%------------------------------------------------------------------------------
% File     : ITP055^1 : TPTP v9.0.0. Released v7.5.0.
% Domain   : Interactive Theorem Proving
% Problem  : Sledgehammer FLPTheorem problem prob_1231__3305662_1
% Version  : Especial.
% English  :

% Refs     : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
%          : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% Source   : [Des21]
% Names    : FLPTheorem/prob_1231__3305662_1 [Des21]

% Status   : Theorem
% Rating   : 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% Syntax   : Number of formulae    :  414 ( 186 unt;  72 typ;   0 def)
%            Number of atoms       :  741 ( 451 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives : 3000 ( 179   ~;  10   |;  38   &;2297   @)
%                                         (   0 <=>; 476  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   7 avg)
%            Number of types       :   15 (  14 usr)
%            Number of type conns  :  520 ( 520   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   59 (  58 usr;  14 con; 0-4 aty)
%            Number of variables   : 1101 (  11   ^;1046   !;  44   ?;1101   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Sledgehammer 2021-02-23 15:32:18.186
%------------------------------------------------------------------------------
% Could-be-implicit typings (14)
thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J_J,type,
    list_l1584713811t_unit: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J,type,
    list_l611321411t_unit: $tType ).

thf(ty_n_t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
    list_c1059388851t_unit: $tType ).

thf(ty_n_t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
    config256849571t_unit: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J_J,type,
    list_l1341496881ge_p_v: $tType ).

thf(ty_n_t__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J,type,
    list_l1619404459ge_p_v: $tType ).

thf(ty_n_t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
    list_message_p_v: $tType ).

thf(ty_n_t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
    message_p_v: $tType ).

thf(ty_n_t__AsynchronousSystem__OmessageValue_Itf__v_J,type,
    messageValue_v: $tType ).

thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
    set_nat: $tType ).

thf(ty_n_t__Nat__Onat,type,
    nat: $tType ).

thf(ty_n_t__Int__Oint,type,
    int: $tType ).

thf(ty_n_tf__s,type,
    s: $tType ).

thf(ty_n_tf__p,type,
    p: $tType ).

% Explicit typings (58)
thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_001tf__p_001tf__s_001tf__v,type,
    fLPThe9398366_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > $o ).

thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_OinfiniteExecutionCfg_001tf__p_001tf__v_001tf__s,type,
    fLPThe1519354920_p_v_s: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > list_c1059388851t_unit ).

thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_OinfiniteExecutionMsg_001tf__p_001tf__v_001tf__s,type,
    fLPThe536531371_p_v_s: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > list_message_p_v ).

thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint,type,
    one_one_int: int ).

thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
    one_one_nat: nat ).

thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Int__Oint,type,
    uminus_uminus_int: int > int ).

thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
    zero_zero_int: int ).

thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
    zero_zero_nat: nat ).

thf(sy_c_Int_Onat,type,
    nat2: int > nat ).

thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
    ring_1_of_int_int: int > int ).

thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
    prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).

thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
    prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o ).

thf(sy_c_ListUtilities_OprefixList_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
    prefix747844452t_unit: list_l611321411t_unit > list_l611321411t_unit > $o ).

thf(sy_c_ListUtilities_OprefixList_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
    prefix1465223476ge_p_v: list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o ).

thf(sy_c_List_Ogen__length_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
    gen_le193291088t_unit: nat > list_c1059388851t_unit > nat ).

thf(sy_c_List_Ogen__length_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
    gen_le697204914ge_p_v: nat > list_message_p_v > nat ).

thf(sy_c_List_Oinsert_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
    insert1308755079t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).

thf(sy_c_List_Oinsert_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
    insert_message_p_v: message_p_v > list_message_p_v > list_message_p_v ).

thf(sy_c_List_Olist_OCons_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
    cons_c1162654829t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).

thf(sy_c_List_Olist_OCons_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
    cons_message_p_v: message_p_v > list_message_p_v > list_message_p_v ).

thf(sy_c_List_Olist_OCons_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
    cons_l1083444861t_unit: list_c1059388851t_unit > list_l611321411t_unit > list_l611321411t_unit ).

thf(sy_c_List_Olist_OCons_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
    cons_l233104475ge_p_v: list_message_p_v > list_l1619404459ge_p_v > list_l1619404459ge_p_v ).

thf(sy_c_List_Olist_OCons_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J,type,
    cons_l1777019405t_unit: list_l611321411t_unit > list_l1584713811t_unit > list_l1584713811t_unit ).

thf(sy_c_List_Olist_OCons_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J,type,
    cons_l1383421281ge_p_v: list_l1619404459ge_p_v > list_l1341496881ge_p_v > list_l1341496881ge_p_v ).

thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
    nil_co1338500125t_unit: list_c1059388851t_unit ).

thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
    nil_message_p_v: list_message_p_v ).

thf(sy_c_List_Olist_ONil_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
    nil_li307996205t_unit: list_l611321411t_unit ).

thf(sy_c_List_Olist_ONil_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
    nil_list_message_p_v: list_l1619404459ge_p_v ).

thf(sy_c_List_Olist_ONil_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J,type,
    nil_li2108369341t_unit: list_l1584713811t_unit ).

thf(sy_c_List_Olist_ONil_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J,type,
    nil_li835338673ge_p_v: list_l1341496881ge_p_v ).

thf(sy_c_List_Olist__ex1_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
    list_e1598815642t_unit: ( config256849571t_unit > $o ) > list_c1059388851t_unit > $o ).

thf(sy_c_List_Olist__ex1_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
    list_ex1_message_p_v: ( message_p_v > $o ) > list_message_p_v > $o ).

thf(sy_c_List_On__lists_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
    n_list1987762709t_unit: nat > list_c1059388851t_unit > list_l611321411t_unit ).

thf(sy_c_List_On__lists_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
    n_lists_message_p_v: nat > list_message_p_v > list_l1619404459ge_p_v ).

thf(sy_c_List_Onths_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
    nths_c890550943t_unit: list_c1059388851t_unit > set_nat > list_c1059388851t_unit ).

thf(sy_c_List_Onths_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
    nths_message_p_v: list_message_p_v > set_nat > list_message_p_v ).

thf(sy_c_List_Oproduct__lists_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
    produc663212148t_unit: list_l611321411t_unit > list_l611321411t_unit ).

thf(sy_c_List_Oproduct__lists_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
    produc1505827982ge_p_v: list_l1619404459ge_p_v > list_l1619404459ge_p_v ).

thf(sy_c_List_Osubseqs_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
    subseq1144048270t_unit: list_c1059388851t_unit > list_l611321411t_unit ).

thf(sy_c_List_Osubseqs_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
    subseqs_message_p_v: list_message_p_v > list_l1619404459ge_p_v ).

thf(sy_c_Nat_OSuc,type,
    suc: nat > nat ).

thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
    semiri2019852685at_int: nat > int ).

thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
    semiri1382578993at_nat: nat > nat ).

thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
    size_s1406904903t_unit: list_c1059388851t_unit > nat ).

thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
    size_s1168481041ge_p_v: list_message_p_v > nat ).

thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J,type,
    size_s503142615t_unit: list_l611321411t_unit > nat ).

thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J,type,
    size_s1809856791ge_p_v: list_l1619404459ge_p_v > nat ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
    ord_less_int: int > int > $o ).

thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
    ord_less_nat: nat > nat > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
    ord_less_eq_int: int > int > $o ).

thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
    collect_nat: ( nat > $o ) > set_nat ).

thf(sy_c_member_001t__Nat__Onat,type,
    member_nat: nat > set_nat > $o ).

thf(sy_v_cfg____,type,
    cfg: config256849571t_unit ).

thf(sy_v_fe____,type,
    fe: nat > list_c1059388851t_unit ).

thf(sy_v_m____,type,
    m: nat ).

thf(sy_v_n____,type,
    n: nat ).

thf(sy_v_na____,type,
    na: nat ).

% Relevant facts (341)
thf(fact_0__092_060open_062m_A_060_An_092_060close_062,axiom,
    ord_less_nat @ m @ na ).

% \<open>m < n\<close>
thf(fact_1_MLessN,axiom,
    ord_less_nat @ m @ n ).

% MLessN
thf(fact_2_IA_I1_J,axiom,
    ( ( ord_less_nat @ m @ na )
   => ( prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) ) ) ).

% IA(1)
thf(fact_3__092_060open_062m_A_061_An_A_092_060or_062_Am_A_060_An_092_060close_062,axiom,
    ( ( m = na )
    | ( ord_less_nat @ m @ na ) ) ).

% \<open>m = n \<or> m < n\<close>
thf(fact_4_IA_I2_J,axiom,
    ord_less_nat @ m @ ( suc @ na ) ).

% IA(2)
thf(fact_5_PrefixListTransitive,axiom,
    ! [L1: list_message_p_v,L2: list_message_p_v,L3: list_message_p_v] :
      ( ( prefix47729710ge_p_v @ L1 @ L2 )
     => ( ( prefix47729710ge_p_v @ L2 @ L3 )
       => ( prefix47729710ge_p_v @ L1 @ L3 ) ) ) ).

% PrefixListTransitive
thf(fact_6_PrefixListTransitive,axiom,
    ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit,L3: list_c1059388851t_unit] :
      ( ( prefix1615116500t_unit @ L1 @ L2 )
     => ( ( prefix1615116500t_unit @ L2 @ L3 )
       => ( prefix1615116500t_unit @ L1 @ L3 ) ) ) ).

% PrefixListTransitive
thf(fact_7_FE_I1_J,axiom,
    ( ( fe @ zero_zero_nat )
    = ( cons_c1162654829t_unit @ cfg @ nil_co1338500125t_unit ) ) ).

% FE(1)
thf(fact_8_prefixList_Ointros_I2_J,axiom,
    ! [Xa: list_l611321411t_unit,Xb: list_l611321411t_unit,X: list_c1059388851t_unit] :
      ( ( prefix747844452t_unit @ Xa @ Xb )
     => ( prefix747844452t_unit @ ( cons_l1083444861t_unit @ X @ Xa ) @ ( cons_l1083444861t_unit @ X @ Xb ) ) ) ).

% prefixList.intros(2)
thf(fact_9_prefixList_Ointros_I2_J,axiom,
    ! [Xa: list_l1619404459ge_p_v,Xb: list_l1619404459ge_p_v,X: list_message_p_v] :
      ( ( prefix1465223476ge_p_v @ Xa @ Xb )
     => ( prefix1465223476ge_p_v @ ( cons_l233104475ge_p_v @ X @ Xa ) @ ( cons_l233104475ge_p_v @ X @ Xb ) ) ) ).

% prefixList.intros(2)
thf(fact_10_prefixList_Ointros_I2_J,axiom,
    ! [Xa: list_message_p_v,Xb: list_message_p_v,X: message_p_v] :
      ( ( prefix47729710ge_p_v @ Xa @ Xb )
     => ( prefix47729710ge_p_v @ ( cons_message_p_v @ X @ Xa ) @ ( cons_message_p_v @ X @ Xb ) ) ) ).

% prefixList.intros(2)
thf(fact_11_prefixList_Ointros_I2_J,axiom,
    ! [Xa: list_c1059388851t_unit,Xb: list_c1059388851t_unit,X: config256849571t_unit] :
      ( ( prefix1615116500t_unit @ Xa @ Xb )
     => ( prefix1615116500t_unit @ ( cons_c1162654829t_unit @ X @ Xa ) @ ( cons_c1162654829t_unit @ X @ Xb ) ) ) ).

% prefixList.intros(2)
thf(fact_12_PrefixListMonotonicity,axiom,
    ! [L1: list_message_p_v,L2: list_message_p_v] :
      ( ( prefix47729710ge_p_v @ L1 @ L2 )
     => ( ord_less_nat @ ( size_s1168481041ge_p_v @ L1 ) @ ( size_s1168481041ge_p_v @ L2 ) ) ) ).

% PrefixListMonotonicity
thf(fact_13_PrefixListMonotonicity,axiom,
    ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit] :
      ( ( prefix1615116500t_unit @ L1 @ L2 )
     => ( ord_less_nat @ ( size_s1406904903t_unit @ L1 ) @ ( size_s1406904903t_unit @ L2 ) ) ) ).

% PrefixListMonotonicity
thf(fact_14_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J,axiom,
    ! [P: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,Q: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,A4: config256849571t_unit,A5: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,A6: list_c1059388851t_unit > list_message_p_v > list_message_p_v,A7: nat] :
      ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( P @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
     => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
            ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
           => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
             => ( P @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
       => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
         => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
                ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
               => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
                 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
           => ( Q @ A4 @ A5 @ A6 @ A7 ) ) ) ) ) ).

% infiniteExecutionCfg_infiniteExecutionMsg.induct(2)
thf(fact_15_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J,axiom,
    ! [P: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,Q: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,A0: config256849571t_unit,A1: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,A2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,A3: nat] :
      ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( P @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
     => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
            ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
           => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
             => ( P @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
       => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
         => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
                ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
               => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
                 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
           => ( P @ A0 @ A1 @ A2 @ A3 ) ) ) ) ) ).

% infiniteExecutionCfg_infiniteExecutionMsg.induct(1)
thf(fact_16_prefixList_Ointros_I1_J,axiom,
    ! [X: list_c1059388851t_unit,Xs: list_l611321411t_unit] : ( prefix747844452t_unit @ nil_li307996205t_unit @ ( cons_l1083444861t_unit @ X @ Xs ) ) ).

% prefixList.intros(1)
thf(fact_17_prefixList_Ointros_I1_J,axiom,
    ! [X: list_message_p_v,Xs: list_l1619404459ge_p_v] : ( prefix1465223476ge_p_v @ nil_list_message_p_v @ ( cons_l233104475ge_p_v @ X @ Xs ) ) ).

% prefixList.intros(1)
thf(fact_18_prefixList_Ointros_I1_J,axiom,
    ! [X: message_p_v,Xs: list_message_p_v] : ( prefix47729710ge_p_v @ nil_message_p_v @ ( cons_message_p_v @ X @ Xs ) ) ).

% prefixList.intros(1)
thf(fact_19_prefixList_Ointros_I1_J,axiom,
    ! [X: config256849571t_unit,Xs: list_c1059388851t_unit] : ( prefix1615116500t_unit @ nil_co1338500125t_unit @ ( cons_c1162654829t_unit @ X @ Xs ) ) ).

% prefixList.intros(1)
thf(fact_20_prefixList_Ocases,axiom,
    ! [A1: list_l611321411t_unit,A2: list_l611321411t_unit] :
      ( ( prefix747844452t_unit @ A1 @ A2 )
     => ( ( ( A1 = nil_li307996205t_unit )
         => ! [X2: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
              ( A2
             != ( cons_l1083444861t_unit @ X2 @ Xs2 ) ) )
       => ~ ! [Xa2: list_l611321411t_unit,Xb2: list_l611321411t_unit,X2: list_c1059388851t_unit] :
              ( ( A1
                = ( cons_l1083444861t_unit @ X2 @ Xa2 ) )
             => ( ( A2
                  = ( cons_l1083444861t_unit @ X2 @ Xb2 ) )
               => ~ ( prefix747844452t_unit @ Xa2 @ Xb2 ) ) ) ) ) ).

% prefixList.cases
thf(fact_21_prefixList_Ocases,axiom,
    ! [A1: list_l1619404459ge_p_v,A2: list_l1619404459ge_p_v] :
      ( ( prefix1465223476ge_p_v @ A1 @ A2 )
     => ( ( ( A1 = nil_list_message_p_v )
         => ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
              ( A2
             != ( cons_l233104475ge_p_v @ X2 @ Xs2 ) ) )
       => ~ ! [Xa2: list_l1619404459ge_p_v,Xb2: list_l1619404459ge_p_v,X2: list_message_p_v] :
              ( ( A1
                = ( cons_l233104475ge_p_v @ X2 @ Xa2 ) )
             => ( ( A2
                  = ( cons_l233104475ge_p_v @ X2 @ Xb2 ) )
               => ~ ( prefix1465223476ge_p_v @ Xa2 @ Xb2 ) ) ) ) ) ).

% prefixList.cases
thf(fact_22_prefixList_Ocases,axiom,
    ! [A1: list_message_p_v,A2: list_message_p_v] :
      ( ( prefix47729710ge_p_v @ A1 @ A2 )
     => ( ( ( A1 = nil_message_p_v )
         => ! [X2: message_p_v,Xs2: list_message_p_v] :
              ( A2
             != ( cons_message_p_v @ X2 @ Xs2 ) ) )
       => ~ ! [Xa2: list_message_p_v,Xb2: list_message_p_v,X2: message_p_v] :
              ( ( A1
                = ( cons_message_p_v @ X2 @ Xa2 ) )
             => ( ( A2
                  = ( cons_message_p_v @ X2 @ Xb2 ) )
               => ~ ( prefix47729710ge_p_v @ Xa2 @ Xb2 ) ) ) ) ) ).

% prefixList.cases
thf(fact_23_prefixList_Ocases,axiom,
    ! [A1: list_c1059388851t_unit,A2: list_c1059388851t_unit] :
      ( ( prefix1615116500t_unit @ A1 @ A2 )
     => ( ( ( A1 = nil_co1338500125t_unit )
         => ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] :
              ( A2
             != ( cons_c1162654829t_unit @ X2 @ Xs2 ) ) )
       => ~ ! [Xa2: list_c1059388851t_unit,Xb2: list_c1059388851t_unit,X2: config256849571t_unit] :
              ( ( A1
                = ( cons_c1162654829t_unit @ X2 @ Xa2 ) )
             => ( ( A2
                  = ( cons_c1162654829t_unit @ X2 @ Xb2 ) )
               => ~ ( prefix1615116500t_unit @ Xa2 @ Xb2 ) ) ) ) ) ).

% prefixList.cases
thf(fact_24_prefixList_Osimps,axiom,
    ( prefix747844452t_unit
    = ( ^ [A12: list_l611321411t_unit,A22: list_l611321411t_unit] :
          ( ? [X3: list_c1059388851t_unit,Xs3: list_l611321411t_unit] :
              ( ( A12 = nil_li307996205t_unit )
              & ( A22
                = ( cons_l1083444861t_unit @ X3 @ Xs3 ) ) )
          | ? [Xa3: list_l611321411t_unit,Xb3: list_l611321411t_unit,X3: list_c1059388851t_unit] :
              ( ( A12
                = ( cons_l1083444861t_unit @ X3 @ Xa3 ) )
              & ( A22
                = ( cons_l1083444861t_unit @ X3 @ Xb3 ) )
              & ( prefix747844452t_unit @ Xa3 @ Xb3 ) ) ) ) ) ).

% prefixList.simps
thf(fact_25_prefixList_Osimps,axiom,
    ( prefix1465223476ge_p_v
    = ( ^ [A12: list_l1619404459ge_p_v,A22: list_l1619404459ge_p_v] :
          ( ? [X3: list_message_p_v,Xs3: list_l1619404459ge_p_v] :
              ( ( A12 = nil_list_message_p_v )
              & ( A22
                = ( cons_l233104475ge_p_v @ X3 @ Xs3 ) ) )
          | ? [Xa3: list_l1619404459ge_p_v,Xb3: list_l1619404459ge_p_v,X3: list_message_p_v] :
              ( ( A12
                = ( cons_l233104475ge_p_v @ X3 @ Xa3 ) )
              & ( A22
                = ( cons_l233104475ge_p_v @ X3 @ Xb3 ) )
              & ( prefix1465223476ge_p_v @ Xa3 @ Xb3 ) ) ) ) ) ).

% prefixList.simps
thf(fact_26_prefixList_Osimps,axiom,
    ( prefix47729710ge_p_v
    = ( ^ [A12: list_message_p_v,A22: list_message_p_v] :
          ( ? [X3: message_p_v,Xs3: list_message_p_v] :
              ( ( A12 = nil_message_p_v )
              & ( A22
                = ( cons_message_p_v @ X3 @ Xs3 ) ) )
          | ? [Xa3: list_message_p_v,Xb3: list_message_p_v,X3: message_p_v] :
              ( ( A12
                = ( cons_message_p_v @ X3 @ Xa3 ) )
              & ( A22
                = ( cons_message_p_v @ X3 @ Xb3 ) )
              & ( prefix47729710ge_p_v @ Xa3 @ Xb3 ) ) ) ) ) ).

% prefixList.simps
thf(fact_27_prefixList_Osimps,axiom,
    ( prefix1615116500t_unit
    = ( ^ [A12: list_c1059388851t_unit,A22: list_c1059388851t_unit] :
          ( ? [X3: config256849571t_unit,Xs3: list_c1059388851t_unit] :
              ( ( A12 = nil_co1338500125t_unit )
              & ( A22
                = ( cons_c1162654829t_unit @ X3 @ Xs3 ) ) )
          | ? [Xa3: list_c1059388851t_unit,Xb3: list_c1059388851t_unit,X3: config256849571t_unit] :
              ( ( A12
                = ( cons_c1162654829t_unit @ X3 @ Xa3 ) )
              & ( A22
                = ( cons_c1162654829t_unit @ X3 @ Xb3 ) )
              & ( prefix1615116500t_unit @ Xa3 @ Xb3 ) ) ) ) ) ).

% prefixList.simps
thf(fact_28_prefixList_Oinducts,axiom,
    ! [X1: list_l611321411t_unit,X22: list_l611321411t_unit,P: list_l611321411t_unit > list_l611321411t_unit > $o] :
      ( ( prefix747844452t_unit @ X1 @ X22 )
     => ( ! [X2: list_c1059388851t_unit,Xs2: list_l611321411t_unit] : ( P @ nil_li307996205t_unit @ ( cons_l1083444861t_unit @ X2 @ Xs2 ) )
       => ( ! [Xa2: list_l611321411t_unit,Xb2: list_l611321411t_unit,X2: list_c1059388851t_unit] :
              ( ( prefix747844452t_unit @ Xa2 @ Xb2 )
             => ( ( P @ Xa2 @ Xb2 )
               => ( P @ ( cons_l1083444861t_unit @ X2 @ Xa2 ) @ ( cons_l1083444861t_unit @ X2 @ Xb2 ) ) ) )
         => ( P @ X1 @ X22 ) ) ) ) ).

% prefixList.inducts
thf(fact_29_prefixList_Oinducts,axiom,
    ! [X1: list_l1619404459ge_p_v,X22: list_l1619404459ge_p_v,P: list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o] :
      ( ( prefix1465223476ge_p_v @ X1 @ X22 )
     => ( ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v] : ( P @ nil_list_message_p_v @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) )
       => ( ! [Xa2: list_l1619404459ge_p_v,Xb2: list_l1619404459ge_p_v,X2: list_message_p_v] :
              ( ( prefix1465223476ge_p_v @ Xa2 @ Xb2 )
             => ( ( P @ Xa2 @ Xb2 )
               => ( P @ ( cons_l233104475ge_p_v @ X2 @ Xa2 ) @ ( cons_l233104475ge_p_v @ X2 @ Xb2 ) ) ) )
         => ( P @ X1 @ X22 ) ) ) ) ).

% prefixList.inducts
thf(fact_30_prefixList_Oinducts,axiom,
    ! [X1: list_message_p_v,X22: list_message_p_v,P: list_message_p_v > list_message_p_v > $o] :
      ( ( prefix47729710ge_p_v @ X1 @ X22 )
     => ( ! [X2: message_p_v,Xs2: list_message_p_v] : ( P @ nil_message_p_v @ ( cons_message_p_v @ X2 @ Xs2 ) )
       => ( ! [Xa2: list_message_p_v,Xb2: list_message_p_v,X2: message_p_v] :
              ( ( prefix47729710ge_p_v @ Xa2 @ Xb2 )
             => ( ( P @ Xa2 @ Xb2 )
               => ( P @ ( cons_message_p_v @ X2 @ Xa2 ) @ ( cons_message_p_v @ X2 @ Xb2 ) ) ) )
         => ( P @ X1 @ X22 ) ) ) ) ).

% prefixList.inducts
thf(fact_31_prefixList_Oinducts,axiom,
    ! [X1: list_c1059388851t_unit,X22: list_c1059388851t_unit,P: list_c1059388851t_unit > list_c1059388851t_unit > $o] :
      ( ( prefix1615116500t_unit @ X1 @ X22 )
     => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) )
       => ( ! [Xa2: list_c1059388851t_unit,Xb2: list_c1059388851t_unit,X2: config256849571t_unit] :
              ( ( prefix1615116500t_unit @ Xa2 @ Xb2 )
             => ( ( P @ Xa2 @ Xb2 )
               => ( P @ ( cons_c1162654829t_unit @ X2 @ Xa2 ) @ ( cons_c1162654829t_unit @ X2 @ Xb2 ) ) ) )
         => ( P @ X1 @ X22 ) ) ) ) ).

% prefixList.inducts
thf(fact_32_NatPredicateTippingPoint,axiom,
    ! [N2: nat,Pr: nat > $o] :
      ( ( ord_less_nat @ zero_zero_nat @ N2 )
     => ( ( Pr @ zero_zero_nat )
       => ( ~ ( Pr @ N2 )
         => ? [N: nat] :
              ( ( ord_less_nat @ N @ N2 )
              & ( Pr @ N )
              & ~ ( Pr @ ( suc @ N ) ) ) ) ) ) ).

% NatPredicateTippingPoint
thf(fact_33_infiniteExecutionCfg_Osimps_I1_J,axiom,
    ! [Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
      ( ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
      = ( cons_c1162654829t_unit @ Cfg2 @ nil_co1338500125t_unit ) ) ).

% infiniteExecutionCfg.simps(1)
thf(fact_34_length__greater__0__conv,axiom,
    ! [Xs: list_l611321411t_unit] :
      ( ( ord_less_nat @ zero_zero_nat @ ( size_s503142615t_unit @ Xs ) )
      = ( Xs != nil_li307996205t_unit ) ) ).

% length_greater_0_conv
thf(fact_35_length__greater__0__conv,axiom,
    ! [Xs: list_l1619404459ge_p_v] :
      ( ( ord_less_nat @ zero_zero_nat @ ( size_s1809856791ge_p_v @ Xs ) )
      = ( Xs != nil_list_message_p_v ) ) ).

% length_greater_0_conv
thf(fact_36_length__greater__0__conv,axiom,
    ! [Xs: list_message_p_v] :
      ( ( ord_less_nat @ zero_zero_nat @ ( size_s1168481041ge_p_v @ Xs ) )
      = ( Xs != nil_message_p_v ) ) ).

% length_greater_0_conv
thf(fact_37_length__greater__0__conv,axiom,
    ! [Xs: list_c1059388851t_unit] :
      ( ( ord_less_nat @ zero_zero_nat @ ( size_s1406904903t_unit @ Xs ) )
      = ( Xs != nil_co1338500125t_unit ) ) ).

% length_greater_0_conv
thf(fact_38_length__0__conv,axiom,
    ! [Xs: list_l611321411t_unit] :
      ( ( ( size_s503142615t_unit @ Xs )
        = zero_zero_nat )
      = ( Xs = nil_li307996205t_unit ) ) ).

% length_0_conv
thf(fact_39_length__0__conv,axiom,
    ! [Xs: list_l1619404459ge_p_v] :
      ( ( ( size_s1809856791ge_p_v @ Xs )
        = zero_zero_nat )
      = ( Xs = nil_list_message_p_v ) ) ).

% length_0_conv
thf(fact_40_length__0__conv,axiom,
    ! [Xs: list_message_p_v] :
      ( ( ( size_s1168481041ge_p_v @ Xs )
        = zero_zero_nat )
      = ( Xs = nil_message_p_v ) ) ).

% length_0_conv
thf(fact_41_length__0__conv,axiom,
    ! [Xs: list_c1059388851t_unit] :
      ( ( ( size_s1406904903t_unit @ Xs )
        = zero_zero_nat )
      = ( Xs = nil_co1338500125t_unit ) ) ).

% length_0_conv
thf(fact_42_less__Suc0,axiom,
    ! [N3: nat] :
      ( ( ord_less_nat @ N3 @ ( suc @ zero_zero_nat ) )
      = ( N3 = zero_zero_nat ) ) ).

% less_Suc0
thf(fact_43_zero__less__Suc,axiom,
    ! [N3: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N3 ) ) ).

% zero_less_Suc
thf(fact_44_lessI,axiom,
    ! [N3: nat] : ( ord_less_nat @ N3 @ ( suc @ N3 ) ) ).

% lessI
thf(fact_45_Suc__mono,axiom,
    ! [M: nat,N3: nat] :
      ( ( ord_less_nat @ M @ N3 )
     => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N3 ) ) ) ).

% Suc_mono
thf(fact_46_Suc__less__eq,axiom,
    ! [M: nat,N3: nat] :
      ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N3 ) )
      = ( ord_less_nat @ M @ N3 ) ) ).

% Suc_less_eq
thf(fact_47_neq0__conv,axiom,
    ! [N3: nat] :
      ( ( N3 != zero_zero_nat )
      = ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).

% neq0_conv
thf(fact_48_less__nat__zero__code,axiom,
    ! [N3: nat] :
      ~ ( ord_less_nat @ N3 @ zero_zero_nat ) ).

% less_nat_zero_code
thf(fact_49_bot__nat__0_Onot__eq__extremum,axiom,
    ! [A: nat] :
      ( ( A != zero_zero_nat )
      = ( ord_less_nat @ zero_zero_nat @ A ) ) ).

% bot_nat_0.not_eq_extremum
thf(fact_50_list_Oinject,axiom,
    ! [X21: message_p_v,X222: list_message_p_v,Y21: message_p_v,Y22: list_message_p_v] :
      ( ( ( cons_message_p_v @ X21 @ X222 )
        = ( cons_message_p_v @ Y21 @ Y22 ) )
      = ( ( X21 = Y21 )
        & ( X222 = Y22 ) ) ) ).

% list.inject
thf(fact_51_list_Oinject,axiom,
    ! [X21: list_c1059388851t_unit,X222: list_l611321411t_unit,Y21: list_c1059388851t_unit,Y22: list_l611321411t_unit] :
      ( ( ( cons_l1083444861t_unit @ X21 @ X222 )
        = ( cons_l1083444861t_unit @ Y21 @ Y22 ) )
      = ( ( X21 = Y21 )
        & ( X222 = Y22 ) ) ) ).

% list.inject
thf(fact_52_list_Oinject,axiom,
    ! [X21: list_message_p_v,X222: list_l1619404459ge_p_v,Y21: list_message_p_v,Y22: list_l1619404459ge_p_v] :
      ( ( ( cons_l233104475ge_p_v @ X21 @ X222 )
        = ( cons_l233104475ge_p_v @ Y21 @ Y22 ) )
      = ( ( X21 = Y21 )
        & ( X222 = Y22 ) ) ) ).

% list.inject
thf(fact_53_list_Oinject,axiom,
    ! [X21: config256849571t_unit,X222: list_c1059388851t_unit,Y21: config256849571t_unit,Y22: list_c1059388851t_unit] :
      ( ( ( cons_c1162654829t_unit @ X21 @ X222 )
        = ( cons_c1162654829t_unit @ Y21 @ Y22 ) )
      = ( ( X21 = Y21 )
        & ( X222 = Y22 ) ) ) ).

% list.inject
thf(fact_54_old_Onat_Oinject,axiom,
    ! [Nat: nat,Nat2: nat] :
      ( ( ( suc @ Nat )
        = ( suc @ Nat2 ) )
      = ( Nat = Nat2 ) ) ).

% old.nat.inject
thf(fact_55_nat_Oinject,axiom,
    ! [X22: nat,Y2: nat] :
      ( ( ( suc @ X22 )
        = ( suc @ Y2 ) )
      = ( X22 = Y2 ) ) ).

% nat.inject
thf(fact_56_not__Cons__self2,axiom,
    ! [X: message_p_v,Xs: list_message_p_v] :
      ( ( cons_message_p_v @ X @ Xs )
     != Xs ) ).

% not_Cons_self2
thf(fact_57_not__Cons__self2,axiom,
    ! [X: list_c1059388851t_unit,Xs: list_l611321411t_unit] :
      ( ( cons_l1083444861t_unit @ X @ Xs )
     != Xs ) ).

% not_Cons_self2
thf(fact_58_not__Cons__self2,axiom,
    ! [X: list_message_p_v,Xs: list_l1619404459ge_p_v] :
      ( ( cons_l233104475ge_p_v @ X @ Xs )
     != Xs ) ).

% not_Cons_self2
thf(fact_59_not__Cons__self2,axiom,
    ! [X: config256849571t_unit,Xs: list_c1059388851t_unit] :
      ( ( cons_c1162654829t_unit @ X @ Xs )
     != Xs ) ).

% not_Cons_self2
thf(fact_60_n__not__Suc__n,axiom,
    ! [N3: nat] :
      ( N3
     != ( suc @ N3 ) ) ).

% n_not_Suc_n
thf(fact_61_Suc__inject,axiom,
    ! [X: nat,Y: nat] :
      ( ( ( suc @ X )
        = ( suc @ Y ) )
     => ( X = Y ) ) ).

% Suc_inject
thf(fact_62_linorder__neqE__nat,axiom,
    ! [X: nat,Y: nat] :
      ( ( X != Y )
     => ( ~ ( ord_less_nat @ X @ Y )
       => ( ord_less_nat @ Y @ X ) ) ) ).

% linorder_neqE_nat
thf(fact_63_infinite__descent,axiom,
    ! [P: nat > $o,N3: nat] :
      ( ! [N: nat] :
          ( ~ ( P @ N )
         => ? [M2: nat] :
              ( ( ord_less_nat @ M2 @ N )
              & ~ ( P @ M2 ) ) )
     => ( P @ N3 ) ) ).

% infinite_descent
thf(fact_64_nat__less__induct,axiom,
    ! [P: nat > $o,N3: nat] :
      ( ! [N: nat] :
          ( ! [M2: nat] :
              ( ( ord_less_nat @ M2 @ N )
             => ( P @ M2 ) )
         => ( P @ N ) )
     => ( P @ N3 ) ) ).

% nat_less_induct
thf(fact_65_less__irrefl__nat,axiom,
    ! [N3: nat] :
      ~ ( ord_less_nat @ N3 @ N3 ) ).

% less_irrefl_nat
thf(fact_66_less__not__refl3,axiom,
    ! [S: nat,T: nat] :
      ( ( ord_less_nat @ S @ T )
     => ( S != T ) ) ).

% less_not_refl3
thf(fact_67_less__not__refl2,axiom,
    ! [N3: nat,M: nat] :
      ( ( ord_less_nat @ N3 @ M )
     => ( M != N3 ) ) ).

% less_not_refl2
thf(fact_68_mem__Collect__eq,axiom,
    ! [A: nat,P: nat > $o] :
      ( ( member_nat @ A @ ( collect_nat @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_69_Collect__mem__eq,axiom,
    ! [A8: set_nat] :
      ( ( collect_nat
        @ ^ [X3: nat] : ( member_nat @ X3 @ A8 ) )
      = A8 ) ).

% Collect_mem_eq
thf(fact_70_less__not__refl,axiom,
    ! [N3: nat] :
      ~ ( ord_less_nat @ N3 @ N3 ) ).

% less_not_refl
thf(fact_71_nat__neq__iff,axiom,
    ! [M: nat,N3: nat] :
      ( ( M != N3 )
      = ( ( ord_less_nat @ M @ N3 )
        | ( ord_less_nat @ N3 @ M ) ) ) ).

% nat_neq_iff
thf(fact_72_size__neq__size__imp__neq,axiom,
    ! [X: list_message_p_v,Y: list_message_p_v] :
      ( ( ( size_s1168481041ge_p_v @ X )
       != ( size_s1168481041ge_p_v @ Y ) )
     => ( X != Y ) ) ).

% size_neq_size_imp_neq
thf(fact_73_size__neq__size__imp__neq,axiom,
    ! [X: list_c1059388851t_unit,Y: list_c1059388851t_unit] :
      ( ( ( size_s1406904903t_unit @ X )
       != ( size_s1406904903t_unit @ Y ) )
     => ( X != Y ) ) ).

% size_neq_size_imp_neq
thf(fact_74_neq__if__length__neq,axiom,
    ! [Xs: list_message_p_v,Ys: list_message_p_v] :
      ( ( ( size_s1168481041ge_p_v @ Xs )
       != ( size_s1168481041ge_p_v @ Ys ) )
     => ( Xs != Ys ) ) ).

% neq_if_length_neq
thf(fact_75_neq__if__length__neq,axiom,
    ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
      ( ( ( size_s1406904903t_unit @ Xs )
       != ( size_s1406904903t_unit @ Ys ) )
     => ( Xs != Ys ) ) ).

% neq_if_length_neq
thf(fact_76_Ex__list__of__length,axiom,
    ! [N3: nat] :
    ? [Xs2: list_message_p_v] :
      ( ( size_s1168481041ge_p_v @ Xs2 )
      = N3 ) ).

% Ex_list_of_length
thf(fact_77_Ex__list__of__length,axiom,
    ! [N3: nat] :
    ? [Xs2: list_c1059388851t_unit] :
      ( ( size_s1406904903t_unit @ Xs2 )
      = N3 ) ).

% Ex_list_of_length
thf(fact_78_not0__implies__Suc,axiom,
    ! [N3: nat] :
      ( ( N3 != zero_zero_nat )
     => ? [M3: nat] :
          ( N3
          = ( suc @ M3 ) ) ) ).

% not0_implies_Suc
thf(fact_79_old_Onat_Oinducts,axiom,
    ! [P: nat > $o,Nat: nat] :
      ( ( P @ zero_zero_nat )
     => ( ! [Nat3: nat] :
            ( ( P @ Nat3 )
           => ( P @ ( suc @ Nat3 ) ) )
       => ( P @ Nat ) ) ) ).

% old.nat.inducts
thf(fact_80_old_Onat_Oexhaust,axiom,
    ! [Y: nat] :
      ( ( Y != zero_zero_nat )
     => ~ ! [Nat3: nat] :
            ( Y
           != ( suc @ Nat3 ) ) ) ).

% old.nat.exhaust
thf(fact_81_Zero__not__Suc,axiom,
    ! [M: nat] :
      ( zero_zero_nat
     != ( suc @ M ) ) ).

% Zero_not_Suc
thf(fact_82_Zero__neq__Suc,axiom,
    ! [M: nat] :
      ( zero_zero_nat
     != ( suc @ M ) ) ).

% Zero_neq_Suc
thf(fact_83_Suc__neq__Zero,axiom,
    ! [M: nat] :
      ( ( suc @ M )
     != zero_zero_nat ) ).

% Suc_neq_Zero
thf(fact_84_zero__induct,axiom,
    ! [P: nat > $o,K: nat] :
      ( ( P @ K )
     => ( ! [N: nat] :
            ( ( P @ ( suc @ N ) )
           => ( P @ N ) )
       => ( P @ zero_zero_nat ) ) ) ).

% zero_induct
thf(fact_85_diff__induct,axiom,
    ! [P: nat > nat > $o,M: nat,N3: nat] :
      ( ! [X2: nat] : ( P @ X2 @ zero_zero_nat )
     => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
       => ( ! [X2: nat,Y3: nat] :
              ( ( P @ X2 @ Y3 )
             => ( P @ ( suc @ X2 ) @ ( suc @ Y3 ) ) )
         => ( P @ M @ N3 ) ) ) ) ).

% diff_induct
thf(fact_86_nat__induct,axiom,
    ! [P: nat > $o,N3: nat] :
      ( ( P @ zero_zero_nat )
     => ( ! [N: nat] :
            ( ( P @ N )
           => ( P @ ( suc @ N ) ) )
       => ( P @ N3 ) ) ) ).

% nat_induct
thf(fact_87_nat_OdiscI,axiom,
    ! [Nat: nat,X22: nat] :
      ( ( Nat
        = ( suc @ X22 ) )
     => ( Nat != zero_zero_nat ) ) ).

% nat.discI
thf(fact_88_old_Onat_Odistinct_I1_J,axiom,
    ! [Nat2: nat] :
      ( zero_zero_nat
     != ( suc @ Nat2 ) ) ).

% old.nat.distinct(1)
thf(fact_89_old_Onat_Odistinct_I2_J,axiom,
    ! [Nat2: nat] :
      ( ( suc @ Nat2 )
     != zero_zero_nat ) ).

% old.nat.distinct(2)
thf(fact_90_nat_Odistinct_I1_J,axiom,
    ! [X22: nat] :
      ( zero_zero_nat
     != ( suc @ X22 ) ) ).

% nat.distinct(1)
thf(fact_91_bot__nat__0_Oextremum__strict,axiom,
    ! [A: nat] :
      ~ ( ord_less_nat @ A @ zero_zero_nat ) ).

% bot_nat_0.extremum_strict
thf(fact_92_infinite__descent0,axiom,
    ! [P: nat > $o,N3: nat] :
      ( ( P @ zero_zero_nat )
     => ( ! [N: nat] :
            ( ( ord_less_nat @ zero_zero_nat @ N )
           => ( ~ ( P @ N )
             => ? [M2: nat] :
                  ( ( ord_less_nat @ M2 @ N )
                  & ~ ( P @ M2 ) ) ) )
       => ( P @ N3 ) ) ) ).

% infinite_descent0
thf(fact_93_gr__implies__not0,axiom,
    ! [M: nat,N3: nat] :
      ( ( ord_less_nat @ M @ N3 )
     => ( N3 != zero_zero_nat ) ) ).

% gr_implies_not0
thf(fact_94_less__zeroE,axiom,
    ! [N3: nat] :
      ~ ( ord_less_nat @ N3 @ zero_zero_nat ) ).

% less_zeroE
thf(fact_95_not__less0,axiom,
    ! [N3: nat] :
      ~ ( ord_less_nat @ N3 @ zero_zero_nat ) ).

% not_less0
thf(fact_96_not__gr0,axiom,
    ! [N3: nat] :
      ( ( ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
      = ( N3 = zero_zero_nat ) ) ).

% not_gr0
thf(fact_97_gr0I,axiom,
    ! [N3: nat] :
      ( ( N3 != zero_zero_nat )
     => ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).

% gr0I
thf(fact_98_not__less__less__Suc__eq,axiom,
    ! [N3: nat,M: nat] :
      ( ~ ( ord_less_nat @ N3 @ M )
     => ( ( ord_less_nat @ N3 @ ( suc @ M ) )
        = ( N3 = M ) ) ) ).

% not_less_less_Suc_eq
thf(fact_99_strict__inc__induct,axiom,
    ! [I: nat,J: nat,P: nat > $o] :
      ( ( ord_less_nat @ I @ J )
     => ( ! [I2: nat] :
            ( ( J
              = ( suc @ I2 ) )
           => ( P @ I2 ) )
       => ( ! [I2: nat] :
              ( ( ord_less_nat @ I2 @ J )
             => ( ( P @ ( suc @ I2 ) )
               => ( P @ I2 ) ) )
         => ( P @ I ) ) ) ) ).

% strict_inc_induct
thf(fact_100_less__Suc__induct,axiom,
    ! [I: nat,J: nat,P: nat > nat > $o] :
      ( ( ord_less_nat @ I @ J )
     => ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
       => ( ! [I2: nat,J2: nat,K2: nat] :
              ( ( ord_less_nat @ I2 @ J2 )
             => ( ( ord_less_nat @ J2 @ K2 )
               => ( ( P @ I2 @ J2 )
                 => ( ( P @ J2 @ K2 )
                   => ( P @ I2 @ K2 ) ) ) ) )
         => ( P @ I @ J ) ) ) ) ).

% less_Suc_induct
thf(fact_101_less__trans__Suc,axiom,
    ! [I: nat,J: nat,K: nat] :
      ( ( ord_less_nat @ I @ J )
     => ( ( ord_less_nat @ J @ K )
       => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).

% less_trans_Suc
thf(fact_102_Suc__less__SucD,axiom,
    ! [M: nat,N3: nat] :
      ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N3 ) )
     => ( ord_less_nat @ M @ N3 ) ) ).

% Suc_less_SucD
thf(fact_103_less__antisym,axiom,
    ! [N3: nat,M: nat] :
      ( ~ ( ord_less_nat @ N3 @ M )
     => ( ( ord_less_nat @ N3 @ ( suc @ M ) )
       => ( M = N3 ) ) ) ).

% less_antisym
thf(fact_104_Suc__less__eq2,axiom,
    ! [N3: nat,M: nat] :
      ( ( ord_less_nat @ ( suc @ N3 ) @ M )
      = ( ? [M4: nat] :
            ( ( M
              = ( suc @ M4 ) )
            & ( ord_less_nat @ N3 @ M4 ) ) ) ) ).

% Suc_less_eq2
thf(fact_105_All__less__Suc,axiom,
    ! [N3: nat,P: nat > $o] :
      ( ( ! [I3: nat] :
            ( ( ord_less_nat @ I3 @ ( suc @ N3 ) )
           => ( P @ I3 ) ) )
      = ( ( P @ N3 )
        & ! [I3: nat] :
            ( ( ord_less_nat @ I3 @ N3 )
           => ( P @ I3 ) ) ) ) ).

% All_less_Suc
thf(fact_106_not__less__eq,axiom,
    ! [M: nat,N3: nat] :
      ( ( ~ ( ord_less_nat @ M @ N3 ) )
      = ( ord_less_nat @ N3 @ ( suc @ M ) ) ) ).

% not_less_eq
thf(fact_107_less__Suc__eq,axiom,
    ! [M: nat,N3: nat] :
      ( ( ord_less_nat @ M @ ( suc @ N3 ) )
      = ( ( ord_less_nat @ M @ N3 )
        | ( M = N3 ) ) ) ).

% less_Suc_eq
thf(fact_108_Ex__less__Suc,axiom,
    ! [N3: nat,P: nat > $o] :
      ( ( ? [I3: nat] :
            ( ( ord_less_nat @ I3 @ ( suc @ N3 ) )
            & ( P @ I3 ) ) )
      = ( ( P @ N3 )
        | ? [I3: nat] :
            ( ( ord_less_nat @ I3 @ N3 )
            & ( P @ I3 ) ) ) ) ).

% Ex_less_Suc
thf(fact_109_less__SucI,axiom,
    ! [M: nat,N3: nat] :
      ( ( ord_less_nat @ M @ N3 )
     => ( ord_less_nat @ M @ ( suc @ N3 ) ) ) ).

% less_SucI
thf(fact_110_less__SucE,axiom,
    ! [M: nat,N3: nat] :
      ( ( ord_less_nat @ M @ ( suc @ N3 ) )
     => ( ~ ( ord_less_nat @ M @ N3 )
       => ( M = N3 ) ) ) ).

% less_SucE
thf(fact_111_Suc__lessI,axiom,
    ! [M: nat,N3: nat] :
      ( ( ord_less_nat @ M @ N3 )
     => ( ( ( suc @ M )
         != N3 )
       => ( ord_less_nat @ ( suc @ M ) @ N3 ) ) ) ).

% Suc_lessI
thf(fact_112_Suc__lessE,axiom,
    ! [I: nat,K: nat] :
      ( ( ord_less_nat @ ( suc @ I ) @ K )
     => ~ ! [J2: nat] :
            ( ( ord_less_nat @ I @ J2 )
           => ( K
             != ( suc @ J2 ) ) ) ) ).

% Suc_lessE
thf(fact_113_Suc__lessD,axiom,
    ! [M: nat,N3: nat] :
      ( ( ord_less_nat @ ( suc @ M ) @ N3 )
     => ( ord_less_nat @ M @ N3 ) ) ).

% Suc_lessD
thf(fact_114_Nat_OlessE,axiom,
    ! [I: nat,K: nat] :
      ( ( ord_less_nat @ I @ K )
     => ( ( K
         != ( suc @ I ) )
       => ~ ! [J2: nat] :
              ( ( ord_less_nat @ I @ J2 )
             => ( K
               != ( suc @ J2 ) ) ) ) ) ).

% Nat.lessE
thf(fact_115_map__tailrec__rev_Oinduct,axiom,
    ! [P: ( message_p_v > config256849571t_unit ) > list_message_p_v > list_c1059388851t_unit > $o,A0: message_p_v > config256849571t_unit,A1: list_message_p_v,A2: list_c1059388851t_unit] :
      ( ! [F: message_p_v > config256849571t_unit,X_1: list_c1059388851t_unit] : ( P @ F @ nil_message_p_v @ X_1 )
     => ( ! [F: message_p_v > config256849571t_unit,A9: message_p_v,As: list_message_p_v,Bs: list_c1059388851t_unit] :
            ( ( P @ F @ As @ ( cons_c1162654829t_unit @ ( F @ A9 ) @ Bs ) )
           => ( P @ F @ ( cons_message_p_v @ A9 @ As ) @ Bs ) )
       => ( P @ A0 @ A1 @ A2 ) ) ) ).

% map_tailrec_rev.induct
thf(fact_116_map__tailrec__rev_Oinduct,axiom,
    ! [P: ( config256849571t_unit > config256849571t_unit ) > list_c1059388851t_unit > list_c1059388851t_unit > $o,A0: config256849571t_unit > config256849571t_unit,A1: list_c1059388851t_unit,A2: list_c1059388851t_unit] :
      ( ! [F: config256849571t_unit > config256849571t_unit,X_1: list_c1059388851t_unit] : ( P @ F @ nil_co1338500125t_unit @ X_1 )
     => ( ! [F: config256849571t_unit > config256849571t_unit,A9: config256849571t_unit,As: list_c1059388851t_unit,Bs: list_c1059388851t_unit] :
            ( ( P @ F @ As @ ( cons_c1162654829t_unit @ ( F @ A9 ) @ Bs ) )
           => ( P @ F @ ( cons_c1162654829t_unit @ A9 @ As ) @ Bs ) )
       => ( P @ A0 @ A1 @ A2 ) ) ) ).

% map_tailrec_rev.induct
thf(fact_117_map__tailrec__rev_Oinduct,axiom,
    ! [P: ( message_p_v > message_p_v ) > list_message_p_v > list_message_p_v > $o,A0: message_p_v > message_p_v,A1: list_message_p_v,A2: list_message_p_v] :
      ( ! [F: message_p_v > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_message_p_v @ X_1 )
     => ( ! [F: message_p_v > message_p_v,A9: message_p_v,As: list_message_p_v,Bs: list_message_p_v] :
            ( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A9 ) @ Bs ) )
           => ( P @ F @ ( cons_message_p_v @ A9 @ As ) @ Bs ) )
       => ( P @ A0 @ A1 @ A2 ) ) ) ).

% map_tailrec_rev.induct
thf(fact_118_map__tailrec__rev_Oinduct,axiom,
    ! [P: ( list_message_p_v > message_p_v ) > list_l1619404459ge_p_v > list_message_p_v > $o,A0: list_message_p_v > message_p_v,A1: list_l1619404459ge_p_v,A2: list_message_p_v] :
      ( ! [F: list_message_p_v > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_list_message_p_v @ X_1 )
     => ( ! [F: list_message_p_v > message_p_v,A9: list_message_p_v,As: list_l1619404459ge_p_v,Bs: list_message_p_v] :
            ( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A9 ) @ Bs ) )
           => ( P @ F @ ( cons_l233104475ge_p_v @ A9 @ As ) @ Bs ) )
       => ( P @ A0 @ A1 @ A2 ) ) ) ).

% map_tailrec_rev.induct
thf(fact_119_map__tailrec__rev_Oinduct,axiom,
    ! [P: ( message_p_v > list_message_p_v ) > list_message_p_v > list_l1619404459ge_p_v > $o,A0: message_p_v > list_message_p_v,A1: list_message_p_v,A2: list_l1619404459ge_p_v] :
      ( ! [F: message_p_v > list_message_p_v,X_1: list_l1619404459ge_p_v] : ( P @ F @ nil_message_p_v @ X_1 )
     => ( ! [F: message_p_v > list_message_p_v,A9: message_p_v,As: list_message_p_v,Bs: list_l1619404459ge_p_v] :
            ( ( P @ F @ As @ ( cons_l233104475ge_p_v @ ( F @ A9 ) @ Bs ) )
           => ( P @ F @ ( cons_message_p_v @ A9 @ As ) @ Bs ) )
       => ( P @ A0 @ A1 @ A2 ) ) ) ).

% map_tailrec_rev.induct
thf(fact_120_map__tailrec__rev_Oinduct,axiom,
    ! [P: ( config256849571t_unit > message_p_v ) > list_c1059388851t_unit > list_message_p_v > $o,A0: config256849571t_unit > message_p_v,A1: list_c1059388851t_unit,A2: list_message_p_v] :
      ( ! [F: config256849571t_unit > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_co1338500125t_unit @ X_1 )
     => ( ! [F: config256849571t_unit > message_p_v,A9: config256849571t_unit,As: list_c1059388851t_unit,Bs: list_message_p_v] :
            ( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A9 ) @ Bs ) )
           => ( P @ F @ ( cons_c1162654829t_unit @ A9 @ As ) @ Bs ) )
       => ( P @ A0 @ A1 @ A2 ) ) ) ).

% map_tailrec_rev.induct
thf(fact_121_map__tailrec__rev_Oinduct,axiom,
    ! [P: ( list_message_p_v > list_message_p_v ) > list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o,A0: list_message_p_v > list_message_p_v,A1: list_l1619404459ge_p_v,A2: list_l1619404459ge_p_v] :
      ( ! [F: list_message_p_v > list_message_p_v,X_1: list_l1619404459ge_p_v] : ( P @ F @ nil_list_message_p_v @ X_1 )
     => ( ! [F: list_message_p_v > list_message_p_v,A9: list_message_p_v,As: list_l1619404459ge_p_v,Bs: list_l1619404459ge_p_v] :
            ( ( P @ F @ As @ ( cons_l233104475ge_p_v @ ( F @ A9 ) @ Bs ) )
           => ( P @ F @ ( cons_l233104475ge_p_v @ A9 @ As ) @ Bs ) )
       => ( P @ A0 @ A1 @ A2 ) ) ) ).

% map_tailrec_rev.induct
thf(fact_122_map__tailrec__rev_Oinduct,axiom,
    ! [P: ( list_message_p_v > config256849571t_unit ) > list_l1619404459ge_p_v > list_c1059388851t_unit > $o,A0: list_message_p_v > config256849571t_unit,A1: list_l1619404459ge_p_v,A2: list_c1059388851t_unit] :
      ( ! [F: list_message_p_v > config256849571t_unit,X_1: list_c1059388851t_unit] : ( P @ F @ nil_list_message_p_v @ X_1 )
     => ( ! [F: list_message_p_v > config256849571t_unit,A9: list_message_p_v,As: list_l1619404459ge_p_v,Bs: list_c1059388851t_unit] :
            ( ( P @ F @ As @ ( cons_c1162654829t_unit @ ( F @ A9 ) @ Bs ) )
           => ( P @ F @ ( cons_l233104475ge_p_v @ A9 @ As ) @ Bs ) )
       => ( P @ A0 @ A1 @ A2 ) ) ) ).

% map_tailrec_rev.induct
thf(fact_123_map__tailrec__rev_Oinduct,axiom,
    ! [P: ( list_c1059388851t_unit > message_p_v ) > list_l611321411t_unit > list_message_p_v > $o,A0: list_c1059388851t_unit > message_p_v,A1: list_l611321411t_unit,A2: list_message_p_v] :
      ( ! [F: list_c1059388851t_unit > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_li307996205t_unit @ X_1 )
     => ( ! [F: list_c1059388851t_unit > message_p_v,A9: list_c1059388851t_unit,As: list_l611321411t_unit,Bs: list_message_p_v] :
            ( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A9 ) @ Bs ) )
           => ( P @ F @ ( cons_l1083444861t_unit @ A9 @ As ) @ Bs ) )
       => ( P @ A0 @ A1 @ A2 ) ) ) ).

% map_tailrec_rev.induct
thf(fact_124_map__tailrec__rev_Oinduct,axiom,
    ! [P: ( message_p_v > list_c1059388851t_unit ) > list_message_p_v > list_l611321411t_unit > $o,A0: message_p_v > list_c1059388851t_unit,A1: list_message_p_v,A2: list_l611321411t_unit] :
      ( ! [F: message_p_v > list_c1059388851t_unit,X_1: list_l611321411t_unit] : ( P @ F @ nil_message_p_v @ X_1 )
     => ( ! [F: message_p_v > list_c1059388851t_unit,A9: message_p_v,As: list_message_p_v,Bs: list_l611321411t_unit] :
            ( ( P @ F @ As @ ( cons_l1083444861t_unit @ ( F @ A9 ) @ Bs ) )
           => ( P @ F @ ( cons_message_p_v @ A9 @ As ) @ Bs ) )
       => ( P @ A0 @ A1 @ A2 ) ) ) ).

% map_tailrec_rev.induct
thf(fact_125_list__nonempty__induct,axiom,
    ! [Xs: list_l611321411t_unit,P: list_l611321411t_unit > $o] :
      ( ( Xs != nil_li307996205t_unit )
     => ( ! [X2: list_c1059388851t_unit] : ( P @ ( cons_l1083444861t_unit @ X2 @ nil_li307996205t_unit ) )
       => ( ! [X2: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
              ( ( Xs2 != nil_li307996205t_unit )
             => ( ( P @ Xs2 )
               => ( P @ ( cons_l1083444861t_unit @ X2 @ Xs2 ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% list_nonempty_induct
thf(fact_126_list__nonempty__induct,axiom,
    ! [Xs: list_l1619404459ge_p_v,P: list_l1619404459ge_p_v > $o] :
      ( ( Xs != nil_list_message_p_v )
     => ( ! [X2: list_message_p_v] : ( P @ ( cons_l233104475ge_p_v @ X2 @ nil_list_message_p_v ) )
       => ( ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
              ( ( Xs2 != nil_list_message_p_v )
             => ( ( P @ Xs2 )
               => ( P @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% list_nonempty_induct
thf(fact_127_list__nonempty__induct,axiom,
    ! [Xs: list_message_p_v,P: list_message_p_v > $o] :
      ( ( Xs != nil_message_p_v )
     => ( ! [X2: message_p_v] : ( P @ ( cons_message_p_v @ X2 @ nil_message_p_v ) )
       => ( ! [X2: message_p_v,Xs2: list_message_p_v] :
              ( ( Xs2 != nil_message_p_v )
             => ( ( P @ Xs2 )
               => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% list_nonempty_induct
thf(fact_128_list__nonempty__induct,axiom,
    ! [Xs: list_c1059388851t_unit,P: list_c1059388851t_unit > $o] :
      ( ( Xs != nil_co1338500125t_unit )
     => ( ! [X2: config256849571t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
       => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] :
              ( ( Xs2 != nil_co1338500125t_unit )
             => ( ( P @ Xs2 )
               => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% list_nonempty_induct
thf(fact_129_successively_Oinduct,axiom,
    ! [P: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_l611321411t_unit > $o,A0: list_c1059388851t_unit > list_c1059388851t_unit > $o,A1: list_l611321411t_unit] :
      ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o] : ( P @ P2 @ nil_li307996205t_unit )
     => ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o,X2: list_c1059388851t_unit] : ( P @ P2 @ ( cons_l1083444861t_unit @ X2 @ nil_li307996205t_unit ) )
       => ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o,X2: list_c1059388851t_unit,Y3: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
              ( ( P @ P2 @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) )
             => ( P @ P2 @ ( cons_l1083444861t_unit @ X2 @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) ) )
         => ( P @ A0 @ A1 ) ) ) ) ).

% successively.induct
thf(fact_130_successively_Oinduct,axiom,
    ! [P: ( list_message_p_v > list_message_p_v > $o ) > list_l1619404459ge_p_v > $o,A0: list_message_p_v > list_message_p_v > $o,A1: list_l1619404459ge_p_v] :
      ( ! [P2: list_message_p_v > list_message_p_v > $o] : ( P @ P2 @ nil_list_message_p_v )
     => ( ! [P2: list_message_p_v > list_message_p_v > $o,X2: list_message_p_v] : ( P @ P2 @ ( cons_l233104475ge_p_v @ X2 @ nil_list_message_p_v ) )
       => ( ! [P2: list_message_p_v > list_message_p_v > $o,X2: list_message_p_v,Y3: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
              ( ( P @ P2 @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) )
             => ( P @ P2 @ ( cons_l233104475ge_p_v @ X2 @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) ) )
         => ( P @ A0 @ A1 ) ) ) ) ).

% successively.induct
thf(fact_131_successively_Oinduct,axiom,
    ! [P: ( message_p_v > message_p_v > $o ) > list_message_p_v > $o,A0: message_p_v > message_p_v > $o,A1: list_message_p_v] :
      ( ! [P2: message_p_v > message_p_v > $o] : ( P @ P2 @ nil_message_p_v )
     => ( ! [P2: message_p_v > message_p_v > $o,X2: message_p_v] : ( P @ P2 @ ( cons_message_p_v @ X2 @ nil_message_p_v ) )
       => ( ! [P2: message_p_v > message_p_v > $o,X2: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
              ( ( P @ P2 @ ( cons_message_p_v @ Y3 @ Xs2 ) )
             => ( P @ P2 @ ( cons_message_p_v @ X2 @ ( cons_message_p_v @ Y3 @ Xs2 ) ) ) )
         => ( P @ A0 @ A1 ) ) ) ) ).

% successively.induct
thf(fact_132_successively_Oinduct,axiom,
    ! [P: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o,A0: config256849571t_unit > config256849571t_unit > $o,A1: list_c1059388851t_unit] :
      ( ! [P2: config256849571t_unit > config256849571t_unit > $o] : ( P @ P2 @ nil_co1338500125t_unit )
     => ( ! [P2: config256849571t_unit > config256849571t_unit > $o,X2: config256849571t_unit] : ( P @ P2 @ ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
       => ( ! [P2: config256849571t_unit > config256849571t_unit > $o,X2: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
              ( ( P @ P2 @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) )
             => ( P @ P2 @ ( cons_c1162654829t_unit @ X2 @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) ) )
         => ( P @ A0 @ A1 ) ) ) ) ).

% successively.induct
thf(fact_133_remdups__adj_Oinduct,axiom,
    ! [P: list_l611321411t_unit > $o,A0: list_l611321411t_unit] :
      ( ( P @ nil_li307996205t_unit )
     => ( ! [X2: list_c1059388851t_unit] : ( P @ ( cons_l1083444861t_unit @ X2 @ nil_li307996205t_unit ) )
       => ( ! [X2: list_c1059388851t_unit,Y3: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
              ( ( ( X2 = Y3 )
               => ( P @ ( cons_l1083444861t_unit @ X2 @ Xs2 ) ) )
             => ( ( ( X2 != Y3 )
                 => ( P @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) )
               => ( P @ ( cons_l1083444861t_unit @ X2 @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) ) ) )
         => ( P @ A0 ) ) ) ) ).

% remdups_adj.induct
thf(fact_134_remdups__adj_Oinduct,axiom,
    ! [P: list_l1619404459ge_p_v > $o,A0: list_l1619404459ge_p_v] :
      ( ( P @ nil_list_message_p_v )
     => ( ! [X2: list_message_p_v] : ( P @ ( cons_l233104475ge_p_v @ X2 @ nil_list_message_p_v ) )
       => ( ! [X2: list_message_p_v,Y3: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
              ( ( ( X2 = Y3 )
               => ( P @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) ) )
             => ( ( ( X2 != Y3 )
                 => ( P @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) )
               => ( P @ ( cons_l233104475ge_p_v @ X2 @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) ) ) )
         => ( P @ A0 ) ) ) ) ).

% remdups_adj.induct
thf(fact_135_remdups__adj_Oinduct,axiom,
    ! [P: list_message_p_v > $o,A0: list_message_p_v] :
      ( ( P @ nil_message_p_v )
     => ( ! [X2: message_p_v] : ( P @ ( cons_message_p_v @ X2 @ nil_message_p_v ) )
       => ( ! [X2: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
              ( ( ( X2 = Y3 )
               => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) ) )
             => ( ( ( X2 != Y3 )
                 => ( P @ ( cons_message_p_v @ Y3 @ Xs2 ) ) )
               => ( P @ ( cons_message_p_v @ X2 @ ( cons_message_p_v @ Y3 @ Xs2 ) ) ) ) )
         => ( P @ A0 ) ) ) ) ).

% remdups_adj.induct
thf(fact_136_remdups__adj_Oinduct,axiom,
    ! [P: list_c1059388851t_unit > $o,A0: list_c1059388851t_unit] :
      ( ( P @ nil_co1338500125t_unit )
     => ( ! [X2: config256849571t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
       => ( ! [X2: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
              ( ( ( X2 = Y3 )
               => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) ) )
             => ( ( ( X2 != Y3 )
                 => ( P @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) )
               => ( P @ ( cons_c1162654829t_unit @ X2 @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) ) ) )
         => ( P @ A0 ) ) ) ) ).

% remdups_adj.induct
thf(fact_137_sorted__wrt_Oinduct,axiom,
    ! [P: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_l611321411t_unit > $o,A0: list_c1059388851t_unit > list_c1059388851t_unit > $o,A1: list_l611321411t_unit] :
      ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o] : ( P @ P2 @ nil_li307996205t_unit )
     => ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o,X2: list_c1059388851t_unit,Ys2: list_l611321411t_unit] :
            ( ( P @ P2 @ Ys2 )
           => ( P @ P2 @ ( cons_l1083444861t_unit @ X2 @ Ys2 ) ) )
       => ( P @ A0 @ A1 ) ) ) ).

% sorted_wrt.induct
thf(fact_138_sorted__wrt_Oinduct,axiom,
    ! [P: ( list_message_p_v > list_message_p_v > $o ) > list_l1619404459ge_p_v > $o,A0: list_message_p_v > list_message_p_v > $o,A1: list_l1619404459ge_p_v] :
      ( ! [P2: list_message_p_v > list_message_p_v > $o] : ( P @ P2 @ nil_list_message_p_v )
     => ( ! [P2: list_message_p_v > list_message_p_v > $o,X2: list_message_p_v,Ys2: list_l1619404459ge_p_v] :
            ( ( P @ P2 @ Ys2 )
           => ( P @ P2 @ ( cons_l233104475ge_p_v @ X2 @ Ys2 ) ) )
       => ( P @ A0 @ A1 ) ) ) ).

% sorted_wrt.induct
thf(fact_139_sorted__wrt_Oinduct,axiom,
    ! [P: ( message_p_v > message_p_v > $o ) > list_message_p_v > $o,A0: message_p_v > message_p_v > $o,A1: list_message_p_v] :
      ( ! [P2: message_p_v > message_p_v > $o] : ( P @ P2 @ nil_message_p_v )
     => ( ! [P2: message_p_v > message_p_v > $o,X2: message_p_v,Ys2: list_message_p_v] :
            ( ( P @ P2 @ Ys2 )
           => ( P @ P2 @ ( cons_message_p_v @ X2 @ Ys2 ) ) )
       => ( P @ A0 @ A1 ) ) ) ).

% sorted_wrt.induct
thf(fact_140_sorted__wrt_Oinduct,axiom,
    ! [P: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o,A0: config256849571t_unit > config256849571t_unit > $o,A1: list_c1059388851t_unit] :
      ( ! [P2: config256849571t_unit > config256849571t_unit > $o] : ( P @ P2 @ nil_co1338500125t_unit )
     => ( ! [P2: config256849571t_unit > config256849571t_unit > $o,X2: config256849571t_unit,Ys2: list_c1059388851t_unit] :
            ( ( P @ P2 @ Ys2 )
           => ( P @ P2 @ ( cons_c1162654829t_unit @ X2 @ Ys2 ) ) )
       => ( P @ A0 @ A1 ) ) ) ).

% sorted_wrt.induct
thf(fact_141_remdups__adj_Ocases,axiom,
    ! [X: list_l611321411t_unit] :
      ( ( X != nil_li307996205t_unit )
     => ( ! [X2: list_c1059388851t_unit] :
            ( X
           != ( cons_l1083444861t_unit @ X2 @ nil_li307996205t_unit ) )
       => ~ ! [X2: list_c1059388851t_unit,Y3: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
              ( X
             != ( cons_l1083444861t_unit @ X2 @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) ) ) ) ).

% remdups_adj.cases
thf(fact_142_remdups__adj_Ocases,axiom,
    ! [X: list_l1619404459ge_p_v] :
      ( ( X != nil_list_message_p_v )
     => ( ! [X2: list_message_p_v] :
            ( X
           != ( cons_l233104475ge_p_v @ X2 @ nil_list_message_p_v ) )
       => ~ ! [X2: list_message_p_v,Y3: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
              ( X
             != ( cons_l233104475ge_p_v @ X2 @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) ) ) ) ).

% remdups_adj.cases
thf(fact_143_remdups__adj_Ocases,axiom,
    ! [X: list_message_p_v] :
      ( ( X != nil_message_p_v )
     => ( ! [X2: message_p_v] :
            ( X
           != ( cons_message_p_v @ X2 @ nil_message_p_v ) )
       => ~ ! [X2: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
              ( X
             != ( cons_message_p_v @ X2 @ ( cons_message_p_v @ Y3 @ Xs2 ) ) ) ) ) ).

% remdups_adj.cases
thf(fact_144_remdups__adj_Ocases,axiom,
    ! [X: list_c1059388851t_unit] :
      ( ( X != nil_co1338500125t_unit )
     => ( ! [X2: config256849571t_unit] :
            ( X
           != ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
       => ~ ! [X2: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
              ( X
             != ( cons_c1162654829t_unit @ X2 @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) ) ) ) ).

% remdups_adj.cases
thf(fact_145_transpose_Ocases,axiom,
    ! [X: list_l1584713811t_unit] :
      ( ( X != nil_li2108369341t_unit )
     => ( ! [Xss: list_l1584713811t_unit] :
            ( X
           != ( cons_l1777019405t_unit @ nil_li307996205t_unit @ Xss ) )
       => ~ ! [X2: list_c1059388851t_unit,Xs2: list_l611321411t_unit,Xss: list_l1584713811t_unit] :
              ( X
             != ( cons_l1777019405t_unit @ ( cons_l1083444861t_unit @ X2 @ Xs2 ) @ Xss ) ) ) ) ).

% transpose.cases
thf(fact_146_transpose_Ocases,axiom,
    ! [X: list_l1341496881ge_p_v] :
      ( ( X != nil_li835338673ge_p_v )
     => ( ! [Xss: list_l1341496881ge_p_v] :
            ( X
           != ( cons_l1383421281ge_p_v @ nil_list_message_p_v @ Xss ) )
       => ~ ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v,Xss: list_l1341496881ge_p_v] :
              ( X
             != ( cons_l1383421281ge_p_v @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) @ Xss ) ) ) ) ).

% transpose.cases
thf(fact_147_transpose_Ocases,axiom,
    ! [X: list_l1619404459ge_p_v] :
      ( ( X != nil_list_message_p_v )
     => ( ! [Xss: list_l1619404459ge_p_v] :
            ( X
           != ( cons_l233104475ge_p_v @ nil_message_p_v @ Xss ) )
       => ~ ! [X2: message_p_v,Xs2: list_message_p_v,Xss: list_l1619404459ge_p_v] :
              ( X
             != ( cons_l233104475ge_p_v @ ( cons_message_p_v @ X2 @ Xs2 ) @ Xss ) ) ) ) ).

% transpose.cases
thf(fact_148_transpose_Ocases,axiom,
    ! [X: list_l611321411t_unit] :
      ( ( X != nil_li307996205t_unit )
     => ( ! [Xss: list_l611321411t_unit] :
            ( X
           != ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ Xss ) )
       => ~ ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Xss: list_l611321411t_unit] :
              ( X
             != ( cons_l1083444861t_unit @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ Xss ) ) ) ) ).

% transpose.cases
thf(fact_149_shuffles_Oinduct,axiom,
    ! [P: list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o,A0: list_l1619404459ge_p_v,A1: list_l1619404459ge_p_v] :
      ( ! [X_1: list_l1619404459ge_p_v] : ( P @ nil_list_message_p_v @ X_1 )
     => ( ! [Xs2: list_l1619404459ge_p_v] : ( P @ Xs2 @ nil_list_message_p_v )
       => ( ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v,Y3: list_message_p_v,Ys2: list_l1619404459ge_p_v] :
              ( ( P @ Xs2 @ ( cons_l233104475ge_p_v @ Y3 @ Ys2 ) )
             => ( ( P @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) @ Ys2 )
               => ( P @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) @ ( cons_l233104475ge_p_v @ Y3 @ Ys2 ) ) ) )
         => ( P @ A0 @ A1 ) ) ) ) ).

% shuffles.induct
thf(fact_150_shuffles_Oinduct,axiom,
    ! [P: list_message_p_v > list_message_p_v > $o,A0: list_message_p_v,A1: list_message_p_v] :
      ( ! [X_1: list_message_p_v] : ( P @ nil_message_p_v @ X_1 )
     => ( ! [Xs2: list_message_p_v] : ( P @ Xs2 @ nil_message_p_v )
       => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v] :
              ( ( P @ Xs2 @ ( cons_message_p_v @ Y3 @ Ys2 ) )
             => ( ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ Ys2 )
               => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) ) )
         => ( P @ A0 @ A1 ) ) ) ) ).

% shuffles.induct
thf(fact_151_shuffles_Oinduct,axiom,
    ! [P: list_c1059388851t_unit > list_c1059388851t_unit > $o,A0: list_c1059388851t_unit,A1: list_c1059388851t_unit] :
      ( ! [X_1: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ X_1 )
     => ( ! [Xs2: list_c1059388851t_unit] : ( P @ Xs2 @ nil_co1338500125t_unit )
       => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
              ( ( P @ Xs2 @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) )
             => ( ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ Ys2 )
               => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) ) )
         => ( P @ A0 @ A1 ) ) ) ) ).

% shuffles.induct
thf(fact_152_induct__list012,axiom,
    ! [P: list_message_p_v > $o,Xs: list_message_p_v] :
      ( ( P @ nil_message_p_v )
     => ( ! [X2: message_p_v] : ( P @ ( cons_message_p_v @ X2 @ nil_message_p_v ) )
       => ( ! [X2: message_p_v,Y3: message_p_v,Zs: list_message_p_v] :
              ( ( P @ Zs )
             => ( ( P @ ( cons_message_p_v @ Y3 @ Zs ) )
               => ( P @ ( cons_message_p_v @ X2 @ ( cons_message_p_v @ Y3 @ Zs ) ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% induct_list012
thf(fact_153_induct__list012,axiom,
    ! [P: list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit] :
      ( ( P @ nil_co1338500125t_unit )
     => ( ! [X2: config256849571t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
       => ( ! [X2: config256849571t_unit,Y3: config256849571t_unit,Zs: list_c1059388851t_unit] :
              ( ( P @ Zs )
             => ( ( P @ ( cons_c1162654829t_unit @ Y3 @ Zs ) )
               => ( P @ ( cons_c1162654829t_unit @ X2 @ ( cons_c1162654829t_unit @ Y3 @ Zs ) ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% induct_list012
thf(fact_154_splice_Oinduct,axiom,
    ! [P: list_message_p_v > list_message_p_v > $o,A0: list_message_p_v,A1: list_message_p_v] :
      ( ! [X_1: list_message_p_v] : ( P @ nil_message_p_v @ X_1 )
     => ( ! [X2: message_p_v,Xs2: list_message_p_v,Ys2: list_message_p_v] :
            ( ( P @ Ys2 @ Xs2 )
           => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ Ys2 ) )
       => ( P @ A0 @ A1 ) ) ) ).

% splice.induct
thf(fact_155_splice_Oinduct,axiom,
    ! [P: list_c1059388851t_unit > list_c1059388851t_unit > $o,A0: list_c1059388851t_unit,A1: list_c1059388851t_unit] :
      ( ! [X_1: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ X_1 )
     => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Ys2: list_c1059388851t_unit] :
            ( ( P @ Ys2 @ Xs2 )
           => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ Ys2 ) )
       => ( P @ A0 @ A1 ) ) ) ).

% splice.induct
thf(fact_156_list__induct2_H,axiom,
    ! [P: list_message_p_v > list_message_p_v > $o,Xs: list_message_p_v,Ys: list_message_p_v] :
      ( ( P @ nil_message_p_v @ nil_message_p_v )
     => ( ! [X2: message_p_v,Xs2: list_message_p_v] : ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ nil_message_p_v )
       => ( ! [Y3: message_p_v,Ys2: list_message_p_v] : ( P @ nil_message_p_v @ ( cons_message_p_v @ Y3 @ Ys2 ) )
         => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v] :
                ( ( P @ Xs2 @ Ys2 )
               => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_157_list__induct2_H,axiom,
    ! [P: list_message_p_v > list_c1059388851t_unit > $o,Xs: list_message_p_v,Ys: list_c1059388851t_unit] :
      ( ( P @ nil_message_p_v @ nil_co1338500125t_unit )
     => ( ! [X2: message_p_v,Xs2: list_message_p_v] : ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ nil_co1338500125t_unit )
       => ( ! [Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] : ( P @ nil_message_p_v @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) )
         => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
                ( ( P @ Xs2 @ Ys2 )
               => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_158_list__induct2_H,axiom,
    ! [P: list_c1059388851t_unit > list_message_p_v > $o,Xs: list_c1059388851t_unit,Ys: list_message_p_v] :
      ( ( P @ nil_co1338500125t_unit @ nil_message_p_v )
     => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ nil_message_p_v )
       => ( ! [Y3: message_p_v,Ys2: list_message_p_v] : ( P @ nil_co1338500125t_unit @ ( cons_message_p_v @ Y3 @ Ys2 ) )
         => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys2: list_message_p_v] :
                ( ( P @ Xs2 @ Ys2 )
               => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_159_list__induct2_H,axiom,
    ! [P: list_c1059388851t_unit > list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
      ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
     => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ nil_co1338500125t_unit )
       => ( ! [Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) )
         => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
                ( ( P @ Xs2 @ Ys2 )
               => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_160_neq__Nil__conv,axiom,
    ! [Xs: list_message_p_v] :
      ( ( Xs != nil_message_p_v )
      = ( ? [Y4: message_p_v,Ys3: list_message_p_v] :
            ( Xs
            = ( cons_message_p_v @ Y4 @ Ys3 ) ) ) ) ).

% neq_Nil_conv
thf(fact_161_neq__Nil__conv,axiom,
    ! [Xs: list_c1059388851t_unit] :
      ( ( Xs != nil_co1338500125t_unit )
      = ( ? [Y4: config256849571t_unit,Ys3: list_c1059388851t_unit] :
            ( Xs
            = ( cons_c1162654829t_unit @ Y4 @ Ys3 ) ) ) ) ).

% neq_Nil_conv
thf(fact_162_list_Oinducts,axiom,
    ! [P: list_message_p_v > $o,List: list_message_p_v] :
      ( ( P @ nil_message_p_v )
     => ( ! [X12: message_p_v,X23: list_message_p_v] :
            ( ( P @ X23 )
           => ( P @ ( cons_message_p_v @ X12 @ X23 ) ) )
       => ( P @ List ) ) ) ).

% list.inducts
thf(fact_163_list_Oinducts,axiom,
    ! [P: list_c1059388851t_unit > $o,List: list_c1059388851t_unit] :
      ( ( P @ nil_co1338500125t_unit )
     => ( ! [X12: config256849571t_unit,X23: list_c1059388851t_unit] :
            ( ( P @ X23 )
           => ( P @ ( cons_c1162654829t_unit @ X12 @ X23 ) ) )
       => ( P @ List ) ) ) ).

% list.inducts
thf(fact_164_list_Oexhaust,axiom,
    ! [Y: list_message_p_v] :
      ( ( Y != nil_message_p_v )
     => ~ ! [X212: message_p_v,X223: list_message_p_v] :
            ( Y
           != ( cons_message_p_v @ X212 @ X223 ) ) ) ).

% list.exhaust
thf(fact_165_list_Oexhaust,axiom,
    ! [Y: list_c1059388851t_unit] :
      ( ( Y != nil_co1338500125t_unit )
     => ~ ! [X212: config256849571t_unit,X223: list_c1059388851t_unit] :
            ( Y
           != ( cons_c1162654829t_unit @ X212 @ X223 ) ) ) ).

% list.exhaust
thf(fact_166_list_OdiscI,axiom,
    ! [List: list_message_p_v,X21: message_p_v,X222: list_message_p_v] :
      ( ( List
        = ( cons_message_p_v @ X21 @ X222 ) )
     => ( List != nil_message_p_v ) ) ).

% list.discI
thf(fact_167_list_OdiscI,axiom,
    ! [List: list_c1059388851t_unit,X21: config256849571t_unit,X222: list_c1059388851t_unit] :
      ( ( List
        = ( cons_c1162654829t_unit @ X21 @ X222 ) )
     => ( List != nil_co1338500125t_unit ) ) ).

% list.discI
thf(fact_168_list_Odistinct_I1_J,axiom,
    ! [X21: message_p_v,X222: list_message_p_v] :
      ( nil_message_p_v
     != ( cons_message_p_v @ X21 @ X222 ) ) ).

% list.distinct(1)
thf(fact_169_list_Odistinct_I1_J,axiom,
    ! [X21: config256849571t_unit,X222: list_c1059388851t_unit] :
      ( nil_co1338500125t_unit
     != ( cons_c1162654829t_unit @ X21 @ X222 ) ) ).

% list.distinct(1)
thf(fact_170_length__induct,axiom,
    ! [P: list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit] :
      ( ! [Xs2: list_c1059388851t_unit] :
          ( ! [Ys4: list_c1059388851t_unit] :
              ( ( ord_less_nat @ ( size_s1406904903t_unit @ Ys4 ) @ ( size_s1406904903t_unit @ Xs2 ) )
             => ( P @ Ys4 ) )
         => ( P @ Xs2 ) )
     => ( P @ Xs ) ) ).

% length_induct
thf(fact_171_lift__Suc__mono__less__iff,axiom,
    ! [F2: nat > nat,N3: nat,M: nat] :
      ( ! [N: nat] : ( ord_less_nat @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
     => ( ( ord_less_nat @ ( F2 @ N3 ) @ ( F2 @ M ) )
        = ( ord_less_nat @ N3 @ M ) ) ) ).

% lift_Suc_mono_less_iff
thf(fact_172_lift__Suc__mono__less__iff,axiom,
    ! [F2: nat > int,N3: nat,M: nat] :
      ( ! [N: nat] : ( ord_less_int @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
     => ( ( ord_less_int @ ( F2 @ N3 ) @ ( F2 @ M ) )
        = ( ord_less_nat @ N3 @ M ) ) ) ).

% lift_Suc_mono_less_iff
thf(fact_173_lift__Suc__mono__less,axiom,
    ! [F2: nat > nat,N3: nat,N4: nat] :
      ( ! [N: nat] : ( ord_less_nat @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
     => ( ( ord_less_nat @ N3 @ N4 )
       => ( ord_less_nat @ ( F2 @ N3 ) @ ( F2 @ N4 ) ) ) ) ).

% lift_Suc_mono_less
thf(fact_174_lift__Suc__mono__less,axiom,
    ! [F2: nat > int,N3: nat,N4: nat] :
      ( ! [N: nat] : ( ord_less_int @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
     => ( ( ord_less_nat @ N3 @ N4 )
       => ( ord_less_int @ ( F2 @ N3 ) @ ( F2 @ N4 ) ) ) ) ).

% lift_Suc_mono_less
thf(fact_175_less__Suc__eq__0__disj,axiom,
    ! [M: nat,N3: nat] :
      ( ( ord_less_nat @ M @ ( suc @ N3 ) )
      = ( ( M = zero_zero_nat )
        | ? [J3: nat] :
            ( ( M
              = ( suc @ J3 ) )
            & ( ord_less_nat @ J3 @ N3 ) ) ) ) ).

% less_Suc_eq_0_disj
thf(fact_176_gr0__implies__Suc,axiom,
    ! [N3: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ N3 )
     => ? [M3: nat] :
          ( N3
          = ( suc @ M3 ) ) ) ).

% gr0_implies_Suc
thf(fact_177_All__less__Suc2,axiom,
    ! [N3: nat,P: nat > $o] :
      ( ( ! [I3: nat] :
            ( ( ord_less_nat @ I3 @ ( suc @ N3 ) )
           => ( P @ I3 ) ) )
      = ( ( P @ zero_zero_nat )
        & ! [I3: nat] :
            ( ( ord_less_nat @ I3 @ N3 )
           => ( P @ ( suc @ I3 ) ) ) ) ) ).

% All_less_Suc2
thf(fact_178_gr0__conv__Suc,axiom,
    ! [N3: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ N3 )
      = ( ? [M5: nat] :
            ( N3
            = ( suc @ M5 ) ) ) ) ).

% gr0_conv_Suc
thf(fact_179_Ex__less__Suc2,axiom,
    ! [N3: nat,P: nat > $o] :
      ( ( ? [I3: nat] :
            ( ( ord_less_nat @ I3 @ ( suc @ N3 ) )
            & ( P @ I3 ) ) )
      = ( ( P @ zero_zero_nat )
        | ? [I3: nat] :
            ( ( ord_less_nat @ I3 @ N3 )
            & ( P @ ( suc @ I3 ) ) ) ) ) ).

% Ex_less_Suc2
thf(fact_180_length__Suc__conv,axiom,
    ! [Xs: list_c1059388851t_unit,N3: nat] :
      ( ( ( size_s1406904903t_unit @ Xs )
        = ( suc @ N3 ) )
      = ( ? [Y4: config256849571t_unit,Ys3: list_c1059388851t_unit] :
            ( ( Xs
              = ( cons_c1162654829t_unit @ Y4 @ Ys3 ) )
            & ( ( size_s1406904903t_unit @ Ys3 )
              = N3 ) ) ) ) ).

% length_Suc_conv
thf(fact_181_Suc__length__conv,axiom,
    ! [N3: nat,Xs: list_c1059388851t_unit] :
      ( ( ( suc @ N3 )
        = ( size_s1406904903t_unit @ Xs ) )
      = ( ? [Y4: config256849571t_unit,Ys3: list_c1059388851t_unit] :
            ( ( Xs
              = ( cons_c1162654829t_unit @ Y4 @ Ys3 ) )
            & ( ( size_s1406904903t_unit @ Ys3 )
              = N3 ) ) ) ) ).

% Suc_length_conv
thf(fact_182_list_Osize_I3_J,axiom,
    ( ( size_s1168481041ge_p_v @ nil_message_p_v )
    = zero_zero_nat ) ).

% list.size(3)
thf(fact_183_list_Osize_I3_J,axiom,
    ( ( size_s1406904903t_unit @ nil_co1338500125t_unit )
    = zero_zero_nat ) ).

% list.size(3)
thf(fact_184_list__induct3,axiom,
    ! [Xs: list_message_p_v,Ys: list_message_p_v,Zs2: list_message_p_v,P: list_message_p_v > list_message_p_v > list_message_p_v > $o] :
      ( ( ( size_s1168481041ge_p_v @ Xs )
        = ( size_s1168481041ge_p_v @ Ys ) )
     => ( ( ( size_s1168481041ge_p_v @ Ys )
          = ( size_s1168481041ge_p_v @ Zs2 ) )
       => ( ( P @ nil_message_p_v @ nil_message_p_v @ nil_message_p_v )
         => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v,Z: message_p_v,Zs: list_message_p_v] :
                ( ( ( size_s1168481041ge_p_v @ Xs2 )
                  = ( size_s1168481041ge_p_v @ Ys2 ) )
               => ( ( ( size_s1168481041ge_p_v @ Ys2 )
                    = ( size_s1168481041ge_p_v @ Zs ) )
                 => ( ( P @ Xs2 @ Ys2 @ Zs )
                   => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
           => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).

% list_induct3
thf(fact_185_list__induct3,axiom,
    ! [Xs: list_message_p_v,Ys: list_message_p_v,Zs2: list_c1059388851t_unit,P: list_message_p_v > list_message_p_v > list_c1059388851t_unit > $o] :
      ( ( ( size_s1168481041ge_p_v @ Xs )
        = ( size_s1168481041ge_p_v @ Ys ) )
     => ( ( ( size_s1168481041ge_p_v @ Ys )
          = ( size_s1406904903t_unit @ Zs2 ) )
       => ( ( P @ nil_message_p_v @ nil_message_p_v @ nil_co1338500125t_unit )
         => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
                ( ( ( size_s1168481041ge_p_v @ Xs2 )
                  = ( size_s1168481041ge_p_v @ Ys2 ) )
               => ( ( ( size_s1168481041ge_p_v @ Ys2 )
                    = ( size_s1406904903t_unit @ Zs ) )
                 => ( ( P @ Xs2 @ Ys2 @ Zs )
                   => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
           => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).

% list_induct3
thf(fact_186_list__induct3,axiom,
    ! [Xs: list_message_p_v,Ys: list_c1059388851t_unit,Zs2: list_message_p_v,P: list_message_p_v > list_c1059388851t_unit > list_message_p_v > $o] :
      ( ( ( size_s1168481041ge_p_v @ Xs )
        = ( size_s1406904903t_unit @ Ys ) )
     => ( ( ( size_s1406904903t_unit @ Ys )
          = ( size_s1168481041ge_p_v @ Zs2 ) )
       => ( ( P @ nil_message_p_v @ nil_co1338500125t_unit @ nil_message_p_v )
         => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit,Z: message_p_v,Zs: list_message_p_v] :
                ( ( ( size_s1168481041ge_p_v @ Xs2 )
                  = ( size_s1406904903t_unit @ Ys2 ) )
               => ( ( ( size_s1406904903t_unit @ Ys2 )
                    = ( size_s1168481041ge_p_v @ Zs ) )
                 => ( ( P @ Xs2 @ Ys2 @ Zs )
                   => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
           => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).

% list_induct3
thf(fact_187_list__induct3,axiom,
    ! [Xs: list_message_p_v,Ys: list_c1059388851t_unit,Zs2: list_c1059388851t_unit,P: list_message_p_v > list_c1059388851t_unit > list_c1059388851t_unit > $o] :
      ( ( ( size_s1168481041ge_p_v @ Xs )
        = ( size_s1406904903t_unit @ Ys ) )
     => ( ( ( size_s1406904903t_unit @ Ys )
          = ( size_s1406904903t_unit @ Zs2 ) )
       => ( ( P @ nil_message_p_v @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
         => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
                ( ( ( size_s1168481041ge_p_v @ Xs2 )
                  = ( size_s1406904903t_unit @ Ys2 ) )
               => ( ( ( size_s1406904903t_unit @ Ys2 )
                    = ( size_s1406904903t_unit @ Zs ) )
                 => ( ( P @ Xs2 @ Ys2 @ Zs )
                   => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
           => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).

% list_induct3
thf(fact_188_list__induct3,axiom,
    ! [Xs: list_c1059388851t_unit,Ys: list_message_p_v,Zs2: list_message_p_v,P: list_c1059388851t_unit > list_message_p_v > list_message_p_v > $o] :
      ( ( ( size_s1406904903t_unit @ Xs )
        = ( size_s1168481041ge_p_v @ Ys ) )
     => ( ( ( size_s1168481041ge_p_v @ Ys )
          = ( size_s1168481041ge_p_v @ Zs2 ) )
       => ( ( P @ nil_co1338500125t_unit @ nil_message_p_v @ nil_message_p_v )
         => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys2: list_message_p_v,Z: message_p_v,Zs: list_message_p_v] :
                ( ( ( size_s1406904903t_unit @ Xs2 )
                  = ( size_s1168481041ge_p_v @ Ys2 ) )
               => ( ( ( size_s1168481041ge_p_v @ Ys2 )
                    = ( size_s1168481041ge_p_v @ Zs ) )
                 => ( ( P @ Xs2 @ Ys2 @ Zs )
                   => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
           => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).

% list_induct3
thf(fact_189_list__induct3,axiom,
    ! [Xs: list_c1059388851t_unit,Ys: list_message_p_v,Zs2: list_c1059388851t_unit,P: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit > $o] :
      ( ( ( size_s1406904903t_unit @ Xs )
        = ( size_s1168481041ge_p_v @ Ys ) )
     => ( ( ( size_s1168481041ge_p_v @ Ys )
          = ( size_s1406904903t_unit @ Zs2 ) )
       => ( ( P @ nil_co1338500125t_unit @ nil_message_p_v @ nil_co1338500125t_unit )
         => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys2: list_message_p_v,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
                ( ( ( size_s1406904903t_unit @ Xs2 )
                  = ( size_s1168481041ge_p_v @ Ys2 ) )
               => ( ( ( size_s1168481041ge_p_v @ Ys2 )
                    = ( size_s1406904903t_unit @ Zs ) )
                 => ( ( P @ Xs2 @ Ys2 @ Zs )
                   => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
           => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).

% list_induct3
thf(fact_190_list__induct3,axiom,
    ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit,Zs2: list_message_p_v,P: list_c1059388851t_unit > list_c1059388851t_unit > list_message_p_v > $o] :
      ( ( ( size_s1406904903t_unit @ Xs )
        = ( size_s1406904903t_unit @ Ys ) )
     => ( ( ( size_s1406904903t_unit @ Ys )
          = ( size_s1168481041ge_p_v @ Zs2 ) )
       => ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit @ nil_message_p_v )
         => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit,Z: message_p_v,Zs: list_message_p_v] :
                ( ( ( size_s1406904903t_unit @ Xs2 )
                  = ( size_s1406904903t_unit @ Ys2 ) )
               => ( ( ( size_s1406904903t_unit @ Ys2 )
                    = ( size_s1168481041ge_p_v @ Zs ) )
                 => ( ( P @ Xs2 @ Ys2 @ Zs )
                   => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
           => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).

% list_induct3
thf(fact_191_list__induct3,axiom,
    ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit,Zs2: list_c1059388851t_unit,P: list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit > $o] :
      ( ( ( size_s1406904903t_unit @ Xs )
        = ( size_s1406904903t_unit @ Ys ) )
     => ( ( ( size_s1406904903t_unit @ Ys )
          = ( size_s1406904903t_unit @ Zs2 ) )
       => ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
         => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
                ( ( ( size_s1406904903t_unit @ Xs2 )
                  = ( size_s1406904903t_unit @ Ys2 ) )
               => ( ( ( size_s1406904903t_unit @ Ys2 )
                    = ( size_s1406904903t_unit @ Zs ) )
                 => ( ( P @ Xs2 @ Ys2 @ Zs )
                   => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
           => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).

% list_induct3
thf(fact_192_list__induct2,axiom,
    ! [Xs: list_message_p_v,Ys: list_message_p_v,P: list_message_p_v > list_message_p_v > $o] :
      ( ( ( size_s1168481041ge_p_v @ Xs )
        = ( size_s1168481041ge_p_v @ Ys ) )
     => ( ( P @ nil_message_p_v @ nil_message_p_v )
       => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v] :
              ( ( ( size_s1168481041ge_p_v @ Xs2 )
                = ( size_s1168481041ge_p_v @ Ys2 ) )
             => ( ( P @ Xs2 @ Ys2 )
               => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) ) )
         => ( P @ Xs @ Ys ) ) ) ) ).

% list_induct2
thf(fact_193_list__induct2,axiom,
    ! [Xs: list_message_p_v,Ys: list_c1059388851t_unit,P: list_message_p_v > list_c1059388851t_unit > $o] :
      ( ( ( size_s1168481041ge_p_v @ Xs )
        = ( size_s1406904903t_unit @ Ys ) )
     => ( ( P @ nil_message_p_v @ nil_co1338500125t_unit )
       => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
              ( ( ( size_s1168481041ge_p_v @ Xs2 )
                = ( size_s1406904903t_unit @ Ys2 ) )
             => ( ( P @ Xs2 @ Ys2 )
               => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) ) )
         => ( P @ Xs @ Ys ) ) ) ) ).

% list_induct2
thf(fact_194_list__induct2,axiom,
    ! [Xs: list_c1059388851t_unit,Ys: list_message_p_v,P: list_c1059388851t_unit > list_message_p_v > $o] :
      ( ( ( size_s1406904903t_unit @ Xs )
        = ( size_s1168481041ge_p_v @ Ys ) )
     => ( ( P @ nil_co1338500125t_unit @ nil_message_p_v )
       => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys2: list_message_p_v] :
              ( ( ( size_s1406904903t_unit @ Xs2 )
                = ( size_s1168481041ge_p_v @ Ys2 ) )
             => ( ( P @ Xs2 @ Ys2 )
               => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) ) )
         => ( P @ Xs @ Ys ) ) ) ) ).

% list_induct2
thf(fact_195_list__induct2,axiom,
    ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit,P: list_c1059388851t_unit > list_c1059388851t_unit > $o] :
      ( ( ( size_s1406904903t_unit @ Xs )
        = ( size_s1406904903t_unit @ Ys ) )
     => ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
       => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
              ( ( ( size_s1406904903t_unit @ Xs2 )
                = ( size_s1406904903t_unit @ Ys2 ) )
             => ( ( P @ Xs2 @ Ys2 )
               => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) ) )
         => ( P @ Xs @ Ys ) ) ) ) ).

% list_induct2
thf(fact_196_infiniteExecutionCfg_Oelims,axiom,
    ! [X: config256849571t_unit,Xa: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,Xb: list_c1059388851t_unit > list_message_p_v > list_message_p_v,Xc: nat,Y: list_c1059388851t_unit] :
      ( ( ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ Xc )
        = Y )
     => ( ( ( Xc = zero_zero_nat )
         => ( Y
           != ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) ) )
       => ~ ! [N: nat] :
              ( ( Xc
                = ( suc @ N ) )
             => ( Y
               != ( Xa @ ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ).

% infiniteExecutionCfg.elims
thf(fact_197_infiniteExecutionMsg_Oelims,axiom,
    ! [X: config256849571t_unit,Xa: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,Xb: list_c1059388851t_unit > list_message_p_v > list_message_p_v,Xc: nat,Y: list_message_p_v] :
      ( ( ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ Xc )
        = Y )
     => ( ( ( Xc = zero_zero_nat )
         => ( Y != nil_message_p_v ) )
       => ~ ! [N: nat] :
              ( ( Xc
                = ( suc @ N ) )
             => ( Y
               != ( Xb @ ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ).

% infiniteExecutionMsg.elims
thf(fact_198_infiniteExecutionMsg_Osimps_I2_J,axiom,
    ! [Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N3: nat] :
      ( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
      = ( FStepMsg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ).

% infiniteExecutionMsg.simps(2)
thf(fact_199_infiniteExecutionCfg_Osimps_I2_J,axiom,
    ! [Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N3: nat] :
      ( ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
      = ( FStepCfg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ).

% infiniteExecutionCfg.simps(2)
thf(fact_200_infiniteExecutionMsg_Osimps_I1_J,axiom,
    ! [Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
      ( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
      = nil_message_p_v ) ).

% infiniteExecutionMsg.simps(1)
thf(fact_201_not__gr__zero,axiom,
    ! [N3: nat] :
      ( ( ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
      = ( N3 = zero_zero_nat ) ) ).

% not_gr_zero
thf(fact_202_length__Cons,axiom,
    ! [X: config256849571t_unit,Xs: list_c1059388851t_unit] :
      ( ( size_s1406904903t_unit @ ( cons_c1162654829t_unit @ X @ Xs ) )
      = ( suc @ ( size_s1406904903t_unit @ Xs ) ) ) ).

% length_Cons
thf(fact_203_zero__reorient,axiom,
    ! [X: nat] :
      ( ( zero_zero_nat = X )
      = ( X = zero_zero_nat ) ) ).

% zero_reorient
thf(fact_204_zero__reorient,axiom,
    ! [X: int] :
      ( ( zero_zero_int = X )
      = ( X = zero_zero_int ) ) ).

% zero_reorient
thf(fact_205_gr__zeroI,axiom,
    ! [N3: nat] :
      ( ( N3 != zero_zero_nat )
     => ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).

% gr_zeroI
thf(fact_206_not__less__zero,axiom,
    ! [N3: nat] :
      ~ ( ord_less_nat @ N3 @ zero_zero_nat ) ).

% not_less_zero
thf(fact_207_gr__implies__not__zero,axiom,
    ! [M: nat,N3: nat] :
      ( ( ord_less_nat @ M @ N3 )
     => ( N3 != zero_zero_nat ) ) ).

% gr_implies_not_zero
thf(fact_208_zero__less__iff__neq__zero,axiom,
    ! [N3: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ N3 )
      = ( N3 != zero_zero_nat ) ) ).

% zero_less_iff_neq_zero
thf(fact_209_n__lists__Nil,axiom,
    ! [N3: nat] :
      ( ( ( N3 = zero_zero_nat )
       => ( ( n_list1987762709t_unit @ N3 @ nil_co1338500125t_unit )
          = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) )
      & ( ( N3 != zero_zero_nat )
       => ( ( n_list1987762709t_unit @ N3 @ nil_co1338500125t_unit )
          = nil_li307996205t_unit ) ) ) ).

% n_lists_Nil
thf(fact_210_n__lists__Nil,axiom,
    ! [N3: nat] :
      ( ( ( N3 = zero_zero_nat )
       => ( ( n_lists_message_p_v @ N3 @ nil_message_p_v )
          = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) )
      & ( ( N3 != zero_zero_nat )
       => ( ( n_lists_message_p_v @ N3 @ nil_message_p_v )
          = nil_list_message_p_v ) ) ) ).

% n_lists_Nil
thf(fact_211_flpPseudoConsensus_OinfiniteExecutionCfg_Oelims,axiom,
    ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,X: config256849571t_unit,Xa: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,Xb: list_c1059388851t_unit > list_message_p_v > list_message_p_v,Xc: nat,Y: list_c1059388851t_unit] :
      ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
     => ( ( ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ Xc )
          = Y )
       => ( ( ( Xc = zero_zero_nat )
           => ( Y
             != ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) ) )
         => ~ ! [N: nat] :
                ( ( Xc
                  = ( suc @ N ) )
               => ( Y
                 != ( Xa @ ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ) ).

% flpPseudoConsensus.infiniteExecutionCfg.elims
thf(fact_212_n__lists_Osimps_I1_J,axiom,
    ! [Xs: list_c1059388851t_unit] :
      ( ( n_list1987762709t_unit @ zero_zero_nat @ Xs )
      = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) ).

% n_lists.simps(1)
thf(fact_213_n__lists_Osimps_I1_J,axiom,
    ! [Xs: list_message_p_v] :
      ( ( n_lists_message_p_v @ zero_zero_nat @ Xs )
      = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) ).

% n_lists.simps(1)
thf(fact_214_flpPseudoConsensus_OinfiniteExecutionMsg_Oelims,axiom,
    ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,X: config256849571t_unit,Xa: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,Xb: list_c1059388851t_unit > list_message_p_v > list_message_p_v,Xc: nat,Y: list_message_p_v] :
      ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
     => ( ( ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ Xc )
          = Y )
       => ( ( ( Xc = zero_zero_nat )
           => ( Y != nil_message_p_v ) )
         => ~ ! [N: nat] :
                ( ( Xc
                  = ( suc @ N ) )
               => ( Y
                 != ( Xb @ ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ) ).

% flpPseudoConsensus.infiniteExecutionMsg.elims
thf(fact_215_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I2_J,axiom,
    ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N3: nat] :
      ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
     => ( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
        = ( FStepMsg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ) ).

% flpPseudoConsensus.infiniteExecutionMsg.simps(2)
thf(fact_216_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I2_J,axiom,
    ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N3: nat] :
      ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
     => ( ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
        = ( FStepCfg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ) ).

% flpPseudoConsensus.infiniteExecutionCfg.simps(2)
thf(fact_217_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I1_J,axiom,
    ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
      ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
     => ( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
        = nil_message_p_v ) ) ).

% flpPseudoConsensus.infiniteExecutionMsg.simps(1)
thf(fact_218_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I1_J,axiom,
    ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
      ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
     => ( ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
        = ( cons_c1162654829t_unit @ Cfg2 @ nil_co1338500125t_unit ) ) ) ).

% flpPseudoConsensus.infiniteExecutionCfg.simps(1)
thf(fact_219_less__numeral__extra_I3_J,axiom,
    ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).

% less_numeral_extra(3)
thf(fact_220_less__numeral__extra_I3_J,axiom,
    ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).

% less_numeral_extra(3)
thf(fact_221_product__lists_Osimps_I1_J,axiom,
    ( ( produc663212148t_unit @ nil_li307996205t_unit )
    = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) ).

% product_lists.simps(1)
thf(fact_222_product__lists_Osimps_I1_J,axiom,
    ( ( produc1505827982ge_p_v @ nil_list_message_p_v )
    = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) ).

% product_lists.simps(1)
thf(fact_223_subseqs_Osimps_I1_J,axiom,
    ( ( subseq1144048270t_unit @ nil_co1338500125t_unit )
    = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) ).

% subseqs.simps(1)
thf(fact_224_subseqs_Osimps_I1_J,axiom,
    ( ( subseqs_message_p_v @ nil_message_p_v )
    = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) ).

% subseqs.simps(1)
thf(fact_225_length__code,axiom,
    ( size_s1406904903t_unit
    = ( gen_le193291088t_unit @ zero_zero_nat ) ) ).

% length_code
thf(fact_226_gen__length__code_I2_J,axiom,
    ! [N3: nat,X: config256849571t_unit,Xs: list_c1059388851t_unit] :
      ( ( gen_le193291088t_unit @ N3 @ ( cons_c1162654829t_unit @ X @ Xs ) )
      = ( gen_le193291088t_unit @ ( suc @ N3 ) @ Xs ) ) ).

% gen_length_code(2)
thf(fact_227_gen__length__code_I1_J,axiom,
    ! [N3: nat] :
      ( ( gen_le193291088t_unit @ N3 @ nil_co1338500125t_unit )
      = N3 ) ).

% gen_length_code(1)
thf(fact_228_gen__length__code_I1_J,axiom,
    ! [N3: nat] :
      ( ( gen_le697204914ge_p_v @ N3 @ nil_message_p_v )
      = N3 ) ).

% gen_length_code(1)
thf(fact_229_insert__Nil,axiom,
    ! [X: message_p_v] :
      ( ( insert_message_p_v @ X @ nil_message_p_v )
      = ( cons_message_p_v @ X @ nil_message_p_v ) ) ).

% insert_Nil
thf(fact_230_insert__Nil,axiom,
    ! [X: config256849571t_unit] :
      ( ( insert1308755079t_unit @ X @ nil_co1338500125t_unit )
      = ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) ) ).

% insert_Nil
thf(fact_231_nths__singleton,axiom,
    ! [A8: set_nat,X: message_p_v] :
      ( ( ( member_nat @ zero_zero_nat @ A8 )
       => ( ( nths_message_p_v @ ( cons_message_p_v @ X @ nil_message_p_v ) @ A8 )
          = ( cons_message_p_v @ X @ nil_message_p_v ) ) )
      & ( ~ ( member_nat @ zero_zero_nat @ A8 )
       => ( ( nths_message_p_v @ ( cons_message_p_v @ X @ nil_message_p_v ) @ A8 )
          = nil_message_p_v ) ) ) ).

% nths_singleton
thf(fact_232_nths__singleton,axiom,
    ! [A8: set_nat,X: config256849571t_unit] :
      ( ( ( member_nat @ zero_zero_nat @ A8 )
       => ( ( nths_c890550943t_unit @ ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) @ A8 )
          = ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) ) )
      & ( ~ ( member_nat @ zero_zero_nat @ A8 )
       => ( ( nths_c890550943t_unit @ ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) @ A8 )
          = nil_co1338500125t_unit ) ) ) ).

% nths_singleton
thf(fact_233_of__nat__0__less__iff,axiom,
    ! [N3: nat] :
      ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N3 ) )
      = ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).

% of_nat_0_less_iff
thf(fact_234_of__nat__0__less__iff,axiom,
    ! [N3: nat] :
      ( ( ord_less_int @ zero_zero_int @ ( semiri2019852685at_int @ N3 ) )
      = ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).

% of_nat_0_less_iff
thf(fact_235_of__nat__eq__iff,axiom,
    ! [M: nat,N3: nat] :
      ( ( ( semiri2019852685at_int @ M )
        = ( semiri2019852685at_int @ N3 ) )
      = ( M = N3 ) ) ).

% of_nat_eq_iff
thf(fact_236_nths__nil,axiom,
    ! [A8: set_nat] :
      ( ( nths_c890550943t_unit @ nil_co1338500125t_unit @ A8 )
      = nil_co1338500125t_unit ) ).

% nths_nil
thf(fact_237_nths__nil,axiom,
    ! [A8: set_nat] :
      ( ( nths_message_p_v @ nil_message_p_v @ A8 )
      = nil_message_p_v ) ).

% nths_nil
thf(fact_238_of__nat__0,axiom,
    ( ( semiri1382578993at_nat @ zero_zero_nat )
    = zero_zero_nat ) ).

% of_nat_0
thf(fact_239_of__nat__0,axiom,
    ( ( semiri2019852685at_int @ zero_zero_nat )
    = zero_zero_int ) ).

% of_nat_0
thf(fact_240_of__nat__0__eq__iff,axiom,
    ! [N3: nat] :
      ( ( zero_zero_nat
        = ( semiri1382578993at_nat @ N3 ) )
      = ( zero_zero_nat = N3 ) ) ).

% of_nat_0_eq_iff
thf(fact_241_of__nat__0__eq__iff,axiom,
    ! [N3: nat] :
      ( ( zero_zero_int
        = ( semiri2019852685at_int @ N3 ) )
      = ( zero_zero_nat = N3 ) ) ).

% of_nat_0_eq_iff
thf(fact_242_of__nat__eq__0__iff,axiom,
    ! [M: nat] :
      ( ( ( semiri1382578993at_nat @ M )
        = zero_zero_nat )
      = ( M = zero_zero_nat ) ) ).

% of_nat_eq_0_iff
thf(fact_243_of__nat__eq__0__iff,axiom,
    ! [M: nat] :
      ( ( ( semiri2019852685at_int @ M )
        = zero_zero_int )
      = ( M = zero_zero_nat ) ) ).

% of_nat_eq_0_iff
thf(fact_244_of__nat__less__iff,axiom,
    ! [M: nat,N3: nat] :
      ( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N3 ) )
      = ( ord_less_nat @ M @ N3 ) ) ).

% of_nat_less_iff
thf(fact_245_of__nat__less__iff,axiom,
    ! [M: nat,N3: nat] :
      ( ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N3 ) )
      = ( ord_less_nat @ M @ N3 ) ) ).

% of_nat_less_iff
thf(fact_246_of__nat__less__0__iff,axiom,
    ! [M: nat] :
      ~ ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat ) ).

% of_nat_less_0_iff
thf(fact_247_of__nat__less__0__iff,axiom,
    ! [M: nat] :
      ~ ( ord_less_int @ ( semiri2019852685at_int @ M ) @ zero_zero_int ) ).

% of_nat_less_0_iff
thf(fact_248_of__nat__neq__0,axiom,
    ! [N3: nat] :
      ( ( semiri1382578993at_nat @ ( suc @ N3 ) )
     != zero_zero_nat ) ).

% of_nat_neq_0
thf(fact_249_of__nat__neq__0,axiom,
    ! [N3: nat] :
      ( ( semiri2019852685at_int @ ( suc @ N3 ) )
     != zero_zero_int ) ).

% of_nat_neq_0
thf(fact_250_less__imp__of__nat__less,axiom,
    ! [M: nat,N3: nat] :
      ( ( ord_less_nat @ M @ N3 )
     => ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N3 ) ) ) ).

% less_imp_of_nat_less
thf(fact_251_less__imp__of__nat__less,axiom,
    ! [M: nat,N3: nat] :
      ( ( ord_less_nat @ M @ N3 )
     => ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N3 ) ) ) ).

% less_imp_of_nat_less
thf(fact_252_of__nat__less__imp__less,axiom,
    ! [M: nat,N3: nat] :
      ( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N3 ) )
     => ( ord_less_nat @ M @ N3 ) ) ).

% of_nat_less_imp_less
thf(fact_253_of__nat__less__imp__less,axiom,
    ! [M: nat,N3: nat] :
      ( ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N3 ) )
     => ( ord_less_nat @ M @ N3 ) ) ).

% of_nat_less_imp_less
thf(fact_254_nths__all,axiom,
    ! [Xs: list_c1059388851t_unit,I4: set_nat] :
      ( ! [I2: nat] :
          ( ( ord_less_nat @ I2 @ ( size_s1406904903t_unit @ Xs ) )
         => ( member_nat @ I2 @ I4 ) )
     => ( ( nths_c890550943t_unit @ Xs @ I4 )
        = Xs ) ) ).

% nths_all
thf(fact_255_pos__int__cases,axiom,
    ! [K: int] :
      ( ( ord_less_int @ zero_zero_int @ K )
     => ~ ! [N: nat] :
            ( ( K
              = ( semiri2019852685at_int @ N ) )
           => ~ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).

% pos_int_cases
thf(fact_256_zero__less__imp__eq__int,axiom,
    ! [K: int] :
      ( ( ord_less_int @ zero_zero_int @ K )
     => ? [N: nat] :
          ( ( ord_less_nat @ zero_zero_nat @ N )
          & ( K
            = ( semiri2019852685at_int @ N ) ) ) ) ).

% zero_less_imp_eq_int
thf(fact_257_list__ex1__simps_I1_J,axiom,
    ! [P: config256849571t_unit > $o] :
      ~ ( list_e1598815642t_unit @ P @ nil_co1338500125t_unit ) ).

% list_ex1_simps(1)
thf(fact_258_list__ex1__simps_I1_J,axiom,
    ! [P: message_p_v > $o] :
      ~ ( list_ex1_message_p_v @ P @ nil_message_p_v ) ).

% list_ex1_simps(1)
thf(fact_259_nat__int__comparison_I2_J,axiom,
    ( ord_less_nat
    = ( ^ [A10: nat,B: nat] : ( ord_less_int @ ( semiri2019852685at_int @ A10 ) @ ( semiri2019852685at_int @ B ) ) ) ) ).

% nat_int_comparison(2)
thf(fact_260_int__ops_I1_J,axiom,
    ( ( semiri2019852685at_int @ zero_zero_nat )
    = zero_zero_int ) ).

% int_ops(1)
thf(fact_261_neg__int__cases,axiom,
    ! [K: int] :
      ( ( ord_less_int @ K @ zero_zero_int )
     => ~ ! [N: nat] :
            ( ( K
              = ( uminus_uminus_int @ ( semiri2019852685at_int @ N ) ) )
           => ~ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).

% neg_int_cases
thf(fact_262_neg__equal__iff__equal,axiom,
    ! [A: int,B2: int] :
      ( ( ( uminus_uminus_int @ A )
        = ( uminus_uminus_int @ B2 ) )
      = ( A = B2 ) ) ).

% neg_equal_iff_equal
thf(fact_263_add_Oinverse__inverse,axiom,
    ! [A: int] :
      ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
      = A ) ).

% add.inverse_inverse
thf(fact_264_add_Oinverse__neutral,axiom,
    ( ( uminus_uminus_int @ zero_zero_int )
    = zero_zero_int ) ).

% add.inverse_neutral
thf(fact_265_neg__0__equal__iff__equal,axiom,
    ! [A: int] :
      ( ( zero_zero_int
        = ( uminus_uminus_int @ A ) )
      = ( zero_zero_int = A ) ) ).

% neg_0_equal_iff_equal
thf(fact_266_neg__equal__0__iff__equal,axiom,
    ! [A: int] :
      ( ( ( uminus_uminus_int @ A )
        = zero_zero_int )
      = ( A = zero_zero_int ) ) ).

% neg_equal_0_iff_equal
thf(fact_267_equal__neg__zero,axiom,
    ! [A: int] :
      ( ( A
        = ( uminus_uminus_int @ A ) )
      = ( A = zero_zero_int ) ) ).

% equal_neg_zero
thf(fact_268_neg__equal__zero,axiom,
    ! [A: int] :
      ( ( ( uminus_uminus_int @ A )
        = A )
      = ( A = zero_zero_int ) ) ).

% neg_equal_zero
thf(fact_269_neg__less__iff__less,axiom,
    ! [B2: int,A: int] :
      ( ( ord_less_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) )
      = ( ord_less_int @ A @ B2 ) ) ).

% neg_less_iff_less
thf(fact_270_less__neg__neg,axiom,
    ! [A: int] :
      ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
      = ( ord_less_int @ A @ zero_zero_int ) ) ).

% less_neg_neg
thf(fact_271_neg__less__pos,axiom,
    ! [A: int] :
      ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
      = ( ord_less_int @ zero_zero_int @ A ) ) ).

% neg_less_pos
thf(fact_272_neg__0__less__iff__less,axiom,
    ! [A: int] :
      ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
      = ( ord_less_int @ A @ zero_zero_int ) ) ).

% neg_0_less_iff_less
thf(fact_273_neg__less__0__iff__less,axiom,
    ! [A: int] :
      ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
      = ( ord_less_int @ zero_zero_int @ A ) ) ).

% neg_less_0_iff_less
thf(fact_274_negative__eq__positive,axiom,
    ! [N3: nat,M: nat] :
      ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ N3 ) )
        = ( semiri2019852685at_int @ M ) )
      = ( ( N3 = zero_zero_nat )
        & ( M = zero_zero_nat ) ) ) ).

% negative_eq_positive
thf(fact_275_negative__zless,axiom,
    ! [N3: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N3 ) ) ) @ ( semiri2019852685at_int @ M ) ) ).

% negative_zless
thf(fact_276_minus__less__iff,axiom,
    ! [A: int,B2: int] :
      ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B2 )
      = ( ord_less_int @ ( uminus_uminus_int @ B2 ) @ A ) ) ).

% minus_less_iff
thf(fact_277_less__minus__iff,axiom,
    ! [A: int,B2: int] :
      ( ( ord_less_int @ A @ ( uminus_uminus_int @ B2 ) )
      = ( ord_less_int @ B2 @ ( uminus_uminus_int @ A ) ) ) ).

% less_minus_iff
thf(fact_278_verit__negate__coefficient_I2_J,axiom,
    ! [A: int,B2: int] :
      ( ( ord_less_int @ A @ B2 )
     => ( ord_less_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) ) ) ).

% verit_negate_coefficient(2)
thf(fact_279_minus__equation__iff,axiom,
    ! [A: int,B2: int] :
      ( ( ( uminus_uminus_int @ A )
        = B2 )
      = ( ( uminus_uminus_int @ B2 )
        = A ) ) ).

% minus_equation_iff
thf(fact_280_equation__minus__iff,axiom,
    ! [A: int,B2: int] :
      ( ( A
        = ( uminus_uminus_int @ B2 ) )
      = ( B2
        = ( uminus_uminus_int @ A ) ) ) ).

% equation_minus_iff
thf(fact_281_int__cases,axiom,
    ! [Z2: int] :
      ( ! [N: nat] :
          ( Z2
         != ( semiri2019852685at_int @ N ) )
     => ~ ! [N: nat] :
            ( Z2
           != ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N ) ) ) ) ) ).

% int_cases
thf(fact_282_int__of__nat__induct,axiom,
    ! [P: int > $o,Z2: int] :
      ( ! [N: nat] : ( P @ ( semiri2019852685at_int @ N ) )
     => ( ! [N: nat] : ( P @ ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N ) ) ) )
       => ( P @ Z2 ) ) ) ).

% int_of_nat_induct
thf(fact_283_int__cases4,axiom,
    ! [M: int] :
      ( ! [N: nat] :
          ( M
         != ( semiri2019852685at_int @ N ) )
     => ~ ! [N: nat] :
            ( ( ord_less_nat @ zero_zero_nat @ N )
           => ( M
             != ( uminus_uminus_int @ ( semiri2019852685at_int @ N ) ) ) ) ) ).

% int_cases4
thf(fact_284_verit__comp__simplify1_I1_J,axiom,
    ! [A: nat] :
      ~ ( ord_less_nat @ A @ A ) ).

% verit_comp_simplify1(1)
thf(fact_285_verit__comp__simplify1_I1_J,axiom,
    ! [A: int] :
      ~ ( ord_less_int @ A @ A ) ).

% verit_comp_simplify1(1)
thf(fact_286_int__cases3,axiom,
    ! [K: int] :
      ( ( K != zero_zero_int )
     => ( ! [N: nat] :
            ( ( K
              = ( semiri2019852685at_int @ N ) )
           => ~ ( ord_less_nat @ zero_zero_nat @ N ) )
       => ~ ! [N: nat] :
              ( ( K
                = ( uminus_uminus_int @ ( semiri2019852685at_int @ N ) ) )
             => ~ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).

% int_cases3
thf(fact_287_negative__zless__0,axiom,
    ! [N3: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N3 ) ) ) @ zero_zero_int ) ).

% negative_zless_0
thf(fact_288_negD,axiom,
    ! [X: int] :
      ( ( ord_less_int @ X @ zero_zero_int )
     => ? [N: nat] :
          ( X
          = ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N ) ) ) ) ) ).

% negD
thf(fact_289_zero__less__nat__eq,axiom,
    ! [Z2: int] :
      ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z2 ) )
      = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).

% zero_less_nat_eq
thf(fact_290_of__int__0__less__iff,axiom,
    ! [Z2: int] :
      ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) )
      = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).

% of_int_0_less_iff
thf(fact_291_of__int__0,axiom,
    ( ( ring_1_of_int_int @ zero_zero_int )
    = zero_zero_int ) ).

% of_int_0
thf(fact_292_of__int__0__eq__iff,axiom,
    ! [Z2: int] :
      ( ( zero_zero_int
        = ( ring_1_of_int_int @ Z2 ) )
      = ( Z2 = zero_zero_int ) ) ).

% of_int_0_eq_iff
thf(fact_293_of__int__eq__0__iff,axiom,
    ! [Z2: int] :
      ( ( ( ring_1_of_int_int @ Z2 )
        = zero_zero_int )
      = ( Z2 = zero_zero_int ) ) ).

% of_int_eq_0_iff
thf(fact_294_of__int__less__iff,axiom,
    ! [W: int,Z2: int] :
      ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z2 ) )
      = ( ord_less_int @ W @ Z2 ) ) ).

% of_int_less_iff
thf(fact_295_zless__nat__conj,axiom,
    ! [W: int,Z2: int] :
      ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z2 ) )
      = ( ( ord_less_int @ zero_zero_int @ Z2 )
        & ( ord_less_int @ W @ Z2 ) ) ) ).

% zless_nat_conj
thf(fact_296_nat__zminus__int,axiom,
    ! [N3: nat] :
      ( ( nat2 @ ( uminus_uminus_int @ ( semiri2019852685at_int @ N3 ) ) )
      = zero_zero_nat ) ).

% nat_zminus_int
thf(fact_297_of__int__less__0__iff,axiom,
    ! [Z2: int] :
      ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ zero_zero_int )
      = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).

% of_int_less_0_iff
thf(fact_298_nat__zero__as__int,axiom,
    ( zero_zero_nat
    = ( nat2 @ zero_zero_int ) ) ).

% nat_zero_as_int
thf(fact_299_nat__mono__iff,axiom,
    ! [Z2: int,W: int] :
      ( ( ord_less_int @ zero_zero_int @ Z2 )
     => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z2 ) )
        = ( ord_less_int @ W @ Z2 ) ) ) ).

% nat_mono_iff
thf(fact_300_zless__nat__eq__int__zless,axiom,
    ! [M: nat,Z2: int] :
      ( ( ord_less_nat @ M @ ( nat2 @ Z2 ) )
      = ( ord_less_int @ ( semiri2019852685at_int @ M ) @ Z2 ) ) ).

% zless_nat_eq_int_zless
thf(fact_301_of__int__pos,axiom,
    ! [Z2: int] :
      ( ( ord_less_int @ zero_zero_int @ Z2 )
     => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).

% of_int_pos
thf(fact_302_of__nat__less__of__int__iff,axiom,
    ! [N3: nat,X: int] :
      ( ( ord_less_int @ ( semiri2019852685at_int @ N3 ) @ ( ring_1_of_int_int @ X ) )
      = ( ord_less_int @ ( semiri2019852685at_int @ N3 ) @ X ) ) ).

% of_nat_less_of_int_iff
thf(fact_303_split__nat,axiom,
    ! [P: nat > $o,I: int] :
      ( ( P @ ( nat2 @ I ) )
      = ( ! [N5: nat] :
            ( ( I
              = ( semiri2019852685at_int @ N5 ) )
           => ( P @ N5 ) )
        & ( ( ord_less_int @ I @ zero_zero_int )
         => ( P @ zero_zero_nat ) ) ) ) ).

% split_nat
thf(fact_304_one__less__nat__eq,axiom,
    ! [Z2: int] :
      ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z2 ) )
      = ( ord_less_int @ one_one_int @ Z2 ) ) ).

% one_less_nat_eq
thf(fact_305_nat__less__iff,axiom,
    ! [W: int,M: nat] :
      ( ( ord_less_eq_int @ zero_zero_int @ W )
     => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
        = ( ord_less_int @ W @ ( semiri2019852685at_int @ M ) ) ) ) ).

% nat_less_iff
thf(fact_306_le__zero__eq,axiom,
    ! [N3: nat] :
      ( ( ord_less_eq_nat @ N3 @ zero_zero_nat )
      = ( N3 = zero_zero_nat ) ) ).

% le_zero_eq
thf(fact_307_neg__le__iff__le,axiom,
    ! [B2: int,A: int] :
      ( ( ord_less_eq_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) )
      = ( ord_less_eq_int @ A @ B2 ) ) ).

% neg_le_iff_le
thf(fact_308_of__nat__le__iff,axiom,
    ! [M: nat,N3: nat] :
      ( ( ord_less_eq_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N3 ) )
      = ( ord_less_eq_nat @ M @ N3 ) ) ).

% of_nat_le_iff
thf(fact_309_of__nat__1,axiom,
    ( ( semiri2019852685at_int @ one_one_nat )
    = one_one_int ) ).

% of_nat_1
thf(fact_310_of__nat__1__eq__iff,axiom,
    ! [N3: nat] :
      ( ( one_one_int
        = ( semiri2019852685at_int @ N3 ) )
      = ( N3 = one_one_nat ) ) ).

% of_nat_1_eq_iff
thf(fact_311_of__nat__eq__1__iff,axiom,
    ! [N3: nat] :
      ( ( ( semiri2019852685at_int @ N3 )
        = one_one_int )
      = ( N3 = one_one_nat ) ) ).

% of_nat_eq_1_iff
thf(fact_312_neg__0__le__iff__le,axiom,
    ! [A: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
      = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).

% neg_0_le_iff_le
thf(fact_313_neg__le__0__iff__le,axiom,
    ! [A: int] :
      ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
      = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).

% neg_le_0_iff_le
thf(fact_314_less__eq__neg__nonpos,axiom,
    ! [A: int] :
      ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
      = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).

% less_eq_neg_nonpos
thf(fact_315_neg__less__eq__nonneg,axiom,
    ! [A: int] :
      ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
      = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).

% neg_less_eq_nonneg
thf(fact_316_of__nat__le__0__iff,axiom,
    ! [M: nat] :
      ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat )
      = ( M = zero_zero_nat ) ) ).

% of_nat_le_0_iff
thf(fact_317_of__nat__le__0__iff,axiom,
    ! [M: nat] :
      ( ( ord_less_eq_int @ ( semiri2019852685at_int @ M ) @ zero_zero_int )
      = ( M = zero_zero_nat ) ) ).

% of_nat_le_0_iff
thf(fact_318_nat__1,axiom,
    ( ( nat2 @ one_one_int )
    = ( suc @ zero_zero_nat ) ) ).

% nat_1
thf(fact_319_nat__le__0,axiom,
    ! [Z2: int] :
      ( ( ord_less_eq_int @ Z2 @ zero_zero_int )
     => ( ( nat2 @ Z2 )
        = zero_zero_nat ) ) ).

% nat_le_0
thf(fact_320_nat__0__iff,axiom,
    ! [I: int] :
      ( ( ( nat2 @ I )
        = zero_zero_nat )
      = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).

% nat_0_iff
thf(fact_321_of__int__le__0__iff,axiom,
    ! [Z2: int] :
      ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z2 ) @ zero_zero_int )
      = ( ord_less_eq_int @ Z2 @ zero_zero_int ) ) ).

% of_int_le_0_iff
thf(fact_322_of__int__0__le__iff,axiom,
    ! [Z2: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) )
      = ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ).

% of_int_0_le_iff
thf(fact_323_of__int__less__1__iff,axiom,
    ! [Z2: int] :
      ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ one_one_int )
      = ( ord_less_int @ Z2 @ one_one_int ) ) ).

% of_int_less_1_iff
thf(fact_324_of__int__1__less__iff,axiom,
    ! [Z2: int] :
      ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z2 ) )
      = ( ord_less_int @ one_one_int @ Z2 ) ) ).

% of_int_1_less_iff
thf(fact_325_of__int__nonneg,axiom,
    ! [Z2: int] :
      ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
     => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).

% of_int_nonneg
thf(fact_326_verit__comp__simplify1_I3_J,axiom,
    ! [B3: nat,A11: nat] :
      ( ( ~ ( ord_less_eq_nat @ B3 @ A11 ) )
      = ( ord_less_nat @ A11 @ B3 ) ) ).

% verit_comp_simplify1(3)
thf(fact_327_verit__comp__simplify1_I3_J,axiom,
    ! [B3: int,A11: int] :
      ( ( ~ ( ord_less_eq_int @ B3 @ A11 ) )
      = ( ord_less_int @ A11 @ B3 ) ) ).

% verit_comp_simplify1(3)
thf(fact_328_le__numeral__extra_I4_J,axiom,
    ord_less_eq_int @ one_one_int @ one_one_int ).

% le_numeral_extra(4)
thf(fact_329_one__reorient,axiom,
    ! [X: int] :
      ( ( one_one_int = X )
      = ( X = one_one_int ) ) ).

% one_reorient
thf(fact_330_lift__Suc__antimono__le,axiom,
    ! [F2: nat > int,N3: nat,N4: nat] :
      ( ! [N: nat] : ( ord_less_eq_int @ ( F2 @ ( suc @ N ) ) @ ( F2 @ N ) )
     => ( ( ord_less_eq_nat @ N3 @ N4 )
       => ( ord_less_eq_int @ ( F2 @ N4 ) @ ( F2 @ N3 ) ) ) ) ).

% lift_Suc_antimono_le
thf(fact_331_lift__Suc__mono__le,axiom,
    ! [F2: nat > int,N3: nat,N4: nat] :
      ( ! [N: nat] : ( ord_less_eq_int @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
     => ( ( ord_less_eq_nat @ N3 @ N4 )
       => ( ord_less_eq_int @ ( F2 @ N3 ) @ ( F2 @ N4 ) ) ) ) ).

% lift_Suc_mono_le
thf(fact_332_zero__le,axiom,
    ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).

% zero_le
thf(fact_333_le__numeral__extra_I3_J,axiom,
    ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).

% le_numeral_extra(3)
thf(fact_334_le__numeral__extra_I3_J,axiom,
    ord_less_eq_int @ zero_zero_int @ zero_zero_int ).

% le_numeral_extra(3)
thf(fact_335_less__numeral__extra_I4_J,axiom,
    ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).

% less_numeral_extra(4)
thf(fact_336_less__numeral__extra_I4_J,axiom,
    ~ ( ord_less_int @ one_one_int @ one_one_int ) ).

% less_numeral_extra(4)
thf(fact_337_of__nat__mono,axiom,
    ! [I: nat,J: nat] :
      ( ( ord_less_eq_nat @ I @ J )
     => ( ord_less_eq_int @ ( semiri2019852685at_int @ I ) @ ( semiri2019852685at_int @ J ) ) ) ).

% of_nat_mono
thf(fact_338_less__minus__one__simps_I4_J,axiom,
    ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).

% less_minus_one_simps(4)
thf(fact_339_less__minus__one__simps_I2_J,axiom,
    ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).

% less_minus_one_simps(2)
thf(fact_340_zero__neq__neg__one,axiom,
    ( zero_zero_int
   != ( uminus_uminus_int @ one_one_int ) ) ).

% zero_neq_neg_one

% Conjectures (1)
thf(conj_0,conjecture,
    prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) ).

%------------------------------------------------------------------------------