thf(fact_940_Inf__fin_Oclosed,axiom,
! [A3: set_se6260736226359567993nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( A3 != bot_bo1488462491386950373nt_int )
=> ( ! [X3: set_Pr958786334691620121nt_int,Y2: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ ( inf_in2269163501485487111nt_int @ X3 @ Y2 ) @ ( insert8897473484851387113nt_int @ X3 @ ( insert8897473484851387113nt_int @ Y2 @ bot_bo1488462491386950373nt_int ) ) )
=> ( member2340774599025711042nt_int @ ( lattic8951152183982934710nt_int @ A3 ) @ A3 ) ) ) ) ).
% Inf_fin.closed
thf(fact_941_Inf__fin_Oinsert__not__elem,axiom,
! [A3: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ~ ( member2340774599025711042nt_int @ X @ A3 )
=> ( ( A3 != bot_bo1488462491386950373nt_int )
=> ( ( lattic8951152183982934710nt_int @ ( insert8897473484851387113nt_int @ X @ A3 ) )
= ( inf_in2269163501485487111nt_int @ X @ ( lattic8951152183982934710nt_int @ A3 ) ) ) ) ) ) ).
% Inf_fin.insert_not_elem
thf(fact_942_Sup__fin_Oinsert__not__elem,axiom,
! [A3: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ~ ( member2340774599025711042nt_int @ X @ A3 )
=> ( ( A3 != bot_bo1488462491386950373nt_int )
=> ( ( lattic1237861848008701264nt_int @ ( insert8897473484851387113nt_int @ X @ A3 ) )
= ( sup_su6024340866399070445nt_int @ X @ ( lattic1237861848008701264nt_int @ A3 ) ) ) ) ) ) ).
% Sup_fin.insert_not_elem
thf(fact_943_Sup__fin_Oclosed,axiom,
! [A3: set_se6260736226359567993nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( A3 != bot_bo1488462491386950373nt_int )
=> ( ! [X3: set_Pr958786334691620121nt_int,Y2: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ ( sup_su6024340866399070445nt_int @ X3 @ Y2 ) @ ( insert8897473484851387113nt_int @ X3 @ ( insert8897473484851387113nt_int @ Y2 @ bot_bo1488462491386950373nt_int ) ) )
=> ( member2340774599025711042nt_int @ ( lattic1237861848008701264nt_int @ A3 ) @ A3 ) ) ) ) ).
% Sup_fin.closed
thf(fact_944_Inf__fin_Ounion,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( A3 != bot_bo1488462491386950373nt_int )
=> ( ( finite8744585540193469122nt_int @ B4 )
=> ( ( B4 != bot_bo1488462491386950373nt_int )
=> ( ( lattic8951152183982934710nt_int @ ( sup_su2047564715030645325nt_int @ A3 @ B4 ) )
= ( inf_in2269163501485487111nt_int @ ( lattic8951152183982934710nt_int @ A3 ) @ ( lattic8951152183982934710nt_int @ B4 ) ) ) ) ) ) ) ).
% Inf_fin.union
thf(fact_945_Sup__fin_Ounion,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( A3 != bot_bo1488462491386950373nt_int )
=> ( ( finite8744585540193469122nt_int @ B4 )
=> ( ( B4 != bot_bo1488462491386950373nt_int )
=> ( ( lattic1237861848008701264nt_int @ ( sup_su2047564715030645325nt_int @ A3 @ B4 ) )
= ( sup_su6024340866399070445nt_int @ ( lattic1237861848008701264nt_int @ A3 ) @ ( lattic1237861848008701264nt_int @ B4 ) ) ) ) ) ) ) ).
% Sup_fin.union
thf(fact_946_Inf__fin_Oinsert__remove,axiom,
! [A3: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( ( ( minus_2612819937483484256nt_int @ A3 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
= bot_bo1488462491386950373nt_int )
=> ( ( lattic8951152183982934710nt_int @ ( insert8897473484851387113nt_int @ X @ A3 ) )
= X ) )
& ( ( ( minus_2612819937483484256nt_int @ A3 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
!= bot_bo1488462491386950373nt_int )
=> ( ( lattic8951152183982934710nt_int @ ( insert8897473484851387113nt_int @ X @ A3 ) )
= ( inf_in2269163501485487111nt_int @ X @ ( lattic8951152183982934710nt_int @ ( minus_2612819937483484256nt_int @ A3 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) ) ) ) ) ) ) ) ).
% Inf_fin.insert_remove
thf(fact_947_finite__Diff__insert,axiom,
! [A3: set_Pr958786334691620121nt_int,A: product_prod_int_int,B4: set_Pr958786334691620121nt_int] :
( ( finite2998713641127702882nt_int @ ( minus_1052850069191792384nt_int @ A3 @ ( insert5033312907999012233nt_int @ A @ B4 ) ) )
= ( finite2998713641127702882nt_int @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) ) ) ).
% finite_Diff_insert
thf(fact_948_finite__Diff2,axiom,
! [B4: set_Pr958786334691620121nt_int,A3: set_Pr958786334691620121nt_int] :
( ( finite2998713641127702882nt_int @ B4 )
=> ( ( finite2998713641127702882nt_int @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) )
= ( finite2998713641127702882nt_int @ A3 ) ) ) ).
% finite_Diff2
thf(fact_949_finite__Diff,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( finite2998713641127702882nt_int @ A3 )
=> ( finite2998713641127702882nt_int @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) ) ) ).
% finite_Diff
thf(fact_950_finite__Un,axiom,
! [F2: set_Pr958786334691620121nt_int,G: set_Pr958786334691620121nt_int] :
( ( finite2998713641127702882nt_int @ ( sup_su6024340866399070445nt_int @ F2 @ G ) )
= ( ( finite2998713641127702882nt_int @ F2 )
& ( finite2998713641127702882nt_int @ G ) ) ) ).
% finite_Un
thf(fact_951_finite__insert,axiom,
! [A: product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( finite2998713641127702882nt_int @ ( insert5033312907999012233nt_int @ A @ A3 ) )
= ( finite2998713641127702882nt_int @ A3 ) ) ).
% finite_insert
thf(fact_952_finite__Int,axiom,
! [F2: set_Pr958786334691620121nt_int,G: set_Pr958786334691620121nt_int] :
( ( ( finite2998713641127702882nt_int @ F2 )
| ( finite2998713641127702882nt_int @ G ) )
=> ( finite2998713641127702882nt_int @ ( inf_in2269163501485487111nt_int @ F2 @ G ) ) ) ).
% finite_Int
thf(fact_953_finite_OemptyI,axiom,
finite2998713641127702882nt_int @ bot_bo1796632182523588997nt_int ).
% finite.emptyI
thf(fact_954_infinite__imp__nonempty,axiom,
! [S: set_Pr958786334691620121nt_int] :
( ~ ( finite2998713641127702882nt_int @ S )
=> ( S != bot_bo1796632182523588997nt_int ) ) ).
% infinite_imp_nonempty
thf(fact_955_finite_OinsertI,axiom,
! [A3: set_Pr958786334691620121nt_int,A: product_prod_int_int] :
( ( finite2998713641127702882nt_int @ A3 )
=> ( finite2998713641127702882nt_int @ ( insert5033312907999012233nt_int @ A @ A3 ) ) ) ).
% finite.insertI
thf(fact_956_infinite__Un,axiom,
! [S: set_Pr958786334691620121nt_int,T: set_Pr958786334691620121nt_int] :
( ( ~ ( finite2998713641127702882nt_int @ ( sup_su6024340866399070445nt_int @ S @ T ) ) )
= ( ~ ( finite2998713641127702882nt_int @ S )
| ~ ( finite2998713641127702882nt_int @ T ) ) ) ).
% infinite_Un
thf(fact_957_Un__infinite,axiom,
! [S: set_Pr958786334691620121nt_int,T: set_Pr958786334691620121nt_int] :
( ~ ( finite2998713641127702882nt_int @ S )
=> ~ ( finite2998713641127702882nt_int @ ( sup_su6024340866399070445nt_int @ S @ T ) ) ) ).
% Un_infinite
thf(fact_958_finite__UnI,axiom,
! [F2: set_Pr958786334691620121nt_int,G: set_Pr958786334691620121nt_int] :
( ( finite2998713641127702882nt_int @ F2 )
=> ( ( finite2998713641127702882nt_int @ G )
=> ( finite2998713641127702882nt_int @ ( sup_su6024340866399070445nt_int @ F2 @ G ) ) ) ) ).
% finite_UnI
thf(fact_959_Diff__infinite__finite,axiom,
! [T: set_Pr958786334691620121nt_int,S: set_Pr958786334691620121nt_int] :
( ( finite2998713641127702882nt_int @ T )
=> ( ~ ( finite2998713641127702882nt_int @ S )
=> ~ ( finite2998713641127702882nt_int @ ( minus_1052850069191792384nt_int @ S @ T ) ) ) ) ).
% Diff_infinite_finite
thf(fact_960_infinite__finite__induct,axiom,
! [P: set_Pr958786334691620121nt_int > $o,A3: set_Pr958786334691620121nt_int] :
( ! [A7: set_Pr958786334691620121nt_int] :
( ~ ( finite2998713641127702882nt_int @ A7 )
=> ( P @ A7 ) )
=> ( ( P @ bot_bo1796632182523588997nt_int )
=> ( ! [X3: product_prod_int_int,F3: set_Pr958786334691620121nt_int] :
( ( finite2998713641127702882nt_int @ F3 )
=> ( ~ ( member5262025264175285858nt_int @ X3 @ F3 )
=> ( ( P @ F3 )
=> ( P @ ( insert5033312907999012233nt_int @ X3 @ F3 ) ) ) ) )
=> ( P @ A3 ) ) ) ) ).
% infinite_finite_induct
thf(fact_961_finite__ne__induct,axiom,
! [F2: set_Pr958786334691620121nt_int,P: set_Pr958786334691620121nt_int > $o] :
( ( finite2998713641127702882nt_int @ F2 )
=> ( ( F2 != bot_bo1796632182523588997nt_int )
=> ( ! [X3: product_prod_int_int] : ( P @ ( insert5033312907999012233nt_int @ X3 @ bot_bo1796632182523588997nt_int ) )
=> ( ! [X3: product_prod_int_int,F3: set_Pr958786334691620121nt_int] :
( ( finite2998713641127702882nt_int @ F3 )
=> ( ( F3 != bot_bo1796632182523588997nt_int )
=> ( ~ ( member5262025264175285858nt_int @ X3 @ F3 )
=> ( ( P @ F3 )
=> ( P @ ( insert5033312907999012233nt_int @ X3 @ F3 ) ) ) ) ) )
=> ( P @ F2 ) ) ) ) ) ).
% finite_ne_induct
thf(fact_962_finite__induct,axiom,
! [F2: set_Pr958786334691620121nt_int,P: set_Pr958786334691620121nt_int > $o] :
( ( finite2998713641127702882nt_int @ F2 )
=> ( ( P @ bot_bo1796632182523588997nt_int )
=> ( ! [X3: product_prod_int_int,F3: set_Pr958786334691620121nt_int] :
( ( finite2998713641127702882nt_int @ F3 )
=> ( ~ ( member5262025264175285858nt_int @ X3 @ F3 )
=> ( ( P @ F3 )
=> ( P @ ( insert5033312907999012233nt_int @ X3 @ F3 ) ) ) ) )
=> ( P @ F2 ) ) ) ) ).
% finite_induct
thf(fact_963_finite_Osimps,axiom,
( finite2998713641127702882nt_int
= ( ^ [A5: set_Pr958786334691620121nt_int] :
( ( A5 = bot_bo1796632182523588997nt_int )
| ? [A4: set_Pr958786334691620121nt_int,B2: product_prod_int_int] :
( ( A5
= ( insert5033312907999012233nt_int @ B2 @ A4 ) )
& ( finite2998713641127702882nt_int @ A4 ) ) ) ) ) ).
% finite.simps
thf(fact_964_finite_Ocases,axiom,
! [A: set_Pr958786334691620121nt_int] :
( ( finite2998713641127702882nt_int @ A )
=> ( ( A != bot_bo1796632182523588997nt_int )
=> ~ ! [A7: set_Pr958786334691620121nt_int] :
( ? [A6: product_prod_int_int] :
( A
= ( insert5033312907999012233nt_int @ A6 @ A7 ) )
=> ~ ( finite2998713641127702882nt_int @ A7 ) ) ) ) ).
% finite.cases
thf(fact_965_infinite__remove,axiom,
! [S: set_Pr958786334691620121nt_int,A: product_prod_int_int] :
( ~ ( finite2998713641127702882nt_int @ S )
=> ~ ( finite2998713641127702882nt_int @ ( minus_1052850069191792384nt_int @ S @ ( insert5033312907999012233nt_int @ A @ bot_bo1796632182523588997nt_int ) ) ) ) ).
% infinite_remove
thf(fact_966_infinite__coinduct,axiom,
! [X5: set_Pr958786334691620121nt_int > $o,A3: set_Pr958786334691620121nt_int] :
( ( X5 @ A3 )
=> ( ! [A7: set_Pr958786334691620121nt_int] :
( ( X5 @ A7 )
=> ? [X4: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X4 @ A7 )
& ( ( X5 @ ( minus_1052850069191792384nt_int @ A7 @ ( insert5033312907999012233nt_int @ X4 @ bot_bo1796632182523588997nt_int ) ) )
| ~ ( finite2998713641127702882nt_int @ ( minus_1052850069191792384nt_int @ A7 @ ( insert5033312907999012233nt_int @ X4 @ bot_bo1796632182523588997nt_int ) ) ) ) ) )
=> ~ ( finite2998713641127702882nt_int @ A3 ) ) ) ).
% infinite_coinduct
thf(fact_967_finite__empty__induct,axiom,
! [A3: set_Pr958786334691620121nt_int,P: set_Pr958786334691620121nt_int > $o] :
( ( finite2998713641127702882nt_int @ A3 )
=> ( ( P @ A3 )
=> ( ! [A6: product_prod_int_int,A7: set_Pr958786334691620121nt_int] :
( ( finite2998713641127702882nt_int @ A7 )
=> ( ( member5262025264175285858nt_int @ A6 @ A7 )
=> ( ( P @ A7 )
=> ( P @ ( minus_1052850069191792384nt_int @ A7 @ ( insert5033312907999012233nt_int @ A6 @ bot_bo1796632182523588997nt_int ) ) ) ) ) )
=> ( P @ bot_bo1796632182523588997nt_int ) ) ) ) ).
% finite_empty_induct
thf(fact_968_min__bot,axiom,
! [X: set_Pr958786334691620121nt_int] :
( ( ord_mi3891036259616950784nt_int @ bot_bo1796632182523588997nt_int @ X )
= bot_bo1796632182523588997nt_int ) ).
% min_bot
thf(fact_969_min__bot2,axiom,
! [X: set_Pr958786334691620121nt_int] :
( ( ord_mi3891036259616950784nt_int @ X @ bot_bo1796632182523588997nt_int )
= bot_bo1796632182523588997nt_int ) ).
% min_bot2
thf(fact_970_Inf__fin__le__Sup__fin,axiom,
! [A3: set_se6260736226359567993nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( A3 != bot_bo1488462491386950373nt_int )
=> ( ord_le2843351958646193337nt_int @ ( lattic8951152183982934710nt_int @ A3 ) @ ( lattic1237861848008701264nt_int @ A3 ) ) ) ) ).
% Inf_fin_le_Sup_fin
thf(fact_971_order__refl,axiom,
! [X: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ X @ X ) ).
% order_refl
thf(fact_972_dual__order_Orefl,axiom,
! [A: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ A @ A ) ).
% dual_order.refl
thf(fact_973_subset__empty,axiom,
! [A3: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ bot_bo1796632182523588997nt_int )
= ( A3 = bot_bo1796632182523588997nt_int ) ) ).
% subset_empty
thf(fact_974_empty__subsetI,axiom,
! [A3: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ bot_bo1796632182523588997nt_int @ A3 ) ).
% empty_subsetI
thf(fact_975_insert__subset,axiom,
! [X: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ ( insert5033312907999012233nt_int @ X @ A3 ) @ B4 )
= ( ( member5262025264175285858nt_int @ X @ B4 )
& ( ord_le2843351958646193337nt_int @ A3 @ B4 ) ) ) ).
% insert_subset
thf(fact_976_Int__subset__iff,axiom,
! [C2: set_Pr958786334691620121nt_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ C2 @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) )
= ( ( ord_le2843351958646193337nt_int @ C2 @ A3 )
& ( ord_le2843351958646193337nt_int @ C2 @ B4 ) ) ) ).
% Int_subset_iff
thf(fact_977_Un__subset__iff,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ ( sup_su6024340866399070445nt_int @ A3 @ B4 ) @ C2 )
= ( ( ord_le2843351958646193337nt_int @ A3 @ C2 )
& ( ord_le2843351958646193337nt_int @ B4 @ C2 ) ) ) ).
% Un_subset_iff
thf(fact_978_le__inf__iff,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X @ ( inf_in2269163501485487111nt_int @ Y @ Z ) )
= ( ( ord_le2843351958646193337nt_int @ X @ Y )
& ( ord_le2843351958646193337nt_int @ X @ Z ) ) ) ).
% le_inf_iff
thf(fact_979_inf_Obounded__iff,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A @ ( inf_in2269163501485487111nt_int @ B @ C ) )
= ( ( ord_le2843351958646193337nt_int @ A @ B )
& ( ord_le2843351958646193337nt_int @ A @ C ) ) ) ).
% inf.bounded_iff
thf(fact_980_le__sup__iff,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ ( sup_su6024340866399070445nt_int @ X @ Y ) @ Z )
= ( ( ord_le2843351958646193337nt_int @ X @ Z )
& ( ord_le2843351958646193337nt_int @ Y @ Z ) ) ) ).
% le_sup_iff
thf(fact_981_sup_Obounded__iff,axiom,
! [B: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ ( sup_su6024340866399070445nt_int @ B @ C ) @ A )
= ( ( ord_le2843351958646193337nt_int @ B @ A )
& ( ord_le2843351958646193337nt_int @ C @ A ) ) ) ).
% sup.bounded_iff
thf(fact_982_singleton__insert__inj__eq_H,axiom,
! [A: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B: product_prod_int_int] :
( ( ( insert5033312907999012233nt_int @ A @ A3 )
= ( insert5033312907999012233nt_int @ B @ bot_bo1796632182523588997nt_int ) )
= ( ( A = B )
& ( ord_le2843351958646193337nt_int @ A3 @ ( insert5033312907999012233nt_int @ B @ bot_bo1796632182523588997nt_int ) ) ) ) ).
% singleton_insert_inj_eq'
thf(fact_983_singleton__insert__inj__eq,axiom,
! [B: product_prod_int_int,A: product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( ( insert5033312907999012233nt_int @ B @ bot_bo1796632182523588997nt_int )
= ( insert5033312907999012233nt_int @ A @ A3 ) )
= ( ( A = B )
& ( ord_le2843351958646193337nt_int @ A3 @ ( insert5033312907999012233nt_int @ B @ bot_bo1796632182523588997nt_int ) ) ) ) ).
% singleton_insert_inj_eq
thf(fact_984_Diff__eq__empty__iff,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ( minus_1052850069191792384nt_int @ A3 @ B4 )
= bot_bo1796632182523588997nt_int )
= ( ord_le2843351958646193337nt_int @ A3 @ B4 ) ) ).
% Diff_eq_empty_iff
thf(fact_985_min__absorb2,axiom,
! [Y: set_Pr958786334691620121nt_int,X: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ Y @ X )
=> ( ( ord_mi3891036259616950784nt_int @ X @ Y )
= Y ) ) ).
% min_absorb2
thf(fact_986_min__absorb1,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X @ Y )
=> ( ( ord_mi3891036259616950784nt_int @ X @ Y )
= X ) ) ).
% min_absorb1
thf(fact_987_min__def,axiom,
( ord_mi3891036259616950784nt_int
= ( ^ [A5: set_Pr958786334691620121nt_int,B2: set_Pr958786334691620121nt_int] : ( if_set4441254072200386271nt_int @ ( ord_le2843351958646193337nt_int @ A5 @ B2 ) @ A5 @ B2 ) ) ) ).
% min_def
thf(fact_988_Inf__fin_Osubset__imp,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( ord_le483042692224249369nt_int @ A3 @ B4 )
=> ( ( A3 != bot_bo1488462491386950373nt_int )
=> ( ( finite8744585540193469122nt_int @ B4 )
=> ( ord_le2843351958646193337nt_int @ ( lattic8951152183982934710nt_int @ B4 ) @ ( lattic8951152183982934710nt_int @ A3 ) ) ) ) ) ).
% Inf_fin.subset_imp
thf(fact_989_Sup__fin_Osubset__imp,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( ord_le483042692224249369nt_int @ A3 @ B4 )
=> ( ( A3 != bot_bo1488462491386950373nt_int )
=> ( ( finite8744585540193469122nt_int @ B4 )
=> ( ord_le2843351958646193337nt_int @ ( lattic1237861848008701264nt_int @ A3 ) @ ( lattic1237861848008701264nt_int @ B4 ) ) ) ) ) ).
% Sup_fin.subset_imp
thf(fact_990_subset__image__iff,axiom,
! [B4: set_Pr958786334691620121nt_int,F: product_prod_int_int > product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ B4 @ ( image_2653370878348428101nt_int @ F @ A3 ) )
= ( ? [AA: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ AA @ A3 )
& ( B4
= ( image_2653370878348428101nt_int @ F @ AA ) ) ) ) ) ).
% subset_image_iff
thf(fact_991_subset__imageE,axiom,
! [B4: set_Pr958786334691620121nt_int,F: product_prod_int_int > product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ B4 @ ( image_2653370878348428101nt_int @ F @ A3 ) )
=> ~ ! [C4: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ C4 @ A3 )
=> ( B4
!= ( image_2653370878348428101nt_int @ F @ C4 ) ) ) ) ).
% subset_imageE
thf(fact_992_image__subsetI,axiom,
! [A3: set_Pr958786334691620121nt_int,F: product_prod_int_int > product_prod_int_int,B4: set_Pr958786334691620121nt_int] :
( ! [X3: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X3 @ A3 )
=> ( member5262025264175285858nt_int @ ( F @ X3 ) @ B4 ) )
=> ( ord_le2843351958646193337nt_int @ ( image_2653370878348428101nt_int @ F @ A3 ) @ B4 ) ) ).
% image_subsetI
thf(fact_993_image__mono,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,F: product_prod_int_int > product_prod_int_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ B4 )
=> ( ord_le2843351958646193337nt_int @ ( image_2653370878348428101nt_int @ F @ A3 ) @ ( image_2653370878348428101nt_int @ F @ B4 ) ) ) ).
% image_mono
thf(fact_994_pairwise__subset,axiom,
! [P: product_prod_int_int > product_prod_int_int > $o,S: set_Pr958786334691620121nt_int,T: set_Pr958786334691620121nt_int] :
( ( pairwi3178678004212613796nt_int @ P @ S )
=> ( ( ord_le2843351958646193337nt_int @ T @ S )
=> ( pairwi3178678004212613796nt_int @ P @ T ) ) ) ).
% pairwise_subset
thf(fact_995_pairwise__mono,axiom,
! [P: product_prod_int_int > product_prod_int_int > $o,A3: set_Pr958786334691620121nt_int,Q: product_prod_int_int > product_prod_int_int > $o,B4: set_Pr958786334691620121nt_int] :
( ( pairwi3178678004212613796nt_int @ P @ A3 )
=> ( ! [X3: product_prod_int_int,Y2: product_prod_int_int] :
( ( P @ X3 @ Y2 )
=> ( Q @ X3 @ Y2 ) )
=> ( ( ord_le2843351958646193337nt_int @ B4 @ A3 )
=> ( pairwi3178678004212613796nt_int @ Q @ B4 ) ) ) ) ).
% pairwise_mono
thf(fact_996_sup_OcoboundedI2,axiom,
! [C: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ C @ B )
=> ( ord_le2843351958646193337nt_int @ C @ ( sup_su6024340866399070445nt_int @ A @ B ) ) ) ).
% sup.coboundedI2
thf(fact_997_sup_OcoboundedI1,axiom,
! [C: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ C @ A )
=> ( ord_le2843351958646193337nt_int @ C @ ( sup_su6024340866399070445nt_int @ A @ B ) ) ) ).
% sup.coboundedI1
thf(fact_998_sup_Oabsorb__iff2,axiom,
( ord_le2843351958646193337nt_int
= ( ^ [A5: set_Pr958786334691620121nt_int,B2: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ A5 @ B2 )
= B2 ) ) ) ).
% sup.absorb_iff2
thf(fact_999_sup_Oabsorb__iff1,axiom,
( ord_le2843351958646193337nt_int
= ( ^ [B2: set_Pr958786334691620121nt_int,A5: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ A5 @ B2 )
= A5 ) ) ) ).
% sup.absorb_iff1
thf(fact_1000_sup_Ocobounded2,axiom,
! [B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ B @ ( sup_su6024340866399070445nt_int @ A @ B ) ) ).
% sup.cobounded2
thf(fact_1001_sup_Ocobounded1,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ A @ ( sup_su6024340866399070445nt_int @ A @ B ) ) ).
% sup.cobounded1
thf(fact_1002_sup_Oorder__iff,axiom,
( ord_le2843351958646193337nt_int
= ( ^ [B2: set_Pr958786334691620121nt_int,A5: set_Pr958786334691620121nt_int] :
( A5
= ( sup_su6024340866399070445nt_int @ A5 @ B2 ) ) ) ) ).
% sup.order_iff
thf(fact_1003_sup_OboundedI,axiom,
! [B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ B @ A )
=> ( ( ord_le2843351958646193337nt_int @ C @ A )
=> ( ord_le2843351958646193337nt_int @ ( sup_su6024340866399070445nt_int @ B @ C ) @ A ) ) ) ).
% sup.boundedI
thf(fact_1004_sup_OboundedE,axiom,
! [B: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ ( sup_su6024340866399070445nt_int @ B @ C ) @ A )
=> ~ ( ( ord_le2843351958646193337nt_int @ B @ A )
=> ~ ( ord_le2843351958646193337nt_int @ C @ A ) ) ) ).
% sup.boundedE
thf(fact_1005_sup__absorb2,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X @ Y )
=> ( ( sup_su6024340866399070445nt_int @ X @ Y )
= Y ) ) ).
% sup_absorb2
thf(fact_1006_sup__absorb1,axiom,
! [Y: set_Pr958786334691620121nt_int,X: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ Y @ X )
=> ( ( sup_su6024340866399070445nt_int @ X @ Y )
= X ) ) ).
% sup_absorb1
thf(fact_1007_sup_Oabsorb2,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A @ B )
=> ( ( sup_su6024340866399070445nt_int @ A @ B )
= B ) ) ).
% sup.absorb2
thf(fact_1008_sup_Oabsorb1,axiom,
! [B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ B @ A )
=> ( ( sup_su6024340866399070445nt_int @ A @ B )
= A ) ) ).
% sup.absorb1
thf(fact_1009_sup__unique,axiom,
! [F: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int,X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ! [X3: set_Pr958786334691620121nt_int,Y2: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ X3 @ ( F @ X3 @ Y2 ) )
=> ( ! [X3: set_Pr958786334691620121nt_int,Y2: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ Y2 @ ( F @ X3 @ Y2 ) )
=> ( ! [X3: set_Pr958786334691620121nt_int,Y2: set_Pr958786334691620121nt_int,Z2: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ Y2 @ X3 )
=> ( ( ord_le2843351958646193337nt_int @ Z2 @ X3 )
=> ( ord_le2843351958646193337nt_int @ ( F @ Y2 @ Z2 ) @ X3 ) ) )
=> ( ( sup_su6024340866399070445nt_int @ X @ Y )
= ( F @ X @ Y ) ) ) ) ) ).
% sup_unique
thf(fact_1010_sup_OorderI,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( A
= ( sup_su6024340866399070445nt_int @ A @ B ) )
=> ( ord_le2843351958646193337nt_int @ B @ A ) ) ).
% sup.orderI
thf(fact_1011_sup_OorderE,axiom,
! [B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ B @ A )
=> ( A
= ( sup_su6024340866399070445nt_int @ A @ B ) ) ) ).
% sup.orderE
thf(fact_1012_le__iff__sup,axiom,
( ord_le2843351958646193337nt_int
= ( ^ [X2: set_Pr958786334691620121nt_int,Y3: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ X2 @ Y3 )
= Y3 ) ) ) ).
% le_iff_sup
thf(fact_1013_sup__least,axiom,
! [Y: set_Pr958786334691620121nt_int,X: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ Y @ X )
=> ( ( ord_le2843351958646193337nt_int @ Z @ X )
=> ( ord_le2843351958646193337nt_int @ ( sup_su6024340866399070445nt_int @ Y @ Z ) @ X ) ) ) ).
% sup_least
thf(fact_1014_sup__mono,axiom,
! [A: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,D: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A @ C )
=> ( ( ord_le2843351958646193337nt_int @ B @ D )
=> ( ord_le2843351958646193337nt_int @ ( sup_su6024340866399070445nt_int @ A @ B ) @ ( sup_su6024340866399070445nt_int @ C @ D ) ) ) ) ).
% sup_mono
thf(fact_1015_sup_Omono,axiom,
! [C: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int,D: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ C @ A )
=> ( ( ord_le2843351958646193337nt_int @ D @ B )
=> ( ord_le2843351958646193337nt_int @ ( sup_su6024340866399070445nt_int @ C @ D ) @ ( sup_su6024340866399070445nt_int @ A @ B ) ) ) ) ).
% sup.mono
thf(fact_1016_le__supI2,axiom,
! [X: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X @ B )
=> ( ord_le2843351958646193337nt_int @ X @ ( sup_su6024340866399070445nt_int @ A @ B ) ) ) ).
% le_supI2
thf(fact_1017_le__supI1,axiom,
! [X: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X @ A )
=> ( ord_le2843351958646193337nt_int @ X @ ( sup_su6024340866399070445nt_int @ A @ B ) ) ) ).
% le_supI1
thf(fact_1018_sup__ge2,axiom,
! [Y: set_Pr958786334691620121nt_int,X: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ Y @ ( sup_su6024340866399070445nt_int @ X @ Y ) ) ).
% sup_ge2
thf(fact_1019_sup__ge1,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ X @ ( sup_su6024340866399070445nt_int @ X @ Y ) ) ).
% sup_ge1
thf(fact_1020_le__supI,axiom,
! [A: set_Pr958786334691620121nt_int,X: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A @ X )
=> ( ( ord_le2843351958646193337nt_int @ B @ X )
=> ( ord_le2843351958646193337nt_int @ ( sup_su6024340866399070445nt_int @ A @ B ) @ X ) ) ) ).
% le_supI
thf(fact_1021_le__supE,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,X: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ ( sup_su6024340866399070445nt_int @ A @ B ) @ X )
=> ~ ( ( ord_le2843351958646193337nt_int @ A @ X )
=> ~ ( ord_le2843351958646193337nt_int @ B @ X ) ) ) ).
% le_supE
thf(fact_1022_inf__sup__ord_I3_J,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ X @ ( sup_su6024340866399070445nt_int @ X @ Y ) ) ).
% inf_sup_ord(3)
thf(fact_1023_inf__sup__ord_I4_J,axiom,
! [Y: set_Pr958786334691620121nt_int,X: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ Y @ ( sup_su6024340866399070445nt_int @ X @ Y ) ) ).
% inf_sup_ord(4)
thf(fact_1024_subset__Un__eq,axiom,
( ord_le2843351958646193337nt_int
= ( ^ [A4: set_Pr958786334691620121nt_int,B5: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ A4 @ B5 )
= B5 ) ) ) ).
% subset_Un_eq
thf(fact_1025_subset__UnE,axiom,
! [C2: set_Pr958786334691620121nt_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ C2 @ ( sup_su6024340866399070445nt_int @ A3 @ B4 ) )
=> ~ ! [A8: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A8 @ A3 )
=> ! [B7: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ B7 @ B4 )
=> ( C2
!= ( sup_su6024340866399070445nt_int @ A8 @ B7 ) ) ) ) ) ).
% subset_UnE
thf(fact_1026_Un__absorb2,axiom,
! [B4: set_Pr958786334691620121nt_int,A3: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ B4 @ A3 )
=> ( ( sup_su6024340866399070445nt_int @ A3 @ B4 )
= A3 ) ) ).
% Un_absorb2
thf(fact_1027_Un__absorb1,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ B4 )
=> ( ( sup_su6024340866399070445nt_int @ A3 @ B4 )
= B4 ) ) ).
% Un_absorb1
thf(fact_1028_Un__upper2,axiom,
! [B4: set_Pr958786334691620121nt_int,A3: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ B4 @ ( sup_su6024340866399070445nt_int @ A3 @ B4 ) ) ).
% Un_upper2
thf(fact_1029_Un__upper1,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ A3 @ ( sup_su6024340866399070445nt_int @ A3 @ B4 ) ) ).
% Un_upper1
thf(fact_1030_Un__least,axiom,
! [A3: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ C2 )
=> ( ( ord_le2843351958646193337nt_int @ B4 @ C2 )
=> ( ord_le2843351958646193337nt_int @ ( sup_su6024340866399070445nt_int @ A3 @ B4 ) @ C2 ) ) ) ).
% Un_least
thf(fact_1031_Un__mono,axiom,
! [A3: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,D2: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ C2 )
=> ( ( ord_le2843351958646193337nt_int @ B4 @ D2 )
=> ( ord_le2843351958646193337nt_int @ ( sup_su6024340866399070445nt_int @ A3 @ B4 ) @ ( sup_su6024340866399070445nt_int @ C2 @ D2 ) ) ) ) ).
% Un_mono
thf(fact_1032_lists__mono,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ B4 )
=> ( ord_le6386220896155801791nt_int @ ( lists_9111190511995884973nt_int @ A3 ) @ ( lists_9111190511995884973nt_int @ B4 ) ) ) ).
% lists_mono
thf(fact_1033_order__class_Oorder__eq__iff,axiom,
( ( ^ [Y4: set_Pr958786334691620121nt_int,Z3: set_Pr958786334691620121nt_int] : ( Y4 = Z3 ) )
= ( ^ [X2: set_Pr958786334691620121nt_int,Y3: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X2 @ Y3 )
& ( ord_le2843351958646193337nt_int @ Y3 @ X2 ) ) ) ) ).
% order_class.order_eq_iff
thf(fact_1034_ord__eq__le__trans,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int] :
( ( A = B )
=> ( ( ord_le2843351958646193337nt_int @ B @ C )
=> ( ord_le2843351958646193337nt_int @ A @ C ) ) ) ).
% ord_eq_le_trans
thf(fact_1035_ord__le__eq__trans,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A @ B )
=> ( ( B = C )
=> ( ord_le2843351958646193337nt_int @ A @ C ) ) ) ).
% ord_le_eq_trans
thf(fact_1036_order__antisym,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X @ Y )
=> ( ( ord_le2843351958646193337nt_int @ Y @ X )
=> ( X = Y ) ) ) ).
% order_antisym
thf(fact_1037_order_Otrans,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A @ B )
=> ( ( ord_le2843351958646193337nt_int @ B @ C )
=> ( ord_le2843351958646193337nt_int @ A @ C ) ) ) ).
% order.trans
thf(fact_1038_order__trans,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X @ Y )
=> ( ( ord_le2843351958646193337nt_int @ Y @ Z )
=> ( ord_le2843351958646193337nt_int @ X @ Z ) ) ) ).
% order_trans
thf(fact_1039_dual__order_Oeq__iff,axiom,
( ( ^ [Y4: set_Pr958786334691620121nt_int,Z3: set_Pr958786334691620121nt_int] : ( Y4 = Z3 ) )
= ( ^ [A5: set_Pr958786334691620121nt_int,B2: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ B2 @ A5 )
& ( ord_le2843351958646193337nt_int @ A5 @ B2 ) ) ) ) ).
% dual_order.eq_iff
thf(fact_1040_dual__order_Oantisym,axiom,
! [B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ B @ A )
=> ( ( ord_le2843351958646193337nt_int @ A @ B )
=> ( A = B ) ) ) ).
% dual_order.antisym
thf(fact_1041_dual__order_Otrans,axiom,
! [B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ B @ A )
=> ( ( ord_le2843351958646193337nt_int @ C @ B )
=> ( ord_le2843351958646193337nt_int @ C @ A ) ) ) ).
% dual_order.trans
thf(fact_1042_antisym,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A @ B )
=> ( ( ord_le2843351958646193337nt_int @ B @ A )
=> ( A = B ) ) ) ).
% antisym
thf(fact_1043_Orderings_Oorder__eq__iff,axiom,
( ( ^ [Y4: set_Pr958786334691620121nt_int,Z3: set_Pr958786334691620121nt_int] : ( Y4 = Z3 ) )
= ( ^ [A5: set_Pr958786334691620121nt_int,B2: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A5 @ B2 )
& ( ord_le2843351958646193337nt_int @ B2 @ A5 ) ) ) ) ).
% Orderings.order_eq_iff
thf(fact_1044_order__subst1,axiom,
! [A: set_Pr958786334691620121nt_int,F: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A @ ( F @ B ) )
=> ( ( ord_le2843351958646193337nt_int @ B @ C )
=> ( ! [X3: set_Pr958786334691620121nt_int,Y2: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X3 @ Y2 )
=> ( ord_le2843351958646193337nt_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
=> ( ord_le2843351958646193337nt_int @ A @ ( F @ C ) ) ) ) ) ).
% order_subst1
thf(fact_1045_order__subst2,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,F: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A @ B )
=> ( ( ord_le2843351958646193337nt_int @ ( F @ B ) @ C )
=> ( ! [X3: set_Pr958786334691620121nt_int,Y2: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X3 @ Y2 )
=> ( ord_le2843351958646193337nt_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
=> ( ord_le2843351958646193337nt_int @ ( F @ A ) @ C ) ) ) ) ).
% order_subst2
thf(fact_1046_order__eq__refl,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ( X = Y )
=> ( ord_le2843351958646193337nt_int @ X @ Y ) ) ).
% order_eq_refl
thf(fact_1047_ord__eq__le__subst,axiom,
! [A: set_Pr958786334691620121nt_int,F: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int] :
( ( A
= ( F @ B ) )
=> ( ( ord_le2843351958646193337nt_int @ B @ C )
=> ( ! [X3: set_Pr958786334691620121nt_int,Y2: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X3 @ Y2 )
=> ( ord_le2843351958646193337nt_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
=> ( ord_le2843351958646193337nt_int @ A @ ( F @ C ) ) ) ) ) ).
% ord_eq_le_subst
thf(fact_1048_ord__le__eq__subst,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,F: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A @ B )
=> ( ( ( F @ B )
= C )
=> ( ! [X3: set_Pr958786334691620121nt_int,Y2: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X3 @ Y2 )
=> ( ord_le2843351958646193337nt_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
=> ( ord_le2843351958646193337nt_int @ ( F @ A ) @ C ) ) ) ) ).
% ord_le_eq_subst
thf(fact_1049_order__antisym__conv,axiom,
! [Y: set_Pr958786334691620121nt_int,X: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ Y @ X )
=> ( ( ord_le2843351958646193337nt_int @ X @ Y )
= ( X = Y ) ) ) ).
% order_antisym_conv
thf(fact_1050_Diff__mono,axiom,
! [A3: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int,D2: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ C2 )
=> ( ( ord_le2843351958646193337nt_int @ D2 @ B4 )
=> ( ord_le2843351958646193337nt_int @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) @ ( minus_1052850069191792384nt_int @ C2 @ D2 ) ) ) ) ).
% Diff_mono
thf(fact_1051_Diff__subset,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) @ A3 ) ).
% Diff_subset
thf(fact_1052_double__diff,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ B4 )
=> ( ( ord_le2843351958646193337nt_int @ B4 @ C2 )
=> ( ( minus_1052850069191792384nt_int @ B4 @ ( minus_1052850069191792384nt_int @ C2 @ A3 ) )
= A3 ) ) ) ).
% double_diff
thf(fact_1053_subset__code_I1_J,axiom,
! [Xs: list_P5707943133018811711nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ ( set_Pr2470121279949933262nt_int @ Xs ) @ B4 )
= ( ! [X2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X2 @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ( member5262025264175285858nt_int @ X2 @ B4 ) ) ) ) ).
% subset_code(1)
thf(fact_1054_insert__mono,axiom,
! [C2: set_Pr958786334691620121nt_int,D2: set_Pr958786334691620121nt_int,A: product_prod_int_int] :
( ( ord_le2843351958646193337nt_int @ C2 @ D2 )
=> ( ord_le2843351958646193337nt_int @ ( insert5033312907999012233nt_int @ A @ C2 ) @ ( insert5033312907999012233nt_int @ A @ D2 ) ) ) ).
% insert_mono
thf(fact_1055_subset__insert,axiom,
! [X: product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ~ ( member5262025264175285858nt_int @ X @ A3 )
=> ( ( ord_le2843351958646193337nt_int @ A3 @ ( insert5033312907999012233nt_int @ X @ B4 ) )
= ( ord_le2843351958646193337nt_int @ A3 @ B4 ) ) ) ).
% subset_insert
thf(fact_1056_subset__insertI,axiom,
! [B4: set_Pr958786334691620121nt_int,A: product_prod_int_int] : ( ord_le2843351958646193337nt_int @ B4 @ ( insert5033312907999012233nt_int @ A @ B4 ) ) ).
% subset_insertI
thf(fact_1057_subset__insertI2,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,B: product_prod_int_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ B4 )
=> ( ord_le2843351958646193337nt_int @ A3 @ ( insert5033312907999012233nt_int @ B @ B4 ) ) ) ).
% subset_insertI2
thf(fact_1058_bot_Oextremum__uniqueI,axiom,
! [A: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A @ bot_bo1796632182523588997nt_int )
=> ( A = bot_bo1796632182523588997nt_int ) ) ).
% bot.extremum_uniqueI
thf(fact_1059_bot_Oextremum__unique,axiom,
! [A: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A @ bot_bo1796632182523588997nt_int )
= ( A = bot_bo1796632182523588997nt_int ) ) ).
% bot.extremum_unique
thf(fact_1060_bot_Oextremum,axiom,
! [A: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ bot_bo1796632182523588997nt_int @ A ) ).
% bot.extremum
thf(fact_1061_inf_OcoboundedI2,axiom,
! [B: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ B @ C )
=> ( ord_le2843351958646193337nt_int @ ( inf_in2269163501485487111nt_int @ A @ B ) @ C ) ) ).
% inf.coboundedI2
thf(fact_1062_inf_OcoboundedI1,axiom,
! [A: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A @ C )
=> ( ord_le2843351958646193337nt_int @ ( inf_in2269163501485487111nt_int @ A @ B ) @ C ) ) ).
% inf.coboundedI1
thf(fact_1063_inf_Oabsorb__iff2,axiom,
( ord_le2843351958646193337nt_int
= ( ^ [B2: set_Pr958786334691620121nt_int,A5: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ A5 @ B2 )
= B2 ) ) ) ).
% inf.absorb_iff2
thf(fact_1064_inf_Oabsorb__iff1,axiom,
( ord_le2843351958646193337nt_int
= ( ^ [A5: set_Pr958786334691620121nt_int,B2: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ A5 @ B2 )
= A5 ) ) ) ).
% inf.absorb_iff1
thf(fact_1065_inf_Ocobounded2,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ ( inf_in2269163501485487111nt_int @ A @ B ) @ B ) ).
% inf.cobounded2
thf(fact_1066_inf_Ocobounded1,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ ( inf_in2269163501485487111nt_int @ A @ B ) @ A ) ).
% inf.cobounded1
thf(fact_1067_inf_Oorder__iff,axiom,
( ord_le2843351958646193337nt_int
= ( ^ [A5: set_Pr958786334691620121nt_int,B2: set_Pr958786334691620121nt_int] :
( A5
= ( inf_in2269163501485487111nt_int @ A5 @ B2 ) ) ) ) ).
% inf.order_iff
thf(fact_1068_inf__greatest,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X @ Y )
=> ( ( ord_le2843351958646193337nt_int @ X @ Z )
=> ( ord_le2843351958646193337nt_int @ X @ ( inf_in2269163501485487111nt_int @ Y @ Z ) ) ) ) ).
% inf_greatest
thf(fact_1069_inf_OboundedI,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A @ B )
=> ( ( ord_le2843351958646193337nt_int @ A @ C )
=> ( ord_le2843351958646193337nt_int @ A @ ( inf_in2269163501485487111nt_int @ B @ C ) ) ) ) ).
% inf.boundedI
thf(fact_1070_inf_OboundedE,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A @ ( inf_in2269163501485487111nt_int @ B @ C ) )
=> ~ ( ( ord_le2843351958646193337nt_int @ A @ B )
=> ~ ( ord_le2843351958646193337nt_int @ A @ C ) ) ) ).
% inf.boundedE
thf(fact_1071_inf__absorb2,axiom,
! [Y: set_Pr958786334691620121nt_int,X: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ Y @ X )
=> ( ( inf_in2269163501485487111nt_int @ X @ Y )
= Y ) ) ).
% inf_absorb2
thf(fact_1072_inf__absorb1,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X @ Y )
=> ( ( inf_in2269163501485487111nt_int @ X @ Y )
= X ) ) ).
% inf_absorb1
thf(fact_1073_inf_Oabsorb2,axiom,
! [B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ B @ A )
=> ( ( inf_in2269163501485487111nt_int @ A @ B )
= B ) ) ).
% inf.absorb2
thf(fact_1074_inf_Oabsorb1,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A @ B )
=> ( ( inf_in2269163501485487111nt_int @ A @ B )
= A ) ) ).
% inf.absorb1
thf(fact_1075_le__iff__inf,axiom,
( ord_le2843351958646193337nt_int
= ( ^ [X2: set_Pr958786334691620121nt_int,Y3: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ X2 @ Y3 )
= X2 ) ) ) ).
% le_iff_inf
thf(fact_1076_inf__unique,axiom,
! [F: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int,X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ! [X3: set_Pr958786334691620121nt_int,Y2: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ ( F @ X3 @ Y2 ) @ X3 )
=> ( ! [X3: set_Pr958786334691620121nt_int,Y2: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ ( F @ X3 @ Y2 ) @ Y2 )
=> ( ! [X3: set_Pr958786334691620121nt_int,Y2: set_Pr958786334691620121nt_int,Z2: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X3 @ Y2 )
=> ( ( ord_le2843351958646193337nt_int @ X3 @ Z2 )
=> ( ord_le2843351958646193337nt_int @ X3 @ ( F @ Y2 @ Z2 ) ) ) )
=> ( ( inf_in2269163501485487111nt_int @ X @ Y )
= ( F @ X @ Y ) ) ) ) ) ).
% inf_unique
thf(fact_1077_inf_OorderI,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( A
= ( inf_in2269163501485487111nt_int @ A @ B ) )
=> ( ord_le2843351958646193337nt_int @ A @ B ) ) ).
% inf.orderI
thf(fact_1078_inf_OorderE,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A @ B )
=> ( A
= ( inf_in2269163501485487111nt_int @ A @ B ) ) ) ).
% inf.orderE
thf(fact_1079_le__infI2,axiom,
! [B: set_Pr958786334691620121nt_int,X: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ B @ X )
=> ( ord_le2843351958646193337nt_int @ ( inf_in2269163501485487111nt_int @ A @ B ) @ X ) ) ).
% le_infI2
thf(fact_1080_le__infI1,axiom,
! [A: set_Pr958786334691620121nt_int,X: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A @ X )
=> ( ord_le2843351958646193337nt_int @ ( inf_in2269163501485487111nt_int @ A @ B ) @ X ) ) ).
% le_infI1
thf(fact_1081_inf__mono,axiom,
! [A: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,D: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A @ C )
=> ( ( ord_le2843351958646193337nt_int @ B @ D )
=> ( ord_le2843351958646193337nt_int @ ( inf_in2269163501485487111nt_int @ A @ B ) @ ( inf_in2269163501485487111nt_int @ C @ D ) ) ) ) ).
% inf_mono
thf(fact_1082_le__infI,axiom,
! [X: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X @ A )
=> ( ( ord_le2843351958646193337nt_int @ X @ B )
=> ( ord_le2843351958646193337nt_int @ X @ ( inf_in2269163501485487111nt_int @ A @ B ) ) ) ) ).
% le_infI
thf(fact_1083_le__infE,axiom,
! [X: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X @ ( inf_in2269163501485487111nt_int @ A @ B ) )
=> ~ ( ( ord_le2843351958646193337nt_int @ X @ A )
=> ~ ( ord_le2843351958646193337nt_int @ X @ B ) ) ) ).
% le_infE
thf(fact_1084_inf__le2,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ ( inf_in2269163501485487111nt_int @ X @ Y ) @ Y ) ).
% inf_le2
thf(fact_1085_inf__le1,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ ( inf_in2269163501485487111nt_int @ X @ Y ) @ X ) ).
% inf_le1
thf(fact_1086_inf__sup__ord_I1_J,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ ( inf_in2269163501485487111nt_int @ X @ Y ) @ X ) ).
% inf_sup_ord(1)
thf(fact_1087_inf__sup__ord_I2_J,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ ( inf_in2269163501485487111nt_int @ X @ Y ) @ Y ) ).
% inf_sup_ord(2)
thf(fact_1088_Int__Collect__mono,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
( ( ord_le2843351958646193337nt_int @ A3 @ B4 )
=> ( ! [X3: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X3 @ A3 )
=> ( ( P @ X3 )
=> ( Q @ X3 ) ) )
=> ( ord_le2843351958646193337nt_int @ ( inf_in2269163501485487111nt_int @ A3 @ ( collec213857154873943460nt_int @ P ) ) @ ( inf_in2269163501485487111nt_int @ B4 @ ( collec213857154873943460nt_int @ Q ) ) ) ) ) ).
% Int_Collect_mono
thf(fact_1089_Int__greatest,axiom,
! [C2: set_Pr958786334691620121nt_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ C2 @ A3 )
=> ( ( ord_le2843351958646193337nt_int @ C2 @ B4 )
=> ( ord_le2843351958646193337nt_int @ C2 @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) ) ) ) ).
% Int_greatest
thf(fact_1090_Int__absorb2,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ B4 )
=> ( ( inf_in2269163501485487111nt_int @ A3 @ B4 )
= A3 ) ) ).
% Int_absorb2
thf(fact_1091_Int__absorb1,axiom,
! [B4: set_Pr958786334691620121nt_int,A3: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ B4 @ A3 )
=> ( ( inf_in2269163501485487111nt_int @ A3 @ B4 )
= B4 ) ) ).
% Int_absorb1
thf(fact_1092_Int__lower2,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) @ B4 ) ).
% Int_lower2
thf(fact_1093_Int__lower1,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) @ A3 ) ).
% Int_lower1
thf(fact_1094_Int__mono,axiom,
! [A3: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,D2: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ C2 )
=> ( ( ord_le2843351958646193337nt_int @ B4 @ D2 )
=> ( ord_le2843351958646193337nt_int @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) @ ( inf_in2269163501485487111nt_int @ C2 @ D2 ) ) ) ) ).
% Int_mono
thf(fact_1095_diff__shunt__var,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ( ( minus_1052850069191792384nt_int @ X @ Y )
= bot_bo1796632182523588997nt_int )
= ( ord_le2843351958646193337nt_int @ X @ Y ) ) ).
% diff_shunt_var
thf(fact_1096_finite__has__maximal,axiom,
! [A3: set_se6260736226359567993nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( A3 != bot_bo1488462491386950373nt_int )
=> ? [X3: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ X3 @ A3 )
& ! [Xa2: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ Xa2 @ A3 )
=> ( ( ord_le2843351958646193337nt_int @ X3 @ Xa2 )
=> ( X3 = Xa2 ) ) ) ) ) ) ).
% finite_has_maximal
thf(fact_1097_finite__has__minimal,axiom,
! [A3: set_se6260736226359567993nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( A3 != bot_bo1488462491386950373nt_int )
=> ? [X3: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ X3 @ A3 )
& ! [Xa2: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ Xa2 @ A3 )
=> ( ( ord_le2843351958646193337nt_int @ Xa2 @ X3 )
=> ( X3 = Xa2 ) ) ) ) ) ) ).
% finite_has_minimal
thf(fact_1098_distrib__inf__le,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ ( sup_su6024340866399070445nt_int @ ( inf_in2269163501485487111nt_int @ X @ Y ) @ ( inf_in2269163501485487111nt_int @ X @ Z ) ) @ ( inf_in2269163501485487111nt_int @ X @ ( sup_su6024340866399070445nt_int @ Y @ Z ) ) ) ).
% distrib_inf_le
thf(fact_1099_distrib__sup__le,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ ( sup_su6024340866399070445nt_int @ X @ ( inf_in2269163501485487111nt_int @ Y @ Z ) ) @ ( inf_in2269163501485487111nt_int @ ( sup_su6024340866399070445nt_int @ X @ Y ) @ ( sup_su6024340866399070445nt_int @ X @ Z ) ) ) ).
% distrib_sup_le
thf(fact_1100_subset__singleton__iff,axiom,
! [X5: set_Pr958786334691620121nt_int,A: product_prod_int_int] :
( ( ord_le2843351958646193337nt_int @ X5 @ ( insert5033312907999012233nt_int @ A @ bot_bo1796632182523588997nt_int ) )
= ( ( X5 = bot_bo1796632182523588997nt_int )
| ( X5
= ( insert5033312907999012233nt_int @ A @ bot_bo1796632182523588997nt_int ) ) ) ) ).
% subset_singleton_iff
thf(fact_1101_subset__singletonD,axiom,
! [A3: set_Pr958786334691620121nt_int,X: product_prod_int_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ ( insert5033312907999012233nt_int @ X @ bot_bo1796632182523588997nt_int ) )
=> ( ( A3 = bot_bo1796632182523588997nt_int )
| ( A3
= ( insert5033312907999012233nt_int @ X @ bot_bo1796632182523588997nt_int ) ) ) ) ).
% subset_singletonD
thf(fact_1102_set__subset__Cons,axiom,
! [Xs: list_P5707943133018811711nt_int,X: product_prod_int_int] : ( ord_le2843351958646193337nt_int @ ( set_Pr2470121279949933262nt_int @ Xs ) @ ( set_Pr2470121279949933262nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) ) ) ).
% set_subset_Cons
thf(fact_1103_image__Int__subset,axiom,
! [F: product_prod_int_int > product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ ( image_2653370878348428101nt_int @ F @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) ) @ ( inf_in2269163501485487111nt_int @ ( image_2653370878348428101nt_int @ F @ A3 ) @ ( image_2653370878348428101nt_int @ F @ B4 ) ) ) ).
% image_Int_subset
thf(fact_1104_image__diff__subset,axiom,
! [F: product_prod_int_int > product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ ( minus_1052850069191792384nt_int @ ( image_2653370878348428101nt_int @ F @ A3 ) @ ( image_2653370878348428101nt_int @ F @ B4 ) ) @ ( image_2653370878348428101nt_int @ F @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) ) ) ).
% image_diff_subset
thf(fact_1105_subset__Diff__insert,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,X: product_prod_int_int,C2: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ ( minus_1052850069191792384nt_int @ B4 @ ( insert5033312907999012233nt_int @ X @ C2 ) ) )
= ( ( ord_le2843351958646193337nt_int @ A3 @ ( minus_1052850069191792384nt_int @ B4 @ C2 ) )
& ~ ( member5262025264175285858nt_int @ X @ A3 ) ) ) ).
% subset_Diff_insert
thf(fact_1106_Un__Int__assoc__eq,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int] :
( ( ( sup_su6024340866399070445nt_int @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) @ C2 )
= ( inf_in2269163501485487111nt_int @ A3 @ ( sup_su6024340866399070445nt_int @ B4 @ C2 ) ) )
= ( ord_le2843351958646193337nt_int @ C2 @ A3 ) ) ).
% Un_Int_assoc_eq
thf(fact_1107_Diff__subset__conv,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) @ C2 )
= ( ord_le2843351958646193337nt_int @ A3 @ ( sup_su6024340866399070445nt_int @ B4 @ C2 ) ) ) ).
% Diff_subset_conv
thf(fact_1108_Diff__partition,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ B4 )
=> ( ( sup_su6024340866399070445nt_int @ A3 @ ( minus_1052850069191792384nt_int @ B4 @ A3 ) )
= B4 ) ) ).
% Diff_partition
thf(fact_1109_set__remove1__subset,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] : ( ord_le2843351958646193337nt_int @ ( set_Pr2470121279949933262nt_int @ ( remove2588356790385189205nt_int @ X @ Xs ) ) @ ( set_Pr2470121279949933262nt_int @ Xs ) ) ).
% set_remove1_subset
thf(fact_1110_subset__code_I2_J,axiom,
! [A3: set_Pr958786334691620121nt_int,Ys: list_P5707943133018811711nt_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ ( coset_3631019413092825772nt_int @ Ys ) )
= ( ! [X2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X2 @ ( set_Pr2470121279949933262nt_int @ Ys ) )
=> ~ ( member5262025264175285858nt_int @ X2 @ A3 ) ) ) ) ).
% subset_code(2)
thf(fact_1111_knights__path__subset,axiom,
! [B_1: set_Pr958786334691620121nt_int,Ps_1: list_P5707943133018811711nt_int,B_2: set_Pr958786334691620121nt_int,Ps_2: list_P5707943133018811711nt_int] :
( ( knights_path @ B_1 @ Ps_1 )
=> ( ( knights_path @ B_2 @ Ps_2 )
=> ( ( ord_le2843351958646193337nt_int @ ( set_Pr2470121279949933262nt_int @ Ps_1 ) @ ( set_Pr2470121279949933262nt_int @ Ps_2 ) )
= ( ord_le2843351958646193337nt_int @ B_1 @ B_2 ) ) ) ) ).
% knights_path_subset
thf(fact_1112_finite__subset__induct_H,axiom,
! [F2: set_Pr958786334691620121nt_int,A3: set_Pr958786334691620121nt_int,P: set_Pr958786334691620121nt_int > $o] :
( ( finite2998713641127702882nt_int @ F2 )
=> ( ( ord_le2843351958646193337nt_int @ F2 @ A3 )
=> ( ( P @ bot_bo1796632182523588997nt_int )
=> ( ! [A6: product_prod_int_int,F3: set_Pr958786334691620121nt_int] :
( ( finite2998713641127702882nt_int @ F3 )
=> ( ( member5262025264175285858nt_int @ A6 @ A3 )
=> ( ( ord_le2843351958646193337nt_int @ F3 @ A3 )
=> ( ~ ( member5262025264175285858nt_int @ A6 @ F3 )
=> ( ( P @ F3 )
=> ( P @ ( insert5033312907999012233nt_int @ A6 @ F3 ) ) ) ) ) ) )
=> ( P @ F2 ) ) ) ) ) ).
% finite_subset_induct'
thf(fact_1113_finite__subset__induct,axiom,
! [F2: set_Pr958786334691620121nt_int,A3: set_Pr958786334691620121nt_int,P: set_Pr958786334691620121nt_int > $o] :
( ( finite2998713641127702882nt_int @ F2 )
=> ( ( ord_le2843351958646193337nt_int @ F2 @ A3 )
=> ( ( P @ bot_bo1796632182523588997nt_int )
=> ( ! [A6: product_prod_int_int,F3: set_Pr958786334691620121nt_int] :
( ( finite2998713641127702882nt_int @ F3 )
=> ( ( member5262025264175285858nt_int @ A6 @ A3 )
=> ( ~ ( member5262025264175285858nt_int @ A6 @ F3 )
=> ( ( P @ F3 )
=> ( P @ ( insert5033312907999012233nt_int @ A6 @ F3 ) ) ) ) ) )
=> ( P @ F2 ) ) ) ) ) ).
% finite_subset_induct
thf(fact_1114_Diff__single__insert,axiom,
! [A3: set_Pr958786334691620121nt_int,X: product_prod_int_int,B4: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ ( minus_1052850069191792384nt_int @ A3 @ ( insert5033312907999012233nt_int @ X @ bot_bo1796632182523588997nt_int ) ) @ B4 )
=> ( ord_le2843351958646193337nt_int @ A3 @ ( insert5033312907999012233nt_int @ X @ B4 ) ) ) ).
% Diff_single_insert
thf(fact_1115_subset__insert__iff,axiom,
! [A3: set_Pr958786334691620121nt_int,X: product_prod_int_int,B4: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ ( insert5033312907999012233nt_int @ X @ B4 ) )
= ( ( ( member5262025264175285858nt_int @ X @ A3 )
=> ( ord_le2843351958646193337nt_int @ ( minus_1052850069191792384nt_int @ A3 @ ( insert5033312907999012233nt_int @ X @ bot_bo1796632182523588997nt_int ) ) @ B4 ) )
& ( ~ ( member5262025264175285858nt_int @ X @ A3 )
=> ( ord_le2843351958646193337nt_int @ A3 @ B4 ) ) ) ) ).
% subset_insert_iff
thf(fact_1116_Sup__fin_Obounded__iff,axiom,
! [A3: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( A3 != bot_bo1488462491386950373nt_int )
=> ( ( ord_le2843351958646193337nt_int @ ( lattic1237861848008701264nt_int @ A3 ) @ X )
= ( ! [X2: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ X2 @ A3 )
=> ( ord_le2843351958646193337nt_int @ X2 @ X ) ) ) ) ) ) ).
% Sup_fin.bounded_iff
thf(fact_1117_Inf__fin_Obounded__iff,axiom,
! [A3: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( A3 != bot_bo1488462491386950373nt_int )
=> ( ( ord_le2843351958646193337nt_int @ X @ ( lattic8951152183982934710nt_int @ A3 ) )
= ( ! [X2: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ X2 @ A3 )
=> ( ord_le2843351958646193337nt_int @ X @ X2 ) ) ) ) ) ) ).
% Inf_fin.bounded_iff
thf(fact_1118_Sup__fin_OboundedI,axiom,
! [A3: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( A3 != bot_bo1488462491386950373nt_int )
=> ( ! [A6: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ A6 @ A3 )
=> ( ord_le2843351958646193337nt_int @ A6 @ X ) )
=> ( ord_le2843351958646193337nt_int @ ( lattic1237861848008701264nt_int @ A3 ) @ X ) ) ) ) ).
% Sup_fin.boundedI
thf(fact_1119_Sup__fin_OboundedE,axiom,
! [A3: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( A3 != bot_bo1488462491386950373nt_int )
=> ( ( ord_le2843351958646193337nt_int @ ( lattic1237861848008701264nt_int @ A3 ) @ X )
=> ! [A9: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ A9 @ A3 )
=> ( ord_le2843351958646193337nt_int @ A9 @ X ) ) ) ) ) ).
% Sup_fin.boundedE
thf(fact_1120_Inf__fin_OboundedI,axiom,
! [A3: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( A3 != bot_bo1488462491386950373nt_int )
=> ( ! [A6: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ A6 @ A3 )
=> ( ord_le2843351958646193337nt_int @ X @ A6 ) )
=> ( ord_le2843351958646193337nt_int @ X @ ( lattic8951152183982934710nt_int @ A3 ) ) ) ) ) ).
% Inf_fin.boundedI
thf(fact_1121_Inf__fin_OboundedE,axiom,
! [A3: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( A3 != bot_bo1488462491386950373nt_int )
=> ( ( ord_le2843351958646193337nt_int @ X @ ( lattic8951152183982934710nt_int @ A3 ) )
=> ! [A9: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ A9 @ A3 )
=> ( ord_le2843351958646193337nt_int @ X @ A9 ) ) ) ) ) ).
% Inf_fin.boundedE
thf(fact_1122_subset__code_I3_J,axiom,
~ ( ord_le2843351958646193337nt_int @ ( coset_3631019413092825772nt_int @ nil_Pr2300489316682597567nt_int ) @ ( set_Pr2470121279949933262nt_int @ nil_Pr2300489316682597567nt_int ) ) ).
% subset_code(3)
thf(fact_1123_Cons__shuffles__subset1,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] : ( ord_le6386220896155801791nt_int @ ( image_689455831346312645nt_int @ ( cons_P3334398858971670639nt_int @ X ) @ ( shuffl1909956583008895700nt_int @ Xs @ Ys ) ) @ ( shuffl1909956583008895700nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) @ Ys ) ) ).
% Cons_shuffles_subset1
thf(fact_1124_Cons__shuffles__subset2,axiom,
! [Y: product_prod_int_int,Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] : ( ord_le6386220896155801791nt_int @ ( image_689455831346312645nt_int @ ( cons_P3334398858971670639nt_int @ Y ) @ ( shuffl1909956583008895700nt_int @ Xs @ Ys ) ) @ ( shuffl1909956583008895700nt_int @ Xs @ ( cons_P3334398858971670639nt_int @ Y @ Ys ) ) ) ).
% Cons_shuffles_subset2
thf(fact_1125_subset__subseqs,axiom,
! [X5: set_Pr958786334691620121nt_int,Xs: list_P5707943133018811711nt_int] :
( ( ord_le2843351958646193337nt_int @ X5 @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ( member2340774599025711042nt_int @ X5 @ ( image_689400715899363487nt_int @ set_Pr2470121279949933262nt_int @ ( set_li2659200638379878868nt_int @ ( subseq1357044202310323342nt_int @ Xs ) ) ) ) ) ).
% subset_subseqs
thf(fact_1126_remove__induct,axiom,
! [P: set_Pr958786334691620121nt_int > $o,B4: set_Pr958786334691620121nt_int] :
( ( P @ bot_bo1796632182523588997nt_int )
=> ( ( ~ ( finite2998713641127702882nt_int @ B4 )
=> ( P @ B4 ) )
=> ( ! [A7: set_Pr958786334691620121nt_int] :
( ( finite2998713641127702882nt_int @ A7 )
=> ( ( A7 != bot_bo1796632182523588997nt_int )
=> ( ( ord_le2843351958646193337nt_int @ A7 @ B4 )
=> ( ! [X4: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X4 @ A7 )
=> ( P @ ( minus_1052850069191792384nt_int @ A7 @ ( insert5033312907999012233nt_int @ X4 @ bot_bo1796632182523588997nt_int ) ) ) )
=> ( P @ A7 ) ) ) ) )
=> ( P @ B4 ) ) ) ) ).
% remove_induct
thf(fact_1127_finite__remove__induct,axiom,
! [B4: set_Pr958786334691620121nt_int,P: set_Pr958786334691620121nt_int > $o] :
( ( finite2998713641127702882nt_int @ B4 )
=> ( ( P @ bot_bo1796632182523588997nt_int )
=> ( ! [A7: set_Pr958786334691620121nt_int] :
( ( finite2998713641127702882nt_int @ A7 )
=> ( ( A7 != bot_bo1796632182523588997nt_int )
=> ( ( ord_le2843351958646193337nt_int @ A7 @ B4 )
=> ( ! [X4: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X4 @ A7 )
=> ( P @ ( minus_1052850069191792384nt_int @ A7 @ ( insert5033312907999012233nt_int @ X4 @ bot_bo1796632182523588997nt_int ) ) ) )
=> ( P @ A7 ) ) ) ) )
=> ( P @ B4 ) ) ) ) ).
% finite_remove_induct
thf(fact_1128_Inf__fin_Osubset,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( B4 != bot_bo1488462491386950373nt_int )
=> ( ( ord_le483042692224249369nt_int @ B4 @ A3 )
=> ( ( inf_in2269163501485487111nt_int @ ( lattic8951152183982934710nt_int @ B4 ) @ ( lattic8951152183982934710nt_int @ A3 ) )
= ( lattic8951152183982934710nt_int @ A3 ) ) ) ) ) ).
% Inf_fin.subset
thf(fact_1129_Sup__fin_Osubset,axiom,
! [A3: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( B4 != bot_bo1488462491386950373nt_int )
=> ( ( ord_le483042692224249369nt_int @ B4 @ A3 )
=> ( ( sup_su6024340866399070445nt_int @ ( lattic1237861848008701264nt_int @ B4 ) @ ( lattic1237861848008701264nt_int @ A3 ) )
= ( lattic1237861848008701264nt_int @ A3 ) ) ) ) ) ).
% Sup_fin.subset
thf(fact_1130_inf__img__fin__dom_H,axiom,
! [F: product_prod_int_int > product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( finite2998713641127702882nt_int @ ( image_2653370878348428101nt_int @ F @ A3 ) )
=> ( ~ ( finite2998713641127702882nt_int @ A3 )
=> ? [X3: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X3 @ ( image_2653370878348428101nt_int @ F @ A3 ) )
& ~ ( finite2998713641127702882nt_int @ ( inf_in2269163501485487111nt_int @ ( vimage9157098373889594107nt_int @ F @ ( insert5033312907999012233nt_int @ X3 @ bot_bo1796632182523588997nt_int ) ) @ A3 ) ) ) ) ) ).
% inf_img_fin_dom'
thf(fact_1131_inf__img__fin__domE_H,axiom,
! [F: product_prod_int_int > product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( finite2998713641127702882nt_int @ ( image_2653370878348428101nt_int @ F @ A3 ) )
=> ( ~ ( finite2998713641127702882nt_int @ A3 )
=> ~ ! [Y2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ Y2 @ ( image_2653370878348428101nt_int @ F @ A3 ) )
=> ( finite2998713641127702882nt_int @ ( inf_in2269163501485487111nt_int @ ( vimage9157098373889594107nt_int @ F @ ( insert5033312907999012233nt_int @ Y2 @ bot_bo1796632182523588997nt_int ) ) @ A3 ) ) ) ) ) ).
% inf_img_fin_domE'
thf(fact_1132_transpose__empty,axiom,
! [Xs: list_l1670014477004246597nt_int] :
( ( ( transp5579559677893564233nt_int @ Xs )
= nil_li8670148097206105925nt_int )
= ( ! [X2: list_P5707943133018811711nt_int] :
( ( member2764346250752101224nt_int @ X2 @ ( set_li2659200638379878868nt_int @ Xs ) )
=> ( X2 = nil_Pr2300489316682597567nt_int ) ) ) ) ).
% transpose_empty
thf(fact_1133_subsetI,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ! [X3: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X3 @ A3 )
=> ( member5262025264175285858nt_int @ X3 @ B4 ) )
=> ( ord_le2843351958646193337nt_int @ A3 @ B4 ) ) ).
% subsetI
thf(fact_1134_subset__antisym,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ B4 )
=> ( ( ord_le2843351958646193337nt_int @ B4 @ A3 )
=> ( A3 = B4 ) ) ) ).
% subset_antisym
thf(fact_1135_vimage__eq,axiom,
! [A: product_prod_int_int,F: product_prod_int_int > product_prod_int_int,B4: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ A @ ( vimage9157098373889594107nt_int @ F @ B4 ) )
= ( member5262025264175285858nt_int @ ( F @ A ) @ B4 ) ) ).
% vimage_eq
thf(fact_1136_vimageI,axiom,
! [F: product_prod_int_int > product_prod_int_int,A: product_prod_int_int,B: product_prod_int_int,B4: set_Pr958786334691620121nt_int] :
( ( ( F @ A )
= B )
=> ( ( member5262025264175285858nt_int @ B @ B4 )
=> ( member5262025264175285858nt_int @ A @ ( vimage9157098373889594107nt_int @ F @ B4 ) ) ) ) ).
% vimageI
thf(fact_1137_vimage__empty,axiom,
! [F: product_prod_int_int > product_prod_int_int] :
( ( vimage9157098373889594107nt_int @ F @ bot_bo1796632182523588997nt_int )
= bot_bo1796632182523588997nt_int ) ).
% vimage_empty
thf(fact_1138_vimage__Int,axiom,
! [F: product_prod_int_int > product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( vimage9157098373889594107nt_int @ F @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) )
= ( inf_in2269163501485487111nt_int @ ( vimage9157098373889594107nt_int @ F @ A3 ) @ ( vimage9157098373889594107nt_int @ F @ B4 ) ) ) ).
% vimage_Int
thf(fact_1139_vimage__Un,axiom,
! [F: product_prod_int_int > product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( vimage9157098373889594107nt_int @ F @ ( sup_su6024340866399070445nt_int @ A3 @ B4 ) )
= ( sup_su6024340866399070445nt_int @ ( vimage9157098373889594107nt_int @ F @ A3 ) @ ( vimage9157098373889594107nt_int @ F @ B4 ) ) ) ).
% vimage_Un
thf(fact_1140_image__subset__iff__subset__vimage,axiom,
! [F: product_prod_int_int > product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ ( image_2653370878348428101nt_int @ F @ A3 ) @ B4 )
= ( ord_le2843351958646193337nt_int @ A3 @ ( vimage9157098373889594107nt_int @ F @ B4 ) ) ) ).
% image_subset_iff_subset_vimage
thf(fact_1141_in__mono,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,X: product_prod_int_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ B4 )
=> ( ( member5262025264175285858nt_int @ X @ A3 )
=> ( member5262025264175285858nt_int @ X @ B4 ) ) ) ).
% in_mono
thf(fact_1142_subsetD,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,C: product_prod_int_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ B4 )
=> ( ( member5262025264175285858nt_int @ C @ A3 )
=> ( member5262025264175285858nt_int @ C @ B4 ) ) ) ).
% subsetD
thf(fact_1143_equalityE,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( A3 = B4 )
=> ~ ( ( ord_le2843351958646193337nt_int @ A3 @ B4 )
=> ~ ( ord_le2843351958646193337nt_int @ B4 @ A3 ) ) ) ).
% equalityE
thf(fact_1144_subset__eq,axiom,
( ord_le2843351958646193337nt_int
= ( ^ [A4: set_Pr958786334691620121nt_int,B5: set_Pr958786334691620121nt_int] :
! [X2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X2 @ A4 )
=> ( member5262025264175285858nt_int @ X2 @ B5 ) ) ) ) ).
% subset_eq
thf(fact_1145_equalityD1,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( A3 = B4 )
=> ( ord_le2843351958646193337nt_int @ A3 @ B4 ) ) ).
% equalityD1
thf(fact_1146_equalityD2,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( A3 = B4 )
=> ( ord_le2843351958646193337nt_int @ B4 @ A3 ) ) ).
% equalityD2
thf(fact_1147_subset__iff,axiom,
( ord_le2843351958646193337nt_int
= ( ^ [A4: set_Pr958786334691620121nt_int,B5: set_Pr958786334691620121nt_int] :
! [T2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ T2 @ A4 )
=> ( member5262025264175285858nt_int @ T2 @ B5 ) ) ) ) ).
% subset_iff
thf(fact_1148_subset__refl,axiom,
! [A3: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ A3 @ A3 ) ).
% subset_refl
thf(fact_1149_vimage__mono,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,F: product_prod_int_int > product_prod_int_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ B4 )
=> ( ord_le2843351958646193337nt_int @ ( vimage9157098373889594107nt_int @ F @ A3 ) @ ( vimage9157098373889594107nt_int @ F @ B4 ) ) ) ).
% vimage_mono
thf(fact_1150_Collect__mono,axiom,
! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
( ! [X3: product_prod_int_int] :
( ( P @ X3 )
=> ( Q @ X3 ) )
=> ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ P ) @ ( collec213857154873943460nt_int @ Q ) ) ) ).
% Collect_mono
thf(fact_1151_subset__trans,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ B4 )
=> ( ( ord_le2843351958646193337nt_int @ B4 @ C2 )
=> ( ord_le2843351958646193337nt_int @ A3 @ C2 ) ) ) ).
% subset_trans
thf(fact_1152_set__eq__subset,axiom,
( ( ^ [Y4: set_Pr958786334691620121nt_int,Z3: set_Pr958786334691620121nt_int] : ( Y4 = Z3 ) )
= ( ^ [A4: set_Pr958786334691620121nt_int,B5: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A4 @ B5 )
& ( ord_le2843351958646193337nt_int @ B5 @ A4 ) ) ) ) ).
% set_eq_subset
thf(fact_1153_Collect__mono__iff,axiom,
! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
( ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ P ) @ ( collec213857154873943460nt_int @ Q ) )
= ( ! [X2: product_prod_int_int] :
( ( P @ X2 )
=> ( Q @ X2 ) ) ) ) ).
% Collect_mono_iff
thf(fact_1154_subset__vimage__iff,axiom,
! [A3: set_Pr958786334691620121nt_int,F: product_prod_int_int > product_prod_int_int,B4: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ ( vimage9157098373889594107nt_int @ F @ B4 ) )
= ( ! [X2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ X2 @ A3 )
=> ( member5262025264175285858nt_int @ ( F @ X2 ) @ B4 ) ) ) ) ).
% subset_vimage_iff
thf(fact_1155_vimageI2,axiom,
! [F: product_prod_int_int > product_prod_int_int,A: product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ ( F @ A ) @ A3 )
=> ( member5262025264175285858nt_int @ A @ ( vimage9157098373889594107nt_int @ F @ A3 ) ) ) ).
% vimageI2
thf(fact_1156_vimageE,axiom,
! [A: product_prod_int_int,F: product_prod_int_int > product_prod_int_int,B4: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ A @ ( vimage9157098373889594107nt_int @ F @ B4 ) )
=> ( member5262025264175285858nt_int @ ( F @ A ) @ B4 ) ) ).
% vimageE
thf(fact_1157_vimageD,axiom,
! [A: product_prod_int_int,F: product_prod_int_int > product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ A @ ( vimage9157098373889594107nt_int @ F @ A3 ) )
=> ( member5262025264175285858nt_int @ ( F @ A ) @ A3 ) ) ).
% vimageD
thf(fact_1158_vimage__Diff,axiom,
! [F: product_prod_int_int > product_prod_int_int,A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( vimage9157098373889594107nt_int @ F @ ( minus_1052850069191792384nt_int @ A3 @ B4 ) )
= ( minus_1052850069191792384nt_int @ ( vimage9157098373889594107nt_int @ F @ A3 ) @ ( vimage9157098373889594107nt_int @ F @ B4 ) ) ) ).
% vimage_Diff
thf(fact_1159_vimage__singleton__eq,axiom,
! [A: product_prod_int_int,F: product_prod_int_int > product_prod_int_int,B: product_prod_int_int] :
( ( member5262025264175285858nt_int @ A @ ( vimage9157098373889594107nt_int @ F @ ( insert5033312907999012233nt_int @ B @ bot_bo1796632182523588997nt_int ) ) )
= ( ( F @ A )
= B ) ) ).
% vimage_singleton_eq
thf(fact_1160_vimage__insert,axiom,
! [F: product_prod_int_int > product_prod_int_int,A: product_prod_int_int,B4: set_Pr958786334691620121nt_int] :
( ( vimage9157098373889594107nt_int @ F @ ( insert5033312907999012233nt_int @ A @ B4 ) )
= ( sup_su6024340866399070445nt_int @ ( vimage9157098373889594107nt_int @ F @ ( insert5033312907999012233nt_int @ A @ bot_bo1796632182523588997nt_int ) ) @ ( vimage9157098373889594107nt_int @ F @ B4 ) ) ) ).
% vimage_insert
thf(fact_1161_transpose_Osimps_I2_J,axiom,
! [Xss2: list_l1670014477004246597nt_int] :
( ( transp5579559677893564233nt_int @ ( cons_l7309679040211256053nt_int @ nil_Pr2300489316682597567nt_int @ Xss2 ) )
= ( transp5579559677893564233nt_int @ Xss2 ) ) ).
% transpose.simps(2)
thf(fact_1162_finite__finite__vimage__IntI,axiom,
! [F2: set_Pr958786334691620121nt_int,H: product_prod_int_int > product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( finite2998713641127702882nt_int @ F2 )
=> ( ! [Y2: product_prod_int_int] :
( ( member5262025264175285858nt_int @ Y2 @ F2 )
=> ( finite2998713641127702882nt_int @ ( inf_in2269163501485487111nt_int @ ( vimage9157098373889594107nt_int @ H @ ( insert5033312907999012233nt_int @ Y2 @ bot_bo1796632182523588997nt_int ) ) @ A3 ) ) )
=> ( finite2998713641127702882nt_int @ ( inf_in2269163501485487111nt_int @ ( vimage9157098373889594107nt_int @ H @ F2 ) @ A3 ) ) ) ) ).
% finite_finite_vimage_IntI
thf(fact_1163_less__by__empty,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( A3 = bot_bo1796632182523588997nt_int )
=> ( ord_le2843351958646193337nt_int @ A3 @ B4 ) ) ).
% less_by_empty
thf(fact_1164_insert__subsetI,axiom,
! [X: product_prod_int_int,A3: set_Pr958786334691620121nt_int,X5: set_Pr958786334691620121nt_int] :
( ( member5262025264175285858nt_int @ X @ A3 )
=> ( ( ord_le2843351958646193337nt_int @ X5 @ A3 )
=> ( ord_le2843351958646193337nt_int @ ( insert5033312907999012233nt_int @ X @ X5 ) @ A3 ) ) ) ).
% insert_subsetI
thf(fact_1165_subset__emptyI,axiom,
! [A3: set_Pr958786334691620121nt_int] :
( ! [X3: product_prod_int_int] :
~ ( member5262025264175285858nt_int @ X3 @ A3 )
=> ( ord_le2843351958646193337nt_int @ A3 @ bot_bo1796632182523588997nt_int ) ) ).
% subset_emptyI
thf(fact_1166_subseqs__powset,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( image_689400715899363487nt_int @ set_Pr2470121279949933262nt_int @ ( set_li2659200638379878868nt_int @ ( subseq1357044202310323342nt_int @ Xs ) ) )
= ( pow_Pr288375884809803734nt_int @ ( set_Pr2470121279949933262nt_int @ Xs ) ) ) ).
% subseqs_powset
thf(fact_1167_Pow__empty,axiom,
( ( pow_Pr288375884809803734nt_int @ bot_bo1796632182523588997nt_int )
= ( insert8897473484851387113nt_int @ bot_bo1796632182523588997nt_int @ bot_bo1488462491386950373nt_int ) ) ).
% Pow_empty
thf(fact_1168_Pow__singleton__iff,axiom,
! [X5: set_Pr958786334691620121nt_int,Y5: set_Pr958786334691620121nt_int] :
( ( ( pow_Pr288375884809803734nt_int @ X5 )
= ( insert8897473484851387113nt_int @ Y5 @ bot_bo1488462491386950373nt_int ) )
= ( ( X5 = bot_bo1796632182523588997nt_int )
& ( Y5 = bot_bo1796632182523588997nt_int ) ) ) ).
% Pow_singleton_iff
thf(fact_1169_PowI,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ B4 )
=> ( member2340774599025711042nt_int @ A3 @ ( pow_Pr288375884809803734nt_int @ B4 ) ) ) ).
% PowI
thf(fact_1170_Pow__iff,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ A3 @ ( pow_Pr288375884809803734nt_int @ B4 ) )
= ( ord_le2843351958646193337nt_int @ A3 @ B4 ) ) ).
% Pow_iff
thf(fact_1171_Pow__Int__eq,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( pow_Pr288375884809803734nt_int @ ( inf_in2269163501485487111nt_int @ A3 @ B4 ) )
= ( inf_in8396524679539076455nt_int @ ( pow_Pr288375884809803734nt_int @ A3 ) @ ( pow_Pr288375884809803734nt_int @ B4 ) ) ) ).
% Pow_Int_eq
thf(fact_1172_Un__Pow__subset,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] : ( ord_le483042692224249369nt_int @ ( sup_su2047564715030645325nt_int @ ( pow_Pr288375884809803734nt_int @ A3 ) @ ( pow_Pr288375884809803734nt_int @ B4 ) ) @ ( pow_Pr288375884809803734nt_int @ ( sup_su6024340866399070445nt_int @ A3 @ B4 ) ) ) ).
% Un_Pow_subset
thf(fact_1173_PowD,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( member2340774599025711042nt_int @ A3 @ ( pow_Pr288375884809803734nt_int @ B4 ) )
=> ( ord_le2843351958646193337nt_int @ A3 @ B4 ) ) ).
% PowD
thf(fact_1174_Pow__mono,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ B4 )
=> ( ord_le483042692224249369nt_int @ ( pow_Pr288375884809803734nt_int @ A3 ) @ ( pow_Pr288375884809803734nt_int @ B4 ) ) ) ).
% Pow_mono
thf(fact_1175_Pow__bottom,axiom,
! [B4: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ bot_bo1796632182523588997nt_int @ ( pow_Pr288375884809803734nt_int @ B4 ) ) ).
% Pow_bottom
thf(fact_1176_Pow__insert,axiom,
! [A: product_prod_int_int,A3: set_Pr958786334691620121nt_int] :
( ( pow_Pr288375884809803734nt_int @ ( insert5033312907999012233nt_int @ A @ A3 ) )
= ( sup_su2047564715030645325nt_int @ ( pow_Pr288375884809803734nt_int @ A3 ) @ ( image_1544889507766666053nt_int @ ( insert5033312907999012233nt_int @ A ) @ ( pow_Pr288375884809803734nt_int @ A3 ) ) ) ) ).
% Pow_insert
thf(fact_1177_union__fold__insert,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( finite2998713641127702882nt_int @ A3 )
=> ( ( sup_su6024340866399070445nt_int @ A3 @ B4 )
= ( finite21431522256130664nt_int @ insert5033312907999012233nt_int @ B4 @ A3 ) ) ) ).
% union_fold_insert
thf(fact_1178_Pow__set_I1_J,axiom,
( ( pow_Pr288375884809803734nt_int @ ( set_Pr2470121279949933262nt_int @ nil_Pr2300489316682597567nt_int ) )
= ( insert8897473484851387113nt_int @ bot_bo1796632182523588997nt_int @ bot_bo1488462491386950373nt_int ) ) ).
% Pow_set(1)
thf(fact_1179_minus__fold__remove,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( finite2998713641127702882nt_int @ A3 )
=> ( ( minus_1052850069191792384nt_int @ B4 @ A3 )
= ( finite21431522256130664nt_int @ remove3288057706648593438nt_int @ B4 @ A3 ) ) ) ).
% minus_fold_remove
thf(fact_1180_Inf__fin_Oeq__fold,axiom,
! [A3: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( lattic8951152183982934710nt_int @ ( insert8897473484851387113nt_int @ X @ A3 ) )
= ( finite7977572941483360520nt_int @ inf_in2269163501485487111nt_int @ X @ A3 ) ) ) ).
% Inf_fin.eq_fold
thf(fact_1181_Sup__fin_Oeq__fold,axiom,
! [A3: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int] :
( ( finite8744585540193469122nt_int @ A3 )
=> ( ( lattic1237861848008701264nt_int @ ( insert8897473484851387113nt_int @ X @ A3 ) )
= ( finite7977572941483360520nt_int @ sup_su6024340866399070445nt_int @ X @ A3 ) ) ) ).
% Sup_fin.eq_fold
thf(fact_1182_remdups__eq__nil__right__iff,axiom,
! [X: list_P5707943133018811711nt_int] :
( ( nil_Pr2300489316682597567nt_int
= ( remdup3392976464123081940nt_int @ X ) )
= ( X = nil_Pr2300489316682597567nt_int ) ) ).
% remdups_eq_nil_right_iff
thf(fact_1183_remdups__eq__nil__iff,axiom,
! [X: list_P5707943133018811711nt_int] :
( ( ( remdup3392976464123081940nt_int @ X )
= nil_Pr2300489316682597567nt_int )
= ( X = nil_Pr2300489316682597567nt_int ) ) ).
% remdups_eq_nil_iff
thf(fact_1184_set__remdups,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( set_Pr2470121279949933262nt_int @ ( remdup3392976464123081940nt_int @ Xs ) )
= ( set_Pr2470121279949933262nt_int @ Xs ) ) ).
% set_remdups
thf(fact_1185_remdups__id__iff__distinct,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( ( remdup3392976464123081940nt_int @ Xs )
= Xs )
= ( distin3744728255968310194nt_int @ Xs ) ) ).
% remdups_id_iff_distinct
thf(fact_1186_distinct__remdups,axiom,
! [Xs: list_P5707943133018811711nt_int] : ( distin3744728255968310194nt_int @ ( remdup3392976464123081940nt_int @ Xs ) ) ).
% distinct_remdups
thf(fact_1187_remdups_Osimps_I2_J,axiom,
! [X: product_prod_int_int,Xs: list_P5707943133018811711nt_int] :
( ( ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ( ( remdup3392976464123081940nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) )
= ( remdup3392976464123081940nt_int @ Xs ) ) )
& ( ~ ( member5262025264175285858nt_int @ X @ ( set_Pr2470121279949933262nt_int @ Xs ) )
=> ( ( remdup3392976464123081940nt_int @ ( cons_P3334398858971670639nt_int @ X @ Xs ) )
= ( cons_P3334398858971670639nt_int @ X @ ( remdup3392976464123081940nt_int @ Xs ) ) ) ) ) ).
% remdups.simps(2)
thf(fact_1188_distinct__remdups__id,axiom,
! [Xs: list_P5707943133018811711nt_int] :
( ( distin3744728255968310194nt_int @ Xs )
=> ( ( remdup3392976464123081940nt_int @ Xs )
= Xs ) ) ).
% distinct_remdups_id
thf(fact_1189_remdups__append2,axiom,
! [Xs: list_P5707943133018811711nt_int,Ys: list_P5707943133018811711nt_int] :
( ( remdup3392976464123081940nt_int @ ( append7030698103840186580nt_int @ Xs @ ( remdup3392976464123081940nt_int @ Ys ) ) )
= ( remdup3392976464123081940nt_int @ ( append7030698103840186580nt_int @ Xs @ Ys ) ) ) ).
% remdups_append2
thf(fact_1190_remdups_Osimps_I1_J,axiom,
( ( remdup3392976464123081940nt_int @ nil_Pr2300489316682597567nt_int )
= nil_Pr2300489316682597567nt_int ) ).
% remdups.simps(1)
thf(fact_1191_remove1__remdups,axiom,
! [Xs: list_P5707943133018811711nt_int,X: product_prod_int_int] :
( ( distin3744728255968310194nt_int @ Xs )
=> ( ( remove2588356790385189205nt_int @ X @ ( remdup3392976464123081940nt_int @ Xs ) )
= ( remdup3392976464123081940nt_int @ ( remove2588356790385189205nt_int @ X @ Xs ) ) ) ) ).
% remove1_remdups
thf(fact_1192_psubset__insert__iff,axiom,
! [A3: set_Pr958786334691620121nt_int,X: product_prod_int_int,B4: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ A3 @ ( insert5033312907999012233nt_int @ X @ B4 ) )
= ( ( ( member5262025264175285858nt_int @ X @ B4 )
=> ( ord_le7563427860532173253nt_int @ A3 @ B4 ) )
& ( ~ ( member5262025264175285858nt_int @ X @ B4 )
=> ( ( ( member5262025264175285858nt_int @ X @ A3 )
=> ( ord_le7563427860532173253nt_int @ ( minus_1052850069191792384nt_int @ A3 @ ( insert5033312907999012233nt_int @ X @ bot_bo1796632182523588997nt_int ) ) @ B4 ) )
& ( ~ ( member5262025264175285858nt_int @ X @ A3 )
=> ( ord_le2843351958646193337nt_int @ A3 @ B4 ) ) ) ) ) ) ).
% psubset_insert_iff
thf(fact_1193_UNIV__I,axiom,
! [X: product_prod_int_int] : ( member5262025264175285858nt_int @ X @ top_to4366644338036079209nt_int ) ).
% UNIV_I
thf(fact_1194_inf__top__left,axiom,
! [X: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ top_to4366644338036079209nt_int @ X )
= X ) ).
% inf_top_left
thf(fact_1195_inf__top__right,axiom,
! [X: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ X @ top_to4366644338036079209nt_int )
= X ) ).
% inf_top_right
thf(fact_1196_inf__eq__top__iff,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ( ( inf_in2269163501485487111nt_int @ X @ Y )
= top_to4366644338036079209nt_int )
= ( ( X = top_to4366644338036079209nt_int )
& ( Y = top_to4366644338036079209nt_int ) ) ) ).
% inf_eq_top_iff
thf(fact_1197_top__eq__inf__iff,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ( top_to4366644338036079209nt_int
= ( inf_in2269163501485487111nt_int @ X @ Y ) )
= ( ( X = top_to4366644338036079209nt_int )
& ( Y = top_to4366644338036079209nt_int ) ) ) ).
% top_eq_inf_iff
thf(fact_1198_inf__top_Oeq__neutr__iff,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ( inf_in2269163501485487111nt_int @ A @ B )
= top_to4366644338036079209nt_int )
= ( ( A = top_to4366644338036079209nt_int )
& ( B = top_to4366644338036079209nt_int ) ) ) ).
% inf_top.eq_neutr_iff
thf(fact_1199_inf__top_Oleft__neutral,axiom,
! [A: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ top_to4366644338036079209nt_int @ A )
= A ) ).
% inf_top.left_neutral
thf(fact_1200_inf__top_Oneutr__eq__iff,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( top_to4366644338036079209nt_int
= ( inf_in2269163501485487111nt_int @ A @ B ) )
= ( ( A = top_to4366644338036079209nt_int )
& ( B = top_to4366644338036079209nt_int ) ) ) ).
% inf_top.neutr_eq_iff
thf(fact_1201_inf__top_Oright__neutral,axiom,
! [A: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ A @ top_to4366644338036079209nt_int )
= A ) ).
% inf_top.right_neutral
thf(fact_1202_sup__top__left,axiom,
! [X: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ top_to4366644338036079209nt_int @ X )
= top_to4366644338036079209nt_int ) ).
% sup_top_left
thf(fact_1203_sup__top__right,axiom,
! [X: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ X @ top_to4366644338036079209nt_int )
= top_to4366644338036079209nt_int ) ).
% sup_top_right
thf(fact_1204_boolean__algebra_Odisj__one__right,axiom,
! [X: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ X @ top_to4366644338036079209nt_int )
= top_to4366644338036079209nt_int ) ).
% boolean_algebra.disj_one_right
thf(fact_1205_boolean__algebra_Odisj__one__left,axiom,
! [X: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ top_to4366644338036079209nt_int @ X )
= top_to4366644338036079209nt_int ) ).
% boolean_algebra.disj_one_left
thf(fact_1206_Int__UNIV,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ( inf_in2269163501485487111nt_int @ A3 @ B4 )
= top_to4366644338036079209nt_int )
= ( ( A3 = top_to4366644338036079209nt_int )
& ( B4 = top_to4366644338036079209nt_int ) ) ) ).
% Int_UNIV
thf(fact_1207_psubsetI,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ B4 )
=> ( ( A3 != B4 )
=> ( ord_le7563427860532173253nt_int @ A3 @ B4 ) ) ) ).
% psubsetI
thf(fact_1208_Diff__UNIV,axiom,
! [A3: set_Pr958786334691620121nt_int] :
( ( minus_1052850069191792384nt_int @ A3 @ top_to4366644338036079209nt_int )
= bot_bo1796632182523588997nt_int ) ).
% Diff_UNIV
thf(fact_1209_sup_Ostrict__coboundedI2,axiom,
! [C: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ C @ B )
=> ( ord_le7563427860532173253nt_int @ C @ ( sup_su6024340866399070445nt_int @ A @ B ) ) ) ).
% sup.strict_coboundedI2
thf(fact_1210_sup_Ostrict__coboundedI1,axiom,
! [C: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ C @ A )
=> ( ord_le7563427860532173253nt_int @ C @ ( sup_su6024340866399070445nt_int @ A @ B ) ) ) ).
% sup.strict_coboundedI1
thf(fact_1211_sup_Ostrict__order__iff,axiom,
( ord_le7563427860532173253nt_int
= ( ^ [B2: set_Pr958786334691620121nt_int,A5: set_Pr958786334691620121nt_int] :
( ( A5
= ( sup_su6024340866399070445nt_int @ A5 @ B2 ) )
& ( A5 != B2 ) ) ) ) ).
% sup.strict_order_iff
thf(fact_1212_sup_Ostrict__boundedE,axiom,
! [B: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ ( sup_su6024340866399070445nt_int @ B @ C ) @ A )
=> ~ ( ( ord_le7563427860532173253nt_int @ B @ A )
=> ~ ( ord_le7563427860532173253nt_int @ C @ A ) ) ) ).
% sup.strict_boundedE
thf(fact_1213_sup_Oabsorb4,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ A @ B )
=> ( ( sup_su6024340866399070445nt_int @ A @ B )
= B ) ) ).
% sup.absorb4
thf(fact_1214_sup_Oabsorb3,axiom,
! [B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ B @ A )
=> ( ( sup_su6024340866399070445nt_int @ A @ B )
= A ) ) ).
% sup.absorb3
thf(fact_1215_less__supI2,axiom,
! [X: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ X @ B )
=> ( ord_le7563427860532173253nt_int @ X @ ( sup_su6024340866399070445nt_int @ A @ B ) ) ) ).
% less_supI2
thf(fact_1216_less__supI1,axiom,
! [X: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ X @ A )
=> ( ord_le7563427860532173253nt_int @ X @ ( sup_su6024340866399070445nt_int @ A @ B ) ) ) ).
% less_supI1
thf(fact_1217_Un__UNIV__right,axiom,
! [A3: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ A3 @ top_to4366644338036079209nt_int )
= top_to4366644338036079209nt_int ) ).
% Un_UNIV_right
thf(fact_1218_Un__UNIV__left,axiom,
! [B4: set_Pr958786334691620121nt_int] :
( ( sup_su6024340866399070445nt_int @ top_to4366644338036079209nt_int @ B4 )
= top_to4366644338036079209nt_int ) ).
% Un_UNIV_left
thf(fact_1219_insert__UNIV,axiom,
! [X: product_prod_int_int] :
( ( insert5033312907999012233nt_int @ X @ top_to4366644338036079209nt_int )
= top_to4366644338036079209nt_int ) ).
% insert_UNIV
thf(fact_1220_empty__not__UNIV,axiom,
bot_bo1796632182523588997nt_int != top_to4366644338036079209nt_int ).
% empty_not_UNIV
thf(fact_1221_not__psubset__empty,axiom,
! [A3: set_Pr958786334691620121nt_int] :
~ ( ord_le7563427860532173253nt_int @ A3 @ bot_bo1796632182523588997nt_int ) ).
% not_psubset_empty
thf(fact_1222_bot_Onot__eq__extremum,axiom,
! [A: set_Pr958786334691620121nt_int] :
( ( A != bot_bo1796632182523588997nt_int )
= ( ord_le7563427860532173253nt_int @ bot_bo1796632182523588997nt_int @ A ) ) ).
% bot.not_eq_extremum
thf(fact_1223_bot_Oextremum__strict,axiom,
! [A: set_Pr958786334691620121nt_int] :
~ ( ord_le7563427860532173253nt_int @ A @ bot_bo1796632182523588997nt_int ) ).
% bot.extremum_strict
thf(fact_1224_inf_Ostrict__coboundedI2,axiom,
! [B: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ B @ C )
=> ( ord_le7563427860532173253nt_int @ ( inf_in2269163501485487111nt_int @ A @ B ) @ C ) ) ).
% inf.strict_coboundedI2
thf(fact_1225_inf_Ostrict__coboundedI1,axiom,
! [A: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ A @ C )
=> ( ord_le7563427860532173253nt_int @ ( inf_in2269163501485487111nt_int @ A @ B ) @ C ) ) ).
% inf.strict_coboundedI1
thf(fact_1226_inf_Ostrict__order__iff,axiom,
( ord_le7563427860532173253nt_int
= ( ^ [A5: set_Pr958786334691620121nt_int,B2: set_Pr958786334691620121nt_int] :
( ( A5
= ( inf_in2269163501485487111nt_int @ A5 @ B2 ) )
& ( A5 != B2 ) ) ) ) ).
% inf.strict_order_iff
thf(fact_1227_inf_Ostrict__boundedE,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ A @ ( inf_in2269163501485487111nt_int @ B @ C ) )
=> ~ ( ( ord_le7563427860532173253nt_int @ A @ B )
=> ~ ( ord_le7563427860532173253nt_int @ A @ C ) ) ) ).
% inf.strict_boundedE
thf(fact_1228_inf_Oabsorb4,axiom,
! [B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ B @ A )
=> ( ( inf_in2269163501485487111nt_int @ A @ B )
= B ) ) ).
% inf.absorb4
thf(fact_1229_inf_Oabsorb3,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ A @ B )
=> ( ( inf_in2269163501485487111nt_int @ A @ B )
= A ) ) ).
% inf.absorb3
thf(fact_1230_less__infI2,axiom,
! [B: set_Pr958786334691620121nt_int,X: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ B @ X )
=> ( ord_le7563427860532173253nt_int @ ( inf_in2269163501485487111nt_int @ A @ B ) @ X ) ) ).
% less_infI2
thf(fact_1231_less__infI1,axiom,
! [A: set_Pr958786334691620121nt_int,X: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ A @ X )
=> ( ord_le7563427860532173253nt_int @ ( inf_in2269163501485487111nt_int @ A @ B ) @ X ) ) ).
% less_infI1
thf(fact_1232_Int__UNIV__right,axiom,
! [A3: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ A3 @ top_to4366644338036079209nt_int )
= A3 ) ).
% Int_UNIV_right
thf(fact_1233_Int__UNIV__left,axiom,
! [B4: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ top_to4366644338036079209nt_int @ B4 )
= B4 ) ).
% Int_UNIV_left
thf(fact_1234_boolean__algebra_Oconj__one__right,axiom,
! [X: set_Pr958786334691620121nt_int] :
( ( inf_in2269163501485487111nt_int @ X @ top_to4366644338036079209nt_int )
= X ) ).
% boolean_algebra.conj_one_right
thf(fact_1235_order__le__imp__less__or__eq,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X @ Y )
=> ( ( ord_le7563427860532173253nt_int @ X @ Y )
| ( X = Y ) ) ) ).
% order_le_imp_less_or_eq
thf(fact_1236_order__less__le__subst1,axiom,
! [A: set_Pr958786334691620121nt_int,F: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ A @ ( F @ B ) )
=> ( ( ord_le2843351958646193337nt_int @ B @ C )
=> ( ! [X3: set_Pr958786334691620121nt_int,Y2: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X3 @ Y2 )
=> ( ord_le2843351958646193337nt_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
=> ( ord_le7563427860532173253nt_int @ A @ ( F @ C ) ) ) ) ) ).
% order_less_le_subst1
thf(fact_1237_order__le__less__subst2,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,F: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A @ B )
=> ( ( ord_le7563427860532173253nt_int @ ( F @ B ) @ C )
=> ( ! [X3: set_Pr958786334691620121nt_int,Y2: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X3 @ Y2 )
=> ( ord_le2843351958646193337nt_int @ ( F @ X3 ) @ ( F @ Y2 ) ) )
=> ( ord_le7563427860532173253nt_int @ ( F @ A ) @ C ) ) ) ) ).
% order_le_less_subst2
thf(fact_1238_order__less__le__trans,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ X @ Y )
=> ( ( ord_le2843351958646193337nt_int @ Y @ Z )
=> ( ord_le7563427860532173253nt_int @ X @ Z ) ) ) ).
% order_less_le_trans
thf(fact_1239_order__le__less__trans,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,Z: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X @ Y )
=> ( ( ord_le7563427860532173253nt_int @ Y @ Z )
=> ( ord_le7563427860532173253nt_int @ X @ Z ) ) ) ).
% order_le_less_trans
thf(fact_1240_order__neq__le__trans,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( A != B )
=> ( ( ord_le2843351958646193337nt_int @ A @ B )
=> ( ord_le7563427860532173253nt_int @ A @ B ) ) ) ).
% order_neq_le_trans
thf(fact_1241_order__le__neq__trans,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A @ B )
=> ( ( A != B )
=> ( ord_le7563427860532173253nt_int @ A @ B ) ) ) ).
% order_le_neq_trans
thf(fact_1242_order__less__imp__le,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ X @ Y )
=> ( ord_le2843351958646193337nt_int @ X @ Y ) ) ).
% order_less_imp_le
thf(fact_1243_order__less__le,axiom,
( ord_le7563427860532173253nt_int
= ( ^ [X2: set_Pr958786334691620121nt_int,Y3: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X2 @ Y3 )
& ( X2 != Y3 ) ) ) ) ).
% order_less_le
thf(fact_1244_order__le__less,axiom,
( ord_le2843351958646193337nt_int
= ( ^ [X2: set_Pr958786334691620121nt_int,Y3: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ X2 @ Y3 )
| ( X2 = Y3 ) ) ) ) ).
% order_le_less
thf(fact_1245_dual__order_Ostrict__implies__order,axiom,
! [B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ B @ A )
=> ( ord_le2843351958646193337nt_int @ B @ A ) ) ).
% dual_order.strict_implies_order
thf(fact_1246_order_Ostrict__implies__order,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ A @ B )
=> ( ord_le2843351958646193337nt_int @ A @ B ) ) ).
% order.strict_implies_order
thf(fact_1247_dual__order_Ostrict__iff__not,axiom,
( ord_le7563427860532173253nt_int
= ( ^ [B2: set_Pr958786334691620121nt_int,A5: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ B2 @ A5 )
& ~ ( ord_le2843351958646193337nt_int @ A5 @ B2 ) ) ) ) ).
% dual_order.strict_iff_not
thf(fact_1248_dual__order_Ostrict__trans2,axiom,
! [B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ B @ A )
=> ( ( ord_le2843351958646193337nt_int @ C @ B )
=> ( ord_le7563427860532173253nt_int @ C @ A ) ) ) ).
% dual_order.strict_trans2
thf(fact_1249_dual__order_Ostrict__trans1,axiom,
! [B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ B @ A )
=> ( ( ord_le7563427860532173253nt_int @ C @ B )
=> ( ord_le7563427860532173253nt_int @ C @ A ) ) ) ).
% dual_order.strict_trans1
thf(fact_1250_dual__order_Ostrict__iff__order,axiom,
( ord_le7563427860532173253nt_int
= ( ^ [B2: set_Pr958786334691620121nt_int,A5: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ B2 @ A5 )
& ( A5 != B2 ) ) ) ) ).
% dual_order.strict_iff_order
thf(fact_1251_dual__order_Oorder__iff__strict,axiom,
( ord_le2843351958646193337nt_int
= ( ^ [B2: set_Pr958786334691620121nt_int,A5: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ B2 @ A5 )
| ( A5 = B2 ) ) ) ) ).
% dual_order.order_iff_strict
thf(fact_1252_top_Oextremum__uniqueI,axiom,
! [A: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ top_to4366644338036079209nt_int @ A )
=> ( A = top_to4366644338036079209nt_int ) ) ).
% top.extremum_uniqueI
thf(fact_1253_order_Ostrict__iff__not,axiom,
( ord_le7563427860532173253nt_int
= ( ^ [A5: set_Pr958786334691620121nt_int,B2: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A5 @ B2 )
& ~ ( ord_le2843351958646193337nt_int @ B2 @ A5 ) ) ) ) ).
% order.strict_iff_not
thf(fact_1254_top_Oextremum__unique,axiom,
! [A: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ top_to4366644338036079209nt_int @ A )
= ( A = top_to4366644338036079209nt_int ) ) ).
% top.extremum_unique
thf(fact_1255_order_Ostrict__trans2,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ A @ B )
=> ( ( ord_le2843351958646193337nt_int @ B @ C )
=> ( ord_le7563427860532173253nt_int @ A @ C ) ) ) ).
% order.strict_trans2
thf(fact_1256_order_Ostrict__trans1,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,C: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A @ B )
=> ( ( ord_le7563427860532173253nt_int @ B @ C )
=> ( ord_le7563427860532173253nt_int @ A @ C ) ) ) ).
% order.strict_trans1
thf(fact_1257_order_Ostrict__iff__order,axiom,
( ord_le7563427860532173253nt_int
= ( ^ [A5: set_Pr958786334691620121nt_int,B2: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A5 @ B2 )
& ( A5 != B2 ) ) ) ) ).
% order.strict_iff_order
thf(fact_1258_order_Oorder__iff__strict,axiom,
( ord_le2843351958646193337nt_int
= ( ^ [A5: set_Pr958786334691620121nt_int,B2: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ A5 @ B2 )
| ( A5 = B2 ) ) ) ) ).
% order.order_iff_strict
thf(fact_1259_less__le__not__le,axiom,
( ord_le7563427860532173253nt_int
= ( ^ [X2: set_Pr958786334691620121nt_int,Y3: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X2 @ Y3 )
& ~ ( ord_le2843351958646193337nt_int @ Y3 @ X2 ) ) ) ) ).
% less_le_not_le
thf(fact_1260_top__greatest,axiom,
! [A: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ A @ top_to4366644338036079209nt_int ) ).
% top_greatest
thf(fact_1261_antisym__conv2,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ X @ Y )
=> ( ( ~ ( ord_le7563427860532173253nt_int @ X @ Y ) )
= ( X = Y ) ) ) ).
% antisym_conv2
thf(fact_1262_antisym__conv1,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ~ ( ord_le7563427860532173253nt_int @ X @ Y )
=> ( ( ord_le2843351958646193337nt_int @ X @ Y )
= ( X = Y ) ) ) ).
% antisym_conv1
thf(fact_1263_nless__le,axiom,
! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int] :
( ( ~ ( ord_le7563427860532173253nt_int @ A @ B ) )
= ( ~ ( ord_le2843351958646193337nt_int @ A @ B )
| ( A = B ) ) ) ).
% nless_le
thf(fact_1264_leD,axiom,
! [Y: set_Pr958786334691620121nt_int,X: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ Y @ X )
=> ~ ( ord_le7563427860532173253nt_int @ X @ Y ) ) ).
% leD
thf(fact_1265_subset__iff__psubset__eq,axiom,
( ord_le2843351958646193337nt_int
= ( ^ [A4: set_Pr958786334691620121nt_int,B5: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ A4 @ B5 )
| ( A4 = B5 ) ) ) ) ).
% subset_iff_psubset_eq
thf(fact_1266_subset__psubset__trans,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A3 @ B4 )
=> ( ( ord_le7563427860532173253nt_int @ B4 @ C2 )
=> ( ord_le7563427860532173253nt_int @ A3 @ C2 ) ) ) ).
% subset_psubset_trans
thf(fact_1267_subset__not__subset__eq,axiom,
( ord_le7563427860532173253nt_int
= ( ^ [A4: set_Pr958786334691620121nt_int,B5: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A4 @ B5 )
& ~ ( ord_le2843351958646193337nt_int @ B5 @ A4 ) ) ) ) ).
% subset_not_subset_eq
thf(fact_1268_psubset__subset__trans,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int,C2: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ A3 @ B4 )
=> ( ( ord_le2843351958646193337nt_int @ B4 @ C2 )
=> ( ord_le7563427860532173253nt_int @ A3 @ C2 ) ) ) ).
% psubset_subset_trans
thf(fact_1269_psubset__imp__subset,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ A3 @ B4 )
=> ( ord_le2843351958646193337nt_int @ A3 @ B4 ) ) ).
% psubset_imp_subset
thf(fact_1270_subset__UNIV,axiom,
! [A3: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ A3 @ top_to4366644338036079209nt_int ) ).
% subset_UNIV
thf(fact_1271_psubset__eq,axiom,
( ord_le7563427860532173253nt_int
= ( ^ [A4: set_Pr958786334691620121nt_int,B5: set_Pr958786334691620121nt_int] :
( ( ord_le2843351958646193337nt_int @ A4 @ B5 )
& ( A4 != B5 ) ) ) ) ).
% psubset_eq
thf(fact_1272_psubsetE,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ A3 @ B4 )
=> ~ ( ( ord_le2843351958646193337nt_int @ A3 @ B4 )
=> ( ord_le2843351958646193337nt_int @ B4 @ A3 ) ) ) ).
% psubsetE
thf(fact_1273_UNIV__coset,axiom,
( top_to4366644338036079209nt_int
= ( coset_3631019413092825772nt_int @ nil_Pr2300489316682597567nt_int ) ) ).
% UNIV_coset
thf(fact_1274_psubset__imp__ex__mem,axiom,
! [A3: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
( ( ord_le7563427860532173253nt_int @ A3 @ B4 )
=> ? [B3: product_prod_int_int] : ( member5262025264175285858nt_int @ B3 @ ( minus_1052850069191792384nt_int @ B4 @ A3 ) ) ) ).
% psubset_imp_ex_mem
% Helper facts (5)
thf(help_If_2_1_If_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ( if_set4441254072200386271nt_int @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
( ( if_set4441254072200386271nt_int @ $true @ X @ Y )
= X ) ).
thf(help_If_3_1_If_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
! [P: $o] :
( ( P = $true )
| ( P = $false ) ) ).
thf(help_If_2_1_If_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
! [X: list_P5707943133018811711nt_int,Y: list_P5707943133018811711nt_int] :
( ( if_lis8883190402267401221nt_int @ $false @ X @ Y )
= Y ) ).
thf(help_If_1_1_If_001t__List__Olist_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
! [X: list_P5707943133018811711nt_int,Y: list_P5707943133018811711nt_int] :
( ( if_lis8883190402267401221nt_int @ $true @ X @ Y )
= X ) ).
% Conjectures (1)
thf(conj_0,conjecture,
( ( knights_path @ b @ ( append7030698103840186580nt_int @ ps @ ( cons_P3334398858971670639nt_int @ s_i @ nil_Pr2300489316682597567nt_int ) ) )
& ( valid_step @ ( last_P3305686521732843992nt_int @ ( append7030698103840186580nt_int @ ps @ ( cons_P3334398858971670639nt_int @ s_i @ nil_Pr2300489316682597567nt_int ) ) ) @ ( hd_Pro282112905867057956nt_int @ ( append7030698103840186580nt_int @ ps @ ( cons_P3334398858971670639nt_int @ s_i @ nil_Pr2300489316682597567nt_int ) ) ) ) ) ).
%------------------------------------------------------------------------------