%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP197^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:56:20 AM UTC 2026
% Result : Theorem 19.84s 4.37s
% Output : Refutation 19.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP197^2 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n003.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 08:30:11 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : ITP197^2 : TPTP v9.2.1. Released v7.5.0.
% 0.29/0.45 % Domain : Interactive Theorem Proving
% 0.29/0.45 % Problem : Sledgehammer Type problem prob_386__3259180_1
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English :
% 0.29/0.45
% 0.29/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.29/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [Des21]
% 0.29/0.45 % Names : Type/prob_386__3259180_1 [Des21]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % Rating : 0.00 v7.5.0
% 0.29/0.45 % Syntax : Number of formulae : 359 ( 148 unt; 60 typ; 0 def)
% 0.29/0.45 % Number of atoms : 713 ( 333 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 11 ( 2 avg)
% 0.29/0.45 % Number of connectives : 3178 ( 107 ~; 22 |; 57 &;2646 @)
% 0.29/0.45 % ( 0 <=>; 346 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 23 ( 7 avg)
% 0.29/0.45 % Number of types : 4 ( 3 usr)
% 0.29/0.45 % Number of type conns : 261 ( 261 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 60 ( 57 usr; 4 con; 0-5 aty)
% 0.29/0.45 % Number of variables : 1051 ( 73 ^; 905 !; 31 ?;1051 :)
% 0.29/0.45 % ( 42 !>; 0 ?*; 0 @-; 0 @+)
% 0.29/0.45 % SPC : TH1_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 16:19:19.244
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % Could-be-implicit typings (5)
% 0.29/0.45 thf(ty_t_Type__Mirabelle__sfxnzmapfi_Otype__scheme,type,
% 0.29/0.45 type_M1610475166scheme: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Type__Mirabelle__sfxnzmapfi_Otyp,type,
% 0.29/0.45 type_Mirabelle_typ: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_List_Olist,type,
% 0.29/0.45 list: $tType > $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Set_Oset,type,
% 0.29/0.45 set: $tType > $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Nat_Onat,type,
% 0.29/0.45 nat: $tType ).
% 0.29/0.45
% 0.29/0.45 % Explicit typings (55)
% 0.29/0.45 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.29/0.45 bounded_lattice:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_HOL_Otype,type,
% 0.29/0.45 type:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Orderings_Obot,type,
% 0.29/0.45 bot:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Orderings_Oord,type,
% 0.29/0.45 ord:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Orderings_Oorder,type,
% 0.29/0.45 order:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Orderings_Ono__bot,type,
% 0.29/0.45 no_bot:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Orderings_Ono__top,type,
% 0.29/0.45 no_top:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Orderings_Olinorder,type,
% 0.29/0.45 linorder:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Orderings_Opreorder,type,
% 0.29/0.45 preorder:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Orderings_Oorder__bot,type,
% 0.29/0.45 order_bot:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Orderings_Owellorder,type,
% 0.29/0.45 wellorder:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Orderings_Odense__order,type,
% 0.29/0.45 dense_order:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.29/0.45 semilattice_sup:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Type__Mirabelle__sfxnzmapfi_Oof__nat,type,
% 0.29/0.45 type_M201404320of_nat:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Type__Mirabelle__sfxnzmapfi_Otyp__of,type,
% 0.29/0.45 type_M1535146424typ_of:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 0.29/0.45 bounde1808546759up_bot:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Type__Mirabelle__sfxnzmapfi_Otype__struct,type,
% 0.29/0.45 type_M1470978233struct:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_HOL_OThe,type,
% 0.29/0.45 the:
% 0.29/0.45 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_If,type,
% 0.29/0.45 if:
% 0.29/0.45 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Lattices_Osemilattice__neutr,type,
% 0.29/0.45 semilattice_neutr:
% 0.29/0.45 !>[A: $tType] : ( ( A > A > A ) > A > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.29/0.45 sup_sup:
% 0.29/0.45 !>[A: $tType] : ( A > A > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_List_Oinsert,type,
% 0.29/0.45 insert:
% 0.29/0.45 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_List_Olist_OCons,type,
% 0.29/0.45 cons:
% 0.29/0.45 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_List_Olist_ONil,type,
% 0.29/0.45 nil:
% 0.29/0.45 !>[A: $tType] : ( list @ A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_List_Oord__class_Olexordp__eq,type,
% 0.29/0.45 ord_lexordp_eq:
% 0.29/0.45 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.29/0.45 bot_bot:
% 0.29/0.45 !>[A: $tType] : A ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.29/0.45 ord_less:
% 0.29/0.45 !>[A: $tType] : ( A > A > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Set_OCollect,type,
% 0.29/0.45 collect:
% 0.29/0.45 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Set_Oinsert,type,
% 0.29/0.45 insert2:
% 0.29/0.45 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Set_Ois__empty,type,
% 0.29/0.45 is_empty:
% 0.29/0.45 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Set_Ois__singleton,type,
% 0.29/0.45 is_singleton:
% 0.29/0.45 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Set_Othe__elem,type,
% 0.29/0.45 the_elem:
% 0.29/0.45 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Ocod,type,
% 0.29/0.45 type_Mirabelle_cod: ( nat > type_Mirabelle_typ ) > ( set @ nat ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Odom,type,
% 0.29/0.45 type_Mirabelle_dom: ( nat > type_Mirabelle_typ ) > ( set @ nat ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Oid__subst,type,
% 0.29/0.45 type_M17369686_subst: nat > type_Mirabelle_typ ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Omk__scheme,type,
% 0.29/0.45 type_M540877363scheme: type_Mirabelle_typ > type_M1610475166scheme ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Onew__tv,type,
% 0.29/0.45 type_M1046766514new_tv:
% 0.29/0.45 !>[A: $tType] : ( nat > A > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Oof__nat__class_Oof__nat,type,
% 0.29/0.45 type_M167561660of_nat:
% 0.29/0.45 !>[A: $tType] : ( nat > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otyp_OFun,type,
% 0.29/0.45 type_Mirabelle_Fun: type_Mirabelle_typ > type_Mirabelle_typ > type_Mirabelle_typ ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otyp_OTVar,type,
% 0.29/0.45 type_Mirabelle_TVar: nat > type_Mirabelle_typ ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otyp_Ocase__typ,type,
% 0.29/0.45 type_M1695911984se_typ:
% 0.29/0.45 !>[A: $tType] : ( ( nat > A ) > ( type_Mirabelle_typ > type_Mirabelle_typ > A ) > type_Mirabelle_typ > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otyp__of__class_Otyp__of,type,
% 0.29/0.45 type_M604437996typ_of:
% 0.29/0.45 !>[A: $tType] : ( A > type_Mirabelle_typ ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__scheme_OBVar,type,
% 0.29/0.45 type_M1264524676e_BVar: nat > type_M1610475166scheme ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__scheme_OFVar,type,
% 0.29/0.45 type_M91906176e_FVar: nat > type_M1610475166scheme ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__scheme_OSFun,type,
% 0.29/0.45 type_M1518733067e_SFun: type_M1610475166scheme > type_M1610475166scheme > type_M1610475166scheme ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__scheme_Ocase__type__scheme,type,
% 0.29/0.45 type_M697345518scheme:
% 0.29/0.45 !>[A: $tType] : ( ( nat > A ) > ( nat > A ) > ( type_M1610475166scheme > type_M1610475166scheme > A ) > type_M1610475166scheme > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__scheme_Orec__type__scheme,type,
% 0.29/0.45 type_M1705333808scheme:
% 0.29/0.45 !>[A: $tType] : ( ( nat > A ) > ( nat > A ) > ( type_M1610475166scheme > type_M1610475166scheme > A > A > A ) > type_M1610475166scheme > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__struct__class_Oapp__subst,type,
% 0.29/0.45 type_M353778473_subst:
% 0.29/0.45 !>[A: $tType] : ( ( nat > type_Mirabelle_typ ) > A > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__struct__class_Obound__tv,type,
% 0.29/0.45 type_M779184887und_tv:
% 0.29/0.45 !>[A: $tType] : ( A > ( set @ nat ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__struct__class_Ofree__tv,type,
% 0.29/0.45 type_M950795831ree_tv:
% 0.29/0.45 !>[A: $tType] : ( A > ( set @ nat ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_member,type,
% 0.29/0.45 member:
% 0.29/0.45 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_v_S1,type,
% 0.29/0.45 s1: nat > type_Mirabelle_typ ).
% 0.29/0.45
% 0.29/0.45 thf(sy_v_S2,type,
% 0.29/0.45 s2: nat > type_Mirabelle_typ ).
% 0.29/0.45
% 0.29/0.45 thf(sy_v_n,type,
% 0.29/0.45 n: nat ).
% 0.29/0.45
% 0.29/0.45 thf(sy_v_x,type,
% 0.29/0.45 x: nat ).
% 0.29/0.45
% 0.29/0.45 % Relevant facts (255)
% 0.29/0.45 thf(fact_0_type__scheme_Oinject_I1_J,axiom,
% 0.29/0.45 ! [X1: nat,Y1: nat] :
% 0.29/0.45 ( ( ( type_M91906176e_FVar @ X1 )
% 0.29/0.45 = ( type_M91906176e_FVar @ Y1 ) )
% 0.29/0.45 = ( X1 = Y1 ) ) ).
% 0.29/0.45
% 0.29/0.45 % type_scheme.inject(1)
% 0.29/0.45 thf(fact_1_eq__free__eq__subst__type__scheme,axiom,
% 0.29/0.45 ! [Sch: type_M1610475166scheme,S1: nat > type_Mirabelle_typ,S2: nat > type_Mirabelle_typ] :
% 0.29/0.45 ( ! [N: nat] :
% 0.29/0.45 ( ( member @ nat @ N @ ( type_M950795831ree_tv @ type_M1610475166scheme @ Sch ) )
% 0.29/0.45 => ( ( S1 @ N )
% 0.29/0.45 = ( S2 @ N ) ) )
% 0.29/0.45 => ( ( type_M353778473_subst @ type_M1610475166scheme @ S1 @ Sch )
% 0.29/0.45 = ( type_M353778473_subst @ type_M1610475166scheme @ S2 @ Sch ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % eq_free_eq_subst_type_scheme
% 0.29/0.45 thf(fact_2_scheme__substitutions__only__on__free__variables,axiom,
% 0.29/0.45 ! [Sch: type_M1610475166scheme,S: nat > type_Mirabelle_typ,S3: nat > type_Mirabelle_typ] :
% 0.29/0.45 ( ! [X: nat] :
% 0.29/0.45 ( ( member @ nat @ X @ ( type_M950795831ree_tv @ type_M1610475166scheme @ Sch ) )
% 0.29/0.45 => ( ( S @ X )
% 0.29/0.45 = ( S3 @ X ) ) )
% 0.29/0.45 => ( ( type_M353778473_subst @ type_M1610475166scheme @ S @ Sch )
% 0.29/0.45 = ( type_M353778473_subst @ type_M1610475166scheme @ S3 @ Sch ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % scheme_substitutions_only_on_free_variables
% 0.29/0.45 thf(fact_3_app__subst__type__scheme_Osimps_I1_J,axiom,
% 0.29/0.45 ! [S: nat > type_Mirabelle_typ,N2: nat] :
% 0.29/0.45 ( ( type_M353778473_subst @ type_M1610475166scheme @ S @ ( type_M91906176e_FVar @ N2 ) )
% 0.29/0.45 = ( type_M540877363scheme @ ( S @ N2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % app_subst_type_scheme.simps(1)
% 0.29/0.45 thf(fact_4_type__scheme_Osimps_I13_J,axiom,
% 0.29/0.45 ! [A: $tType,F1: nat > A,F2: nat > A,F3: type_M1610475166scheme > type_M1610475166scheme > A > A > A,X1: nat] :
% 0.29/0.45 ( ( type_M1705333808scheme @ A @ F1 @ F2 @ F3 @ ( type_M91906176e_FVar @ X1 ) )
% 0.29/0.45 = ( F1 @ X1 ) ) ).
% 0.29/0.45
% 0.29/0.45 % type_scheme.simps(13)
% 0.29/0.45 thf(fact_5_type__scheme_Osimps_I10_J,axiom,
% 0.29/0.45 ! [A: $tType,F1: nat > A,F2: nat > A,F3: type_M1610475166scheme > type_M1610475166scheme > A,X1: nat] :
% 0.29/0.45 ( ( type_M697345518scheme @ A @ F1 @ F2 @ F3 @ ( type_M91906176e_FVar @ X1 ) )
% 0.29/0.45 = ( F1 @ X1 ) ) ).
% 0.29/0.45
% 0.29/0.45 % type_scheme.simps(10)
% 0.29/0.45 thf(fact_6_app__subst__type__scheme_Osimps_I2_J,axiom,
% 0.29/0.45 ! [S: nat > type_Mirabelle_typ,N2: nat] :
% 0.29/0.45 ( ( type_M353778473_subst @ type_M1610475166scheme @ S @ ( type_M1264524676e_BVar @ N2 ) )
% 0.29/0.45 = ( type_M1264524676e_BVar @ N2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % app_subst_type_scheme.simps(2)
% 0.29/0.45 thf(fact_7_app__subst__type__scheme_Osimps_I3_J,axiom,
% 0.29/0.45 ! [S: nat > type_Mirabelle_typ,Sch1: type_M1610475166scheme,Sch2: type_M1610475166scheme] :
% 0.29/0.45 ( ( type_M353778473_subst @ type_M1610475166scheme @ S @ ( type_M1518733067e_SFun @ Sch1 @ Sch2 ) )
% 0.29/0.45 = ( type_M1518733067e_SFun @ ( type_M353778473_subst @ type_M1610475166scheme @ S @ Sch1 ) @ ( type_M353778473_subst @ type_M1610475166scheme @ S @ Sch2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % app_subst_type_scheme.simps(3)
% 0.29/0.45 thf(fact_8_type__scheme_Odistinct_I1_J,axiom,
% 0.29/0.45 ! [X1: nat,X2: nat] :
% 0.29/0.45 ( ( type_M91906176e_FVar @ X1 )
% 0.29/0.45 != ( type_M1264524676e_BVar @ X2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % type_scheme.distinct(1)
% 0.29/0.45 thf(fact_9_type__scheme_Odistinct_I3_J,axiom,
% 0.29/0.45 ! [X1: nat,X31: type_M1610475166scheme,X32: type_M1610475166scheme] :
% 0.29/0.45 ( ( type_M91906176e_FVar @ X1 )
% 0.29/0.45 != ( type_M1518733067e_SFun @ X31 @ X32 ) ) ).
% 0.29/0.45
% 0.29/0.45 % type_scheme.distinct(3)
% 0.29/0.45 thf(fact_10_app__subst__Cons,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( type_M1470978233struct @ A )
% 0.29/0.45 => ! [S: nat > type_Mirabelle_typ,X3: A,L: list @ A] :
% 0.29/0.45 ( ( type_M353778473_subst @ ( list @ A ) @ S @ ( cons @ A @ X3 @ L ) )
% 0.29/0.45 = ( cons @ A @ ( type_M353778473_subst @ A @ S @ X3 ) @ ( type_M353778473_subst @ ( list @ A ) @ S @ L ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % app_subst_Cons
% 0.29/0.45 thf(fact_11_free__tv__mk__scheme,axiom,
% 0.29/0.45 ! [T: type_Mirabelle_typ] :
% 0.29/0.45 ( ( type_M950795831ree_tv @ type_M1610475166scheme @ ( type_M540877363scheme @ T ) )
% 0.29/0.45 = ( type_M950795831ree_tv @ type_Mirabelle_typ @ T ) ) ).
% 0.29/0.45
% 0.29/0.45 % free_tv_mk_scheme
% 0.29/0.45 thf(fact_12_free__tv__type__scheme_Osimps_I1_J,axiom,
% 0.29/0.45 ! [M: nat] :
% 0.29/0.45 ( ( type_M950795831ree_tv @ type_M1610475166scheme @ ( type_M91906176e_FVar @ M ) )
% 0.29/0.45 = ( insert2 @ nat @ M @ ( bot_bot @ ( set @ nat ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % free_tv_type_scheme.simps(1)
% 0.29/0.45 thf(fact_13_new__if__subst__type__scheme,axiom,
% 0.29/0.45 ! [N2: nat,Sch: type_M1610475166scheme,S: nat > type_Mirabelle_typ,S3: nat > type_Mirabelle_typ] :
% 0.29/0.45 ( ( type_M1046766514new_tv @ type_M1610475166scheme @ N2 @ Sch )
% 0.29/0.45 => ( ( type_M353778473_subst @ type_M1610475166scheme
% 0.29/0.45 @ ^ [K: nat] : ( if @ type_Mirabelle_typ @ ( ord_less @ nat @ K @ N2 ) @ ( S @ K ) @ ( S3 @ K ) )
% 0.29/0.45 @ Sch )
% 0.29/0.45 = ( type_M353778473_subst @ type_M1610475166scheme @ S @ Sch ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % new_if_subst_type_scheme
% 0.29/0.45 thf(fact_14_typ_Ocase__distrib,axiom,
% 0.29/0.45 ! [A: $tType,B: $tType,H: A > B,F1: nat > A,F2: type_Mirabelle_typ > type_Mirabelle_typ > A,Typ: type_Mirabelle_typ] :
% 0.29/0.45 ( ( H @ ( type_M1695911984se_typ @ A @ F1 @ F2 @ Typ ) )
% 0.29/0.45 = ( type_M1695911984se_typ @ B
% 0.29/0.45 @ ^ [X4: nat] : ( H @ ( F1 @ X4 ) )
% 0.29/0.45 @ ^ [X12: type_Mirabelle_typ,X22: type_Mirabelle_typ] : ( H @ ( F2 @ X12 @ X22 ) )
% 0.29/0.45 @ Typ ) ) ).
% 0.29/0.45
% 0.29/0.45 % typ.case_distrib
% 0.29/0.45 thf(fact_15_type__scheme_Oinject_I3_J,axiom,
% 0.29/0.45 ! [X31: type_M1610475166scheme,X32: type_M1610475166scheme,Y31: type_M1610475166scheme,Y32: type_M1610475166scheme] :
% 0.29/0.45 ( ( ( type_M1518733067e_SFun @ X31 @ X32 )
% 0.29/0.45 = ( type_M1518733067e_SFun @ Y31 @ Y32 ) )
% 0.29/0.45 = ( ( X31 = Y31 )
% 0.29/0.45 & ( X32 = Y32 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % type_scheme.inject(3)
% 0.29/0.45 thf(fact_16_type__scheme_Oinject_I2_J,axiom,
% 0.29/0.45 ! [X2: nat,Y2: nat] :
% 0.29/0.45 ( ( ( type_M1264524676e_BVar @ X2 )
% 0.29/0.45 = ( type_M1264524676e_BVar @ Y2 ) )
% 0.29/0.45 = ( X2 = Y2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % type_scheme.inject(2)
% 0.29/0.45 thf(fact_17_new__tv__Cons,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( type_M1470978233struct @ A )
% 0.29/0.45 => ! [N2: nat,X3: A,L: list @ A] :
% 0.29/0.45 ( ( type_M1046766514new_tv @ ( list @ A ) @ N2 @ ( cons @ A @ X3 @ L ) )
% 0.29/0.45 = ( ( type_M1046766514new_tv @ A @ N2 @ X3 )
% 0.29/0.45 & ( type_M1046766514new_tv @ ( list @ A ) @ N2 @ L ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % new_tv_Cons
% 0.29/0.45 thf(fact_18_subst__mk__scheme,axiom,
% 0.29/0.45 ! [S: nat > type_Mirabelle_typ,T: type_Mirabelle_typ] :
% 0.29/0.45 ( ( type_M353778473_subst @ type_M1610475166scheme @ S @ ( type_M540877363scheme @ T ) )
% 0.29/0.45 = ( type_M540877363scheme @ ( type_M353778473_subst @ type_Mirabelle_typ @ S @ T ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % subst_mk_scheme
% 0.29/0.45 thf(fact_19_new__tv__Fun2,axiom,
% 0.29/0.45 ! [N2: nat,T1: type_M1610475166scheme,T2: type_M1610475166scheme] :
% 0.29/0.45 ( ( type_M1046766514new_tv @ type_M1610475166scheme @ N2 @ ( type_M1518733067e_SFun @ T1 @ T2 ) )
% 0.29/0.45 = ( ( type_M1046766514new_tv @ type_M1610475166scheme @ N2 @ T1 )
% 0.29/0.45 & ( type_M1046766514new_tv @ type_M1610475166scheme @ N2 @ T2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % new_tv_Fun2
% 0.29/0.45 thf(fact_20_new__tv__BVar,axiom,
% 0.29/0.45 ! [N2: nat,M: nat] : ( type_M1046766514new_tv @ type_M1610475166scheme @ N2 @ ( type_M1264524676e_BVar @ M ) ) ).
% 0.29/0.45
% 0.29/0.45 % new_tv_BVar
% 0.29/0.45 thf(fact_21_new__tv__FVar,axiom,
% 0.29/0.45 ! [N2: nat,M: nat] :
% 0.29/0.45 ( ( type_M1046766514new_tv @ type_M1610475166scheme @ N2 @ ( type_M91906176e_FVar @ M ) )
% 0.29/0.45 = ( ord_less @ nat @ M @ N2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % new_tv_FVar
% 0.29/0.45 thf(fact_22_type__scheme_Osimps_I15_J,axiom,
% 0.29/0.45 ! [A: $tType,F1: nat > A,F2: nat > A,F3: type_M1610475166scheme > type_M1610475166scheme > A > A > A,X31: type_M1610475166scheme,X32: type_M1610475166scheme] :
% 0.29/0.45 ( ( type_M1705333808scheme @ A @ F1 @ F2 @ F3 @ ( type_M1518733067e_SFun @ X31 @ X32 ) )
% 0.29/0.45 = ( F3 @ X31 @ X32 @ ( type_M1705333808scheme @ A @ F1 @ F2 @ F3 @ X31 ) @ ( type_M1705333808scheme @ A @ F1 @ F2 @ F3 @ X32 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % type_scheme.simps(15)
% 0.29/0.45 thf(fact_23_type__scheme_Osimps_I14_J,axiom,
% 0.29/0.45 ! [A: $tType,F1: nat > A,F2: nat > A,F3: type_M1610475166scheme > type_M1610475166scheme > A > A > A,X2: nat] :
% 0.29/0.45 ( ( type_M1705333808scheme @ A @ F1 @ F2 @ F3 @ ( type_M1264524676e_BVar @ X2 ) )
% 0.29/0.45 = ( F2 @ X2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % type_scheme.simps(14)
% 0.29/0.45 thf(fact_24_type__scheme_Osimps_I12_J,axiom,
% 0.29/0.45 ! [A: $tType,F1: nat > A,F2: nat > A,F3: type_M1610475166scheme > type_M1610475166scheme > A,X31: type_M1610475166scheme,X32: type_M1610475166scheme] :
% 0.29/0.45 ( ( type_M697345518scheme @ A @ F1 @ F2 @ F3 @ ( type_M1518733067e_SFun @ X31 @ X32 ) )
% 0.29/0.45 = ( F3 @ X31 @ X32 ) ) ).
% 0.29/0.45
% 0.29/0.45 % type_scheme.simps(12)
% 0.29/0.45 thf(fact_25_type__scheme_Osimps_I11_J,axiom,
% 0.29/0.45 ! [A: $tType,F1: nat > A,F2: nat > A,F3: type_M1610475166scheme > type_M1610475166scheme > A,X2: nat] :
% 0.29/0.45 ( ( type_M697345518scheme @ A @ F1 @ F2 @ F3 @ ( type_M1264524676e_BVar @ X2 ) )
% 0.29/0.45 = ( F2 @ X2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % type_scheme.simps(11)
% 0.29/0.45 thf(fact_26_type__scheme_Odistinct_I5_J,axiom,
% 0.29/0.45 ! [X2: nat,X31: type_M1610475166scheme,X32: type_M1610475166scheme] :
% 0.29/0.45 ( ( type_M1264524676e_BVar @ X2 )
% 0.29/0.45 != ( type_M1518733067e_SFun @ X31 @ X32 ) ) ).
% 0.29/0.45
% 0.29/0.45 % type_scheme.distinct(5)
% 0.29/0.45 thf(fact_27_mk__scheme__Fun,axiom,
% 0.29/0.45 ! [T: type_Mirabelle_typ,Sch1: type_M1610475166scheme,Sch2: type_M1610475166scheme] :
% 0.29/0.45 ( ( ( type_M540877363scheme @ T )
% 0.29/0.45 = ( type_M1518733067e_SFun @ Sch1 @ Sch2 ) )
% 0.29/0.45 => ? [T12: type_Mirabelle_typ,T22: type_Mirabelle_typ] :
% 0.29/0.45 ( ( Sch1
% 0.29/0.45 = ( type_M540877363scheme @ T12 ) )
% 0.29/0.45 & ( Sch2
% 0.29/0.45 = ( type_M540877363scheme @ T22 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mk_scheme_Fun
% 0.29/0.45 thf(fact_28_eq__free__eq__subst__te,axiom,
% 0.29/0.45 ! [T: type_Mirabelle_typ,S1: nat > type_Mirabelle_typ,S2: nat > type_Mirabelle_typ] :
% 0.29/0.45 ( ! [N: nat] :
% 0.29/0.45 ( ( member @ nat @ N @ ( type_M950795831ree_tv @ type_Mirabelle_typ @ T ) )
% 0.29/0.45 => ( ( S1 @ N )
% 0.29/0.45 = ( S2 @ N ) ) )
% 0.29/0.45 => ( ( type_M353778473_subst @ type_Mirabelle_typ @ S1 @ T )
% 0.29/0.45 = ( type_M353778473_subst @ type_Mirabelle_typ @ S2 @ T ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % eq_free_eq_subst_te
% 0.29/0.45 thf(fact_29_eq__subst__te__eq__free,axiom,
% 0.29/0.45 ! [S1: nat > type_Mirabelle_typ,T: type_Mirabelle_typ,S2: nat > type_Mirabelle_typ,N2: nat] :
% 0.29/0.45 ( ( ( type_M353778473_subst @ type_Mirabelle_typ @ S1 @ T )
% 0.29/0.45 = ( type_M353778473_subst @ type_Mirabelle_typ @ S2 @ T ) )
% 0.29/0.45 => ( ( member @ nat @ N2 @ ( type_M950795831ree_tv @ type_Mirabelle_typ @ T ) )
% 0.29/0.45 => ( ( S1 @ N2 )
% 0.29/0.45 = ( S2 @ N2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % eq_subst_te_eq_free
% 0.29/0.45 thf(fact_30_typ__substitutions__only__on__free__variables,axiom,
% 0.29/0.45 ! [T: type_Mirabelle_typ,S: nat > type_Mirabelle_typ,S3: nat > type_Mirabelle_typ] :
% 0.29/0.45 ( ! [X: nat] :
% 0.29/0.45 ( ( member @ nat @ X @ ( type_M950795831ree_tv @ type_Mirabelle_typ @ T ) )
% 0.29/0.45 => ( ( S @ X )
% 0.29/0.45 = ( S3 @ X ) ) )
% 0.29/0.45 => ( ( type_M353778473_subst @ type_Mirabelle_typ @ S @ T )
% 0.29/0.45 = ( type_M353778473_subst @ type_Mirabelle_typ @ S3 @ T ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % typ_substitutions_only_on_free_variables
% 0.29/0.45 thf(fact_31_mk__scheme__injective,axiom,
% 0.29/0.45 ! [T: type_Mirabelle_typ,T3: type_Mirabelle_typ] :
% 0.29/0.45 ( ( ( type_M540877363scheme @ T )
% 0.29/0.45 = ( type_M540877363scheme @ T3 ) )
% 0.29/0.45 => ( T = T3 ) ) ).
% 0.29/0.45
% 0.29/0.45 % mk_scheme_injective
% 0.29/0.45 thf(fact_32_free__tv__type__scheme_Osimps_I2_J,axiom,
% 0.29/0.45 ! [M: nat] :
% 0.29/0.45 ( ( type_M950795831ree_tv @ type_M1610475166scheme @ ( type_M1264524676e_BVar @ M ) )
% 0.29/0.45 = ( bot_bot @ ( set @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % free_tv_type_scheme.simps(2)
% 0.29/0.45 thf(fact_33_type__scheme_Oexhaust,axiom,
% 0.29/0.45 ! [Y: type_M1610475166scheme] :
% 0.29/0.45 ( ! [X13: nat] :
% 0.29/0.45 ( Y
% 0.29/0.45 != ( type_M91906176e_FVar @ X13 ) )
% 0.29/0.45 => ( ! [X23: nat] :
% 0.29/0.45 ( Y
% 0.29/0.45 != ( type_M1264524676e_BVar @ X23 ) )
% 0.29/0.45 => ~ ! [X312: type_M1610475166scheme,X322: type_M1610475166scheme] :
% 0.29/0.45 ( Y
% 0.29/0.45 != ( type_M1518733067e_SFun @ X312 @ X322 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % type_scheme.exhaust
% 0.29/0.45 thf(fact_34_type__scheme_Oinduct,axiom,
% 0.29/0.45 ! [P: type_M1610475166scheme > $o,Type_scheme: type_M1610475166scheme] :
% 0.29/0.45 ( ! [X: nat] : ( P @ ( type_M91906176e_FVar @ X ) )
% 0.29/0.45 => ( ! [X: nat] : ( P @ ( type_M1264524676e_BVar @ X ) )
% 0.29/0.45 => ( ! [X1a: type_M1610475166scheme,X2a: type_M1610475166scheme] :
% 0.29/0.45 ( ( P @ X1a )
% 0.29/0.45 => ( ( P @ X2a )
% 0.29/0.45 => ( P @ ( type_M1518733067e_SFun @ X1a @ X2a ) ) ) )
% 0.29/0.45 => ( P @ Type_scheme ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % type_scheme.induct
% 0.29/0.45 thf(fact_35_new__tv__def,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( type_M1470978233struct @ A )
% 0.29/0.45 => ( ( type_M1046766514new_tv @ A )
% 0.29/0.45 = ( ^ [N3: nat,Ts: A] :
% 0.29/0.45 ! [M2: nat] :
% 0.29/0.45 ( ( member @ nat @ M2 @ ( type_M950795831ree_tv @ A @ Ts ) )
% 0.29/0.45 => ( ord_less @ nat @ M2 @ N3 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % new_tv_def
% 0.29/0.45 thf(fact_36_type__scheme_Ocase__distrib,axiom,
% 0.29/0.45 ! [A: $tType,B: $tType,H: A > B,F1: nat > A,F2: nat > A,F3: type_M1610475166scheme > type_M1610475166scheme > A,Type_scheme: type_M1610475166scheme] :
% 0.29/0.45 ( ( H @ ( type_M697345518scheme @ A @ F1 @ F2 @ F3 @ Type_scheme ) )
% 0.29/0.45 = ( type_M697345518scheme @ B
% 0.29/0.45 @ ^ [X4: nat] : ( H @ ( F1 @ X4 ) )
% 0.29/0.45 @ ^ [X4: nat] : ( H @ ( F2 @ X4 ) )
% 0.29/0.45 @ ^ [X12: type_M1610475166scheme,X22: type_M1610475166scheme] : ( H @ ( F3 @ X12 @ X22 ) )
% 0.29/0.45 @ Type_scheme ) ) ).
% 0.29/0.45
% 0.29/0.45 % type_scheme.case_distrib
% 0.29/0.45 thf(fact_37_singleton__conv,axiom,
% 0.29/0.45 ! [A: $tType,A2: A] :
% 0.29/0.45 ( ( collect @ A
% 0.29/0.45 @ ^ [X4: A] : ( X4 = A2 ) )
% 0.29/0.45 = ( insert2 @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % singleton_conv
% 0.29/0.45 thf(fact_38_singleton__conv2,axiom,
% 0.29/0.45 ! [A: $tType,A2: A] :
% 0.29/0.45 ( ( collect @ A
% 0.29/0.45 @ ( ^ [Y3: A,Z: A] : ( Y3 = Z )
% 0.29/0.45 @ A2 ) )
% 0.29/0.45 = ( insert2 @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % singleton_conv2
% 0.29/0.45 thf(fact_39_singletonI,axiom,
% 0.29/0.45 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert2 @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % singletonI
% 0.29/0.45 thf(fact_40_insertCI,axiom,
% 0.29/0.45 ! [A: $tType,A2: A,B2: set @ A,B3: A] :
% 0.29/0.45 ( ( ~ ( member @ A @ A2 @ B2 )
% 0.29/0.45 => ( A2 = B3 ) )
% 0.29/0.45 => ( member @ A @ A2 @ ( insert2 @ A @ B3 @ B2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % insertCI
% 0.29/0.45 thf(fact_41_insert__iff,axiom,
% 0.29/0.45 ! [A: $tType,A2: A,B3: A,A3: set @ A] :
% 0.29/0.45 ( ( member @ A @ A2 @ ( insert2 @ A @ B3 @ A3 ) )
% 0.29/0.45 = ( ( A2 = B3 )
% 0.29/0.45 | ( member @ A @ A2 @ A3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % insert_iff
% 0.29/0.45 thf(fact_42_insert__absorb2,axiom,
% 0.29/0.45 ! [A: $tType,X3: A,A3: set @ A] :
% 0.29/0.45 ( ( insert2 @ A @ X3 @ ( insert2 @ A @ X3 @ A3 ) )
% 0.29/0.45 = ( insert2 @ A @ X3 @ A3 ) ) ).
% 0.29/0.45
% 0.29/0.45 % insert_absorb2
% 0.29/0.45 thf(fact_43_list_Oinject,axiom,
% 0.29/0.45 ! [A: $tType,X21: A,X222: list @ A,Y21: A,Y22: list @ A] :
% 0.29/0.45 ( ( ( cons @ A @ X21 @ X222 )
% 0.29/0.45 = ( cons @ A @ Y21 @ Y22 ) )
% 0.29/0.45 = ( ( X21 = Y21 )
% 0.29/0.45 & ( X222 = Y22 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % list.inject
% 0.29/0.45 thf(fact_44_empty__iff,axiom,
% 0.29/0.45 ! [A: $tType,C: A] :
% 0.29/0.45 ~ ( member @ A @ C @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % empty_iff
% 0.29/0.45 thf(fact_45_mem__Collect__eq,axiom,
% 0.29/0.45 ! [A: $tType,A2: A,P: A > $o] :
% 0.29/0.45 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.29/0.45 = ( P @ A2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % mem_Collect_eq
% 0.29/0.45 thf(fact_46_Collect__mem__eq,axiom,
% 0.29/0.45 ! [A: $tType,A3: set @ A] :
% 0.29/0.45 ( ( collect @ A
% 0.29/0.45 @ ^ [X4: A] : ( member @ A @ X4 @ A3 ) )
% 0.29/0.45 = A3 ) ).
% 0.29/0.45
% 0.29/0.45 % Collect_mem_eq
% 0.29/0.45 thf(fact_47_Collect__cong,axiom,
% 0.29/0.45 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.29/0.45 ( ! [X: A] :
% 0.29/0.45 ( ( P @ X )
% 0.29/0.45 = ( Q @ X ) )
% 0.29/0.45 => ( ( collect @ A @ P )
% 0.29/0.45 = ( collect @ A @ Q ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Collect_cong
% 0.29/0.45 thf(fact_48_ext,axiom,
% 0.29/0.45 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.29/0.45 ( ! [X: A] :
% 0.29/0.45 ( ( F @ X )
% 0.29/0.45 = ( G @ X ) )
% 0.29/0.45 => ( F = G ) ) ).
% 0.29/0.45
% 0.29/0.45 % ext
% 0.29/0.45 thf(fact_49_all__not__in__conv,axiom,
% 0.29/0.45 ! [A: $tType,A3: set @ A] :
% 0.29/0.45 ( ( ! [X4: A] :
% 0.29/0.45 ~ ( member @ A @ X4 @ A3 ) )
% 0.29/0.45 = ( A3
% 0.29/0.45 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % all_not_in_conv
% 0.29/0.45 thf(fact_50_Collect__empty__eq,axiom,
% 0.29/0.45 ! [A: $tType,P: A > $o] :
% 0.29/0.45 ( ( ( collect @ A @ P )
% 0.29/0.45 = ( bot_bot @ ( set @ A ) ) )
% 0.29/0.45 = ( ! [X4: A] :
% 0.29/0.45 ~ ( P @ X4 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Collect_empty_eq
% 0.29/0.45 thf(fact_51_empty__Collect__eq,axiom,
% 0.29/0.45 ! [A: $tType,P: A > $o] :
% 0.29/0.45 ( ( ( bot_bot @ ( set @ A ) )
% 0.29/0.45 = ( collect @ A @ P ) )
% 0.29/0.45 = ( ! [X4: A] :
% 0.29/0.45 ~ ( P @ X4 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % empty_Collect_eq
% 0.29/0.45 thf(fact_52_new__if__subst__type__scheme__list,axiom,
% 0.29/0.45 ! [N2: nat,A3: list @ type_M1610475166scheme,S: nat > type_Mirabelle_typ,S3: nat > type_Mirabelle_typ] :
% 0.29/0.45 ( ( type_M1046766514new_tv @ ( list @ type_M1610475166scheme ) @ N2 @ A3 )
% 0.29/0.45 => ( ( type_M353778473_subst @ ( list @ type_M1610475166scheme )
% 0.29/0.45 @ ^ [K: nat] : ( if @ type_Mirabelle_typ @ ( ord_less @ nat @ K @ N2 ) @ ( S @ K ) @ ( S3 @ K ) )
% 0.29/0.45 @ A3 )
% 0.29/0.45 = ( type_M353778473_subst @ ( list @ type_M1610475166scheme ) @ S @ A3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % new_if_subst_type_scheme_list
% 0.29/0.45 thf(fact_53_ex__in__conv,axiom,
% 0.29/0.45 ! [A: $tType,A3: set @ A] :
% 0.29/0.45 ( ( ? [X4: A] : ( member @ A @ X4 @ A3 ) )
% 0.29/0.45 = ( A3
% 0.29/0.45 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % ex_in_conv
% 0.29/0.45 thf(fact_54_equals0I,axiom,
% 0.29/0.45 ! [A: $tType,A3: set @ A] :
% 0.29/0.45 ( ! [Y4: A] :
% 0.29/0.45 ~ ( member @ A @ Y4 @ A3 )
% 0.29/0.45 => ( A3
% 0.29/0.45 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % equals0I
% 0.29/0.45 thf(fact_55_equals0D,axiom,
% 0.29/0.45 ! [A: $tType,A3: set @ A,A2: A] :
% 0.29/0.45 ( ( A3
% 0.29/0.45 = ( bot_bot @ ( set @ A ) ) )
% 0.29/0.45 => ~ ( member @ A @ A2 @ A3 ) ) ).
% 0.29/0.45
% 0.29/0.45 % equals0D
% 0.29/0.45 thf(fact_56_emptyE,axiom,
% 0.29/0.45 ! [A: $tType,A2: A] :
% 0.29/0.45 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % emptyE
% 0.29/0.45 thf(fact_57_not__Cons__self2,axiom,
% 0.29/0.45 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.29/0.45 ( ( cons @ A @ X3 @ Xs )
% 0.29/0.45 != Xs ) ).
% 0.29/0.45
% 0.29/0.45 % not_Cons_self2
% 0.29/0.45 thf(fact_58_mk__disjoint__insert,axiom,
% 0.29/0.45 ! [A: $tType,A2: A,A3: set @ A] :
% 0.29/0.45 ( ( member @ A @ A2 @ A3 )
% 0.29/0.45 => ? [B4: set @ A] :
% 0.29/0.45 ( ( A3
% 0.29/0.45 = ( insert2 @ A @ A2 @ B4 ) )
% 0.29/0.45 & ~ ( member @ A @ A2 @ B4 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mk_disjoint_insert
% 0.29/0.45 thf(fact_59_insert__commute,axiom,
% 0.29/0.45 ! [A: $tType,X3: A,Y: A,A3: set @ A] :
% 0.29/0.45 ( ( insert2 @ A @ X3 @ ( insert2 @ A @ Y @ A3 ) )
% 0.29/0.45 = ( insert2 @ A @ Y @ ( insert2 @ A @ X3 @ A3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % insert_commute
% 0.29/0.45 thf(fact_60_insert__eq__iff,axiom,
% 0.29/0.45 ! [A: $tType,A2: A,A3: set @ A,B3: A,B2: set @ A] :
% 0.29/0.45 ( ~ ( member @ A @ A2 @ A3 )
% 0.29/0.45 => ( ~ ( member @ A @ B3 @ B2 )
% 0.29/0.45 => ( ( ( insert2 @ A @ A2 @ A3 )
% 0.29/0.45 = ( insert2 @ A @ B3 @ B2 ) )
% 0.29/0.45 = ( ( ( A2 = B3 )
% 0.29/0.45 => ( A3 = B2 ) )
% 0.29/0.45 & ( ( A2 != B3 )
% 0.29/0.45 => ? [C2: set @ A] :
% 0.29/0.45 ( ( A3
% 0.29/0.45 = ( insert2 @ A @ B3 @ C2 ) )
% 0.29/0.45 & ~ ( member @ A @ B3 @ C2 )
% 0.29/0.45 & ( B2
% 0.29/0.45 = ( insert2 @ A @ A2 @ C2 ) )
% 0.29/0.45 & ~ ( member @ A @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % insert_eq_iff
% 0.29/0.45 thf(fact_61_insert__absorb,axiom,
% 0.29/0.45 ! [A: $tType,A2: A,A3: set @ A] :
% 0.29/0.45 ( ( member @ A @ A2 @ A3 )
% 0.29/0.45 => ( ( insert2 @ A @ A2 @ A3 )
% 0.29/0.45 = A3 ) ) ).
% 0.29/0.45
% 0.29/0.45 % insert_absorb
% 0.29/0.45 thf(fact_62_insert__ident,axiom,
% 0.29/0.45 ! [A: $tType,X3: A,A3: set @ A,B2: set @ A] :
% 0.29/0.45 ( ~ ( member @ A @ X3 @ A3 )
% 0.29/0.45 => ( ~ ( member @ A @ X3 @ B2 )
% 0.29/0.45 => ( ( ( insert2 @ A @ X3 @ A3 )
% 0.29/0.45 = ( insert2 @ A @ X3 @ B2 ) )
% 0.29/0.45 = ( A3 = B2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % insert_ident
% 0.29/0.45 thf(fact_63_Set_Oset__insert,axiom,
% 0.29/0.45 ! [A: $tType,X3: A,A3: set @ A] :
% 0.29/0.45 ( ( member @ A @ X3 @ A3 )
% 0.29/0.45 => ~ ! [B4: set @ A] :
% 0.29/0.45 ( ( A3
% 0.29/0.45 = ( insert2 @ A @ X3 @ B4 ) )
% 0.29/0.45 => ( member @ A @ X3 @ B4 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Set.set_insert
% 0.29/0.45 thf(fact_64_insertI2,axiom,
% 0.29/0.45 ! [A: $tType,A2: A,B2: set @ A,B3: A] :
% 0.29/0.45 ( ( member @ A @ A2 @ B2 )
% 0.29/0.45 => ( member @ A @ A2 @ ( insert2 @ A @ B3 @ B2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % insertI2
% 0.29/0.45 thf(fact_65_insertI1,axiom,
% 0.29/0.45 ! [A: $tType,A2: A,B2: set @ A] : ( member @ A @ A2 @ ( insert2 @ A @ A2 @ B2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % insertI1
% 0.29/0.45 thf(fact_66_insertE,axiom,
% 0.29/0.45 ! [A: $tType,A2: A,B3: A,A3: set @ A] :
% 0.29/0.45 ( ( member @ A @ A2 @ ( insert2 @ A @ B3 @ A3 ) )
% 0.29/0.45 => ( ( A2 != B3 )
% 0.29/0.45 => ( member @ A @ A2 @ A3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % insertE
% 0.29/0.45 thf(fact_67_empty__def,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( bot_bot @ ( set @ A ) )
% 0.29/0.45 = ( collect @ A
% 0.29/0.45 @ ^ [X4: A] : $false ) ) ).
% 0.29/0.45
% 0.29/0.45 % empty_def
% 0.29/0.45 thf(fact_68_insert__Collect,axiom,
% 0.29/0.45 ! [A: $tType,A2: A,P: A > $o] :
% 0.29/0.45 ( ( insert2 @ A @ A2 @ ( collect @ A @ P ) )
% 0.29/0.45 = ( collect @ A
% 0.29/0.45 @ ^ [U: A] :
% 0.29/0.45 ( ( U != A2 )
% 0.29/0.45 => ( P @ U ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % insert_Collect
% 0.29/0.45 thf(fact_69_insert__compr,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( insert2 @ A )
% 0.29/0.45 = ( ^ [A4: A,B5: set @ A] :
% 0.29/0.45 ( collect @ A
% 0.29/0.45 @ ^ [X4: A] :
% 0.29/0.45 ( ( X4 = A4 )
% 0.29/0.45 | ( member @ A @ X4 @ B5 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % insert_compr
% 0.29/0.45 thf(fact_70_singleton__inject,axiom,
% 0.29/0.45 ! [A: $tType,A2: A,B3: A] :
% 0.29/0.45 ( ( ( insert2 @ A @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.29/0.45 = ( insert2 @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.29/0.45 => ( A2 = B3 ) ) ).
% 0.29/0.45
% 0.29/0.45 % singleton_inject
% 0.29/0.45 thf(fact_71_insert__not__empty,axiom,
% 0.29/0.45 ! [A: $tType,A2: A,A3: set @ A] :
% 0.29/0.45 ( ( insert2 @ A @ A2 @ A3 )
% 0.29/0.45 != ( bot_bot @ ( set @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % insert_not_empty
% 0.29/0.45 thf(fact_72_doubleton__eq__iff,axiom,
% 0.29/0.45 ! [A: $tType,A2: A,B3: A,C: A,D: A] :
% 0.29/0.45 ( ( ( insert2 @ A @ A2 @ ( insert2 @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.29/0.45 = ( insert2 @ A @ C @ ( insert2 @ A @ D @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.29/0.45 = ( ( ( A2 = C )
% 0.29/0.45 & ( B3 = D ) )
% 0.29/0.45 | ( ( A2 = D )
% 0.29/0.45 & ( B3 = C ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % doubleton_eq_iff
% 0.29/0.45 thf(fact_73_singleton__iff,axiom,
% 0.29/0.45 ! [A: $tType,B3: A,A2: A] :
% 0.29/0.45 ( ( member @ A @ B3 @ ( insert2 @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.29/0.45 = ( B3 = A2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % singleton_iff
% 0.29/0.45 thf(fact_74_singletonD,axiom,
% 0.29/0.45 ! [A: $tType,B3: A,A2: A] :
% 0.29/0.45 ( ( member @ A @ B3 @ ( insert2 @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.29/0.45 => ( B3 = A2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % singletonD
% 0.29/0.45 thf(fact_75_Collect__conv__if2,axiom,
% 0.29/0.45 ! [A: $tType,P: A > $o,A2: A] :
% 0.29/0.45 ( ( ( P @ A2 )
% 0.29/0.45 => ( ( collect @ A
% 0.29/0.45 @ ^ [X4: A] :
% 0.29/0.45 ( ( A2 = X4 )
% 0.29/0.45 & ( P @ X4 ) ) )
% 0.29/0.45 = ( insert2 @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.29/0.45 & ( ~ ( P @ A2 )
% 0.29/0.45 => ( ( collect @ A
% 0.29/0.45 @ ^ [X4: A] :
% 0.29/0.45 ( ( A2 = X4 )
% 0.29/0.45 & ( P @ X4 ) ) )
% 0.29/0.45 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Collect_conv_if2
% 0.29/0.45 thf(fact_76_Collect__conv__if,axiom,
% 0.29/0.45 ! [A: $tType,P: A > $o,A2: A] :
% 0.29/0.45 ( ( ( P @ A2 )
% 0.29/0.45 => ( ( collect @ A
% 0.29/0.45 @ ^ [X4: A] :
% 0.29/0.45 ( ( X4 = A2 )
% 0.29/0.45 & ( P @ X4 ) ) )
% 0.29/0.45 = ( insert2 @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.29/0.45 & ( ~ ( P @ A2 )
% 0.29/0.45 => ( ( collect @ A
% 0.29/0.45 @ ^ [X4: A] :
% 0.29/0.45 ( ( X4 = A2 )
% 0.29/0.45 & ( P @ X4 ) ) )
% 0.29/0.45 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Collect_conv_if
% 0.29/0.45 thf(fact_77_the__elem__eq,axiom,
% 0.29/0.45 ! [A: $tType,X3: A] :
% 0.29/0.45 ( ( the_elem @ A @ ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.29/0.45 = X3 ) ).
% 0.29/0.45
% 0.29/0.45 % the_elem_eq
% 0.29/0.45 thf(fact_78_bot__apply,axiom,
% 0.29/0.45 ! [C3: $tType,D2: $tType] :
% 0.29/0.45 ( ( bot @ C3 )
% 0.29/0.45 => ( ( bot_bot @ ( D2 > C3 ) )
% 0.29/0.45 = ( ^ [X4: D2] : ( bot_bot @ C3 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % bot_apply
% 0.29/0.45 thf(fact_79_bound__tv__type__scheme_Osimps_I2_J,axiom,
% 0.29/0.45 ! [M: nat] :
% 0.29/0.45 ( ( type_M779184887und_tv @ type_M1610475166scheme @ ( type_M1264524676e_BVar @ M ) )
% 0.29/0.45 = ( insert2 @ nat @ M @ ( bot_bot @ ( set @ nat ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % bound_tv_type_scheme.simps(2)
% 0.29/0.45 thf(fact_80_is__singletonI,axiom,
% 0.29/0.45 ! [A: $tType,X3: A] : ( is_singleton @ A @ ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % is_singletonI
% 0.29/0.45 thf(fact_81_bot_Onot__eq__extremum,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( order_bot @ A )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( A2
% 0.29/0.45 != ( bot_bot @ A ) )
% 0.29/0.45 = ( ord_less @ A @ ( bot_bot @ A ) @ A2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % bot.not_eq_extremum
% 0.29/0.45 thf(fact_82_bot_Oextremum__strict,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( order_bot @ A )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ~ ( ord_less @ A @ A2 @ ( bot_bot @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % bot.extremum_strict
% 0.29/0.45 thf(fact_83_free__tv__TVar,axiom,
% 0.29/0.45 ! [M: nat] :
% 0.29/0.45 ( ( type_M950795831ree_tv @ type_Mirabelle_typ @ ( type_Mirabelle_TVar @ M ) )
% 0.29/0.45 = ( insert2 @ nat @ M @ ( bot_bot @ ( set @ nat ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % free_tv_TVar
% 0.29/0.45 thf(fact_84_bound__tv__type__scheme_Osimps_I1_J,axiom,
% 0.29/0.45 ! [M: nat] :
% 0.29/0.45 ( ( type_M779184887und_tv @ type_M1610475166scheme @ ( type_M91906176e_FVar @ M ) )
% 0.29/0.45 = ( bot_bot @ ( set @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % bound_tv_type_scheme.simps(1)
% 0.29/0.45 thf(fact_85_typ_Oinject_I1_J,axiom,
% 0.29/0.45 ! [X1: nat,Y1: nat] :
% 0.29/0.45 ( ( ( type_Mirabelle_TVar @ X1 )
% 0.29/0.45 = ( type_Mirabelle_TVar @ Y1 ) )
% 0.29/0.45 = ( X1 = Y1 ) ) ).
% 0.29/0.45
% 0.29/0.45 % typ.inject(1)
% 0.29/0.45 thf(fact_86_new__tv__TVar,axiom,
% 0.29/0.45 ! [N2: nat,M: nat] :
% 0.29/0.45 ( ( type_M1046766514new_tv @ type_Mirabelle_typ @ N2 @ ( type_Mirabelle_TVar @ M ) )
% 0.29/0.45 = ( ord_less @ nat @ M @ N2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % new_tv_TVar
% 0.29/0.45 thf(fact_87_new__tv__TVar__subst,axiom,
% 0.29/0.45 ! [N2: nat] : ( type_M1046766514new_tv @ ( nat > type_Mirabelle_typ ) @ N2 @ type_Mirabelle_TVar ) ).
% 0.29/0.45
% 0.29/0.45 % new_tv_TVar_subst
% 0.29/0.45 thf(fact_88_eq__free__eq__subst__scheme__list,axiom,
% 0.29/0.45 ! [A3: list @ type_M1610475166scheme,S1: nat > type_Mirabelle_typ,S2: nat > type_Mirabelle_typ] :
% 0.29/0.45 ( ! [N: nat] :
% 0.29/0.45 ( ( member @ nat @ N @ ( type_M950795831ree_tv @ ( list @ type_M1610475166scheme ) @ A3 ) )
% 0.29/0.45 => ( ( S1 @ N )
% 0.29/0.45 = ( S2 @ N ) ) )
% 0.29/0.45 => ( ( type_M353778473_subst @ ( list @ type_M1610475166scheme ) @ S1 @ A3 )
% 0.29/0.45 = ( type_M353778473_subst @ ( list @ type_M1610475166scheme ) @ S2 @ A3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % eq_free_eq_subst_scheme_list
% 0.29/0.45 thf(fact_89_scheme__list__substitutions__only__on__free__variables,axiom,
% 0.29/0.45 ! [A3: list @ type_M1610475166scheme,S: nat > type_Mirabelle_typ,S3: nat > type_Mirabelle_typ] :
% 0.29/0.45 ( ! [X: nat] :
% 0.29/0.45 ( ( member @ nat @ X @ ( type_M950795831ree_tv @ ( list @ type_M1610475166scheme ) @ A3 ) )
% 0.29/0.45 => ( ( S @ X )
% 0.29/0.45 = ( S3 @ X ) ) )
% 0.29/0.45 => ( ( type_M353778473_subst @ ( list @ type_M1610475166scheme ) @ S @ A3 )
% 0.29/0.45 = ( type_M353778473_subst @ ( list @ type_M1610475166scheme ) @ S3 @ A3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % scheme_list_substitutions_only_on_free_variables
% 0.29/0.45 thf(fact_90_bot__set__def,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( bot_bot @ ( set @ A ) )
% 0.29/0.45 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % bot_set_def
% 0.29/0.45 thf(fact_91_not__psubset__empty,axiom,
% 0.29/0.45 ! [A: $tType,A3: set @ A] :
% 0.29/0.45 ~ ( ord_less @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % not_psubset_empty
% 0.29/0.45 thf(fact_92_app__subst__TVar,axiom,
% 0.29/0.45 ! [S: nat > type_Mirabelle_typ,N2: nat] :
% 0.29/0.45 ( ( type_M353778473_subst @ type_Mirabelle_typ @ S @ ( type_Mirabelle_TVar @ N2 ) )
% 0.29/0.45 = ( S @ N2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % app_subst_TVar
% 0.29/0.45 thf(fact_93_is__singleton__the__elem,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( is_singleton @ A )
% 0.29/0.45 = ( ^ [A5: set @ A] :
% 0.29/0.45 ( A5
% 0.29/0.45 = ( insert2 @ A @ ( the_elem @ A @ A5 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % is_singleton_the_elem
% 0.29/0.45 thf(fact_94_typ_Osimps_I5_J,axiom,
% 0.29/0.45 ! [A: $tType,F1: nat > A,F2: type_Mirabelle_typ > type_Mirabelle_typ > A,X1: nat] :
% 0.29/0.45 ( ( type_M1695911984se_typ @ A @ F1 @ F2 @ ( type_Mirabelle_TVar @ X1 ) )
% 0.29/0.45 = ( F1 @ X1 ) ) ).
% 0.29/0.45
% 0.29/0.45 % typ.simps(5)
% 0.29/0.45 thf(fact_95_is__singletonI_H,axiom,
% 0.29/0.45 ! [A: $tType,A3: set @ A] :
% 0.29/0.45 ( ( A3
% 0.29/0.45 != ( bot_bot @ ( set @ A ) ) )
% 0.29/0.45 => ( ! [X: A,Y4: A] :
% 0.29/0.45 ( ( member @ A @ X @ A3 )
% 0.29/0.45 => ( ( member @ A @ Y4 @ A3 )
% 0.29/0.45 => ( X = Y4 ) ) )
% 0.29/0.45 => ( is_singleton @ A @ A3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % is_singletonI'
% 0.29/0.45 thf(fact_96_ord__eq__less__subst,axiom,
% 0.29/0.45 ! [A: $tType,B: $tType] :
% 0.29/0.45 ( ( ( ord @ B )
% 0.29/0.45 & ( ord @ A ) )
% 0.29/0.45 => ! [A2: A,F: B > A,B3: B,C: B] :
% 0.29/0.45 ( ( A2
% 0.29/0.45 = ( F @ B3 ) )
% 0.29/0.45 => ( ( ord_less @ B @ B3 @ C )
% 0.29/0.45 => ( ! [X: B,Y4: B] :
% 0.29/0.45 ( ( ord_less @ B @ X @ Y4 )
% 0.29/0.45 => ( ord_less @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/0.45 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % ord_eq_less_subst
% 0.29/0.45 thf(fact_97_ord__less__eq__subst,axiom,
% 0.29/0.45 ! [A: $tType,B: $tType] :
% 0.29/0.45 ( ( ( ord @ B )
% 0.29/0.45 & ( ord @ A ) )
% 0.29/0.45 => ! [A2: A,B3: A,F: A > B,C: B] :
% 0.29/0.45 ( ( ord_less @ A @ A2 @ B3 )
% 0.29/0.45 => ( ( ( F @ B3 )
% 0.29/0.45 = C )
% 0.29/0.45 => ( ! [X: A,Y4: A] :
% 0.29/0.45 ( ( ord_less @ A @ X @ Y4 )
% 0.29/0.45 => ( ord_less @ B @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/0.45 => ( ord_less @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % ord_less_eq_subst
% 0.29/0.45 thf(fact_98_order__less__subst1,axiom,
% 0.29/0.45 ! [A: $tType,B: $tType] :
% 0.29/0.45 ( ( ( order @ B )
% 0.29/0.45 & ( order @ A ) )
% 0.29/0.45 => ! [A2: A,F: B > A,B3: B,C: B] :
% 0.29/0.45 ( ( ord_less @ A @ A2 @ ( F @ B3 ) )
% 0.29/0.45 => ( ( ord_less @ B @ B3 @ C )
% 0.29/0.45 => ( ! [X: B,Y4: B] :
% 0.29/0.45 ( ( ord_less @ B @ X @ Y4 )
% 0.29/0.45 => ( ord_less @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/0.45 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % order_less_subst1
% 0.29/0.45 thf(fact_99_order__less__subst2,axiom,
% 0.29/0.45 ! [A: $tType,C3: $tType] :
% 0.29/0.45 ( ( ( order @ C3 )
% 0.29/0.45 & ( order @ A ) )
% 0.29/0.45 => ! [A2: A,B3: A,F: A > C3,C: C3] :
% 0.29/0.45 ( ( ord_less @ A @ A2 @ B3 )
% 0.29/0.45 => ( ( ord_less @ C3 @ ( F @ B3 ) @ C )
% 0.29/0.45 => ( ! [X: A,Y4: A] :
% 0.29/0.45 ( ( ord_less @ A @ X @ Y4 )
% 0.29/0.45 => ( ord_less @ C3 @ ( F @ X ) @ ( F @ Y4 ) ) )
% 0.29/0.45 => ( ord_less @ C3 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % order_less_subst2
% 0.29/0.45 thf(fact_100_lt__ex,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( no_bot @ A )
% 0.29/0.45 => ! [X3: A] :
% 0.29/0.45 ? [Y4: A] : ( ord_less @ A @ Y4 @ X3 ) ) ).
% 0.29/0.45
% 0.29/0.45 % lt_ex
% 0.29/0.45 thf(fact_101_gt__ex,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( no_top @ A )
% 0.29/0.45 => ! [X3: A] :
% 0.29/0.45 ? [X_1: A] : ( ord_less @ A @ X3 @ X_1 ) ) ).
% 0.29/0.45
% 0.29/0.45 % gt_ex
% 0.29/0.45 thf(fact_102_neqE,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linorder @ A )
% 0.29/0.45 => ! [X3: A,Y: A] :
% 0.29/0.45 ( ( X3 != Y )
% 0.29/0.45 => ( ~ ( ord_less @ A @ X3 @ Y )
% 0.29/0.45 => ( ord_less @ A @ Y @ X3 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % neqE
% 0.29/0.45 thf(fact_103_neq__iff,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linorder @ A )
% 0.29/0.45 => ! [X3: A,Y: A] :
% 0.29/0.45 ( ( X3 != Y )
% 0.29/0.45 = ( ( ord_less @ A @ X3 @ Y )
% 0.29/0.45 | ( ord_less @ A @ Y @ X3 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % neq_iff
% 0.29/0.45 thf(fact_104_order_Oasym,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( order @ A )
% 0.29/0.45 => ! [A2: A,B3: A] :
% 0.29/0.45 ( ( ord_less @ A @ A2 @ B3 )
% 0.29/0.45 => ~ ( ord_less @ A @ B3 @ A2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % order.asym
% 0.29/0.45 thf(fact_105_dense,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( dense_order @ A )
% 0.29/0.45 => ! [X3: A,Y: A] :
% 0.29/0.45 ( ( ord_less @ A @ X3 @ Y )
% 0.29/0.45 => ? [Z2: A] :
% 0.29/0.45 ( ( ord_less @ A @ X3 @ Z2 )
% 0.29/0.45 & ( ord_less @ A @ Z2 @ Y ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % dense
% 0.29/0.45 thf(fact_106_less__imp__neq,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( order @ A )
% 0.29/0.45 => ! [X3: A,Y: A] :
% 0.29/0.45 ( ( ord_less @ A @ X3 @ Y )
% 0.29/0.45 => ( X3 != Y ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % less_imp_neq
% 0.29/0.45 thf(fact_107_less__asym,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( preorder @ A )
% 0.29/0.45 => ! [X3: A,Y: A] :
% 0.29/0.45 ( ( ord_less @ A @ X3 @ Y )
% 0.29/0.45 => ~ ( ord_less @ A @ Y @ X3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % less_asym
% 0.29/0.45 thf(fact_108_less__asym_H,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( preorder @ A )
% 0.29/0.45 => ! [A2: A,B3: A] :
% 0.29/0.45 ( ( ord_less @ A @ A2 @ B3 )
% 0.29/0.45 => ~ ( ord_less @ A @ B3 @ A2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % less_asym'
% 0.29/0.45 thf(fact_109_less__trans,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( preorder @ A )
% 0.29/0.45 => ! [X3: A,Y: A,Z3: A] :
% 0.29/0.45 ( ( ord_less @ A @ X3 @ Y )
% 0.29/0.45 => ( ( ord_less @ A @ Y @ Z3 )
% 0.29/0.45 => ( ord_less @ A @ X3 @ Z3 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % less_trans
% 0.29/0.45 thf(fact_110_less__linear,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linorder @ A )
% 0.29/0.45 => ! [X3: A,Y: A] :
% 0.29/0.45 ( ( ord_less @ A @ X3 @ Y )
% 0.29/0.45 | ( X3 = Y )
% 0.29/0.45 | ( ord_less @ A @ Y @ X3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % less_linear
% 0.29/0.45 thf(fact_111_less__irrefl,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( preorder @ A )
% 0.29/0.45 => ! [X3: A] :
% 0.29/0.45 ~ ( ord_less @ A @ X3 @ X3 ) ) ).
% 0.29/0.45
% 0.29/0.45 % less_irrefl
% 0.29/0.45 thf(fact_112_ord__eq__less__trans,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ord @ A )
% 0.29/0.45 => ! [A2: A,B3: A,C: A] :
% 0.29/0.45 ( ( A2 = B3 )
% 0.29/0.45 => ( ( ord_less @ A @ B3 @ C )
% 0.29/0.45 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % ord_eq_less_trans
% 0.29/0.45 thf(fact_113_ord__less__eq__trans,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ord @ A )
% 0.29/0.45 => ! [A2: A,B3: A,C: A] :
% 0.29/0.45 ( ( ord_less @ A @ A2 @ B3 )
% 0.29/0.45 => ( ( B3 = C )
% 0.29/0.45 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % ord_less_eq_trans
% 0.29/0.45 thf(fact_114_dual__order_Oasym,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( order @ A )
% 0.29/0.45 => ! [B3: A,A2: A] :
% 0.29/0.45 ( ( ord_less @ A @ B3 @ A2 )
% 0.29/0.45 => ~ ( ord_less @ A @ A2 @ B3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % dual_order.asym
% 0.29/0.45 thf(fact_115_less__imp__not__eq,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( order @ A )
% 0.29/0.45 => ! [X3: A,Y: A] :
% 0.29/0.45 ( ( ord_less @ A @ X3 @ Y )
% 0.29/0.45 => ( X3 != Y ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % less_imp_not_eq
% 0.29/0.45 thf(fact_116_less__not__sym,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( preorder @ A )
% 0.29/0.45 => ! [X3: A,Y: A] :
% 0.29/0.45 ( ( ord_less @ A @ X3 @ Y )
% 0.29/0.45 => ~ ( ord_less @ A @ Y @ X3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % less_not_sym
% 0.29/0.45 thf(fact_117_less__induct,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( wellorder @ A )
% 0.29/0.45 => ! [P: A > $o,A2: A] :
% 0.29/0.45 ( ! [X: A] :
% 0.29/0.45 ( ! [Y5: A] :
% 0.29/0.45 ( ( ord_less @ A @ Y5 @ X )
% 0.29/0.45 => ( P @ Y5 ) )
% 0.29/0.45 => ( P @ X ) )
% 0.29/0.45 => ( P @ A2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % less_induct
% 0.29/0.45 thf(fact_118_antisym__conv3,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linorder @ A )
% 0.29/0.45 => ! [Y: A,X3: A] :
% 0.29/0.45 ( ~ ( ord_less @ A @ Y @ X3 )
% 0.29/0.45 => ( ( ~ ( ord_less @ A @ X3 @ Y ) )
% 0.29/0.45 = ( X3 = Y ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % antisym_conv3
% 0.29/0.45 thf(fact_119_less__imp__not__eq2,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( order @ A )
% 0.29/0.45 => ! [X3: A,Y: A] :
% 0.29/0.45 ( ( ord_less @ A @ X3 @ Y )
% 0.29/0.45 => ( Y != X3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % less_imp_not_eq2
% 0.29/0.45 thf(fact_120_less__imp__triv,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( preorder @ A )
% 0.29/0.45 => ! [X3: A,Y: A,P: $o] :
% 0.29/0.45 ( ( ord_less @ A @ X3 @ Y )
% 0.29/0.45 => ( ( ord_less @ A @ Y @ X3 )
% 0.29/0.45 => P ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % less_imp_triv
% 0.29/0.45 thf(fact_121_linorder__cases,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linorder @ A )
% 0.29/0.45 => ! [X3: A,Y: A] :
% 0.29/0.45 ( ~ ( ord_less @ A @ X3 @ Y )
% 0.29/0.45 => ( ( X3 != Y )
% 0.29/0.45 => ( ord_less @ A @ Y @ X3 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % linorder_cases
% 0.29/0.45 thf(fact_122_dual__order_Oirrefl,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( order @ A )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % dual_order.irrefl
% 0.29/0.45 thf(fact_123_order_Ostrict__trans,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( order @ A )
% 0.29/0.45 => ! [A2: A,B3: A,C: A] :
% 0.29/0.45 ( ( ord_less @ A @ A2 @ B3 )
% 0.29/0.45 => ( ( ord_less @ A @ B3 @ C )
% 0.29/0.45 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % order.strict_trans
% 0.29/0.45 thf(fact_124_less__imp__not__less,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( preorder @ A )
% 0.29/0.45 => ! [X3: A,Y: A] :
% 0.29/0.45 ( ( ord_less @ A @ X3 @ Y )
% 0.29/0.45 => ~ ( ord_less @ A @ Y @ X3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % less_imp_not_less
% 0.29/0.45 thf(fact_125_exists__least__iff,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( wellorder @ A )
% 0.29/0.45 => ( ( ^ [P2: A > $o] :
% 0.29/0.45 ? [X5: A] : ( P2 @ X5 ) )
% 0.29/0.45 = ( ^ [P3: A > $o] :
% 0.29/0.45 ? [N3: A] :
% 0.29/0.45 ( ( P3 @ N3 )
% 0.29/0.45 & ! [M2: A] :
% 0.29/0.45 ( ( ord_less @ A @ M2 @ N3 )
% 0.29/0.45 => ~ ( P3 @ M2 ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % exists_least_iff
% 0.29/0.45 thf(fact_126_linorder__less__wlog,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linorder @ A )
% 0.29/0.45 => ! [P: A > A > $o,A2: A,B3: A] :
% 0.29/0.45 ( ! [A6: A,B6: A] :
% 0.29/0.45 ( ( ord_less @ A @ A6 @ B6 )
% 0.29/0.45 => ( P @ A6 @ B6 ) )
% 0.29/0.45 => ( ! [A6: A] : ( P @ A6 @ A6 )
% 0.29/0.45 => ( ! [A6: A,B6: A] :
% 0.29/0.45 ( ( P @ B6 @ A6 )
% 0.29/0.45 => ( P @ A6 @ B6 ) )
% 0.29/0.45 => ( P @ A2 @ B3 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % linorder_less_wlog
% 0.29/0.45 thf(fact_127_dual__order_Ostrict__trans,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( order @ A )
% 0.29/0.45 => ! [B3: A,A2: A,C: A] :
% 0.29/0.45 ( ( ord_less @ A @ B3 @ A2 )
% 0.29/0.45 => ( ( ord_less @ A @ C @ B3 )
% 0.29/0.45 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % dual_order.strict_trans
% 0.29/0.45 thf(fact_128_not__less__iff__gr__or__eq,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linorder @ A )
% 0.29/0.45 => ! [X3: A,Y: A] :
% 0.29/0.45 ( ( ~ ( ord_less @ A @ X3 @ Y ) )
% 0.29/0.45 = ( ( ord_less @ A @ Y @ X3 )
% 0.29/0.45 | ( X3 = Y ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % not_less_iff_gr_or_eq
% 0.29/0.45 thf(fact_129_order_Ostrict__implies__not__eq,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( order @ A )
% 0.29/0.45 => ! [A2: A,B3: A] :
% 0.29/0.45 ( ( ord_less @ A @ A2 @ B3 )
% 0.29/0.45 => ( A2 != B3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % order.strict_implies_not_eq
% 0.29/0.45 thf(fact_130_dual__order_Ostrict__implies__not__eq,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( order @ A )
% 0.29/0.45 => ! [B3: A,A2: A] :
% 0.29/0.45 ( ( ord_less @ A @ B3 @ A2 )
% 0.29/0.45 => ( A2 != B3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % dual_order.strict_implies_not_eq
% 0.29/0.45 thf(fact_131_bot__fun__def,axiom,
% 0.29/0.45 ! [B: $tType,A: $tType] :
% 0.29/0.45 ( ( bot @ B )
% 0.29/0.45 => ( ( bot_bot @ ( A > B ) )
% 0.29/0.45 = ( ^ [X4: A] : ( bot_bot @ B ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % bot_fun_def
% 0.29/0.45 thf(fact_132_mk__scheme_Osimps_I1_J,axiom,
% 0.29/0.45 ! [N2: nat] :
% 0.29/0.45 ( ( type_M540877363scheme @ ( type_Mirabelle_TVar @ N2 ) )
% 0.29/0.45 = ( type_M91906176e_FVar @ N2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % mk_scheme.simps(1)
% 0.29/0.45 thf(fact_133_is__singletonE,axiom,
% 0.29/0.45 ! [A: $tType,A3: set @ A] :
% 0.29/0.45 ( ( is_singleton @ A @ A3 )
% 0.29/0.45 => ~ ! [X: A] :
% 0.29/0.45 ( A3
% 0.29/0.45 != ( insert2 @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % is_singletonE
% 0.29/0.45 thf(fact_134_is__singleton__def,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( is_singleton @ A )
% 0.29/0.45 = ( ^ [A5: set @ A] :
% 0.29/0.45 ? [X4: A] :
% 0.29/0.45 ( A5
% 0.29/0.45 = ( insert2 @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % is_singleton_def
% 0.29/0.45 thf(fact_135_free__tv__id__subst,axiom,
% 0.29/0.45 ( ( type_M950795831ree_tv @ ( nat > type_Mirabelle_typ ) @ type_M17369686_subst )
% 0.29/0.45 = ( bot_bot @ ( set @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % free_tv_id_subst
% 0.29/0.45 thf(fact_136_Set_Ois__empty__def,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( is_empty @ A )
% 0.29/0.45 = ( ^ [A5: set @ A] :
% 0.29/0.45 ( A5
% 0.29/0.45 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Set.is_empty_def
% 0.29/0.45 thf(fact_137_the__elem__def,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( the_elem @ A )
% 0.29/0.45 = ( ^ [X6: set @ A] :
% 0.29/0.45 ( the @ A
% 0.29/0.45 @ ^ [X4: A] :
% 0.29/0.45 ( X6
% 0.29/0.45 = ( insert2 @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % the_elem_def
% 0.29/0.45 thf(fact_138_mk__scheme_Osimps_I2_J,axiom,
% 0.29/0.45 ! [T1: type_Mirabelle_typ,T2: type_Mirabelle_typ] :
% 0.29/0.45 ( ( type_M540877363scheme @ ( type_Mirabelle_Fun @ T1 @ T2 ) )
% 0.29/0.45 = ( type_M1518733067e_SFun @ ( type_M540877363scheme @ T1 ) @ ( type_M540877363scheme @ T2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mk_scheme.simps(2)
% 0.29/0.45 thf(fact_139_Type__Mirabelle__sfxnzmapfi_Odom__def,axiom,
% 0.29/0.45 ( type_Mirabelle_dom
% 0.29/0.45 = ( ^ [S4: nat > type_Mirabelle_typ] :
% 0.29/0.45 ( collect @ nat
% 0.29/0.45 @ ^ [N3: nat] :
% 0.29/0.45 ( ( S4 @ N3 )
% 0.29/0.45 != ( type_Mirabelle_TVar @ N3 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Type_Mirabelle_sfxnzmapfi.dom_def
% 0.29/0.45 thf(fact_140_id__subst__def,axiom,
% 0.29/0.45 type_M17369686_subst = type_Mirabelle_TVar ).
% 0.29/0.45
% 0.29/0.45 % id_subst_def
% 0.29/0.45 thf(fact_141_typ_Oinject_I2_J,axiom,
% 0.29/0.45 ! [X21: type_Mirabelle_typ,X222: type_Mirabelle_typ,Y21: type_Mirabelle_typ,Y22: type_Mirabelle_typ] :
% 0.29/0.45 ( ( ( type_Mirabelle_Fun @ X21 @ X222 )
% 0.29/0.45 = ( type_Mirabelle_Fun @ Y21 @ Y22 ) )
% 0.29/0.45 = ( ( X21 = Y21 )
% 0.29/0.45 & ( X222 = Y22 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % typ.inject(2)
% 0.29/0.45 thf(fact_142_new__tv__Fun,axiom,
% 0.29/0.45 ! [N2: nat,T1: type_Mirabelle_typ,T2: type_Mirabelle_typ] :
% 0.29/0.45 ( ( type_M1046766514new_tv @ type_Mirabelle_typ @ N2 @ ( type_Mirabelle_Fun @ T1 @ T2 ) )
% 0.29/0.45 = ( ( type_M1046766514new_tv @ type_Mirabelle_typ @ N2 @ T1 )
% 0.29/0.45 & ( type_M1046766514new_tv @ type_Mirabelle_typ @ N2 @ T2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % new_tv_Fun
% 0.29/0.45 thf(fact_143_dom__id__subst,axiom,
% 0.29/0.45 ( ( type_Mirabelle_dom @ type_M17369686_subst )
% 0.29/0.45 = ( bot_bot @ ( set @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % dom_id_subst
% 0.29/0.45 thf(fact_144_psubsetD,axiom,
% 0.29/0.45 ! [A: $tType,A3: set @ A,B2: set @ A,C: A] :
% 0.29/0.45 ( ( ord_less @ ( set @ A ) @ A3 @ B2 )
% 0.29/0.45 => ( ( member @ A @ C @ A3 )
% 0.29/0.45 => ( member @ A @ C @ B2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % psubsetD
% 0.29/0.45 thf(fact_145_less__set__def,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ord_less @ ( set @ A ) )
% 0.29/0.45 = ( ^ [A5: set @ A,B5: set @ A] :
% 0.29/0.45 ( ord_less @ ( A > $o )
% 0.29/0.45 @ ^ [X4: A] : ( member @ A @ X4 @ A5 )
% 0.29/0.45 @ ^ [X4: A] : ( member @ A @ X4 @ B5 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % less_set_def
% 0.29/0.45 thf(fact_146_psubset__trans,axiom,
% 0.29/0.45 ! [A: $tType,A3: set @ A,B2: set @ A,C4: set @ A] :
% 0.29/0.45 ( ( ord_less @ ( set @ A ) @ A3 @ B2 )
% 0.29/0.45 => ( ( ord_less @ ( set @ A ) @ B2 @ C4 )
% 0.29/0.45 => ( ord_less @ ( set @ A ) @ A3 @ C4 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % psubset_trans
% 0.29/0.45 thf(fact_147_new__tv__id__subst,axiom,
% 0.29/0.45 ! [N2: nat] : ( type_M1046766514new_tv @ ( nat > type_Mirabelle_typ ) @ N2 @ type_M17369686_subst ) ).
% 0.29/0.45
% 0.29/0.45 % new_tv_id_subst
% 0.29/0.45 thf(fact_148_app__subst__Fun,axiom,
% 0.29/0.45 ! [S: nat > type_Mirabelle_typ,T1: type_Mirabelle_typ,T2: type_Mirabelle_typ] :
% 0.29/0.45 ( ( type_M353778473_subst @ type_Mirabelle_typ @ S @ ( type_Mirabelle_Fun @ T1 @ T2 ) )
% 0.29/0.45 = ( type_Mirabelle_Fun @ ( type_M353778473_subst @ type_Mirabelle_typ @ S @ T1 ) @ ( type_M353778473_subst @ type_Mirabelle_typ @ S @ T2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % app_subst_Fun
% 0.29/0.45 thf(fact_149_typ_Oexhaust,axiom,
% 0.29/0.45 ! [Y: type_Mirabelle_typ] :
% 0.29/0.46 ( ! [X13: nat] :
% 0.29/0.46 ( Y
% 0.29/0.46 != ( type_Mirabelle_TVar @ X13 ) )
% 0.29/0.46 => ~ ! [X212: type_Mirabelle_typ,X223: type_Mirabelle_typ] :
% 0.29/0.46 ( Y
% 0.29/0.46 != ( type_Mirabelle_Fun @ X212 @ X223 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % typ.exhaust
% 0.29/0.46 thf(fact_150_typ_Oinduct,axiom,
% 0.29/0.46 ! [P: type_Mirabelle_typ > $o,Typ: type_Mirabelle_typ] :
% 0.29/0.46 ( ! [X: nat] : ( P @ ( type_Mirabelle_TVar @ X ) )
% 0.29/0.46 => ( ! [X1a: type_Mirabelle_typ,X23: type_Mirabelle_typ] :
% 0.29/0.46 ( ( P @ X1a )
% 0.29/0.46 => ( ( P @ X23 )
% 0.29/0.46 => ( P @ ( type_Mirabelle_Fun @ X1a @ X23 ) ) ) )
% 0.29/0.46 => ( P @ Typ ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % typ.induct
% 0.29/0.46 thf(fact_151_typ_Odistinct_I1_J,axiom,
% 0.29/0.46 ! [X1: nat,X21: type_Mirabelle_typ,X222: type_Mirabelle_typ] :
% 0.29/0.46 ( ( type_Mirabelle_TVar @ X1 )
% 0.29/0.46 != ( type_Mirabelle_Fun @ X21 @ X222 ) ) ).
% 0.29/0.46
% 0.29/0.46 % typ.distinct(1)
% 0.29/0.46 thf(fact_152_typ_Osimps_I6_J,axiom,
% 0.29/0.46 ! [A: $tType,F1: nat > A,F2: type_Mirabelle_typ > type_Mirabelle_typ > A,X21: type_Mirabelle_typ,X222: type_Mirabelle_typ] :
% 0.29/0.46 ( ( type_M1695911984se_typ @ A @ F1 @ F2 @ ( type_Mirabelle_Fun @ X21 @ X222 ) )
% 0.29/0.46 = ( F2 @ X21 @ X222 ) ) ).
% 0.29/0.46
% 0.29/0.46 % typ.simps(6)
% 0.29/0.46 thf(fact_153_the__sym__eq__trivial,axiom,
% 0.29/0.46 ! [A: $tType,X3: A] :
% 0.29/0.46 ( ( the @ A
% 0.29/0.46 @ ( ^ [Y3: A,Z: A] : ( Y3 = Z )
% 0.29/0.46 @ X3 ) )
% 0.29/0.46 = X3 ) ).
% 0.29/0.46
% 0.29/0.46 % the_sym_eq_trivial
% 0.29/0.46 thf(fact_154_the__eq__trivial,axiom,
% 0.29/0.46 ! [A: $tType,A2: A] :
% 0.29/0.46 ( ( the @ A
% 0.29/0.46 @ ^ [X4: A] : ( X4 = A2 ) )
% 0.29/0.46 = A2 ) ).
% 0.29/0.46
% 0.29/0.46 % the_eq_trivial
% 0.29/0.46 thf(fact_155_the__equality,axiom,
% 0.29/0.46 ! [A: $tType,P: A > $o,A2: A] :
% 0.29/0.46 ( ( P @ A2 )
% 0.29/0.46 => ( ! [X: A] :
% 0.29/0.46 ( ( P @ X )
% 0.29/0.46 => ( X = A2 ) )
% 0.29/0.46 => ( ( the @ A @ P )
% 0.29/0.46 = A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % the_equality
% 0.29/0.46 thf(fact_156_cod__id__subst,axiom,
% 0.29/0.46 ( ( type_Mirabelle_cod @ type_M17369686_subst )
% 0.29/0.46 = ( bot_bot @ ( set @ nat ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % cod_id_subst
% 0.29/0.46 thf(fact_157_theI,axiom,
% 0.29/0.46 ! [A: $tType,P: A > $o,A2: A] :
% 0.29/0.46 ( ( P @ A2 )
% 0.29/0.46 => ( ! [X: A] :
% 0.29/0.46 ( ( P @ X )
% 0.29/0.46 => ( X = A2 ) )
% 0.29/0.46 => ( P @ ( the @ A @ P ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % theI
% 0.29/0.46 thf(fact_158_theI_H,axiom,
% 0.29/0.46 ! [A: $tType,P: A > $o] :
% 0.29/0.46 ( ? [X7: A] :
% 0.29/0.46 ( ( P @ X7 )
% 0.29/0.46 & ! [Y4: A] :
% 0.29/0.46 ( ( P @ Y4 )
% 0.29/0.46 => ( Y4 = X7 ) ) )
% 0.29/0.46 => ( P @ ( the @ A @ P ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % theI'
% 0.29/0.46 thf(fact_159_theI2,axiom,
% 0.29/0.46 ! [A: $tType,P: A > $o,A2: A,Q: A > $o] :
% 0.29/0.46 ( ( P @ A2 )
% 0.29/0.46 => ( ! [X: A] :
% 0.29/0.46 ( ( P @ X )
% 0.29/0.46 => ( X = A2 ) )
% 0.29/0.46 => ( ! [X: A] :
% 0.29/0.46 ( ( P @ X )
% 0.29/0.46 => ( Q @ X ) )
% 0.29/0.46 => ( Q @ ( the @ A @ P ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % theI2
% 0.29/0.46 thf(fact_160_If__def,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( if @ A )
% 0.29/0.46 = ( ^ [P3: $o,X4: A,Y6: A] :
% 0.29/0.46 ( the @ A
% 0.29/0.46 @ ^ [Z4: A] :
% 0.29/0.46 ( ( P3
% 0.29/0.46 => ( Z4 = X4 ) )
% 0.29/0.46 & ( ~ P3
% 0.29/0.46 => ( Z4 = Y6 ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % If_def
% 0.29/0.46 thf(fact_161_the1I2,axiom,
% 0.29/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.29/0.46 ( ? [X7: A] :
% 0.29/0.46 ( ( P @ X7 )
% 0.29/0.46 & ! [Y4: A] :
% 0.29/0.46 ( ( P @ Y4 )
% 0.29/0.46 => ( Y4 = X7 ) ) )
% 0.29/0.46 => ( ! [X: A] :
% 0.29/0.46 ( ( P @ X )
% 0.29/0.46 => ( Q @ X ) )
% 0.29/0.46 => ( Q @ ( the @ A @ P ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % the1I2
% 0.29/0.46 thf(fact_162_the1__equality,axiom,
% 0.29/0.46 ! [A: $tType,P: A > $o,A2: A] :
% 0.29/0.46 ( ? [X7: A] :
% 0.29/0.46 ( ( P @ X7 )
% 0.29/0.46 & ! [Y4: A] :
% 0.29/0.46 ( ( P @ Y4 )
% 0.29/0.46 => ( Y4 = X7 ) ) )
% 0.29/0.46 => ( ( P @ A2 )
% 0.29/0.46 => ( ( the @ A @ P )
% 0.29/0.46 = A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % the1_equality
% 0.29/0.46 thf(fact_163_Collect__empty__eq__bot,axiom,
% 0.29/0.46 ! [A: $tType,P: A > $o] :
% 0.29/0.46 ( ( ( collect @ A @ P )
% 0.29/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.29/0.46 = ( P
% 0.29/0.46 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Collect_empty_eq_bot
% 0.29/0.46 thf(fact_164_bot__empty__eq,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( bot_bot @ ( A > $o ) )
% 0.29/0.46 = ( ^ [X4: A] : ( member @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % bot_empty_eq
% 0.29/0.46 thf(fact_165_free__tv__subst,axiom,
% 0.29/0.46 ( ( type_M950795831ree_tv @ ( nat > type_Mirabelle_typ ) )
% 0.29/0.46 = ( ^ [S4: nat > type_Mirabelle_typ] : ( sup_sup @ ( set @ nat ) @ ( type_Mirabelle_dom @ S4 ) @ ( type_Mirabelle_cod @ S4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % free_tv_subst
% 0.29/0.46 thf(fact_166_UnCI,axiom,
% 0.29/0.46 ! [A: $tType,C: A,B2: set @ A,A3: set @ A] :
% 0.29/0.46 ( ( ~ ( member @ A @ C @ B2 )
% 0.29/0.46 => ( member @ A @ C @ A3 ) )
% 0.29/0.46 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % UnCI
% 0.29/0.46 thf(fact_167_Un__iff,axiom,
% 0.29/0.46 ! [A: $tType,C: A,A3: set @ A,B2: set @ A] :
% 0.29/0.46 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 0.29/0.46 = ( ( member @ A @ C @ A3 )
% 0.29/0.46 | ( member @ A @ C @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_iff
% 0.29/0.46 thf(fact_168_Un__empty,axiom,
% 0.29/0.46 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 0.29/0.46 ( ( ( sup_sup @ ( set @ A ) @ A3 @ B2 )
% 0.29/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.29/0.46 = ( ( A3
% 0.29/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.29/0.46 & ( B2
% 0.29/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_empty
% 0.29/0.46 thf(fact_169_Un__insert__left,axiom,
% 0.29/0.46 ! [A: $tType,A2: A,B2: set @ A,C4: set @ A] :
% 0.29/0.46 ( ( sup_sup @ ( set @ A ) @ ( insert2 @ A @ A2 @ B2 ) @ C4 )
% 0.29/0.46 = ( insert2 @ A @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_insert_left
% 0.29/0.46 thf(fact_170_Un__insert__right,axiom,
% 0.29/0.46 ! [A: $tType,A3: set @ A,A2: A,B2: set @ A] :
% 0.29/0.46 ( ( sup_sup @ ( set @ A ) @ A3 @ ( insert2 @ A @ A2 @ B2 ) )
% 0.29/0.46 = ( insert2 @ A @ A2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_insert_right
% 0.29/0.46 thf(fact_171_weaken__asm__Un,axiom,
% 0.29/0.46 ! [A: $tType,A3: set @ A,P: A > $o,Q: $o,B2: set @ A] :
% 0.29/0.46 ( ( ! [X7: A] :
% 0.29/0.46 ( ( member @ A @ X7 @ A3 )
% 0.29/0.46 => ( P @ X7 ) )
% 0.29/0.46 => Q )
% 0.29/0.46 => ( ! [X: A] :
% 0.29/0.46 ( ( member @ A @ X @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 0.29/0.46 => ( P @ X ) )
% 0.29/0.46 => Q ) ) ).
% 0.29/0.46
% 0.29/0.46 % weaken_asm_Un
% 0.29/0.46 thf(fact_172_UnE,axiom,
% 0.29/0.46 ! [A: $tType,C: A,A3: set @ A,B2: set @ A] :
% 0.29/0.46 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 0.29/0.46 => ( ~ ( member @ A @ C @ A3 )
% 0.29/0.46 => ( member @ A @ C @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % UnE
% 0.29/0.46 thf(fact_173_UnI1,axiom,
% 0.29/0.46 ! [A: $tType,C: A,A3: set @ A,B2: set @ A] :
% 0.29/0.46 ( ( member @ A @ C @ A3 )
% 0.29/0.46 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % UnI1
% 0.29/0.46 thf(fact_174_UnI2,axiom,
% 0.29/0.46 ! [A: $tType,C: A,B2: set @ A,A3: set @ A] :
% 0.29/0.46 ( ( member @ A @ C @ B2 )
% 0.29/0.46 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % UnI2
% 0.29/0.46 thf(fact_175_Un__def,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( sup_sup @ ( set @ A ) )
% 0.29/0.46 = ( ^ [A5: set @ A,B5: set @ A] :
% 0.29/0.46 ( collect @ A
% 0.29/0.46 @ ^ [X4: A] :
% 0.29/0.46 ( ( member @ A @ X4 @ A5 )
% 0.29/0.46 | ( member @ A @ X4 @ B5 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_def
% 0.29/0.46 thf(fact_176_bex__Un,axiom,
% 0.29/0.46 ! [A: $tType,A3: set @ A,B2: set @ A,P: A > $o] :
% 0.29/0.46 ( ( ? [X4: A] :
% 0.29/0.46 ( ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 0.29/0.46 & ( P @ X4 ) ) )
% 0.29/0.46 = ( ? [X4: A] :
% 0.29/0.46 ( ( member @ A @ X4 @ A3 )
% 0.29/0.46 & ( P @ X4 ) )
% 0.29/0.46 | ? [X4: A] :
% 0.29/0.46 ( ( member @ A @ X4 @ B2 )
% 0.29/0.46 & ( P @ X4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % bex_Un
% 0.29/0.46 thf(fact_177_ball__Un,axiom,
% 0.29/0.46 ! [A: $tType,A3: set @ A,B2: set @ A,P: A > $o] :
% 0.29/0.46 ( ( ! [X4: A] :
% 0.29/0.46 ( ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 0.29/0.46 => ( P @ X4 ) ) )
% 0.29/0.46 = ( ! [X4: A] :
% 0.29/0.46 ( ( member @ A @ X4 @ A3 )
% 0.29/0.46 => ( P @ X4 ) )
% 0.29/0.46 & ! [X4: A] :
% 0.29/0.46 ( ( member @ A @ X4 @ B2 )
% 0.29/0.46 => ( P @ X4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % ball_Un
% 0.29/0.46 thf(fact_178_Un__assoc,axiom,
% 0.29/0.46 ! [A: $tType,A3: set @ A,B2: set @ A,C4: set @ A] :
% 0.29/0.46 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) @ C4 )
% 0.29/0.46 = ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_assoc
% 0.29/0.46 thf(fact_179_Un__absorb,axiom,
% 0.29/0.46 ! [A: $tType,A3: set @ A] :
% 0.29/0.46 ( ( sup_sup @ ( set @ A ) @ A3 @ A3 )
% 0.29/0.46 = A3 ) ).
% 0.29/0.46
% 0.29/0.46 % Un_absorb
% 0.29/0.46 thf(fact_180_Un__commute,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( sup_sup @ ( set @ A ) )
% 0.29/0.46 = ( ^ [A5: set @ A,B5: set @ A] : ( sup_sup @ ( set @ A ) @ B5 @ A5 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_commute
% 0.29/0.46 thf(fact_181_Un__left__absorb,axiom,
% 0.29/0.46 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 0.29/0.46 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 0.29/0.46 = ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_left_absorb
% 0.29/0.46 thf(fact_182_Collect__disj__eq,axiom,
% 0.29/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.29/0.46 ( ( collect @ A
% 0.29/0.46 @ ^ [X4: A] :
% 0.29/0.46 ( ( P @ X4 )
% 0.29/0.46 | ( Q @ X4 ) ) )
% 0.29/0.46 = ( sup_sup @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Collect_disj_eq
% 0.29/0.46 thf(fact_183_Un__left__commute,axiom,
% 0.29/0.46 ! [A: $tType,A3: set @ A,B2: set @ A,C4: set @ A] :
% 0.29/0.46 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) )
% 0.29/0.46 = ( sup_sup @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A3 @ C4 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_left_commute
% 0.29/0.46 thf(fact_184_insert__def,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( insert2 @ A )
% 0.29/0.46 = ( ^ [A4: A] :
% 0.29/0.46 ( sup_sup @ ( set @ A )
% 0.29/0.46 @ ( collect @ A
% 0.29/0.46 @ ^ [X4: A] : ( X4 = A4 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % insert_def
% 0.29/0.46 thf(fact_185_Un__empty__left,axiom,
% 0.29/0.46 ! [A: $tType,B2: set @ A] :
% 0.29/0.46 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B2 )
% 0.29/0.46 = B2 ) ).
% 0.29/0.46
% 0.29/0.46 % Un_empty_left
% 0.29/0.46 thf(fact_186_Un__empty__right,axiom,
% 0.29/0.46 ! [A: $tType,A3: set @ A] :
% 0.29/0.46 ( ( sup_sup @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.29/0.46 = A3 ) ).
% 0.29/0.46
% 0.29/0.46 % Un_empty_right
% 0.29/0.46 thf(fact_187_singleton__Un__iff,axiom,
% 0.29/0.46 ! [A: $tType,X3: A,A3: set @ A,B2: set @ A] :
% 0.29/0.46 ( ( ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) )
% 0.29/0.46 = ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 0.29/0.46 = ( ( ( A3
% 0.29/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.29/0.46 & ( B2
% 0.29/0.46 = ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.29/0.46 | ( ( A3
% 0.29/0.46 = ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.29/0.46 & ( B2
% 0.29/0.46 = ( bot_bot @ ( set @ A ) ) ) )
% 0.29/0.46 | ( ( A3
% 0.29/0.46 = ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.29/0.46 & ( B2
% 0.29/0.46 = ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % singleton_Un_iff
% 0.29/0.46 thf(fact_188_Un__singleton__iff,axiom,
% 0.29/0.46 ! [A: $tType,A3: set @ A,B2: set @ A,X3: A] :
% 0.29/0.46 ( ( ( sup_sup @ ( set @ A ) @ A3 @ B2 )
% 0.29/0.46 = ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.29/0.46 = ( ( ( A3
% 0.29/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.29/0.46 & ( B2
% 0.29/0.46 = ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.29/0.46 | ( ( A3
% 0.29/0.46 = ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.29/0.46 & ( B2
% 0.29/0.46 = ( bot_bot @ ( set @ A ) ) ) )
% 0.29/0.46 | ( ( A3
% 0.29/0.46 = ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.29/0.46 & ( B2
% 0.29/0.46 = ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Un_singleton_iff
% 0.29/0.46 thf(fact_189_insert__is__Un,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( insert2 @ A )
% 0.29/0.46 = ( ^ [A4: A] : ( sup_sup @ ( set @ A ) @ ( insert2 @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % insert_is_Un
% 0.29/0.46 thf(fact_190_bound__tv__list_Osimps_I2_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( type_M1470978233struct @ A )
% 0.29/0.46 => ! [X3: A,L: list @ A] :
% 0.29/0.46 ( ( type_M779184887und_tv @ ( list @ A ) @ ( cons @ A @ X3 @ L ) )
% 0.29/0.46 = ( sup_sup @ ( set @ nat ) @ ( type_M779184887und_tv @ A @ X3 ) @ ( type_M779184887und_tv @ ( list @ A ) @ L ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % bound_tv_list.simps(2)
% 0.29/0.46 thf(fact_191_free__tv__Fun,axiom,
% 0.29/0.46 ! [T1: type_Mirabelle_typ,T2: type_Mirabelle_typ] :
% 0.29/0.46 ( ( type_M950795831ree_tv @ type_Mirabelle_typ @ ( type_Mirabelle_Fun @ T1 @ T2 ) )
% 0.29/0.46 = ( sup_sup @ ( set @ nat ) @ ( type_M950795831ree_tv @ type_Mirabelle_typ @ T1 ) @ ( type_M950795831ree_tv @ type_Mirabelle_typ @ T2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % free_tv_Fun
% 0.29/0.46 thf(fact_192_free__tv__type__scheme_Osimps_I3_J,axiom,
% 0.29/0.46 ! [S1: type_M1610475166scheme,S2: type_M1610475166scheme] :
% 0.29/0.46 ( ( type_M950795831ree_tv @ type_M1610475166scheme @ ( type_M1518733067e_SFun @ S1 @ S2 ) )
% 0.29/0.46 = ( sup_sup @ ( set @ nat ) @ ( type_M950795831ree_tv @ type_M1610475166scheme @ S1 ) @ ( type_M950795831ree_tv @ type_M1610475166scheme @ S2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % free_tv_type_scheme.simps(3)
% 0.29/0.46 thf(fact_193_bound__tv__type__scheme_Osimps_I3_J,axiom,
% 0.29/0.46 ! [S1: type_M1610475166scheme,S2: type_M1610475166scheme] :
% 0.29/0.46 ( ( type_M779184887und_tv @ type_M1610475166scheme @ ( type_M1518733067e_SFun @ S1 @ S2 ) )
% 0.29/0.46 = ( sup_sup @ ( set @ nat ) @ ( type_M779184887und_tv @ type_M1610475166scheme @ S1 ) @ ( type_M779184887und_tv @ type_M1610475166scheme @ S2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % bound_tv_type_scheme.simps(3)
% 0.29/0.46 thf(fact_194_free__tv__list_Osimps_I2_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( type_M1470978233struct @ A )
% 0.29/0.46 => ! [X3: A,L: list @ A] :
% 0.29/0.46 ( ( type_M950795831ree_tv @ ( list @ A ) @ ( cons @ A @ X3 @ L ) )
% 0.29/0.46 = ( sup_sup @ ( set @ nat ) @ ( type_M950795831ree_tv @ A @ X3 ) @ ( type_M950795831ree_tv @ ( list @ A ) @ L ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % free_tv_list.simps(2)
% 0.29/0.46 thf(fact_195_free__tv__fun__def,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( ( type_M201404320of_nat @ A )
% 0.29/0.46 & ( type_M1535146424typ_of @ B ) )
% 0.29/0.46 => ( ( type_M950795831ree_tv @ ( A > B ) )
% 0.29/0.46 = ( ^ [F4: A > B] :
% 0.29/0.46 ( sup_sup @ ( set @ nat )
% 0.29/0.46 @ ( type_Mirabelle_dom
% 0.29/0.46 @ ^ [N3: nat] : ( type_M604437996typ_of @ B @ ( F4 @ ( type_M167561660of_nat @ A @ N3 ) ) ) )
% 0.29/0.46 @ ( type_Mirabelle_cod
% 0.29/0.46 @ ^ [N3: nat] : ( type_M604437996typ_of @ B @ ( F4 @ ( type_M167561660of_nat @ A @ N3 ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % free_tv_fun_def
% 0.29/0.46 thf(fact_196_sup__bot__left,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( bounde1808546759up_bot @ A )
% 0.29/0.46 => ! [X3: A] :
% 0.29/0.46 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X3 )
% 0.29/0.46 = X3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_bot_left
% 0.29/0.46 thf(fact_197_sup__bot__right,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( bounde1808546759up_bot @ A )
% 0.29/0.46 => ! [X3: A] :
% 0.29/0.46 ( ( sup_sup @ A @ X3 @ ( bot_bot @ A ) )
% 0.29/0.46 = X3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_bot_right
% 0.29/0.46 thf(fact_198_sup__bot_Oright__neutral,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( bounde1808546759up_bot @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( sup_sup @ A @ A2 @ ( bot_bot @ A ) )
% 0.29/0.46 = A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_bot.right_neutral
% 0.29/0.46 thf(fact_199_sup__bot_Oneutr__eq__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( bounde1808546759up_bot @ A )
% 0.29/0.46 => ! [A2: A,B3: A] :
% 0.29/0.46 ( ( ( bot_bot @ A )
% 0.29/0.46 = ( sup_sup @ A @ A2 @ B3 ) )
% 0.29/0.46 = ( ( A2
% 0.29/0.46 = ( bot_bot @ A ) )
% 0.29/0.46 & ( B3
% 0.29/0.46 = ( bot_bot @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_bot.neutr_eq_iff
% 0.29/0.46 thf(fact_200_sup__bot_Oleft__neutral,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( bounde1808546759up_bot @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A2 )
% 0.29/0.46 = A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_bot.left_neutral
% 0.29/0.46 thf(fact_201_sup__bot_Oeq__neutr__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( bounde1808546759up_bot @ A )
% 0.29/0.46 => ! [A2: A,B3: A] :
% 0.29/0.46 ( ( ( sup_sup @ A @ A2 @ B3 )
% 0.29/0.46 = ( bot_bot @ A ) )
% 0.29/0.46 = ( ( A2
% 0.29/0.46 = ( bot_bot @ A ) )
% 0.29/0.46 & ( B3
% 0.29/0.46 = ( bot_bot @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_bot.eq_neutr_iff
% 0.29/0.46 thf(fact_202_sup__eq__bot__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( bounde1808546759up_bot @ A )
% 0.29/0.46 => ! [X3: A,Y: A] :
% 0.29/0.46 ( ( ( sup_sup @ A @ X3 @ Y )
% 0.29/0.46 = ( bot_bot @ A ) )
% 0.29/0.46 = ( ( X3
% 0.29/0.46 = ( bot_bot @ A ) )
% 0.29/0.46 & ( Y
% 0.29/0.46 = ( bot_bot @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_eq_bot_iff
% 0.29/0.46 thf(fact_203_bot__eq__sup__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( bounde1808546759up_bot @ A )
% 0.29/0.46 => ! [X3: A,Y: A] :
% 0.29/0.46 ( ( ( bot_bot @ A )
% 0.29/0.46 = ( sup_sup @ A @ X3 @ Y ) )
% 0.29/0.46 = ( ( X3
% 0.29/0.46 = ( bot_bot @ A ) )
% 0.29/0.46 & ( Y
% 0.29/0.46 = ( bot_bot @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % bot_eq_sup_iff
% 0.29/0.46 thf(fact_204_sup__Un__eq,axiom,
% 0.29/0.46 ! [A: $tType,R: set @ A,S: set @ A] :
% 0.29/0.46 ( ( sup_sup @ ( A > $o )
% 0.29/0.46 @ ^ [X4: A] : ( member @ A @ X4 @ R )
% 0.29/0.46 @ ^ [X4: A] : ( member @ A @ X4 @ S ) )
% 0.29/0.46 = ( ^ [X4: A] : ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ R @ S ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_Un_eq
% 0.29/0.46 thf(fact_205_sup__set__def,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( sup_sup @ ( set @ A ) )
% 0.29/0.46 = ( ^ [A5: set @ A,B5: set @ A] :
% 0.29/0.46 ( collect @ A
% 0.29/0.46 @ ( sup_sup @ ( A > $o )
% 0.29/0.46 @ ^ [X4: A] : ( member @ A @ X4 @ A5 )
% 0.29/0.46 @ ^ [X4: A] : ( member @ A @ X4 @ B5 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_set_def
% 0.29/0.46 thf(fact_206_less__supI1,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semilattice_sup @ A )
% 0.29/0.46 => ! [X3: A,A2: A,B3: A] :
% 0.29/0.46 ( ( ord_less @ A @ X3 @ A2 )
% 0.29/0.46 => ( ord_less @ A @ X3 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_supI1
% 0.29/0.46 thf(fact_207_less__supI2,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semilattice_sup @ A )
% 0.29/0.46 => ! [X3: A,B3: A,A2: A] :
% 0.29/0.46 ( ( ord_less @ A @ X3 @ B3 )
% 0.29/0.46 => ( ord_less @ A @ X3 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_supI2
% 0.29/0.46 thf(fact_208_sup_Ostrict__boundedE,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semilattice_sup @ A )
% 0.29/0.46 => ! [B3: A,C: A,A2: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( sup_sup @ A @ B3 @ C ) @ A2 )
% 0.29/0.46 => ~ ( ( ord_less @ A @ B3 @ A2 )
% 0.29/0.46 => ~ ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup.strict_boundedE
% 0.29/0.46 thf(fact_209_sup_Ostrict__order__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semilattice_sup @ A )
% 0.29/0.46 => ( ( ord_less @ A )
% 0.29/0.46 = ( ^ [B7: A,A4: A] :
% 0.29/0.46 ( ( A4
% 0.29/0.46 = ( sup_sup @ A @ A4 @ B7 ) )
% 0.29/0.46 & ( A4 != B7 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup.strict_order_iff
% 0.29/0.46 thf(fact_210_sup_Ostrict__coboundedI1,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semilattice_sup @ A )
% 0.29/0.46 => ! [C: A,A2: A,B3: A] :
% 0.29/0.46 ( ( ord_less @ A @ C @ A2 )
% 0.29/0.46 => ( ord_less @ A @ C @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup.strict_coboundedI1
% 0.29/0.46 thf(fact_211_sup_Ostrict__coboundedI2,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( semilattice_sup @ A )
% 0.29/0.46 => ! [C: A,B3: A,A2: A] :
% 0.29/0.46 ( ( ord_less @ A @ C @ B3 )
% 0.29/0.46 => ( ord_less @ A @ C @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup.strict_coboundedI2
% 0.29/0.46 thf(fact_212_Nitpick_OThe__psimp,axiom,
% 0.29/0.46 ! [A: $tType,P: A > $o,X3: A] :
% 0.29/0.46 ( ( P
% 0.29/0.46 = ( ^ [Y3: A,Z: A] : ( Y3 = Z )
% 0.29/0.46 @ X3 ) )
% 0.29/0.46 => ( ( the @ A @ P )
% 0.29/0.46 = X3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % Nitpick.The_psimp
% 0.29/0.46 thf(fact_213_theI__unique,axiom,
% 0.29/0.46 ! [A: $tType,P: A > $o,X3: A] :
% 0.29/0.46 ( ? [X7: A] :
% 0.29/0.46 ( ( P @ X7 )
% 0.29/0.46 & ! [Y4: A] :
% 0.29/0.46 ( ( P @ Y4 )
% 0.29/0.46 => ( Y4 = X7 ) ) )
% 0.29/0.46 => ( ( P @ X3 )
% 0.29/0.46 = ( X3
% 0.29/0.46 = ( the @ A @ P ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % theI_unique
% 0.29/0.46 thf(fact_214_sup__bot_Osemilattice__neutr__axioms,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( bounde1808546759up_bot @ A )
% 0.29/0.46 => ( semilattice_neutr @ A @ ( sup_sup @ A ) @ ( bot_bot @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sup_bot.semilattice_neutr_axioms
% 0.29/0.46 thf(fact_215_lexordp__eq__simps_I4_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ord @ A )
% 0.29/0.46 => ! [X3: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 0.29/0.46 ( ( ord_lexordp_eq @ A @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 0.29/0.46 = ( ( ord_less @ A @ X3 @ Y )
% 0.29/0.46 | ( ~ ( ord_less @ A @ Y @ X3 )
% 0.29/0.46 & ( ord_lexordp_eq @ A @ Xs @ Ys ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % lexordp_eq_simps(4)
% 0.29/0.46 thf(fact_216_lexordp__eq_OCons__eq,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ord @ A )
% 0.29/0.46 => ! [X3: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 0.29/0.46 ( ~ ( ord_less @ A @ X3 @ Y )
% 0.29/0.46 => ( ~ ( ord_less @ A @ Y @ X3 )
% 0.29/0.46 => ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 0.29/0.46 => ( ord_lexordp_eq @ A @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % lexordp_eq.Cons_eq
% 0.29/0.46 thf(fact_217_lexordp__eq_OCons,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ord @ A )
% 0.29/0.46 => ! [X3: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 0.29/0.46 ( ( ord_less @ A @ X3 @ Y )
% 0.29/0.46 => ( ord_lexordp_eq @ A @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % lexordp_eq.Cons
% 0.29/0.46 thf(fact_218_lexordp__eq__antisym,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linorder @ A )
% 0.29/0.46 => ! [Xs: list @ A,Ys: list @ A] :
% 0.29/0.46 ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 0.29/0.46 => ( ( ord_lexordp_eq @ A @ Ys @ Xs )
% 0.29/0.46 => ( Xs = Ys ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % lexordp_eq_antisym
% 0.29/0.46 thf(fact_219_lexordp__eq__linear,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linorder @ A )
% 0.29/0.46 => ! [Xs: list @ A,Ys: list @ A] :
% 0.29/0.46 ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 0.29/0.46 | ( ord_lexordp_eq @ A @ Ys @ Xs ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % lexordp_eq_linear
% 0.29/0.46 thf(fact_220_lexordp__eq__trans,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linorder @ A )
% 0.29/0.46 => ! [Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 0.29/0.46 ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 0.29/0.46 => ( ( ord_lexordp_eq @ A @ Ys @ Zs )
% 0.29/0.46 => ( ord_lexordp_eq @ A @ Xs @ Zs ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % lexordp_eq_trans
% 0.29/0.46 thf(fact_221_lexordp__eq__refl,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ord @ A )
% 0.29/0.46 => ! [Xs: list @ A] : ( ord_lexordp_eq @ A @ Xs @ Xs ) ) ).
% 0.29/0.46
% 0.29/0.46 % lexordp_eq_refl
% 0.29/0.46 thf(fact_222_lexordp__eq_Ocases,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ord @ A )
% 0.29/0.46 => ! [A1: list @ A,A22: list @ A] :
% 0.29/0.46 ( ( ord_lexordp_eq @ A @ A1 @ A22 )
% 0.29/0.46 => ( ( A1
% 0.29/0.46 != ( nil @ A ) )
% 0.29/0.46 => ( ! [X: A] :
% 0.29/0.46 ( ? [Xs2: list @ A] :
% 0.29/0.46 ( A1
% 0.29/0.46 = ( cons @ A @ X @ Xs2 ) )
% 0.29/0.46 => ! [Y4: A] :
% 0.29/0.46 ( ? [Ys2: list @ A] :
% 0.29/0.46 ( A22
% 0.29/0.46 = ( cons @ A @ Y4 @ Ys2 ) )
% 0.29/0.46 => ~ ( ord_less @ A @ X @ Y4 ) ) )
% 0.29/0.46 => ~ ! [X: A,Y4: A,Xs2: list @ A] :
% 0.29/0.46 ( ( A1
% 0.29/0.46 = ( cons @ A @ X @ Xs2 ) )
% 0.29/0.46 => ! [Ys2: list @ A] :
% 0.29/0.46 ( ( A22
% 0.29/0.46 = ( cons @ A @ Y4 @ Ys2 ) )
% 0.29/0.46 => ( ~ ( ord_less @ A @ X @ Y4 )
% 0.29/0.46 => ( ~ ( ord_less @ A @ Y4 @ X )
% 0.29/0.46 => ~ ( ord_lexordp_eq @ A @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % lexordp_eq.cases
% 0.29/0.46 thf(fact_223_lexordp__eq_Osimps,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ord @ A )
% 0.29/0.46 => ( ( ord_lexordp_eq @ A )
% 0.29/0.46 = ( ^ [A12: list @ A,A23: list @ A] :
% 0.29/0.46 ( ? [Ys3: list @ A] :
% 0.29/0.46 ( ( A12
% 0.29/0.46 = ( nil @ A ) )
% 0.29/0.46 & ( A23 = Ys3 ) )
% 0.29/0.46 | ? [X4: A,Y6: A,Xs3: list @ A,Ys3: list @ A] :
% 0.29/0.46 ( ( A12
% 0.29/0.46 = ( cons @ A @ X4 @ Xs3 ) )
% 0.29/0.46 & ( A23
% 0.29/0.46 = ( cons @ A @ Y6 @ Ys3 ) )
% 0.29/0.46 & ( ord_less @ A @ X4 @ Y6 ) )
% 0.29/0.46 | ? [X4: A,Y6: A,Xs3: list @ A,Ys3: list @ A] :
% 0.29/0.46 ( ( A12
% 0.29/0.46 = ( cons @ A @ X4 @ Xs3 ) )
% 0.29/0.46 & ( A23
% 0.29/0.46 = ( cons @ A @ Y6 @ Ys3 ) )
% 0.29/0.46 & ~ ( ord_less @ A @ X4 @ Y6 )
% 0.29/0.46 & ~ ( ord_less @ A @ Y6 @ X4 )
% 0.29/0.46 & ( ord_lexordp_eq @ A @ Xs3 @ Ys3 ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % lexordp_eq.simps
% 0.29/0.46 thf(fact_224_lexordp__eq__simps_I1_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ord @ A )
% 0.29/0.46 => ! [Ys: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys ) ) ).
% 0.29/0.46
% 0.29/0.46 % lexordp_eq_simps(1)
% 0.29/0.46 thf(fact_225_lexordp__eq__simps_I2_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ord @ A )
% 0.29/0.46 => ! [Xs: list @ A] :
% 0.29/0.46 ( ( ord_lexordp_eq @ A @ Xs @ ( nil @ A ) )
% 0.29/0.46 = ( Xs
% 0.29/0.46 = ( nil @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % lexordp_eq_simps(2)
% 0.29/0.46 thf(fact_226_app__subst__Nil,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( type_M1470978233struct @ A )
% 0.29/0.46 => ! [S: nat > type_Mirabelle_typ] :
% 0.29/0.46 ( ( type_M353778473_subst @ ( list @ A ) @ S @ ( nil @ A ) )
% 0.29/0.46 = ( nil @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % app_subst_Nil
% 0.29/0.46 thf(fact_227_lexordp__eq__simps_I3_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ord @ A )
% 0.29/0.46 => ! [X3: A,Xs: list @ A] :
% 0.29/0.46 ~ ( ord_lexordp_eq @ A @ ( cons @ A @ X3 @ Xs ) @ ( nil @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % lexordp_eq_simps(3)
% 0.29/0.46 thf(fact_228_lexordp__eq_ONil,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ord @ A )
% 0.29/0.46 => ! [Ys: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys ) ) ).
% 0.29/0.46
% 0.29/0.46 % lexordp_eq.Nil
% 0.29/0.46 thf(fact_229_new__tv__Nil,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( type_M1470978233struct @ A )
% 0.29/0.46 => ! [N2: nat] : ( type_M1046766514new_tv @ ( list @ A ) @ N2 @ ( nil @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % new_tv_Nil
% 0.29/0.46 thf(fact_230_transpose_Ocases,axiom,
% 0.29/0.46 ! [A: $tType,X3: list @ ( list @ A )] :
% 0.29/0.46 ( ( X3
% 0.29/0.46 != ( nil @ ( list @ A ) ) )
% 0.29/0.46 => ( ! [Xss: list @ ( list @ A )] :
% 0.29/0.46 ( X3
% 0.29/0.46 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.29/0.46 => ~ ! [X: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 0.29/0.46 ( X3
% 0.29/0.46 != ( cons @ ( list @ A ) @ ( cons @ A @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % transpose.cases
% 0.29/0.46 thf(fact_231_list_Odistinct_I1_J,axiom,
% 0.29/0.46 ! [A: $tType,X21: A,X222: list @ A] :
% 0.29/0.46 ( ( nil @ A )
% 0.29/0.46 != ( cons @ A @ X21 @ X222 ) ) ).
% 0.29/0.46
% 0.29/0.46 % list.distinct(1)
% 0.29/0.46 thf(fact_232_list_OdiscI,axiom,
% 0.29/0.46 ! [A: $tType,List: list @ A,X21: A,X222: list @ A] :
% 0.29/0.46 ( ( List
% 0.29/0.46 = ( cons @ A @ X21 @ X222 ) )
% 0.29/0.46 => ( List
% 0.29/0.46 != ( nil @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % list.discI
% 0.29/0.46 thf(fact_233_list_Oexhaust,axiom,
% 0.29/0.46 ! [A: $tType,Y: list @ A] :
% 0.29/0.46 ( ( Y
% 0.29/0.46 != ( nil @ A ) )
% 0.29/0.46 => ~ ! [X212: A,X223: list @ A] :
% 0.29/0.46 ( Y
% 0.29/0.46 != ( cons @ A @ X212 @ X223 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % list.exhaust
% 0.29/0.46 thf(fact_234_list_Oinducts,axiom,
% 0.29/0.46 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 0.29/0.46 ( ( P @ ( nil @ A ) )
% 0.29/0.46 => ( ! [X13: A,X23: list @ A] :
% 0.29/0.46 ( ( P @ X23 )
% 0.29/0.46 => ( P @ ( cons @ A @ X13 @ X23 ) ) )
% 0.29/0.46 => ( P @ List ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % list.inducts
% 0.29/0.46 thf(fact_235_neq__Nil__conv,axiom,
% 0.29/0.46 ! [A: $tType,Xs: list @ A] :
% 0.29/0.46 ( ( Xs
% 0.29/0.46 != ( nil @ A ) )
% 0.29/0.46 = ( ? [Y6: A,Ys3: list @ A] :
% 0.29/0.46 ( Xs
% 0.29/0.46 = ( cons @ A @ Y6 @ Ys3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % neq_Nil_conv
% 0.29/0.46 thf(fact_236_list__induct2_H,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 0.29/0.46 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.29/0.46 => ( ! [X: A,Xs2: list @ A] : ( P @ ( cons @ A @ X @ Xs2 ) @ ( nil @ B ) )
% 0.29/0.46 => ( ! [Y4: B,Ys2: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y4 @ Ys2 ) )
% 0.29/0.46 => ( ! [X: A,Xs2: list @ A,Y4: B,Ys2: list @ B] :
% 0.29/0.46 ( ( P @ Xs2 @ Ys2 )
% 0.29/0.46 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ B @ Y4 @ Ys2 ) ) )
% 0.29/0.46 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % list_induct2'
% 0.29/0.46 thf(fact_237_splice_Oinduct,axiom,
% 0.29/0.46 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.29/0.46 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.29/0.46 => ( ! [X: A,Xs2: list @ A,Ys2: list @ A] :
% 0.29/0.46 ( ( P @ Ys2 @ Xs2 )
% 0.29/0.46 => ( P @ ( cons @ A @ X @ Xs2 ) @ Ys2 ) )
% 0.29/0.46 => ( P @ A0 @ A1 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % splice.induct
% 0.29/0.46 thf(fact_238_induct__list012,axiom,
% 0.29/0.46 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.29/0.46 ( ( P @ ( nil @ A ) )
% 0.29/0.46 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.29/0.46 => ( ! [X: A,Y4: A,Zs2: list @ A] :
% 0.29/0.46 ( ( P @ Zs2 )
% 0.29/0.46 => ( ( P @ ( cons @ A @ Y4 @ Zs2 ) )
% 0.29/0.46 => ( P @ ( cons @ A @ X @ ( cons @ A @ Y4 @ Zs2 ) ) ) ) )
% 0.29/0.46 => ( P @ Xs ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % induct_list012
% 0.29/0.46 thf(fact_239_min__list_Ocases,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ord @ A )
% 0.29/0.46 => ! [X3: list @ A] :
% 0.29/0.46 ( ! [X: A,Xs2: list @ A] :
% 0.29/0.46 ( X3
% 0.29/0.46 != ( cons @ A @ X @ Xs2 ) )
% 0.29/0.46 => ( X3
% 0.29/0.46 = ( nil @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % min_list.cases
% 0.29/0.46 thf(fact_240_min__list_Oinduct,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ord @ A )
% 0.29/0.46 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.29/0.46 ( ! [X: A,Xs2: list @ A] :
% 0.29/0.46 ( ! [X213: A,X224: list @ A] :
% 0.29/0.46 ( ( Xs2
% 0.29/0.46 = ( cons @ A @ X213 @ X224 ) )
% 0.29/0.46 => ( P @ Xs2 ) )
% 0.29/0.46 => ( P @ ( cons @ A @ X @ Xs2 ) ) )
% 0.29/0.46 => ( ( P @ ( nil @ A ) )
% 0.29/0.46 => ( P @ A0 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % min_list.induct
% 0.29/0.46 thf(fact_241_shuffles_Oinduct,axiom,
% 0.29/0.46 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.29/0.46 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.29/0.46 => ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ A ) )
% 0.29/0.46 => ( ! [X: A,Xs2: list @ A,Y4: A,Ys2: list @ A] :
% 0.29/0.46 ( ( P @ Xs2 @ ( cons @ A @ Y4 @ Ys2 ) )
% 0.29/0.46 => ( ( P @ ( cons @ A @ X @ Xs2 ) @ Ys2 )
% 0.29/0.46 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y4 @ Ys2 ) ) ) )
% 0.29/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % shuffles.induct
% 0.29/0.46 thf(fact_242_remdups__adj_Ocases,axiom,
% 0.29/0.46 ! [A: $tType,X3: list @ A] :
% 0.29/0.46 ( ( X3
% 0.29/0.46 != ( nil @ A ) )
% 0.29/0.46 => ( ! [X: A] :
% 0.29/0.46 ( X3
% 0.29/0.46 != ( cons @ A @ X @ ( nil @ A ) ) )
% 0.29/0.46 => ~ ! [X: A,Y4: A,Xs2: list @ A] :
% 0.29/0.46 ( X3
% 0.29/0.46 != ( cons @ A @ X @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % remdups_adj.cases
% 0.29/0.46 thf(fact_243_sorted__wrt_Oinduct,axiom,
% 0.29/0.46 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.29/0.46 ( ! [P4: A > A > $o] : ( P @ P4 @ ( nil @ A ) )
% 0.29/0.46 => ( ! [P4: A > A > $o,X: A,Ys2: list @ A] :
% 0.29/0.46 ( ( P @ P4 @ Ys2 )
% 0.29/0.46 => ( P @ P4 @ ( cons @ A @ X @ Ys2 ) ) )
% 0.29/0.46 => ( P @ A0 @ A1 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sorted_wrt.induct
% 0.29/0.46 thf(fact_244_remdups__adj_Oinduct,axiom,
% 0.29/0.46 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 0.29/0.46 ( ( P @ ( nil @ A ) )
% 0.29/0.46 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.29/0.46 => ( ! [X: A,Y4: A,Xs2: list @ A] :
% 0.29/0.46 ( ( ( X = Y4 )
% 0.29/0.46 => ( P @ ( cons @ A @ X @ Xs2 ) ) )
% 0.29/0.46 => ( ( ( X != Y4 )
% 0.29/0.46 => ( P @ ( cons @ A @ Y4 @ Xs2 ) ) )
% 0.29/0.46 => ( P @ ( cons @ A @ X @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) )
% 0.29/0.46 => ( P @ A0 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % remdups_adj.induct
% 0.29/0.46 thf(fact_245_arg__min__list_Oinduct,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( linorder @ B )
% 0.29/0.46 => ! [P: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 0.29/0.46 ( ! [F5: A > B,X: A] : ( P @ F5 @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.29/0.46 => ( ! [F5: A > B,X: A,Y4: A,Zs2: list @ A] :
% 0.29/0.46 ( ( P @ F5 @ ( cons @ A @ Y4 @ Zs2 ) )
% 0.29/0.46 => ( P @ F5 @ ( cons @ A @ X @ ( cons @ A @ Y4 @ Zs2 ) ) ) )
% 0.29/0.46 => ( ! [A6: A > B] : ( P @ A6 @ ( nil @ A ) )
% 0.29/0.46 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % arg_min_list.induct
% 0.29/0.46 thf(fact_246_successively_Oinduct,axiom,
% 0.29/0.46 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.29/0.46 ( ! [P4: A > A > $o] : ( P @ P4 @ ( nil @ A ) )
% 0.29/0.46 => ( ! [P4: A > A > $o,X: A] : ( P @ P4 @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.29/0.46 => ( ! [P4: A > A > $o,X: A,Y4: A,Xs2: list @ A] :
% 0.29/0.46 ( ( P @ P4 @ ( cons @ A @ Y4 @ Xs2 ) )
% 0.29/0.46 => ( P @ P4 @ ( cons @ A @ X @ ( cons @ A @ Y4 @ Xs2 ) ) ) )
% 0.29/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % successively.induct
% 0.29/0.46 thf(fact_247_list__nonempty__induct,axiom,
% 0.29/0.46 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.29/0.46 ( ( Xs
% 0.29/0.46 != ( nil @ A ) )
% 0.29/0.46 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.29/0.46 => ( ! [X: A,Xs2: list @ A] :
% 0.29/0.46 ( ( Xs2
% 0.29/0.46 != ( nil @ A ) )
% 0.29/0.46 => ( ( P @ Xs2 )
% 0.29/0.46 => ( P @ ( cons @ A @ X @ Xs2 ) ) ) )
% 0.29/0.46 => ( P @ Xs ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % list_nonempty_induct
% 0.29/0.46 thf(fact_248_map__tailrec__rev_Oinduct,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 0.29/0.46 ( ! [F5: A > B,X_1: list @ B] : ( P @ F5 @ ( nil @ A ) @ X_1 )
% 0.29/0.46 => ( ! [F5: A > B,A6: A,As: list @ A,Bs: list @ B] :
% 0.29/0.46 ( ( P @ F5 @ As @ ( cons @ B @ ( F5 @ A6 ) @ Bs ) )
% 0.29/0.46 => ( P @ F5 @ ( cons @ A @ A6 @ As ) @ Bs ) )
% 0.29/0.46 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % map_tailrec_rev.induct
% 0.29/0.46 thf(fact_249_strict__sorted_Ocases,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linorder @ A )
% 0.29/0.46 => ! [X3: list @ A] :
% 0.29/0.46 ( ( X3
% 0.29/0.46 != ( nil @ A ) )
% 0.29/0.46 => ~ ! [X: A,Ys2: list @ A] :
% 0.29/0.46 ( X3
% 0.29/0.46 != ( cons @ A @ X @ Ys2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % strict_sorted.cases
% 0.29/0.46 thf(fact_250_strict__sorted_Oinduct,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linorder @ A )
% 0.29/0.46 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.29/0.46 ( ( P @ ( nil @ A ) )
% 0.29/0.46 => ( ! [X: A,Ys2: list @ A] :
% 0.29/0.46 ( ( P @ Ys2 )
% 0.29/0.46 => ( P @ ( cons @ A @ X @ Ys2 ) ) )
% 0.29/0.46 => ( P @ A0 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % strict_sorted.induct
% 0.29/0.46 thf(fact_251_free__tv__list_Osimps_I1_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( type_M1470978233struct @ A )
% 0.29/0.46 => ( ( type_M950795831ree_tv @ ( list @ A ) @ ( nil @ A ) )
% 0.29/0.46 = ( bot_bot @ ( set @ nat ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % free_tv_list.simps(1)
% 0.29/0.46 thf(fact_252_bound__tv__list_Osimps_I1_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( type_M1470978233struct @ A )
% 0.29/0.46 => ( ( type_M779184887und_tv @ ( list @ A ) @ ( nil @ A ) )
% 0.29/0.46 = ( bot_bot @ ( set @ nat ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % bound_tv_list.simps(1)
% 0.29/0.46 thf(fact_253_lexordp__eq_Oinducts,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ord @ A )
% 0.29/0.46 => ! [X1: list @ A,X2: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 0.29/0.46 ( ( ord_lexordp_eq @ A @ X1 @ X2 )
% 0.29/0.46 => ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.29/0.46 => ( ! [X: A,Y4: A,Xs2: list @ A,Ys2: list @ A] :
% 0.29/0.46 ( ( ord_less @ A @ X @ Y4 )
% 0.29/0.46 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y4 @ Ys2 ) ) )
% 0.29/0.46 => ( ! [X: A,Y4: A,Xs2: list @ A,Ys2: list @ A] :
% 0.29/0.46 ( ~ ( ord_less @ A @ X @ Y4 )
% 0.29/0.46 => ( ~ ( ord_less @ A @ Y4 @ X )
% 0.29/0.46 => ( ( ord_lexordp_eq @ A @ Xs2 @ Ys2 )
% 0.29/0.46 => ( ( P @ Xs2 @ Ys2 )
% 0.29/0.46 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y4 @ Ys2 ) ) ) ) ) )
% 0.29/0.46 => ( P @ X1 @ X2 ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % lexordp_eq.inducts
% 0.29/0.46 thf(fact_254_insert__Nil,axiom,
% 0.29/0.46 ! [A: $tType,X3: A] :
% 0.29/0.46 ( ( insert @ A @ X3 @ ( nil @ A ) )
% 0.29/0.46 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % insert_Nil
% 0.29/0.46
% 0.29/0.46 % Type constructors (40)
% 0.29/0.46 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.29/0.46 bounded_lattice @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.29/0.46 ! [A7: $tType] : ( bounded_lattice @ ( set @ A7 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.29/0.46 ! [A7: $tType,A8: $tType] :
% 0.29/0.46 ( ( bounded_lattice @ A8 )
% 0.29/0.46 => ( bounded_lattice @ ( A7 > A8 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Type__Mirabelle__sfxnzmapfi_Otype__struct,axiom,
% 0.29/0.46 ! [A7: $tType,A8: $tType] :
% 0.29/0.46 ( ( ( type_M201404320of_nat @ A7 )
% 0.29/0.46 & ( type_M1535146424typ_of @ A8 ) )
% 0.29/0.46 => ( type_M1470978233struct @ ( A7 > A8 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 0.29/0.46 ! [A7: $tType,A8: $tType] :
% 0.29/0.46 ( ( bounded_lattice @ A8 )
% 0.29/0.46 => ( bounde1808546759up_bot @ ( A7 > A8 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.29/0.46 ! [A7: $tType,A8: $tType] :
% 0.29/0.46 ( ( semilattice_sup @ A8 )
% 0.29/0.46 => ( semilattice_sup @ ( A7 > A8 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 0.29/0.46 ! [A7: $tType,A8: $tType] :
% 0.29/0.46 ( ( order_bot @ A8 )
% 0.29/0.46 => ( order_bot @ ( A7 > A8 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.29/0.46 ! [A7: $tType,A8: $tType] :
% 0.29/0.46 ( ( preorder @ A8 )
% 0.29/0.46 => ( preorder @ ( A7 > A8 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.29/0.46 ! [A7: $tType,A8: $tType] :
% 0.29/0.46 ( ( order @ A8 )
% 0.29/0.46 => ( order @ ( A7 > A8 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Orderings_Oord,axiom,
% 0.29/0.46 ! [A7: $tType,A8: $tType] :
% 0.29/0.46 ( ( ord @ A8 )
% 0.29/0.46 => ( ord @ ( A7 > A8 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Orderings_Obot,axiom,
% 0.29/0.46 ! [A7: $tType,A8: $tType] :
% 0.29/0.46 ( ( bot @ A8 )
% 0.29/0.46 => ( bot @ ( A7 > A8 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Type__Mirabelle__sfxnzmapfi_Oof__nat,axiom,
% 0.29/0.46 type_M201404320of_nat @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Lattices_Osemilattice__sup_3,axiom,
% 0.29/0.46 semilattice_sup @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.29/0.46 wellorder @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Orderings_Oorder__bot_4,axiom,
% 0.29/0.46 order_bot @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Orderings_Opreorder_5,axiom,
% 0.29/0.46 preorder @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.29/0.46 linorder @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 0.29/0.46 no_top @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Orderings_Oorder_6,axiom,
% 0.29/0.46 order @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Orderings_Oord_7,axiom,
% 0.29/0.46 ord @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Orderings_Obot_8,axiom,
% 0.29/0.46 bot @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_9,axiom,
% 0.29/0.46 ! [A7: $tType] : ( bounde1808546759up_bot @ ( set @ A7 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_10,axiom,
% 0.29/0.46 ! [A7: $tType] : ( semilattice_sup @ ( set @ A7 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___Orderings_Oorder__bot_11,axiom,
% 0.29/0.46 ! [A7: $tType] : ( order_bot @ ( set @ A7 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___Orderings_Opreorder_12,axiom,
% 0.29/0.46 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___Orderings_Oorder_13,axiom,
% 0.29/0.46 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___Orderings_Oord_14,axiom,
% 0.29/0.46 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Set_Oset___Orderings_Obot_15,axiom,
% 0.29/0.46 ! [A7: $tType] : ( bot @ ( set @ A7 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_16,axiom,
% 0.29/0.46 bounde1808546759up_bot @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_17,axiom,
% 0.29/0.46 semilattice_sup @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Orderings_Oorder__bot_18,axiom,
% 0.29/0.46 order_bot @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Orderings_Opreorder_19,axiom,
% 0.29/0.46 preorder @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Orderings_Olinorder_20,axiom,
% 0.29/0.46 linorder @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Orderings_Oorder_21,axiom,
% 0.29/0.46 order @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Orderings_Oord_22,axiom,
% 0.29/0.46 ord @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Orderings_Obot_23,axiom,
% 0.29/0.46 bot @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_List_Olist___Type__Mirabelle__sfxnzmapfi_Otype__struct_24,axiom,
% 0.29/0.46 ! [A7: $tType] :
% 0.29/0.46 ( ( type_M1470978233struct @ A7 )
% 0.29/0.46 => ( type_M1470978233struct @ ( list @ A7 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Type__Mirabelle__sfxnzmapfi_Otyp___Type__Mirabelle__sfxnzmapfi_Otype__struct_25,axiom,
% 0.29/0.46 type_M1470978233struct @ type_Mirabelle_typ ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Type__Mirabelle__sfxnzmapfi_Otyp___Type__Mirabelle__sfxnzmapfi_Otyp__of,axiom,
% 0.29/0.46 type_M1535146424typ_of @ type_Mirabelle_typ ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Type__Mirabelle__sfxnzmapfi_Otype__scheme___Type__Mirabelle__sfxnzmapfi_Otype__struct_26,axiom,
% 0.29/0.46 type_M1470978233struct @ type_M1610475166scheme ).
% 0.29/0.46
% 0.29/0.46 % Helper facts (3)
% 0.29/0.46 thf(help_If_3_1_T,axiom,
% 0.29/0.46 ! [P: $o] :
% 0.29/0.46 ( ( P = $true )
% 0.29/0.46 | ( P = $false ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(help_If_2_1_T,axiom,
% 0.29/0.46 ! [A: $tType,X3: A,Y: A] :
% 0.29/0.46 ( ( if @ A @ $false @ X3 @ Y )
% 0.29/0.46 = Y ) ).
% 0.29/0.46
% 0.29/0.46 thf(help_If_1_1_T,axiom,
% 0.29/0.46 ! [A: $tType,X3: A,Y: A] :
% 0.29/0.46 ( ( if @ A @ $true @ X3 @ Y )
% 0.29/0.46 = X3 ) ).
% 0.29/0.46
% 0.29/0.46 % Conjectures (1)
% 0.29/0.46 thf(conj_0,conjecture,
% 0.29/0.46 ( ( ( type_M353778473_subst @ type_M1610475166scheme @ s1 @ ( type_M91906176e_FVar @ x ) )
% 0.29/0.46 != ( type_M353778473_subst @ type_M1610475166scheme @ s2 @ ( type_M91906176e_FVar @ x ) ) )
% 0.29/0.46 | ~ ( member @ nat @ n @ ( type_M950795831ree_tv @ type_M1610475166scheme @ ( type_M91906176e_FVar @ x ) ) )
% 0.29/0.46 | ( ( s1 @ n )
% 0.29/0.46 = ( s2 @ n ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 3.37/1.86 ---- Embedded in THF ---
% 3.37/1.86 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.37/1.86 %%% Generated on Tue Feb 24 08:30:12 EST 2026
% 3.37/1.86 %%% using '$$dhol' embedding, version 1.3.0.
% 3.37/1.86 %%% Logic specification used:
% 3.37/1.86 %%% thf(spec, logic, $$dhol).
% 3.37/1.86
% 3.37/1.86 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.98HAT0fbB4/DTF2DTF4446.p
% 3.37/1.86 thf(ty_t_Type__Mirabelle__sfxnzmapfi_Otype__scheme, type, type_M1610475166scheme: $tType).
% 3.37/1.86 thf(ty_t_Type__Mirabelle__sfxnzmapfi_Otyp, type, type_Mirabelle_typ: $tType).
% 3.37/1.86 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 3.37/1.86 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 3.37/1.86 thf(ty_t_Nat_Onat, type, nat: $tType).
% 3.37/1.86 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: ($o))).
% 3.37/1.86 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 3.37/1.86 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: ($o))).
% 3.37/1.86 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 3.37/1.86 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 3.37/1.86 thf(sy_cl_Orderings_Ono__bot, type, no_bot: (!> [A:$tType]: ($o))).
% 3.37/1.86 thf(sy_cl_Orderings_Ono__top, type, no_top: (!> [A:$tType]: ($o))).
% 3.37/1.86 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 3.37/1.86 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 3.37/1.86 thf(sy_cl_Orderings_Oorder__bot, type, order_bot: (!> [A:$tType]: ($o))).
% 3.37/1.86 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: ($o))).
% 3.37/1.86 thf(sy_cl_Orderings_Odense__order, type, dense_order: (!> [A:$tType]: ($o))).
% 3.37/1.86 thf(sy_cl_Lattices_Osemilattice__sup, type, semilattice_sup: (!> [A:$tType]: ($o))).
% 3.37/1.86 thf(sy_cl_Type__Mirabelle__sfxnzmapfi_Oof__nat, type, type_M201404320of_nat: (!> [A:$tType]: ($o))).
% 3.37/1.86 thf(sy_cl_Type__Mirabelle__sfxnzmapfi_Otyp__of, type, type_M1535146424typ_of: (!> [A:$tType]: ($o))).
% 3.37/1.86 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot, type, bounde1808546759up_bot: (!> [A:$tType]: ($o))).
% 3.37/1.86 thf(sy_cl_Type__Mirabelle__sfxnzmapfi_Otype__struct, type, type_M1470978233struct: (!> [A:$tType]: ($o))).
% 3.37/1.86 thf(sy_c_HOL_OThe, type, the: (!> [A:$tType]: (((A > $o) > A)))).
% 3.37/1.86 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 3.37/1.86 thf(sy_c_Lattices_Osemilattice__neutr, type, semilattice_neutr: (!> [A:$tType]: (((A > (A > A)) > (A > $o))))).
% 3.37/1.86 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 3.37/1.86 thf(sy_c_List_Oinsert, type, insert: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 3.37/1.86 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 3.37/1.86 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 3.37/1.86 thf(sy_c_List_Oord__class_Olexordp__eq, type, ord_lexordp_eq: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 3.37/1.86 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 3.37/1.86 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 3.37/1.86 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 3.37/1.86 thf(sy_c_Set_Oinsert, type, insert2: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 3.37/1.86 thf(sy_c_Set_Ois__empty, type, is_empty: (!> [A:$tType]: (((set @ A) > $o)))).
% 3.37/1.86 thf(sy_c_Set_Ois__singleton, type, is_singleton: (!> [A:$tType]: (((set @ A) > $o)))).
% 3.37/1.86 thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 3.37/1.86 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Ocod, type, type_Mirabelle_cod: ((nat > type_Mirabelle_typ) > (set @ nat))).
% 3.37/1.86 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Odom, type, type_Mirabelle_dom: ((nat > type_Mirabelle_typ) > (set @ nat))).
% 3.37/1.86 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Oid__subst, type, type_M17369686_subst: (nat > type_Mirabelle_typ)).
% 3.37/1.86 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Omk__scheme, type, type_M540877363scheme: (type_Mirabelle_typ > type_M1610475166scheme)).
% 3.37/1.86 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Onew__tv, type, type_M1046766514new_tv: (!> [A:$tType]: ((nat > (A > $o))))).
% 3.37/1.86 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Oof__nat__class_Oof__nat, type, type_M167561660of_nat: (!> [A:$tType]: ((nat > A)))).
% 3.37/1.86 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otyp_OFun, type, type_Mirabelle_Fun: (type_Mirabelle_typ > (type_Mirabelle_typ > type_Mirabelle_typ))).
% 3.37/1.86 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otyp_OTVar, type, type_Mirabelle_TVar: (nat > type_Mirabelle_typ)).
% 3.37/1.86 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otyp_Ocase__typ, type, type_M1695911984se_typ: (!> [A:$tType]: (((nat > A) > ((type_Mirabelle_typ > (type_Mirabelle_typ > A)) > (type_Mirabelle_typ > A)))))).
% 3.37/1.86 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otyp__of__class_Otyp__of, type, type_M604437996typ_of: (!> [A:$tType]: ((A > type_Mirabelle_typ)))).
% 3.37/1.86 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__scheme_OBVar, type, type_M1264524676e_BVar: (nat > type_M1610475166scheme)).
% 3.37/1.86 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__scheme_OFVar, type, type_M91906176e_FVar: (nat > type_M1610475166scheme)).
% 3.37/1.86 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__scheme_OSFun, type, type_M1518733067e_SFun: (type_M1610475166scheme > (type_M1610475166scheme > type_M1610475166scheme))).
% 3.37/1.86 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__scheme_Ocase__type__scheme, type, type_M697345518scheme: (!> [A:$tType]: (((nat > A) > ((nat > A) > ((type_M1610475166scheme > (type_M1610475166scheme > A)) > (type_M1610475166scheme > A))))))).
% 3.37/1.86 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__scheme_Orec__type__scheme, type, type_M1705333808scheme: (!> [A:$tType]: (((nat > A) > ((nat > A) > ((type_M1610475166scheme > (type_M1610475166scheme > (A > (A > A)))) > (type_M1610475166scheme > A))))))).
% 3.37/1.86 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__struct__class_Oapp__subst, type, type_M353778473_subst: (!> [A:$tType]: (((nat > type_Mirabelle_typ) > (A > A))))).
% 3.37/1.86 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__struct__class_Obound__tv, type, type_M779184887und_tv: (!> [A:$tType]: ((A > (set @ nat))))).
% 3.37/1.86 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__struct__class_Ofree__tv, type, type_M950795831ree_tv: (!> [A:$tType]: ((A > (set @ nat))))).
% 3.37/1.86 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 3.37/1.86 thf(sy_v_S1, type, s1: (nat > type_Mirabelle_typ)).
% 3.37/1.86 thf(sy_v_S2, type, s2: (nat > type_Mirabelle_typ)).
% 3.37/1.86 thf(sy_v_n, type, n: nat).
% 3.37/1.86 thf(sy_v_x, type, x: nat).
% 3.37/1.86 thf(fact_0_type__scheme_Oinject_I1_J, axiom, (! [X1:nat,Y1:nat]: ((((type_M91906176e_FVar @ X1) = (type_M91906176e_FVar @ Y1)) = (X1 = Y1))))).
% 3.37/1.86 thf(fact_1_eq__free__eq__subst__type__scheme, axiom, (! [Sch:type_M1610475166scheme,S1:(nat > type_Mirabelle_typ),S2:(nat > type_Mirabelle_typ)]: (((! [N:nat]: (((((member @ nat) @ N) @ ((type_M950795831ree_tv @ type_M1610475166scheme) @ Sch)) => ((S1 @ N) = (S2 @ N))))) => ((((type_M353778473_subst @ type_M1610475166scheme) @ S1) @ Sch) = (((type_M353778473_subst @ type_M1610475166scheme) @ S2) @ Sch)))))).
% 3.37/1.86 thf(fact_2_scheme__substitutions__only__on__free__variables, axiom, (! [Sch:type_M1610475166scheme,S:(nat > type_Mirabelle_typ),S3:(nat > type_Mirabelle_typ)]: (((! [X:nat]: (((((member @ nat) @ X) @ ((type_M950795831ree_tv @ type_M1610475166scheme) @ Sch)) => ((S @ X) = (S3 @ X))))) => ((((type_M353778473_subst @ type_M1610475166scheme) @ S) @ Sch) = (((type_M353778473_subst @ type_M1610475166scheme) @ S3) @ Sch)))))).
% 3.37/1.86 thf(fact_3_app__subst__type__scheme_Osimps_I1_J, axiom, (! [S:(nat > type_Mirabelle_typ),N2:nat]: (((((type_M353778473_subst @ type_M1610475166scheme) @ S) @ (type_M91906176e_FVar @ N2)) = (type_M540877363scheme @ (S @ N2)))))).
% 3.37/1.86 thf(fact_4_type__scheme_Osimps_I13_J, axiom, (! [A:$tType,F1:(nat > A),F2:(nat > A),F3:(type_M1610475166scheme > (type_M1610475166scheme > (A > (A > A)))),X1:nat]: (((((((type_M1705333808scheme @ A) @ F1) @ F2) @ F3) @ (type_M91906176e_FVar @ X1)) = (F1 @ X1))))).
% 3.37/1.86 thf(fact_5_type__scheme_Osimps_I10_J, axiom, (! [A:$tType,F1:(nat > A),F2:(nat > A),F3:(type_M1610475166scheme > (type_M1610475166scheme > A)),X1:nat]: (((((((type_M697345518scheme @ A) @ F1) @ F2) @ F3) @ (type_M91906176e_FVar @ X1)) = (F1 @ X1))))).
% 3.37/1.86 thf(fact_6_app__subst__type__scheme_Osimps_I2_J, axiom, (! [S:(nat > type_Mirabelle_typ),N2:nat]: (((((type_M353778473_subst @ type_M1610475166scheme) @ S) @ (type_M1264524676e_BVar @ N2)) = (type_M1264524676e_BVar @ N2))))).
% 3.37/1.86 thf(fact_7_app__subst__type__scheme_Osimps_I3_J, axiom, (! [S:(nat > type_Mirabelle_typ),Sch1:type_M1610475166scheme,Sch2:type_M1610475166scheme]: (((((type_M353778473_subst @ type_M1610475166scheme) @ S) @ ((type_M1518733067e_SFun @ Sch1) @ Sch2)) = ((type_M1518733067e_SFun @ (((type_M353778473_subst @ type_M1610475166scheme) @ S) @ Sch1)) @ (((type_M353778473_subst @ type_M1610475166scheme) @ S) @ Sch2)))))).
% 3.37/1.86 thf(fact_8_type__scheme_Odistinct_I1_J, axiom, (! [X1:nat,X2:nat]: (((type_M91906176e_FVar @ X1) != (type_M1264524676e_BVar @ X2))))).
% 3.37/1.86 thf(fact_9_type__scheme_Odistinct_I3_J, axiom, (! [X1:nat,X31:type_M1610475166scheme,X32:type_M1610475166scheme]: (((type_M91906176e_FVar @ X1) != ((type_M1518733067e_SFun @ X31) @ X32))))).
% 3.37/1.86 thf(fact_10_app__subst__Cons, axiom, (! [A:$tType]: (((type_M1470978233struct @ A) => (! [S:(nat > type_Mirabelle_typ),X3:A,L:(list @ A)]: (((((type_M353778473_subst @ (list @ A)) @ S) @ (((cons @ A) @ X3) @ L)) = (((cons @ A) @ (((type_M353778473_subst @ A) @ S) @ X3)) @ (((type_M353778473_subst @ (list @ A)) @ S) @ L))))))))).
% 3.37/1.86 thf(fact_11_free__tv__mk__scheme, axiom, (! [T:type_Mirabelle_typ]: ((((type_M950795831ree_tv @ type_M1610475166scheme) @ (type_M540877363scheme @ T)) = ((type_M950795831ree_tv @ type_Mirabelle_typ) @ T))))).
% 3.37/1.86 thf(fact_12_free__tv__type__scheme_Osimps_I1_J, axiom, (! [M:nat]: ((((type_M950795831ree_tv @ type_M1610475166scheme) @ (type_M91906176e_FVar @ M)) = (((insert2 @ nat) @ M) @ (bot_bot @ (set @ nat))))))).
% 3.37/1.86 thf(fact_13_new__if__subst__type__scheme, axiom, (! [N2:nat,Sch:type_M1610475166scheme,S:(nat > type_Mirabelle_typ),S3:(nat > type_Mirabelle_typ)]: (((((type_M1046766514new_tv @ type_M1610475166scheme) @ N2) @ Sch) => ((((type_M353778473_subst @ type_M1610475166scheme) @ (^ [K:nat]: (((((if @ type_Mirabelle_typ) @ (((ord_less @ nat) @ K) @ N2)) @ (S @ K)) @ (S3 @ K))))) @ Sch) = (((type_M353778473_subst @ type_M1610475166scheme) @ S) @ Sch)))))).
% 3.37/1.86 thf(fact_14_typ_Ocase__distrib, axiom, (! [A:$tType,B:$tType,H:(A > B),F1:(nat > A),F2:(type_Mirabelle_typ > (type_Mirabelle_typ > A)),Typ:type_Mirabelle_typ]: (((H @ ((((type_M1695911984se_typ @ A) @ F1) @ F2) @ Typ)) = ((((type_M1695911984se_typ @ B) @ (^ [X4:nat]: ((H @ (F1 @ X4))))) @ (^ [X12:type_Mirabelle_typ,X22:type_Mirabelle_typ]: ((H @ ((F2 @ X12) @ X22))))) @ Typ))))).
% 3.37/1.86 thf(fact_15_type__scheme_Oinject_I3_J, axiom, (! [X31:type_M1610475166scheme,X32:type_M1610475166scheme,Y31:type_M1610475166scheme,Y32:type_M1610475166scheme]: (((((type_M1518733067e_SFun @ X31) @ X32) = ((type_M1518733067e_SFun @ Y31) @ Y32)) = ((X31 = Y31) & (X32 = Y32)))))).
% 3.37/1.86 thf(fact_16_type__scheme_Oinject_I2_J, axiom, (! [X2:nat,Y2:nat]: ((((type_M1264524676e_BVar @ X2) = (type_M1264524676e_BVar @ Y2)) = (X2 = Y2))))).
% 3.37/1.86 thf(fact_17_new__tv__Cons, axiom, (! [A:$tType]: (((type_M1470978233struct @ A) => (! [N2:nat,X3:A,L:(list @ A)]: (((((type_M1046766514new_tv @ (list @ A)) @ N2) @ (((cons @ A) @ X3) @ L)) = ((((type_M1046766514new_tv @ A) @ N2) @ X3) & (((type_M1046766514new_tv @ (list @ A)) @ N2) @ L))))))))).
% 3.37/1.86 thf(fact_18_subst__mk__scheme, axiom, (! [S:(nat > type_Mirabelle_typ),T:type_Mirabelle_typ]: (((((type_M353778473_subst @ type_M1610475166scheme) @ S) @ (type_M540877363scheme @ T)) = (type_M540877363scheme @ (((type_M353778473_subst @ type_Mirabelle_typ) @ S) @ T)))))).
% 3.37/1.86 thf(fact_19_new__tv__Fun2, axiom, (! [N2:nat,T1:type_M1610475166scheme,T2:type_M1610475166scheme]: (((((type_M1046766514new_tv @ type_M1610475166scheme) @ N2) @ ((type_M1518733067e_SFun @ T1) @ T2)) = ((((type_M1046766514new_tv @ type_M1610475166scheme) @ N2) @ T1) & (((type_M1046766514new_tv @ type_M1610475166scheme) @ N2) @ T2)))))).
% 3.37/1.86 thf(fact_20_new__tv__BVar, axiom, (! [N2:nat,M:nat]: ((((type_M1046766514new_tv @ type_M1610475166scheme) @ N2) @ (type_M1264524676e_BVar @ M))))).
% 3.37/1.86 thf(fact_21_new__tv__FVar, axiom, (! [N2:nat,M:nat]: (((((type_M1046766514new_tv @ type_M1610475166scheme) @ N2) @ (type_M91906176e_FVar @ M)) = (((ord_less @ nat) @ M) @ N2))))).
% 3.37/1.86 thf(fact_22_type__scheme_Osimps_I15_J, axiom, (! [A:$tType,F1:(nat > A),F2:(nat > A),F3:(type_M1610475166scheme > (type_M1610475166scheme > (A > (A > A)))),X31:type_M1610475166scheme,X32:type_M1610475166scheme]: (((((((type_M1705333808scheme @ A) @ F1) @ F2) @ F3) @ ((type_M1518733067e_SFun @ X31) @ X32)) = ((((F3 @ X31) @ X32) @ (((((type_M1705333808scheme @ A) @ F1) @ F2) @ F3) @ X31)) @ (((((type_M1705333808scheme @ A) @ F1) @ F2) @ F3) @ X32)))))).
% 3.37/1.86 thf(fact_23_type__scheme_Osimps_I14_J, axiom, (! [A:$tType,F1:(nat > A),F2:(nat > A),F3:(type_M1610475166scheme > (type_M1610475166scheme > (A > (A > A)))),X2:nat]: (((((((type_M1705333808scheme @ A) @ F1) @ F2) @ F3) @ (type_M1264524676e_BVar @ X2)) = (F2 @ X2))))).
% 3.37/1.86 thf(fact_24_type__scheme_Osimps_I12_J, axiom, (! [A:$tType,F1:(nat > A),F2:(nat > A),F3:(type_M1610475166scheme > (type_M1610475166scheme > A)),X31:type_M1610475166scheme,X32:type_M1610475166scheme]: (((((((type_M697345518scheme @ A) @ F1) @ F2) @ F3) @ ((type_M1518733067e_SFun @ X31) @ X32)) = ((F3 @ X31) @ X32))))).
% 3.37/1.86 thf(fact_25_type__scheme_Osimps_I11_J, axiom, (! [A:$tType,F1:(nat > A),F2:(nat > A),F3:(type_M1610475166scheme > (type_M1610475166scheme > A)),X2:nat]: (((((((type_M697345518scheme @ A) @ F1) @ F2) @ F3) @ (type_M1264524676e_BVar @ X2)) = (F2 @ X2))))).
% 3.37/1.86 thf(fact_26_type__scheme_Odistinct_I5_J, axiom, (! [X2:nat,X31:type_M1610475166scheme,X32:type_M1610475166scheme]: (((type_M1264524676e_BVar @ X2) != ((type_M1518733067e_SFun @ X31) @ X32))))).
% 3.37/1.86 thf(fact_27_mk__scheme__Fun, axiom, (! [T:type_Mirabelle_typ,Sch1:type_M1610475166scheme,Sch2:type_M1610475166scheme]: ((((type_M540877363scheme @ T) = ((type_M1518733067e_SFun @ Sch1) @ Sch2)) => (? [T12:type_Mirabelle_typ,T22:type_Mirabelle_typ]: (((Sch1 = (type_M540877363scheme @ T12)) & (Sch2 = (type_M540877363scheme @ T22))))))))).
% 3.37/1.86 thf(fact_28_eq__free__eq__subst__te, axiom, (! [T:type_Mirabelle_typ,S1:(nat > type_Mirabelle_typ),S2:(nat > type_Mirabelle_typ)]: (((! [N:nat]: (((((member @ nat) @ N) @ ((type_M950795831ree_tv @ type_Mirabelle_typ) @ T)) => ((S1 @ N) = (S2 @ N))))) => ((((type_M353778473_subst @ type_Mirabelle_typ) @ S1) @ T) = (((type_M353778473_subst @ type_Mirabelle_typ) @ S2) @ T)))))).
% 3.37/1.86 thf(fact_29_eq__subst__te__eq__free, axiom, (! [S1:(nat > type_Mirabelle_typ),T:type_Mirabelle_typ,S2:(nat > type_Mirabelle_typ),N2:nat]: ((((((type_M353778473_subst @ type_Mirabelle_typ) @ S1) @ T) = (((type_M353778473_subst @ type_Mirabelle_typ) @ S2) @ T)) => ((((member @ nat) @ N2) @ ((type_M950795831ree_tv @ type_Mirabelle_typ) @ T)) => ((S1 @ N2) = (S2 @ N2))))))).
% 3.37/1.86 thf(fact_30_typ__substitutions__only__on__free__variables, axiom, (! [T:type_Mirabelle_typ,S:(nat > type_Mirabelle_typ),S3:(nat > type_Mirabelle_typ)]: (((! [X:nat]: (((((member @ nat) @ X) @ ((type_M950795831ree_tv @ type_Mirabelle_typ) @ T)) => ((S @ X) = (S3 @ X))))) => ((((type_M353778473_subst @ type_Mirabelle_typ) @ S) @ T) = (((type_M353778473_subst @ type_Mirabelle_typ) @ S3) @ T)))))).
% 3.37/1.86 thf(fact_31_mk__scheme__injective, axiom, (! [T:type_Mirabelle_typ,T3:type_Mirabelle_typ]: ((((type_M540877363scheme @ T) = (type_M540877363scheme @ T3)) => (T = T3))))).
% 3.37/1.86 thf(fact_32_free__tv__type__scheme_Osimps_I2_J, axiom, (! [M:nat]: ((((type_M950795831ree_tv @ type_M1610475166scheme) @ (type_M1264524676e_BVar @ M)) = (bot_bot @ (set @ nat)))))).
% 3.37/1.86 thf(fact_33_type__scheme_Oexhaust, axiom, (! [Y:type_M1610475166scheme]: (((! [X13:nat]: ((Y != (type_M91906176e_FVar @ X13)))) => ((! [X23:nat]: ((Y != (type_M1264524676e_BVar @ X23)))) => (~ ((! [X312:type_M1610475166scheme,X322:type_M1610475166scheme]: ((Y != ((type_M1518733067e_SFun @ X312) @ X322))))))))))).
% 3.37/1.86 thf(fact_34_type__scheme_Oinduct, axiom, (! [P:(type_M1610475166scheme > $o),Type_scheme:type_M1610475166scheme]: (((! [X:nat]: ((P @ (type_M91906176e_FVar @ X)))) => ((! [X:nat]: ((P @ (type_M1264524676e_BVar @ X)))) => ((! [X1a:type_M1610475166scheme,X2a:type_M1610475166scheme]: (((P @ X1a) => ((P @ X2a) => (P @ ((type_M1518733067e_SFun @ X1a) @ X2a)))))) => (P @ Type_scheme))))))).
% 3.37/1.86 thf(fact_35_new__tv__def, axiom, (! [A:$tType]: (((type_M1470978233struct @ A) => ((type_M1046766514new_tv @ A) = (^ [N3:nat,Ts:A]: ((! [M2:nat]: (((((member @ nat) @ M2) @ ((type_M950795831ree_tv @ A) @ Ts)) => (((ord_less @ nat) @ M2) @ N3))))))))))).
% 3.37/1.86 thf(fact_36_type__scheme_Ocase__distrib, axiom, (! [A:$tType,B:$tType,H:(A > B),F1:(nat > A),F2:(nat > A),F3:(type_M1610475166scheme > (type_M1610475166scheme > A)),Type_scheme:type_M1610475166scheme]: (((H @ (((((type_M697345518scheme @ A) @ F1) @ F2) @ F3) @ Type_scheme)) = (((((type_M697345518scheme @ B) @ (^ [X4:nat]: ((H @ (F1 @ X4))))) @ (^ [X4:nat]: ((H @ (F2 @ X4))))) @ (^ [X12:type_M1610475166scheme,X22:type_M1610475166scheme]: ((H @ ((F3 @ X12) @ X22))))) @ Type_scheme))))).
% 3.37/1.86 thf(fact_37_singleton__conv, axiom, (! [A:$tType,A2:A]: ((((collect @ A) @ (^ [X4:A]: ((X4 = A2)))) = (((insert2 @ A) @ A2) @ (bot_bot @ (set @ A))))))).
% 3.37/1.86 thf(fact_38_singleton__conv2, axiom, (! [A:$tType,A2:A]: ((((collect @ A) @ ((^ [Y3:A,Z:A]: ((Y3 = Z))) @ A2)) = (((insert2 @ A) @ A2) @ (bot_bot @ (set @ A))))))).
% 3.37/1.86 thf(fact_39_singletonI, axiom, (! [A:$tType,A2:A]: ((((member @ A) @ A2) @ (((insert2 @ A) @ A2) @ (bot_bot @ (set @ A))))))).
% 3.37/1.86 thf(fact_40_insertCI, axiom, (! [A:$tType,A2:A,B2:(set @ A),B3:A]: ((((~ ((((member @ A) @ A2) @ B2))) => (A2 = B3)) => (((member @ A) @ A2) @ (((insert2 @ A) @ B3) @ B2)))))).
% 3.37/1.86 thf(fact_41_insert__iff, axiom, (! [A:$tType,A2:A,B3:A,A3:(set @ A)]: (((((member @ A) @ A2) @ (((insert2 @ A) @ B3) @ A3)) = ((A2 = B3) | (((member @ A) @ A2) @ A3)))))).
% 3.37/1.86 thf(fact_42_insert__absorb2, axiom, (! [A:$tType,X3:A,A3:(set @ A)]: (((((insert2 @ A) @ X3) @ (((insert2 @ A) @ X3) @ A3)) = (((insert2 @ A) @ X3) @ A3))))).
% 3.37/1.86 thf(fact_43_list_Oinject, axiom, (! [A:$tType,X21:A,X222:(list @ A),Y21:A,Y22:(list @ A)]: ((((((cons @ A) @ X21) @ X222) = (((cons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X222 = Y22)))))).
% 3.37/1.86 thf(fact_44_empty__iff, axiom, (! [A:$tType,C:A]: ((~ ((((member @ A) @ C) @ (bot_bot @ (set @ A)))))))).
% 3.37/1.86 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 3.37/1.86 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X4:A]: ((((member @ A) @ X4) @ A3)))) = A3)))).
% 3.37/1.86 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X:A]: (((P @ X) = (Q @ X)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 3.37/1.86 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X:A]: (((F @ X) = (G @ X)))) => (F = G))))).
% 3.37/1.86 thf(fact_49_all__not__in__conv, axiom, (! [A:$tType,A3:(set @ A)]: (((! [X4:A]: ((~ ((((member @ A) @ X4) @ A3))))) = (A3 = (bot_bot @ (set @ A))))))).
% 3.37/1.86 thf(fact_50_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X4:A]: ((~ ((P @ X4))))))))).
% 3.37/1.86 thf(fact_51_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X4:A]: ((~ ((P @ X4))))))))).
% 3.37/1.86 thf(fact_52_new__if__subst__type__scheme__list, axiom, (! [N2:nat,A3:(list @ type_M1610475166scheme),S:(nat > type_Mirabelle_typ),S3:(nat > type_Mirabelle_typ)]: (((((type_M1046766514new_tv @ (list @ type_M1610475166scheme)) @ N2) @ A3) => ((((type_M353778473_subst @ (list @ type_M1610475166scheme)) @ (^ [K:nat]: (((((if @ type_Mirabelle_typ) @ (((ord_less @ nat) @ K) @ N2)) @ (S @ K)) @ (S3 @ K))))) @ A3) = (((type_M353778473_subst @ (list @ type_M1610475166scheme)) @ S) @ A3)))))).
% 3.37/1.86 thf(fact_53_ex__in__conv, axiom, (! [A:$tType,A3:(set @ A)]: (((? [X4:A]: ((((member @ A) @ X4) @ A3))) = (A3 != (bot_bot @ (set @ A))))))).
% 3.37/1.86 thf(fact_54_equals0I, axiom, (! [A:$tType,A3:(set @ A)]: (((! [Y4:A]: ((~ ((((member @ A) @ Y4) @ A3))))) => (A3 = (bot_bot @ (set @ A))))))).
% 3.37/1.86 thf(fact_55_equals0D, axiom, (! [A:$tType,A3:(set @ A),A2:A]: (((A3 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A2) @ A3))))))).
% 3.37/1.86 thf(fact_56_emptyE, axiom, (! [A:$tType,A2:A]: ((~ ((((member @ A) @ A2) @ (bot_bot @ (set @ A)))))))).
% 3.37/1.86 thf(fact_57_not__Cons__self2, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: (((((cons @ A) @ X3) @ Xs) != Xs)))).
% 3.37/1.86 thf(fact_58_mk__disjoint__insert, axiom, (! [A:$tType,A2:A,A3:(set @ A)]: (((((member @ A) @ A2) @ A3) => (? [B4:(set @ A)]: (((A3 = (((insert2 @ A) @ A2) @ B4)) & (~ ((((member @ A) @ A2) @ B4)))))))))).
% 3.37/1.86 thf(fact_59_insert__commute, axiom, (! [A:$tType,X3:A,Y:A,A3:(set @ A)]: (((((insert2 @ A) @ X3) @ (((insert2 @ A) @ Y) @ A3)) = (((insert2 @ A) @ Y) @ (((insert2 @ A) @ X3) @ A3)))))).
% 3.37/1.86 thf(fact_60_insert__eq__iff, axiom, (! [A:$tType,A2:A,A3:(set @ A),B3:A,B2:(set @ A)]: (((~ ((((member @ A) @ A2) @ A3))) => ((~ ((((member @ A) @ B3) @ B2))) => (((((insert2 @ A) @ A2) @ A3) = (((insert2 @ A) @ B3) @ B2)) = (((A2 = B3) => (A3 = B2)) & ((A2 != B3) => (? [C2:(set @ A)]: (((A3 = (((insert2 @ A) @ B3) @ C2)) & ((~ ((((member @ A) @ B3) @ C2))) & ((B2 = (((insert2 @ A) @ A2) @ C2)) & (~ ((((member @ A) @ A2) @ C2)))))))))))))))).
% 3.37/1.86 thf(fact_61_insert__absorb, axiom, (! [A:$tType,A2:A,A3:(set @ A)]: (((((member @ A) @ A2) @ A3) => ((((insert2 @ A) @ A2) @ A3) = A3))))).
% 3.37/1.86 thf(fact_62_insert__ident, axiom, (! [A:$tType,X3:A,A3:(set @ A),B2:(set @ A)]: (((~ ((((member @ A) @ X3) @ A3))) => ((~ ((((member @ A) @ X3) @ B2))) => (((((insert2 @ A) @ X3) @ A3) = (((insert2 @ A) @ X3) @ B2)) = (A3 = B2))))))).
% 3.37/1.86 thf(fact_63_Set_Oset__insert, axiom, (! [A:$tType,X3:A,A3:(set @ A)]: (((((member @ A) @ X3) @ A3) => (~ ((! [B4:(set @ A)]: (((A3 = (((insert2 @ A) @ X3) @ B4)) => (((member @ A) @ X3) @ B4)))))))))).
% 3.37/1.86 thf(fact_64_insertI2, axiom, (! [A:$tType,A2:A,B2:(set @ A),B3:A]: (((((member @ A) @ A2) @ B2) => (((member @ A) @ A2) @ (((insert2 @ A) @ B3) @ B2)))))).
% 3.37/1.86 thf(fact_65_insertI1, axiom, (! [A:$tType,A2:A,B2:(set @ A)]: ((((member @ A) @ A2) @ (((insert2 @ A) @ A2) @ B2))))).
% 3.37/1.86 thf(fact_66_insertE, axiom, (! [A:$tType,A2:A,B3:A,A3:(set @ A)]: (((((member @ A) @ A2) @ (((insert2 @ A) @ B3) @ A3)) => ((A2 != B3) => (((member @ A) @ A2) @ A3)))))).
% 3.37/1.86 thf(fact_67_empty__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (^ [X4:A]: ($false))))))).
% 3.37/1.86 thf(fact_68_insert__Collect, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((insert2 @ A) @ A2) @ ((collect @ A) @ P)) = ((collect @ A) @ (^ [U:A]: (((U != A2) => (P @ U))))))))).
% 3.37/1.86 thf(fact_69_insert__compr, axiom, (! [A:$tType]: (((insert2 @ A) = (^ [A4:A,B5:(set @ A)]: (((collect @ A) @ (^ [X4:A]: (((X4 = A4) | (((member @ A) @ X4) @ B5))))))))))).
% 3.37/1.86 thf(fact_70_singleton__inject, axiom, (! [A:$tType,A2:A,B3:A]: ((((((insert2 @ A) @ A2) @ (bot_bot @ (set @ A))) = (((insert2 @ A) @ B3) @ (bot_bot @ (set @ A)))) => (A2 = B3))))).
% 3.37/1.86 thf(fact_71_insert__not__empty, axiom, (! [A:$tType,A2:A,A3:(set @ A)]: (((((insert2 @ A) @ A2) @ A3) != (bot_bot @ (set @ A)))))).
% 3.37/1.86 thf(fact_72_doubleton__eq__iff, axiom, (! [A:$tType,A2:A,B3:A,C:A,D:A]: ((((((insert2 @ A) @ A2) @ (((insert2 @ A) @ B3) @ (bot_bot @ (set @ A)))) = (((insert2 @ A) @ C) @ (((insert2 @ A) @ D) @ (bot_bot @ (set @ A))))) = (((A2 = C) & (B3 = D)) | ((A2 = D) & (B3 = C))))))).
% 3.37/1.86 thf(fact_73_singleton__iff, axiom, (! [A:$tType,B3:A,A2:A]: (((((member @ A) @ B3) @ (((insert2 @ A) @ A2) @ (bot_bot @ (set @ A)))) = (B3 = A2))))).
% 3.37/1.86 thf(fact_74_singletonD, axiom, (! [A:$tType,B3:A,A2:A]: (((((member @ A) @ B3) @ (((insert2 @ A) @ A2) @ (bot_bot @ (set @ A)))) => (B3 = A2))))).
% 3.37/1.86 thf(fact_75_Collect__conv__if2, axiom, (! [A:$tType,P:(A > $o),A2:A]: ((((P @ A2) => (((collect @ A) @ (^ [X4:A]: (((A2 = X4) & (P @ X4))))) = (((insert2 @ A) @ A2) @ (bot_bot @ (set @ A))))) & ((~ ((P @ A2))) => (((collect @ A) @ (^ [X4:A]: (((A2 = X4) & (P @ X4))))) = (bot_bot @ (set @ A)))))))).
% 3.37/1.86 thf(fact_76_Collect__conv__if, axiom, (! [A:$tType,P:(A > $o),A2:A]: ((((P @ A2) => (((collect @ A) @ (^ [X4:A]: (((X4 = A2) & (P @ X4))))) = (((insert2 @ A) @ A2) @ (bot_bot @ (set @ A))))) & ((~ ((P @ A2))) => (((collect @ A) @ (^ [X4:A]: (((X4 = A2) & (P @ X4))))) = (bot_bot @ (set @ A)))))))).
% 3.37/1.86 thf(fact_77_the__elem__eq, axiom, (! [A:$tType,X3:A]: ((((the_elem @ A) @ (((insert2 @ A) @ X3) @ (bot_bot @ (set @ A)))) = X3)))).
% 3.37/1.86 thf(fact_78_bot__apply, axiom, (! [C3:$tType,D2:$tType]: (((bot @ C3) => ((bot_bot @ (D2 > C3)) = (^ [X4:D2]: ((bot_bot @ C3)))))))).
% 3.37/1.86 thf(fact_79_bound__tv__type__scheme_Osimps_I2_J, axiom, (! [M:nat]: ((((type_M779184887und_tv @ type_M1610475166scheme) @ (type_M1264524676e_BVar @ M)) = (((insert2 @ nat) @ M) @ (bot_bot @ (set @ nat))))))).
% 3.37/1.86 thf(fact_80_is__singletonI, axiom, (! [A:$tType,X3:A]: (((is_singleton @ A) @ (((insert2 @ A) @ X3) @ (bot_bot @ (set @ A))))))).
% 3.37/1.86 thf(fact_81_bot_Onot__eq__extremum, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A2:A]: (((A2 != (bot_bot @ A)) = (((ord_less @ A) @ (bot_bot @ A)) @ A2)))))))).
% 3.37/1.86 thf(fact_82_bot_Oextremum__strict, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A2:A]: ((~ ((((ord_less @ A) @ A2) @ (bot_bot @ A)))))))))).
% 3.37/1.86 thf(fact_83_free__tv__TVar, axiom, (! [M:nat]: ((((type_M950795831ree_tv @ type_Mirabelle_typ) @ (type_Mirabelle_TVar @ M)) = (((insert2 @ nat) @ M) @ (bot_bot @ (set @ nat))))))).
% 3.37/1.86 thf(fact_84_bound__tv__type__scheme_Osimps_I1_J, axiom, (! [M:nat]: ((((type_M779184887und_tv @ type_M1610475166scheme) @ (type_M91906176e_FVar @ M)) = (bot_bot @ (set @ nat)))))).
% 3.37/1.86 thf(fact_85_typ_Oinject_I1_J, axiom, (! [X1:nat,Y1:nat]: ((((type_Mirabelle_TVar @ X1) = (type_Mirabelle_TVar @ Y1)) = (X1 = Y1))))).
% 3.37/1.86 thf(fact_86_new__tv__TVar, axiom, (! [N2:nat,M:nat]: (((((type_M1046766514new_tv @ type_Mirabelle_typ) @ N2) @ (type_Mirabelle_TVar @ M)) = (((ord_less @ nat) @ M) @ N2))))).
% 3.37/1.86 thf(fact_87_new__tv__TVar__subst, axiom, (! [N2:nat]: ((((type_M1046766514new_tv @ (nat > type_Mirabelle_typ)) @ N2) @ type_Mirabelle_TVar)))).
% 3.37/1.86 thf(fact_88_eq__free__eq__subst__scheme__list, axiom, (! [A3:(list @ type_M1610475166scheme),S1:(nat > type_Mirabelle_typ),S2:(nat > type_Mirabelle_typ)]: (((! [N:nat]: (((((member @ nat) @ N) @ ((type_M950795831ree_tv @ (list @ type_M1610475166scheme)) @ A3)) => ((S1 @ N) = (S2 @ N))))) => ((((type_M353778473_subst @ (list @ type_M1610475166scheme)) @ S1) @ A3) = (((type_M353778473_subst @ (list @ type_M1610475166scheme)) @ S2) @ A3)))))).
% 3.37/1.86 thf(fact_89_scheme__list__substitutions__only__on__free__variables, axiom, (! [A3:(list @ type_M1610475166scheme),S:(nat > type_Mirabelle_typ),S3:(nat > type_Mirabelle_typ)]: (((! [X:nat]: (((((member @ nat) @ X) @ ((type_M950795831ree_tv @ (list @ type_M1610475166scheme)) @ A3)) => ((S @ X) = (S3 @ X))))) => ((((type_M353778473_subst @ (list @ type_M1610475166scheme)) @ S) @ A3) = (((type_M353778473_subst @ (list @ type_M1610475166scheme)) @ S3) @ A3)))))).
% 3.37/1.86 thf(fact_90_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 3.37/1.86 thf(fact_91_not__psubset__empty, axiom, (! [A:$tType,A3:(set @ A)]: ((~ ((((ord_less @ (set @ A)) @ A3) @ (bot_bot @ (set @ A)))))))).
% 3.37/1.86 thf(fact_92_app__subst__TVar, axiom, (! [S:(nat > type_Mirabelle_typ),N2:nat]: (((((type_M353778473_subst @ type_Mirabelle_typ) @ S) @ (type_Mirabelle_TVar @ N2)) = (S @ N2))))).
% 3.37/1.86 thf(fact_93_is__singleton__the__elem, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A5:(set @ A)]: ((A5 = (((insert2 @ A) @ ((the_elem @ A) @ A5)) @ (bot_bot @ (set @ A)))))))))).
% 3.37/1.86 thf(fact_94_typ_Osimps_I5_J, axiom, (! [A:$tType,F1:(nat > A),F2:(type_Mirabelle_typ > (type_Mirabelle_typ > A)),X1:nat]: ((((((type_M1695911984se_typ @ A) @ F1) @ F2) @ (type_Mirabelle_TVar @ X1)) = (F1 @ X1))))).
% 3.37/1.86 thf(fact_95_is__singletonI_H, axiom, (! [A:$tType,A3:(set @ A)]: (((A3 != (bot_bot @ (set @ A))) => ((! [X:A,Y4:A]: (((((member @ A) @ X) @ A3) => ((((member @ A) @ Y4) @ A3) => (X = Y4))))) => ((is_singleton @ A) @ A3)))))).
% 3.37/1.86 thf(fact_96_ord__eq__less__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,F:(B > A),B3:B,C:B]: (((A2 = (F @ B3)) => ((((ord_less @ B) @ B3) @ C) => ((! [X:B,Y4:B]: (((((ord_less @ B) @ X) @ Y4) => (((ord_less @ A) @ (F @ X)) @ (F @ Y4))))) => (((ord_less @ A) @ A2) @ (F @ C))))))))))).
% 3.37/1.86 thf(fact_97_ord__less__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,B3:A,F:(A > B),C:B]: (((((ord_less @ A) @ A2) @ B3) => (((F @ B3) = C) => ((! [X:A,Y4:A]: (((((ord_less @ A) @ X) @ Y4) => (((ord_less @ B) @ (F @ X)) @ (F @ Y4))))) => (((ord_less @ B) @ (F @ A2)) @ C)))))))))).
% 3.37/1.86 thf(fact_98_order__less__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F:(B > A),B3:B,C:B]: (((((ord_less @ A) @ A2) @ (F @ B3)) => ((((ord_less @ B) @ B3) @ C) => ((! [X:B,Y4:B]: (((((ord_less @ B) @ X) @ Y4) => (((ord_less @ A) @ (F @ X)) @ (F @ Y4))))) => (((ord_less @ A) @ A2) @ (F @ C))))))))))).
% 3.37/1.86 thf(fact_99_order__less__subst2, axiom, (! [A:$tType,C3:$tType]: ((((order @ C3) & (order @ A)) => (! [A2:A,B3:A,F:(A > C3),C:C3]: (((((ord_less @ A) @ A2) @ B3) => ((((ord_less @ C3) @ (F @ B3)) @ C) => ((! [X:A,Y4:A]: (((((ord_less @ A) @ X) @ Y4) => (((ord_less @ C3) @ (F @ X)) @ (F @ Y4))))) => (((ord_less @ C3) @ (F @ A2)) @ C)))))))))).
% 3.37/1.86 thf(fact_100_lt__ex, axiom, (! [A:$tType]: (((no_bot @ A) => (! [X3:A]: ((? [Y4:A]: ((((ord_less @ A) @ Y4) @ X3))))))))).
% 3.37/1.86 thf(fact_101_gt__ex, axiom, (! [A:$tType]: (((no_top @ A) => (! [X3:A]: ((? [X_1:A]: ((((ord_less @ A) @ X3) @ X_1))))))))).
% 3.37/1.86 thf(fact_102_neqE, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y:A]: (((X3 != Y) => ((~ ((((ord_less @ A) @ X3) @ Y))) => (((ord_less @ A) @ Y) @ X3))))))))).
% 3.37/1.86 thf(fact_103_neq__iff, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y:A]: (((X3 != Y) = ((((ord_less @ A) @ X3) @ Y) | (((ord_less @ A) @ Y) @ X3))))))))).
% 3.37/1.86 thf(fact_104_order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B3:A]: (((((ord_less @ A) @ A2) @ B3) => (~ ((((ord_less @ A) @ B3) @ A2)))))))))).
% 3.37/1.86 thf(fact_105_dense, axiom, (! [A:$tType]: (((dense_order @ A) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) => (? [Z2:A]: (((((ord_less @ A) @ X3) @ Z2) & (((ord_less @ A) @ Z2) @ Y))))))))))).
% 3.37/1.86 thf(fact_106_less__imp__neq, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) => (X3 != Y)))))))).
% 3.37/1.86 thf(fact_107_less__asym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) => (~ ((((ord_less @ A) @ Y) @ X3)))))))))).
% 3.37/1.86 thf(fact_108_less__asym_H, axiom, (! [A:$tType]: (((preorder @ A) => (! [A2:A,B3:A]: (((((ord_less @ A) @ A2) @ B3) => (~ ((((ord_less @ A) @ B3) @ A2)))))))))).
% 3.37/1.86 thf(fact_109_less__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y:A,Z3:A]: (((((ord_less @ A) @ X3) @ Y) => ((((ord_less @ A) @ Y) @ Z3) => (((ord_less @ A) @ X3) @ Z3))))))))).
% 3.37/1.86 thf(fact_110_less__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) | ((X3 = Y) | (((ord_less @ A) @ Y) @ X3))))))))).
% 3.37/1.86 thf(fact_111_less__irrefl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A]: ((~ ((((ord_less @ A) @ X3) @ X3))))))))).
% 3.37/1.86 thf(fact_112_ord__eq__less__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B3:A,C:A]: (((A2 = B3) => ((((ord_less @ A) @ B3) @ C) => (((ord_less @ A) @ A2) @ C))))))))).
% 3.37/1.86 thf(fact_113_ord__less__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B3:A,C:A]: (((((ord_less @ A) @ A2) @ B3) => ((B3 = C) => (((ord_less @ A) @ A2) @ C))))))))).
% 3.37/1.86 thf(fact_114_dual__order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A2:A]: (((((ord_less @ A) @ B3) @ A2) => (~ ((((ord_less @ A) @ A2) @ B3)))))))))).
% 3.37/1.86 thf(fact_115_less__imp__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) => (X3 != Y)))))))).
% 3.37/1.86 thf(fact_116_less__not__sym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) => (~ ((((ord_less @ A) @ Y) @ X3)))))))))).
% 3.37/1.86 thf(fact_117_less__induct, axiom, (! [A:$tType]: (((wellorder @ A) => (! [P:(A > $o),A2:A]: (((! [X:A]: (((! [Y5:A]: (((((ord_less @ A) @ Y5) @ X) => (P @ Y5)))) => (P @ X)))) => (P @ A2)))))))).
% 3.37/1.86 thf(fact_118_antisym__conv3, axiom, (! [A:$tType]: (((linorder @ A) => (! [Y:A,X3:A]: (((~ ((((ord_less @ A) @ Y) @ X3))) => ((~ ((((ord_less @ A) @ X3) @ Y))) = (X3 = Y))))))))).
% 3.37/1.86 thf(fact_119_less__imp__not__eq2, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) => (Y != X3)))))))).
% 3.37/1.86 thf(fact_120_less__imp__triv, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y:A,P:$o]: (((((ord_less @ A) @ X3) @ Y) => ((((ord_less @ A) @ Y) @ X3) => P)))))))).
% 3.37/1.86 thf(fact_121_linorder__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y:A]: (((~ ((((ord_less @ A) @ X3) @ Y))) => ((X3 != Y) => (((ord_less @ A) @ Y) @ X3))))))))).
% 3.37/1.86 thf(fact_122_dual__order_Oirrefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((~ ((((ord_less @ A) @ A2) @ A2))))))))).
% 3.37/1.86 thf(fact_123_order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B3:A,C:A]: (((((ord_less @ A) @ A2) @ B3) => ((((ord_less @ A) @ B3) @ C) => (((ord_less @ A) @ A2) @ C))))))))).
% 3.37/1.86 thf(fact_124_less__imp__not__less, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y:A]: (((((ord_less @ A) @ X3) @ Y) => (~ ((((ord_less @ A) @ Y) @ X3)))))))))).
% 3.37/1.86 thf(fact_125_exists__least__iff, axiom, (! [A:$tType]: (((wellorder @ A) => ((^ [P2:(A > $o)]: ((? [X5:A]: ((P2 @ X5))))) = (^ [P3:(A > $o)]: ((? [N3:A]: (((P3 @ N3) & (! [M2:A]: (((((ord_less @ A) @ M2) @ N3) => (~ ((P3 @ M2)))))))))))))))).
% 3.37/1.86 thf(fact_126_linorder__less__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A2:A,B3:A]: (((! [A6:A,B6:A]: (((((ord_less @ A) @ A6) @ B6) => ((P @ A6) @ B6)))) => ((! [A6:A]: (((P @ A6) @ A6))) => ((! [A6:A,B6:A]: ((((P @ B6) @ A6) => ((P @ A6) @ B6)))) => ((P @ A2) @ B3)))))))))).
% 3.37/1.86 thf(fact_127_dual__order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A2:A,C:A]: (((((ord_less @ A) @ B3) @ A2) => ((((ord_less @ A) @ C) @ B3) => (((ord_less @ A) @ C) @ A2))))))))).
% 3.37/1.86 thf(fact_128_not__less__iff__gr__or__eq, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y:A]: (((~ ((((ord_less @ A) @ X3) @ Y))) = ((((ord_less @ A) @ Y) @ X3) | (X3 = Y))))))))).
% 3.37/1.86 thf(fact_129_order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B3:A]: (((((ord_less @ A) @ A2) @ B3) => (A2 != B3)))))))).
% 3.37/1.86 thf(fact_130_dual__order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A2:A]: (((((ord_less @ A) @ B3) @ A2) => (A2 != B3)))))))).
% 3.37/1.86 thf(fact_131_bot__fun__def, axiom, (! [B:$tType,A:$tType]: (((bot @ B) => ((bot_bot @ (A > B)) = (^ [X4:A]: ((bot_bot @ B)))))))).
% 3.37/1.86 thf(fact_132_mk__scheme_Osimps_I1_J, axiom, (! [N2:nat]: (((type_M540877363scheme @ (type_Mirabelle_TVar @ N2)) = (type_M91906176e_FVar @ N2))))).
% 3.37/1.86 thf(fact_133_is__singletonE, axiom, (! [A:$tType,A3:(set @ A)]: ((((is_singleton @ A) @ A3) => (~ ((! [X:A]: ((A3 != (((insert2 @ A) @ X) @ (bot_bot @ (set @ A)))))))))))).
% 3.37/1.86 thf(fact_134_is__singleton__def, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A5:(set @ A)]: ((? [X4:A]: ((A5 = (((insert2 @ A) @ X4) @ (bot_bot @ (set @ A)))))))))))).
% 3.37/1.86 thf(fact_135_free__tv__id__subst, axiom, (((type_M950795831ree_tv @ (nat > type_Mirabelle_typ)) @ type_M17369686_subst) = (bot_bot @ (set @ nat)))).
% 3.37/1.86 thf(fact_136_Set_Ois__empty__def, axiom, (! [A:$tType]: (((is_empty @ A) = (^ [A5:(set @ A)]: ((A5 = (bot_bot @ (set @ A))))))))).
% 3.37/1.86 thf(fact_137_the__elem__def, axiom, (! [A:$tType]: (((the_elem @ A) = (^ [X6:(set @ A)]: (((the @ A) @ (^ [X4:A]: ((X6 = (((insert2 @ A) @ X4) @ (bot_bot @ (set @ A))))))))))))).
% 3.37/1.86 thf(fact_138_mk__scheme_Osimps_I2_J, axiom, (! [T1:type_Mirabelle_typ,T2:type_Mirabelle_typ]: (((type_M540877363scheme @ ((type_Mirabelle_Fun @ T1) @ T2)) = ((type_M1518733067e_SFun @ (type_M540877363scheme @ T1)) @ (type_M540877363scheme @ T2)))))).
% 3.37/1.86 thf(fact_139_Type__Mirabelle__sfxnzmapfi_Odom__def, axiom, (type_Mirabelle_dom = (^ [S4:(nat > type_Mirabelle_typ)]: (((collect @ nat) @ (^ [N3:nat]: (((S4 @ N3) != (type_Mirabelle_TVar @ N3))))))))).
% 3.37/1.86 thf(fact_140_id__subst__def, axiom, (type_M17369686_subst = type_Mirabelle_TVar)).
% 3.37/1.86 thf(fact_141_typ_Oinject_I2_J, axiom, (! [X21:type_Mirabelle_typ,X222:type_Mirabelle_typ,Y21:type_Mirabelle_typ,Y22:type_Mirabelle_typ]: (((((type_Mirabelle_Fun @ X21) @ X222) = ((type_Mirabelle_Fun @ Y21) @ Y22)) = ((X21 = Y21) & (X222 = Y22)))))).
% 3.37/1.86 thf(fact_142_new__tv__Fun, axiom, (! [N2:nat,T1:type_Mirabelle_typ,T2:type_Mirabelle_typ]: (((((type_M1046766514new_tv @ type_Mirabelle_typ) @ N2) @ ((type_Mirabelle_Fun @ T1) @ T2)) = ((((type_M1046766514new_tv @ type_Mirabelle_typ) @ N2) @ T1) & (((type_M1046766514new_tv @ type_Mirabelle_typ) @ N2) @ T2)))))).
% 3.37/1.86 thf(fact_143_dom__id__subst, axiom, ((type_Mirabelle_dom @ type_M17369686_subst) = (bot_bot @ (set @ nat)))).
% 3.37/1.86 thf(fact_144_psubsetD, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A),C:A]: (((((ord_less @ (set @ A)) @ A3) @ B2) => ((((member @ A) @ C) @ A3) => (((member @ A) @ C) @ B2)))))).
% 3.37/1.86 thf(fact_145_less__set__def, axiom, (! [A:$tType]: (((ord_less @ (set @ A)) = (^ [A5:(set @ A),B5:(set @ A)]: ((((ord_less @ (A > $o)) @ (^ [X4:A]: ((((member @ A) @ X4) @ A5)))) @ (^ [X4:A]: ((((member @ A) @ X4) @ B5)))))))))).
% 3.37/1.86 thf(fact_146_psubset__trans, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A),C4:(set @ A)]: (((((ord_less @ (set @ A)) @ A3) @ B2) => ((((ord_less @ (set @ A)) @ B2) @ C4) => (((ord_less @ (set @ A)) @ A3) @ C4)))))).
% 3.37/1.86 thf(fact_147_new__tv__id__subst, axiom, (! [N2:nat]: ((((type_M1046766514new_tv @ (nat > type_Mirabelle_typ)) @ N2) @ type_M17369686_subst)))).
% 3.37/1.86 thf(fact_148_app__subst__Fun, axiom, (! [S:(nat > type_Mirabelle_typ),T1:type_Mirabelle_typ,T2:type_Mirabelle_typ]: (((((type_M353778473_subst @ type_Mirabelle_typ) @ S) @ ((type_Mirabelle_Fun @ T1) @ T2)) = ((type_Mirabelle_Fun @ (((type_M353778473_subst @ type_Mirabelle_typ) @ S) @ T1)) @ (((type_M353778473_subst @ type_Mirabelle_typ) @ S) @ T2)))))).
% 3.37/1.86 thf(fact_149_typ_Oexhaust, axiom, (! [Y:type_Mirabelle_typ]: (((! [X13:nat]: ((Y != (type_Mirabelle_TVar @ X13)))) => (~ ((! [X212:type_Mirabelle_typ,X223:type_Mirabelle_typ]: ((Y != ((type_Mirabelle_Fun @ X212) @ X223)))))))))).
% 3.37/1.86 thf(fact_150_typ_Oinduct, axiom, (! [P:(type_Mirabelle_typ > $o),Typ:type_Mirabelle_typ]: (((! [X:nat]: ((P @ (type_Mirabelle_TVar @ X)))) => ((! [X1a:type_Mirabelle_typ,X23:type_Mirabelle_typ]: (((P @ X1a) => ((P @ X23) => (P @ ((type_Mirabelle_Fun @ X1a) @ X23)))))) => (P @ Typ)))))).
% 3.37/1.86 thf(fact_151_typ_Odistinct_I1_J, axiom, (! [X1:nat,X21:type_Mirabelle_typ,X222:type_Mirabelle_typ]: (((type_Mirabelle_TVar @ X1) != ((type_Mirabelle_Fun @ X21) @ X222))))).
% 3.37/1.86 thf(fact_152_typ_Osimps_I6_J, axiom, (! [A:$tType,F1:(nat > A),F2:(type_Mirabelle_typ > (type_Mirabelle_typ > A)),X21:type_Mirabelle_typ,X222:type_Mirabelle_typ]: ((((((type_M1695911984se_typ @ A) @ F1) @ F2) @ ((type_Mirabelle_Fun @ X21) @ X222)) = ((F2 @ X21) @ X222))))).
% 3.37/1.86 thf(fact_153_the__sym__eq__trivial, axiom, (! [A:$tType,X3:A]: ((((the @ A) @ ((^ [Y3:A,Z:A]: ((Y3 = Z))) @ X3)) = X3)))).
% 3.37/1.86 thf(fact_154_the__eq__trivial, axiom, (! [A:$tType,A2:A]: ((((the @ A) @ (^ [X4:A]: ((X4 = A2)))) = A2)))).
% 3.37/1.86 thf(fact_155_the__equality, axiom, (! [A:$tType,P:(A > $o),A2:A]: (((P @ A2) => ((! [X:A]: (((P @ X) => (X = A2)))) => (((the @ A) @ P) = A2)))))).
% 3.37/1.86 thf(fact_156_cod__id__subst, axiom, ((type_Mirabelle_cod @ type_M17369686_subst) = (bot_bot @ (set @ nat)))).
% 3.37/1.86 thf(fact_157_theI, axiom, (! [A:$tType,P:(A > $o),A2:A]: (((P @ A2) => ((! [X:A]: (((P @ X) => (X = A2)))) => (P @ ((the @ A) @ P))))))).
% 3.37/1.86 thf(fact_158_theI_H, axiom, (! [A:$tType,P:(A > $o)]: (((? [X7:A]: (((P @ X7) & (! [Y4:A]: (((P @ Y4) => (Y4 = X7))))))) => (P @ ((the @ A) @ P)))))).
% 3.37/1.86 thf(fact_159_theI2, axiom, (! [A:$tType,P:(A > $o),A2:A,Q:(A > $o)]: (((P @ A2) => ((! [X:A]: (((P @ X) => (X = A2)))) => ((! [X:A]: (((P @ X) => (Q @ X)))) => (Q @ ((the @ A) @ P)))))))).
% 3.37/1.86 thf(fact_160_If__def, axiom, (! [A:$tType]: (((if @ A) = (^ [P3:$o,X4:A,Y6:A]: (((the @ A) @ (^ [Z4:A]: (((P3 => (Z4 = X4)) & ((~ (P3)) => (Z4 = Y6)))))))))))).
% 3.37/1.86 thf(fact_161_the1I2, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((? [X7:A]: (((P @ X7) & (! [Y4:A]: (((P @ Y4) => (Y4 = X7))))))) => ((! [X:A]: (((P @ X) => (Q @ X)))) => (Q @ ((the @ A) @ P))))))).
% 3.37/1.86 thf(fact_162_the1__equality, axiom, (! [A:$tType,P:(A > $o),A2:A]: (((? [X7:A]: (((P @ X7) & (! [Y4:A]: (((P @ Y4) => (Y4 = X7))))))) => ((P @ A2) => (((the @ A) @ P) = A2)))))).
% 3.37/1.86 thf(fact_163_Collect__empty__eq__bot, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (P = (bot_bot @ (A > $o))))))).
% 3.37/1.86 thf(fact_164_bot__empty__eq, axiom, (! [A:$tType]: (((bot_bot @ (A > $o)) = (^ [X4:A]: ((((member @ A) @ X4) @ (bot_bot @ (set @ A))))))))).
% 3.37/1.86 thf(fact_165_free__tv__subst, axiom, ((type_M950795831ree_tv @ (nat > type_Mirabelle_typ)) = (^ [S4:(nat > type_Mirabelle_typ)]: ((((sup_sup @ (set @ nat)) @ (type_Mirabelle_dom @ S4)) @ (type_Mirabelle_cod @ S4)))))).
% 3.37/1.86 thf(fact_166_UnCI, axiom, (! [A:$tType,C:A,B2:(set @ A),A3:(set @ A)]: ((((~ ((((member @ A) @ C) @ B2))) => (((member @ A) @ C) @ A3)) => (((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A3) @ B2)))))).
% 3.37/1.86 thf(fact_167_Un__iff, axiom, (! [A:$tType,C:A,A3:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A3) @ B2)) = ((((member @ A) @ C) @ A3) | (((member @ A) @ C) @ B2)))))).
% 3.37/1.86 thf(fact_168_Un__empty, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A)]: ((((((sup_sup @ (set @ A)) @ A3) @ B2) = (bot_bot @ (set @ A))) = ((A3 = (bot_bot @ (set @ A))) & (B2 = (bot_bot @ (set @ A)))))))).
% 3.37/1.86 thf(fact_169_Un__insert__left, axiom, (! [A:$tType,A2:A,B2:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((insert2 @ A) @ A2) @ B2)) @ C4) = (((insert2 @ A) @ A2) @ (((sup_sup @ (set @ A)) @ B2) @ C4)))))).
% 3.37/1.86 thf(fact_170_Un__insert__right, axiom, (! [A:$tType,A3:(set @ A),A2:A,B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (((insert2 @ A) @ A2) @ B2)) = (((insert2 @ A) @ A2) @ (((sup_sup @ (set @ A)) @ A3) @ B2)))))).
% 3.37/1.86 thf(fact_171_weaken__asm__Un, axiom, (! [A:$tType,A3:(set @ A),P:(A > $o),Q:$o,B2:(set @ A)]: ((((! [X7:A]: (((((member @ A) @ X7) @ A3) => (P @ X7)))) => Q) => ((! [X:A]: (((((member @ A) @ X) @ (((sup_sup @ (set @ A)) @ A3) @ B2)) => (P @ X)))) => Q))))).
% 3.37/1.86 thf(fact_172_UnE, axiom, (! [A:$tType,C:A,A3:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A3) @ B2)) => ((~ ((((member @ A) @ C) @ A3))) => (((member @ A) @ C) @ B2)))))).
% 3.37/1.86 thf(fact_173_UnI1, axiom, (! [A:$tType,C:A,A3:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ A3) => (((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A3) @ B2)))))).
% 3.37/1.86 thf(fact_174_UnI2, axiom, (! [A:$tType,C:A,B2:(set @ A),A3:(set @ A)]: (((((member @ A) @ C) @ B2) => (((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A3) @ B2)))))).
% 3.37/1.86 thf(fact_175_Un__def, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A5:(set @ A),B5:(set @ A)]: (((collect @ A) @ (^ [X4:A]: (((((member @ A) @ X4) @ A5) | (((member @ A) @ X4) @ B5))))))))))).
% 3.37/1.86 thf(fact_176_bex__Un, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ (((sup_sup @ (set @ A)) @ A3) @ B2)) & (P @ X4)))) = ((? [X4:A]: (((((member @ A) @ X4) @ A3) & (P @ X4)))) | (? [X4:A]: (((((member @ A) @ X4) @ B2) & (P @ X4))))))))).
% 3.37/1.86 thf(fact_177_ball__Un, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A),P:(A > $o)]: (((! [X4:A]: (((((member @ A) @ X4) @ (((sup_sup @ (set @ A)) @ A3) @ B2)) => (P @ X4)))) = ((! [X4:A]: (((((member @ A) @ X4) @ A3) => (P @ X4)))) & (! [X4:A]: (((((member @ A) @ X4) @ B2) => (P @ X4))))))))).
% 3.37/1.86 thf(fact_178_Un__assoc, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A3) @ B2)) @ C4) = (((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ B2) @ C4)))))).
% 3.37/1.86 thf(fact_179_Un__absorb, axiom, (! [A:$tType,A3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ A3) = A3)))).
% 3.37/1.86 thf(fact_180_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A5:(set @ A),B5:(set @ A)]: ((((sup_sup @ (set @ A)) @ B5) @ A5))))))).
% 3.37/1.86 thf(fact_181_Un__left__absorb, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ A3) @ B2)) = (((sup_sup @ (set @ A)) @ A3) @ B2))))).
% 3.37/1.86 thf(fact_182_Collect__disj__eq, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: ((((collect @ A) @ (^ [X4:A]: (((P @ X4) | (Q @ X4))))) = (((sup_sup @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 3.37/1.86 thf(fact_183_Un__left__commute, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (((sup_sup @ (set @ A)) @ B2) @ C4)) = (((sup_sup @ (set @ A)) @ B2) @ (((sup_sup @ (set @ A)) @ A3) @ C4)))))).
% 3.37/1.86 thf(fact_184_insert__def, axiom, (! [A:$tType]: (((insert2 @ A) = (^ [A4:A]: (((sup_sup @ (set @ A)) @ ((collect @ A) @ (^ [X4:A]: ((X4 = A4))))))))))).
% 3.37/1.86 thf(fact_185_Un__empty__left, axiom, (! [A:$tType,B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ (bot_bot @ (set @ A))) @ B2) = B2)))).
% 3.37/1.86 thf(fact_186_Un__empty__right, axiom, (! [A:$tType,A3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A3) @ (bot_bot @ (set @ A))) = A3)))).
% 3.37/1.86 thf(fact_187_singleton__Un__iff, axiom, (! [A:$tType,X3:A,A3:(set @ A),B2:(set @ A)]: ((((((insert2 @ A) @ X3) @ (bot_bot @ (set @ A))) = (((sup_sup @ (set @ A)) @ A3) @ B2)) = (((A3 = (bot_bot @ (set @ A))) & (B2 = (((insert2 @ A) @ X3) @ (bot_bot @ (set @ A))))) | (((A3 = (((insert2 @ A) @ X3) @ (bot_bot @ (set @ A)))) & (B2 = (bot_bot @ (set @ A)))) | ((A3 = (((insert2 @ A) @ X3) @ (bot_bot @ (set @ A)))) & (B2 = (((insert2 @ A) @ X3) @ (bot_bot @ (set @ A))))))))))).
% 3.37/1.86 thf(fact_188_Un__singleton__iff, axiom, (! [A:$tType,A3:(set @ A),B2:(set @ A),X3:A]: ((((((sup_sup @ (set @ A)) @ A3) @ B2) = (((insert2 @ A) @ X3) @ (bot_bot @ (set @ A)))) = (((A3 = (bot_bot @ (set @ A))) & (B2 = (((insert2 @ A) @ X3) @ (bot_bot @ (set @ A))))) | (((A3 = (((insert2 @ A) @ X3) @ (bot_bot @ (set @ A)))) & (B2 = (bot_bot @ (set @ A)))) | ((A3 = (((insert2 @ A) @ X3) @ (bot_bot @ (set @ A)))) & (B2 = (((insert2 @ A) @ X3) @ (bot_bot @ (set @ A))))))))))).
% 3.37/1.86 thf(fact_189_insert__is__Un, axiom, (! [A:$tType]: (((insert2 @ A) = (^ [A4:A]: (((sup_sup @ (set @ A)) @ (((insert2 @ A) @ A4) @ (bot_bot @ (set @ A)))))))))).
% 3.37/1.86 thf(fact_190_bound__tv__list_Osimps_I2_J, axiom, (! [A:$tType]: (((type_M1470978233struct @ A) => (! [X3:A,L:(list @ A)]: ((((type_M779184887und_tv @ (list @ A)) @ (((cons @ A) @ X3) @ L)) = (((sup_sup @ (set @ nat)) @ ((type_M779184887und_tv @ A) @ X3)) @ ((type_M779184887und_tv @ (list @ A)) @ L))))))))).
% 3.37/1.86 thf(fact_191_free__tv__Fun, axiom, (! [T1:type_Mirabelle_typ,T2:type_Mirabelle_typ]: ((((type_M950795831ree_tv @ type_Mirabelle_typ) @ ((type_Mirabelle_Fun @ T1) @ T2)) = (((sup_sup @ (set @ nat)) @ ((type_M950795831ree_tv @ type_Mirabelle_typ) @ T1)) @ ((type_M950795831ree_tv @ type_Mirabelle_typ) @ T2)))))).
% 3.37/1.86 thf(fact_192_free__tv__type__scheme_Osimps_I3_J, axiom, (! [S1:type_M1610475166scheme,S2:type_M1610475166scheme]: ((((type_M950795831ree_tv @ type_M1610475166scheme) @ ((type_M1518733067e_SFun @ S1) @ S2)) = (((sup_sup @ (set @ nat)) @ ((type_M950795831ree_tv @ type_M1610475166scheme) @ S1)) @ ((type_M950795831ree_tv @ type_M1610475166scheme) @ S2)))))).
% 3.37/1.86 thf(fact_193_bound__tv__type__scheme_Osimps_I3_J, axiom, (! [S1:type_M1610475166scheme,S2:type_M1610475166scheme]: ((((type_M779184887und_tv @ type_M1610475166scheme) @ ((type_M1518733067e_SFun @ S1) @ S2)) = (((sup_sup @ (set @ nat)) @ ((type_M779184887und_tv @ type_M1610475166scheme) @ S1)) @ ((type_M779184887und_tv @ type_M1610475166scheme) @ S2)))))).
% 3.37/1.86 thf(fact_194_free__tv__list_Osimps_I2_J, axiom, (! [A:$tType]: (((type_M1470978233struct @ A) => (! [X3:A,L:(list @ A)]: ((((type_M950795831ree_tv @ (list @ A)) @ (((cons @ A) @ X3) @ L)) = (((sup_sup @ (set @ nat)) @ ((type_M950795831ree_tv @ A) @ X3)) @ ((type_M950795831ree_tv @ (list @ A)) @ L))))))))).
% 3.37/1.86 thf(fact_195_free__tv__fun__def, axiom, (! [B:$tType,A:$tType]: ((((type_M201404320of_nat @ A) & (type_M1535146424typ_of @ B)) => ((type_M950795831ree_tv @ (A > B)) = (^ [F4:(A > B)]: ((((sup_sup @ (set @ nat)) @ (type_Mirabelle_dom @ (^ [N3:nat]: (((type_M604437996typ_of @ B) @ (F4 @ ((type_M167561660of_nat @ A) @ N3))))))) @ (type_Mirabelle_cod @ (^ [N3:nat]: (((type_M604437996typ_of @ B) @ (F4 @ ((type_M167561660of_nat @ A) @ N3)))))))))))))).
% 3.37/1.86 thf(fact_196_sup__bot__left, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X3:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ X3) = X3))))))).
% 3.37/1.86 thf(fact_197_sup__bot__right, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X3:A]: (((((sup_sup @ A) @ X3) @ (bot_bot @ A)) = X3))))))).
% 3.37/1.86 thf(fact_198_sup__bot_Oright__neutral, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A2:A]: (((((sup_sup @ A) @ A2) @ (bot_bot @ A)) = A2))))))).
% 3.37/1.86 thf(fact_199_sup__bot_Oneutr__eq__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A2:A,B3:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ A2) @ B3)) = ((A2 = (bot_bot @ A)) & (B3 = (bot_bot @ A)))))))))).
% 3.37/1.86 thf(fact_200_sup__bot_Oleft__neutral, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A2:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ A2) = A2))))))).
% 3.37/1.86 thf(fact_201_sup__bot_Oeq__neutr__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A2:A,B3:A]: ((((((sup_sup @ A) @ A2) @ B3) = (bot_bot @ A)) = ((A2 = (bot_bot @ A)) & (B3 = (bot_bot @ A)))))))))).
% 3.37/1.86 thf(fact_202_sup__eq__bot__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X3:A,Y:A]: ((((((sup_sup @ A) @ X3) @ Y) = (bot_bot @ A)) = ((X3 = (bot_bot @ A)) & (Y = (bot_bot @ A)))))))))).
% 3.37/1.86 thf(fact_203_bot__eq__sup__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X3:A,Y:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ X3) @ Y)) = ((X3 = (bot_bot @ A)) & (Y = (bot_bot @ A)))))))))).
% 3.37/1.86 thf(fact_204_sup__Un__eq, axiom, (! [A:$tType,R:(set @ A),S:(set @ A)]: (((((sup_sup @ (A > $o)) @ (^ [X4:A]: ((((member @ A) @ X4) @ R)))) @ (^ [X4:A]: ((((member @ A) @ X4) @ S)))) = (^ [X4:A]: ((((member @ A) @ X4) @ (((sup_sup @ (set @ A)) @ R) @ S)))))))).
% 3.37/1.86 thf(fact_205_sup__set__def, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A5:(set @ A),B5:(set @ A)]: (((collect @ A) @ (((sup_sup @ (A > $o)) @ (^ [X4:A]: ((((member @ A) @ X4) @ A5)))) @ (^ [X4:A]: ((((member @ A) @ X4) @ B5))))))))))).
% 3.37/1.86 thf(fact_206_less__supI1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X3:A,A2:A,B3:A]: (((((ord_less @ A) @ X3) @ A2) => (((ord_less @ A) @ X3) @ (((sup_sup @ A) @ A2) @ B3))))))))).
% 3.37/1.86 thf(fact_207_less__supI2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [X3:A,B3:A,A2:A]: (((((ord_less @ A) @ X3) @ B3) => (((ord_less @ A) @ X3) @ (((sup_sup @ A) @ A2) @ B3))))))))).
% 3.37/1.86 thf(fact_208_sup_Ostrict__boundedE, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [B3:A,C:A,A2:A]: (((((ord_less @ A) @ (((sup_sup @ A) @ B3) @ C)) @ A2) => (~ (((((ord_less @ A) @ B3) @ A2) => (~ ((((ord_less @ A) @ C) @ A2))))))))))))).
% 3.37/1.86 thf(fact_209_sup_Ostrict__order__iff, axiom, (! [A:$tType]: (((semilattice_sup @ A) => ((ord_less @ A) = (^ [B7:A,A4:A]: (((A4 = (((sup_sup @ A) @ A4) @ B7)) & (A4 != B7))))))))).
% 3.37/1.86 thf(fact_210_sup_Ostrict__coboundedI1, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [C:A,A2:A,B3:A]: (((((ord_less @ A) @ C) @ A2) => (((ord_less @ A) @ C) @ (((sup_sup @ A) @ A2) @ B3))))))))).
% 3.37/1.86 thf(fact_211_sup_Ostrict__coboundedI2, axiom, (! [A:$tType]: (((semilattice_sup @ A) => (! [C:A,B3:A,A2:A]: (((((ord_less @ A) @ C) @ B3) => (((ord_less @ A) @ C) @ (((sup_sup @ A) @ A2) @ B3))))))))).
% 3.37/1.86 thf(fact_212_Nitpick_OThe__psimp, axiom, (! [A:$tType,P:(A > $o),X3:A]: (((P = ((^ [Y3:A,Z:A]: ((Y3 = Z))) @ X3)) => (((the @ A) @ P) = X3))))).
% 3.37/1.86 thf(fact_213_theI__unique, axiom, (! [A:$tType,P:(A > $o),X3:A]: (((? [X7:A]: (((P @ X7) & (! [Y4:A]: (((P @ Y4) => (Y4 = X7))))))) => ((P @ X3) = (X3 = ((the @ A) @ P))))))).
% 3.37/1.86 thf(fact_214_sup__bot_Osemilattice__neutr__axioms, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (((semilattice_neutr @ A) @ (sup_sup @ A)) @ (bot_bot @ A)))))).
% 3.37/1.86 thf(fact_215_lexordp__eq__simps_I4_J, axiom, (! [A:$tType]: (((ord @ A) => (! [X3:A,Xs:(list @ A),Y:A,Ys:(list @ A)]: (((((ord_lexordp_eq @ A) @ (((cons @ A) @ X3) @ Xs)) @ (((cons @ A) @ Y) @ Ys)) = ((((ord_less @ A) @ X3) @ Y) | ((~ ((((ord_less @ A) @ Y) @ X3))) & (((ord_lexordp_eq @ A) @ Xs) @ Ys)))))))))).
% 3.37/1.86 thf(fact_216_lexordp__eq_OCons__eq, axiom, (! [A:$tType]: (((ord @ A) => (! [X3:A,Y:A,Xs:(list @ A),Ys:(list @ A)]: (((~ ((((ord_less @ A) @ X3) @ Y))) => ((~ ((((ord_less @ A) @ Y) @ X3))) => ((((ord_lexordp_eq @ A) @ Xs) @ Ys) => (((ord_lexordp_eq @ A) @ (((cons @ A) @ X3) @ Xs)) @ (((cons @ A) @ Y) @ Ys))))))))))).
% 3.37/1.86 thf(fact_217_lexordp__eq_OCons, axiom, (! [A:$tType]: (((ord @ A) => (! [X3:A,Y:A,Xs:(list @ A),Ys:(list @ A)]: (((((ord_less @ A) @ X3) @ Y) => (((ord_lexordp_eq @ A) @ (((cons @ A) @ X3) @ Xs)) @ (((cons @ A) @ Y) @ Ys))))))))).
% 3.37/1.86 thf(fact_218_lexordp__eq__antisym, axiom, (! [A:$tType]: (((linorder @ A) => (! [Xs:(list @ A),Ys:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ Ys) => ((((ord_lexordp_eq @ A) @ Ys) @ Xs) => (Xs = Ys))))))))).
% 3.37/1.86 thf(fact_219_lexordp__eq__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [Xs:(list @ A),Ys:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ Ys) | (((ord_lexordp_eq @ A) @ Ys) @ Xs)))))))).
% 3.37/1.86 thf(fact_220_lexordp__eq__trans, axiom, (! [A:$tType]: (((linorder @ A) => (! [Xs:(list @ A),Ys:(list @ A),Zs:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ Ys) => ((((ord_lexordp_eq @ A) @ Ys) @ Zs) => (((ord_lexordp_eq @ A) @ Xs) @ Zs))))))))).
% 3.37/1.86 thf(fact_221_lexordp__eq__refl, axiom, (! [A:$tType]: (((ord @ A) => (! [Xs:(list @ A)]: ((((ord_lexordp_eq @ A) @ Xs) @ Xs))))))).
% 3.37/1.86 thf(fact_222_lexordp__eq_Ocases, axiom, (! [A:$tType]: (((ord @ A) => (! [A1:(list @ A),A22:(list @ A)]: (((((ord_lexordp_eq @ A) @ A1) @ A22) => ((A1 != (nil @ A)) => ((! [X:A]: (((? [Xs2:(list @ A)]: ((A1 = (((cons @ A) @ X) @ Xs2)))) => (! [Y4:A]: (((? [Ys2:(list @ A)]: ((A22 = (((cons @ A) @ Y4) @ Ys2)))) => (~ ((((ord_less @ A) @ X) @ Y4))))))))) => (~ ((! [X:A,Y4:A,Xs2:(list @ A)]: (((A1 = (((cons @ A) @ X) @ Xs2)) => (! [Ys2:(list @ A)]: (((A22 = (((cons @ A) @ Y4) @ Ys2)) => ((~ ((((ord_less @ A) @ X) @ Y4))) => ((~ ((((ord_less @ A) @ Y4) @ X))) => (~ ((((ord_lexordp_eq @ A) @ Xs2) @ Ys2)))))))))))))))))))))).
% 3.37/1.86 thf(fact_223_lexordp__eq_Osimps, axiom, (! [A:$tType]: (((ord @ A) => ((ord_lexordp_eq @ A) = (^ [A12:(list @ A),A23:(list @ A)]: (((? [Ys3:(list @ A)]: (((A12 = (nil @ A)) & (A23 = Ys3)))) | ((? [X4:A,Y6:A,Xs3:(list @ A),Ys3:(list @ A)]: (((A12 = (((cons @ A) @ X4) @ Xs3)) & ((A23 = (((cons @ A) @ Y6) @ Ys3)) & (((ord_less @ A) @ X4) @ Y6))))) | (? [X4:A,Y6:A,Xs3:(list @ A),Ys3:(list @ A)]: (((A12 = (((cons @ A) @ X4) @ Xs3)) & ((A23 = (((cons @ A) @ Y6) @ Ys3)) & ((~ ((((ord_less @ A) @ X4) @ Y6))) & ((~ ((((ord_less @ A) @ Y6) @ X4))) & (((ord_lexordp_eq @ A) @ Xs3) @ Ys3)))))))))))))))).
% 3.37/1.86 thf(fact_224_lexordp__eq__simps_I1_J, axiom, (! [A:$tType]: (((ord @ A) => (! [Ys:(list @ A)]: ((((ord_lexordp_eq @ A) @ (nil @ A)) @ Ys))))))).
% 3.37/1.86 thf(fact_225_lexordp__eq__simps_I2_J, axiom, (! [A:$tType]: (((ord @ A) => (! [Xs:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ (nil @ A)) = (Xs = (nil @ A))))))))).
% 3.37/1.86 thf(fact_226_app__subst__Nil, axiom, (! [A:$tType]: (((type_M1470978233struct @ A) => (! [S:(nat > type_Mirabelle_typ)]: (((((type_M353778473_subst @ (list @ A)) @ S) @ (nil @ A)) = (nil @ A)))))))).
% 3.37/1.86 thf(fact_227_lexordp__eq__simps_I3_J, axiom, (! [A:$tType]: (((ord @ A) => (! [X3:A,Xs:(list @ A)]: ((~ ((((ord_lexordp_eq @ A) @ (((cons @ A) @ X3) @ Xs)) @ (nil @ A)))))))))).
% 3.37/1.86 thf(fact_228_lexordp__eq_ONil, axiom, (! [A:$tType]: (((ord @ A) => (! [Ys:(list @ A)]: ((((ord_lexordp_eq @ A) @ (nil @ A)) @ Ys))))))).
% 3.37/1.86 thf(fact_229_new__tv__Nil, axiom, (! [A:$tType]: (((type_M1470978233struct @ A) => (! [N2:nat]: ((((type_M1046766514new_tv @ (list @ A)) @ N2) @ (nil @ A)))))))).
% 3.37/1.86 thf(fact_230_transpose_Ocases, axiom, (! [A:$tType,X3:(list @ (list @ A))]: (((X3 != (nil @ (list @ A))) => ((! [Xss:(list @ (list @ A))]: ((X3 != (((cons @ (list @ A)) @ (nil @ A)) @ Xss)))) => (~ ((! [X:A,Xs2:(list @ A),Xss:(list @ (list @ A))]: ((X3 != (((cons @ (list @ A)) @ (((cons @ A) @ X) @ Xs2)) @ Xss))))))))))).
% 3.37/1.86 thf(fact_231_list_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X222:(list @ A)]: (((nil @ A) != (((cons @ A) @ X21) @ X222))))).
% 3.37/1.86 thf(fact_232_list_OdiscI, axiom, (! [A:$tType,List:(list @ A),X21:A,X222:(list @ A)]: (((List = (((cons @ A) @ X21) @ X222)) => (List != (nil @ A)))))).
% 3.37/1.86 thf(fact_233_list_Oexhaust, axiom, (! [A:$tType,Y:(list @ A)]: (((Y != (nil @ A)) => (~ ((! [X212:A,X223:(list @ A)]: ((Y != (((cons @ A) @ X212) @ X223)))))))))).
% 3.37/1.86 thf(fact_234_list_Oinducts, axiom, (! [A:$tType,P:((list @ A) > $o),List:(list @ A)]: (((P @ (nil @ A)) => ((! [X13:A,X23:(list @ A)]: (((P @ X23) => (P @ (((cons @ A) @ X13) @ X23))))) => (P @ List)))))).
% 3.37/1.86 thf(fact_235_neq__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) = (? [Y6:A,Ys3:(list @ A)]: ((Xs = (((cons @ A) @ Y6) @ Ys3)))))))).
% 3.37/1.86 thf(fact_236_list__induct2_H, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),Xs:(list @ A),Ys:(list @ B)]: ((((P @ (nil @ A)) @ (nil @ B)) => ((! [X:A,Xs2:(list @ A)]: (((P @ (((cons @ A) @ X) @ Xs2)) @ (nil @ B)))) => ((! [Y4:B,Ys2:(list @ B)]: (((P @ (nil @ A)) @ (((cons @ B) @ Y4) @ Ys2)))) => ((! [X:A,Xs2:(list @ A),Y4:B,Ys2:(list @ B)]: ((((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ B) @ Y4) @ Ys2))))) => ((P @ Xs) @ Ys)))))))).
% 3.37/1.86 thf(fact_237_splice_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [X:A,Xs2:(list @ A),Ys2:(list @ A)]: ((((P @ Ys2) @ Xs2) => ((P @ (((cons @ A) @ X) @ Xs2)) @ Ys2)))) => ((P @ A0) @ A1)))))).
% 3.37/1.86 thf(fact_238_induct__list012, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X:A]: ((P @ (((cons @ A) @ X) @ (nil @ A))))) => ((! [X:A,Y4:A,Zs2:(list @ A)]: (((P @ Zs2) => ((P @ (((cons @ A) @ Y4) @ Zs2)) => (P @ (((cons @ A) @ X) @ (((cons @ A) @ Y4) @ Zs2))))))) => (P @ Xs))))))).
% 3.37/1.86 thf(fact_239_min__list_Ocases, axiom, (! [A:$tType]: (((ord @ A) => (! [X3:(list @ A)]: (((! [X:A,Xs2:(list @ A)]: ((X3 != (((cons @ A) @ X) @ Xs2)))) => (X3 = (nil @ A))))))))).
% 3.37/1.86 thf(fact_240_min__list_Oinduct, axiom, (! [A:$tType]: (((ord @ A) => (! [P:((list @ A) > $o),A0:(list @ A)]: (((! [X:A,Xs2:(list @ A)]: (((! [X213:A,X224:(list @ A)]: (((Xs2 = (((cons @ A) @ X213) @ X224)) => (P @ Xs2)))) => (P @ (((cons @ A) @ X) @ Xs2))))) => ((P @ (nil @ A)) => (P @ A0))))))))).
% 3.37/1.86 thf(fact_241_shuffles_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [Xs2:(list @ A)]: (((P @ Xs2) @ (nil @ A)))) => ((! [X:A,Xs2:(list @ A),Y4:A,Ys2:(list @ A)]: ((((P @ Xs2) @ (((cons @ A) @ Y4) @ Ys2)) => (((P @ (((cons @ A) @ X) @ Xs2)) @ Ys2) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ A) @ Y4) @ Ys2)))))) => ((P @ A0) @ A1))))))).
% 3.37/1.86 thf(fact_242_remdups__adj_Ocases, axiom, (! [A:$tType,X3:(list @ A)]: (((X3 != (nil @ A)) => ((! [X:A]: ((X3 != (((cons @ A) @ X) @ (nil @ A))))) => (~ ((! [X:A,Y4:A,Xs2:(list @ A)]: ((X3 != (((cons @ A) @ X) @ (((cons @ A) @ Y4) @ Xs2)))))))))))).
% 3.37/1.86 thf(fact_243_sorted__wrt_Oinduct, axiom, (! [A:$tType,P:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P4:(A > (A > $o))]: (((P @ P4) @ (nil @ A)))) => ((! [P4:(A > (A > $o)),X:A,Ys2:(list @ A)]: ((((P @ P4) @ Ys2) => ((P @ P4) @ (((cons @ A) @ X) @ Ys2))))) => ((P @ A0) @ A1)))))).
% 3.37/1.86 thf(fact_244_remdups__adj_Oinduct, axiom, (! [A:$tType,P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X:A]: ((P @ (((cons @ A) @ X) @ (nil @ A))))) => ((! [X:A,Y4:A,Xs2:(list @ A)]: ((((X = Y4) => (P @ (((cons @ A) @ X) @ Xs2))) => (((X != Y4) => (P @ (((cons @ A) @ Y4) @ Xs2))) => (P @ (((cons @ A) @ X) @ (((cons @ A) @ Y4) @ Xs2))))))) => (P @ A0))))))).
% 3.37/1.86 thf(fact_245_arg__min__list_Oinduct, axiom, (! [B:$tType,A:$tType]: (((linorder @ B) => (! [P:((A > B) > ((list @ A) > $o)),A0:(A > B),A1:(list @ A)]: (((! [F5:(A > B),X:A]: (((P @ F5) @ (((cons @ A) @ X) @ (nil @ A))))) => ((! [F5:(A > B),X:A,Y4:A,Zs2:(list @ A)]: ((((P @ F5) @ (((cons @ A) @ Y4) @ Zs2)) => ((P @ F5) @ (((cons @ A) @ X) @ (((cons @ A) @ Y4) @ Zs2)))))) => ((! [A6:(A > B)]: (((P @ A6) @ (nil @ A)))) => ((P @ A0) @ A1)))))))))).
% 3.37/1.86 thf(fact_246_successively_Oinduct, axiom, (! [A:$tType,P:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P4:(A > (A > $o))]: (((P @ P4) @ (nil @ A)))) => ((! [P4:(A > (A > $o)),X:A]: (((P @ P4) @ (((cons @ A) @ X) @ (nil @ A))))) => ((! [P4:(A > (A > $o)),X:A,Y4:A,Xs2:(list @ A)]: ((((P @ P4) @ (((cons @ A) @ Y4) @ Xs2)) => ((P @ P4) @ (((cons @ A) @ X) @ (((cons @ A) @ Y4) @ Xs2)))))) => ((P @ A0) @ A1))))))).
% 3.37/1.86 thf(fact_247_list__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X:A]: ((P @ (((cons @ A) @ X) @ (nil @ A))))) => ((! [X:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((cons @ A) @ X) @ Xs2)))))) => (P @ Xs))))))).
% 3.37/1.86 thf(fact_248_map__tailrec__rev_Oinduct, axiom, (! [A:$tType,B:$tType,P:((A > B) > ((list @ A) > ((list @ B) > $o))),A0:(A > B),A1:(list @ A),A22:(list @ B)]: (((! [F5:(A > B),X_1:(list @ B)]: ((((P @ F5) @ (nil @ A)) @ X_1))) => ((! [F5:(A > B),A6:A,As:(list @ A),Bs:(list @ B)]: (((((P @ F5) @ As) @ (((cons @ B) @ (F5 @ A6)) @ Bs)) => (((P @ F5) @ (((cons @ A) @ A6) @ As)) @ Bs)))) => (((P @ A0) @ A1) @ A22)))))).
% 3.37/1.86 thf(fact_249_strict__sorted_Ocases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:(list @ A)]: (((X3 != (nil @ A)) => (~ ((! [X:A,Ys2:(list @ A)]: ((X3 != (((cons @ A) @ X) @ Ys2))))))))))))).
% 3.37/1.86 thf(fact_250_strict__sorted_Oinduct, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X:A,Ys2:(list @ A)]: (((P @ Ys2) => (P @ (((cons @ A) @ X) @ Ys2))))) => (P @ A0))))))))).
% 3.37/1.86 thf(fact_251_free__tv__list_Osimps_I1_J, axiom, (! [A:$tType]: (((type_M1470978233struct @ A) => (((type_M950795831ree_tv @ (list @ A)) @ (nil @ A)) = (bot_bot @ (set @ nat))))))).
% 3.37/1.86 thf(fact_252_bound__tv__list_Osimps_I1_J, axiom, (! [A:$tType]: (((type_M1470978233struct @ A) => (((type_M779184887und_tv @ (list @ A)) @ (nil @ A)) = (bot_bot @ (set @ nat))))))).
% 3.37/1.86 thf(fact_253_lexordp__eq_Oinducts, axiom, (! [A:$tType]: (((ord @ A) => (! [X1:(list @ A),X2:(list @ A),P:((list @ A) > ((list @ A) > $o))]: (((((ord_lexordp_eq @ A) @ X1) @ X2) => ((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [X:A,Y4:A,Xs2:(list @ A),Ys2:(list @ A)]: (((((ord_less @ A) @ X) @ Y4) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ A) @ Y4) @ Ys2))))) => ((! [X:A,Y4:A,Xs2:(list @ A),Ys2:(list @ A)]: (((~ ((((ord_less @ A) @ X) @ Y4))) => ((~ ((((ord_less @ A) @ Y4) @ X))) => ((((ord_lexordp_eq @ A) @ Xs2) @ Ys2) => (((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ A) @ Y4) @ Ys2)))))))) => ((P @ X1) @ X2))))))))))).
% 3.37/1.86 thf(fact_254_insert__Nil, axiom, (! [A:$tType,X3:A]: (((((insert @ A) @ X3) @ (nil @ A)) = (((cons @ A) @ X3) @ (nil @ A)))))).
% 3.37/1.86 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, (bounded_lattice @ $o)).
% 3.37/1.86 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A7:$tType]: ((bounded_lattice @ (set @ A7))))).
% 3.37/1.86 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A7:$tType,A8:$tType]: (((bounded_lattice @ A8) => (bounded_lattice @ (A7 > A8)))))).
% 3.37/1.86 thf(tcon_fun___Type__Mirabelle__sfxnzmapfi_Otype__struct, axiom, (! [A7:$tType,A8:$tType]: ((((type_M201404320of_nat @ A7) & (type_M1535146424typ_of @ A8)) => (type_M1470978233struct @ (A7 > A8)))))).
% 3.37/1.86 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot, axiom, (! [A7:$tType,A8:$tType]: (((bounded_lattice @ A8) => (bounde1808546759up_bot @ (A7 > A8)))))).
% 3.37/1.86 thf(tcon_fun___Lattices_Osemilattice__sup, axiom, (! [A7:$tType,A8:$tType]: (((semilattice_sup @ A8) => (semilattice_sup @ (A7 > A8)))))).
% 3.37/1.86 thf(tcon_fun___Orderings_Oorder__bot, axiom, (! [A7:$tType,A8:$tType]: (((order_bot @ A8) => (order_bot @ (A7 > A8)))))).
% 3.37/1.86 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A7:$tType,A8:$tType]: (((preorder @ A8) => (preorder @ (A7 > A8)))))).
% 3.37/1.86 thf(tcon_fun___Orderings_Oorder, axiom, (! [A7:$tType,A8:$tType]: (((order @ A8) => (order @ (A7 > A8)))))).
% 3.37/1.86 thf(tcon_fun___Orderings_Oord, axiom, (! [A7:$tType,A8:$tType]: (((ord @ A8) => (ord @ (A7 > A8)))))).
% 3.37/1.86 thf(tcon_fun___Orderings_Obot, axiom, (! [A7:$tType,A8:$tType]: (((bot @ A8) => (bot @ (A7 > A8)))))).
% 3.37/1.86 thf(tcon_Nat_Onat___Type__Mirabelle__sfxnzmapfi_Oof__nat, axiom, (type_M201404320of_nat @ nat)).
% 3.37/1.86 thf(tcon_Nat_Onat___Lattices_Osemilattice__sup_3, axiom, (semilattice_sup @ nat)).
% 3.37/1.86 thf(tcon_Nat_Onat___Orderings_Owellorder, axiom, (wellorder @ nat)).
% 3.37/1.86 thf(tcon_Nat_Onat___Orderings_Oorder__bot_4, axiom, (order_bot @ nat)).
% 3.37/1.86 thf(tcon_Nat_Onat___Orderings_Opreorder_5, axiom, (preorder @ nat)).
% 3.37/1.86 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, (linorder @ nat)).
% 3.37/1.86 thf(tcon_Nat_Onat___Orderings_Ono__top, axiom, (no_top @ nat)).
% 3.37/1.86 thf(tcon_Nat_Onat___Orderings_Oorder_6, axiom, (order @ nat)).
% 3.37/1.86 thf(tcon_Nat_Onat___Orderings_Oord_7, axiom, (ord @ nat)).
% 3.37/1.86 thf(tcon_Nat_Onat___Orderings_Obot_8, axiom, (bot @ nat)).
% 3.37/1.86 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_9, axiom, (! [A7:$tType]: ((bounde1808546759up_bot @ (set @ A7))))).
% 3.37/1.86 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_10, axiom, (! [A7:$tType]: ((semilattice_sup @ (set @ A7))))).
% 3.37/1.86 thf(tcon_Set_Oset___Orderings_Oorder__bot_11, axiom, (! [A7:$tType]: ((order_bot @ (set @ A7))))).
% 3.37/1.86 thf(tcon_Set_Oset___Orderings_Opreorder_12, axiom, (! [A7:$tType]: ((preorder @ (set @ A7))))).
% 3.37/1.86 thf(tcon_Set_Oset___Orderings_Oorder_13, axiom, (! [A7:$tType]: ((order @ (set @ A7))))).
% 3.37/1.86 thf(tcon_Set_Oset___Orderings_Oord_14, axiom, (! [A7:$tType]: ((ord @ (set @ A7))))).
% 3.37/1.86 thf(tcon_Set_Oset___Orderings_Obot_15, axiom, (! [A7:$tType]: ((bot @ (set @ A7))))).
% 3.37/1.86 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_16, axiom, (bounde1808546759up_bot @ $o)).
% 3.37/1.86 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_17, axiom, (semilattice_sup @ $o)).
% 3.37/1.86 thf(tcon_HOL_Obool___Orderings_Oorder__bot_18, axiom, (order_bot @ $o)).
% 3.37/1.86 thf(tcon_HOL_Obool___Orderings_Opreorder_19, axiom, (preorder @ $o)).
% 3.37/1.86 thf(tcon_HOL_Obool___Orderings_Olinorder_20, axiom, (linorder @ $o)).
% 3.37/1.86 thf(tcon_HOL_Obool___Orderings_Oorder_21, axiom, (order @ $o)).
% 3.37/1.86 thf(tcon_HOL_Obool___Orderings_Oord_22, axiom, (ord @ $o)).
% 3.37/1.86 thf(tcon_HOL_Obool___Orderings_Obot_23, axiom, (bot @ $o)).
% 3.37/1.86 thf(tcon_List_Olist___Type__Mirabelle__sfxnzmapfi_Otype__struct_24, axiom, (! [A7:$tType]: (((type_M1470978233struct @ A7) => (type_M1470978233struct @ (list @ A7)))))).
% 3.37/1.86 thf(tcon_Type__Mirabelle__sfxnzmapfi_Otyp___Type__Mirabelle__sfxnzmapfi_Otype__struct_25, axiom, (type_M1470978233struct @ type_Mirabelle_typ)).
% 3.37/1.86 thf(tcon_Type__Mirabelle__sfxnzmapfi_Otyp___Type__Mirabelle__sfxnzmapfi_Otyp__of, axiom, (type_M1535146424typ_of @ type_Mirabelle_typ)).
% 3.37/1.86 thf(tcon_Type__Mirabelle__sfxnzmapfi_Otype__scheme___Type__Mirabelle__sfxnzmapfi_Otype__struct_26, axiom, (type_M1470978233struct @ type_M1610475166scheme)).
% 3.37/1.86 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 3.37/1.86 thf(help_If_2_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $false) @ X3) @ Y) = Y)))).
% 3.37/1.86 thf(help_If_1_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $true) @ X3) @ Y) = X3)))).
% 3.37/1.86 thf(conj_0, conjecture, (((((type_M353778473_subst @ type_M1610475166scheme) @ s1) @ (type_M91906176e_FVar @ x)) != (((type_M353778473_subst @ type_M1610475166scheme) @ s2) @ (type_M91906176e_FVar @ x))) | ((~ ((((member @ nat) @ n) @ ((type_M950795831ree_tv @ type_M1610475166scheme) @ (type_M91906176e_FVar @ x))))) | ((s1 @ n) = (s2 @ n))))).
% 3.37/1.86 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.98HAT0fbB4/DTF2DTF4446.p
% 3.37/1.86 ------------------------
% 3.49/1.90 ---- Cleaned THF ---
% 3.49/1.90 thf(ty_t_Type__Mirabelle__sfxnzmapfi_Otype__scheme,type,
% 3.49/1.90 type_M1610475166scheme: $tType ).
% 3.49/1.90
% 3.49/1.90 thf(ty_t_Type__Mirabelle__sfxnzmapfi_Otyp,type,
% 3.49/1.90 type_Mirabelle_typ: $tType ).
% 3.49/1.90
% 3.49/1.90 thf(ty_t_List_Olist,type,
% 3.49/1.90 list: $tType > $tType ).
% 3.49/1.90
% 3.49/1.90 thf(ty_t_Set_Oset,type,
% 3.49/1.90 set: $tType > $tType ).
% 3.49/1.90
% 3.49/1.90 thf(ty_t_Nat_Onat,type,
% 3.49/1.90 nat: $tType ).
% 3.49/1.90
% 3.49/1.90 thf(sy_cl_Lattices_Obounded__lattice,type,
% 3.49/1.90 bounded_lattice:
% 3.49/1.90 !>[A: $tType] : $o ).
% 3.49/1.90
% 3.49/1.90 thf(sy_cl_HOL_Otype,type,
% 3.49/1.90 type:
% 3.49/1.90 !>[A: $tType] : $o ).
% 3.49/1.90
% 3.49/1.90 thf(sy_cl_Orderings_Obot,type,
% 3.49/1.90 bot:
% 3.49/1.90 !>[A: $tType] : $o ).
% 3.49/1.90
% 3.49/1.90 thf(sy_cl_Orderings_Oord,type,
% 3.49/1.90 ord:
% 3.49/1.90 !>[A: $tType] : $o ).
% 3.49/1.90
% 3.49/1.90 thf(sy_cl_Orderings_Oorder,type,
% 3.49/1.90 order:
% 3.49/1.90 !>[A: $tType] : $o ).
% 3.49/1.90
% 3.49/1.90 thf(sy_cl_Orderings_Ono__bot,type,
% 3.49/1.90 no_bot:
% 3.49/1.90 !>[A: $tType] : $o ).
% 3.49/1.90
% 3.49/1.90 thf(sy_cl_Orderings_Ono__top,type,
% 3.49/1.90 no_top:
% 3.49/1.90 !>[A: $tType] : $o ).
% 3.49/1.90
% 3.49/1.90 thf(sy_cl_Orderings_Olinorder,type,
% 3.49/1.90 linorder:
% 3.49/1.90 !>[A: $tType] : $o ).
% 3.49/1.90
% 3.49/1.90 thf(sy_cl_Orderings_Opreorder,type,
% 3.49/1.90 preorder:
% 3.49/1.90 !>[A: $tType] : $o ).
% 3.49/1.90
% 3.49/1.90 thf(sy_cl_Orderings_Oorder__bot,type,
% 3.49/1.90 order_bot:
% 3.49/1.90 !>[A: $tType] : $o ).
% 3.49/1.90
% 3.49/1.90 thf(sy_cl_Orderings_Owellorder,type,
% 3.49/1.90 wellorder:
% 3.49/1.90 !>[A: $tType] : $o ).
% 3.49/1.90
% 3.49/1.90 thf(sy_cl_Orderings_Odense__order,type,
% 3.49/1.90 dense_order:
% 3.49/1.90 !>[A: $tType] : $o ).
% 3.49/1.90
% 3.49/1.90 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 3.49/1.90 semilattice_sup:
% 3.49/1.90 !>[A: $tType] : $o ).
% 3.49/1.90
% 3.49/1.90 thf(sy_cl_Type__Mirabelle__sfxnzmapfi_Oof__nat,type,
% 3.49/1.90 type_M201404320of_nat:
% 3.49/1.90 !>[A: $tType] : $o ).
% 3.49/1.90
% 3.49/1.90 thf(sy_cl_Type__Mirabelle__sfxnzmapfi_Otyp__of,type,
% 3.49/1.90 type_M1535146424typ_of:
% 3.49/1.90 !>[A: $tType] : $o ).
% 3.49/1.90
% 3.49/1.90 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 3.49/1.90 bounde1808546759up_bot:
% 3.49/1.90 !>[A: $tType] : $o ).
% 3.49/1.90
% 3.49/1.90 thf(sy_cl_Type__Mirabelle__sfxnzmapfi_Otype__struct,type,
% 3.49/1.90 type_M1470978233struct:
% 3.49/1.90 !>[A: $tType] : $o ).
% 3.49/1.90
% 3.49/1.90 thf(sy_c_HOL_OThe,type,
% 3.49/1.90 the:
% 3.49/1.90 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 3.49/1.90
% 3.49/1.90 thf(sy_c_If,type,
% 3.49/1.90 if:
% 3.49/1.90 !>[A: $tType] : ( $o > A > A > A ) ).
% 3.49/1.90
% 3.49/1.90 thf(sy_c_Lattices_Osemilattice__neutr,type,
% 3.49/1.90 semilattice_neutr:
% 3.49/1.90 !>[A: $tType] : ( ( A > A > A ) > A > $o ) ).
% 3.49/1.90
% 3.49/1.90 thf(sy_c_Lattices_Osup__class_Osup,type,
% 3.49/1.90 sup_sup:
% 3.49/1.90 !>[A: $tType] : ( A > A > A ) ).
% 3.49/1.90
% 3.49/1.90 thf(sy_c_List_Oinsert,type,
% 3.49/1.90 insert:
% 3.49/1.90 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 3.49/1.90
% 3.49/1.90 thf(sy_c_List_Olist_OCons,type,
% 3.49/1.90 cons:
% 3.49/1.90 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 3.49/1.90
% 3.49/1.90 thf(sy_c_List_Olist_ONil,type,
% 3.49/1.90 nil:
% 3.49/1.90 !>[A: $tType] : ( list @ A ) ).
% 3.49/1.90
% 3.49/1.90 thf(sy_c_List_Oord__class_Olexordp__eq,type,
% 3.49/1.90 ord_lexordp_eq:
% 3.49/1.90 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 3.49/1.90
% 3.49/1.90 thf(sy_c_Orderings_Obot__class_Obot,type,
% 3.49/1.90 bot_bot:
% 3.49/1.90 !>[A: $tType] : A ).
% 3.49/1.90
% 3.49/1.90 thf(sy_c_Orderings_Oord__class_Oless,type,
% 3.49/1.90 ord_less:
% 3.49/1.90 !>[A: $tType] : ( A > A > $o ) ).
% 3.49/1.90
% 3.49/1.90 thf(sy_c_Set_OCollect,type,
% 3.49/1.90 collect:
% 3.49/1.90 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.49/1.90
% 3.49/1.90 thf(sy_c_Set_Oinsert,type,
% 3.49/1.90 insert2:
% 3.49/1.90 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 3.49/1.90
% 3.49/1.90 thf(sy_c_Set_Ois__empty,type,
% 3.49/1.90 is_empty:
% 3.49/1.90 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 3.49/1.91
% 3.49/1.91 thf(sy_c_Set_Ois__singleton,type,
% 3.49/1.91 is_singleton:
% 3.49/1.91 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 3.49/1.91
% 3.49/1.91 thf(sy_c_Set_Othe__elem,type,
% 3.49/1.91 the_elem:
% 3.49/1.91 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 3.49/1.91
% 3.49/1.91 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Ocod,type,
% 3.49/1.91 type_Mirabelle_cod: ( nat > type_Mirabelle_typ ) > ( set @ nat ) ).
% 3.49/1.91
% 3.49/1.91 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Odom,type,
% 3.49/1.91 type_Mirabelle_dom: ( nat > type_Mirabelle_typ ) > ( set @ nat ) ).
% 3.49/1.91
% 3.49/1.91 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Oid__subst,type,
% 3.49/1.91 type_M17369686_subst: nat > type_Mirabelle_typ ).
% 3.49/1.91
% 3.49/1.91 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Omk__scheme,type,
% 3.49/1.91 type_M540877363scheme: type_Mirabelle_typ > type_M1610475166scheme ).
% 3.49/1.91
% 3.49/1.91 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Onew__tv,type,
% 3.49/1.91 type_M1046766514new_tv:
% 3.49/1.91 !>[A: $tType] : ( nat > A > $o ) ).
% 3.49/1.91
% 3.49/1.91 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Oof__nat__class_Oof__nat,type,
% 3.49/1.91 type_M167561660of_nat:
% 3.49/1.91 !>[A: $tType] : ( nat > A ) ).
% 3.49/1.91
% 3.49/1.91 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otyp_OFun,type,
% 3.49/1.91 type_Mirabelle_Fun: type_Mirabelle_typ > type_Mirabelle_typ > type_Mirabelle_typ ).
% 3.49/1.91
% 3.49/1.91 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otyp_OTVar,type,
% 3.49/1.91 type_Mirabelle_TVar: nat > type_Mirabelle_typ ).
% 3.49/1.91
% 3.49/1.91 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otyp_Ocase__typ,type,
% 3.49/1.91 type_M1695911984se_typ:
% 3.49/1.91 !>[A: $tType] : ( ( nat > A ) > ( type_Mirabelle_typ > type_Mirabelle_typ > A ) > type_Mirabelle_typ > A ) ).
% 3.49/1.91
% 3.49/1.91 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otyp__of__class_Otyp__of,type,
% 3.49/1.91 type_M604437996typ_of:
% 3.49/1.91 !>[A: $tType] : ( A > type_Mirabelle_typ ) ).
% 3.49/1.91
% 3.49/1.91 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__scheme_OBVar,type,
% 3.49/1.91 type_M1264524676e_BVar: nat > type_M1610475166scheme ).
% 3.49/1.91
% 3.49/1.91 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__scheme_OFVar,type,
% 3.49/1.91 type_M91906176e_FVar: nat > type_M1610475166scheme ).
% 3.49/1.91
% 3.49/1.91 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__scheme_OSFun,type,
% 3.49/1.91 type_M1518733067e_SFun: type_M1610475166scheme > type_M1610475166scheme > type_M1610475166scheme ).
% 3.49/1.91
% 3.49/1.91 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__scheme_Ocase__type__scheme,type,
% 3.49/1.91 type_M697345518scheme:
% 3.49/1.91 !>[A: $tType] : ( ( nat > A ) > ( nat > A ) > ( type_M1610475166scheme > type_M1610475166scheme > A ) > type_M1610475166scheme > A ) ).
% 3.49/1.91
% 3.49/1.91 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__scheme_Orec__type__scheme,type,
% 3.49/1.91 type_M1705333808scheme:
% 3.49/1.91 !>[A: $tType] : ( ( nat > A ) > ( nat > A ) > ( type_M1610475166scheme > type_M1610475166scheme > A > A > A ) > type_M1610475166scheme > A ) ).
% 3.49/1.91
% 3.49/1.91 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__struct__class_Oapp__subst,type,
% 3.49/1.91 type_M353778473_subst:
% 3.49/1.91 !>[A: $tType] : ( ( nat > type_Mirabelle_typ ) > A > A ) ).
% 3.49/1.91
% 3.49/1.91 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__struct__class_Obound__tv,type,
% 3.49/1.91 type_M779184887und_tv:
% 3.49/1.91 !>[A: $tType] : ( A > ( set @ nat ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(sy_c_Type__Mirabelle__sfxnzmapfi_Otype__struct__class_Ofree__tv,type,
% 3.49/1.91 type_M950795831ree_tv:
% 3.49/1.91 !>[A: $tType] : ( A > ( set @ nat ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(sy_c_member,type,
% 3.49/1.91 member:
% 3.49/1.91 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.49/1.91
% 3.49/1.91 thf(sy_v_S1,type,
% 3.49/1.91 s1: nat > type_Mirabelle_typ ).
% 3.49/1.91
% 3.49/1.91 thf(sy_v_S2,type,
% 3.49/1.91 s2: nat > type_Mirabelle_typ ).
% 3.49/1.91
% 3.49/1.91 thf(sy_v_n,type,
% 3.49/1.91 n: nat ).
% 3.49/1.91
% 3.49/1.91 thf(sy_v_x,type,
% 3.49/1.91 x: nat ).
% 3.49/1.91
% 3.49/1.91 thf(fact_0_type__scheme_Oinject_I1_J,axiom,
% 3.49/1.91 ! [X1: nat,Y1: nat] :
% 3.49/1.91 ( ( ( type_M91906176e_FVar @ X1 )
% 3.49/1.91 = ( type_M91906176e_FVar @ Y1 ) )
% 3.49/1.91 = ( X1 = Y1 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_1_eq__free__eq__subst__type__scheme,axiom,
% 3.49/1.91 ! [Sch: type_M1610475166scheme,S1: nat > type_Mirabelle_typ,S2: nat > type_Mirabelle_typ] :
% 3.49/1.91 ( ! [N: nat] :
% 3.49/1.91 ( ( member @ nat @ N @ ( type_M950795831ree_tv @ type_M1610475166scheme @ Sch ) )
% 3.49/1.91 => ( ( S1 @ N )
% 3.49/1.91 = ( S2 @ N ) ) )
% 3.49/1.91 => ( ( type_M353778473_subst @ type_M1610475166scheme @ S1 @ Sch )
% 3.49/1.91 = ( type_M353778473_subst @ type_M1610475166scheme @ S2 @ Sch ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_2_scheme__substitutions__only__on__free__variables,axiom,
% 3.49/1.91 ! [Sch: type_M1610475166scheme,S: nat > type_Mirabelle_typ,S3: nat > type_Mirabelle_typ] :
% 3.49/1.91 ( ! [X: nat] :
% 3.49/1.91 ( ( member @ nat @ X @ ( type_M950795831ree_tv @ type_M1610475166scheme @ Sch ) )
% 3.49/1.91 => ( ( S @ X )
% 3.49/1.91 = ( S3 @ X ) ) )
% 3.49/1.91 => ( ( type_M353778473_subst @ type_M1610475166scheme @ S @ Sch )
% 3.49/1.91 = ( type_M353778473_subst @ type_M1610475166scheme @ S3 @ Sch ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_3_app__subst__type__scheme_Osimps_I1_J,axiom,
% 3.49/1.91 ! [S: nat > type_Mirabelle_typ,N2: nat] :
% 3.49/1.91 ( ( type_M353778473_subst @ type_M1610475166scheme @ S @ ( type_M91906176e_FVar @ N2 ) )
% 3.49/1.91 = ( type_M540877363scheme @ ( S @ N2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_4_type__scheme_Osimps_I13_J,axiom,
% 3.49/1.91 ! [A: $tType,F1: nat > A,F2: nat > A,F3: type_M1610475166scheme > type_M1610475166scheme > A > A > A,X1: nat] :
% 3.49/1.91 ( ( type_M1705333808scheme @ A @ F1 @ F2 @ F3 @ ( type_M91906176e_FVar @ X1 ) )
% 3.49/1.91 = ( F1 @ X1 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_5_type__scheme_Osimps_I10_J,axiom,
% 3.49/1.91 ! [A: $tType,F1: nat > A,F2: nat > A,F3: type_M1610475166scheme > type_M1610475166scheme > A,X1: nat] :
% 3.49/1.91 ( ( type_M697345518scheme @ A @ F1 @ F2 @ F3 @ ( type_M91906176e_FVar @ X1 ) )
% 3.49/1.91 = ( F1 @ X1 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_6_app__subst__type__scheme_Osimps_I2_J,axiom,
% 3.49/1.91 ! [S: nat > type_Mirabelle_typ,N2: nat] :
% 3.49/1.91 ( ( type_M353778473_subst @ type_M1610475166scheme @ S @ ( type_M1264524676e_BVar @ N2 ) )
% 3.49/1.91 = ( type_M1264524676e_BVar @ N2 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_7_app__subst__type__scheme_Osimps_I3_J,axiom,
% 3.49/1.91 ! [S: nat > type_Mirabelle_typ,Sch1: type_M1610475166scheme,Sch2: type_M1610475166scheme] :
% 3.49/1.91 ( ( type_M353778473_subst @ type_M1610475166scheme @ S @ ( type_M1518733067e_SFun @ Sch1 @ Sch2 ) )
% 3.49/1.91 = ( type_M1518733067e_SFun @ ( type_M353778473_subst @ type_M1610475166scheme @ S @ Sch1 ) @ ( type_M353778473_subst @ type_M1610475166scheme @ S @ Sch2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_8_type__scheme_Odistinct_I1_J,axiom,
% 3.49/1.91 ! [X1: nat,X2: nat] :
% 3.49/1.91 ( ( type_M91906176e_FVar @ X1 )
% 3.49/1.91 != ( type_M1264524676e_BVar @ X2 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_9_type__scheme_Odistinct_I3_J,axiom,
% 3.49/1.91 ! [X1: nat,X31: type_M1610475166scheme,X32: type_M1610475166scheme] :
% 3.49/1.91 ( ( type_M91906176e_FVar @ X1 )
% 3.49/1.91 != ( type_M1518733067e_SFun @ X31 @ X32 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_10_app__subst__Cons,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( type_M1470978233struct @ A )
% 3.49/1.91 => ! [S: nat > type_Mirabelle_typ,X3: A,L: list @ A] :
% 3.49/1.91 ( ( type_M353778473_subst @ ( list @ A ) @ S @ ( cons @ A @ X3 @ L ) )
% 3.49/1.91 = ( cons @ A @ ( type_M353778473_subst @ A @ S @ X3 ) @ ( type_M353778473_subst @ ( list @ A ) @ S @ L ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_11_free__tv__mk__scheme,axiom,
% 3.49/1.91 ! [T: type_Mirabelle_typ] :
% 3.49/1.91 ( ( type_M950795831ree_tv @ type_M1610475166scheme @ ( type_M540877363scheme @ T ) )
% 3.49/1.91 = ( type_M950795831ree_tv @ type_Mirabelle_typ @ T ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_12_free__tv__type__scheme_Osimps_I1_J,axiom,
% 3.49/1.91 ! [M: nat] :
% 3.49/1.91 ( ( type_M950795831ree_tv @ type_M1610475166scheme @ ( type_M91906176e_FVar @ M ) )
% 3.49/1.91 = ( insert2 @ nat @ M @ ( bot_bot @ ( set @ nat ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_13_new__if__subst__type__scheme,axiom,
% 3.49/1.91 ! [N2: nat,Sch: type_M1610475166scheme,S: nat > type_Mirabelle_typ,S3: nat > type_Mirabelle_typ] :
% 3.49/1.91 ( ( type_M1046766514new_tv @ type_M1610475166scheme @ N2 @ Sch )
% 3.49/1.91 => ( ( type_M353778473_subst @ type_M1610475166scheme
% 3.49/1.91 @ ^ [K: nat] : ( if @ type_Mirabelle_typ @ ( ord_less @ nat @ K @ N2 ) @ ( S @ K ) @ ( S3 @ K ) )
% 3.49/1.91 @ Sch )
% 3.49/1.91 = ( type_M353778473_subst @ type_M1610475166scheme @ S @ Sch ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_14_typ_Ocase__distrib,axiom,
% 3.49/1.91 ! [A: $tType,B: $tType,H: A > B,F1: nat > A,F2: type_Mirabelle_typ > type_Mirabelle_typ > A,Typ: type_Mirabelle_typ] :
% 3.49/1.91 ( ( H @ ( type_M1695911984se_typ @ A @ F1 @ F2 @ Typ ) )
% 3.49/1.91 = ( type_M1695911984se_typ @ B
% 3.49/1.91 @ ^ [X4: nat] : ( H @ ( F1 @ X4 ) )
% 3.49/1.91 @ ^ [X12: type_Mirabelle_typ,X22: type_Mirabelle_typ] : ( H @ ( F2 @ X12 @ X22 ) )
% 3.49/1.91 @ Typ ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_15_type__scheme_Oinject_I3_J,axiom,
% 3.49/1.91 ! [X31: type_M1610475166scheme,X32: type_M1610475166scheme,Y31: type_M1610475166scheme,Y32: type_M1610475166scheme] :
% 3.49/1.91 ( ( ( type_M1518733067e_SFun @ X31 @ X32 )
% 3.49/1.91 = ( type_M1518733067e_SFun @ Y31 @ Y32 ) )
% 3.49/1.91 = ( ( X31 = Y31 )
% 3.49/1.91 & ( X32 = Y32 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_16_type__scheme_Oinject_I2_J,axiom,
% 3.49/1.91 ! [X2: nat,Y2: nat] :
% 3.49/1.91 ( ( ( type_M1264524676e_BVar @ X2 )
% 3.49/1.91 = ( type_M1264524676e_BVar @ Y2 ) )
% 3.49/1.91 = ( X2 = Y2 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_17_new__tv__Cons,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( type_M1470978233struct @ A )
% 3.49/1.91 => ! [N2: nat,X3: A,L: list @ A] :
% 3.49/1.91 ( ( type_M1046766514new_tv @ ( list @ A ) @ N2 @ ( cons @ A @ X3 @ L ) )
% 3.49/1.91 = ( ( type_M1046766514new_tv @ A @ N2 @ X3 )
% 3.49/1.91 & ( type_M1046766514new_tv @ ( list @ A ) @ N2 @ L ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_18_subst__mk__scheme,axiom,
% 3.49/1.91 ! [S: nat > type_Mirabelle_typ,T: type_Mirabelle_typ] :
% 3.49/1.91 ( ( type_M353778473_subst @ type_M1610475166scheme @ S @ ( type_M540877363scheme @ T ) )
% 3.49/1.91 = ( type_M540877363scheme @ ( type_M353778473_subst @ type_Mirabelle_typ @ S @ T ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_19_new__tv__Fun2,axiom,
% 3.49/1.91 ! [N2: nat,T1: type_M1610475166scheme,T2: type_M1610475166scheme] :
% 3.49/1.91 ( ( type_M1046766514new_tv @ type_M1610475166scheme @ N2 @ ( type_M1518733067e_SFun @ T1 @ T2 ) )
% 3.49/1.91 = ( ( type_M1046766514new_tv @ type_M1610475166scheme @ N2 @ T1 )
% 3.49/1.91 & ( type_M1046766514new_tv @ type_M1610475166scheme @ N2 @ T2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_20_new__tv__BVar,axiom,
% 3.49/1.91 ! [N2: nat,M: nat] : ( type_M1046766514new_tv @ type_M1610475166scheme @ N2 @ ( type_M1264524676e_BVar @ M ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_21_new__tv__FVar,axiom,
% 3.49/1.91 ! [N2: nat,M: nat] :
% 3.49/1.91 ( ( type_M1046766514new_tv @ type_M1610475166scheme @ N2 @ ( type_M91906176e_FVar @ M ) )
% 3.49/1.91 = ( ord_less @ nat @ M @ N2 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_22_type__scheme_Osimps_I15_J,axiom,
% 3.49/1.91 ! [A: $tType,F1: nat > A,F2: nat > A,F3: type_M1610475166scheme > type_M1610475166scheme > A > A > A,X31: type_M1610475166scheme,X32: type_M1610475166scheme] :
% 3.49/1.91 ( ( type_M1705333808scheme @ A @ F1 @ F2 @ F3 @ ( type_M1518733067e_SFun @ X31 @ X32 ) )
% 3.49/1.91 = ( F3 @ X31 @ X32 @ ( type_M1705333808scheme @ A @ F1 @ F2 @ F3 @ X31 ) @ ( type_M1705333808scheme @ A @ F1 @ F2 @ F3 @ X32 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_23_type__scheme_Osimps_I14_J,axiom,
% 3.49/1.91 ! [A: $tType,F1: nat > A,F2: nat > A,F3: type_M1610475166scheme > type_M1610475166scheme > A > A > A,X2: nat] :
% 3.49/1.91 ( ( type_M1705333808scheme @ A @ F1 @ F2 @ F3 @ ( type_M1264524676e_BVar @ X2 ) )
% 3.49/1.91 = ( F2 @ X2 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_24_type__scheme_Osimps_I12_J,axiom,
% 3.49/1.91 ! [A: $tType,F1: nat > A,F2: nat > A,F3: type_M1610475166scheme > type_M1610475166scheme > A,X31: type_M1610475166scheme,X32: type_M1610475166scheme] :
% 3.49/1.91 ( ( type_M697345518scheme @ A @ F1 @ F2 @ F3 @ ( type_M1518733067e_SFun @ X31 @ X32 ) )
% 3.49/1.91 = ( F3 @ X31 @ X32 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_25_type__scheme_Osimps_I11_J,axiom,
% 3.49/1.91 ! [A: $tType,F1: nat > A,F2: nat > A,F3: type_M1610475166scheme > type_M1610475166scheme > A,X2: nat] :
% 3.49/1.91 ( ( type_M697345518scheme @ A @ F1 @ F2 @ F3 @ ( type_M1264524676e_BVar @ X2 ) )
% 3.49/1.91 = ( F2 @ X2 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_26_type__scheme_Odistinct_I5_J,axiom,
% 3.49/1.91 ! [X2: nat,X31: type_M1610475166scheme,X32: type_M1610475166scheme] :
% 3.49/1.91 ( ( type_M1264524676e_BVar @ X2 )
% 3.49/1.91 != ( type_M1518733067e_SFun @ X31 @ X32 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_27_mk__scheme__Fun,axiom,
% 3.49/1.91 ! [T: type_Mirabelle_typ,Sch1: type_M1610475166scheme,Sch2: type_M1610475166scheme] :
% 3.49/1.91 ( ( ( type_M540877363scheme @ T )
% 3.49/1.91 = ( type_M1518733067e_SFun @ Sch1 @ Sch2 ) )
% 3.49/1.91 => ? [T12: type_Mirabelle_typ,T22: type_Mirabelle_typ] :
% 3.49/1.91 ( ( Sch1
% 3.49/1.91 = ( type_M540877363scheme @ T12 ) )
% 3.49/1.91 & ( Sch2
% 3.49/1.91 = ( type_M540877363scheme @ T22 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_28_eq__free__eq__subst__te,axiom,
% 3.49/1.91 ! [T: type_Mirabelle_typ,S1: nat > type_Mirabelle_typ,S2: nat > type_Mirabelle_typ] :
% 3.49/1.91 ( ! [N: nat] :
% 3.49/1.91 ( ( member @ nat @ N @ ( type_M950795831ree_tv @ type_Mirabelle_typ @ T ) )
% 3.49/1.91 => ( ( S1 @ N )
% 3.49/1.91 = ( S2 @ N ) ) )
% 3.49/1.91 => ( ( type_M353778473_subst @ type_Mirabelle_typ @ S1 @ T )
% 3.49/1.91 = ( type_M353778473_subst @ type_Mirabelle_typ @ S2 @ T ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_29_eq__subst__te__eq__free,axiom,
% 3.49/1.91 ! [S1: nat > type_Mirabelle_typ,T: type_Mirabelle_typ,S2: nat > type_Mirabelle_typ,N2: nat] :
% 3.49/1.91 ( ( ( type_M353778473_subst @ type_Mirabelle_typ @ S1 @ T )
% 3.49/1.91 = ( type_M353778473_subst @ type_Mirabelle_typ @ S2 @ T ) )
% 3.49/1.91 => ( ( member @ nat @ N2 @ ( type_M950795831ree_tv @ type_Mirabelle_typ @ T ) )
% 3.49/1.91 => ( ( S1 @ N2 )
% 3.49/1.91 = ( S2 @ N2 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_30_typ__substitutions__only__on__free__variables,axiom,
% 3.49/1.91 ! [T: type_Mirabelle_typ,S: nat > type_Mirabelle_typ,S3: nat > type_Mirabelle_typ] :
% 3.49/1.91 ( ! [X: nat] :
% 3.49/1.91 ( ( member @ nat @ X @ ( type_M950795831ree_tv @ type_Mirabelle_typ @ T ) )
% 3.49/1.91 => ( ( S @ X )
% 3.49/1.91 = ( S3 @ X ) ) )
% 3.49/1.91 => ( ( type_M353778473_subst @ type_Mirabelle_typ @ S @ T )
% 3.49/1.91 = ( type_M353778473_subst @ type_Mirabelle_typ @ S3 @ T ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_31_mk__scheme__injective,axiom,
% 3.49/1.91 ! [T: type_Mirabelle_typ,T3: type_Mirabelle_typ] :
% 3.49/1.91 ( ( ( type_M540877363scheme @ T )
% 3.49/1.91 = ( type_M540877363scheme @ T3 ) )
% 3.49/1.91 => ( T = T3 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_32_free__tv__type__scheme_Osimps_I2_J,axiom,
% 3.49/1.91 ! [M: nat] :
% 3.49/1.91 ( ( type_M950795831ree_tv @ type_M1610475166scheme @ ( type_M1264524676e_BVar @ M ) )
% 3.49/1.91 = ( bot_bot @ ( set @ nat ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_33_type__scheme_Oexhaust,axiom,
% 3.49/1.91 ! [Y: type_M1610475166scheme] :
% 3.49/1.91 ( ! [X13: nat] :
% 3.49/1.91 ( Y
% 3.49/1.91 != ( type_M91906176e_FVar @ X13 ) )
% 3.49/1.91 => ( ! [X23: nat] :
% 3.49/1.91 ( Y
% 3.49/1.91 != ( type_M1264524676e_BVar @ X23 ) )
% 3.49/1.91 => ~ ! [X312: type_M1610475166scheme,X322: type_M1610475166scheme] :
% 3.49/1.91 ( Y
% 3.49/1.91 != ( type_M1518733067e_SFun @ X312 @ X322 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_34_type__scheme_Oinduct,axiom,
% 3.49/1.91 ! [P: type_M1610475166scheme > $o,Type_scheme: type_M1610475166scheme] :
% 3.49/1.91 ( ! [X: nat] : ( P @ ( type_M91906176e_FVar @ X ) )
% 3.49/1.91 => ( ! [X: nat] : ( P @ ( type_M1264524676e_BVar @ X ) )
% 3.49/1.91 => ( ! [X1a: type_M1610475166scheme,X2a: type_M1610475166scheme] :
% 3.49/1.91 ( ( P @ X1a )
% 3.49/1.91 => ( ( P @ X2a )
% 3.49/1.91 => ( P @ ( type_M1518733067e_SFun @ X1a @ X2a ) ) ) )
% 3.49/1.91 => ( P @ Type_scheme ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_35_new__tv__def,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( type_M1470978233struct @ A )
% 3.49/1.91 => ( ( type_M1046766514new_tv @ A )
% 3.49/1.91 = ( ^ [N3: nat,Ts: A] :
% 3.49/1.91 ! [M2: nat] :
% 3.49/1.91 ( ( member @ nat @ M2 @ ( type_M950795831ree_tv @ A @ Ts ) )
% 3.49/1.91 => ( ord_less @ nat @ M2 @ N3 ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_36_type__scheme_Ocase__distrib,axiom,
% 3.49/1.91 ! [A: $tType,B: $tType,H: A > B,F1: nat > A,F2: nat > A,F3: type_M1610475166scheme > type_M1610475166scheme > A,Type_scheme: type_M1610475166scheme] :
% 3.49/1.91 ( ( H @ ( type_M697345518scheme @ A @ F1 @ F2 @ F3 @ Type_scheme ) )
% 3.49/1.91 = ( type_M697345518scheme @ B
% 3.49/1.91 @ ^ [X4: nat] : ( H @ ( F1 @ X4 ) )
% 3.49/1.91 @ ^ [X4: nat] : ( H @ ( F2 @ X4 ) )
% 3.49/1.91 @ ^ [X12: type_M1610475166scheme,X22: type_M1610475166scheme] : ( H @ ( F3 @ X12 @ X22 ) )
% 3.49/1.91 @ Type_scheme ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_37_singleton__conv,axiom,
% 3.49/1.91 ! [A: $tType,A2: A] :
% 3.49/1.91 ( ( collect @ A
% 3.49/1.91 @ ^ [X4: A] : ( X4 = A2 ) )
% 3.49/1.91 = ( insert2 @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_38_singleton__conv2,axiom,
% 3.49/1.91 ! [A: $tType,A2: A] :
% 3.49/1.91 ( ( collect @ A
% 3.49/1.91 @ ( ^ [Y3: A,Z: A] : ( Y3 = Z )
% 3.49/1.91 @ A2 ) )
% 3.49/1.91 = ( insert2 @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_39_singletonI,axiom,
% 3.49/1.91 ! [A: $tType,A2: A] : ( member @ A @ A2 @ ( insert2 @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_40_insertCI,axiom,
% 3.49/1.91 ! [A: $tType,A2: A,B2: set @ A,B3: A] :
% 3.49/1.91 ( ( ~ ( member @ A @ A2 @ B2 )
% 3.49/1.91 => ( A2 = B3 ) )
% 3.49/1.91 => ( member @ A @ A2 @ ( insert2 @ A @ B3 @ B2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_41_insert__iff,axiom,
% 3.49/1.91 ! [A: $tType,A2: A,B3: A,A3: set @ A] :
% 3.49/1.91 ( ( member @ A @ A2 @ ( insert2 @ A @ B3 @ A3 ) )
% 3.49/1.91 = ( ( A2 = B3 )
% 3.49/1.91 | ( member @ A @ A2 @ A3 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_42_insert__absorb2,axiom,
% 3.49/1.91 ! [A: $tType,X3: A,A3: set @ A] :
% 3.49/1.91 ( ( insert2 @ A @ X3 @ ( insert2 @ A @ X3 @ A3 ) )
% 3.49/1.91 = ( insert2 @ A @ X3 @ A3 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_43_list_Oinject,axiom,
% 3.49/1.91 ! [A: $tType,X21: A,X222: list @ A,Y21: A,Y22: list @ A] :
% 3.49/1.91 ( ( ( cons @ A @ X21 @ X222 )
% 3.49/1.91 = ( cons @ A @ Y21 @ Y22 ) )
% 3.49/1.91 = ( ( X21 = Y21 )
% 3.49/1.91 & ( X222 = Y22 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_44_empty__iff,axiom,
% 3.49/1.91 ! [A: $tType,C: A] :
% 3.49/1.91 ~ ( member @ A @ C @ ( bot_bot @ ( set @ A ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_45_mem__Collect__eq,axiom,
% 3.49/1.91 ! [A: $tType,A2: A,P: A > $o] :
% 3.49/1.91 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 3.49/1.91 = ( P @ A2 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_46_Collect__mem__eq,axiom,
% 3.49/1.91 ! [A: $tType,A3: set @ A] :
% 3.49/1.91 ( ( collect @ A
% 3.49/1.91 @ ^ [X4: A] : ( member @ A @ X4 @ A3 ) )
% 3.49/1.91 = A3 ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_47_Collect__cong,axiom,
% 3.49/1.91 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.49/1.91 ( ! [X: A] :
% 3.49/1.91 ( ( P @ X )
% 3.49/1.91 = ( Q @ X ) )
% 3.49/1.91 => ( ( collect @ A @ P )
% 3.49/1.91 = ( collect @ A @ Q ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_48_ext,axiom,
% 3.49/1.91 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 3.49/1.91 ( ! [X: A] :
% 3.49/1.91 ( ( F @ X )
% 3.49/1.91 = ( G @ X ) )
% 3.49/1.91 => ( F = G ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_49_all__not__in__conv,axiom,
% 3.49/1.91 ! [A: $tType,A3: set @ A] :
% 3.49/1.91 ( ( ! [X4: A] :
% 3.49/1.91 ~ ( member @ A @ X4 @ A3 ) )
% 3.49/1.91 = ( A3
% 3.49/1.91 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_50_Collect__empty__eq,axiom,
% 3.49/1.91 ! [A: $tType,P: A > $o] :
% 3.49/1.91 ( ( ( collect @ A @ P )
% 3.49/1.91 = ( bot_bot @ ( set @ A ) ) )
% 3.49/1.91 = ( ! [X4: A] :
% 3.49/1.91 ~ ( P @ X4 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_51_empty__Collect__eq,axiom,
% 3.49/1.91 ! [A: $tType,P: A > $o] :
% 3.49/1.91 ( ( ( bot_bot @ ( set @ A ) )
% 3.49/1.91 = ( collect @ A @ P ) )
% 3.49/1.91 = ( ! [X4: A] :
% 3.49/1.91 ~ ( P @ X4 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_52_new__if__subst__type__scheme__list,axiom,
% 3.49/1.91 ! [N2: nat,A3: list @ type_M1610475166scheme,S: nat > type_Mirabelle_typ,S3: nat > type_Mirabelle_typ] :
% 3.49/1.91 ( ( type_M1046766514new_tv @ ( list @ type_M1610475166scheme ) @ N2 @ A3 )
% 3.49/1.91 => ( ( type_M353778473_subst @ ( list @ type_M1610475166scheme )
% 3.49/1.91 @ ^ [K: nat] : ( if @ type_Mirabelle_typ @ ( ord_less @ nat @ K @ N2 ) @ ( S @ K ) @ ( S3 @ K ) )
% 3.49/1.91 @ A3 )
% 3.49/1.91 = ( type_M353778473_subst @ ( list @ type_M1610475166scheme ) @ S @ A3 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_53_ex__in__conv,axiom,
% 3.49/1.91 ! [A: $tType,A3: set @ A] :
% 3.49/1.91 ( ( ? [X4: A] : ( member @ A @ X4 @ A3 ) )
% 3.49/1.91 = ( A3
% 3.49/1.91 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_54_equals0I,axiom,
% 3.49/1.91 ! [A: $tType,A3: set @ A] :
% 3.49/1.91 ( ! [Y4: A] :
% 3.49/1.91 ~ ( member @ A @ Y4 @ A3 )
% 3.49/1.91 => ( A3
% 3.49/1.91 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_55_equals0D,axiom,
% 3.49/1.91 ! [A: $tType,A3: set @ A,A2: A] :
% 3.49/1.91 ( ( A3
% 3.49/1.91 = ( bot_bot @ ( set @ A ) ) )
% 3.49/1.91 => ~ ( member @ A @ A2 @ A3 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_56_emptyE,axiom,
% 3.49/1.91 ! [A: $tType,A2: A] :
% 3.49/1.91 ~ ( member @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_57_not__Cons__self2,axiom,
% 3.49/1.91 ! [A: $tType,X3: A,Xs: list @ A] :
% 3.49/1.91 ( ( cons @ A @ X3 @ Xs )
% 3.49/1.91 != Xs ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_58_mk__disjoint__insert,axiom,
% 3.49/1.91 ! [A: $tType,A2: A,A3: set @ A] :
% 3.49/1.91 ( ( member @ A @ A2 @ A3 )
% 3.49/1.91 => ? [B4: set @ A] :
% 3.49/1.91 ( ( A3
% 3.49/1.91 = ( insert2 @ A @ A2 @ B4 ) )
% 3.49/1.91 & ~ ( member @ A @ A2 @ B4 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_59_insert__commute,axiom,
% 3.49/1.91 ! [A: $tType,X3: A,Y: A,A3: set @ A] :
% 3.49/1.91 ( ( insert2 @ A @ X3 @ ( insert2 @ A @ Y @ A3 ) )
% 3.49/1.91 = ( insert2 @ A @ Y @ ( insert2 @ A @ X3 @ A3 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_60_insert__eq__iff,axiom,
% 3.49/1.91 ! [A: $tType,A2: A,A3: set @ A,B3: A,B2: set @ A] :
% 3.49/1.91 ( ~ ( member @ A @ A2 @ A3 )
% 3.49/1.91 => ( ~ ( member @ A @ B3 @ B2 )
% 3.49/1.91 => ( ( ( insert2 @ A @ A2 @ A3 )
% 3.49/1.91 = ( insert2 @ A @ B3 @ B2 ) )
% 3.49/1.91 = ( ( ( A2 = B3 )
% 3.49/1.91 => ( A3 = B2 ) )
% 3.49/1.91 & ( ( A2 != B3 )
% 3.49/1.91 => ? [C2: set @ A] :
% 3.49/1.91 ( ( A3
% 3.49/1.91 = ( insert2 @ A @ B3 @ C2 ) )
% 3.49/1.91 & ~ ( member @ A @ B3 @ C2 )
% 3.49/1.91 & ( B2
% 3.49/1.91 = ( insert2 @ A @ A2 @ C2 ) )
% 3.49/1.91 & ~ ( member @ A @ A2 @ C2 ) ) ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_61_insert__absorb,axiom,
% 3.49/1.91 ! [A: $tType,A2: A,A3: set @ A] :
% 3.49/1.91 ( ( member @ A @ A2 @ A3 )
% 3.49/1.91 => ( ( insert2 @ A @ A2 @ A3 )
% 3.49/1.91 = A3 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_62_insert__ident,axiom,
% 3.49/1.91 ! [A: $tType,X3: A,A3: set @ A,B2: set @ A] :
% 3.49/1.91 ( ~ ( member @ A @ X3 @ A3 )
% 3.49/1.91 => ( ~ ( member @ A @ X3 @ B2 )
% 3.49/1.91 => ( ( ( insert2 @ A @ X3 @ A3 )
% 3.49/1.91 = ( insert2 @ A @ X3 @ B2 ) )
% 3.49/1.91 = ( A3 = B2 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_63_Set_Oset__insert,axiom,
% 3.49/1.91 ! [A: $tType,X3: A,A3: set @ A] :
% 3.49/1.91 ( ( member @ A @ X3 @ A3 )
% 3.49/1.91 => ~ ! [B4: set @ A] :
% 3.49/1.91 ( ( A3
% 3.49/1.91 = ( insert2 @ A @ X3 @ B4 ) )
% 3.49/1.91 => ( member @ A @ X3 @ B4 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_64_insertI2,axiom,
% 3.49/1.91 ! [A: $tType,A2: A,B2: set @ A,B3: A] :
% 3.49/1.91 ( ( member @ A @ A2 @ B2 )
% 3.49/1.91 => ( member @ A @ A2 @ ( insert2 @ A @ B3 @ B2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_65_insertI1,axiom,
% 3.49/1.91 ! [A: $tType,A2: A,B2: set @ A] : ( member @ A @ A2 @ ( insert2 @ A @ A2 @ B2 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_66_insertE,axiom,
% 3.49/1.91 ! [A: $tType,A2: A,B3: A,A3: set @ A] :
% 3.49/1.91 ( ( member @ A @ A2 @ ( insert2 @ A @ B3 @ A3 ) )
% 3.49/1.91 => ( ( A2 != B3 )
% 3.49/1.91 => ( member @ A @ A2 @ A3 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_67_empty__def,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( bot_bot @ ( set @ A ) )
% 3.49/1.91 = ( collect @ A
% 3.49/1.91 @ ^ [X4: A] : $false ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_68_insert__Collect,axiom,
% 3.49/1.91 ! [A: $tType,A2: A,P: A > $o] :
% 3.49/1.91 ( ( insert2 @ A @ A2 @ ( collect @ A @ P ) )
% 3.49/1.91 = ( collect @ A
% 3.49/1.91 @ ^ [U: A] :
% 3.49/1.91 ( ( U != A2 )
% 3.49/1.91 => ( P @ U ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_69_insert__compr,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( insert2 @ A )
% 3.49/1.91 = ( ^ [A4: A,B5: set @ A] :
% 3.49/1.91 ( collect @ A
% 3.49/1.91 @ ^ [X4: A] :
% 3.49/1.91 ( ( X4 = A4 )
% 3.49/1.91 | ( member @ A @ X4 @ B5 ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_70_singleton__inject,axiom,
% 3.49/1.91 ! [A: $tType,A2: A,B3: A] :
% 3.49/1.91 ( ( ( insert2 @ A @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 3.49/1.91 = ( insert2 @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.49/1.91 => ( A2 = B3 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_71_insert__not__empty,axiom,
% 3.49/1.91 ! [A: $tType,A2: A,A3: set @ A] :
% 3.49/1.91 ( ( insert2 @ A @ A2 @ A3 )
% 3.49/1.91 != ( bot_bot @ ( set @ A ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_72_doubleton__eq__iff,axiom,
% 3.49/1.91 ! [A: $tType,A2: A,B3: A,C: A,D: A] :
% 3.49/1.91 ( ( ( insert2 @ A @ A2 @ ( insert2 @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.49/1.91 = ( insert2 @ A @ C @ ( insert2 @ A @ D @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.49/1.91 = ( ( ( A2 = C )
% 3.49/1.91 & ( B3 = D ) )
% 3.49/1.91 | ( ( A2 = D )
% 3.49/1.91 & ( B3 = C ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_73_singleton__iff,axiom,
% 3.49/1.91 ! [A: $tType,B3: A,A2: A] :
% 3.49/1.91 ( ( member @ A @ B3 @ ( insert2 @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.49/1.91 = ( B3 = A2 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_74_singletonD,axiom,
% 3.49/1.91 ! [A: $tType,B3: A,A2: A] :
% 3.49/1.91 ( ( member @ A @ B3 @ ( insert2 @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.49/1.91 => ( B3 = A2 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_75_Collect__conv__if2,axiom,
% 3.49/1.91 ! [A: $tType,P: A > $o,A2: A] :
% 3.49/1.91 ( ( ( P @ A2 )
% 3.49/1.91 => ( ( collect @ A
% 3.49/1.91 @ ^ [X4: A] :
% 3.49/1.91 ( ( A2 = X4 )
% 3.49/1.91 & ( P @ X4 ) ) )
% 3.49/1.91 = ( insert2 @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.49/1.91 & ( ~ ( P @ A2 )
% 3.49/1.91 => ( ( collect @ A
% 3.49/1.91 @ ^ [X4: A] :
% 3.49/1.91 ( ( A2 = X4 )
% 3.49/1.91 & ( P @ X4 ) ) )
% 3.49/1.91 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_76_Collect__conv__if,axiom,
% 3.49/1.91 ! [A: $tType,P: A > $o,A2: A] :
% 3.49/1.91 ( ( ( P @ A2 )
% 3.49/1.91 => ( ( collect @ A
% 3.49/1.91 @ ^ [X4: A] :
% 3.49/1.91 ( ( X4 = A2 )
% 3.49/1.91 & ( P @ X4 ) ) )
% 3.49/1.91 = ( insert2 @ A @ A2 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.49/1.91 & ( ~ ( P @ A2 )
% 3.49/1.91 => ( ( collect @ A
% 3.49/1.91 @ ^ [X4: A] :
% 3.49/1.91 ( ( X4 = A2 )
% 3.49/1.91 & ( P @ X4 ) ) )
% 3.49/1.91 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_77_the__elem__eq,axiom,
% 3.49/1.91 ! [A: $tType,X3: A] :
% 3.49/1.91 ( ( the_elem @ A @ ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.49/1.91 = X3 ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_78_bot__apply,axiom,
% 3.49/1.91 ! [C3: $tType,D2: $tType] :
% 3.49/1.91 ( ( bot @ C3 )
% 3.49/1.91 => ( ( bot_bot @ ( D2 > C3 ) )
% 3.49/1.91 = ( ^ [X4: D2] : ( bot_bot @ C3 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_79_bound__tv__type__scheme_Osimps_I2_J,axiom,
% 3.49/1.91 ! [M: nat] :
% 3.49/1.91 ( ( type_M779184887und_tv @ type_M1610475166scheme @ ( type_M1264524676e_BVar @ M ) )
% 3.49/1.91 = ( insert2 @ nat @ M @ ( bot_bot @ ( set @ nat ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_80_is__singletonI,axiom,
% 3.49/1.91 ! [A: $tType,X3: A] : ( is_singleton @ A @ ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_81_bot_Onot__eq__extremum,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( order_bot @ A )
% 3.49/1.91 => ! [A2: A] :
% 3.49/1.91 ( ( A2
% 3.49/1.91 != ( bot_bot @ A ) )
% 3.49/1.91 = ( ord_less @ A @ ( bot_bot @ A ) @ A2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_82_bot_Oextremum__strict,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( order_bot @ A )
% 3.49/1.91 => ! [A2: A] :
% 3.49/1.91 ~ ( ord_less @ A @ A2 @ ( bot_bot @ A ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_83_free__tv__TVar,axiom,
% 3.49/1.91 ! [M: nat] :
% 3.49/1.91 ( ( type_M950795831ree_tv @ type_Mirabelle_typ @ ( type_Mirabelle_TVar @ M ) )
% 3.49/1.91 = ( insert2 @ nat @ M @ ( bot_bot @ ( set @ nat ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_84_bound__tv__type__scheme_Osimps_I1_J,axiom,
% 3.49/1.91 ! [M: nat] :
% 3.49/1.91 ( ( type_M779184887und_tv @ type_M1610475166scheme @ ( type_M91906176e_FVar @ M ) )
% 3.49/1.91 = ( bot_bot @ ( set @ nat ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_85_typ_Oinject_I1_J,axiom,
% 3.49/1.91 ! [X1: nat,Y1: nat] :
% 3.49/1.91 ( ( ( type_Mirabelle_TVar @ X1 )
% 3.49/1.91 = ( type_Mirabelle_TVar @ Y1 ) )
% 3.49/1.91 = ( X1 = Y1 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_86_new__tv__TVar,axiom,
% 3.49/1.91 ! [N2: nat,M: nat] :
% 3.49/1.91 ( ( type_M1046766514new_tv @ type_Mirabelle_typ @ N2 @ ( type_Mirabelle_TVar @ M ) )
% 3.49/1.91 = ( ord_less @ nat @ M @ N2 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_87_new__tv__TVar__subst,axiom,
% 3.49/1.91 ! [N2: nat] : ( type_M1046766514new_tv @ ( nat > type_Mirabelle_typ ) @ N2 @ type_Mirabelle_TVar ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_88_eq__free__eq__subst__scheme__list,axiom,
% 3.49/1.91 ! [A3: list @ type_M1610475166scheme,S1: nat > type_Mirabelle_typ,S2: nat > type_Mirabelle_typ] :
% 3.49/1.91 ( ! [N: nat] :
% 3.49/1.91 ( ( member @ nat @ N @ ( type_M950795831ree_tv @ ( list @ type_M1610475166scheme ) @ A3 ) )
% 3.49/1.91 => ( ( S1 @ N )
% 3.49/1.91 = ( S2 @ N ) ) )
% 3.49/1.91 => ( ( type_M353778473_subst @ ( list @ type_M1610475166scheme ) @ S1 @ A3 )
% 3.49/1.91 = ( type_M353778473_subst @ ( list @ type_M1610475166scheme ) @ S2 @ A3 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_89_scheme__list__substitutions__only__on__free__variables,axiom,
% 3.49/1.91 ! [A3: list @ type_M1610475166scheme,S: nat > type_Mirabelle_typ,S3: nat > type_Mirabelle_typ] :
% 3.49/1.91 ( ! [X: nat] :
% 3.49/1.91 ( ( member @ nat @ X @ ( type_M950795831ree_tv @ ( list @ type_M1610475166scheme ) @ A3 ) )
% 3.49/1.91 => ( ( S @ X )
% 3.49/1.91 = ( S3 @ X ) ) )
% 3.49/1.91 => ( ( type_M353778473_subst @ ( list @ type_M1610475166scheme ) @ S @ A3 )
% 3.49/1.91 = ( type_M353778473_subst @ ( list @ type_M1610475166scheme ) @ S3 @ A3 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_90_bot__set__def,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( bot_bot @ ( set @ A ) )
% 3.49/1.91 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_91_not__psubset__empty,axiom,
% 3.49/1.91 ! [A: $tType,A3: set @ A] :
% 3.49/1.91 ~ ( ord_less @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_92_app__subst__TVar,axiom,
% 3.49/1.91 ! [S: nat > type_Mirabelle_typ,N2: nat] :
% 3.49/1.91 ( ( type_M353778473_subst @ type_Mirabelle_typ @ S @ ( type_Mirabelle_TVar @ N2 ) )
% 3.49/1.91 = ( S @ N2 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_93_is__singleton__the__elem,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( is_singleton @ A )
% 3.49/1.91 = ( ^ [A5: set @ A] :
% 3.49/1.91 ( A5
% 3.49/1.91 = ( insert2 @ A @ ( the_elem @ A @ A5 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_94_typ_Osimps_I5_J,axiom,
% 3.49/1.91 ! [A: $tType,F1: nat > A,F2: type_Mirabelle_typ > type_Mirabelle_typ > A,X1: nat] :
% 3.49/1.91 ( ( type_M1695911984se_typ @ A @ F1 @ F2 @ ( type_Mirabelle_TVar @ X1 ) )
% 3.49/1.91 = ( F1 @ X1 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_95_is__singletonI_H,axiom,
% 3.49/1.91 ! [A: $tType,A3: set @ A] :
% 3.49/1.91 ( ( A3
% 3.49/1.91 != ( bot_bot @ ( set @ A ) ) )
% 3.49/1.91 => ( ! [X: A,Y4: A] :
% 3.49/1.91 ( ( member @ A @ X @ A3 )
% 3.49/1.91 => ( ( member @ A @ Y4 @ A3 )
% 3.49/1.91 => ( X = Y4 ) ) )
% 3.49/1.91 => ( is_singleton @ A @ A3 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_96_ord__eq__less__subst,axiom,
% 3.49/1.91 ! [A: $tType,B: $tType] :
% 3.49/1.91 ( ( ( ord @ B )
% 3.49/1.91 & ( ord @ A ) )
% 3.49/1.91 => ! [A2: A,F: B > A,B3: B,C: B] :
% 3.49/1.91 ( ( A2
% 3.49/1.91 = ( F @ B3 ) )
% 3.49/1.91 => ( ( ord_less @ B @ B3 @ C )
% 3.49/1.91 => ( ! [X: B,Y4: B] :
% 3.49/1.91 ( ( ord_less @ B @ X @ Y4 )
% 3.49/1.91 => ( ord_less @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 3.49/1.91 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_97_ord__less__eq__subst,axiom,
% 3.49/1.91 ! [A: $tType,B: $tType] :
% 3.49/1.91 ( ( ( ord @ B )
% 3.49/1.91 & ( ord @ A ) )
% 3.49/1.91 => ! [A2: A,B3: A,F: A > B,C: B] :
% 3.49/1.91 ( ( ord_less @ A @ A2 @ B3 )
% 3.49/1.91 => ( ( ( F @ B3 )
% 3.49/1.91 = C )
% 3.49/1.91 => ( ! [X: A,Y4: A] :
% 3.49/1.91 ( ( ord_less @ A @ X @ Y4 )
% 3.49/1.91 => ( ord_less @ B @ ( F @ X ) @ ( F @ Y4 ) ) )
% 3.49/1.91 => ( ord_less @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_98_order__less__subst1,axiom,
% 3.49/1.91 ! [A: $tType,B: $tType] :
% 3.49/1.91 ( ( ( order @ B )
% 3.49/1.91 & ( order @ A ) )
% 3.49/1.91 => ! [A2: A,F: B > A,B3: B,C: B] :
% 3.49/1.91 ( ( ord_less @ A @ A2 @ ( F @ B3 ) )
% 3.49/1.91 => ( ( ord_less @ B @ B3 @ C )
% 3.49/1.91 => ( ! [X: B,Y4: B] :
% 3.49/1.91 ( ( ord_less @ B @ X @ Y4 )
% 3.49/1.91 => ( ord_less @ A @ ( F @ X ) @ ( F @ Y4 ) ) )
% 3.49/1.91 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_99_order__less__subst2,axiom,
% 3.49/1.91 ! [A: $tType,C3: $tType] :
% 3.49/1.91 ( ( ( order @ C3 )
% 3.49/1.91 & ( order @ A ) )
% 3.49/1.91 => ! [A2: A,B3: A,F: A > C3,C: C3] :
% 3.49/1.91 ( ( ord_less @ A @ A2 @ B3 )
% 3.49/1.91 => ( ( ord_less @ C3 @ ( F @ B3 ) @ C )
% 3.49/1.91 => ( ! [X: A,Y4: A] :
% 3.49/1.91 ( ( ord_less @ A @ X @ Y4 )
% 3.49/1.91 => ( ord_less @ C3 @ ( F @ X ) @ ( F @ Y4 ) ) )
% 3.49/1.91 => ( ord_less @ C3 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_100_lt__ex,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( no_bot @ A )
% 3.49/1.91 => ! [X3: A] :
% 3.49/1.91 ? [Y4: A] : ( ord_less @ A @ Y4 @ X3 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_101_gt__ex,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( no_top @ A )
% 3.49/1.91 => ! [X3: A] :
% 3.49/1.91 ? [X_1: A] : ( ord_less @ A @ X3 @ X_1 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_102_neqE,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( linorder @ A )
% 3.49/1.91 => ! [X3: A,Y: A] :
% 3.49/1.91 ( ( X3 != Y )
% 3.49/1.91 => ( ~ ( ord_less @ A @ X3 @ Y )
% 3.49/1.91 => ( ord_less @ A @ Y @ X3 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_103_neq__iff,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( linorder @ A )
% 3.49/1.91 => ! [X3: A,Y: A] :
% 3.49/1.91 ( ( X3 != Y )
% 3.49/1.91 = ( ( ord_less @ A @ X3 @ Y )
% 3.49/1.91 | ( ord_less @ A @ Y @ X3 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_104_order_Oasym,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( order @ A )
% 3.49/1.91 => ! [A2: A,B3: A] :
% 3.49/1.91 ( ( ord_less @ A @ A2 @ B3 )
% 3.49/1.91 => ~ ( ord_less @ A @ B3 @ A2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_105_dense,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( dense_order @ A )
% 3.49/1.91 => ! [X3: A,Y: A] :
% 3.49/1.91 ( ( ord_less @ A @ X3 @ Y )
% 3.49/1.91 => ? [Z2: A] :
% 3.49/1.91 ( ( ord_less @ A @ X3 @ Z2 )
% 3.49/1.91 & ( ord_less @ A @ Z2 @ Y ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_106_less__imp__neq,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( order @ A )
% 3.49/1.91 => ! [X3: A,Y: A] :
% 3.49/1.91 ( ( ord_less @ A @ X3 @ Y )
% 3.49/1.91 => ( X3 != Y ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_107_less__asym,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( preorder @ A )
% 3.49/1.91 => ! [X3: A,Y: A] :
% 3.49/1.91 ( ( ord_less @ A @ X3 @ Y )
% 3.49/1.91 => ~ ( ord_less @ A @ Y @ X3 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_108_less__asym_H,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( preorder @ A )
% 3.49/1.91 => ! [A2: A,B3: A] :
% 3.49/1.91 ( ( ord_less @ A @ A2 @ B3 )
% 3.49/1.91 => ~ ( ord_less @ A @ B3 @ A2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_109_less__trans,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( preorder @ A )
% 3.49/1.91 => ! [X3: A,Y: A,Z3: A] :
% 3.49/1.91 ( ( ord_less @ A @ X3 @ Y )
% 3.49/1.91 => ( ( ord_less @ A @ Y @ Z3 )
% 3.49/1.91 => ( ord_less @ A @ X3 @ Z3 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_110_less__linear,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( linorder @ A )
% 3.49/1.91 => ! [X3: A,Y: A] :
% 3.49/1.91 ( ( ord_less @ A @ X3 @ Y )
% 3.49/1.91 | ( X3 = Y )
% 3.49/1.91 | ( ord_less @ A @ Y @ X3 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_111_less__irrefl,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( preorder @ A )
% 3.49/1.91 => ! [X3: A] :
% 3.49/1.91 ~ ( ord_less @ A @ X3 @ X3 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_112_ord__eq__less__trans,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( ord @ A )
% 3.49/1.91 => ! [A2: A,B3: A,C: A] :
% 3.49/1.91 ( ( A2 = B3 )
% 3.49/1.91 => ( ( ord_less @ A @ B3 @ C )
% 3.49/1.91 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_113_ord__less__eq__trans,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( ord @ A )
% 3.49/1.91 => ! [A2: A,B3: A,C: A] :
% 3.49/1.91 ( ( ord_less @ A @ A2 @ B3 )
% 3.49/1.91 => ( ( B3 = C )
% 3.49/1.91 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_114_dual__order_Oasym,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( order @ A )
% 3.49/1.91 => ! [B3: A,A2: A] :
% 3.49/1.91 ( ( ord_less @ A @ B3 @ A2 )
% 3.49/1.91 => ~ ( ord_less @ A @ A2 @ B3 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_115_less__imp__not__eq,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( order @ A )
% 3.49/1.91 => ! [X3: A,Y: A] :
% 3.49/1.91 ( ( ord_less @ A @ X3 @ Y )
% 3.49/1.91 => ( X3 != Y ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_116_less__not__sym,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( preorder @ A )
% 3.49/1.91 => ! [X3: A,Y: A] :
% 3.49/1.91 ( ( ord_less @ A @ X3 @ Y )
% 3.49/1.91 => ~ ( ord_less @ A @ Y @ X3 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_117_less__induct,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( wellorder @ A )
% 3.49/1.91 => ! [P: A > $o,A2: A] :
% 3.49/1.91 ( ! [X: A] :
% 3.49/1.91 ( ! [Y5: A] :
% 3.49/1.91 ( ( ord_less @ A @ Y5 @ X )
% 3.49/1.91 => ( P @ Y5 ) )
% 3.49/1.91 => ( P @ X ) )
% 3.49/1.91 => ( P @ A2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_118_antisym__conv3,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( linorder @ A )
% 3.49/1.91 => ! [Y: A,X3: A] :
% 3.49/1.91 ( ~ ( ord_less @ A @ Y @ X3 )
% 3.49/1.91 => ( ( ~ ( ord_less @ A @ X3 @ Y ) )
% 3.49/1.91 = ( X3 = Y ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_119_less__imp__not__eq2,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( order @ A )
% 3.49/1.91 => ! [X3: A,Y: A] :
% 3.49/1.91 ( ( ord_less @ A @ X3 @ Y )
% 3.49/1.91 => ( Y != X3 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_120_less__imp__triv,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( preorder @ A )
% 3.49/1.91 => ! [X3: A,Y: A,P: $o] :
% 3.49/1.91 ( ( ord_less @ A @ X3 @ Y )
% 3.49/1.91 => ( ( ord_less @ A @ Y @ X3 )
% 3.49/1.91 => P ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_121_linorder__cases,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( linorder @ A )
% 3.49/1.91 => ! [X3: A,Y: A] :
% 3.49/1.91 ( ~ ( ord_less @ A @ X3 @ Y )
% 3.49/1.91 => ( ( X3 != Y )
% 3.49/1.91 => ( ord_less @ A @ Y @ X3 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_122_dual__order_Oirrefl,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( order @ A )
% 3.49/1.91 => ! [A2: A] :
% 3.49/1.91 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_123_order_Ostrict__trans,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( order @ A )
% 3.49/1.91 => ! [A2: A,B3: A,C: A] :
% 3.49/1.91 ( ( ord_less @ A @ A2 @ B3 )
% 3.49/1.91 => ( ( ord_less @ A @ B3 @ C )
% 3.49/1.91 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_124_less__imp__not__less,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( preorder @ A )
% 3.49/1.91 => ! [X3: A,Y: A] :
% 3.49/1.91 ( ( ord_less @ A @ X3 @ Y )
% 3.49/1.91 => ~ ( ord_less @ A @ Y @ X3 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_125_exists__least__iff,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( wellorder @ A )
% 3.49/1.91 => ( ( ^ [P2: A > $o] :
% 3.49/1.91 ? [X5: A] : ( P2 @ X5 ) )
% 3.49/1.91 = ( ^ [P3: A > $o] :
% 3.49/1.91 ? [N3: A] :
% 3.49/1.91 ( ( P3 @ N3 )
% 3.49/1.91 & ! [M2: A] :
% 3.49/1.91 ( ( ord_less @ A @ M2 @ N3 )
% 3.49/1.91 => ~ ( P3 @ M2 ) ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_126_linorder__less__wlog,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( linorder @ A )
% 3.49/1.91 => ! [P: A > A > $o,A2: A,B3: A] :
% 3.49/1.91 ( ! [A6: A,B6: A] :
% 3.49/1.91 ( ( ord_less @ A @ A6 @ B6 )
% 3.49/1.91 => ( P @ A6 @ B6 ) )
% 3.49/1.91 => ( ! [A6: A] : ( P @ A6 @ A6 )
% 3.49/1.91 => ( ! [A6: A,B6: A] :
% 3.49/1.91 ( ( P @ B6 @ A6 )
% 3.49/1.91 => ( P @ A6 @ B6 ) )
% 3.49/1.91 => ( P @ A2 @ B3 ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_127_dual__order_Ostrict__trans,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( order @ A )
% 3.49/1.91 => ! [B3: A,A2: A,C: A] :
% 3.49/1.91 ( ( ord_less @ A @ B3 @ A2 )
% 3.49/1.91 => ( ( ord_less @ A @ C @ B3 )
% 3.49/1.91 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_128_not__less__iff__gr__or__eq,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( linorder @ A )
% 3.49/1.91 => ! [X3: A,Y: A] :
% 3.49/1.91 ( ( ~ ( ord_less @ A @ X3 @ Y ) )
% 3.49/1.91 = ( ( ord_less @ A @ Y @ X3 )
% 3.49/1.91 | ( X3 = Y ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_129_order_Ostrict__implies__not__eq,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( order @ A )
% 3.49/1.91 => ! [A2: A,B3: A] :
% 3.49/1.91 ( ( ord_less @ A @ A2 @ B3 )
% 3.49/1.91 => ( A2 != B3 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_130_dual__order_Ostrict__implies__not__eq,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( order @ A )
% 3.49/1.91 => ! [B3: A,A2: A] :
% 3.49/1.91 ( ( ord_less @ A @ B3 @ A2 )
% 3.49/1.91 => ( A2 != B3 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_131_bot__fun__def,axiom,
% 3.49/1.91 ! [B: $tType,A: $tType] :
% 3.49/1.91 ( ( bot @ B )
% 3.49/1.91 => ( ( bot_bot @ ( A > B ) )
% 3.49/1.91 = ( ^ [X4: A] : ( bot_bot @ B ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_132_mk__scheme_Osimps_I1_J,axiom,
% 3.49/1.91 ! [N2: nat] :
% 3.49/1.91 ( ( type_M540877363scheme @ ( type_Mirabelle_TVar @ N2 ) )
% 3.49/1.91 = ( type_M91906176e_FVar @ N2 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_133_is__singletonE,axiom,
% 3.49/1.91 ! [A: $tType,A3: set @ A] :
% 3.49/1.91 ( ( is_singleton @ A @ A3 )
% 3.49/1.91 => ~ ! [X: A] :
% 3.49/1.91 ( A3
% 3.49/1.91 != ( insert2 @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_134_is__singleton__def,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( is_singleton @ A )
% 3.49/1.91 = ( ^ [A5: set @ A] :
% 3.49/1.91 ? [X4: A] :
% 3.49/1.91 ( A5
% 3.49/1.91 = ( insert2 @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_135_free__tv__id__subst,axiom,
% 3.49/1.91 ( ( type_M950795831ree_tv @ ( nat > type_Mirabelle_typ ) @ type_M17369686_subst )
% 3.49/1.91 = ( bot_bot @ ( set @ nat ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_136_Set_Ois__empty__def,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( is_empty @ A )
% 3.49/1.91 = ( ^ [A5: set @ A] :
% 3.49/1.91 ( A5
% 3.49/1.91 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_137_the__elem__def,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( the_elem @ A )
% 3.49/1.91 = ( ^ [X6: set @ A] :
% 3.49/1.91 ( the @ A
% 3.49/1.91 @ ^ [X4: A] :
% 3.49/1.91 ( X6
% 3.49/1.91 = ( insert2 @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_138_mk__scheme_Osimps_I2_J,axiom,
% 3.49/1.91 ! [T1: type_Mirabelle_typ,T2: type_Mirabelle_typ] :
% 3.49/1.91 ( ( type_M540877363scheme @ ( type_Mirabelle_Fun @ T1 @ T2 ) )
% 3.49/1.91 = ( type_M1518733067e_SFun @ ( type_M540877363scheme @ T1 ) @ ( type_M540877363scheme @ T2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_139_Type__Mirabelle__sfxnzmapfi_Odom__def,axiom,
% 3.49/1.91 ( type_Mirabelle_dom
% 3.49/1.91 = ( ^ [S4: nat > type_Mirabelle_typ] :
% 3.49/1.91 ( collect @ nat
% 3.49/1.91 @ ^ [N3: nat] :
% 3.49/1.91 ( ( S4 @ N3 )
% 3.49/1.91 != ( type_Mirabelle_TVar @ N3 ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_140_id__subst__def,axiom,
% 3.49/1.91 type_M17369686_subst = type_Mirabelle_TVar ).
% 3.49/1.91
% 3.49/1.91 thf(fact_141_typ_Oinject_I2_J,axiom,
% 3.49/1.91 ! [X21: type_Mirabelle_typ,X222: type_Mirabelle_typ,Y21: type_Mirabelle_typ,Y22: type_Mirabelle_typ] :
% 3.49/1.91 ( ( ( type_Mirabelle_Fun @ X21 @ X222 )
% 3.49/1.91 = ( type_Mirabelle_Fun @ Y21 @ Y22 ) )
% 3.49/1.91 = ( ( X21 = Y21 )
% 3.49/1.91 & ( X222 = Y22 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_142_new__tv__Fun,axiom,
% 3.49/1.91 ! [N2: nat,T1: type_Mirabelle_typ,T2: type_Mirabelle_typ] :
% 3.49/1.91 ( ( type_M1046766514new_tv @ type_Mirabelle_typ @ N2 @ ( type_Mirabelle_Fun @ T1 @ T2 ) )
% 3.49/1.91 = ( ( type_M1046766514new_tv @ type_Mirabelle_typ @ N2 @ T1 )
% 3.49/1.91 & ( type_M1046766514new_tv @ type_Mirabelle_typ @ N2 @ T2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_143_dom__id__subst,axiom,
% 3.49/1.91 ( ( type_Mirabelle_dom @ type_M17369686_subst )
% 3.49/1.91 = ( bot_bot @ ( set @ nat ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_144_psubsetD,axiom,
% 3.49/1.91 ! [A: $tType,A3: set @ A,B2: set @ A,C: A] :
% 3.49/1.91 ( ( ord_less @ ( set @ A ) @ A3 @ B2 )
% 3.49/1.91 => ( ( member @ A @ C @ A3 )
% 3.49/1.91 => ( member @ A @ C @ B2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_145_less__set__def,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( ord_less @ ( set @ A ) )
% 3.49/1.91 = ( ^ [A5: set @ A,B5: set @ A] :
% 3.49/1.91 ( ord_less @ ( A > $o )
% 3.49/1.91 @ ^ [X4: A] : ( member @ A @ X4 @ A5 )
% 3.49/1.91 @ ^ [X4: A] : ( member @ A @ X4 @ B5 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_146_psubset__trans,axiom,
% 3.49/1.91 ! [A: $tType,A3: set @ A,B2: set @ A,C4: set @ A] :
% 3.49/1.91 ( ( ord_less @ ( set @ A ) @ A3 @ B2 )
% 3.49/1.91 => ( ( ord_less @ ( set @ A ) @ B2 @ C4 )
% 3.49/1.91 => ( ord_less @ ( set @ A ) @ A3 @ C4 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_147_new__tv__id__subst,axiom,
% 3.49/1.91 ! [N2: nat] : ( type_M1046766514new_tv @ ( nat > type_Mirabelle_typ ) @ N2 @ type_M17369686_subst ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_148_app__subst__Fun,axiom,
% 3.49/1.91 ! [S: nat > type_Mirabelle_typ,T1: type_Mirabelle_typ,T2: type_Mirabelle_typ] :
% 3.49/1.91 ( ( type_M353778473_subst @ type_Mirabelle_typ @ S @ ( type_Mirabelle_Fun @ T1 @ T2 ) )
% 3.49/1.91 = ( type_Mirabelle_Fun @ ( type_M353778473_subst @ type_Mirabelle_typ @ S @ T1 ) @ ( type_M353778473_subst @ type_Mirabelle_typ @ S @ T2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_149_typ_Oexhaust,axiom,
% 3.49/1.91 ! [Y: type_Mirabelle_typ] :
% 3.49/1.91 ( ! [X13: nat] :
% 3.49/1.91 ( Y
% 3.49/1.91 != ( type_Mirabelle_TVar @ X13 ) )
% 3.49/1.91 => ~ ! [X212: type_Mirabelle_typ,X223: type_Mirabelle_typ] :
% 3.49/1.91 ( Y
% 3.49/1.91 != ( type_Mirabelle_Fun @ X212 @ X223 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_150_typ_Oinduct,axiom,
% 3.49/1.91 ! [P: type_Mirabelle_typ > $o,Typ: type_Mirabelle_typ] :
% 3.49/1.91 ( ! [X: nat] : ( P @ ( type_Mirabelle_TVar @ X ) )
% 3.49/1.91 => ( ! [X1a: type_Mirabelle_typ,X23: type_Mirabelle_typ] :
% 3.49/1.91 ( ( P @ X1a )
% 3.49/1.91 => ( ( P @ X23 )
% 3.49/1.91 => ( P @ ( type_Mirabelle_Fun @ X1a @ X23 ) ) ) )
% 3.49/1.91 => ( P @ Typ ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_151_typ_Odistinct_I1_J,axiom,
% 3.49/1.91 ! [X1: nat,X21: type_Mirabelle_typ,X222: type_Mirabelle_typ] :
% 3.49/1.91 ( ( type_Mirabelle_TVar @ X1 )
% 3.49/1.91 != ( type_Mirabelle_Fun @ X21 @ X222 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_152_typ_Osimps_I6_J,axiom,
% 3.49/1.91 ! [A: $tType,F1: nat > A,F2: type_Mirabelle_typ > type_Mirabelle_typ > A,X21: type_Mirabelle_typ,X222: type_Mirabelle_typ] :
% 3.49/1.91 ( ( type_M1695911984se_typ @ A @ F1 @ F2 @ ( type_Mirabelle_Fun @ X21 @ X222 ) )
% 3.49/1.91 = ( F2 @ X21 @ X222 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_153_the__sym__eq__trivial,axiom,
% 3.49/1.91 ! [A: $tType,X3: A] :
% 3.49/1.91 ( ( the @ A
% 3.49/1.91 @ ( ^ [Y3: A,Z: A] : ( Y3 = Z )
% 3.49/1.91 @ X3 ) )
% 3.49/1.91 = X3 ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_154_the__eq__trivial,axiom,
% 3.49/1.91 ! [A: $tType,A2: A] :
% 3.49/1.91 ( ( the @ A
% 3.49/1.91 @ ^ [X4: A] : ( X4 = A2 ) )
% 3.49/1.91 = A2 ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_155_the__equality,axiom,
% 3.49/1.91 ! [A: $tType,P: A > $o,A2: A] :
% 3.49/1.91 ( ( P @ A2 )
% 3.49/1.91 => ( ! [X: A] :
% 3.49/1.91 ( ( P @ X )
% 3.49/1.91 => ( X = A2 ) )
% 3.49/1.91 => ( ( the @ A @ P )
% 3.49/1.91 = A2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_156_cod__id__subst,axiom,
% 3.49/1.91 ( ( type_Mirabelle_cod @ type_M17369686_subst )
% 3.49/1.91 = ( bot_bot @ ( set @ nat ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_157_theI,axiom,
% 3.49/1.91 ! [A: $tType,P: A > $o,A2: A] :
% 3.49/1.91 ( ( P @ A2 )
% 3.49/1.91 => ( ! [X: A] :
% 3.49/1.91 ( ( P @ X )
% 3.49/1.91 => ( X = A2 ) )
% 3.49/1.91 => ( P @ ( the @ A @ P ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_158_theI_H,axiom,
% 3.49/1.91 ! [A: $tType,P: A > $o] :
% 3.49/1.91 ( ? [X7: A] :
% 3.49/1.91 ( ( P @ X7 )
% 3.49/1.91 & ! [Y4: A] :
% 3.49/1.91 ( ( P @ Y4 )
% 3.49/1.91 => ( Y4 = X7 ) ) )
% 3.49/1.91 => ( P @ ( the @ A @ P ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_159_theI2,axiom,
% 3.49/1.91 ! [A: $tType,P: A > $o,A2: A,Q: A > $o] :
% 3.49/1.91 ( ( P @ A2 )
% 3.49/1.91 => ( ! [X: A] :
% 3.49/1.91 ( ( P @ X )
% 3.49/1.91 => ( X = A2 ) )
% 3.49/1.91 => ( ! [X: A] :
% 3.49/1.91 ( ( P @ X )
% 3.49/1.91 => ( Q @ X ) )
% 3.49/1.91 => ( Q @ ( the @ A @ P ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_160_If__def,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( if @ A )
% 3.49/1.91 = ( ^ [P3: $o,X4: A,Y6: A] :
% 3.49/1.91 ( the @ A
% 3.49/1.91 @ ^ [Z4: A] :
% 3.49/1.91 ( ( P3
% 3.49/1.91 => ( Z4 = X4 ) )
% 3.49/1.91 & ( ~ P3
% 3.49/1.91 => ( Z4 = Y6 ) ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_161_the1I2,axiom,
% 3.49/1.91 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.49/1.91 ( ? [X7: A] :
% 3.49/1.91 ( ( P @ X7 )
% 3.49/1.91 & ! [Y4: A] :
% 3.49/1.91 ( ( P @ Y4 )
% 3.49/1.91 => ( Y4 = X7 ) ) )
% 3.49/1.91 => ( ! [X: A] :
% 3.49/1.91 ( ( P @ X )
% 3.49/1.91 => ( Q @ X ) )
% 3.49/1.91 => ( Q @ ( the @ A @ P ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_162_the1__equality,axiom,
% 3.49/1.91 ! [A: $tType,P: A > $o,A2: A] :
% 3.49/1.91 ( ? [X7: A] :
% 3.49/1.91 ( ( P @ X7 )
% 3.49/1.91 & ! [Y4: A] :
% 3.49/1.91 ( ( P @ Y4 )
% 3.49/1.91 => ( Y4 = X7 ) ) )
% 3.49/1.91 => ( ( P @ A2 )
% 3.49/1.91 => ( ( the @ A @ P )
% 3.49/1.91 = A2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_163_Collect__empty__eq__bot,axiom,
% 3.49/1.91 ! [A: $tType,P: A > $o] :
% 3.49/1.91 ( ( ( collect @ A @ P )
% 3.49/1.91 = ( bot_bot @ ( set @ A ) ) )
% 3.49/1.91 = ( P
% 3.49/1.91 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_164_bot__empty__eq,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( bot_bot @ ( A > $o ) )
% 3.49/1.91 = ( ^ [X4: A] : ( member @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_165_free__tv__subst,axiom,
% 3.49/1.91 ( ( type_M950795831ree_tv @ ( nat > type_Mirabelle_typ ) )
% 3.49/1.91 = ( ^ [S4: nat > type_Mirabelle_typ] : ( sup_sup @ ( set @ nat ) @ ( type_Mirabelle_dom @ S4 ) @ ( type_Mirabelle_cod @ S4 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_166_UnCI,axiom,
% 3.49/1.91 ! [A: $tType,C: A,B2: set @ A,A3: set @ A] :
% 3.49/1.91 ( ( ~ ( member @ A @ C @ B2 )
% 3.49/1.91 => ( member @ A @ C @ A3 ) )
% 3.49/1.91 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_167_Un__iff,axiom,
% 3.49/1.91 ! [A: $tType,C: A,A3: set @ A,B2: set @ A] :
% 3.49/1.91 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 3.49/1.91 = ( ( member @ A @ C @ A3 )
% 3.49/1.91 | ( member @ A @ C @ B2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_168_Un__empty,axiom,
% 3.49/1.91 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 3.49/1.91 ( ( ( sup_sup @ ( set @ A ) @ A3 @ B2 )
% 3.49/1.91 = ( bot_bot @ ( set @ A ) ) )
% 3.49/1.91 = ( ( A3
% 3.49/1.91 = ( bot_bot @ ( set @ A ) ) )
% 3.49/1.91 & ( B2
% 3.49/1.91 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_169_Un__insert__left,axiom,
% 3.49/1.91 ! [A: $tType,A2: A,B2: set @ A,C4: set @ A] :
% 3.49/1.91 ( ( sup_sup @ ( set @ A ) @ ( insert2 @ A @ A2 @ B2 ) @ C4 )
% 3.49/1.91 = ( insert2 @ A @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_170_Un__insert__right,axiom,
% 3.49/1.91 ! [A: $tType,A3: set @ A,A2: A,B2: set @ A] :
% 3.49/1.91 ( ( sup_sup @ ( set @ A ) @ A3 @ ( insert2 @ A @ A2 @ B2 ) )
% 3.49/1.91 = ( insert2 @ A @ A2 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_171_weaken__asm__Un,axiom,
% 3.49/1.91 ! [A: $tType,A3: set @ A,P: A > $o,Q: $o,B2: set @ A] :
% 3.49/1.91 ( ( ! [X7: A] :
% 3.49/1.91 ( ( member @ A @ X7 @ A3 )
% 3.49/1.91 => ( P @ X7 ) )
% 3.49/1.91 => Q )
% 3.49/1.91 => ( ! [X: A] :
% 3.49/1.91 ( ( member @ A @ X @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 3.49/1.91 => ( P @ X ) )
% 3.49/1.91 => Q ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_172_UnE,axiom,
% 3.49/1.91 ! [A: $tType,C: A,A3: set @ A,B2: set @ A] :
% 3.49/1.91 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 3.49/1.91 => ( ~ ( member @ A @ C @ A3 )
% 3.49/1.91 => ( member @ A @ C @ B2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_173_UnI1,axiom,
% 3.49/1.91 ! [A: $tType,C: A,A3: set @ A,B2: set @ A] :
% 3.49/1.91 ( ( member @ A @ C @ A3 )
% 3.49/1.91 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_174_UnI2,axiom,
% 3.49/1.91 ! [A: $tType,C: A,B2: set @ A,A3: set @ A] :
% 3.49/1.91 ( ( member @ A @ C @ B2 )
% 3.49/1.91 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_175_Un__def,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( sup_sup @ ( set @ A ) )
% 3.49/1.91 = ( ^ [A5: set @ A,B5: set @ A] :
% 3.49/1.91 ( collect @ A
% 3.49/1.91 @ ^ [X4: A] :
% 3.49/1.91 ( ( member @ A @ X4 @ A5 )
% 3.49/1.91 | ( member @ A @ X4 @ B5 ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_176_bex__Un,axiom,
% 3.49/1.91 ! [A: $tType,A3: set @ A,B2: set @ A,P: A > $o] :
% 3.49/1.91 ( ( ? [X4: A] :
% 3.49/1.91 ( ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 3.49/1.91 & ( P @ X4 ) ) )
% 3.49/1.91 = ( ? [X4: A] :
% 3.49/1.91 ( ( member @ A @ X4 @ A3 )
% 3.49/1.91 & ( P @ X4 ) )
% 3.49/1.91 | ? [X4: A] :
% 3.49/1.91 ( ( member @ A @ X4 @ B2 )
% 3.49/1.91 & ( P @ X4 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_177_ball__Un,axiom,
% 3.49/1.91 ! [A: $tType,A3: set @ A,B2: set @ A,P: A > $o] :
% 3.49/1.91 ( ( ! [X4: A] :
% 3.49/1.91 ( ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 3.49/1.91 => ( P @ X4 ) ) )
% 3.49/1.91 = ( ! [X4: A] :
% 3.49/1.91 ( ( member @ A @ X4 @ A3 )
% 3.49/1.91 => ( P @ X4 ) )
% 3.49/1.91 & ! [X4: A] :
% 3.49/1.91 ( ( member @ A @ X4 @ B2 )
% 3.49/1.91 => ( P @ X4 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_178_Un__assoc,axiom,
% 3.49/1.91 ! [A: $tType,A3: set @ A,B2: set @ A,C4: set @ A] :
% 3.49/1.91 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) @ C4 )
% 3.49/1.91 = ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_179_Un__absorb,axiom,
% 3.49/1.91 ! [A: $tType,A3: set @ A] :
% 3.49/1.91 ( ( sup_sup @ ( set @ A ) @ A3 @ A3 )
% 3.49/1.91 = A3 ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_180_Un__commute,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( sup_sup @ ( set @ A ) )
% 3.49/1.91 = ( ^ [A5: set @ A,B5: set @ A] : ( sup_sup @ ( set @ A ) @ B5 @ A5 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_181_Un__left__absorb,axiom,
% 3.49/1.91 ! [A: $tType,A3: set @ A,B2: set @ A] :
% 3.49/1.91 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 3.49/1.91 = ( sup_sup @ ( set @ A ) @ A3 @ B2 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_182_Collect__disj__eq,axiom,
% 3.49/1.91 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.49/1.91 ( ( collect @ A
% 3.49/1.91 @ ^ [X4: A] :
% 3.49/1.91 ( ( P @ X4 )
% 3.49/1.91 | ( Q @ X4 ) ) )
% 3.49/1.91 = ( sup_sup @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_183_Un__left__commute,axiom,
% 3.49/1.91 ! [A: $tType,A3: set @ A,B2: set @ A,C4: set @ A] :
% 3.49/1.91 ( ( sup_sup @ ( set @ A ) @ A3 @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) )
% 3.49/1.91 = ( sup_sup @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A3 @ C4 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_184_insert__def,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( insert2 @ A )
% 3.49/1.91 = ( ^ [A4: A] :
% 3.49/1.91 ( sup_sup @ ( set @ A )
% 3.49/1.91 @ ( collect @ A
% 3.49/1.91 @ ^ [X4: A] : ( X4 = A4 ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_185_Un__empty__left,axiom,
% 3.49/1.91 ! [A: $tType,B2: set @ A] :
% 3.49/1.91 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B2 )
% 3.49/1.91 = B2 ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_186_Un__empty__right,axiom,
% 3.49/1.91 ! [A: $tType,A3: set @ A] :
% 3.49/1.91 ( ( sup_sup @ ( set @ A ) @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 3.49/1.91 = A3 ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_187_singleton__Un__iff,axiom,
% 3.49/1.91 ! [A: $tType,X3: A,A3: set @ A,B2: set @ A] :
% 3.49/1.91 ( ( ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) )
% 3.49/1.91 = ( sup_sup @ ( set @ A ) @ A3 @ B2 ) )
% 3.49/1.91 = ( ( ( A3
% 3.49/1.91 = ( bot_bot @ ( set @ A ) ) )
% 3.49/1.91 & ( B2
% 3.49/1.91 = ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.49/1.91 | ( ( A3
% 3.49/1.91 = ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.49/1.91 & ( B2
% 3.49/1.91 = ( bot_bot @ ( set @ A ) ) ) )
% 3.49/1.91 | ( ( A3
% 3.49/1.91 = ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.49/1.91 & ( B2
% 3.49/1.91 = ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_188_Un__singleton__iff,axiom,
% 3.49/1.91 ! [A: $tType,A3: set @ A,B2: set @ A,X3: A] :
% 3.49/1.91 ( ( ( sup_sup @ ( set @ A ) @ A3 @ B2 )
% 3.49/1.91 = ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.49/1.91 = ( ( ( A3
% 3.49/1.91 = ( bot_bot @ ( set @ A ) ) )
% 3.49/1.91 & ( B2
% 3.49/1.91 = ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.49/1.91 | ( ( A3
% 3.49/1.91 = ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.49/1.91 & ( B2
% 3.49/1.91 = ( bot_bot @ ( set @ A ) ) ) )
% 3.49/1.91 | ( ( A3
% 3.49/1.91 = ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.49/1.91 & ( B2
% 3.49/1.91 = ( insert2 @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_189_insert__is__Un,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( insert2 @ A )
% 3.49/1.91 = ( ^ [A4: A] : ( sup_sup @ ( set @ A ) @ ( insert2 @ A @ A4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_190_bound__tv__list_Osimps_I2_J,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( type_M1470978233struct @ A )
% 3.49/1.91 => ! [X3: A,L: list @ A] :
% 3.49/1.91 ( ( type_M779184887und_tv @ ( list @ A ) @ ( cons @ A @ X3 @ L ) )
% 3.49/1.91 = ( sup_sup @ ( set @ nat ) @ ( type_M779184887und_tv @ A @ X3 ) @ ( type_M779184887und_tv @ ( list @ A ) @ L ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_191_free__tv__Fun,axiom,
% 3.49/1.91 ! [T1: type_Mirabelle_typ,T2: type_Mirabelle_typ] :
% 3.49/1.91 ( ( type_M950795831ree_tv @ type_Mirabelle_typ @ ( type_Mirabelle_Fun @ T1 @ T2 ) )
% 3.49/1.91 = ( sup_sup @ ( set @ nat ) @ ( type_M950795831ree_tv @ type_Mirabelle_typ @ T1 ) @ ( type_M950795831ree_tv @ type_Mirabelle_typ @ T2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_192_free__tv__type__scheme_Osimps_I3_J,axiom,
% 3.49/1.91 ! [S1: type_M1610475166scheme,S2: type_M1610475166scheme] :
% 3.49/1.91 ( ( type_M950795831ree_tv @ type_M1610475166scheme @ ( type_M1518733067e_SFun @ S1 @ S2 ) )
% 3.49/1.91 = ( sup_sup @ ( set @ nat ) @ ( type_M950795831ree_tv @ type_M1610475166scheme @ S1 ) @ ( type_M950795831ree_tv @ type_M1610475166scheme @ S2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_193_bound__tv__type__scheme_Osimps_I3_J,axiom,
% 3.49/1.91 ! [S1: type_M1610475166scheme,S2: type_M1610475166scheme] :
% 3.49/1.91 ( ( type_M779184887und_tv @ type_M1610475166scheme @ ( type_M1518733067e_SFun @ S1 @ S2 ) )
% 3.49/1.91 = ( sup_sup @ ( set @ nat ) @ ( type_M779184887und_tv @ type_M1610475166scheme @ S1 ) @ ( type_M779184887und_tv @ type_M1610475166scheme @ S2 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_194_free__tv__list_Osimps_I2_J,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( type_M1470978233struct @ A )
% 3.49/1.91 => ! [X3: A,L: list @ A] :
% 3.49/1.91 ( ( type_M950795831ree_tv @ ( list @ A ) @ ( cons @ A @ X3 @ L ) )
% 3.49/1.91 = ( sup_sup @ ( set @ nat ) @ ( type_M950795831ree_tv @ A @ X3 ) @ ( type_M950795831ree_tv @ ( list @ A ) @ L ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_195_free__tv__fun__def,axiom,
% 3.49/1.91 ! [B: $tType,A: $tType] :
% 3.49/1.91 ( ( ( type_M201404320of_nat @ A )
% 3.49/1.91 & ( type_M1535146424typ_of @ B ) )
% 3.49/1.91 => ( ( type_M950795831ree_tv @ ( A > B ) )
% 3.49/1.91 = ( ^ [F4: A > B] :
% 3.49/1.91 ( sup_sup @ ( set @ nat )
% 3.49/1.91 @ ( type_Mirabelle_dom
% 3.49/1.91 @ ^ [N3: nat] : ( type_M604437996typ_of @ B @ ( F4 @ ( type_M167561660of_nat @ A @ N3 ) ) ) )
% 3.49/1.91 @ ( type_Mirabelle_cod
% 3.49/1.91 @ ^ [N3: nat] : ( type_M604437996typ_of @ B @ ( F4 @ ( type_M167561660of_nat @ A @ N3 ) ) ) ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_196_sup__bot__left,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( bounde1808546759up_bot @ A )
% 3.49/1.91 => ! [X3: A] :
% 3.49/1.91 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X3 )
% 3.49/1.91 = X3 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_197_sup__bot__right,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( bounde1808546759up_bot @ A )
% 3.49/1.91 => ! [X3: A] :
% 3.49/1.91 ( ( sup_sup @ A @ X3 @ ( bot_bot @ A ) )
% 3.49/1.91 = X3 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_198_sup__bot_Oright__neutral,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( bounde1808546759up_bot @ A )
% 3.49/1.91 => ! [A2: A] :
% 3.49/1.91 ( ( sup_sup @ A @ A2 @ ( bot_bot @ A ) )
% 3.49/1.91 = A2 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_199_sup__bot_Oneutr__eq__iff,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( bounde1808546759up_bot @ A )
% 3.49/1.91 => ! [A2: A,B3: A] :
% 3.49/1.91 ( ( ( bot_bot @ A )
% 3.49/1.91 = ( sup_sup @ A @ A2 @ B3 ) )
% 3.49/1.91 = ( ( A2
% 3.49/1.91 = ( bot_bot @ A ) )
% 3.49/1.91 & ( B3
% 3.49/1.91 = ( bot_bot @ A ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_200_sup__bot_Oleft__neutral,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( bounde1808546759up_bot @ A )
% 3.49/1.91 => ! [A2: A] :
% 3.49/1.91 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A2 )
% 3.49/1.91 = A2 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_201_sup__bot_Oeq__neutr__iff,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( bounde1808546759up_bot @ A )
% 3.49/1.91 => ! [A2: A,B3: A] :
% 3.49/1.91 ( ( ( sup_sup @ A @ A2 @ B3 )
% 3.49/1.91 = ( bot_bot @ A ) )
% 3.49/1.91 = ( ( A2
% 3.49/1.91 = ( bot_bot @ A ) )
% 3.49/1.91 & ( B3
% 3.49/1.91 = ( bot_bot @ A ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_202_sup__eq__bot__iff,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( bounde1808546759up_bot @ A )
% 3.49/1.91 => ! [X3: A,Y: A] :
% 3.49/1.91 ( ( ( sup_sup @ A @ X3 @ Y )
% 3.49/1.91 = ( bot_bot @ A ) )
% 3.49/1.91 = ( ( X3
% 3.49/1.91 = ( bot_bot @ A ) )
% 3.49/1.91 & ( Y
% 3.49/1.91 = ( bot_bot @ A ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_203_bot__eq__sup__iff,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( bounde1808546759up_bot @ A )
% 3.49/1.91 => ! [X3: A,Y: A] :
% 3.49/1.91 ( ( ( bot_bot @ A )
% 3.49/1.91 = ( sup_sup @ A @ X3 @ Y ) )
% 3.49/1.91 = ( ( X3
% 3.49/1.91 = ( bot_bot @ A ) )
% 3.49/1.91 & ( Y
% 3.49/1.91 = ( bot_bot @ A ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_204_sup__Un__eq,axiom,
% 3.49/1.91 ! [A: $tType,R: set @ A,S: set @ A] :
% 3.49/1.91 ( ( sup_sup @ ( A > $o )
% 3.49/1.91 @ ^ [X4: A] : ( member @ A @ X4 @ R )
% 3.49/1.91 @ ^ [X4: A] : ( member @ A @ X4 @ S ) )
% 3.49/1.91 = ( ^ [X4: A] : ( member @ A @ X4 @ ( sup_sup @ ( set @ A ) @ R @ S ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_205_sup__set__def,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( sup_sup @ ( set @ A ) )
% 3.49/1.91 = ( ^ [A5: set @ A,B5: set @ A] :
% 3.49/1.91 ( collect @ A
% 3.49/1.91 @ ( sup_sup @ ( A > $o )
% 3.49/1.91 @ ^ [X4: A] : ( member @ A @ X4 @ A5 )
% 3.49/1.91 @ ^ [X4: A] : ( member @ A @ X4 @ B5 ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_206_less__supI1,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( semilattice_sup @ A )
% 3.49/1.91 => ! [X3: A,A2: A,B3: A] :
% 3.49/1.91 ( ( ord_less @ A @ X3 @ A2 )
% 3.49/1.91 => ( ord_less @ A @ X3 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_207_less__supI2,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( semilattice_sup @ A )
% 3.49/1.91 => ! [X3: A,B3: A,A2: A] :
% 3.49/1.91 ( ( ord_less @ A @ X3 @ B3 )
% 3.49/1.91 => ( ord_less @ A @ X3 @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_208_sup_Ostrict__boundedE,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( semilattice_sup @ A )
% 3.49/1.91 => ! [B3: A,C: A,A2: A] :
% 3.49/1.91 ( ( ord_less @ A @ ( sup_sup @ A @ B3 @ C ) @ A2 )
% 3.49/1.91 => ~ ( ( ord_less @ A @ B3 @ A2 )
% 3.49/1.91 => ~ ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_209_sup_Ostrict__order__iff,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( semilattice_sup @ A )
% 3.49/1.91 => ( ( ord_less @ A )
% 3.49/1.91 = ( ^ [B7: A,A4: A] :
% 3.49/1.91 ( ( A4
% 3.49/1.91 = ( sup_sup @ A @ A4 @ B7 ) )
% 3.49/1.91 & ( A4 != B7 ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_210_sup_Ostrict__coboundedI1,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( semilattice_sup @ A )
% 3.49/1.91 => ! [C: A,A2: A,B3: A] :
% 3.49/1.91 ( ( ord_less @ A @ C @ A2 )
% 3.49/1.91 => ( ord_less @ A @ C @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_211_sup_Ostrict__coboundedI2,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( semilattice_sup @ A )
% 3.49/1.91 => ! [C: A,B3: A,A2: A] :
% 3.49/1.91 ( ( ord_less @ A @ C @ B3 )
% 3.49/1.91 => ( ord_less @ A @ C @ ( sup_sup @ A @ A2 @ B3 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_212_Nitpick_OThe__psimp,axiom,
% 3.49/1.91 ! [A: $tType,P: A > $o,X3: A] :
% 3.49/1.91 ( ( P
% 3.49/1.91 = ( ^ [Y3: A,Z: A] : ( Y3 = Z )
% 3.49/1.91 @ X3 ) )
% 3.49/1.91 => ( ( the @ A @ P )
% 3.49/1.91 = X3 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_213_theI__unique,axiom,
% 3.49/1.91 ! [A: $tType,P: A > $o,X3: A] :
% 3.49/1.91 ( ? [X7: A] :
% 3.49/1.91 ( ( P @ X7 )
% 3.49/1.91 & ! [Y4: A] :
% 3.49/1.91 ( ( P @ Y4 )
% 3.49/1.91 => ( Y4 = X7 ) ) )
% 3.49/1.91 => ( ( P @ X3 )
% 3.49/1.91 = ( X3
% 3.49/1.91 = ( the @ A @ P ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_214_sup__bot_Osemilattice__neutr__axioms,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( bounde1808546759up_bot @ A )
% 3.49/1.91 => ( semilattice_neutr @ A @ ( sup_sup @ A ) @ ( bot_bot @ A ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_215_lexordp__eq__simps_I4_J,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( ord @ A )
% 3.49/1.91 => ! [X3: A,Xs: list @ A,Y: A,Ys: list @ A] :
% 3.49/1.91 ( ( ord_lexordp_eq @ A @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys ) )
% 3.49/1.91 = ( ( ord_less @ A @ X3 @ Y )
% 3.49/1.91 | ( ~ ( ord_less @ A @ Y @ X3 )
% 3.49/1.91 & ( ord_lexordp_eq @ A @ Xs @ Ys ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_216_lexordp__eq_OCons__eq,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( ord @ A )
% 3.49/1.91 => ! [X3: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 3.49/1.91 ( ~ ( ord_less @ A @ X3 @ Y )
% 3.49/1.91 => ( ~ ( ord_less @ A @ Y @ X3 )
% 3.49/1.91 => ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 3.49/1.91 => ( ord_lexordp_eq @ A @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_217_lexordp__eq_OCons,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( ord @ A )
% 3.49/1.91 => ! [X3: A,Y: A,Xs: list @ A,Ys: list @ A] :
% 3.49/1.91 ( ( ord_less @ A @ X3 @ Y )
% 3.49/1.91 => ( ord_lexordp_eq @ A @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_218_lexordp__eq__antisym,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( linorder @ A )
% 3.49/1.91 => ! [Xs: list @ A,Ys: list @ A] :
% 3.49/1.91 ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 3.49/1.91 => ( ( ord_lexordp_eq @ A @ Ys @ Xs )
% 3.49/1.91 => ( Xs = Ys ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_219_lexordp__eq__linear,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( linorder @ A )
% 3.49/1.91 => ! [Xs: list @ A,Ys: list @ A] :
% 3.49/1.91 ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 3.49/1.91 | ( ord_lexordp_eq @ A @ Ys @ Xs ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_220_lexordp__eq__trans,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( linorder @ A )
% 3.49/1.91 => ! [Xs: list @ A,Ys: list @ A,Zs: list @ A] :
% 3.49/1.91 ( ( ord_lexordp_eq @ A @ Xs @ Ys )
% 3.49/1.91 => ( ( ord_lexordp_eq @ A @ Ys @ Zs )
% 3.49/1.91 => ( ord_lexordp_eq @ A @ Xs @ Zs ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_221_lexordp__eq__refl,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( ord @ A )
% 3.49/1.91 => ! [Xs: list @ A] : ( ord_lexordp_eq @ A @ Xs @ Xs ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_222_lexordp__eq_Ocases,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( ord @ A )
% 3.49/1.91 => ! [A1: list @ A,A22: list @ A] :
% 3.49/1.91 ( ( ord_lexordp_eq @ A @ A1 @ A22 )
% 3.49/1.91 => ( ( A1
% 3.49/1.91 != ( nil @ A ) )
% 3.49/1.91 => ( ! [X: A] :
% 3.49/1.91 ( ? [Xs2: list @ A] :
% 3.49/1.91 ( A1
% 3.49/1.91 = ( cons @ A @ X @ Xs2 ) )
% 3.49/1.91 => ! [Y4: A] :
% 3.49/1.91 ( ? [Ys2: list @ A] :
% 3.49/1.91 ( A22
% 3.49/1.91 = ( cons @ A @ Y4 @ Ys2 ) )
% 3.49/1.91 => ~ ( ord_less @ A @ X @ Y4 ) ) )
% 3.49/1.91 => ~ ! [X: A,Y4: A,Xs2: list @ A] :
% 3.49/1.91 ( ( A1
% 3.49/1.91 = ( cons @ A @ X @ Xs2 ) )
% 3.49/1.91 => ! [Ys2: list @ A] :
% 3.49/1.91 ( ( A22
% 3.49/1.91 = ( cons @ A @ Y4 @ Ys2 ) )
% 3.49/1.91 => ( ~ ( ord_less @ A @ X @ Y4 )
% 3.49/1.91 => ( ~ ( ord_less @ A @ Y4 @ X )
% 3.49/1.91 => ~ ( ord_lexordp_eq @ A @ Xs2 @ Ys2 ) ) ) ) ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_223_lexordp__eq_Osimps,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( ord @ A )
% 3.49/1.91 => ( ( ord_lexordp_eq @ A )
% 3.49/1.91 = ( ^ [A12: list @ A,A23: list @ A] :
% 3.49/1.91 ( ? [Ys3: list @ A] :
% 3.49/1.91 ( ( A12
% 3.49/1.91 = ( nil @ A ) )
% 3.49/1.91 & ( A23 = Ys3 ) )
% 3.49/1.91 | ? [X4: A,Y6: A,Xs3: list @ A,Ys3: list @ A] :
% 3.49/1.91 ( ( A12
% 3.49/1.91 = ( cons @ A @ X4 @ Xs3 ) )
% 3.49/1.91 & ( A23
% 3.49/1.91 = ( cons @ A @ Y6 @ Ys3 ) )
% 3.49/1.91 & ( ord_less @ A @ X4 @ Y6 ) )
% 3.49/1.91 | ? [X4: A,Y6: A,Xs3: list @ A,Ys3: list @ A] :
% 3.49/1.91 ( ( A12
% 3.49/1.91 = ( cons @ A @ X4 @ Xs3 ) )
% 3.49/1.91 & ( A23
% 3.49/1.91 = ( cons @ A @ Y6 @ Ys3 ) )
% 3.49/1.91 & ~ ( ord_less @ A @ X4 @ Y6 )
% 3.49/1.91 & ~ ( ord_less @ A @ Y6 @ X4 )
% 3.49/1.91 & ( ord_lexordp_eq @ A @ Xs3 @ Ys3 ) ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_224_lexordp__eq__simps_I1_J,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( ord @ A )
% 3.49/1.91 => ! [Ys: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_225_lexordp__eq__simps_I2_J,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( ord @ A )
% 3.49/1.91 => ! [Xs: list @ A] :
% 3.49/1.91 ( ( ord_lexordp_eq @ A @ Xs @ ( nil @ A ) )
% 3.49/1.91 = ( Xs
% 3.49/1.91 = ( nil @ A ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_226_app__subst__Nil,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( type_M1470978233struct @ A )
% 3.49/1.91 => ! [S: nat > type_Mirabelle_typ] :
% 3.49/1.91 ( ( type_M353778473_subst @ ( list @ A ) @ S @ ( nil @ A ) )
% 3.49/1.91 = ( nil @ A ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_227_lexordp__eq__simps_I3_J,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( ord @ A )
% 3.49/1.91 => ! [X3: A,Xs: list @ A] :
% 3.49/1.91 ~ ( ord_lexordp_eq @ A @ ( cons @ A @ X3 @ Xs ) @ ( nil @ A ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_228_lexordp__eq_ONil,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( ord @ A )
% 3.49/1.91 => ! [Ys: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_229_new__tv__Nil,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( type_M1470978233struct @ A )
% 3.49/1.91 => ! [N2: nat] : ( type_M1046766514new_tv @ ( list @ A ) @ N2 @ ( nil @ A ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_230_transpose_Ocases,axiom,
% 3.49/1.91 ! [A: $tType,X3: list @ ( list @ A )] :
% 3.49/1.91 ( ( X3
% 3.49/1.91 != ( nil @ ( list @ A ) ) )
% 3.49/1.91 => ( ! [Xss: list @ ( list @ A )] :
% 3.49/1.91 ( X3
% 3.49/1.91 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 3.49/1.91 => ~ ! [X: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 3.49/1.91 ( X3
% 3.49/1.91 != ( cons @ ( list @ A ) @ ( cons @ A @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_231_list_Odistinct_I1_J,axiom,
% 3.49/1.91 ! [A: $tType,X21: A,X222: list @ A] :
% 3.49/1.91 ( ( nil @ A )
% 3.49/1.91 != ( cons @ A @ X21 @ X222 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_232_list_OdiscI,axiom,
% 3.49/1.91 ! [A: $tType,List: list @ A,X21: A,X222: list @ A] :
% 3.49/1.91 ( ( List
% 3.49/1.91 = ( cons @ A @ X21 @ X222 ) )
% 3.49/1.91 => ( List
% 3.49/1.91 != ( nil @ A ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_233_list_Oexhaust,axiom,
% 3.49/1.91 ! [A: $tType,Y: list @ A] :
% 3.49/1.91 ( ( Y
% 3.49/1.91 != ( nil @ A ) )
% 3.49/1.91 => ~ ! [X212: A,X223: list @ A] :
% 3.49/1.91 ( Y
% 3.49/1.91 != ( cons @ A @ X212 @ X223 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_234_list_Oinducts,axiom,
% 3.49/1.91 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 3.49/1.91 ( ( P @ ( nil @ A ) )
% 3.49/1.91 => ( ! [X13: A,X23: list @ A] :
% 3.49/1.91 ( ( P @ X23 )
% 3.49/1.91 => ( P @ ( cons @ A @ X13 @ X23 ) ) )
% 3.49/1.91 => ( P @ List ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_235_neq__Nil__conv,axiom,
% 3.49/1.91 ! [A: $tType,Xs: list @ A] :
% 3.49/1.91 ( ( Xs
% 3.49/1.91 != ( nil @ A ) )
% 3.49/1.91 = ( ? [Y6: A,Ys3: list @ A] :
% 3.49/1.91 ( Xs
% 3.49/1.91 = ( cons @ A @ Y6 @ Ys3 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_236_list__induct2_H,axiom,
% 3.49/1.91 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 3.49/1.91 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 3.49/1.91 => ( ! [X: A,Xs2: list @ A] : ( P @ ( cons @ A @ X @ Xs2 ) @ ( nil @ B ) )
% 3.49/1.91 => ( ! [Y4: B,Ys2: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y4 @ Ys2 ) )
% 3.49/1.91 => ( ! [X: A,Xs2: list @ A,Y4: B,Ys2: list @ B] :
% 3.49/1.91 ( ( P @ Xs2 @ Ys2 )
% 3.49/1.91 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ B @ Y4 @ Ys2 ) ) )
% 3.49/1.91 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_237_splice_Oinduct,axiom,
% 3.49/1.91 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 3.49/1.91 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 3.49/1.91 => ( ! [X: A,Xs2: list @ A,Ys2: list @ A] :
% 3.49/1.91 ( ( P @ Ys2 @ Xs2 )
% 3.49/1.91 => ( P @ ( cons @ A @ X @ Xs2 ) @ Ys2 ) )
% 3.49/1.91 => ( P @ A0 @ A1 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_238_induct__list012,axiom,
% 3.49/1.91 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 3.49/1.91 ( ( P @ ( nil @ A ) )
% 3.49/1.91 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 3.49/1.91 => ( ! [X: A,Y4: A,Zs2: list @ A] :
% 3.49/1.91 ( ( P @ Zs2 )
% 3.49/1.91 => ( ( P @ ( cons @ A @ Y4 @ Zs2 ) )
% 3.49/1.91 => ( P @ ( cons @ A @ X @ ( cons @ A @ Y4 @ Zs2 ) ) ) ) )
% 3.49/1.91 => ( P @ Xs ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_239_min__list_Ocases,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( ord @ A )
% 3.49/1.91 => ! [X3: list @ A] :
% 3.49/1.91 ( ! [X: A,Xs2: list @ A] :
% 3.49/1.91 ( X3
% 3.49/1.91 != ( cons @ A @ X @ Xs2 ) )
% 3.49/1.91 => ( X3
% 3.49/1.91 = ( nil @ A ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_240_min__list_Oinduct,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( ord @ A )
% 3.49/1.91 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 3.49/1.91 ( ! [X: A,Xs2: list @ A] :
% 3.49/1.91 ( ! [X213: A,X224: list @ A] :
% 3.49/1.91 ( ( Xs2
% 3.49/1.91 = ( cons @ A @ X213 @ X224 ) )
% 3.49/1.91 => ( P @ Xs2 ) )
% 3.49/1.91 => ( P @ ( cons @ A @ X @ Xs2 ) ) )
% 3.49/1.91 => ( ( P @ ( nil @ A ) )
% 3.49/1.91 => ( P @ A0 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_241_shuffles_Oinduct,axiom,
% 3.49/1.91 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 3.49/1.91 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 3.49/1.91 => ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ A ) )
% 3.49/1.91 => ( ! [X: A,Xs2: list @ A,Y4: A,Ys2: list @ A] :
% 3.49/1.91 ( ( P @ Xs2 @ ( cons @ A @ Y4 @ Ys2 ) )
% 3.49/1.91 => ( ( P @ ( cons @ A @ X @ Xs2 ) @ Ys2 )
% 3.49/1.91 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y4 @ Ys2 ) ) ) )
% 3.49/1.91 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_242_remdups__adj_Ocases,axiom,
% 3.49/1.91 ! [A: $tType,X3: list @ A] :
% 3.49/1.91 ( ( X3
% 3.49/1.91 != ( nil @ A ) )
% 3.49/1.91 => ( ! [X: A] :
% 3.49/1.91 ( X3
% 3.49/1.91 != ( cons @ A @ X @ ( nil @ A ) ) )
% 3.49/1.91 => ~ ! [X: A,Y4: A,Xs2: list @ A] :
% 3.49/1.91 ( X3
% 3.49/1.91 != ( cons @ A @ X @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_243_sorted__wrt_Oinduct,axiom,
% 3.49/1.91 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 3.49/1.91 ( ! [P4: A > A > $o] : ( P @ P4 @ ( nil @ A ) )
% 3.49/1.91 => ( ! [P4: A > A > $o,X: A,Ys2: list @ A] :
% 3.49/1.91 ( ( P @ P4 @ Ys2 )
% 3.49/1.91 => ( P @ P4 @ ( cons @ A @ X @ Ys2 ) ) )
% 3.49/1.91 => ( P @ A0 @ A1 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_244_remdups__adj_Oinduct,axiom,
% 3.49/1.91 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 3.49/1.91 ( ( P @ ( nil @ A ) )
% 3.49/1.91 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 3.49/1.91 => ( ! [X: A,Y4: A,Xs2: list @ A] :
% 3.49/1.91 ( ( ( X = Y4 )
% 3.49/1.91 => ( P @ ( cons @ A @ X @ Xs2 ) ) )
% 3.49/1.91 => ( ( ( X != Y4 )
% 3.49/1.91 => ( P @ ( cons @ A @ Y4 @ Xs2 ) ) )
% 3.49/1.91 => ( P @ ( cons @ A @ X @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) )
% 3.49/1.91 => ( P @ A0 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_245_arg__min__list_Oinduct,axiom,
% 3.49/1.91 ! [B: $tType,A: $tType] :
% 3.49/1.91 ( ( linorder @ B )
% 3.49/1.91 => ! [P: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 3.49/1.91 ( ! [F5: A > B,X: A] : ( P @ F5 @ ( cons @ A @ X @ ( nil @ A ) ) )
% 3.49/1.91 => ( ! [F5: A > B,X: A,Y4: A,Zs2: list @ A] :
% 3.49/1.91 ( ( P @ F5 @ ( cons @ A @ Y4 @ Zs2 ) )
% 3.49/1.91 => ( P @ F5 @ ( cons @ A @ X @ ( cons @ A @ Y4 @ Zs2 ) ) ) )
% 3.49/1.91 => ( ! [A6: A > B] : ( P @ A6 @ ( nil @ A ) )
% 3.49/1.91 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_246_successively_Oinduct,axiom,
% 3.49/1.91 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 3.49/1.91 ( ! [P4: A > A > $o] : ( P @ P4 @ ( nil @ A ) )
% 3.49/1.91 => ( ! [P4: A > A > $o,X: A] : ( P @ P4 @ ( cons @ A @ X @ ( nil @ A ) ) )
% 3.49/1.91 => ( ! [P4: A > A > $o,X: A,Y4: A,Xs2: list @ A] :
% 3.49/1.91 ( ( P @ P4 @ ( cons @ A @ Y4 @ Xs2 ) )
% 3.49/1.91 => ( P @ P4 @ ( cons @ A @ X @ ( cons @ A @ Y4 @ Xs2 ) ) ) )
% 3.49/1.91 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_247_list__nonempty__induct,axiom,
% 3.49/1.91 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 3.49/1.91 ( ( Xs
% 3.49/1.91 != ( nil @ A ) )
% 3.49/1.91 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 3.49/1.91 => ( ! [X: A,Xs2: list @ A] :
% 3.49/1.91 ( ( Xs2
% 3.49/1.91 != ( nil @ A ) )
% 3.49/1.91 => ( ( P @ Xs2 )
% 3.49/1.91 => ( P @ ( cons @ A @ X @ Xs2 ) ) ) )
% 3.49/1.91 => ( P @ Xs ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_248_map__tailrec__rev_Oinduct,axiom,
% 3.49/1.91 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 3.49/1.91 ( ! [F5: A > B,X_1: list @ B] : ( P @ F5 @ ( nil @ A ) @ X_1 )
% 3.49/1.91 => ( ! [F5: A > B,A6: A,As: list @ A,Bs: list @ B] :
% 3.49/1.91 ( ( P @ F5 @ As @ ( cons @ B @ ( F5 @ A6 ) @ Bs ) )
% 3.49/1.91 => ( P @ F5 @ ( cons @ A @ A6 @ As ) @ Bs ) )
% 3.49/1.91 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_249_strict__sorted_Ocases,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( linorder @ A )
% 3.49/1.91 => ! [X3: list @ A] :
% 3.49/1.91 ( ( X3
% 3.49/1.91 != ( nil @ A ) )
% 3.49/1.91 => ~ ! [X: A,Ys2: list @ A] :
% 3.49/1.91 ( X3
% 3.49/1.91 != ( cons @ A @ X @ Ys2 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_250_strict__sorted_Oinduct,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( linorder @ A )
% 3.49/1.91 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 3.49/1.91 ( ( P @ ( nil @ A ) )
% 3.49/1.91 => ( ! [X: A,Ys2: list @ A] :
% 3.49/1.91 ( ( P @ Ys2 )
% 3.49/1.91 => ( P @ ( cons @ A @ X @ Ys2 ) ) )
% 3.49/1.91 => ( P @ A0 ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_251_free__tv__list_Osimps_I1_J,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( type_M1470978233struct @ A )
% 3.49/1.91 => ( ( type_M950795831ree_tv @ ( list @ A ) @ ( nil @ A ) )
% 3.49/1.91 = ( bot_bot @ ( set @ nat ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_252_bound__tv__list_Osimps_I1_J,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( type_M1470978233struct @ A )
% 3.49/1.91 => ( ( type_M779184887und_tv @ ( list @ A ) @ ( nil @ A ) )
% 3.49/1.91 = ( bot_bot @ ( set @ nat ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_253_lexordp__eq_Oinducts,axiom,
% 3.49/1.91 ! [A: $tType] :
% 3.49/1.91 ( ( ord @ A )
% 3.49/1.91 => ! [X1: list @ A,X2: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 3.49/1.91 ( ( ord_lexordp_eq @ A @ X1 @ X2 )
% 3.49/1.91 => ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 3.49/1.91 => ( ! [X: A,Y4: A,Xs2: list @ A,Ys2: list @ A] :
% 3.49/1.91 ( ( ord_less @ A @ X @ Y4 )
% 3.49/1.91 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y4 @ Ys2 ) ) )
% 3.49/1.91 => ( ! [X: A,Y4: A,Xs2: list @ A,Ys2: list @ A] :
% 3.49/1.91 ( ~ ( ord_less @ A @ X @ Y4 )
% 3.49/1.91 => ( ~ ( ord_less @ A @ Y4 @ X )
% 3.49/1.91 => ( ( ord_lexordp_eq @ A @ Xs2 @ Ys2 )
% 3.49/1.91 => ( ( P @ Xs2 @ Ys2 )
% 3.49/1.91 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y4 @ Ys2 ) ) ) ) ) )
% 3.49/1.91 => ( P @ X1 @ X2 ) ) ) ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(fact_254_insert__Nil,axiom,
% 3.49/1.91 ! [A: $tType,X3: A] :
% 3.49/1.91 ( ( insert @ A @ X3 @ ( nil @ A ) )
% 3.49/1.91 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 3.49/1.91 bounded_lattice @ $o ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 3.49/1.91 ! [A7: $tType] : ( bounded_lattice @ ( set @ A7 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 3.49/1.91 ! [A7: $tType,A8: $tType] :
% 3.49/1.91 ( ( bounded_lattice @ A8 )
% 3.49/1.91 => ( bounded_lattice @ ( A7 > A8 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_fun___Type__Mirabelle__sfxnzmapfi_Otype__struct,axiom,
% 3.49/1.91 ! [A7: $tType,A8: $tType] :
% 3.49/1.91 ( ( ( type_M201404320of_nat @ A7 )
% 3.49/1.91 & ( type_M1535146424typ_of @ A8 ) )
% 3.49/1.91 => ( type_M1470978233struct @ ( A7 > A8 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 3.49/1.91 ! [A7: $tType,A8: $tType] :
% 3.49/1.91 ( ( bounded_lattice @ A8 )
% 3.49/1.91 => ( bounde1808546759up_bot @ ( A7 > A8 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 3.49/1.91 ! [A7: $tType,A8: $tType] :
% 3.49/1.91 ( ( semilattice_sup @ A8 )
% 3.49/1.91 => ( semilattice_sup @ ( A7 > A8 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 3.49/1.91 ! [A7: $tType,A8: $tType] :
% 3.49/1.91 ( ( order_bot @ A8 )
% 3.49/1.91 => ( order_bot @ ( A7 > A8 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_fun___Orderings_Opreorder,axiom,
% 3.49/1.91 ! [A7: $tType,A8: $tType] :
% 3.49/1.91 ( ( preorder @ A8 )
% 3.49/1.91 => ( preorder @ ( A7 > A8 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_fun___Orderings_Oorder,axiom,
% 3.49/1.91 ! [A7: $tType,A8: $tType] :
% 3.49/1.91 ( ( order @ A8 )
% 3.49/1.91 => ( order @ ( A7 > A8 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_fun___Orderings_Oord,axiom,
% 3.49/1.91 ! [A7: $tType,A8: $tType] :
% 3.49/1.91 ( ( ord @ A8 )
% 3.49/1.91 => ( ord @ ( A7 > A8 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_fun___Orderings_Obot,axiom,
% 3.49/1.91 ! [A7: $tType,A8: $tType] :
% 3.49/1.91 ( ( bot @ A8 )
% 3.49/1.91 => ( bot @ ( A7 > A8 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_Nat_Onat___Type__Mirabelle__sfxnzmapfi_Oof__nat,axiom,
% 3.49/1.91 type_M201404320of_nat @ nat ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_Nat_Onat___Lattices_Osemilattice__sup_3,axiom,
% 3.49/1.91 semilattice_sup @ nat ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 3.49/1.91 wellorder @ nat ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_Nat_Onat___Orderings_Oorder__bot_4,axiom,
% 3.49/1.91 order_bot @ nat ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_Nat_Onat___Orderings_Opreorder_5,axiom,
% 3.49/1.91 preorder @ nat ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 3.49/1.91 linorder @ nat ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 3.49/1.91 no_top @ nat ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_Nat_Onat___Orderings_Oorder_6,axiom,
% 3.49/1.91 order @ nat ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_Nat_Onat___Orderings_Oord_7,axiom,
% 3.49/1.91 ord @ nat ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_Nat_Onat___Orderings_Obot_8,axiom,
% 3.49/1.91 bot @ nat ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_9,axiom,
% 3.49/1.91 ! [A7: $tType] : ( bounde1808546759up_bot @ ( set @ A7 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_10,axiom,
% 3.49/1.91 ! [A7: $tType] : ( semilattice_sup @ ( set @ A7 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_Set_Oset___Orderings_Oorder__bot_11,axiom,
% 3.49/1.91 ! [A7: $tType] : ( order_bot @ ( set @ A7 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_Set_Oset___Orderings_Opreorder_12,axiom,
% 3.49/1.91 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_Set_Oset___Orderings_Oorder_13,axiom,
% 3.49/1.91 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_Set_Oset___Orderings_Oord_14,axiom,
% 3.49/1.91 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_Set_Oset___Orderings_Obot_15,axiom,
% 3.49/1.91 ! [A7: $tType] : ( bot @ ( set @ A7 ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_16,axiom,
% 3.49/1.91 bounde1808546759up_bot @ $o ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_17,axiom,
% 3.49/1.91 semilattice_sup @ $o ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_HOL_Obool___Orderings_Oorder__bot_18,axiom,
% 3.49/1.91 order_bot @ $o ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_HOL_Obool___Orderings_Opreorder_19,axiom,
% 3.49/1.91 preorder @ $o ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_HOL_Obool___Orderings_Olinorder_20,axiom,
% 3.49/1.91 linorder @ $o ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_HOL_Obool___Orderings_Oorder_21,axiom,
% 3.49/1.91 order @ $o ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_HOL_Obool___Orderings_Oord_22,axiom,
% 3.49/1.91 ord @ $o ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_HOL_Obool___Orderings_Obot_23,axiom,
% 3.49/1.91 bot @ $o ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_List_Olist___Type__Mirabelle__sfxnzmapfi_Otype__struct_24,axiom,
% 3.49/1.91 ! [A7: $tType] :
% 3.49/1.91 ( ( type_M1470978233struct @ A7 )
% 3.49/1.91 => ( type_M1470978233struct @ ( list @ A7 ) ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_Type__Mirabelle__sfxnzmapfi_Otyp___Type__Mirabelle__sfxnzmapfi_Otype__struct_25,axiom,
% 3.49/1.91 type_M1470978233struct @ type_Mirabelle_typ ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_Type__Mirabelle__sfxnzmapfi_Otyp___Type__Mirabelle__sfxnzmapfi_Otyp__of,axiom,
% 3.49/1.91 type_M1535146424typ_of @ type_Mirabelle_typ ).
% 3.49/1.91
% 3.49/1.91 thf(tcon_Type__Mirabelle__sfxnzmapfi_Otype__scheme___Type__Mirabelle__sfxnzmapfi_Otype__struct_26,axiom,
% 3.49/1.91 type_M1470978233struct @ type_M1610475166scheme ).
% 3.49/1.91
% 3.49/1.91 thf(help_If_3_1_T,axiom,
% 3.49/1.91 ! [P: $o] :
% 3.49/1.91 ( ( P = $true )
% 3.49/1.91 | ( P = $false ) ) ).
% 3.49/1.91
% 3.49/1.91 thf(help_If_2_1_T,axiom,
% 3.49/1.91 ! [A: $tType,X3: A,Y: A] :
% 3.49/1.91 ( ( if @ A @ $false @ X3 @ Y )
% 3.49/1.91 = Y ) ).
% 3.49/1.91
% 3.49/1.91 thf(help_If_1_1_T,axiom,
% 3.49/1.91 ! [A: $tType,X3: A,Y: A] :
% 3.49/1.91 ( ( if @ A @ $true @ X3 @ Y )
% 3.49/1.91 = X3 ) ).
% 3.49/1.91
% 3.49/1.91 thf(conj_0,conjecture,
% 3.49/1.91 ( ( ( type_M353778473_subst @ type_M1610475166scheme @ s1 @ ( type_M91906176e_FVar @ x ) )
% 3.49/1.91 != ( type_M353778473_subst @ type_M1610475166scheme @ s2 @ ( type_M91906176e_FVar @ x ) ) )
% 3.49/1.91 | ~ ( member @ nat @ n @ ( type_M950795831ree_tv @ type_M1610475166scheme @ ( type_M91906176e_FVar @ x ) ) )
% 3.49/1.91 | ( ( s1 @ n )
% 3.49/1.91 = ( s2 @ n ) ) ) ).
% 3.49/1.91 ------------------------
% 3.49/1.94 % (4555)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4446 for (2999ds/2Mi)
% 3.49/1.94 % (4553)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_4446 for (2999ds/4Mi)
% 3.49/1.94 % (4557)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_4446 for (2999ds/275Mi)
% 3.49/1.94 % (4552)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4446 for (2999ds/183Mi)
% 3.49/1.94 % (4558)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4446 for (2999ds/18Mi)
% 3.49/1.94 % (4554)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_4446 for (2999ds/27Mi)
% 3.49/1.94 % (4556)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_4446 for (2999ds/2Mi)
% 3.49/1.94 % (4555)Instruction limit reached!
% 3.49/1.94 % (4555)------------------------------
% 3.49/1.94 % (4555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.49/1.94 % (4555)Termination reason: Unknown
% 3.49/1.94 % (4555)Termination phase: shuffling
% 3.49/1.94
% 3.49/1.94 % (4556)Instruction limit reached!
% 3.49/1.94 % (4556)------------------------------
% 3.49/1.94 % (4556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.49/1.94 % (4556)Termination reason: Unknown
% 3.49/1.94 % (4556)Termination phase: shuffling
% 3.49/1.94
% 3.49/1.94 % (4556)Memory used [KB]: 1407
% 3.49/1.94 % (4556)Time elapsed: 0.003 s
% 3.49/1.94 % (4556)Instructions burned: 3 (million)
% 3.49/1.94 % (4556)------------------------------
% 3.49/1.94 % (4556)------------------------------
% 3.49/1.94 % (4555)Memory used [KB]: 1407
% 3.49/1.94 % (4555)Time elapsed: 0.003 s
% 3.49/1.94 % (4555)Instructions burned: 2 (million)
% 3.49/1.94 % (4555)------------------------------
% 3.49/1.94 % (4555)------------------------------
% 3.49/1.94 % (4553)Instruction limit reached!
% 3.49/1.94 % (4553)------------------------------
% 3.49/1.94 % (4553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.49/1.94 % (4553)Termination reason: Unknown
% 3.49/1.94 % (4553)Termination phase: shuffling
% 3.49/1.94
% 3.49/1.94 % (4553)Memory used [KB]: 1407
% 3.49/1.94 % (4553)Time elapsed: 0.004 s
% 3.49/1.94 % (4553)Instructions burned: 4 (million)
% 3.49/1.94 % (4553)------------------------------
% 3.49/1.94 % (4553)------------------------------
% 3.49/1.95 % (4558)Instruction limit reached!
% 3.49/1.95 % (4558)------------------------------
% 3.49/1.95 % (4558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.49/1.95 % (4558)Termination reason: Unknown
% 3.49/1.95 % (4558)Termination phase: Property scanning
% 3.49/1.95
% 3.49/1.95 % (4558)Memory used [KB]: 1791
% 3.49/1.95 % (4558)Time elapsed: 0.013 s
% 3.49/1.95 % (4558)Instructions burned: 19 (million)
% 3.49/1.95 % (4558)------------------------------
% 3.49/1.95 % (4558)------------------------------
% 3.49/1.96 % (4554)Instruction limit reached!
% 3.49/1.96 % (4554)------------------------------
% 3.49/1.96 % (4554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.49/1.96 % (4554)Termination reason: Unknown
% 3.49/1.96 % (4554)Termination phase: Property scanning
% 3.49/1.96
% 3.49/1.96 % (4554)Memory used [KB]: 1918
% 3.49/1.96 % (4554)Time elapsed: 0.015 s
% 3.49/1.96 % (4554)Instructions burned: 27 (million)
% 3.49/1.96 % (4554)------------------------------
% 3.49/1.96 % (4554)------------------------------
% 3.49/1.96 % (4559)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4446 for (2999ds/3Mi)
% 3.49/1.96 % (4560)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_4446 for (2999ds/37Mi)
% 3.49/1.96 % (4561)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_4446 for (2999ds/15Mi)
% 3.49/1.96 % (4559)Instruction limit reached!
% 3.49/1.96 % (4559)------------------------------
% 3.49/1.96 % (4559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.49/1.96 % (4559)Termination reason: Unknown
% 3.49/1.96 % (4559)Termination phase: shuffling
% 3.49/1.96
% 3.49/1.96 % (4559)Memory used [KB]: 1407
% 3.49/1.96 % (4559)Time elapsed: 0.004 s
% 3.49/1.96 % (4559)Instructions burned: 3 (million)
% 3.49/1.96 % (4559)------------------------------
% 3.49/1.96 % (4559)------------------------------
% 3.49/1.97 % (4561)Instruction limit reached!
% 3.49/1.97 % (4561)------------------------------
% 3.49/1.97 % (4561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.49/1.97 % (4561)Termination reason: Unknown
% 3.49/1.97 % (4561)Termination phase: shuffling
% 3.49/1.97
% 3.49/1.97 % (4561)Memory used [KB]: 1663
% 3.49/1.97 % (4561)Time elapsed: 0.010 s
% 3.49/1.97 % (4561)Instructions burned: 15 (million)
% 3.49/1.97 % (4561)------------------------------
% 3.49/1.97 % (4561)------------------------------
% 3.49/1.97 % (4562)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4446 for (2999ds/3Mi)
% 3.49/1.97 % (4562)Instruction limit reached!
% 3.49/1.97 % (4562)------------------------------
% 3.49/1.97 % (4562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.49/1.97 % (4562)Termination reason: Unknown
% 3.49/1.97 % (4562)Termination phase: shuffling
% 3.49/1.97
% 3.49/1.97 % (4562)Memory used [KB]: 1407
% 3.49/1.97 % (4562)Time elapsed: 0.004 s
% 3.49/1.97 % (4562)Instructions burned: 3 (million)
% 3.49/1.97 % (4562)------------------------------
% 3.49/1.97 % (4562)------------------------------
% 3.49/1.97 % (4563)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_4446 for (2999ds/1041Mi)
% 3.49/1.98 % (4564)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_4446 for (2999ds/7Mi)
% 3.49/1.98 % (4560)Instruction limit reached!
% 3.49/1.98 % (4560)------------------------------
% 3.49/1.98 % (4560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.49/1.98 % (4560)Termination reason: Unknown
% 3.49/1.98 % (4560)Termination phase: shuffling
% 3.49/1.98
% 3.49/1.98 % (4560)Memory used [KB]: 2174
% 3.49/1.98 % (4560)Time elapsed: 0.021 s
% 3.49/1.98 % (4560)Instructions burned: 38 (million)
% 3.49/1.98 % (4560)------------------------------
% 3.49/1.98 % (4560)------------------------------
% 3.49/1.98 % (4564)Instruction limit reached!
% 3.49/1.98 % (4564)------------------------------
% 3.49/1.98 % (4564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.49/1.98 % (4564)Termination reason: Unknown
% 3.49/1.98 % (4564)Termination phase: shuffling
% 3.49/1.98
% 3.49/1.98 % (4564)Memory used [KB]: 1535
% 3.49/1.98 % (4564)Time elapsed: 0.006 s
% 3.49/1.98 % (4564)Instructions burned: 7 (million)
% 3.49/1.98 % (4564)------------------------------
% 3.49/1.98 % (4564)------------------------------
% 3.49/1.98 % (4565)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_4446 for (2999ds/16Mi)
% 3.49/1.99 % (4566)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_4446 for (2999ds/3Mi)
% 3.49/1.99 % (4566)Instruction limit reached!
% 3.49/1.99 % (4566)------------------------------
% 3.49/1.99 % (4566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.49/1.99 % (4566)Termination reason: Unknown
% 3.49/1.99 % (4566)Termination phase: shuffling
% 3.49/1.99
% 3.49/1.99 % (4566)Memory used [KB]: 1407
% 3.49/1.99 % (4566)Time elapsed: 0.004 s
% 3.49/1.99 % (4566)Instructions burned: 3 (million)
% 3.49/1.99 % (4566)------------------------------
% 3.49/1.99 % (4566)------------------------------
% 3.49/1.99 % (4565)Instruction limit reached!
% 3.49/1.99 % (4565)------------------------------
% 3.49/1.99 % (4565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.49/1.99 % (4565)Termination reason: Unknown
% 3.49/1.99 % (4565)Termination phase: shuffling
% 3.49/1.99
% 3.49/1.99 % (4565)Memory used [KB]: 1791
% 3.49/1.99 % (4565)Time elapsed: 0.011 s
% 3.49/1.99 % (4565)Instructions burned: 17 (million)
% 3.49/1.99 % (4565)------------------------------
% 3.49/1.99 % (4565)------------------------------
% 3.49/1.99 % (4567)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_4446 for (2999ds/3Mi)
% 3.49/2.00 % (4568)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_4446 for (2999ds/7Mi)
% 3.49/2.00 % (4567)Instruction limit reached!
% 3.49/2.00 % (4567)------------------------------
% 3.49/2.00 % (4567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.49/2.00 % (4567)Termination reason: Unknown
% 3.49/2.00 % (4567)Termination phase: shuffling
% 3.49/2.00
% 3.49/2.00 % (4567)Memory used [KB]: 1407
% 3.49/2.00 % (4567)Time elapsed: 0.004 s
% 3.49/2.00 % (4567)Instructions burned: 3 (million)
% 3.49/2.00 % (4567)------------------------------
% 3.49/2.00 % (4567)------------------------------
% 3.49/2.00 % (4568)Instruction limit reached!
% 3.49/2.00 % (4568)------------------------------
% 3.49/2.00 % (4568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.49/2.00 % (4568)Termination reason: Unknown
% 3.49/2.00 % (4568)Termination phase: shuffling
% 3.49/2.00
% 3.49/2.00 % (4568)Memory used [KB]: 1535
% 3.49/2.00 % (4568)Time elapsed: 0.006 s
% 3.49/2.00 % (4568)Instructions burned: 7 (million)
% 3.49/2.00 % (4568)------------------------------
% 3.49/2.00 % (4568)------------------------------
% 3.49/2.00 % (4569)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_4446 for (2999ds/3Mi)
% 3.49/2.01 % (4569)Instruction limit reached!
% 3.49/2.01 % (4569)------------------------------
% 3.49/2.01 % (4569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.49/2.01 % (4569)Termination reason: Unknown
% 3.49/2.01 % (4569)Termination phase: shuffling
% 3.49/2.01
% 3.49/2.01 % (4569)Memory used [KB]: 1407
% 3.49/2.01 % (4569)Time elapsed: 0.004 s
% 3.49/2.01 % (4569)Instructions burned: 4 (million)
% 3.49/2.01 % (4569)------------------------------
% 3.49/2.01 % (4569)------------------------------
% 3.49/2.01 % (4570)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_4446 for (2999ds/4Mi)
% 3.49/2.01 % (4570)Instruction limit reached!
% 3.49/2.01 % (4570)------------------------------
% 3.49/2.01 % (4570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.49/2.01 % (4570)Termination reason: Unknown
% 3.49/2.01 % (4570)Termination phase: shuffling
% 3.49/2.01
% 3.49/2.01 % (4570)Memory used [KB]: 1407
% 3.49/2.01 % (4570)Time elapsed: 0.004 s
% 3.49/2.01 % (4570)Instructions burned: 4 (million)
% 3.49/2.01 % (4570)------------------------------
% 3.49/2.01 % (4570)------------------------------
% 3.49/2.01 % (4571)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_4446 for (2999ds/18Mi)
% 3.49/2.02 % (4572)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_4446 for (2999ds/710Mi)
% 3.49/2.02 % (4573)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_4446 for (2999ds/6Mi)
% 3.49/2.02 % (4571)Instruction limit reached!
% 3.49/2.02 % (4571)------------------------------
% 3.49/2.02 % (4571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.49/2.02 % (4571)Termination reason: Unknown
% 3.49/2.02 % (4571)Termination phase: shuffling
% 3.49/2.02
% 3.49/2.02 % (4571)Memory used [KB]: 1791
% 3.49/2.02 % (4571)Time elapsed: 0.012 s
% 3.49/2.02 % (4571)Instructions burned: 18 (million)
% 3.49/2.02 % (4571)------------------------------
% 3.49/2.02 % (4571)------------------------------
% 3.49/2.03 % (4573)Instruction limit reached!
% 3.49/2.03 % (4573)------------------------------
% 3.49/2.03 % (4573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.49/2.03 % (4573)Termination reason: Unknown
% 3.49/2.03 % (4573)Termination phase: shuffling
% 3.49/2.03
% 3.49/2.03 % (4573)Memory used [KB]: 1535
% 3.49/2.03 % (4573)Time elapsed: 0.006 s
% 3.49/2.03 % (4573)Instructions burned: 7 (million)
% 3.49/2.03 % (4573)------------------------------
% 3.49/2.03 % (4573)------------------------------
% 4.12/2.03 % (4574)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_4446 for (2999ds/902Mi)
% 4.12/2.03 % (4552)Instruction limit reached!
% 4.12/2.03 % (4552)------------------------------
% 4.12/2.03 % (4552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.12/2.03 % (4552)Termination reason: Unknown
% 4.12/2.03 % (4552)Termination phase: Saturation
% 4.12/2.03
% 4.12/2.03 % (4552)Memory used [KB]: 7291
% 4.12/2.03 % (4552)Time elapsed: 0.094 s
% 4.12/2.03 % (4552)Instructions burned: 184 (million)
% 4.12/2.03 % (4552)------------------------------
% 4.12/2.03 % (4552)------------------------------
% 4.12/2.04 % (4575)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_4446 for (2998ds/21Mi)
% 4.12/2.04 % (4576)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_4446 for (2998ds/5Mi)
% 4.12/2.04 % (4576)Instruction limit reached!
% 4.12/2.04 % (4576)------------------------------
% 4.12/2.04 % (4576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.12/2.04 % (4576)Termination reason: Unknown
% 4.12/2.04 % (4576)Termination phase: shuffling
% 4.12/2.04
% 4.12/2.04 % (4576)Memory used [KB]: 1535
% 4.12/2.04 % (4576)Time elapsed: 0.005 s
% 4.12/2.04 % (4576)Instructions burned: 6 (million)
% 4.12/2.04 % (4576)------------------------------
% 4.12/2.04 % (4576)------------------------------
% 4.12/2.05 % (4577)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_4446 for (2998ds/6Mi)
% 4.12/2.05 % (4575)Instruction limit reached!
% 4.12/2.05 % (4575)------------------------------
% 4.12/2.05 % (4575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.12/2.05 % (4575)Termination reason: Unknown
% 4.12/2.05 % (4575)Termination phase: shuffling
% 4.12/2.05
% 4.12/2.05 % (4575)Memory used [KB]: 1918
% 4.12/2.05 % (4575)Time elapsed: 0.014 s
% 4.12/2.05 % (4575)Instructions burned: 22 (million)
% 4.12/2.05 % (4575)------------------------------
% 4.12/2.05 % (4575)------------------------------
% 4.12/2.05 % (4577)Instruction limit reached!
% 4.12/2.05 % (4577)------------------------------
% 4.12/2.05 % (4577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.12/2.05 % (4577)Termination reason: Unknown
% 4.12/2.05 % (4577)Termination phase: shuffling
% 4.12/2.05
% 4.12/2.05 % (4577)Memory used [KB]: 1407
% 4.12/2.05 % (4577)Time elapsed: 0.005 s
% 4.12/2.05 % (4577)Instructions burned: 6 (million)
% 4.12/2.05 % (4577)------------------------------
% 4.12/2.05 % (4577)------------------------------
% 4.12/2.06 % (4578)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_4446 for (2998ds/377Mi)
% 4.12/2.07 % (4579)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_4446 for (2998ds/779Mi)
% 4.12/2.07 % (4580)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_4446 for (2998ds/19Mi)
% 4.12/2.08 % (4580)Instruction limit reached!
% 4.12/2.08 % (4580)------------------------------
% 4.12/2.08 % (4580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.12/2.08 % (4580)Termination reason: Unknown
% 4.12/2.08 % (4580)Termination phase: shuffling
% 4.12/2.08
% 4.12/2.08 % (4580)Memory used [KB]: 1791
% 4.12/2.08 % (4580)Time elapsed: 0.012 s
% 4.12/2.08 % (4580)Instructions burned: 20 (million)
% 4.12/2.08 % (4580)------------------------------
% 4.12/2.08 % (4580)------------------------------
% 4.12/2.08 % (4557)Instruction limit reached!
% 4.12/2.08 % (4557)------------------------------
% 4.12/2.08 % (4557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.12/2.08 % (4557)Termination reason: Unknown
% 4.12/2.08 % (4557)Termination phase: Saturation
% 4.12/2.08
% 4.12/2.08 % (4557)Memory used [KB]: 6908
% 4.12/2.08 % (4557)Time elapsed: 0.143 s
% 4.12/2.08 % (4557)Instructions burned: 275 (million)
% 4.12/2.08 % (4557)------------------------------
% 4.12/2.08 % (4557)------------------------------
% 4.12/2.09 % (4581)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_4446 for (2998ds/879Mi)
% 4.12/2.10 % (4582)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_4446 for (2998ds/17Mi)
% 4.12/2.11 % (4582)Instruction limit reached!
% 4.12/2.11 % (4582)------------------------------
% 4.12/2.11 % (4582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.12/2.11 % (4582)Termination reason: Unknown
% 4.12/2.11 % (4582)Termination phase: shuffling
% 4.12/2.11
% 4.12/2.11 % (4582)Memory used [KB]: 1791
% 4.12/2.11 % (4582)Time elapsed: 0.012 s
% 4.12/2.11 % (4582)Instructions burned: 18 (million)
% 4.12/2.11 % (4582)------------------------------
% 4.12/2.11 % (4582)------------------------------
% 4.12/2.12 % (4583)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_4446 for (2997ds/3Mi)
% 4.46/2.13 % (4583)Instruction limit reached!
% 4.46/2.13 % (4583)------------------------------
% 4.46/2.13 % (4583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.46/2.13 % (4583)Termination reason: Unknown
% 4.46/2.13 % (4583)Termination phase: shuffling
% 4.46/2.13
% 4.46/2.13 % (4583)Memory used [KB]: 1407
% 4.46/2.13 % (4583)Time elapsed: 0.004 s
% 4.46/2.13 % (4583)Instructions burned: 3 (million)
% 4.46/2.13 % (4583)------------------------------
% 4.46/2.13 % (4583)------------------------------
% 4.46/2.14 % (4584)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_4446 for (2997ds/30Mi)
% 4.46/2.16 % (4584)Instruction limit reached!
% 4.46/2.16 % (4584)------------------------------
% 4.46/2.16 % (4584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.46/2.16 % (4584)Termination reason: Unknown
% 4.46/2.16 % (4584)Termination phase: Property scanning
% 4.46/2.16
% 4.46/2.16 % (4584)Memory used [KB]: 1918
% 4.46/2.16 % (4584)Time elapsed: 0.018 s
% 4.46/2.16 % (4584)Instructions burned: 31 (million)
% 4.46/2.16 % (4584)------------------------------
% 4.46/2.16 % (4584)------------------------------
% 4.46/2.17 % (4585)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_4446 for (2997ds/127Mi)
% 4.58/2.24 % (4585)Instruction limit reached!
% 4.58/2.24 % (4585)------------------------------
% 4.58/2.24 % (4585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.58/2.24 % (4585)Termination reason: Unknown
% 4.58/2.24 % (4585)Termination phase: Saturation
% 4.58/2.24
% 4.58/2.24 % (4585)Memory used [KB]: 7036
% 4.58/2.24 % (4585)Time elapsed: 0.064 s
% 4.58/2.24 % (4585)Instructions burned: 127 (million)
% 4.58/2.24 % (4585)------------------------------
% 4.58/2.24 % (4585)------------------------------
% 4.58/2.25 % (4586)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_4446 for (2996ds/100Mi)
% 4.58/2.26 % (4578)Instruction limit reached!
% 4.58/2.26 % (4578)------------------------------
% 4.58/2.26 % (4578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.58/2.26 % (4578)Termination reason: Unknown
% 4.58/2.26 % (4578)Termination phase: Saturation
% 4.58/2.26
% 4.58/2.26 % (4578)Memory used [KB]: 8315
% 4.58/2.26 % (4578)Time elapsed: 0.224 s
% 4.58/2.26 % (4578)Instructions burned: 377 (million)
% 4.58/2.26 % (4578)------------------------------
% 4.58/2.26 % (4578)------------------------------
% 4.58/2.28 % (4587)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_4446 for (2996ds/3Mi)
% 4.58/2.28 % (4587)Instruction limit reached!
% 4.58/2.28 % (4587)------------------------------
% 4.58/2.28 % (4587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.58/2.28 % (4587)Termination reason: Unknown
% 4.58/2.28 % (4587)Termination phase: shuffling
% 4.58/2.28
% 4.58/2.28 % (4587)Memory used [KB]: 1407
% 4.58/2.28 % (4587)Time elapsed: 0.004 s
% 4.58/2.28 % (4587)Instructions burned: 3 (million)
% 4.58/2.28 % (4587)------------------------------
% 4.58/2.28 % (4587)------------------------------
% 4.58/2.29 % (4588)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_4446 for (2996ds/20Mi)
% 5.00/2.30 % (4586)Instruction limit reached!
% 5.00/2.30 % (4586)------------------------------
% 5.00/2.30 % (4586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.00/2.30 % (4586)Termination reason: Unknown
% 5.00/2.30 % (4586)Termination phase: Property scanning
% 5.00/2.30
% 5.00/2.30 % (4586)Memory used [KB]: 2302
% 5.00/2.30 % (4586)Time elapsed: 0.048 s
% 5.00/2.30 % (4586)Instructions burned: 100 (million)
% 5.00/2.30 % (4586)------------------------------
% 5.00/2.30 % (4586)------------------------------
% 5.00/2.30 % (4588)Instruction limit reached!
% 5.00/2.30 % (4588)------------------------------
% 5.00/2.30 % (4588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.00/2.30 % (4588)Termination reason: Unknown
% 5.00/2.30 % (4588)Termination phase: Property scanning
% 5.00/2.30
% 5.00/2.30 % (4588)Memory used [KB]: 1791
% 5.00/2.30 % (4588)Time elapsed: 0.013 s
% 5.00/2.30 % (4588)Instructions burned: 20 (million)
% 5.00/2.30 % (4588)------------------------------
% 5.00/2.30 % (4588)------------------------------
% 5.00/2.31 % (4589)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_4446 for (2996ds/86Mi)
% 5.00/2.32 % (4590)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_4446 for (2996ds/107Mi)
% 5.00/2.35 % (4589)Instruction limit reached!
% 5.00/2.35 % (4589)------------------------------
% 5.00/2.35 % (4589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.00/2.35 % (4589)Termination reason: Unknown
% 5.00/2.35 % (4589)Termination phase: Saturation
% 5.00/2.35
% 5.00/2.35 % (4589)Memory used [KB]: 6780
% 5.00/2.35 % (4589)Time elapsed: 0.040 s
% 5.00/2.35 % (4589)Instructions burned: 87 (million)
% 5.00/2.35 % (4589)------------------------------
% 5.00/2.35 % (4589)------------------------------
% 5.00/2.37 % (4591)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_4446 for (2995ds/39Mi)
% 5.00/2.37 % (4590)Instruction limit reached!
% 5.00/2.37 % (4590)------------------------------
% 5.00/2.37 % (4590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.00/2.37 % (4590)Termination reason: Unknown
% 5.00/2.37 % (4590)Termination phase: Saturation
% 5.00/2.37
% 5.00/2.37 % (4590)Memory used [KB]: 6908
% 5.00/2.37 % (4590)Time elapsed: 0.055 s
% 5.00/2.37 % (4590)Instructions burned: 108 (million)
% 5.00/2.37 % (4590)------------------------------
% 5.00/2.37 % (4590)------------------------------
% 5.00/2.38 % (4572)Instruction limit reached!
% 5.00/2.38 % (4572)------------------------------
% 5.00/2.38 % (4572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.00/2.38 % (4572)Termination reason: Unknown
% 5.00/2.38 % (4572)Termination phase: Saturation
% 5.00/2.38
% 5.00/2.38 % (4572)Memory used [KB]: 8315
% 5.00/2.38 % (4572)Time elapsed: 0.366 s
% 5.00/2.38 % (4572)Instructions burned: 711 (million)
% 5.00/2.38 % (4572)------------------------------
% 5.00/2.38 % (4572)------------------------------
% 5.00/2.39 % (4592)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_4446 for (2995ds/448Mi)
% 5.00/2.39 % (4591)Instruction limit reached!
% 5.00/2.39 % (4591)------------------------------
% 5.00/2.39 % (4591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.00/2.39 % (4591)Termination reason: Unknown
% 5.00/2.39 % (4591)Termination phase: shuffling
% 5.00/2.39
% 5.00/2.39 % (4591)Memory used [KB]: 2174
% 5.00/2.39 % (4591)Time elapsed: 0.022 s
% 5.00/2.39 % (4591)Instructions burned: 40 (million)
% 5.00/2.39 % (4591)------------------------------
% 5.00/2.39 % (4591)------------------------------
% 5.72/2.40 % (4593)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_4446 for (2995ds/46Mi)
% 5.72/2.41 % (4594)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_4446 for (2995ds/98Mi)
% 5.72/2.42 % (4593)Instruction limit reached!
% 5.72/2.42 % (4593)------------------------------
% 5.72/2.42 % (4593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.72/2.42 % (4593)Termination reason: Unknown
% 5.72/2.42 % (4593)Termination phase: Preprocessing 3
% 5.72/2.42
% 5.72/2.42 % (4593)Memory used [KB]: 2046
% 5.72/2.42 % (4593)Time elapsed: 0.025 s
% 5.72/2.42 % (4593)Instructions burned: 46 (million)
% 5.72/2.42 % (4593)------------------------------
% 5.72/2.42 % (4593)------------------------------
% 5.72/2.44 % (4595)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_4446 for (2994ds/507Mi)
% 5.72/2.45 % (4594)Instruction limit reached!
% 5.72/2.45 % (4594)------------------------------
% 5.72/2.45 % (4594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.72/2.45 % (4594)Termination reason: Unknown
% 5.72/2.45 % (4594)Termination phase: Property scanning
% 5.72/2.45
% 5.72/2.45 % (4594)Memory used [KB]: 2302
% 5.72/2.45 % (4594)Time elapsed: 0.047 s
% 5.72/2.45 % (4594)Instructions burned: 98 (million)
% 5.72/2.45 % (4594)------------------------------
% 5.72/2.45 % (4594)------------------------------
% 5.72/2.46 % (4579)Instruction limit reached!
% 5.72/2.46 % (4579)------------------------------
% 5.72/2.46 % (4579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.72/2.46 % (4579)Termination reason: Unknown
% 5.72/2.46 % (4579)Termination phase: Saturation
% 5.72/2.46
% 5.72/2.46 % (4579)Memory used [KB]: 8315
% 5.72/2.46 % (4579)Time elapsed: 0.422 s
% 5.72/2.46 % (4579)Instructions burned: 779 (million)
% 5.72/2.46 % (4579)------------------------------
% 5.72/2.46 % (4579)------------------------------
% 5.72/2.47 % (4596)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_4446 for (2994ds/149Mi)
% 5.72/2.48 % (4597)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_4446 for (2994ds/39Mi)
% 5.72/2.48 % (4574)Instruction limit reached!
% 5.72/2.48 % (4574)------------------------------
% 5.72/2.48 % (4574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.72/2.48 % (4574)Termination reason: Unknown
% 5.72/2.48 % (4574)Termination phase: Saturation
% 5.72/2.48
% 5.72/2.48 % (4574)Memory used [KB]: 8827
% 5.72/2.48 % (4574)Time elapsed: 0.459 s
% 5.72/2.48 % (4574)Instructions burned: 902 (million)
% 5.72/2.48 % (4574)------------------------------
% 5.72/2.48 % (4574)------------------------------
% 6.81/2.50 % (4598)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_4446 for (2994ds/6Mi)
% 6.81/2.50 % (4597)Instruction limit reached!
% 6.81/2.50 % (4597)------------------------------
% 6.81/2.50 % (4597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.50 % (4597)Termination reason: Unknown
% 6.81/2.50 % (4597)Termination phase: Preprocessing 3
% 6.81/2.50
% 6.81/2.50 % (4597)Memory used [KB]: 2046
% 6.81/2.50 % (4597)Time elapsed: 0.023 s
% 6.81/2.50 % (4597)Instructions burned: 39 (million)
% 6.81/2.50 % (4597)------------------------------
% 6.81/2.50 % (4597)------------------------------
% 6.81/2.50 % (4598)Instruction limit reached!
% 6.81/2.50 % (4598)------------------------------
% 6.81/2.50 % (4598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.50 % (4598)Termination reason: Unknown
% 6.81/2.50 % (4598)Termination phase: shuffling
% 6.81/2.50
% 6.81/2.50 % (4598)Memory used [KB]: 1535
% 6.81/2.50 % (4598)Time elapsed: 0.006 s
% 6.81/2.50 % (4598)Instructions burned: 7 (million)
% 6.81/2.50 % (4598)------------------------------
% 6.81/2.50 % (4598)------------------------------
% 6.81/2.52 % (4599)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_4446 for (2994ds/1087Mi)
% 6.81/2.52 % (4600)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_4446 for (2994ds/47Mi)
% 6.81/2.53 % (4563)Instruction limit reached!
% 6.81/2.53 % (4563)------------------------------
% 6.81/2.53 % (4563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.53 % (4563)Termination reason: Unknown
% 6.81/2.53 % (4563)Termination phase: Saturation
% 6.81/2.53
% 6.81/2.53 % (4563)Memory used [KB]: 9978
% 6.81/2.53 % (4563)Time elapsed: 0.555 s
% 6.81/2.53 % (4563)Instructions burned: 1041 (million)
% 6.81/2.53 % (4563)------------------------------
% 6.81/2.53 % (4563)------------------------------
% 6.81/2.54 % (4601)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_4446 for (2993ds/44Mi)
% 6.81/2.54 % (4600)Instruction limit reached!
% 6.81/2.54 % (4600)------------------------------
% 6.81/2.54 % (4600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.54 % (4600)Termination reason: Unknown
% 6.81/2.54 % (4600)Termination phase: Preprocessing 3
% 6.81/2.54
% 6.81/2.54 % (4600)Memory used [KB]: 2174
% 6.81/2.54 % (4600)Time elapsed: 0.026 s
% 6.81/2.54 % (4600)Instructions burned: 47 (million)
% 6.81/2.54 % (4600)------------------------------
% 6.81/2.54 % (4600)------------------------------
% 6.81/2.55 % (4596)Instruction limit reached!
% 6.81/2.55 % (4596)------------------------------
% 6.81/2.55 % (4596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.55 % (4596)Termination reason: Unknown
% 6.81/2.55 % (4596)Termination phase: Saturation
% 6.81/2.55
% 6.81/2.55 % (4596)Memory used [KB]: 7291
% 6.81/2.55 % (4596)Time elapsed: 0.080 s
% 6.81/2.55 % (4596)Instructions burned: 149 (million)
% 6.81/2.55 % (4596)------------------------------
% 6.81/2.55 % (4596)------------------------------
% 6.81/2.55 % (4581)Instruction limit reached!
% 6.81/2.55 % (4581)------------------------------
% 6.81/2.55 % (4581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.55 % (4581)Termination reason: Unknown
% 6.81/2.55 % (4581)Termination phase: Saturation
% 6.81/2.55
% 6.81/2.55 % (4581)Memory used [KB]: 8059
% 6.81/2.55 % (4581)Time elapsed: 0.458 s
% 6.81/2.55 % (4581)Instructions burned: 879 (million)
% 6.81/2.55 % (4581)------------------------------
% 6.81/2.55 % (4581)------------------------------
% 6.81/2.56 % (4602)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_4446 for (2993ds/432Mi)
% 6.81/2.56 % (4603)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_4446 for (2993ds/62Mi)
% 6.81/2.57 % (4601)Instruction limit reached!
% 6.81/2.57 % (4601)------------------------------
% 6.81/2.57 % (4601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.57 % (4601)Termination reason: Unknown
% 6.81/2.57 % (4601)Termination phase: Property scanning
% 6.81/2.57
% 6.81/2.57 % (4601)Memory used [KB]: 2174
% 6.81/2.57 % (4601)Time elapsed: 0.024 s
% 6.81/2.57 % (4601)Instructions burned: 45 (million)
% 6.81/2.57 % (4601)------------------------------
% 6.81/2.57 % (4601)------------------------------
% 6.81/2.57 % (4604)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_4446 for (2993ds/31Mi)
% 6.81/2.59 % (4604)Instruction limit reached!
% 6.81/2.59 % (4604)------------------------------
% 6.81/2.59 % (4604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.59 % (4604)Termination reason: Unknown
% 6.81/2.59 % (4604)Termination phase: Preprocessing 1
% 6.81/2.59
% 6.81/2.59 % (4604)Memory used [KB]: 1918
% 6.81/2.59 % (4604)Time elapsed: 0.019 s
% 6.81/2.59 % (4604)Instructions burned: 32 (million)
% 6.81/2.59 % (4604)------------------------------
% 6.81/2.59 % (4604)------------------------------
% 6.81/2.59 % (4605)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_4446 for (2993ds/96Mi)
% 6.81/2.59 % (4603)Instruction limit reached!
% 6.81/2.59 % (4603)------------------------------
% 6.81/2.59 % (4603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.59 % (4603)Termination reason: Unknown
% 6.81/2.59 % (4603)Termination phase: Property scanning
% 6.81/2.59
% 6.81/2.59 % (4603)Memory used [KB]: 2174
% 6.81/2.59 % (4603)Time elapsed: 0.032 s
% 6.81/2.59 % (4603)Instructions burned: 62 (million)
% 6.81/2.59 % (4603)------------------------------
% 6.81/2.59 % (4603)------------------------------
% 7.64/2.60 % (4606)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_4446 for (2993ds/453Mi)
% 7.64/2.61 % (4607)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_4446 for (2993ds/71Mi)
% 7.64/2.62 % (4592)Instruction limit reached!
% 7.64/2.62 % (4592)------------------------------
% 7.64/2.62 % (4592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.64/2.62 % (4592)Termination reason: Unknown
% 7.64/2.62 % (4592)Termination phase: Saturation
% 7.64/2.62
% 7.64/2.62 % (4592)Memory used [KB]: 8443
% 7.64/2.62 % (4592)Time elapsed: 0.231 s
% 7.64/2.62 % (4592)Instructions burned: 449 (million)
% 7.64/2.62 % (4592)------------------------------
% 7.64/2.62 % (4592)------------------------------
% 7.64/2.64 % (4608)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_4446 for (2992ds/83Mi)
% 7.64/2.64 % (4607)Instruction limit reached!
% 7.64/2.64 % (4607)------------------------------
% 7.64/2.64 % (4607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.64/2.64 % (4607)Termination reason: Unknown
% 7.64/2.64 % (4607)Termination phase: Property scanning
% 7.64/2.64
% 7.64/2.64 % (4607)Memory used [KB]: 2302
% 7.64/2.64 % (4607)Time elapsed: 0.034 s
% 7.64/2.64 % (4607)Instructions burned: 72 (million)
% 7.64/2.64 % (4607)------------------------------
% 7.64/2.64 % (4607)------------------------------
% 7.64/2.65 % (4605)Instruction limit reached!
% 7.64/2.65 % (4605)------------------------------
% 7.64/2.65 % (4605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.64/2.65 % (4605)Termination reason: Unknown
% 7.64/2.65 % (4605)Termination phase: Saturation
% 7.64/2.65
% 7.64/2.65 % (4605)Memory used [KB]: 6908
% 7.64/2.65 % (4605)Time elapsed: 0.039 s
% 7.64/2.65 % (4605)Instructions burned: 97 (million)
% 7.64/2.65 % (4605)------------------------------
% 7.64/2.65 % (4605)------------------------------
% 7.64/2.66 % (4609)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_4446 for (2992ds/11Mi)
% 7.64/2.66 % (4610)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_4446 for (2992ds/41Mi)
% 7.64/2.66 % (4609)Instruction limit reached!
% 7.64/2.66 % (4609)------------------------------
% 7.64/2.66 % (4609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.64/2.66 % (4609)Termination reason: Unknown
% 7.64/2.66 % (4609)Termination phase: shuffling
% 7.64/2.66
% 7.64/2.66 % (4609)Memory used [KB]: 1663
% 7.64/2.66 % (4609)Time elapsed: 0.007 s
% 7.64/2.66 % (4609)Instructions burned: 12 (million)
% 7.64/2.66 % (4609)------------------------------
% 7.64/2.66 % (4609)------------------------------
% 7.64/2.67 % (4610)Instruction limit reached!
% 7.64/2.67 % (4610)------------------------------
% 7.64/2.67 % (4610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.64/2.67 % (4610)Termination reason: Unknown
% 7.64/2.67 % (4610)Termination phase: Property scanning
% 7.64/2.67
% 7.64/2.67 % (4610)Memory used [KB]: 2174
% 7.64/2.67 % (4610)Time elapsed: 0.014 s
% 7.64/2.67 % (4610)Instructions burned: 44 (million)
% 7.64/2.67 % (4610)------------------------------
% 7.64/2.67 % (4610)------------------------------
% 7.64/2.68 % (4611)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_4446 for (2992ds/6Mi)
% 7.64/2.68 % (4611)Instruction limit reached!
% 7.64/2.68 % (4611)------------------------------
% 7.64/2.68 % (4611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.64/2.68 % (4611)Termination reason: Unknown
% 7.64/2.68 % (4611)Termination phase: shuffling
% 7.64/2.68
% 7.64/2.68 % (4611)Memory used [KB]: 1535
% 7.64/2.68 % (4611)Time elapsed: 0.004 s
% 7.64/2.68 % (4611)Instructions burned: 8 (million)
% 7.64/2.68 % (4611)------------------------------
% 7.64/2.68 % (4611)------------------------------
% 7.64/2.68 % (4608)Instruction limit reached!
% 7.64/2.68 % (4608)------------------------------
% 7.64/2.68 % (4608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.64/2.68 % (4608)Termination reason: Unknown
% 7.64/2.68 % (4608)Termination phase: Saturation
% 7.64/2.68
% 7.64/2.68 % (4608)Memory used [KB]: 6652
% 7.64/2.68 % (4608)Time elapsed: 0.047 s
% 7.64/2.68 % (4608)Instructions burned: 83 (million)
% 7.64/2.68 % (4608)------------------------------
% 7.64/2.68 % (4608)------------------------------
% 7.64/2.68 % (4612)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_4446 for (2992ds/150Mi)
% 7.64/2.69 % (4613)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_4446 for (2992ds/343Mi)
% 7.64/2.70 % (4614)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_4446 for (2992ds/109Mi)
% 8.11/2.70 % (4595)Instruction limit reached!
% 8.11/2.70 % (4595)------------------------------
% 8.11/2.70 % (4595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.11/2.70 % (4595)Termination reason: Unknown
% 8.11/2.70 % (4595)Termination phase: Saturation
% 8.11/2.70
% 8.11/2.70 % (4595)Memory used [KB]: 8443
% 8.11/2.70 % (4595)Time elapsed: 0.265 s
% 8.11/2.70 % (4595)Instructions burned: 508 (million)
% 8.11/2.70 % (4595)------------------------------
% 8.11/2.70 % (4595)------------------------------
% 8.11/2.72 % (4615)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_4446 for (2992ds/253Mi)
% 8.11/2.73 % (4614)Instruction limit reached!
% 8.11/2.73 % (4614)------------------------------
% 8.11/2.73 % (4614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.11/2.73 % (4614)Termination reason: Unknown
% 8.11/2.73 % (4614)Termination phase: Saturation
% 8.11/2.73
% 8.11/2.73 % (4614)Memory used [KB]: 7036
% 8.11/2.73 % (4614)Time elapsed: 0.034 s
% 8.11/2.73 % (4614)Instructions burned: 110 (million)
% 8.11/2.73 % (4614)------------------------------
% 8.11/2.73 % (4614)------------------------------
% 8.11/2.73 % (4612)Instruction limit reached!
% 8.11/2.73 % (4612)------------------------------
% 8.11/2.73 % (4612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.11/2.73 % (4612)Termination reason: Unknown
% 8.11/2.73 % (4612)Termination phase: Saturation
% 8.11/2.73
% 8.11/2.73 % (4612)Memory used [KB]: 7291
% 8.11/2.73 % (4612)Time elapsed: 0.053 s
% 8.11/2.73 % (4612)Instructions burned: 151 (million)
% 8.11/2.73 % (4612)------------------------------
% 8.11/2.73 % (4612)------------------------------
% 8.11/2.74 % (4616)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_4446 for (2991ds/140Mi)
% 8.11/2.75 % (4617)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_4446 for (2991ds/614Mi)
% 8.11/2.76 % (4602)Instruction limit reached!
% 8.11/2.76 % (4602)------------------------------
% 8.11/2.76 % (4602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.11/2.76 % (4602)Termination reason: Unknown
% 8.11/2.76 % (4602)Termination phase: Saturation
% 8.11/2.76
% 8.11/2.76 % (4602)Memory used [KB]: 3709
% 8.11/2.76 % (4602)Time elapsed: 0.199 s
% 8.11/2.76 % (4602)Instructions burned: 432 (million)
% 8.11/2.76 % (4602)------------------------------
% 8.11/2.76 % (4602)------------------------------
% 8.11/2.77 % (4606)Instruction limit reached!
% 8.11/2.77 % (4606)------------------------------
% 8.11/2.77 % (4606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.11/2.77 % (4606)Termination reason: Unknown
% 8.11/2.77 % (4606)Termination phase: Saturation
% 8.11/2.77
% 8.11/2.77 % (4606)Memory used [KB]: 7803
% 8.11/2.77 % (4606)Time elapsed: 0.167 s
% 8.11/2.77 % (4606)Instructions burned: 453 (million)
% 8.11/2.77 % (4606)------------------------------
% 8.11/2.77 % (4606)------------------------------
% 8.11/2.77 % (4618)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_4446 for (2991ds/202Mi)
% 8.11/2.78 % (4619)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_4446 for (2991ds/339Mi)
% 8.11/2.79 % (4616)Instruction limit reached!
% 8.11/2.79 % (4616)------------------------------
% 8.11/2.79 % (4616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.11/2.79 % (4616)Termination reason: Unknown
% 8.11/2.79 % (4616)Termination phase: Saturation
% 8.11/2.79
% 8.11/2.79 % (4616)Memory used [KB]: 7036
% 8.11/2.79 % (4616)Time elapsed: 0.074 s
% 8.11/2.79 % (4616)Instructions burned: 141 (million)
% 8.11/2.79 % (4616)------------------------------
% 8.11/2.79 % (4616)------------------------------
% 8.11/2.79 % (4613)Instruction limit reached!
% 8.11/2.79 % (4613)------------------------------
% 8.11/2.79 % (4613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.11/2.79 % (4613)Termination reason: Unknown
% 8.11/2.79 % (4613)Termination phase: Saturation
% 8.11/2.79
% 8.11/2.79 % (4613)Memory used [KB]: 7547
% 8.11/2.79 % (4613)Time elapsed: 0.106 s
% 8.11/2.79 % (4613)Instructions burned: 343 (million)
% 8.11/2.79 % (4613)------------------------------
% 8.11/2.79 % (4613)------------------------------
% 9.07/2.80 % (4618)Refutation not found, incomplete strategy
% 9.07/2.80 % (4618)------------------------------
% 9.07/2.80 % (4618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.07/2.80 % (4618)Termination reason: Refutation not found, incomplete strategy
% 9.07/2.80
% 9.07/2.80
% 9.07/2.80 % (4618)Memory used [KB]: 6780
% 9.07/2.80 % (4618)Time elapsed: 0.030 s
% 9.07/2.80 % (4618)Instructions burned: 67 (million)
% 9.07/2.80 % (4618)------------------------------
% 9.07/2.80 % (4618)------------------------------
% 9.07/2.80 % (4620)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_4446 for (2991ds/283Mi)
% 9.07/2.80 % (4621)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_4446 for (2991ds/134Mi)
% 9.07/2.81 % (4622)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_4446 for (2991ds/298Mi)
% 9.07/2.81 % (4615)Instruction limit reached!
% 9.07/2.81 % (4615)------------------------------
% 9.07/2.81 % (4615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.07/2.81 % (4615)Termination reason: Unknown
% 9.07/2.81 % (4615)Termination phase: Saturation
% 9.07/2.81
% 9.07/2.81 % (4615)Memory used [KB]: 7291
% 9.07/2.81 % (4615)Time elapsed: 0.115 s
% 9.07/2.81 % (4615)Instructions burned: 255 (million)
% 9.07/2.81 % (4615)------------------------------
% 9.07/2.81 % (4615)------------------------------
% 9.07/2.82 % (4623)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_4446 for (2990ds/192Mi)
% 9.07/2.84 % (4621)Instruction limit reached!
% 9.07/2.84 % (4621)------------------------------
% 9.07/2.84 % (4621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.07/2.84 % (4621)Termination reason: Unknown
% 9.07/2.84 % (4621)Termination phase: Saturation
% 9.07/2.84
% 9.07/2.84 % (4621)Memory used [KB]: 7036
% 9.07/2.84 % (4621)Time elapsed: 0.040 s
% 9.07/2.84 % (4621)Instructions burned: 134 (million)
% 9.07/2.84 % (4621)------------------------------
% 9.07/2.84 % (4621)------------------------------
% 9.07/2.85 % (4624)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_4446 for (2990ds/258Mi)
% 9.07/2.87 % (4619)Instruction limit reached!
% 9.07/2.87 % (4619)------------------------------
% 9.07/2.87 % (4619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.07/2.87 % (4619)Termination reason: Unknown
% 9.07/2.87 % (4619)Termination phase: Saturation
% 9.07/2.87
% 9.07/2.87 % (4619)Memory used [KB]: 7547
% 9.07/2.87 % (4619)Time elapsed: 0.098 s
% 9.07/2.87 % (4619)Instructions burned: 342 (million)
% 9.07/2.87 % (4619)------------------------------
% 9.07/2.87 % (4619)------------------------------
% 9.07/2.88 % (4625)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_4446 for (2990ds/90Mi)
% 9.07/2.88 % (4623)Instruction limit reached!
% 9.07/2.88 % (4623)------------------------------
% 9.07/2.88 % (4623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.07/2.88 % (4623)Termination reason: Unknown
% 9.07/2.88 % (4623)Termination phase: Saturation
% 9.07/2.88
% 9.07/2.88 % (4623)Memory used [KB]: 8315
% 9.07/2.88 % (4623)Time elapsed: 0.066 s
% 9.07/2.88 % (4623)Instructions burned: 194 (million)
% 9.07/2.88 % (4623)------------------------------
% 9.07/2.88 % (4623)------------------------------
% 9.07/2.89 % (4622)Instruction limit reached!
% 9.07/2.89 % (4622)------------------------------
% 9.07/2.89 % (4622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.07/2.89 % (4622)Termination reason: Unknown
% 9.07/2.89 % (4622)Termination phase: Saturation
% 9.07/2.89
% 9.07/2.89 % (4622)Memory used [KB]: 7931
% 9.07/2.89 % (4622)Time elapsed: 0.086 s
% 9.07/2.89 % (4622)Instructions burned: 300 (million)
% 9.07/2.89 % (4622)------------------------------
% 9.07/2.89 % (4622)------------------------------
% 9.07/2.89 % (4626)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_4446 for (2990ds/231Mi)
% 9.53/2.90 % (4627)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_4446 for (2990ds/458Mi)
% 9.53/2.90 % (4620)Instruction limit reached!
% 9.53/2.90 % (4620)------------------------------
% 9.53/2.90 % (4620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/2.90 % (4620)Termination reason: Unknown
% 9.53/2.90 % (4620)Termination phase: Saturation
% 9.53/2.90
% 9.53/2.90 % (4620)Memory used [KB]: 7675
% 9.53/2.90 % (4620)Time elapsed: 0.105 s
% 9.53/2.90 % (4620)Instructions burned: 283 (million)
% 9.53/2.90 % (4620)------------------------------
% 9.53/2.90 % (4620)------------------------------
% 9.53/2.91 % (4599)Instruction limit reached!
% 9.53/2.91 % (4599)------------------------------
% 9.53/2.91 % (4599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/2.91 % (4599)Termination reason: Unknown
% 9.53/2.91 % (4599)Termination phase: Saturation
% 9.53/2.91
% 9.53/2.91 % (4599)Memory used [KB]: 8571
% 9.53/2.91 % (4599)Time elapsed: 0.392 s
% 9.53/2.91 % (4599)Instructions burned: 1089 (million)
% 9.53/2.91 % (4599)------------------------------
% 9.53/2.91 % (4599)------------------------------
% 9.53/2.91 % (4625)Instruction limit reached!
% 9.53/2.91 % (4625)------------------------------
% 9.53/2.91 % (4625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/2.91 % (4625)Termination reason: Unknown
% 9.53/2.91 % (4625)Termination phase: Saturation
% 9.53/2.91
% 9.53/2.91 % (4625)Memory used [KB]: 6908
% 9.53/2.91 % (4625)Time elapsed: 0.028 s
% 9.53/2.91 % (4625)Instructions burned: 92 (million)
% 9.53/2.91 % (4625)------------------------------
% 9.53/2.91 % (4625)------------------------------
% 9.53/2.91 % (4628)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_4446 for (2990ds/31Mi)
% 9.53/2.92 % (4629)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_4446 for (2989ds/297Mi)
% 9.53/2.92 % (4630)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_4446 for (2989ds/987Mi)
% 9.53/2.92 % (4628)Instruction limit reached!
% 9.53/2.92 % (4628)------------------------------
% 9.53/2.92 % (4628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/2.92 % (4628)Termination reason: Unknown
% 9.53/2.92 % (4628)Termination phase: Preprocessing 1
% 9.53/2.92
% 9.53/2.92 % (4628)Memory used [KB]: 1918
% 9.53/2.92 % (4628)Time elapsed: 0.011 s
% 9.53/2.92 % (4628)Instructions burned: 33 (million)
% 9.53/2.92 % (4628)------------------------------
% 9.53/2.92 % (4628)------------------------------
% 9.53/2.93 % (4624)Instruction limit reached!
% 9.53/2.93 % (4624)------------------------------
% 9.53/2.93 % (4624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/2.93 % (4624)Termination reason: Unknown
% 9.53/2.93 % (4624)Termination phase: Saturation
% 9.53/2.93
% 9.53/2.93 % (4624)Memory used [KB]: 7675
% 9.53/2.93 % (4624)Time elapsed: 0.080 s
% 9.53/2.93 % (4624)Instructions burned: 258 (million)
% 9.53/2.93 % (4624)------------------------------
% 9.53/2.93 % (4624)------------------------------
% 9.53/2.93 % (4631)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_4446 for (2989ds/182Mi)
% 9.53/2.94 % (4632)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_4446 for (2989ds/182Mi)
% 9.53/2.95 % (4617)Instruction limit reached!
% 9.53/2.95 % (4617)------------------------------
% 9.53/2.95 % (4617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/2.95 % (4617)Termination reason: Unknown
% 9.53/2.95 % (4617)Termination phase: Saturation
% 9.53/2.95
% 9.53/2.95 % (4617)Memory used [KB]: 8827
% 9.53/2.95 % (4617)Time elapsed: 0.227 s
% 9.53/2.95 % (4617)Instructions burned: 615 (million)
% 9.53/2.95 % (4617)------------------------------
% 9.53/2.95 % (4617)------------------------------
% 9.53/2.96 % (4626)Instruction limit reached!
% 9.53/2.96 % (4626)------------------------------
% 9.53/2.96 % (4626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/2.96 % (4626)Termination reason: Unknown
% 9.53/2.96 % (4626)Termination phase: Saturation
% 9.53/2.96
% 9.53/2.96 % (4626)Memory used [KB]: 7036
% 9.53/2.96 % (4626)Time elapsed: 0.063 s
% 9.53/2.96 % (4626)Instructions burned: 233 (million)
% 9.53/2.96 % (4626)------------------------------
% 9.53/2.96 % (4626)------------------------------
% 9.53/2.96 % (4633)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_4446 for (2989ds/154Mi)
% 9.53/2.97 % (4634)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_4446 for (2989ds/79Mi)
% 9.53/2.99 % (4631)Instruction limit reached!
% 9.53/2.99 % (4631)------------------------------
% 9.53/2.99 % (4631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/2.99 % (4631)Termination reason: Unknown
% 9.53/2.99 % (4631)Termination phase: Saturation
% 9.53/2.99
% 9.53/2.99 % (4631)Memory used [KB]: 7291
% 9.53/2.99 % (4631)Time elapsed: 0.055 s
% 9.53/2.99 % (4631)Instructions burned: 184 (million)
% 9.53/2.99 % (4631)------------------------------
% 9.53/2.99 % (4631)------------------------------
% 9.53/2.99 % (4634)Instruction limit reached!
% 9.53/2.99 % (4634)------------------------------
% 9.53/2.99 % (4634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/2.99 % (4634)Termination reason: Unknown
% 9.53/2.99 % (4634)Termination phase: Property scanning
% 9.53/2.99
% 9.53/2.99 % (4634)Memory used [KB]: 2302
% 9.53/2.99 % (4634)Time elapsed: 0.024 s
% 9.53/2.99 % (4634)Instructions burned: 79 (million)
% 9.53/2.99 % (4634)------------------------------
% 9.53/2.99 % (4634)------------------------------
% 9.53/3.00 % (4632)Instruction limit reached!
% 9.53/3.00 % (4632)------------------------------
% 9.53/3.00 % (4632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/3.00 % (4632)Termination reason: Unknown
% 9.53/3.00 % (4632)Termination phase: Saturation
% 9.53/3.00
% 9.53/3.00 % (4632)Memory used [KB]: 7419
% 9.53/3.00 % (4632)Time elapsed: 0.057 s
% 9.53/3.00 % (4632)Instructions burned: 182 (million)
% 9.53/3.00 % (4632)------------------------------
% 9.53/3.00 % (4632)------------------------------
% 9.53/3.00 % (4635)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_4446 for (2989ds/216Mi)
% 9.53/3.00 % (4636)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_4446 for (2989ds/114Mi)
% 9.53/3.00 % (4633)Instruction limit reached!
% 9.53/3.00 % (4633)------------------------------
% 9.53/3.00 % (4633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.53/3.00 % (4633)Termination reason: Unknown
% 9.53/3.00 % (4633)Termination phase: Saturation
% 9.53/3.00
% 9.53/3.00 % (4633)Memory used [KB]: 2558
% 9.53/3.00 % (4633)Time elapsed: 0.044 s
% 9.53/3.00 % (4633)Instructions burned: 157 (million)
% 9.53/3.00 % (4633)------------------------------
% 9.53/3.00 % (4633)------------------------------
% 9.53/3.00 % (4637)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_4446 for (2989ds/922Mi)
% 11.01/3.02 % (4629)Instruction limit reached!
% 11.01/3.02 % (4629)------------------------------
% 11.01/3.02 % (4629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.01/3.02 % (4629)Termination reason: Unknown
% 11.01/3.02 % (4629)Termination phase: Saturation
% 11.01/3.02
% 11.01/3.02 % (4629)Memory used [KB]: 7675
% 11.01/3.02 % (4629)Time elapsed: 0.101 s
% 11.01/3.02 % (4629)Instructions burned: 297 (million)
% 11.01/3.02 % (4629)------------------------------
% 11.01/3.02 % (4629)------------------------------
% 11.01/3.02 % (4638)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_4446 for (2989ds/182Mi)
% 11.01/3.03 % (4639)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_4446 for (2988ds/164Mi)
% 11.01/3.04 % (4627)Refutation not found, non-redundant clauses discarded% (4627)------------------------------
% 11.01/3.04 % (4627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.01/3.04 % (4627)Termination reason: Refutation not found, non-redundant clauses discarded
% 11.01/3.04
% 11.01/3.04 % (4627)Memory used [KB]: 8187
% 11.01/3.04 % (4627)Time elapsed: 0.139 s
% 11.01/3.04 % (4627)Instructions burned: 446 (million)
% 11.01/3.04 % (4627)------------------------------
% 11.01/3.04 % (4627)------------------------------
% 11.01/3.05 % (4640)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_4446 for (2988ds/50Mi)
% 11.01/3.06 % (4635)Instruction limit reached!
% 11.01/3.06 % (4635)------------------------------
% 11.01/3.06 % (4635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.01/3.06 % (4635)Termination reason: Unknown
% 11.01/3.06 % (4635)Termination phase: Saturation
% 11.01/3.06
% 11.01/3.06 % (4635)Memory used [KB]: 7419
% 11.01/3.06 % (4635)Time elapsed: 0.063 s
% 11.01/3.06 % (4635)Instructions burned: 216 (million)
% 11.01/3.06 % (4635)------------------------------
% 11.01/3.06 % (4635)------------------------------
% 11.01/3.06 % (4636)Instruction limit reached!
% 11.01/3.06 % (4636)------------------------------
% 11.01/3.06 % (4636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.01/3.06 % (4636)Termination reason: Unknown
% 11.01/3.06 % (4636)Termination phase: Saturation
% 11.01/3.06
% 11.01/3.06 % (4636)Memory used [KB]: 7036
% 11.01/3.06 % (4636)Time elapsed: 0.059 s
% 11.01/3.06 % (4636)Instructions burned: 115 (million)
% 11.01/3.06 % (4636)------------------------------
% 11.01/3.06 % (4636)------------------------------
% 11.01/3.06 % (4640)Instruction limit reached!
% 11.01/3.06 % (4640)------------------------------
% 11.01/3.06 % (4640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.01/3.06 % (4640)Termination reason: Unknown
% 11.01/3.06 % (4640)Termination phase: Property scanning
% 11.01/3.06
% 11.01/3.06 % (4640)Memory used [KB]: 2174
% 11.01/3.06 % (4640)Time elapsed: 0.015 s
% 11.01/3.06 % (4640)Instructions burned: 51 (million)
% 11.01/3.06 % (4640)------------------------------
% 11.01/3.06 % (4640)------------------------------
% 11.01/3.07 % (4641)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_4446 for (2988ds/368Mi)
% 11.01/3.07 % (4642)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_4446 for (2988ds/1021Mi)
% 11.01/3.07 % (4638)Instruction limit reached!
% 11.01/3.07 % (4638)------------------------------
% 11.01/3.07 % (4638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.01/3.07 % (4638)Termination reason: Unknown
% 11.01/3.07 % (4638)Termination phase: Saturation
% 11.01/3.07
% 11.01/3.07 % (4638)Memory used [KB]: 7036
% 11.01/3.07 % (4638)Time elapsed: 0.052 s
% 11.01/3.07 % (4638)Instructions burned: 183 (million)
% 11.01/3.07 % (4638)------------------------------
% 11.01/3.07 % (4638)------------------------------
% 11.01/3.07 % (4643)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_4446 for (2988ds/267Mi)
% 11.01/3.08 % (4639)Instruction limit reached!
% 11.01/3.08 % (4639)------------------------------
% 11.01/3.08 % (4639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.01/3.08 % (4639)Termination reason: Unknown
% 11.01/3.08 % (4639)Termination phase: Saturation
% 11.01/3.08
% 11.01/3.08 % (4639)Memory used [KB]: 2558
% 11.01/3.08 % (4639)Time elapsed: 0.049 s
% 11.01/3.08 % (4639)Instructions burned: 166 (million)
% 11.01/3.08 % (4639)------------------------------
% 11.01/3.08 % (4639)------------------------------
% 11.01/3.08 % (4644)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_4446 for (2988ds/204Mi)
% 11.01/3.09 % (4645)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_4446 for (2988ds/26Mi)
% 11.01/3.09 % (4645)Instruction limit reached!
% 11.01/3.09 % (4645)------------------------------
% 11.01/3.09 % (4645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.01/3.09 % (4645)Termination reason: Unknown
% 11.01/3.09 % (4645)Termination phase: shuffling
% 11.01/3.09
% 11.01/3.09 % (4645)Memory used [KB]: 2046
% 11.01/3.09 % (4645)Time elapsed: 0.009 s
% 11.01/3.09 % (4645)Instructions burned: 28 (million)
% 11.01/3.09 % (4645)------------------------------
% 11.01/3.09 % (4645)------------------------------
% 11.01/3.10 % (4646)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_4446 for (2988ds/53Mi)
% 11.53/3.12 % (4646)Instruction limit reached!
% 11.53/3.12 % (4646)------------------------------
% 11.53/3.12 % (4646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.53/3.12 % (4646)Termination reason: Unknown
% 11.53/3.12 % (4646)Termination phase: Property scanning
% 11.53/3.12
% 11.53/3.12 % (4646)Memory used [KB]: 2174
% 11.53/3.12 % (4646)Time elapsed: 0.016 s
% 11.53/3.12 % (4646)Instructions burned: 55 (million)
% 11.53/3.12 % (4646)------------------------------
% 11.53/3.12 % (4646)------------------------------
% 11.53/3.13 % (4647)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_4446 for (2987ds/4436Mi)
% 11.53/3.14 % (4644)Instruction limit reached!
% 11.53/3.14 % (4644)------------------------------
% 11.53/3.14 % (4644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.53/3.14 % (4644)Termination reason: Unknown
% 11.53/3.14 % (4644)Termination phase: Saturation
% 11.53/3.14
% 11.53/3.14 % (4644)Memory used [KB]: 7291
% 11.53/3.14 % (4644)Time elapsed: 0.063 s
% 11.53/3.14 % (4644)Instructions burned: 204 (million)
% 11.53/3.14 % (4644)------------------------------
% 11.53/3.14 % (4644)------------------------------
% 11.53/3.15 % (4648)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_4446 for (2987ds/1539Mi)
% 11.53/3.15 % (4643)Instruction limit reached!
% 11.53/3.15 % (4643)------------------------------
% 11.53/3.15 % (4643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.53/3.15 % (4643)Termination reason: Unknown
% 11.53/3.15 % (4643)Termination phase: Saturation
% 11.53/3.15
% 11.53/3.15 % (4643)Memory used [KB]: 7547
% 11.53/3.15 % (4643)Time elapsed: 0.081 s
% 11.53/3.15 % (4643)Instructions burned: 269 (million)
% 11.53/3.15 % (4643)------------------------------
% 11.53/3.15 % (4643)------------------------------
% 11.53/3.16 % (4649)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_4446 for (2987ds/408Mi)
% 11.53/3.18 % (4641)Instruction limit reached!
% 11.53/3.18 % (4641)------------------------------
% 11.53/3.18 % (4641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.53/3.18 % (4641)Termination reason: Unknown
% 11.53/3.18 % (4641)Termination phase: Saturation
% 11.53/3.18
% 11.53/3.18 % (4641)Memory used [KB]: 8187
% 11.53/3.18 % (4641)Time elapsed: 0.115 s
% 11.53/3.18 % (4641)Instructions burned: 370 (million)
% 11.53/3.18 % (4641)------------------------------
% 11.53/3.18 % (4641)------------------------------
% 11.53/3.19 % (4650)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_4446 for (2987ds/5205Mi)
% 12.01/3.22 % (4630)Instruction limit reached!
% 12.01/3.22 % (4630)------------------------------
% 12.01/3.22 % (4630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.01/3.22 % (4630)Termination reason: Unknown
% 12.01/3.22 % (4630)Termination phase: Saturation
% 12.01/3.22
% 12.01/3.22 % (4630)Memory used [KB]: 9722
% 12.01/3.22 % (4630)Time elapsed: 0.303 s
% 12.01/3.22 % (4630)Instructions burned: 988 (million)
% 12.01/3.22 % (4630)------------------------------
% 12.01/3.22 % (4630)------------------------------
% 12.01/3.23 % (4651)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_4446 for (2986ds/1913Mi)
% 12.01/3.29 % (4649)Instruction limit reached!
% 12.01/3.29 % (4649)------------------------------
% 12.01/3.29 % (4649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.01/3.29 % (4649)Termination reason: Unknown
% 12.01/3.29 % (4649)Termination phase: Saturation
% 12.01/3.29
% 12.01/3.29 % (4649)Memory used [KB]: 8571
% 12.01/3.29 % (4649)Time elapsed: 0.123 s
% 12.01/3.29 % (4649)Instructions burned: 408 (million)
% 12.01/3.29 % (4649)------------------------------
% 12.01/3.29 % (4649)------------------------------
% 12.01/3.29 % (4637)Instruction limit reached!
% 12.01/3.29 % (4637)------------------------------
% 12.01/3.29 % (4637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.01/3.29 % (4637)Termination reason: Unknown
% 12.01/3.29 % (4637)Termination phase: Saturation
% 12.01/3.29
% 12.01/3.29 % (4637)Memory used [KB]: 7547
% 12.01/3.29 % (4637)Time elapsed: 0.285 s
% 12.01/3.29 % (4637)Instructions burned: 922 (million)
% 12.01/3.29 % (4637)------------------------------
% 12.01/3.29 % (4637)------------------------------
% 12.01/3.30 % (4652)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_4446 for (2986ds/4350Mi)
% 12.28/3.30 % (4653)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_4446 for (2986ds/68Mi)
% 12.28/3.32 % (4653)Instruction limit reached!
% 12.28/3.32 % (4653)------------------------------
% 12.28/3.32 % (4653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.28/3.32 % (4653)Termination reason: Unknown
% 12.28/3.32 % (4653)Termination phase: Function definition elimination
% 12.28/3.32
% 12.28/3.32 % (4653)Memory used [KB]: 2302
% 12.28/3.32 % (4653)Time elapsed: 0.022 s
% 12.28/3.32 % (4653)Instructions burned: 69 (million)
% 12.28/3.32 % (4653)------------------------------
% 12.28/3.32 % (4653)------------------------------
% 12.28/3.33 % (4654)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_4446 for (2985ds/358Mi)
% 12.28/3.38 % (4642)Instruction limit reached!
% 12.28/3.38 % (4642)------------------------------
% 12.28/3.38 % (4642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.28/3.38 % (4642)Termination reason: Unknown
% 12.28/3.38 % (4642)Termination phase: Saturation
% 12.28/3.38
% 12.28/3.38 % (4642)Memory used [KB]: 8699
% 12.28/3.38 % (4642)Time elapsed: 0.308 s
% 12.28/3.38 % (4642)Instructions burned: 1023 (million)
% 12.28/3.38 % (4642)------------------------------
% 12.28/3.38 % (4642)------------------------------
% 12.28/3.38 % (4655)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_4446 for (2985ds/31Mi)
% 12.28/3.39 % (4655)Instruction limit reached!
% 12.28/3.39 % (4655)------------------------------
% 12.28/3.39 % (4655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.28/3.39 % (4655)Termination reason: Unknown
% 12.28/3.39 % (4655)Termination phase: Preprocessing 1
% 12.28/3.39
% 12.28/3.39 % (4655)Memory used [KB]: 1918
% 12.28/3.39 % (4655)Time elapsed: 0.011 s
% 12.28/3.39 % (4655)Instructions burned: 32 (million)
% 12.28/3.39 % (4655)------------------------------
% 12.28/3.39 % (4655)------------------------------
% 12.64/3.40 % (4656)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_4446 for (2985ds/279Mi)
% 12.64/3.44 % (4654)Instruction limit reached!
% 12.64/3.44 % (4654)------------------------------
% 12.64/3.44 % (4654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.64/3.44 % (4654)Termination reason: Unknown
% 12.64/3.44 % (4654)Termination phase: Saturation
% 12.64/3.44
% 12.64/3.44 % (4654)Memory used [KB]: 7675
% 12.64/3.44 % (4654)Time elapsed: 0.113 s
% 12.64/3.44 % (4654)Instructions burned: 360 (million)
% 12.64/3.44 % (4654)------------------------------
% 12.64/3.44 % (4654)------------------------------
% 12.64/3.44 % (4656)Refutation not found, incomplete strategy
% 12.64/3.44 % (4656)------------------------------
% 12.64/3.44 % (4656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.64/3.44 % (4656)Termination reason: Refutation not found, incomplete strategy
% 12.64/3.44
% 12.64/3.44
% 12.64/3.44 % (4656)Memory used [KB]: 7036
% 12.64/3.44 % (4656)Time elapsed: 0.038 s
% 12.64/3.44 % (4656)Instructions burned: 130 (million)
% 12.64/3.44 % (4656)------------------------------
% 12.64/3.44 % (4656)------------------------------
% 12.64/3.45 % (4657)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_4446 for (2984ds/258Mi)
% 12.64/3.45 % (4658)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_4446 for (2984ds/26Mi)
% 12.64/3.46 % (4658)Instruction limit reached!
% 12.64/3.46 % (4658)------------------------------
% 12.64/3.46 % (4658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.64/3.46 % (4658)Termination reason: Unknown
% 12.64/3.46 % (4658)Termination phase: shuffling
% 12.64/3.46
% 12.64/3.46 % (4658)Memory used [KB]: 2046
% 12.64/3.46 % (4658)Time elapsed: 0.009 s
% 12.64/3.46 % (4658)Instructions burned: 28 (million)
% 12.64/3.46 % (4658)------------------------------
% 12.64/3.46 % (4658)------------------------------
% 12.64/3.47 % (4659)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_4446 for (2984ds/995Mi)
% 12.82/3.53 % (4657)Instruction limit reached!
% 12.82/3.53 % (4657)------------------------------
% 12.82/3.53 % (4657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.82/3.53 % (4657)Termination reason: Unknown
% 12.82/3.53 % (4657)Termination phase: Saturation
% 12.82/3.53
% 12.82/3.53 % (4657)Memory used [KB]: 7547
% 12.82/3.53 % (4657)Time elapsed: 0.079 s
% 12.82/3.53 % (4657)Instructions burned: 258 (million)
% 12.82/3.53 % (4657)------------------------------
% 12.82/3.53 % (4657)------------------------------
% 12.82/3.54 % (4660)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_4446 for (2983ds/373Mi)
% 12.93/3.62 % (4648)Instruction limit reached!
% 12.93/3.62 % (4648)------------------------------
% 12.93/3.62 % (4648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.93/3.62 % (4648)Termination reason: Unknown
% 12.93/3.62 % (4648)Termination phase: Saturation
% 12.93/3.62
% 12.93/3.62 % (4648)Memory used [KB]: 10746
% 12.93/3.62 % (4648)Time elapsed: 0.472 s
% 12.93/3.62 % (4648)Instructions burned: 1541 (million)
% 12.93/3.62 % (4648)------------------------------
% 12.93/3.62 % (4648)------------------------------
% 12.93/3.63 % (4661)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_4446 for (2982ds/253Mi)
% 12.93/3.65 % (4660)Instruction limit reached!
% 12.93/3.65 % (4660)------------------------------
% 12.93/3.65 % (4660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.93/3.65 % (4660)Termination reason: Unknown
% 12.93/3.65 % (4660)Termination phase: Saturation
% 12.93/3.65
% 12.93/3.65 % (4660)Memory used [KB]: 8955
% 12.93/3.65 % (4660)Time elapsed: 0.115 s
% 12.93/3.65 % (4660)Instructions burned: 374 (million)
% 12.93/3.65 % (4660)------------------------------
% 12.93/3.65 % (4660)------------------------------
% 12.93/3.66 % (4662)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_4446 for (2982ds/832Mi)
% 13.52/3.71 % (4661)Instruction limit reached!
% 13.52/3.71 % (4661)------------------------------
% 13.52/3.71 % (4661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.52/3.71 % (4661)Termination reason: Unknown
% 13.52/3.71 % (4661)Termination phase: Saturation
% 13.52/3.71
% 13.52/3.71 % (4661)Memory used [KB]: 7675
% 13.52/3.71 % (4661)Time elapsed: 0.073 s
% 13.52/3.71 % (4661)Instructions burned: 254 (million)
% 13.52/3.71 % (4661)------------------------------
% 13.52/3.71 % (4661)------------------------------
% 13.52/3.72 % (4663)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_4446 for (2981ds/668Mi)
% 13.52/3.76 % (4659)Instruction limit reached!
% 13.52/3.76 % (4659)------------------------------
% 13.52/3.76 % (4659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.52/3.76 % (4659)Termination reason: Unknown
% 13.52/3.76 % (4659)Termination phase: Saturation
% 13.52/3.76
% 13.52/3.76 % (4659)Memory used [KB]: 9722
% 13.52/3.76 % (4659)Time elapsed: 0.295 s
% 13.52/3.76 % (4659)Instructions burned: 995 (million)
% 13.52/3.76 % (4659)------------------------------
% 13.52/3.76 % (4659)------------------------------
% 13.52/3.77 % (4651)Instruction limit reached!
% 13.52/3.77 % (4651)------------------------------
% 13.52/3.77 % (4651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.52/3.77 % (4651)Termination reason: Unknown
% 13.52/3.77 % (4651)Termination phase: Saturation
% 13.52/3.77
% 13.52/3.77 % (4651)Memory used [KB]: 5373
% 13.52/3.77 % (4651)Time elapsed: 0.535 s
% 13.52/3.77 % (4651)Instructions burned: 1915 (million)
% 13.52/3.77 % (4651)------------------------------
% 13.52/3.77 % (4651)------------------------------
% 13.52/3.77 % (4664)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_4446 for (2981ds/40Mi)
% 13.52/3.78 % (4665)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_4446 for (2981ds/294Mi)
% 13.52/3.78 % (4664)Instruction limit reached!
% 13.52/3.78 % (4664)------------------------------
% 13.52/3.78 % (4664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.52/3.78 % (4664)Termination reason: Unknown
% 13.52/3.78 % (4664)Termination phase: Property scanning
% 13.52/3.78
% 13.52/3.78 % (4664)Memory used [KB]: 2174
% 13.52/3.78 % (4664)Time elapsed: 0.013 s
% 13.52/3.78 % (4664)Instructions burned: 42 (million)
% 13.52/3.78 % (4664)------------------------------
% 13.52/3.78 % (4664)------------------------------
% 13.52/3.79 % (4666)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_4446 for (2981ds/187Mi)
% 14.47/3.80 % (4665)Refutation not found, incomplete strategy
% 14.47/3.80 % (4665)------------------------------
% 14.47/3.80 % (4665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.47/3.80 % (4665)Termination reason: Refutation not found, incomplete strategy
% 14.47/3.80
% 14.47/3.80
% 14.47/3.80 % (4665)Memory used [KB]: 6908
% 14.47/3.80 % (4665)Time elapsed: 0.028 s
% 14.47/3.80 % (4665)Instructions burned: 97 (million)
% 14.47/3.80 % (4665)------------------------------
% 14.47/3.80 % (4665)------------------------------
% 14.47/3.81 % (4667)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_4446 for (2981ds/371Mi)
% 14.47/3.85 % (4666)Instruction limit reached!
% 14.47/3.85 % (4666)------------------------------
% 14.47/3.85 % (4666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.47/3.85 % (4666)Termination reason: Unknown
% 14.47/3.85 % (4666)Termination phase: Saturation
% 14.47/3.85
% 14.47/3.85 % (4666)Memory used [KB]: 7419
% 14.47/3.85 % (4666)Time elapsed: 0.057 s
% 14.47/3.85 % (4666)Instructions burned: 187 (million)
% 14.47/3.85 % (4666)------------------------------
% 14.47/3.85 % (4666)------------------------------
% 14.47/3.86 % (4668)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_4446 for (2980ds/1827Mi)
% 14.57/3.91 % (4663)Instruction limit reached!
% 14.57/3.91 % (4663)------------------------------
% 14.57/3.91 % (4663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.57/3.91 % (4663)Termination reason: Unknown
% 14.57/3.91 % (4663)Termination phase: Saturation
% 14.57/3.91
% 14.57/3.91 % (4663)Memory used [KB]: 13944
% 14.57/3.91 % (4663)Time elapsed: 0.199 s
% 14.57/3.91 % (4663)Instructions burned: 671 (million)
% 14.57/3.91 % (4663)------------------------------
% 14.57/3.91 % (4663)------------------------------
% 14.57/3.91 % (4662)Instruction limit reached!
% 14.57/3.91 % (4662)------------------------------
% 14.57/3.91 % (4662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.57/3.91 % (4662)Termination reason: Unknown
% 14.57/3.91 % (4662)Termination phase: Saturation
% 14.57/3.91
% 14.57/3.91 % (4662)Memory used [KB]: 8443
% 14.57/3.91 % (4662)Time elapsed: 0.254 s
% 14.57/3.91 % (4662)Instructions burned: 834 (million)
% 14.57/3.91 % (4662)------------------------------
% 14.57/3.91 % (4662)------------------------------
% 14.57/3.92 % (4669)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_4446 for (2979ds/70Mi)
% 14.57/3.92 % (4670)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_4446 for (2979ds/316Mi)
% 14.57/3.93 % (4667)Instruction limit reached!
% 14.57/3.93 % (4667)------------------------------
% 14.57/3.93 % (4667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.57/3.93 % (4667)Termination reason: Unknown
% 14.57/3.93 % (4667)Termination phase: Saturation
% 14.57/3.93
% 14.57/3.93 % (4667)Memory used [KB]: 7675
% 14.57/3.93 % (4667)Time elapsed: 0.119 s
% 14.57/3.93 % (4667)Instructions burned: 371 (million)
% 14.57/3.93 % (4667)------------------------------
% 14.57/3.93 % (4667)------------------------------
% 14.57/3.94 % (4671)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_4446 for (2979ds/932Mi)
% 14.57/3.94 % (4669)Instruction limit reached!
% 14.57/3.94 % (4669)------------------------------
% 14.57/3.94 % (4669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.57/3.94 % (4669)Termination reason: Unknown
% 14.57/3.94 % (4669)Termination phase: Preprocessing 3
% 14.57/3.94
% 14.57/3.94 % (4669)Memory used [KB]: 2302
% 14.57/3.94 % (4669)Time elapsed: 0.021 s
% 14.57/3.94 % (4669)Instructions burned: 72 (million)
% 14.57/3.94 % (4669)------------------------------
% 14.57/3.94 % (4669)------------------------------
% 14.57/3.96 % (4672)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_4446 for (2979ds/4714Mi)
% 14.57/3.98 % (4670)Refutation not found, incomplete strategy
% 14.57/3.98 % (4670)------------------------------
% 14.57/3.98 % (4670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.57/3.98 % (4670)Termination reason: Refutation not found, incomplete strategy
% 14.57/3.98
% 14.57/3.98
% 14.57/3.98 % (4670)Memory used [KB]: 7547
% 14.57/3.98 % (4670)Time elapsed: 0.056 s
% 14.57/3.98 % (4670)Instructions burned: 200 (million)
% 14.57/3.98 % (4670)------------------------------
% 14.57/3.98 % (4670)------------------------------
% 14.57/3.99 % (4673)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_4446 for (2979ds/8250Mi)
% 17.98/4.04 % (4672)Refutation not found, incomplete strategy
% 17.98/4.04 % (4672)------------------------------
% 17.98/4.04 % (4672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.98/4.04 % (4672)Termination reason: Refutation not found, incomplete strategy
% 17.98/4.04
% 17.98/4.04
% 17.98/4.04 % (4672)Memory used [KB]: 7675
% 17.98/4.04 % (4672)Time elapsed: 0.093 s
% 17.98/4.04 % (4672)Instructions burned: 221 (million)
% 17.98/4.04 % (4672)------------------------------
% 17.98/4.04 % (4672)------------------------------
% 17.98/4.05 % (4674)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_4446 for (2978ds/770Mi)
% 19.14/4.21 % (4671)Instruction limit reached!
% 19.14/4.21 % (4671)------------------------------
% 19.14/4.21 % (4671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.14/4.21 % (4671)Termination reason: Unknown
% 19.14/4.21 % (4671)Termination phase: Saturation
% 19.14/4.21
% 19.14/4.21 % (4671)Memory used [KB]: 9594
% 19.14/4.21 % (4671)Time elapsed: 0.270 s
% 19.14/4.21 % (4671)Instructions burned: 932 (million)
% 19.14/4.21 % (4671)------------------------------
% 19.14/4.21 % (4671)------------------------------
% 19.14/4.22 % (4675)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_4446 for (2977ds/794Mi)
% 19.14/4.25 % (4674)Instruction limit reached!
% 19.14/4.25 % (4674)------------------------------
% 19.14/4.25 % (4674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.14/4.25 % (4674)Termination reason: Unknown
% 19.14/4.25 % (4674)Termination phase: Saturation
% 19.14/4.25
% 19.14/4.25 % (4674)Memory used [KB]: 7164
% 19.14/4.25 % (4674)Time elapsed: 0.195 s
% 19.14/4.25 % (4674)Instructions burned: 771 (million)
% 19.14/4.25 % (4674)------------------------------
% 19.14/4.25 % (4674)------------------------------
% 19.14/4.26 % (4676)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_4446 for (2976ds/464Mi)
% 19.84/4.36 % (4668)First to succeed.
% 19.84/4.37 % (4668)Refutation found. Thanks to Tanya!
% 19.84/4.37 % SZS status Theorem for DTF2THF_4446
% 19.84/4.37 % SZS output start Proof for DTF2THF_4446
% 19.84/4.37 thf(type_def_6, type, list: ($tType) > $tType).
% 19.84/4.37 thf(type_def_7, type, set: ($tType) > $tType).
% 19.84/4.37 thf(type_def_8, type, nat: $tType).
% 19.84/4.37 thf(type_def_9, type, type_Mirabelle_typ: $tType).
% 19.84/4.37 thf(type_def_10, type, type_M1610475166scheme: $tType).
% 19.84/4.37 thf(func_def_0, type, type_M1610475166scheme: $tType).
% 19.84/4.37 thf(func_def_1, type, type_Mirabelle_typ: $tType).
% 19.84/4.37 thf(func_def_2, type, list: ($tType) > $tType).
% 19.84/4.37 thf(func_def_3, type, set: ($tType) > $tType).
% 19.84/4.37 thf(func_def_4, type, nat: $tType).
% 19.84/4.37 thf(func_def_5, type, bounded_lattice: !>[X0: $tType]:($o)).
% 19.84/4.37 thf(func_def_6, type, type: !>[X0: $tType]:($o)).
% 19.84/4.37 thf(func_def_7, type, bot: !>[X0: $tType]:($o)).
% 19.84/4.37 thf(func_def_8, type, ord: !>[X0: $tType]:($o)).
% 19.84/4.37 thf(func_def_9, type, order: !>[X0: $tType]:($o)).
% 19.84/4.37 thf(func_def_10, type, no_bot: !>[X0: $tType]:($o)).
% 19.84/4.37 thf(func_def_11, type, no_top: !>[X0: $tType]:($o)).
% 19.84/4.37 thf(func_def_12, type, linorder: !>[X0: $tType]:($o)).
% 19.84/4.37 thf(func_def_13, type, preorder: !>[X0: $tType]:($o)).
% 19.84/4.37 thf(func_def_14, type, order_bot: !>[X0: $tType]:($o)).
% 19.84/4.37 thf(func_def_15, type, wellorder: !>[X0: $tType]:($o)).
% 19.84/4.37 thf(func_def_16, type, dense_order: !>[X0: $tType]:($o)).
% 19.84/4.37 thf(func_def_17, type, semilattice_sup: !>[X0: $tType]:($o)).
% 19.84/4.37 thf(func_def_18, type, type_M201404320of_nat: !>[X0: $tType]:($o)).
% 19.84/4.37 thf(func_def_19, type, type_M1535146424typ_of: !>[X0: $tType]:($o)).
% 19.84/4.37 thf(func_def_20, type, bounde1808546759up_bot: !>[X0: $tType]:($o)).
% 19.84/4.37 thf(func_def_21, type, type_M1470978233struct: !>[X0: $tType]:($o)).
% 19.84/4.37 thf(func_def_22, type, the: !>[X0: $tType]:((X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_23, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 19.84/4.37 thf(func_def_24, type, semilattice_neutr: !>[X0: $tType]:((X0 > X0 > X0) > X0 > $o)).
% 19.84/4.37 thf(func_def_25, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 19.84/4.37 thf(func_def_26, type, insert: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 19.84/4.37 thf(func_def_27, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 19.84/4.37 thf(func_def_28, type, nil: !>[X0: $tType]:(list @ X0)).
% 19.84/4.37 thf(func_def_29, type, ord_lexordp_eq: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 19.84/4.37 thf(func_def_30, type, bot_bot: !>[X0: $tType]:(X0)).
% 19.84/4.37 thf(func_def_31, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 19.84/4.37 thf(func_def_32, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 19.84/4.37 thf(func_def_33, type, insert2: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 19.84/4.37 thf(func_def_34, type, is_empty: !>[X0: $tType]:(set @ X0 > $o)).
% 19.84/4.37 thf(func_def_35, type, is_singleton: !>[X0: $tType]:(set @ X0 > $o)).
% 19.84/4.37 thf(func_def_36, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 19.84/4.37 thf(func_def_37, type, type_Mirabelle_cod: (nat > type_Mirabelle_typ) > set @ nat).
% 19.84/4.37 thf(func_def_38, type, type_Mirabelle_dom: (nat > type_Mirabelle_typ) > set @ nat).
% 19.84/4.37 thf(func_def_39, type, type_M17369686_subst: nat > type_Mirabelle_typ).
% 19.84/4.37 thf(func_def_40, type, type_M540877363scheme: type_Mirabelle_typ > type_M1610475166scheme).
% 19.84/4.37 thf(func_def_41, type, type_M1046766514new_tv: !>[X0: $tType]:(nat > X0 > $o)).
% 19.84/4.37 thf(func_def_42, type, type_M167561660of_nat: !>[X0: $tType]:(nat > X0)).
% 19.84/4.37 thf(func_def_43, type, type_Mirabelle_Fun: type_Mirabelle_typ > type_Mirabelle_typ > type_Mirabelle_typ).
% 19.84/4.37 thf(func_def_44, type, type_Mirabelle_TVar: nat > type_Mirabelle_typ).
% 19.84/4.37 thf(func_def_45, type, type_M1695911984se_typ: !>[X0: $tType]:((nat > X0) > (type_Mirabelle_typ > type_Mirabelle_typ > X0) > type_Mirabelle_typ > X0)).
% 19.84/4.37 thf(func_def_46, type, type_M604437996typ_of: !>[X0: $tType]:(X0 > type_Mirabelle_typ)).
% 19.84/4.37 thf(func_def_47, type, type_M1264524676e_BVar: nat > type_M1610475166scheme).
% 19.84/4.37 thf(func_def_48, type, type_M91906176e_FVar: nat > type_M1610475166scheme).
% 19.84/4.37 thf(func_def_49, type, type_M1518733067e_SFun: type_M1610475166scheme > type_M1610475166scheme > type_M1610475166scheme).
% 19.84/4.37 thf(func_def_50, type, type_M697345518scheme: !>[X0: $tType]:((nat > X0) > (nat > X0) > (type_M1610475166scheme > type_M1610475166scheme > X0) > type_M1610475166scheme > X0)).
% 19.84/4.37 thf(func_def_51, type, type_M1705333808scheme: !>[X0: $tType]:((nat > X0) > (nat > X0) > (type_M1610475166scheme > type_M1610475166scheme > X0 > X0 > X0) > type_M1610475166scheme > X0)).
% 19.84/4.37 thf(func_def_52, type, type_M353778473_subst: !>[X0: $tType]:((nat > type_Mirabelle_typ) > X0 > X0)).
% 19.84/4.37 thf(func_def_53, type, type_M779184887und_tv: !>[X0: $tType]:(X0 > set @ nat)).
% 19.84/4.37 thf(func_def_54, type, type_M950795831ree_tv: !>[X0: $tType]:(X0 > set @ nat)).
% 19.84/4.37 thf(func_def_55, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 19.84/4.37 thf(func_def_56, type, s1: nat > type_Mirabelle_typ).
% 19.84/4.37 thf(func_def_57, type, s2: nat > type_Mirabelle_typ).
% 19.84/4.37 thf(func_def_58, type, n: nat).
% 19.84/4.37 thf(func_def_59, type, x: nat).
% 19.84/4.37 thf(func_def_77, type, sP0: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > $o)).
% 19.84/4.37 thf(func_def_78, type, sP1: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 19.84/4.37 thf(func_def_79, type, sK2: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_80, type, sK3: (nat > type_Mirabelle_typ) > (nat > type_Mirabelle_typ) > type_M1610475166scheme > nat).
% 19.84/4.37 thf(func_def_81, type, sK4: type_M1610475166scheme > type_M1610475166scheme).
% 19.84/4.37 thf(func_def_82, type, sK5: type_M1610475166scheme > type_M1610475166scheme).
% 19.84/4.37 thf(func_def_83, type, sK6: type_M1610475166scheme > nat).
% 19.84/4.37 thf(func_def_84, type, sK7: type_M1610475166scheme > nat).
% 19.84/4.37 thf(func_def_85, type, sK8: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 19.84/4.37 thf(func_def_86, type, sK9: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 19.84/4.37 thf(func_def_87, type, sK10: !>[X0: $tType]:(list @ X0 > X0)).
% 19.84/4.37 thf(func_def_88, type, sK11: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 19.84/4.37 thf(func_def_89, type, sK12: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_90, type, sK13: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 19.84/4.37 thf(func_def_91, type, sK14: type_M1610475166scheme > type_M1610475166scheme > type_Mirabelle_typ).
% 19.84/4.37 thf(func_def_92, type, sK15: type_M1610475166scheme > type_M1610475166scheme > type_Mirabelle_typ).
% 19.84/4.37 thf(func_def_93, type, sK16: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 19.84/4.37 thf(func_def_94, type, sK17: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 19.84/4.37 thf(func_def_95, type, sK18: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 19.84/4.37 thf(func_def_96, type, sK19: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0)).
% 19.84/4.37 thf(func_def_97, type, sK20: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X0)).
% 19.84/4.37 thf(func_def_98, type, sK21: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 19.84/4.37 thf(func_def_99, type, sK22: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 19.84/4.37 thf(func_def_100, type, sK23: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 19.84/4.37 thf(func_def_101, type, sK24: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_102, type, sK25: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_103, type, sK26: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 19.84/4.37 thf(func_def_104, type, sK27: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 19.84/4.37 thf(func_def_105, type, sK28: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_106, type, sK29: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_107, type, sK30: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 19.84/4.37 thf(func_def_108, type, sK31: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 19.84/4.37 thf(func_def_109, type, sK32: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 19.84/4.37 thf(func_def_110, type, sK33: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_111, type, sK34: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 19.84/4.37 thf(func_def_112, type, sK35: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 19.84/4.37 thf(func_def_113, type, sK36: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 19.84/4.37 thf(func_def_114, type, sK37: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_115, type, sK38: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > list @ X0)).
% 19.84/4.37 thf(func_def_116, type, sK39: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 19.84/4.37 thf(func_def_117, type, sK40: type_Mirabelle_typ > nat).
% 19.84/4.37 thf(func_def_118, type, sK41: type_Mirabelle_typ > type_Mirabelle_typ).
% 19.84/4.37 thf(func_def_119, type, sK42: type_Mirabelle_typ > type_Mirabelle_typ).
% 19.84/4.37 thf(func_def_120, type, sK43: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 19.84/4.37 thf(func_def_121, type, sK44: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 19.84/4.37 thf(func_def_122, type, sK45: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 19.84/4.37 thf(func_def_123, type, sK46: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 19.84/4.37 thf(func_def_124, type, sK47: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 19.84/4.37 thf(func_def_125, type, sK48: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 19.84/4.37 thf(func_def_126, type, sK49: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 19.84/4.37 thf(func_def_127, type, sK50: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 19.84/4.37 thf(func_def_128, type, sK51: (type_Mirabelle_typ > $o) > type_Mirabelle_typ).
% 19.84/4.37 thf(func_def_129, type, sK52: (type_Mirabelle_typ > $o) > type_Mirabelle_typ).
% 19.84/4.37 thf(func_def_130, type, sK53: (type_Mirabelle_typ > $o) > nat).
% 19.84/4.37 thf(func_def_131, type, sK54: !>[X0: $tType]:(set @ X0 > X0)).
% 19.84/4.37 thf(func_def_132, type, sK55: !>[X0: $tType]:(set @ X0 > X0)).
% 19.84/4.37 thf(func_def_133, type, sK56: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_134, type, sK57: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_135, type, sK58: (nat > type_Mirabelle_typ) > (nat > type_Mirabelle_typ) > type_Mirabelle_typ > nat).
% 19.84/4.37 thf(func_def_136, type, sK59: !>[X0: $tType]:((X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_137, type, sK60: (nat > type_Mirabelle_typ) > (nat > type_Mirabelle_typ) > list @ type_M1610475166scheme > nat).
% 19.84/4.37 thf(func_def_138, type, sK61: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 19.84/4.37 thf(func_def_139, type, sK62: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_140, type, sK63: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 19.84/4.37 thf(func_def_141, type, sK64: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 19.84/4.37 thf(func_def_142, type, sK65: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_143, type, sK66: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 19.84/4.37 thf(func_def_144, type, sK67: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 19.84/4.37 thf(func_def_145, type, sK68: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_146, type, sK69: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_147, type, sK70: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > list @ X0)).
% 19.84/4.37 thf(func_def_148, type, sK71: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_149, type, sK72: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_150, type, sK73: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_151, type, sK74: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 19.84/4.37 thf(func_def_152, type, sK75: !>[X0: $tType]:(X0 > X0)).
% 19.84/4.37 thf(func_def_153, type, sK76: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 19.84/4.37 thf(func_def_154, type, sK77: !>[X0: $tType]:(list @ X0 > X0)).
% 19.84/4.37 thf(func_def_155, type, sK78: !>[X0: $tType]:(list @ X0 > X0)).
% 19.84/4.37 thf(func_def_156, type, sK79: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 19.84/4.37 thf(func_def_157, type, sK80: !>[X0: $tType]:(list @ X0 > X0)).
% 19.84/4.37 thf(func_def_158, type, sK81: !>[X0: $tType]:(X0 > X0 > X0)).
% 19.84/4.37 thf(func_def_159, type, sK82: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 19.84/4.37 thf(func_def_160, type, sK83: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 19.84/4.37 thf(func_def_161, type, sK84: !>[X0: $tType]:(set @ X0 > X0)).
% 19.84/4.37 thf(func_def_162, type, sK85: !>[X0: $tType]:(list @ X0 > X0)).
% 19.84/4.37 thf(func_def_163, type, sK86: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 19.84/4.37 thf(func_def_164, type, sK87: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 19.84/4.37 thf(func_def_165, type, sK88: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 19.84/4.37 thf(func_def_166, type, sK89: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_167, type, sK90: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_168, type, sK91: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 19.84/4.37 thf(func_def_169, type, sK92: (nat > type_Mirabelle_typ) > (nat > type_Mirabelle_typ) > type_M1610475166scheme > nat).
% 19.84/4.37 thf(func_def_170, type, sK93: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_171, type, sK94: !>[X0: $tType]:(set @ X0 > X0)).
% 19.84/4.37 thf(func_def_172, type, sK95: (nat > type_Mirabelle_typ) > (nat > type_Mirabelle_typ) > type_Mirabelle_typ > nat).
% 19.84/4.37 thf(func_def_173, type, sK96: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 19.84/4.37 thf(func_def_174, type, sK97: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 19.84/4.37 thf(func_def_175, type, sK98: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_176, type, sK99: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 19.84/4.37 thf(func_def_177, type, sK100: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_178, type, sK101: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 19.84/4.37 thf(func_def_179, type, sK102: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_180, type, sK103: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_181, type, sK104: !>[X0: $tType]:(list @ list @ X0 > X0)).
% 19.84/4.37 thf(func_def_182, type, sK105: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 19.84/4.37 thf(func_def_183, type, sK106: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 19.84/4.37 thf(func_def_184, type, sK107: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 19.84/4.37 thf(func_def_185, type, sK108: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 19.84/4.37 thf(func_def_186, type, sK109: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 19.84/4.37 thf(func_def_187, type, sK110: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 19.84/4.37 thf(func_def_188, type, sK111: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 19.84/4.37 thf(func_def_189, type, sK112: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 19.84/4.37 thf(func_def_190, type, sK113: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 19.84/4.37 thf(func_def_191, type, sK114: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 19.84/4.37 thf(func_def_192, type, sK115: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 19.84/4.37 thf(func_def_193, type, sK116: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_194, type, sK117: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_195, type, sK118: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_196, type, sK119: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 19.84/4.37 thf(func_def_197, type, sK120: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1 > X0)).
% 19.84/4.37 thf(func_def_198, type, sK121: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1)).
% 19.84/4.37 thf(func_def_199, type, sK122: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1)).
% 19.84/4.37 thf(func_def_200, type, sK123: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > list @ X1)).
% 19.84/4.37 thf(func_def_201, type, sK124: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1 > X0)).
% 19.84/4.37 thf(func_def_202, type, sK125: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1 > X0)).
% 19.84/4.37 thf(func_def_203, type, sK126: !>[X0: $tType, X1: $tType]:(((X1 > X0) > list @ X1 > $o) > X1)).
% 19.84/4.37 thf(func_def_204, type, sK127: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_205, type, sK128: (type_M1610475166scheme > $o) > nat).
% 19.84/4.37 thf(func_def_206, type, sK129: (type_M1610475166scheme > $o) > nat).
% 19.84/4.37 thf(func_def_207, type, sK130: (type_M1610475166scheme > $o) > type_M1610475166scheme).
% 19.84/4.37 thf(func_def_208, type, sK131: (type_M1610475166scheme > $o) > type_M1610475166scheme).
% 19.84/4.37 thf(func_def_209, type, sK132: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_210, type, sK133: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 19.84/4.37 thf(func_def_211, type, sK134: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 19.84/4.37 thf(func_def_212, type, sK135: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 19.84/4.37 thf(func_def_213, type, sK136: !>[X0: $tType]:(X0 > X0)).
% 19.84/4.37 thf(func_def_214, type, sK137: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_215, type, sK138: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_216, type, sK139: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_217, type, sK140: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_218, type, sK141: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_219, type, sK142: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_220, type, sK143: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_221, type, sK144: !>[X0: $tType]:(list @ X0 > X0)).
% 19.84/4.37 thf(func_def_222, type, sK145: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 19.84/4.37 thf(func_def_223, type, sK146: (nat > type_Mirabelle_typ) > (nat > type_Mirabelle_typ) > list @ type_M1610475166scheme > nat).
% 19.84/4.37 thf(func_def_224, type, sK147: !>[X0: $tType]:(set @ X0 > (X0 > $o) > set @ X0 > X0)).
% 19.84/4.37 thf(func_def_225, type, sK148: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_227, type, sK150: !>[X0: $tType]:((X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_228, type, sK151: !>[X0: $tType]:(X0 > set @ X0 > X0 > set @ X0 > set @ X0)).
% 19.84/4.37 thf(func_def_229, type, sK152: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 19.84/4.37 thf(func_def_230, type, sK153: !>[X0: $tType]:(list @ X0 > X0)).
% 19.84/4.37 thf(func_def_231, type, sK154: !>[X0: $tType]:(set @ X0 > X0)).
% 19.84/4.37 thf(func_def_232, type, sK155: !>[X0: $tType]:(set @ X0 > (X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_233, type, sK156: !>[X0: $tType]:(set @ X0 > (X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_234, type, sK157: !>[X0: $tType]:(set @ X0 > (X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_235, type, sK158: !>[X0: $tType]:(set @ X0 > (X0 > $o) > set @ X0 > X0)).
% 19.84/4.37 thf(func_def_236, type, sK159: !>[X0: $tType]:(set @ X0 > (X0 > $o) > set @ X0 > X0)).
% 19.84/4.37 thf(func_def_237, type, sK160: !>[X0: $tType]:((X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_238, type, sK161: !>[X0: $tType]:(set @ X0 > X0)).
% 19.84/4.37 thf(func_def_239, type, sK162: !>[X0: $tType]:(set @ X0 > (X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_240, type, sK163: !>[X0: $tType]:(set @ X0 > (X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_241, type, sK164: !>[X0: $tType]:(set @ X0 > (X0 > $o) > X0)).
% 19.84/4.37 thf(func_def_242, type, sK165: !>[X0: $tType]:(set @ X0 > (X0 > $o) > set @ X0 > X0)).
% 19.84/4.37 thf(func_def_243, type, ph166: !>[X0: $tType]:(X0)).
% 19.84/4.37 thf(func_def_244, type, sK167: !>[X0: $tType]:(set @ X0 > X0)).
% 19.84/4.37 thf(f6441,plain,(
% 19.84/4.37 $false),
% 19.84/4.37 inference(equality_resolution,[status(thm)],[f6393])).
% 19.84/4.37 thf(f6393,plain,(
% 19.84/4.37 ( ! [X0 : nat > type_Mirabelle_typ] : (((s1 @ x) != (X0 @ x))) )),
% 19.84/4.37 inference(subsumption_resolution,[status(thm)],[f6389,f6059])).
% 19.84/4.37 thf(f6059,plain,(
% 19.84/4.37 ( ! [X0 : nat > type_Mirabelle_typ,X1 : nat > type_Mirabelle_typ] : (((X1 @ n) = (X0 @ n)) | ((X0 @ x) != (X1 @ x))) )),
% 19.84/4.37 inference(superposition,[status(thm)],[f6055,f3925])).
% 19.84/4.37 thf(f3925,plain,(
% 19.84/4.37 ( ! [X0 : nat > type_Mirabelle_typ,X1 : nat] : (((type_M353778473_subst @ type_Mirabelle_typ @ X0 @ (type_M17369686_subst @ X1)) = (X0 @ X1))) )),
% 19.84/4.37 inference(backward_demodulation,[status(thm)],[f1389,f2218])).
% 19.84/4.37 thf(f2218,plain,(
% 19.84/4.37 ( ! [X1 : nat] : (((type_Mirabelle_TVar @ X1) = (type_M17369686_subst @ X1))) )),
% 19.84/4.37 inference(argument_congruence,[status(thm)],[f1436])).
% 19.84/4.37 thf(f1436,plain,(
% 19.84/4.37 (type_Mirabelle_TVar = type_M17369686_subst)),
% 19.84/4.37 inference(cnf_transformation,[status(thm)],[f141])).
% 19.84/4.37 thf(f141,axiom,(
% 19.84/4.37 (type_Mirabelle_TVar = type_M17369686_subst)),
% 19.84/4.37 file('/export/starexec/sandbox2/tmp/tmp.98HAT0fbB4/DTF2THF_4446.p',fact_140_id__subst__def)).
% 19.84/4.37 thf(f1389,plain,(
% 19.84/4.37 ( ! [X0 : nat > type_Mirabelle_typ,X1 : nat] : (((X0 @ X1) = (type_M353778473_subst @ type_Mirabelle_typ @ X0 @ (type_Mirabelle_TVar @ X1)))) )),
% 19.84/4.37 inference(cnf_transformation,[status(thm)],[f817])).
% 19.84/4.37 thf(f817,plain,(
% 19.84/4.37 ! [X0 : nat > type_Mirabelle_typ,X1 : nat] : ((X0 @ X1) = (type_M353778473_subst @ type_Mirabelle_typ @ X0 @ (type_Mirabelle_TVar @ X1)))),
% 19.84/4.37 inference(rectify,[status(thm)],[f93])).
% 19.84/4.37 thf(f93,axiom,(
% 19.84/4.37 ! [X7 : nat > type_Mirabelle_typ,X10 : nat] : ((X7 @ X10) = (type_M353778473_subst @ type_Mirabelle_typ @ X7 @ (type_Mirabelle_TVar @ X10)))),
% 19.84/4.37 file('/export/starexec/sandbox2/tmp/tmp.98HAT0fbB4/DTF2THF_4446.p',fact_92_app__subst__TVar)).
% 19.84/4.37 thf(f6055,plain,(
% 19.84/4.37 ( ! [X0 : nat > type_Mirabelle_typ,X1 : nat > type_Mirabelle_typ] : (((type_M353778473_subst @ type_Mirabelle_typ @ X1 @ (type_M17369686_subst @ x)) != (X0 @ x)) | ((X1 @ n) = (X0 @ n))) )),
% 19.84/4.37 inference(superposition,[status(thm)],[f6051,f3925])).
% 19.84/4.37 thf(f6051,plain,(
% 19.84/4.37 ( ! [X0 : nat > type_Mirabelle_typ,X1 : nat > type_Mirabelle_typ] : (((type_M353778473_subst @ type_Mirabelle_typ @ X1 @ (type_M17369686_subst @ x)) != (type_M353778473_subst @ type_Mirabelle_typ @ X0 @ (type_M17369686_subst @ x))) | ((X1 @ n) = (X0 @ n))) )),
% 19.84/4.37 inference(trivial_inequality_removal,[status(thm)],[f6029])).
% 19.84/4.37 thf(f6029,plain,(
% 19.84/4.37 ( ! [X0 : nat > type_Mirabelle_typ,X1 : nat > type_Mirabelle_typ] : (((type_M353778473_subst @ type_Mirabelle_typ @ X1 @ (type_M17369686_subst @ x)) != (type_M353778473_subst @ type_Mirabelle_typ @ X0 @ (type_M17369686_subst @ x))) | ($true != $true) | ((X1 @ n) = (X0 @ n))) )),
% 19.84/4.37 inference(superposition,[status(thm)],[f1249,f3932])).
% 19.84/4.37 thf(f3932,plain,(
% 19.84/4.37 ((member @ nat @ n @ (type_M950795831ree_tv @ type_Mirabelle_typ @ (type_M17369686_subst @ x))) = $true)),
% 19.84/4.37 inference(backward_demodulation,[status(thm)],[f3185,f2218])).
% 19.84/4.37 thf(f3185,plain,(
% 19.84/4.37 ((member @ nat @ n @ (type_M950795831ree_tv @ type_Mirabelle_typ @ (type_Mirabelle_TVar @ x))) = $true)),
% 19.84/4.37 inference(backward_demodulation,[status(thm)],[f1268,f3172])).
% 19.84/4.37 thf(f3172,plain,(
% 19.84/4.37 ( ! [X0 : nat] : (((type_M950795831ree_tv @ type_Mirabelle_typ @ (type_Mirabelle_TVar @ X0)) = (type_M950795831ree_tv @ type_M1610475166scheme @ (type_M91906176e_FVar @ X0)))) )),
% 19.84/4.37 inference(backward_demodulation,[status(thm)],[f1407,f1540])).
% 19.84/4.37 thf(f1540,plain,(
% 19.84/4.37 ( ! [X0 : nat] : (((type_M950795831ree_tv @ type_Mirabelle_typ @ (type_Mirabelle_TVar @ X0)) = (insert2 @ nat @ X0 @ bot_bot @ set @ nat))) )),
% 19.84/4.37 inference(cnf_transformation,[status(thm)],[f822])).
% 19.84/4.37 thf(f822,plain,(
% 19.84/4.37 ! [X0 : nat] : ((type_M950795831ree_tv @ type_Mirabelle_typ @ (type_Mirabelle_TVar @ X0)) = (insert2 @ nat @ X0 @ bot_bot @ set @ nat))),
% 19.84/4.37 inference(rectify,[status(thm)],[f84])).
% 19.84/4.37 thf(f84,axiom,(
% 19.84/4.37 ! [X22 : nat] : ((insert2 @ nat @ X22 @ bot_bot @ set @ nat) = (type_M950795831ree_tv @ type_Mirabelle_typ @ (type_Mirabelle_TVar @ X22)))),
% 19.84/4.37 file('/export/starexec/sandbox2/tmp/tmp.98HAT0fbB4/DTF2THF_4446.p',fact_83_free__tv__TVar)).
% 19.84/4.37 thf(f1407,plain,(
% 19.84/4.37 ( ! [X0 : nat] : (((type_M950795831ree_tv @ type_M1610475166scheme @ (type_M91906176e_FVar @ X0)) = (insert2 @ nat @ X0 @ bot_bot @ set @ nat))) )),
% 19.84/4.37 inference(cnf_transformation,[status(thm)],[f850])).
% 19.84/4.37 thf(f850,plain,(
% 19.84/4.37 ! [X0 : nat] : ((type_M950795831ree_tv @ type_M1610475166scheme @ (type_M91906176e_FVar @ X0)) = (insert2 @ nat @ X0 @ bot_bot @ set @ nat))),
% 19.84/4.37 inference(rectify,[status(thm)],[f13])).
% 19.84/4.37 thf(f13,axiom,(
% 19.84/4.37 ! [X22 : nat] : ((type_M950795831ree_tv @ type_M1610475166scheme @ (type_M91906176e_FVar @ X22)) = (insert2 @ nat @ X22 @ bot_bot @ set @ nat))),
% 19.84/4.37 file('/export/starexec/sandbox2/tmp/tmp.98HAT0fbB4/DTF2THF_4446.p',fact_12_free__tv__type__scheme_Osimps_I1_J)).
% 19.84/4.37 thf(f1268,plain,(
% 19.84/4.37 ((member @ nat @ n @ (type_M950795831ree_tv @ type_M1610475166scheme @ (type_M91906176e_FVar @ x))) = $true)),
% 19.84/4.37 inference(cnf_transformation,[status(thm)],[f990])).
% 19.84/4.37 thf(f990,plain,(
% 19.84/4.37 ((s1 @ n) != (s2 @ n)) & ((member @ nat @ n @ (type_M950795831ree_tv @ type_M1610475166scheme @ (type_M91906176e_FVar @ x))) = $true) & ((type_M353778473_subst @ type_M1610475166scheme @ s1 @ (type_M91906176e_FVar @ x)) = (type_M353778473_subst @ type_M1610475166scheme @ s2 @ (type_M91906176e_FVar @ x)))),
% 19.84/4.37 inference(ennf_transformation,[status(thm)],[f809])).
% 19.84/4.37 thf(f809,plain,(
% 19.84/4.37 ~(((member @ nat @ n @ (type_M950795831ree_tv @ type_M1610475166scheme @ (type_M91906176e_FVar @ x))) != $true) | ((s1 @ n) = (s2 @ n)) | ((type_M353778473_subst @ type_M1610475166scheme @ s1 @ (type_M91906176e_FVar @ x)) != (type_M353778473_subst @ type_M1610475166scheme @ s2 @ (type_M91906176e_FVar @ x))))),
% 19.84/4.37 inference(flattening,[status(thm)],[f473])).
% 19.84/4.37 thf(f473,plain,(
% 19.84/4.37 ~(((type_M353778473_subst @ type_M1610475166scheme @ s1 @ (type_M91906176e_FVar @ x)) != (type_M353778473_subst @ type_M1610475166scheme @ s2 @ (type_M91906176e_FVar @ x))) | ~((member @ nat @ n @ (type_M950795831ree_tv @ type_M1610475166scheme @ (type_M91906176e_FVar @ x))) = $true) | ((s1 @ n) = (s2 @ n)))),
% 19.84/4.37 inference(fool_elimination,[status(thm)],[f472])).
% 19.84/4.37 thf(f472,plain,(
% 19.84/4.37 ~(((type_M353778473_subst @ type_M1610475166scheme @ s1 @ (type_M91906176e_FVar @ x)) != (type_M353778473_subst @ type_M1610475166scheme @ s2 @ (type_M91906176e_FVar @ x))) | ~(member @ nat @ n @ (type_M950795831ree_tv @ type_M1610475166scheme @ (type_M91906176e_FVar @ x))) | ((s1 @ n) = (s2 @ n)))),
% 19.84/4.37 inference(rectify,[status(thm)],[f300])).
% 19.84/4.37 thf(f300,negated_conjecture,(
% 19.84/4.37 ~(((type_M353778473_subst @ type_M1610475166scheme @ s1 @ (type_M91906176e_FVar @ x)) != (type_M353778473_subst @ type_M1610475166scheme @ s2 @ (type_M91906176e_FVar @ x))) | ~(member @ nat @ n @ (type_M950795831ree_tv @ type_M1610475166scheme @ (type_M91906176e_FVar @ x))) | ((s1 @ n) = (s2 @ n)))),
% 19.84/4.37 inference(negated_conjecture,[status(cth)],[f299])).
% 19.84/4.37 thf(f299,conjecture,(
% 19.84/4.37 ((type_M353778473_subst @ type_M1610475166scheme @ s1 @ (type_M91906176e_FVar @ x)) != (type_M353778473_subst @ type_M1610475166scheme @ s2 @ (type_M91906176e_FVar @ x))) | ~(member @ nat @ n @ (type_M950795831ree_tv @ type_M1610475166scheme @ (type_M91906176e_FVar @ x))) | ((s1 @ n) = (s2 @ n))),
% 19.84/4.37 file('/export/starexec/sandbox2/tmp/tmp.98HAT0fbB4/DTF2THF_4446.p',conj_0)).
% 19.84/4.37 thf(f1249,plain,(
% 19.84/4.37 ( ! [X2 : nat > type_Mirabelle_typ,X3 : nat,X0 : nat > type_Mirabelle_typ,X1 : type_Mirabelle_typ] : (((member @ nat @ X3 @ (type_M950795831ree_tv @ type_Mirabelle_typ @ X1)) != $true) | ((X2 @ X3) = (X0 @ X3)) | ((type_M353778473_subst @ type_Mirabelle_typ @ X0 @ X1) != (type_M353778473_subst @ type_Mirabelle_typ @ X2 @ X1))) )),
% 19.84/4.37 inference(cnf_transformation,[status(thm)],[f938])).
% 19.84/4.37 thf(f938,plain,(
% 19.84/4.37 ! [X0 : nat > type_Mirabelle_typ,X1 : type_Mirabelle_typ,X2 : nat > type_Mirabelle_typ,X3 : nat] : (((member @ nat @ X3 @ (type_M950795831ree_tv @ type_Mirabelle_typ @ X1)) != $true) | ((X2 @ X3) = (X0 @ X3)) | ((type_M353778473_subst @ type_Mirabelle_typ @ X0 @ X1) != (type_M353778473_subst @ type_Mirabelle_typ @ X2 @ X1)))),
% 19.84/4.37 inference(flattening,[status(thm)],[f937])).
% 19.84/4.37 thf(f937,plain,(
% 19.84/4.37 ! [X0 : nat > type_Mirabelle_typ,X1 : type_Mirabelle_typ,X2 : nat > type_Mirabelle_typ,X3 : nat] : ((((X2 @ X3) = (X0 @ X3)) | ((member @ nat @ X3 @ (type_M950795831ree_tv @ type_Mirabelle_typ @ X1)) != $true)) | ((type_M353778473_subst @ type_Mirabelle_typ @ X0 @ X1) != (type_M353778473_subst @ type_Mirabelle_typ @ X2 @ X1)))),
% 19.84/4.37 inference(ennf_transformation,[status(thm)],[f401])).
% 19.84/4.37 thf(f401,plain,(
% 19.84/4.37 ! [X0 : nat > type_Mirabelle_typ,X1 : type_Mirabelle_typ,X2 : nat > type_Mirabelle_typ,X3 : nat] : (((type_M353778473_subst @ type_Mirabelle_typ @ X0 @ X1) = (type_M353778473_subst @ type_Mirabelle_typ @ X2 @ X1)) => (((member @ nat @ X3 @ (type_M950795831ree_tv @ type_Mirabelle_typ @ X1)) = $true) => ((X2 @ X3) = (X0 @ X3))))),
% 19.84/4.37 inference(fool_elimination,[status(thm)],[f400])).
% 19.84/4.37 thf(f400,plain,(
% 19.84/4.37 ! [X0 : nat > type_Mirabelle_typ,X1 : type_Mirabelle_typ,X2 : nat > type_Mirabelle_typ,X3 : nat] : (((type_M353778473_subst @ type_Mirabelle_typ @ X0 @ X1) = (type_M353778473_subst @ type_Mirabelle_typ @ X2 @ X1)) => ((member @ nat @ X3 @ (type_M950795831ree_tv @ type_Mirabelle_typ @ X1)) => ((X2 @ X3) = (X0 @ X3))))),
% 19.84/4.37 inference(rectify,[status(thm)],[f30])).
% 19.84/4.37 thf(f30,axiom,(
% 19.84/4.37 ! [X4 : nat > type_Mirabelle_typ,X21 : type_Mirabelle_typ,X5 : nat > type_Mirabelle_typ,X10 : nat] : (((type_M353778473_subst @ type_Mirabelle_typ @ X4 @ X21) = (type_M353778473_subst @ type_Mirabelle_typ @ X5 @ X21)) => ((member @ nat @ X10 @ (type_M950795831ree_tv @ type_Mirabelle_typ @ X21)) => ((X4 @ X10) = (X5 @ X10))))),
% 19.84/4.37 file('/export/starexec/sandbox2/tmp/tmp.98HAT0fbB4/DTF2THF_4446.p',fact_29_eq__subst__te__eq__free)).
% 19.84/4.37 thf(f6389,plain,(
% 19.84/4.37 ( ! [X0 : nat > type_Mirabelle_typ] : (((s1 @ n) != (X0 @ n)) | ((s1 @ x) != (X0 @ x))) )),
% 19.84/4.37 inference(superposition,[status(thm)],[f6080,f3070])).
% 19.84/4.37 thf(f3070,plain,(
% 19.84/4.37 ((s2 @ x) = (s1 @ x))),
% 19.84/4.37 inference(equality_resolution,[status(thm)],[f3065])).
% 19.84/4.37 thf(f3065,plain,(
% 19.84/4.37 ( ! [X0 : type_Mirabelle_typ] : (((type_M540877363scheme @ (s1 @ x)) != (type_M540877363scheme @ X0)) | ((s2 @ x) = X0)) )),
% 19.84/4.37 inference(superposition,[status(thm)],[f1607,f3063])).
% 19.84/4.37 thf(f3063,plain,(
% 19.84/4.37 ((type_M540877363scheme @ (s2 @ x)) = (type_M540877363scheme @ (s1 @ x)))),
% 19.84/4.37 inference(forward_demodulation,[status(thm)],[f3062,f1542])).
% 19.84/4.37 thf(f1542,plain,(
% 19.84/4.37 ( ! [X0 : nat > type_Mirabelle_typ,X1 : nat] : (((type_M353778473_subst @ type_M1610475166scheme @ X0 @ (type_M91906176e_FVar @ X1)) = (type_M540877363scheme @ (X0 @ X1)))) )),
% 19.84/4.37 inference(cnf_transformation,[status(thm)],[f775])).
% 19.84/4.37 thf(f775,plain,(
% 19.84/4.37 ! [X0 : nat > type_Mirabelle_typ,X1 : nat] : ((type_M353778473_subst @ type_M1610475166scheme @ X0 @ (type_M91906176e_FVar @ X1)) = (type_M540877363scheme @ (X0 @ X1)))),
% 19.84/4.37 inference(rectify,[status(thm)],[f4])).
% 19.84/4.37 thf(f4,axiom,(
% 19.84/4.37 ! [X7 : nat > type_Mirabelle_typ,X10 : nat] : ((type_M353778473_subst @ type_M1610475166scheme @ X7 @ (type_M91906176e_FVar @ X10)) = (type_M540877363scheme @ (X7 @ X10)))),
% 19.84/4.37 file('/export/starexec/sandbox2/tmp/tmp.98HAT0fbB4/DTF2THF_4446.p',fact_3_app__subst__type__scheme_Osimps_I1_J)).
% 19.84/4.37 thf(f3062,plain,(
% 19.84/4.37 ((type_M353778473_subst @ type_M1610475166scheme @ s1 @ (type_M91906176e_FVar @ x)) = (type_M540877363scheme @ (s2 @ x)))),
% 19.84/4.37 inference(backward_demodulation,[status(thm)],[f1267,f1542])).
% 19.84/4.37 thf(f1267,plain,(
% 19.84/4.37 ((type_M353778473_subst @ type_M1610475166scheme @ s1 @ (type_M91906176e_FVar @ x)) = (type_M353778473_subst @ type_M1610475166scheme @ s2 @ (type_M91906176e_FVar @ x)))),
% 19.84/4.37 inference(cnf_transformation,[status(thm)],[f990])).
% 19.84/4.37 thf(f1607,plain,(
% 19.84/4.37 ( ! [X0 : type_Mirabelle_typ,X1 : type_Mirabelle_typ] : (((type_M540877363scheme @ X1) != (type_M540877363scheme @ X0)) | (X0 = X1)) )),
% 19.84/4.37 inference(cnf_transformation,[status(thm)],[f879])).
% 19.84/4.37 thf(f879,plain,(
% 19.84/4.37 ! [X0 : type_Mirabelle_typ,X1 : type_Mirabelle_typ] : (((type_M540877363scheme @ X1) != (type_M540877363scheme @ X0)) | (X0 = X1))),
% 19.84/4.37 inference(ennf_transformation,[status(thm)],[f847])).
% 19.84/4.37 thf(f847,plain,(
% 19.84/4.37 ! [X0 : type_Mirabelle_typ,X1 : type_Mirabelle_typ] : (((type_M540877363scheme @ X1) = (type_M540877363scheme @ X0)) => (X0 = X1))),
% 19.84/4.37 inference(rectify,[status(thm)],[f32])).
% 19.84/4.37 thf(f32,axiom,(
% 19.84/4.37 ! [X21 : type_Mirabelle_typ,X37 : type_Mirabelle_typ] : (((type_M540877363scheme @ X21) = (type_M540877363scheme @ X37)) => (X21 = X37))),
% 19.84/4.37 file('/export/starexec/sandbox2/tmp/tmp.98HAT0fbB4/DTF2THF_4446.p',fact_31_mk__scheme__injective)).
% 19.84/4.37 thf(f6080,plain,(
% 19.84/4.37 ( ! [X0 : nat > type_Mirabelle_typ] : (((s2 @ x) != (X0 @ x)) | ((s1 @ n) != (X0 @ n))) )),
% 19.84/4.37 inference(superposition,[status(thm)],[f1269,f6059])).
% 19.84/4.37 thf(f1269,plain,(
% 19.84/4.37 ((s1 @ n) != (s2 @ n))),
% 19.84/4.37 inference(cnf_transformation,[status(thm)],[f990])).
% 19.84/4.37 % SZS output end Proof for DTF2THF_4446
% 19.84/4.37 % (4668)------------------------------
% 19.84/4.37 % (4668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.84/4.37 % (4668)Termination reason: Refutation
% 19.84/4.37
% 19.84/4.37 % (4668)Memory used [KB]: 10490
% 19.84/4.37 % (4668)Time elapsed: 0.506 s
% 19.84/4.37 % (4668)Instructions burned: 1582 (million)
% 19.84/4.37 % (4668)------------------------------
% 19.84/4.37 % (4668)------------------------------
% 19.84/4.37 % (4551)Success in time 2.454 s
%------------------------------------------------------------------------------