%------------------------------------------------------------------------------
% File     : SLH0000^1 : TPTP v8.2.0. Released v8.2.0.
% Domain   : Archive of Formal Proofs
% Problem  :
% Version  : Especial.
% English  :

% Refs     : [Des23] Desharnais (2023), Email to Geoff Sutcliffe
% Source   : [Des23]
% Names    : FSM_Tests/0062_SPY_Framework/prob_00202_010965__20762330_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 1526 ( 192 unt; 648 typ;   0 def)
%            Number of atoms       : 4235 (1072 equ;   0 cnn)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives : 19079 ( 462   ~;  15   |; 604   &;15518   @)
%                                         (   0 <=>;2480  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (  10 avg)
%            Number of types       :  141 ( 140 usr)
%            Number of type conns  : 1125 (1125   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  511 ( 508 usr;  21 con; 0-9 aty)
%            Number of variables   : 3334 ( 131   ^;3017   !; 186   ?;3334   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 11:29:54.587
%------------------------------------------------------------------------------
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thf(ty_n_t__FSM__Ofsm_Itf__a_Mtf__b_Mtf__b_J,type,
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thf(ty_n_t__FSM__Ofsm_Itf__a_Mtf__a_Mtf__a_J,type,
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thf(ty_n_t__List__Olist_Itf__c_J,type,
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thf(ty_n_t__List__Olist_Itf__a_J,type,
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thf(ty_n_t__Set__Oset_Itf__e_J,type,
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thf(ty_n_tf__e,type,
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thf(ty_n_tf__d,type,
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thf(ty_n_tf__c,type,
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thf(ty_n_tf__b,type,
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thf(ty_n_tf__a,type,
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% Explicit typings (508)
thf(sy_c_AList_Omap__default_001t__Prefix____Tree__Oprefix____tree_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_001tf__d,type,
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thf(sy_c_AList_Omap__default_001tf__b_001tf__c,type,
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thf(sy_c_AList_Omap__default__rel_001t__Prefix____Tree__Oprefix____tree_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_001tf__d,type,
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thf(sy_c_AList_Omap__default__rel_001tf__b_001tf__c,type,
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thf(sy_c_AList_Omap__entry_001t__Prefix____Tree__Oprefix____tree_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_001tf__d,type,
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thf(sy_c_AList_Omap__entry_001tf__b_001tf__c,type,
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thf(sy_c_AList_Oupdate__with__aux_001tf__c_001tf__b,type,
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thf(sy_c_AList_Oupdate__with__aux_001tf__d_001t__Prefix____Tree__Oprefix____tree_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J,type,
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thf(sy_c_Convergence_Oconverge_001t__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_001tf__b_001tf__c,type,
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thf(sy_c_Convergence_Oconverge_001tf__a_001tf__b_001tf__c,type,
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thf(sy_c_Convergence_Oconverge_001tf__b_001tf__b_001tf__c,type,
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thf(sy_c_Convergence_Oconverge_001tf__c_001tf__b_001tf__c,type,
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thf(sy_c_Convergence_Oconverge_001tf__e_001tf__b_001tf__c,type,
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thf(sy_c_Convergence_Opreserves__convergence_001tf__a_001tf__b_001tf__c_001tf__a,type,
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thf(sy_c_Convergence_Opreserves__convergence_001tf__a_001tf__b_001tf__c_001tf__e,type,
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thf(sy_c_Convergence_Opreserves__convergence_001tf__e_001tf__b_001tf__c_001tf__a,type,
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thf(sy_c_Convergence_Opreserves__convergence_001tf__e_001tf__b_001tf__c_001tf__e,type,
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thf(sy_c_Convergence_Opreserves__divergence_001tf__a_001tf__b_001tf__c_001tf__a,type,
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thf(sy_c_Convergence_Opreserves__divergence_001tf__a_001tf__b_001tf__c_001tf__e,type,
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thf(sy_c_Convergence_Opreserves__divergence_001tf__e_001tf__b_001tf__c_001tf__a,type,
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thf(sy_c_Convergence_Opreserves__divergence_001tf__e_001tf__b_001tf__c_001tf__e,type,
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thf(sy_c_Convergence_Otransition__cover_001tf__a_001tf__b_001tf__c,type,
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thf(sy_c_Convergence_Otransition__cover_001tf__e_001tf__b_001tf__c,type,
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thf(sy_c_Convergence__Graph_Oconvergence__graph__initial__invar_001tf__a_001tf__b_001tf__c_001tf__e_001tf__d,type,
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thf(sy_c_Convergence__Graph_Oconvergence__graph__insert__invar_001tf__a_001tf__b_001tf__c_001tf__e_001tf__d,type,
    conver9163591880137905914_c_e_d: fsm_a_b_c > fsm_e_b_c > ( d > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c ) > ( d > list_P903359562653991662od_b_c > d ) > $o ).

thf(sy_c_Convergence__Graph_Oconvergence__graph__lookup__invar_001tf__a_001tf__b_001tf__c_001tf__e_001tf__d,type,
    conver4302099639658809211_c_e_d: fsm_a_b_c > fsm_e_b_c > ( d > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c ) > d > $o ).

thf(sy_c_Convergence__Graph_Oconvergence__graph__merge__invar_001tf__a_001tf__b_001tf__c_001tf__e_001tf__d,type,
    conver4668632057843472301_c_e_d: fsm_a_b_c > fsm_e_b_c > ( d > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c ) > ( d > list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > d ) > $o ).

thf(sy_c_FSM_OLS_001t__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_001tf__b_001tf__c,type,
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thf(sy_c_FSM_OLS_001tf__a_001tf__b_001tf__c,type,
    lS_a_b_c: fsm_a_b_c > a > set_li6436108459499378894od_b_c ).

thf(sy_c_FSM_OLS_001tf__b_001tf__b_001tf__c,type,
    lS_b_b_c: fsm_b_b_c > b > set_li6436108459499378894od_b_c ).

thf(sy_c_FSM_OLS_001tf__c_001tf__b_001tf__c,type,
    lS_c_b_c: fsm_c_b_c > c > set_li6436108459499378894od_b_c ).

thf(sy_c_FSM_OLS_001tf__e_001tf__b_001tf__c,type,
    lS_e_b_c: fsm_e_b_c > e > set_li6436108459499378894od_b_c ).

thf(sy_c_FSM_OLS__acyclic_001tf__a_001tf__b_001tf__c,type,
    lS_acyclic_a_b_c: fsm_a_b_c > a > set_li6436108459499378894od_b_c ).

thf(sy_c_FSM_OLS__acyclic_001tf__e_001tf__b_001tf__c,type,
    lS_acyclic_e_b_c: fsm_e_b_c > e > set_li6436108459499378894od_b_c ).

thf(sy_c_FSM_Oacyclic_001tf__a_001tf__b_001tf__c,type,
    acyclic_a_b_c: fsm_a_b_c > $o ).

thf(sy_c_FSM_Oacyclic_001tf__e_001tf__b_001tf__c,type,
    acyclic_e_b_c: fsm_e_b_c > $o ).

thf(sy_c_FSM_Oadd__transition_001tf__a_001tf__a_001tf__a,type,
    add_transition_a_a_a: fsm_a_a_a > produc7928013997122480633od_a_a > fsm_a_a_a ).

thf(sy_c_FSM_Oadd__transition_001tf__a_001tf__a_001tf__b,type,
    add_transition_a_a_b: fsm_a_a_b > produc1355312390766300472od_b_a > fsm_a_a_b ).

thf(sy_c_FSM_Oadd__transition_001tf__a_001tf__a_001tf__c,type,
    add_transition_a_a_c: fsm_a_a_c > produc4005982821264896119od_c_a > fsm_a_a_c ).

thf(sy_c_FSM_Oadd__transition_001tf__a_001tf__b_001tf__a,type,
    add_transition_a_b_a: fsm_a_b_a > produc6591963377169786296od_a_a > fsm_a_b_a ).

thf(sy_c_FSM_Oadd__transition_001tf__a_001tf__b_001tf__b,type,
    add_transition_a_b_b: fsm_a_b_b > produc19261770813606135od_b_a > fsm_a_b_b ).

thf(sy_c_FSM_Oadd__transition_001tf__a_001tf__c_001tf__a,type,
    add_transition_a_c_a: fsm_a_c_a > produc5255912757217091959od_a_a > fsm_a_c_a ).

thf(sy_c_FSM_Oadd__transition_001tf__a_001tf__c_001tf__b,type,
    add_transition_a_c_b: fsm_a_c_b > produc7906583187715687606od_b_a > fsm_a_c_b ).

thf(sy_c_FSM_Oadd__transition_001tf__a_001tf__c_001tf__c,type,
    add_transition_a_c_c: fsm_a_c_c > produc1333881581359507445od_c_a > fsm_a_c_c ).

thf(sy_c_FSM_Oadd__transition_001tf__b_001tf__a_001tf__a,type,
    add_transition_b_a_a: fsm_b_a_a > produc1355512071451634873od_a_b > fsm_b_a_a ).

thf(sy_c_FSM_Oadd__transition_001tf__b_001tf__a_001tf__b,type,
    add_transition_b_a_b: fsm_b_a_b > produc4006182501950230520od_b_b > fsm_b_a_b ).

thf(sy_c_FSM_Oadd__transition__with__components_001tf__a_001tf__b_001tf__c,type,
    add_tr8224572408740125824_a_b_c: fsm_a_b_c > produc2669932201312201782od_c_a > fsm_a_b_c ).

thf(sy_c_FSM_Oadd__transition__with__components_001tf__e_001tf__b_001tf__c,type,
    add_tr2939330758928321156_e_b_c: fsm_e_b_c > produc4050040609193146166od_c_e > fsm_e_b_c ).

thf(sy_c_FSM_Oadd__transitions_001tf__a_001tf__a_001tf__a,type,
    add_tr3755657074655224972_a_a_a: fsm_a_a_a > set_Pr625025929086095065od_a_a > fsm_a_a_a ).

thf(sy_c_FSM_Oadd__transitions_001tf__a_001tf__a_001tf__b,type,
    add_tr3755657074655224973_a_a_b: fsm_a_a_b > set_Pr172305270015935128od_b_a > fsm_a_a_b ).

thf(sy_c_FSM_Oadd__transitions_001tf__a_001tf__a_001tf__c,type,
    add_tr3755657074655224974_a_a_c: fsm_a_a_c > set_Pr8942956647800550999od_c_a > fsm_a_a_c ).

thf(sy_c_FSM_Oadd__transitions_001tf__a_001tf__b_001tf__a,type,
    add_tr968201492682548939_a_b_a: fsm_a_b_a > set_Pr39693332076387096od_a_a > fsm_a_b_a ).

thf(sy_c_FSM_Oadd__transitions_001tf__a_001tf__b_001tf__b,type,
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thf(sy_c_FSM_Oobservable_001tf__b_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Oobservable_001tf__c_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Oobservable_001tf__e_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Ooutputs_001tf__a_001tf__a_001tf__b,type,
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thf(sy_c_FSM_Ooutputs_001tf__a_001tf__a_001tf__c,type,
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thf(sy_c_FSM_Ooutputs_001tf__a_001tf__b_001tf__a,type,
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thf(sy_c_FSM_Ooutputs_001tf__a_001tf__b_001tf__b,type,
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thf(sy_c_FSM_Ooutputs_001tf__a_001tf__c_001tf__a,type,
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thf(sy_c_FSM_Ooutputs_001tf__a_001tf__c_001tf__c,type,
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thf(sy_c_FSM_Ooutputs_001tf__b_001tf__a_001tf__a,type,
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thf(sy_c_FSM_Ooutputs_001tf__b_001tf__a_001tf__b,type,
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thf(sy_c_FSM_Ooutputs_001tf__e_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Opass__io__set_001tf__a_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Osize_001tf__a_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Osize_001tf__e_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Ostates_001tf__a_001tf__a_001tf__b,type,
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thf(sy_c_FSM_Ostates_001tf__b_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Ostates_001tf__c_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Ostates_001tf__e_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Otransitions_001tf__a_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Otransitions_001tf__a_001tf__c_001tf__a,type,
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thf(sy_c_FSM_Otransitions_001tf__a_001tf__c_001tf__b,type,
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thf(sy_c_FSM_Otransitions_001tf__a_001tf__c_001tf__c,type,
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thf(sy_c_FSM_Otransitions_001tf__b_001tf__a_001tf__a,type,
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thf(sy_c_FSM_Otransitions_001tf__b_001tf__a_001tf__b,type,
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thf(sy_c_FSM_Otransitions_001tf__b_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Otransitions_001tf__c_001tf__b_001tf__c,type,
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thf(sy_c_FSM_Otransitions_001tf__e_001tf__b_001tf__c,type,
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    state_7672330573471793359_a_b_c @ m1 @ v ).

% a07
thf(fact_5_a13,axiom,
    conver4302099639658809211_c_e_d @ m1 @ m2 @ cg_lookup @ g ).

% a13
thf(fact_6_a01,axiom,
    observable_a_b_c @ m1 ).

% a01
thf(fact_7_a02,axiom,
    observable_e_b_c @ m2 ).

% a02
thf(fact_8__C_K_C,axiom,
    ? [Alpha: list_P903359562653991662od_b_c] :
      ( ( converge_a_b_c @ m1 @ Alpha @ ( v @ q ) )
      & ( converge_e_b_c @ m2 @ Alpha @ ( v @ q ) )
      & ( member6330420149250801815od_b_c @ Alpha @ ( prefix9085958534787526401od_b_c @ ( produc1447154562020694006_b_c_d @ ( f @ m1 @ v @ t @ g @ cg_insert @ cg_lookup @ q @ x @ y ) ) ) )
      & ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ x @ y ) @ nil_Product_prod_b_c ) ) @ ( prefix9085958534787526401od_b_c @ ( produc1447154562020694006_b_c_d @ ( f @ m1 @ v @ t @ g @ cg_insert @ cg_lookup @ q @ x @ y ) ) ) ) ) ).

% "*"
thf(fact_9_a10,axiom,
    member_a @ q @ ( reacha1620305530751930115_a_b_c @ m1 ) ).

% a10
thf(fact_10_a11,axiom,
    member_b @ x @ ( inputs_a_b_c @ m1 ) ).

% a11
thf(fact_11_a12,axiom,
    member_c @ y @ ( outputs_a_b_c @ m1 ) ).

% a12
thf(fact_12__C_K_K_K_C,axiom,
    ! [T: prefix425356687782099470od_b_c,V: a > list_P903359562653991662od_b_c,G: d,Q: a,X: b,Y: c] :
      ( ( prefix6767660319289835678od_b_c @ T )
     => ( prefix6767660319289835678od_b_c @ ( produc1447154562020694006_b_c_d @ ( f @ m1 @ V @ T @ G @ cg_insert @ cg_lookup @ Q @ X @ Y ) ) ) ) ).

% "***"
thf(fact_13_append1__eq__conv,axiom,
    ! [Xs: list_P903359562653991662od_b_c,X: product_prod_b_c,Ys: list_P903359562653991662od_b_c,Y: product_prod_b_c] :
      ( ( ( append2547753245680614915od_b_c @ Xs @ ( cons_P4529483553340347422od_b_c @ X @ nil_Product_prod_b_c ) )
        = ( append2547753245680614915od_b_c @ Ys @ ( cons_P4529483553340347422od_b_c @ Y @ nil_Product_prod_b_c ) ) )
      = ( ( Xs = Ys )
        & ( X = Y ) ) ) ).

% append1_eq_conv
thf(fact_14__C_K_K_C,axiom,
    conver4302099639658809211_c_e_d @ m1 @ m2 @ cg_lookup @ ( produc6779600879576379960_b_c_d @ ( f @ m1 @ v @ t @ g @ cg_insert @ cg_lookup @ q @ x @ y ) ) ).

% "**"
thf(fact_15_append_Oright__neutral,axiom,
    ! [A: list_P903359562653991662od_b_c] :
      ( ( append2547753245680614915od_b_c @ A @ nil_Product_prod_b_c )
      = A ) ).

% append.right_neutral
thf(fact_16_append__Nil2,axiom,
    ! [Xs: list_P903359562653991662od_b_c] :
      ( ( append2547753245680614915od_b_c @ Xs @ nil_Product_prod_b_c )
      = Xs ) ).

% append_Nil2
thf(fact_17_append__self__conv,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( ( append2547753245680614915od_b_c @ Xs @ Ys )
        = Xs )
      = ( Ys = nil_Product_prod_b_c ) ) ).

% append_self_conv
thf(fact_18_self__append__conv,axiom,
    ! [Y: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( Y
        = ( append2547753245680614915od_b_c @ Y @ Ys ) )
      = ( Ys = nil_Product_prod_b_c ) ) ).

% self_append_conv
thf(fact_19_append__self__conv2,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( ( append2547753245680614915od_b_c @ Xs @ Ys )
        = Ys )
      = ( Xs = nil_Product_prod_b_c ) ) ).

% append_self_conv2
thf(fact_20_self__append__conv2,axiom,
    ! [Y: list_P903359562653991662od_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( Y
        = ( append2547753245680614915od_b_c @ Xs @ Y ) )
      = ( Xs = nil_Product_prod_b_c ) ) ).

% self_append_conv2
thf(fact_21_Nil__is__append__conv,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( nil_Product_prod_b_c
        = ( append2547753245680614915od_b_c @ Xs @ Ys ) )
      = ( ( Xs = nil_Product_prod_b_c )
        & ( Ys = nil_Product_prod_b_c ) ) ) ).

% Nil_is_append_conv
thf(fact_22_append__is__Nil__conv,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( ( append2547753245680614915od_b_c @ Xs @ Ys )
        = nil_Product_prod_b_c )
      = ( ( Xs = nil_Product_prod_b_c )
        & ( Ys = nil_Product_prod_b_c ) ) ) ).

% append_is_Nil_conv
thf(fact_23_list_Oinject,axiom,
    ! [X21: product_prod_b_c,X22: list_P903359562653991662od_b_c,Y21: product_prod_b_c,Y22: list_P903359562653991662od_b_c] :
      ( ( ( cons_P4529483553340347422od_b_c @ X21 @ X22 )
        = ( cons_P4529483553340347422od_b_c @ Y21 @ Y22 ) )
      = ( ( X21 = Y21 )
        & ( X22 = Y22 ) ) ) ).

% list.inject
thf(fact_24_same__append__eq,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,Zs: list_P903359562653991662od_b_c] :
      ( ( ( append2547753245680614915od_b_c @ Xs @ Ys )
        = ( append2547753245680614915od_b_c @ Xs @ Zs ) )
      = ( Ys = Zs ) ) ).

% same_append_eq
thf(fact_25_append__same__eq,axiom,
    ! [Ys: list_P903359562653991662od_b_c,Xs: list_P903359562653991662od_b_c,Zs: list_P903359562653991662od_b_c] :
      ( ( ( append2547753245680614915od_b_c @ Ys @ Xs )
        = ( append2547753245680614915od_b_c @ Zs @ Xs ) )
      = ( Ys = Zs ) ) ).

% append_same_eq
thf(fact_26_append__assoc,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,Zs: list_P903359562653991662od_b_c] :
      ( ( append2547753245680614915od_b_c @ ( append2547753245680614915od_b_c @ Xs @ Ys ) @ Zs )
      = ( append2547753245680614915od_b_c @ Xs @ ( append2547753245680614915od_b_c @ Ys @ Zs ) ) ) ).

% append_assoc
thf(fact_27_append_Oassoc,axiom,
    ! [A: list_P903359562653991662od_b_c,B: list_P903359562653991662od_b_c,C: list_P903359562653991662od_b_c] :
      ( ( append2547753245680614915od_b_c @ ( append2547753245680614915od_b_c @ A @ B ) @ C )
      = ( append2547753245680614915od_b_c @ A @ ( append2547753245680614915od_b_c @ B @ C ) ) ) ).

% append.assoc
thf(fact_28_a05,axiom,
    ( ( inputs_e_b_c @ m2 )
    = ( inputs_a_b_c @ m1 ) ) ).

% a05
thf(fact_29_a06,axiom,
    ( ( outputs_e_b_c @ m2 )
    = ( outputs_a_b_c @ m1 ) ) ).

% a06
thf(fact_30_not__Cons__self2,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( cons_P4529483553340347422od_b_c @ X @ Xs )
     != Xs ) ).

% not_Cons_self2
thf(fact_31_append__eq__append__conv2,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,Zs: list_P903359562653991662od_b_c,Ts: list_P903359562653991662od_b_c] :
      ( ( ( append2547753245680614915od_b_c @ Xs @ Ys )
        = ( append2547753245680614915od_b_c @ Zs @ Ts ) )
      = ( ? [Us: list_P903359562653991662od_b_c] :
            ( ( ( Xs
                = ( append2547753245680614915od_b_c @ Zs @ Us ) )
              & ( ( append2547753245680614915od_b_c @ Us @ Ys )
                = Ts ) )
            | ( ( ( append2547753245680614915od_b_c @ Xs @ Us )
                = Zs )
              & ( Ys
                = ( append2547753245680614915od_b_c @ Us @ Ts ) ) ) ) ) ) ).

% append_eq_append_conv2
thf(fact_32_append__eq__appendI,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Xs1: list_P903359562653991662od_b_c,Zs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,Us2: list_P903359562653991662od_b_c] :
      ( ( ( append2547753245680614915od_b_c @ Xs @ Xs1 )
        = Zs )
     => ( ( Ys
          = ( append2547753245680614915od_b_c @ Xs1 @ Us2 ) )
       => ( ( append2547753245680614915od_b_c @ Xs @ Ys )
          = ( append2547753245680614915od_b_c @ Zs @ Us2 ) ) ) ) ).

% append_eq_appendI
thf(fact_33_list__nonempty__induct,axiom,
    ! [Xs: list_P903359562653991662od_b_c,P: list_P903359562653991662od_b_c > $o] :
      ( ( Xs != nil_Product_prod_b_c )
     => ( ! [X2: product_prod_b_c] : ( P @ ( cons_P4529483553340347422od_b_c @ X2 @ nil_Product_prod_b_c ) )
       => ( ! [X2: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
              ( ( Xs2 != nil_Product_prod_b_c )
             => ( ( P @ Xs2 )
               => ( P @ ( cons_P4529483553340347422od_b_c @ X2 @ Xs2 ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% list_nonempty_induct
thf(fact_34_list__induct2_H,axiom,
    ! [P: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > $o,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( P @ nil_Product_prod_b_c @ nil_Product_prod_b_c )
     => ( ! [X2: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] : ( P @ ( cons_P4529483553340347422od_b_c @ X2 @ Xs2 ) @ nil_Product_prod_b_c )
       => ( ! [Y2: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] : ( P @ nil_Product_prod_b_c @ ( cons_P4529483553340347422od_b_c @ Y2 @ Ys2 ) )
         => ( ! [X2: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y2: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] :
                ( ( P @ Xs2 @ Ys2 )
               => ( P @ ( cons_P4529483553340347422od_b_c @ X2 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y2 @ Ys2 ) ) )
           => ( P @ Xs @ Ys ) ) ) ) ) ).

% list_induct2'
thf(fact_35_neq__Nil__conv,axiom,
    ! [Xs: list_P903359562653991662od_b_c] :
      ( ( Xs != nil_Product_prod_b_c )
      = ( ? [Y3: product_prod_b_c,Ys3: list_P903359562653991662od_b_c] :
            ( Xs
            = ( cons_P4529483553340347422od_b_c @ Y3 @ Ys3 ) ) ) ) ).

% neq_Nil_conv
thf(fact_36_remdups__adj_Ocases,axiom,
    ! [X: list_P903359562653991662od_b_c] :
      ( ( X != nil_Product_prod_b_c )
     => ( ! [X2: product_prod_b_c] :
            ( X
           != ( cons_P4529483553340347422od_b_c @ X2 @ nil_Product_prod_b_c ) )
       => ~ ! [X2: product_prod_b_c,Y2: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
              ( X
             != ( cons_P4529483553340347422od_b_c @ X2 @ ( cons_P4529483553340347422od_b_c @ Y2 @ Xs2 ) ) ) ) ) ).

% remdups_adj.cases
thf(fact_37_mem__Collect__eq,axiom,
    ! [A: list_P903359562653991662od_b_c,P: list_P903359562653991662od_b_c > $o] :
      ( ( member6330420149250801815od_b_c @ A @ ( collec2280997390073109977od_b_c @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_38_mem__Collect__eq,axiom,
    ! [A: a,P: a > $o] :
      ( ( member_a @ A @ ( collect_a @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_39_mem__Collect__eq,axiom,
    ! [A: b,P: b > $o] :
      ( ( member_b @ A @ ( collect_b @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_40_mem__Collect__eq,axiom,
    ! [A: c,P: c > $o] :
      ( ( member_c @ A @ ( collect_c @ P ) )
      = ( P @ A ) ) ).

% mem_Collect_eq
thf(fact_41_Collect__mem__eq,axiom,
    ! [A2: set_li6436108459499378894od_b_c] :
      ( ( collec2280997390073109977od_b_c
        @ ^ [X3: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ X3 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_42_Collect__mem__eq,axiom,
    ! [A2: set_a] :
      ( ( collect_a
        @ ^ [X3: a] : ( member_a @ X3 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_43_Collect__mem__eq,axiom,
    ! [A2: set_b] :
      ( ( collect_b
        @ ^ [X3: b] : ( member_b @ X3 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_44_Collect__mem__eq,axiom,
    ! [A2: set_c] :
      ( ( collect_c
        @ ^ [X3: c] : ( member_c @ X3 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_45_transpose_Ocases,axiom,
    ! [X: list_l8907847357763382004od_b_c] :
      ( ( X != nil_li8071162985807626740od_b_c )
     => ( ! [Xss: list_l8907847357763382004od_b_c] :
            ( X
           != ( cons_l342771267123639716od_b_c @ nil_Product_prod_b_c @ Xss ) )
       => ~ ! [X2: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Xss: list_l8907847357763382004od_b_c] :
              ( X
             != ( cons_l342771267123639716od_b_c @ ( cons_P4529483553340347422od_b_c @ X2 @ Xs2 ) @ Xss ) ) ) ) ).

% transpose.cases
thf(fact_46_min__list_Ocases,axiom,
    ! [X: list_P903359562653991662od_b_c] :
      ( ! [X2: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
          ( X
         != ( cons_P4529483553340347422od_b_c @ X2 @ Xs2 ) )
     => ( X = nil_Product_prod_b_c ) ) ).

% min_list.cases
thf(fact_47_list_Oexhaust,axiom,
    ! [Y: list_P903359562653991662od_b_c] :
      ( ( Y != nil_Product_prod_b_c )
     => ~ ! [X212: product_prod_b_c,X222: list_P903359562653991662od_b_c] :
            ( Y
           != ( cons_P4529483553340347422od_b_c @ X212 @ X222 ) ) ) ).

% list.exhaust
thf(fact_48_list_OdiscI,axiom,
    ! [List: list_P903359562653991662od_b_c,X21: product_prod_b_c,X22: list_P903359562653991662od_b_c] :
      ( ( List
        = ( cons_P4529483553340347422od_b_c @ X21 @ X22 ) )
     => ( List != nil_Product_prod_b_c ) ) ).

% list.discI
thf(fact_49_list_Odistinct_I1_J,axiom,
    ! [X21: product_prod_b_c,X22: list_P903359562653991662od_b_c] :
      ( nil_Product_prod_b_c
     != ( cons_P4529483553340347422od_b_c @ X21 @ X22 ) ) ).

% list.distinct(1)
thf(fact_50_Cons__eq__appendI,axiom,
    ! [X: product_prod_b_c,Xs1: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,Xs: list_P903359562653991662od_b_c,Zs: list_P903359562653991662od_b_c] :
      ( ( ( cons_P4529483553340347422od_b_c @ X @ Xs1 )
        = Ys )
     => ( ( Xs
          = ( append2547753245680614915od_b_c @ Xs1 @ Zs ) )
       => ( ( cons_P4529483553340347422od_b_c @ X @ Xs )
          = ( append2547753245680614915od_b_c @ Ys @ Zs ) ) ) ) ).

% Cons_eq_appendI
thf(fact_51_append__Cons,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) @ Ys )
      = ( cons_P4529483553340347422od_b_c @ X @ ( append2547753245680614915od_b_c @ Xs @ Ys ) ) ) ).

% append_Cons
thf(fact_52_eq__Nil__appendI,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( Xs = Ys )
     => ( Xs
        = ( append2547753245680614915od_b_c @ nil_Product_prod_b_c @ Ys ) ) ) ).

% eq_Nil_appendI
thf(fact_53_append_Oleft__neutral,axiom,
    ! [A: list_P903359562653991662od_b_c] :
      ( ( append2547753245680614915od_b_c @ nil_Product_prod_b_c @ A )
      = A ) ).

% append.left_neutral
thf(fact_54_append__Nil,axiom,
    ! [Ys: list_P903359562653991662od_b_c] :
      ( ( append2547753245680614915od_b_c @ nil_Product_prod_b_c @ Ys )
      = Ys ) ).

% append_Nil
thf(fact_55_clearjunk_Ocases,axiom,
    ! [X: list_P903359562653991662od_b_c] :
      ( ( X != nil_Product_prod_b_c )
     => ~ ! [P2: product_prod_b_c,Ps: list_P903359562653991662od_b_c] :
            ( X
           != ( cons_P4529483553340347422od_b_c @ P2 @ Ps ) ) ) ).

% clearjunk.cases
thf(fact_56_rev__nonempty__induct,axiom,
    ! [Xs: list_P903359562653991662od_b_c,P: list_P903359562653991662od_b_c > $o] :
      ( ( Xs != nil_Product_prod_b_c )
     => ( ! [X2: product_prod_b_c] : ( P @ ( cons_P4529483553340347422od_b_c @ X2 @ nil_Product_prod_b_c ) )
       => ( ! [X2: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
              ( ( Xs2 != nil_Product_prod_b_c )
             => ( ( P @ Xs2 )
               => ( P @ ( append2547753245680614915od_b_c @ Xs2 @ ( cons_P4529483553340347422od_b_c @ X2 @ nil_Product_prod_b_c ) ) ) ) )
         => ( P @ Xs ) ) ) ) ).

% rev_nonempty_induct
thf(fact_57_append__eq__Cons__conv,axiom,
    ! [Ys: list_P903359562653991662od_b_c,Zs: list_P903359562653991662od_b_c,X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( ( append2547753245680614915od_b_c @ Ys @ Zs )
        = ( cons_P4529483553340347422od_b_c @ X @ Xs ) )
      = ( ( ( Ys = nil_Product_prod_b_c )
          & ( Zs
            = ( cons_P4529483553340347422od_b_c @ X @ Xs ) ) )
        | ? [Ys4: list_P903359562653991662od_b_c] :
            ( ( Ys
              = ( cons_P4529483553340347422od_b_c @ X @ Ys4 ) )
            & ( ( append2547753245680614915od_b_c @ Ys4 @ Zs )
              = Xs ) ) ) ) ).

% append_eq_Cons_conv
thf(fact_58_Cons__eq__append__conv,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,Zs: list_P903359562653991662od_b_c] :
      ( ( ( cons_P4529483553340347422od_b_c @ X @ Xs )
        = ( append2547753245680614915od_b_c @ Ys @ Zs ) )
      = ( ( ( Ys = nil_Product_prod_b_c )
          & ( ( cons_P4529483553340347422od_b_c @ X @ Xs )
            = Zs ) )
        | ? [Ys4: list_P903359562653991662od_b_c] :
            ( ( ( cons_P4529483553340347422od_b_c @ X @ Ys4 )
              = Ys )
            & ( Xs
              = ( append2547753245680614915od_b_c @ Ys4 @ Zs ) ) ) ) ) ).

% Cons_eq_append_conv
thf(fact_59_rev__exhaust,axiom,
    ! [Xs: list_P903359562653991662od_b_c] :
      ( ( Xs != nil_Product_prod_b_c )
     => ~ ! [Ys2: list_P903359562653991662od_b_c,Y2: product_prod_b_c] :
            ( Xs
           != ( append2547753245680614915od_b_c @ Ys2 @ ( cons_P4529483553340347422od_b_c @ Y2 @ nil_Product_prod_b_c ) ) ) ) ).

% rev_exhaust
thf(fact_60_rev__induct,axiom,
    ! [P: list_P903359562653991662od_b_c > $o,Xs: list_P903359562653991662od_b_c] :
      ( ( P @ nil_Product_prod_b_c )
     => ( ! [X2: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
            ( ( P @ Xs2 )
           => ( P @ ( append2547753245680614915od_b_c @ Xs2 @ ( cons_P4529483553340347422od_b_c @ X2 @ nil_Product_prod_b_c ) ) ) )
       => ( P @ Xs ) ) ) ).

% rev_induct
thf(fact_61_delete__aux_Ocases,axiom,
    ! [X: produc6475121930738208726od_b_c] :
      ( ! [K: b] :
          ( X
         != ( produc561751498933632326od_b_c @ K @ nil_Product_prod_b_c ) )
     => ~ ! [K: b,K2: b,V2: c,Xs2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc561751498933632326od_b_c @ K @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ K2 @ V2 ) @ Xs2 ) ) ) ) ).

% delete_aux.cases
thf(fact_62_prod_Ocollapse,axiom,
    ! [Prod: product_prod_b_c] :
      ( ( product_Pair_b_c @ ( product_fst_b_c @ Prod ) @ ( product_snd_b_c @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_63_prod_Ocollapse,axiom,
    ! [Prod: produc4534891791806675482_b_c_d] :
      ( ( produc2511600812177743882_b_c_d @ ( produc1447154562020694006_b_c_d @ Prod ) @ ( produc6779600879576379960_b_c_d @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_64_state__cover__assignment__diverges,axiom,
    ! [M: fsm_e_b_c,F: e > list_P903359562653991662od_b_c,Q1: e,Q2: e] :
      ( ( observable_e_b_c @ M )
     => ( ( minimal_e_b_c @ M )
       => ( ( state_2387088923659988691_e_b_c @ M @ F )
         => ( ( member_e @ Q1 @ ( reacha5558435917794901255_e_b_c @ M ) )
           => ( ( member_e @ Q2 @ ( reacha5558435917794901255_e_b_c @ M ) )
             => ( ( Q1 != Q2 )
               => ~ ( converge_e_b_c @ M @ ( F @ Q1 ) @ ( F @ Q2 ) ) ) ) ) ) ) ) ).

% state_cover_assignment_diverges
thf(fact_65_state__cover__assignment__diverges,axiom,
    ! [M: fsm_a_b_c,F: a > list_P903359562653991662od_b_c,Q1: a,Q2: a] :
      ( ( observable_a_b_c @ M )
     => ( ( minimal_a_b_c @ M )
       => ( ( state_7672330573471793359_a_b_c @ M @ F )
         => ( ( member_a @ Q1 @ ( reacha1620305530751930115_a_b_c @ M ) )
           => ( ( member_a @ Q2 @ ( reacha1620305530751930115_a_b_c @ M ) )
             => ( ( Q1 != Q2 )
               => ~ ( converge_a_b_c @ M @ ( F @ Q1 ) @ ( F @ Q2 ) ) ) ) ) ) ) ) ).

% state_cover_assignment_diverges
thf(fact_66_converge__trans__2_I1_J,axiom,
    ! [M: fsm_a_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,W1: list_P903359562653991662od_b_c,W2: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( minimal_a_b_c @ M )
       => ( ( converge_a_b_c @ M @ U @ V3 )
         => ( ( converge_a_b_c @ M @ ( append2547753245680614915od_b_c @ U @ W1 ) @ ( append2547753245680614915od_b_c @ U @ W2 ) )
            = ( converge_a_b_c @ M @ ( append2547753245680614915od_b_c @ V3 @ W1 ) @ ( append2547753245680614915od_b_c @ V3 @ W2 ) ) ) ) ) ) ).

% converge_trans_2(1)
thf(fact_67_converge__trans__2_I1_J,axiom,
    ! [M: fsm_e_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,W1: list_P903359562653991662od_b_c,W2: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( minimal_e_b_c @ M )
       => ( ( converge_e_b_c @ M @ U @ V3 )
         => ( ( converge_e_b_c @ M @ ( append2547753245680614915od_b_c @ U @ W1 ) @ ( append2547753245680614915od_b_c @ U @ W2 ) )
            = ( converge_e_b_c @ M @ ( append2547753245680614915od_b_c @ V3 @ W1 ) @ ( append2547753245680614915od_b_c @ V3 @ W2 ) ) ) ) ) ) ).

% converge_trans_2(1)
thf(fact_68_converge__trans__2_I2_J,axiom,
    ! [M: fsm_a_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,W1: list_P903359562653991662od_b_c,W2: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( minimal_a_b_c @ M )
       => ( ( converge_a_b_c @ M @ U @ V3 )
         => ( ( converge_a_b_c @ M @ ( append2547753245680614915od_b_c @ U @ W1 ) @ ( append2547753245680614915od_b_c @ U @ W2 ) )
            = ( converge_a_b_c @ M @ ( append2547753245680614915od_b_c @ U @ W1 ) @ ( append2547753245680614915od_b_c @ V3 @ W2 ) ) ) ) ) ) ).

% converge_trans_2(2)
thf(fact_69_converge__trans__2_I2_J,axiom,
    ! [M: fsm_e_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,W1: list_P903359562653991662od_b_c,W2: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( minimal_e_b_c @ M )
       => ( ( converge_e_b_c @ M @ U @ V3 )
         => ( ( converge_e_b_c @ M @ ( append2547753245680614915od_b_c @ U @ W1 ) @ ( append2547753245680614915od_b_c @ U @ W2 ) )
            = ( converge_e_b_c @ M @ ( append2547753245680614915od_b_c @ U @ W1 ) @ ( append2547753245680614915od_b_c @ V3 @ W2 ) ) ) ) ) ) ).

% converge_trans_2(2)
thf(fact_70_converge__trans__2_I3_J,axiom,
    ! [M: fsm_a_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,W1: list_P903359562653991662od_b_c,W2: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( minimal_a_b_c @ M )
       => ( ( converge_a_b_c @ M @ U @ V3 )
         => ( ( converge_a_b_c @ M @ ( append2547753245680614915od_b_c @ U @ W1 ) @ ( append2547753245680614915od_b_c @ U @ W2 ) )
            = ( converge_a_b_c @ M @ ( append2547753245680614915od_b_c @ V3 @ W1 ) @ ( append2547753245680614915od_b_c @ U @ W2 ) ) ) ) ) ) ).

% converge_trans_2(3)
thf(fact_71_converge__trans__2_I3_J,axiom,
    ! [M: fsm_e_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,W1: list_P903359562653991662od_b_c,W2: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( minimal_e_b_c @ M )
       => ( ( converge_e_b_c @ M @ U @ V3 )
         => ( ( converge_e_b_c @ M @ ( append2547753245680614915od_b_c @ U @ W1 ) @ ( append2547753245680614915od_b_c @ U @ W2 ) )
            = ( converge_e_b_c @ M @ ( append2547753245680614915od_b_c @ V3 @ W1 ) @ ( append2547753245680614915od_b_c @ U @ W2 ) ) ) ) ) ) ).

% converge_trans_2(3)
thf(fact_72_state__cover__assignment__inj,axiom,
    ! [M: fsm_e_b_c,V: e > list_P903359562653991662od_b_c,Q1: e,Q2: e] :
      ( ( state_2387088923659988691_e_b_c @ M @ V )
     => ( ( observable_e_b_c @ M )
       => ( ( member_e @ Q1 @ ( reacha5558435917794901255_e_b_c @ M ) )
         => ( ( member_e @ Q2 @ ( reacha5558435917794901255_e_b_c @ M ) )
           => ( ( Q1 != Q2 )
             => ( ( V @ Q1 )
               != ( V @ Q2 ) ) ) ) ) ) ) ).

% state_cover_assignment_inj
thf(fact_73_state__cover__assignment__inj,axiom,
    ! [M: fsm_a_b_c,V: a > list_P903359562653991662od_b_c,Q1: a,Q2: a] :
      ( ( state_7672330573471793359_a_b_c @ M @ V )
     => ( ( observable_a_b_c @ M )
       => ( ( member_a @ Q1 @ ( reacha1620305530751930115_a_b_c @ M ) )
         => ( ( member_a @ Q2 @ ( reacha1620305530751930115_a_b_c @ M ) )
           => ( ( Q1 != Q2 )
             => ( ( V @ Q1 )
               != ( V @ Q2 ) ) ) ) ) ) ) ).

% state_cover_assignment_inj
thf(fact_74_converge__append__iff,axiom,
    ! [M: fsm_a_b_c,Alpha2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,Omega: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( converge_a_b_c @ M @ Alpha2 @ Beta )
       => ( ( converge_a_b_c @ M @ Gamma @ ( append2547753245680614915od_b_c @ Alpha2 @ Omega ) )
          = ( converge_a_b_c @ M @ Gamma @ ( append2547753245680614915od_b_c @ Beta @ Omega ) ) ) ) ) ).

% converge_append_iff
thf(fact_75_converge__append__iff,axiom,
    ! [M: fsm_e_b_c,Alpha2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,Omega: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( converge_e_b_c @ M @ Alpha2 @ Beta )
       => ( ( converge_e_b_c @ M @ Gamma @ ( append2547753245680614915od_b_c @ Alpha2 @ Omega ) )
          = ( converge_e_b_c @ M @ Gamma @ ( append2547753245680614915od_b_c @ Beta @ Omega ) ) ) ) ) ).

% converge_append_iff
thf(fact_76_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: b > c > $o,X: b,Y: c,A: product_prod_b_c] :
      ( ( P @ X @ Y )
     => ( ( A
          = ( product_Pair_b_c @ X @ Y ) )
       => ( P @ ( product_fst_b_c @ A ) @ ( product_snd_b_c @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_77_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
    ! [P: prefix425356687782099470od_b_c > d > $o,X: prefix425356687782099470od_b_c,Y: d,A: produc4534891791806675482_b_c_d] :
      ( ( P @ X @ Y )
     => ( ( A
          = ( produc2511600812177743882_b_c_d @ X @ Y ) )
       => ( P @ ( produc1447154562020694006_b_c_d @ A ) @ ( produc6779600879576379960_b_c_d @ A ) ) ) ) ).

% BNF_Greatest_Fixpoint.subst_Pair
thf(fact_78_prod_Oinject,axiom,
    ! [X1: b,X23: c,Y1: b,Y23: c] :
      ( ( ( product_Pair_b_c @ X1 @ X23 )
        = ( product_Pair_b_c @ Y1 @ Y23 ) )
      = ( ( X1 = Y1 )
        & ( X23 = Y23 ) ) ) ).

% prod.inject
thf(fact_79_old_Oprod_Oinject,axiom,
    ! [A: b,B: c,A3: b,B2: c] :
      ( ( ( product_Pair_b_c @ A @ B )
        = ( product_Pair_b_c @ A3 @ B2 ) )
      = ( ( A = A3 )
        & ( B = B2 ) ) ) ).

% old.prod.inject
thf(fact_80_map__default_Ocases,axiom,
    ! [X: produc2009451851958091931od_b_c] :
      ( ! [K: b,V2: c,F2: c > c] :
          ( X
         != ( produc1384939585547926677od_b_c @ K @ ( produc3590379597927054951od_b_c @ V2 @ ( produc1101678828523717360od_b_c @ F2 @ nil_Product_prod_b_c ) ) ) )
     => ~ ! [K: b,V2: c,F2: c > c,P2: product_prod_b_c,Ps: list_P903359562653991662od_b_c] :
            ( X
           != ( produc1384939585547926677od_b_c @ K @ ( produc3590379597927054951od_b_c @ V2 @ ( produc1101678828523717360od_b_c @ F2 @ ( cons_P4529483553340347422od_b_c @ P2 @ Ps ) ) ) ) ) ) ).

% map_default.cases
thf(fact_81_find__remove_H_Ocases,axiom,
    ! [X: produc5559707038353031495od_b_c] :
      ( ! [P3: product_prod_b_c > $o,Uu: list_P903359562653991662od_b_c] :
          ( X
         != ( produc1005531610559690873od_b_c @ P3 @ ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ Uu ) ) )
     => ~ ! [P3: product_prod_b_c > $o,X2: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Prev: list_P903359562653991662od_b_c] :
            ( X
           != ( produc1005531610559690873od_b_c @ P3 @ ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ X2 @ Xs2 ) @ Prev ) ) ) ) ).

% find_remove'.cases
thf(fact_82_map__entry_Ocases,axiom,
    ! [X: produc6452300523622238572od_b_c] :
      ( ! [K: b,F2: c > c] :
          ( X
         != ( produc7015427828931889894od_b_c @ K @ ( produc1101678828523717360od_b_c @ F2 @ nil_Product_prod_b_c ) ) )
     => ~ ! [K: b,F2: c > c,P2: product_prod_b_c,Ps: list_P903359562653991662od_b_c] :
            ( X
           != ( produc7015427828931889894od_b_c @ K @ ( produc1101678828523717360od_b_c @ F2 @ ( cons_P4529483553340347422od_b_c @ P2 @ Ps ) ) ) ) ) ).

% map_entry.cases
thf(fact_83_find__index_Ocases,axiom,
    ! [X: produc7816210539016439438od_b_c] :
      ( ! [F2: product_prod_b_c > $o] :
          ( X
         != ( produc7392021306980666816od_b_c @ F2 @ nil_Product_prod_b_c ) )
     => ~ ! [F2: product_prod_b_c > $o,X2: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc7392021306980666816od_b_c @ F2 @ ( cons_P4529483553340347422od_b_c @ X2 @ Xs2 ) ) ) ) ).

% find_index.cases
thf(fact_84_is__prefix_Ocases,axiom,
    ! [X: produc5878855887281848999od_b_c] :
      ( ! [Uu: list_P903359562653991662od_b_c] :
          ( X
         != ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ Uu ) )
     => ( ! [X2: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ X2 @ Xs2 ) @ nil_Product_prod_b_c ) )
       => ~ ! [X2: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y2: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] :
              ( X
             != ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ X2 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y2 @ Ys2 ) ) ) ) ) ).

% is_prefix.cases
thf(fact_85_sorted__wrt_Ocases,axiom,
    ! [X: produc2416979464461413415od_b_c] :
      ( ! [P3: product_prod_b_c > product_prod_b_c > $o] :
          ( X
         != ( produc6092892548594537111od_b_c @ P3 @ nil_Product_prod_b_c ) )
     => ~ ! [P3: product_prod_b_c > product_prod_b_c > $o,X2: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc6092892548594537111od_b_c @ P3 @ ( cons_P4529483553340347422od_b_c @ X2 @ Ys2 ) ) ) ) ).

% sorted_wrt.cases
thf(fact_86_successively_Ocases,axiom,
    ! [X: produc2416979464461413415od_b_c] :
      ( ! [P3: product_prod_b_c > product_prod_b_c > $o] :
          ( X
         != ( produc6092892548594537111od_b_c @ P3 @ nil_Product_prod_b_c ) )
     => ( ! [P3: product_prod_b_c > product_prod_b_c > $o,X2: product_prod_b_c] :
            ( X
           != ( produc6092892548594537111od_b_c @ P3 @ ( cons_P4529483553340347422od_b_c @ X2 @ nil_Product_prod_b_c ) ) )
       => ~ ! [P3: product_prod_b_c > product_prod_b_c > $o,X2: product_prod_b_c,Y2: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
              ( X
             != ( produc6092892548594537111od_b_c @ P3 @ ( cons_P4529483553340347422od_b_c @ X2 @ ( cons_P4529483553340347422od_b_c @ Y2 @ Xs2 ) ) ) ) ) ) ).

% successively.cases
thf(fact_87_splice_Ocases,axiom,
    ! [X: produc5878855887281848999od_b_c] :
      ( ! [Ys2: list_P903359562653991662od_b_c] :
          ( X
         != ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ Ys2 ) )
     => ~ ! [X2: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Ys2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ X2 @ Xs2 ) @ Ys2 ) ) ) ).

% splice.cases
thf(fact_88_shuffles_Ocases,axiom,
    ! [X: produc5878855887281848999od_b_c] :
      ( ! [Ys2: list_P903359562653991662od_b_c] :
          ( X
         != ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ Ys2 ) )
     => ( ! [Xs2: list_P903359562653991662od_b_c] :
            ( X
           != ( produc3076307724246486423od_b_c @ Xs2 @ nil_Product_prod_b_c ) )
       => ~ ! [X2: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y2: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] :
              ( X
             != ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ X2 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y2 @ Ys2 ) ) ) ) ) ).

% shuffles.cases
thf(fact_89_old_Oprod_Oexhaust,axiom,
    ! [Y: product_prod_b_c] :
      ~ ! [A4: b,B3: c] :
          ( Y
         != ( product_Pair_b_c @ A4 @ B3 ) ) ).

% old.prod.exhaust
thf(fact_90_surj__pair,axiom,
    ! [P4: product_prod_b_c] :
    ? [X2: b,Y2: c] :
      ( P4
      = ( product_Pair_b_c @ X2 @ Y2 ) ) ).

% surj_pair
thf(fact_91_prod__cases,axiom,
    ! [P: product_prod_b_c > $o,P4: product_prod_b_c] :
      ( ! [A4: b,B3: c] : ( P @ ( product_Pair_b_c @ A4 @ B3 ) )
     => ( P @ P4 ) ) ).

% prod_cases
thf(fact_92_Pair__inject,axiom,
    ! [A: b,B: c,A3: b,B2: c] :
      ( ( ( product_Pair_b_c @ A @ B )
        = ( product_Pair_b_c @ A3 @ B2 ) )
     => ~ ( ( A = A3 )
         => ( B != B2 ) ) ) ).

% Pair_inject
thf(fact_93_converge__sym,axiom,
    ( converge_a_b_c
    = ( ^ [M2: fsm_a_b_c,U2: list_P903359562653991662od_b_c,V4: list_P903359562653991662od_b_c] : ( converge_a_b_c @ M2 @ V4 @ U2 ) ) ) ).

% converge_sym
thf(fact_94_converge__sym,axiom,
    ( converge_e_b_c
    = ( ^ [M2: fsm_e_b_c,U2: list_P903359562653991662od_b_c,V4: list_P903359562653991662od_b_c] : ( converge_e_b_c @ M2 @ V4 @ U2 ) ) ) ).

% converge_sym
thf(fact_95_snd__eqD,axiom,
    ! [X: b,Y: c,A: c] :
      ( ( ( product_snd_b_c @ ( product_Pair_b_c @ X @ Y ) )
        = A )
     => ( Y = A ) ) ).

% snd_eqD
thf(fact_96_snd__eqD,axiom,
    ! [X: prefix425356687782099470od_b_c,Y: d,A: d] :
      ( ( ( produc6779600879576379960_b_c_d @ ( produc2511600812177743882_b_c_d @ X @ Y ) )
        = A )
     => ( Y = A ) ) ).

% snd_eqD
thf(fact_97_snd__conv,axiom,
    ! [X1: b,X23: c] :
      ( ( product_snd_b_c @ ( product_Pair_b_c @ X1 @ X23 ) )
      = X23 ) ).

% snd_conv
thf(fact_98_snd__conv,axiom,
    ! [X1: prefix425356687782099470od_b_c,X23: d] :
      ( ( produc6779600879576379960_b_c_d @ ( produc2511600812177743882_b_c_d @ X1 @ X23 ) )
      = X23 ) ).

% snd_conv
thf(fact_99_fst__eqD,axiom,
    ! [X: b,Y: c,A: b] :
      ( ( ( product_fst_b_c @ ( product_Pair_b_c @ X @ Y ) )
        = A )
     => ( X = A ) ) ).

% fst_eqD
thf(fact_100_fst__eqD,axiom,
    ! [X: prefix425356687782099470od_b_c,Y: d,A: prefix425356687782099470od_b_c] :
      ( ( ( produc1447154562020694006_b_c_d @ ( produc2511600812177743882_b_c_d @ X @ Y ) )
        = A )
     => ( X = A ) ) ).

% fst_eqD
thf(fact_101_fst__conv,axiom,
    ! [X1: b,X23: c] :
      ( ( product_fst_b_c @ ( product_Pair_b_c @ X1 @ X23 ) )
      = X1 ) ).

% fst_conv
thf(fact_102_fst__conv,axiom,
    ! [X1: prefix425356687782099470od_b_c,X23: d] :
      ( ( produc1447154562020694006_b_c_d @ ( produc2511600812177743882_b_c_d @ X1 @ X23 ) )
      = X1 ) ).

% fst_conv
thf(fact_103_linear__order__from__list__position_H_Ocases,axiom,
    ! [X: list_P903359562653991662od_b_c] :
      ( ( X != nil_Product_prod_b_c )
     => ~ ! [X2: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
            ( X
           != ( cons_P4529483553340347422od_b_c @ X2 @ Xs2 ) ) ) ).

% linear_order_from_list_position'.cases
thf(fact_104_prod_Oexpand,axiom,
    ! [Prod: produc4534891791806675482_b_c_d,Prod2: produc4534891791806675482_b_c_d] :
      ( ( ( ( produc1447154562020694006_b_c_d @ Prod )
          = ( produc1447154562020694006_b_c_d @ Prod2 ) )
        & ( ( produc6779600879576379960_b_c_d @ Prod )
          = ( produc6779600879576379960_b_c_d @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_105_prod__eqI,axiom,
    ! [P4: produc4534891791806675482_b_c_d,Q: produc4534891791806675482_b_c_d] :
      ( ( ( produc1447154562020694006_b_c_d @ P4 )
        = ( produc1447154562020694006_b_c_d @ Q ) )
     => ( ( ( produc6779600879576379960_b_c_d @ P4 )
          = ( produc6779600879576379960_b_c_d @ Q ) )
       => ( P4 = Q ) ) ) ).

% prod_eqI
thf(fact_106_prod__eq__iff,axiom,
    ( ( ^ [Y4: produc4534891791806675482_b_c_d,Z: produc4534891791806675482_b_c_d] : ( Y4 = Z ) )
    = ( ^ [S: produc4534891791806675482_b_c_d,T2: produc4534891791806675482_b_c_d] :
          ( ( ( produc1447154562020694006_b_c_d @ S )
            = ( produc1447154562020694006_b_c_d @ T2 ) )
          & ( ( produc6779600879576379960_b_c_d @ S )
            = ( produc6779600879576379960_b_c_d @ T2 ) ) ) ) ) ).

% prod_eq_iff
thf(fact_107_prod_Oexhaust__sel,axiom,
    ! [Prod: product_prod_b_c] :
      ( Prod
      = ( product_Pair_b_c @ ( product_fst_b_c @ Prod ) @ ( product_snd_b_c @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_108_prod_Oexhaust__sel,axiom,
    ! [Prod: produc4534891791806675482_b_c_d] :
      ( Prod
      = ( produc2511600812177743882_b_c_d @ ( produc1447154562020694006_b_c_d @ Prod ) @ ( produc6779600879576379960_b_c_d @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_109_surjective__pairing,axiom,
    ! [T3: product_prod_b_c] :
      ( T3
      = ( product_Pair_b_c @ ( product_fst_b_c @ T3 ) @ ( product_snd_b_c @ T3 ) ) ) ).

% surjective_pairing
thf(fact_110_surjective__pairing,axiom,
    ! [T3: produc4534891791806675482_b_c_d] :
      ( T3
      = ( produc2511600812177743882_b_c_d @ ( produc1447154562020694006_b_c_d @ T3 ) @ ( produc6779600879576379960_b_c_d @ T3 ) ) ) ).

% surjective_pairing
thf(fact_111_exI__realizer,axiom,
    ! [P: c > b > $o,Y: c,X: b] :
      ( ( P @ Y @ X )
     => ( P @ ( product_snd_b_c @ ( product_Pair_b_c @ X @ Y ) ) @ ( product_fst_b_c @ ( product_Pair_b_c @ X @ Y ) ) ) ) ).

% exI_realizer
thf(fact_112_exI__realizer,axiom,
    ! [P: d > prefix425356687782099470od_b_c > $o,Y: d,X: prefix425356687782099470od_b_c] :
      ( ( P @ Y @ X )
     => ( P @ ( produc6779600879576379960_b_c_d @ ( produc2511600812177743882_b_c_d @ X @ Y ) ) @ ( produc1447154562020694006_b_c_d @ ( produc2511600812177743882_b_c_d @ X @ Y ) ) ) ) ).

% exI_realizer
thf(fact_113_conjI__realizer,axiom,
    ! [P: b > $o,P4: b,Q3: c > $o,Q: c] :
      ( ( P @ P4 )
     => ( ( Q3 @ Q )
       => ( ( P @ ( product_fst_b_c @ ( product_Pair_b_c @ P4 @ Q ) ) )
          & ( Q3 @ ( product_snd_b_c @ ( product_Pair_b_c @ P4 @ Q ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_114_conjI__realizer,axiom,
    ! [P: prefix425356687782099470od_b_c > $o,P4: prefix425356687782099470od_b_c,Q3: d > $o,Q: d] :
      ( ( P @ P4 )
     => ( ( Q3 @ Q )
       => ( ( P @ ( produc1447154562020694006_b_c_d @ ( produc2511600812177743882_b_c_d @ P4 @ Q ) ) )
          & ( Q3 @ ( produc6779600879576379960_b_c_d @ ( produc2511600812177743882_b_c_d @ P4 @ Q ) ) ) ) ) ) ).

% conjI_realizer
thf(fact_115_state__cover__transition__converges,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,V: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,T3: produc596031391177498678od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( state_2362830510734323903_c_b_c @ M @ V )
       => ( ( member8124909232574984543od_b_c @ T3 @ ( transi3161963839906981764_c_b_c @ M ) )
         => ( ( member6330420149250801815od_b_c @ ( produc5084291339869529746od_b_c @ T3 ) @ ( reacha8116992257183400179_c_b_c @ M ) )
           => ( conver6852411701971397450_c_b_c @ M @ ( append2547753245680614915od_b_c @ ( V @ ( produc5084291339869529746od_b_c @ T3 ) ) @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc4488652850390612441od_b_c @ ( produc829356566976367572od_b_c @ T3 ) ) @ ( produc5388473464130769137od_b_c @ ( produc3182598933741882395od_b_c @ ( produc829356566976367572od_b_c @ T3 ) ) ) ) @ nil_Product_prod_b_c ) ) @ ( V @ ( produc8475728678562477363od_b_c @ ( produc3182598933741882395od_b_c @ ( produc829356566976367572od_b_c @ T3 ) ) ) ) ) ) ) ) ) ).

% state_cover_transition_converges
thf(fact_116_state__cover__transition__converges,axiom,
    ! [M: fsm_b_b_c,V: b > list_P903359562653991662od_b_c,T3: produc5320802312496131830od_c_b] :
      ( ( observable_b_b_c @ M )
     => ( ( state_4045177151805148240_b_b_c @ M @ V )
       => ( ( member8152910379392791327od_c_b @ T3 @ ( transitions_b_b_c @ M ) )
         => ( ( member_b @ ( produc245660266982166738od_c_b @ T3 ) @ ( reacha7216524145940060804_b_b_c @ M ) )
           => ( converge_b_b_c @ M @ ( append2547753245680614915od_b_c @ ( V @ ( produc245660266982166738od_c_b @ T3 ) ) @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949079049814378od_c_b @ ( produc4107847022047063060od_c_b @ T3 ) ) @ ( product_fst_c_b @ ( produc5221446328463814316od_c_b @ ( produc4107847022047063060od_c_b @ T3 ) ) ) ) @ nil_Product_prod_b_c ) ) @ ( V @ ( product_snd_c_b @ ( produc5221446328463814316od_c_b @ ( produc4107847022047063060od_c_b @ T3 ) ) ) ) ) ) ) ) ) ).

% state_cover_transition_converges
thf(fact_117_state__cover__transition__converges,axiom,
    ! [M: fsm_c_b_c,V: c > list_P903359562653991662od_b_c,T3: produc7971672423680061878od_c_c] :
      ( ( observable_c_b_c @ M )
     => ( ( state_418023730138503121_c_b_c @ M @ V )
       => ( ( member1580408453721945567od_c_c @ T3 @ ( transitions_c_b_c @ M ) )
         => ( ( member_c @ ( produc5488748936501478418od_c_c @ T3 ) @ ( reacha3589370724273415685_c_b_c @ M ) )
           => ( converge_c_b_c @ M @ ( append2547753245680614915od_b_c @ ( V @ ( produc5488748936501478418od_c_c @ T3 ) ) @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949083353043179od_c_c @ ( produc127563654711598932od_c_c @ T3 ) ) @ ( product_fst_c_c @ ( produc5221446332767043117od_c_c @ ( produc127563654711598932od_c_c @ T3 ) ) ) ) @ nil_Product_prod_b_c ) ) @ ( V @ ( product_snd_c_c @ ( produc5221446332767043117od_c_c @ ( produc127563654711598932od_c_c @ T3 ) ) ) ) ) ) ) ) ) ).

% state_cover_transition_converges
thf(fact_118_state__cover__transition__converges,axiom,
    ! [M: fsm_e_b_c,V: e > list_P903359562653991662od_b_c,T3: produc4050040609193146166od_c_e] :
      ( ( observable_e_b_c @ M )
     => ( ( state_2387088923659988691_e_b_c @ M @ V )
       => ( ( member6882148676089805663od_c_e @ T3 @ ( transitions_e_b_c @ M ) )
         => ( ( member_e @ ( produc6751554238685325970od_c_e @ T3 ) @ ( reacha5558435917794901255_e_b_c @ M ) )
           => ( converge_e_b_c @ M @ ( append2547753245680614915od_b_c @ ( V @ ( produc6751554238685325970od_c_e @ T3 ) ) @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) @ ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) ) ) @ nil_Product_prod_b_c ) ) @ ( V @ ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) ) ) ) ) ) ) ) ).

% state_cover_transition_converges
thf(fact_119_state__cover__transition__converges,axiom,
    ! [M: fsm_a_b_c,V: a > list_P903359562653991662od_b_c,T3: produc2669932201312201782od_c_a] :
      ( ( observable_a_b_c @ M )
     => ( ( state_7672330573471793359_a_b_c @ M @ V )
       => ( ( member5502040268208861279od_c_a @ T3 @ ( transitions_a_b_c @ M ) )
         => ( ( member_a @ ( produc4225943634317630866od_c_a @ T3 ) @ ( reacha1620305530751930115_a_b_c @ M ) )
           => ( converge_a_b_c @ M @ ( append2547753245680614915od_b_c @ ( V @ ( produc4225943634317630866od_c_a @ T3 ) ) @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) ) ) @ nil_Product_prod_b_c ) ) @ ( V @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) ) ) ) ) ) ) ) ).

% state_cover_transition_converges
thf(fact_120_map__entry_Oelims,axiom,
    ! [X: b,Xa: c > c,Xb: list_P903359562653991662od_b_c,Y: list_P903359562653991662od_b_c] :
      ( ( ( map_entry_b_c @ X @ Xa @ Xb )
        = Y )
     => ( ( ( Xb = nil_Product_prod_b_c )
         => ( Y != nil_Product_prod_b_c ) )
       => ~ ! [P2: product_prod_b_c,Ps: list_P903359562653991662od_b_c] :
              ( ( Xb
                = ( cons_P4529483553340347422od_b_c @ P2 @ Ps ) )
             => ~ ( ( ( ( product_fst_b_c @ P2 )
                      = X )
                   => ( Y
                      = ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ ( Xa @ ( product_snd_b_c @ P2 ) ) ) @ Ps ) ) )
                  & ( ( ( product_fst_b_c @ P2 )
                     != X )
                   => ( Y
                      = ( cons_P4529483553340347422od_b_c @ P2 @ ( map_entry_b_c @ X @ Xa @ Ps ) ) ) ) ) ) ) ) ).

% map_entry.elims
thf(fact_121_map__entry_Oelims,axiom,
    ! [X: prefix425356687782099470od_b_c,Xa: d > d,Xb: list_P197655048861356576_b_c_d,Y: list_P197655048861356576_b_c_d] :
      ( ( ( map_en7111768261497259452_b_c_d @ X @ Xa @ Xb )
        = Y )
     => ( ( ( Xb = nil_Pr3869772434330527008_b_c_d )
         => ( Y != nil_Pr3869772434330527008_b_c_d ) )
       => ~ ! [P2: produc4534891791806675482_b_c_d,Ps: list_P197655048861356576_b_c_d] :
              ( ( Xb
                = ( cons_P1373155234573727952_b_c_d @ P2 @ Ps ) )
             => ~ ( ( ( ( produc1447154562020694006_b_c_d @ P2 )
                      = X )
                   => ( Y
                      = ( cons_P1373155234573727952_b_c_d @ ( produc2511600812177743882_b_c_d @ X @ ( Xa @ ( produc6779600879576379960_b_c_d @ P2 ) ) ) @ Ps ) ) )
                  & ( ( ( produc1447154562020694006_b_c_d @ P2 )
                     != X )
                   => ( Y
                      = ( cons_P1373155234573727952_b_c_d @ P2 @ ( map_en7111768261497259452_b_c_d @ X @ Xa @ Ps ) ) ) ) ) ) ) ) ).

% map_entry.elims
thf(fact_122_map__default_Oelims,axiom,
    ! [X: b,Xa: c,Xb: c > c,Xc: list_P903359562653991662od_b_c,Y: list_P903359562653991662od_b_c] :
      ( ( ( map_default_b_c @ X @ Xa @ Xb @ Xc )
        = Y )
     => ( ( ( Xc = nil_Product_prod_b_c )
         => ( Y
           != ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Xa ) @ nil_Product_prod_b_c ) ) )
       => ~ ! [P2: product_prod_b_c,Ps: list_P903359562653991662od_b_c] :
              ( ( Xc
                = ( cons_P4529483553340347422od_b_c @ P2 @ Ps ) )
             => ~ ( ( ( ( product_fst_b_c @ P2 )
                      = X )
                   => ( Y
                      = ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ ( Xb @ ( product_snd_b_c @ P2 ) ) ) @ Ps ) ) )
                  & ( ( ( product_fst_b_c @ P2 )
                     != X )
                   => ( Y
                      = ( cons_P4529483553340347422od_b_c @ P2 @ ( map_default_b_c @ X @ Xa @ Xb @ Ps ) ) ) ) ) ) ) ) ).

% map_default.elims
thf(fact_123_map__default_Oelims,axiom,
    ! [X: prefix425356687782099470od_b_c,Xa: d,Xb: d > d,Xc: list_P197655048861356576_b_c_d,Y: list_P197655048861356576_b_c_d] :
      ( ( ( map_de7650936251494337739_b_c_d @ X @ Xa @ Xb @ Xc )
        = Y )
     => ( ( ( Xc = nil_Pr3869772434330527008_b_c_d )
         => ( Y
           != ( cons_P1373155234573727952_b_c_d @ ( produc2511600812177743882_b_c_d @ X @ Xa ) @ nil_Pr3869772434330527008_b_c_d ) ) )
       => ~ ! [P2: produc4534891791806675482_b_c_d,Ps: list_P197655048861356576_b_c_d] :
              ( ( Xc
                = ( cons_P1373155234573727952_b_c_d @ P2 @ Ps ) )
             => ~ ( ( ( ( produc1447154562020694006_b_c_d @ P2 )
                      = X )
                   => ( Y
                      = ( cons_P1373155234573727952_b_c_d @ ( produc2511600812177743882_b_c_d @ X @ ( Xb @ ( produc6779600879576379960_b_c_d @ P2 ) ) ) @ Ps ) ) )
                  & ( ( ( produc1447154562020694006_b_c_d @ P2 )
                     != X )
                   => ( Y
                      = ( cons_P1373155234573727952_b_c_d @ P2 @ ( map_de7650936251494337739_b_c_d @ X @ Xa @ Xb @ Ps ) ) ) ) ) ) ) ) ).

% map_default.elims
thf(fact_124_suffixes_Oelims,axiom,
    ! [X: list_P903359562653991662od_b_c,Y: list_l8907847357763382004od_b_c] :
      ( ( ( suffix2151784340763841114od_b_c @ X )
        = Y )
     => ( ( ( X = nil_Product_prod_b_c )
         => ( Y
           != ( cons_l342771267123639716od_b_c @ nil_Product_prod_b_c @ nil_li8071162985807626740od_b_c ) ) )
       => ~ ! [X2: product_prod_b_c,Xs2: list_P903359562653991662od_b_c] :
              ( ( X
                = ( cons_P4529483553340347422od_b_c @ X2 @ Xs2 ) )
             => ( Y
               != ( append6992831555715836169od_b_c @ ( suffix2151784340763841114od_b_c @ Xs2 ) @ ( cons_l342771267123639716od_b_c @ ( cons_P4529483553340347422od_b_c @ X2 @ Xs2 ) @ nil_li8071162985807626740od_b_c ) ) ) ) ) ) ).

% suffixes.elims
thf(fact_125_finite__tree__set__eq,axiom,
    ! [T1: prefix425356687782099470od_b_c,T22: prefix425356687782099470od_b_c] :
      ( ( ( prefix9085958534787526401od_b_c @ T1 )
        = ( prefix9085958534787526401od_b_c @ T22 ) )
     => ( ( prefix6767660319289835678od_b_c @ T1 )
       => ( T1 = T22 ) ) ) ).

% finite_tree_set_eq
thf(fact_126_update__with__aux_Osimps_I2_J,axiom,
    ! [P4: product_prod_b_c,K3: b,V3: c,F: c > c,Ps2: list_P903359562653991662od_b_c] :
      ( ( ( ( product_fst_b_c @ P4 )
          = K3 )
       => ( ( update_with_aux_c_b @ V3 @ K3 @ F @ ( cons_P4529483553340347422od_b_c @ P4 @ Ps2 ) )
          = ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ K3 @ ( F @ ( product_snd_b_c @ P4 ) ) ) @ Ps2 ) ) )
      & ( ( ( product_fst_b_c @ P4 )
         != K3 )
       => ( ( update_with_aux_c_b @ V3 @ K3 @ F @ ( cons_P4529483553340347422od_b_c @ P4 @ Ps2 ) )
          = ( cons_P4529483553340347422od_b_c @ P4 @ ( update_with_aux_c_b @ V3 @ K3 @ F @ Ps2 ) ) ) ) ) ).

% update_with_aux.simps(2)
thf(fact_127_update__with__aux_Osimps_I2_J,axiom,
    ! [P4: produc4534891791806675482_b_c_d,K3: prefix425356687782099470od_b_c,V3: d,F: d > d,Ps2: list_P197655048861356576_b_c_d] :
      ( ( ( ( produc1447154562020694006_b_c_d @ P4 )
          = K3 )
       => ( ( update6326457734613818831od_b_c @ V3 @ K3 @ F @ ( cons_P1373155234573727952_b_c_d @ P4 @ Ps2 ) )
          = ( cons_P1373155234573727952_b_c_d @ ( produc2511600812177743882_b_c_d @ K3 @ ( F @ ( produc6779600879576379960_b_c_d @ P4 ) ) ) @ Ps2 ) ) )
      & ( ( ( produc1447154562020694006_b_c_d @ P4 )
         != K3 )
       => ( ( update6326457734613818831od_b_c @ V3 @ K3 @ F @ ( cons_P1373155234573727952_b_c_d @ P4 @ Ps2 ) )
          = ( cons_P1373155234573727952_b_c_d @ P4 @ ( update6326457734613818831od_b_c @ V3 @ K3 @ F @ Ps2 ) ) ) ) ) ).

% update_with_aux.simps(2)
thf(fact_128_fsm__transition__input,axiom,
    ! [T3: produc2669932201312201782od_c_a,M: fsm_a_b_c] :
      ( ( member5502040268208861279od_c_a @ T3 @ ( transitions_a_b_c @ M ) )
     => ( member_b @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) @ ( inputs_a_b_c @ M ) ) ) ).

% fsm_transition_input
thf(fact_129_fsm__transition__input,axiom,
    ! [T3: produc4050040609193146166od_c_e,M: fsm_e_b_c] :
      ( ( member6882148676089805663od_c_e @ T3 @ ( transitions_e_b_c @ M ) )
     => ( member_b @ ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) @ ( inputs_e_b_c @ M ) ) ) ).

% fsm_transition_input
thf(fact_130_fsm__transition__output,axiom,
    ! [T3: produc2669932201312201782od_c_a,M: fsm_a_b_c] :
      ( ( member5502040268208861279od_c_a @ T3 @ ( transitions_a_b_c @ M ) )
     => ( member_c @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) ) @ ( outputs_a_b_c @ M ) ) ) ).

% fsm_transition_output
thf(fact_131_fsm__transition__output,axiom,
    ! [T3: produc4050040609193146166od_c_e,M: fsm_e_b_c] :
      ( ( member6882148676089805663od_c_e @ T3 @ ( transitions_e_b_c @ M ) )
     => ( member_c @ ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) ) @ ( outputs_e_b_c @ M ) ) ) ).

% fsm_transition_output
thf(fact_132_reachable__states__next,axiom,
    ! [Q: a,M: fsm_a_b_c,T3: produc2669932201312201782od_c_a] :
      ( ( member_a @ Q @ ( reacha1620305530751930115_a_b_c @ M ) )
     => ( ( member5502040268208861279od_c_a @ T3 @ ( transitions_a_b_c @ M ) )
       => ( ( ( produc4225943634317630866od_c_a @ T3 )
            = Q )
         => ( member_a @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) ) @ ( reacha1620305530751930115_a_b_c @ M ) ) ) ) ) ).

% reachable_states_next
thf(fact_133_observable__transition__unique,axiom,
    ! [M: fsm_a_b_c,T3: produc2669932201312201782od_c_a] :
      ( ( observable_a_b_c @ M )
     => ( ( member5502040268208861279od_c_a @ T3 @ ( transitions_a_b_c @ M ) )
       => ? [X2: produc2669932201312201782od_c_a] :
            ( ( member5502040268208861279od_c_a @ X2 @ ( transitions_a_b_c @ M ) )
            & ( ( produc4225943634317630866od_c_a @ X2 )
              = ( produc4225943634317630866od_c_a @ T3 ) )
            & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) )
              = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) )
            & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) ) )
              = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) ) )
            & ! [Y5: produc2669932201312201782od_c_a] :
                ( ( ( member5502040268208861279od_c_a @ Y5 @ ( transitions_a_b_c @ M ) )
                  & ( ( produc4225943634317630866od_c_a @ Y5 )
                    = ( produc4225943634317630866od_c_a @ T3 ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Y5 ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) )
                  & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Y5 ) ) )
                    = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) ) ) )
               => ( Y5 = X2 ) ) ) ) ) ).

% observable_transition_unique
thf(fact_134_observable__transition__unique,axiom,
    ! [M: fsm_e_b_c,T3: produc4050040609193146166od_c_e] :
      ( ( observable_e_b_c @ M )
     => ( ( member6882148676089805663od_c_e @ T3 @ ( transitions_e_b_c @ M ) )
       => ? [X2: produc4050040609193146166od_c_e] :
            ( ( member6882148676089805663od_c_e @ X2 @ ( transitions_e_b_c @ M ) )
            & ( ( produc6751554238685325970od_c_e @ X2 )
              = ( produc6751554238685325970od_c_e @ T3 ) )
            & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ X2 ) )
              = ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) )
            & ( ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ X2 ) ) )
              = ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) ) )
            & ! [Y5: produc4050040609193146166od_c_e] :
                ( ( ( member6882148676089805663od_c_e @ Y5 @ ( transitions_e_b_c @ M ) )
                  & ( ( produc6751554238685325970od_c_e @ Y5 )
                    = ( produc6751554238685325970od_c_e @ T3 ) )
                  & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Y5 ) )
                    = ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) )
                  & ( ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ Y5 ) ) )
                    = ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) ) ) )
               => ( Y5 = X2 ) ) ) ) ) ).

% observable_transition_unique
thf(fact_135_map__entry_Osimps_I1_J,axiom,
    ! [K3: b,F: c > c] :
      ( ( map_entry_b_c @ K3 @ F @ nil_Product_prod_b_c )
      = nil_Product_prod_b_c ) ).

% map_entry.simps(1)
thf(fact_136_observable_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ~ ( observable_a_b_c @ X )
     => ~ ! [X2: produc2669932201312201782od_c_a] :
            ( ( member5502040268208861279od_c_a @ X2 @ ( transitions_a_b_c @ X ) )
           => ! [Xa2: produc2669932201312201782od_c_a] :
                ( ( member5502040268208861279od_c_a @ Xa2 @ ( transitions_a_b_c @ X ) )
               => ( ( ( ( produc4225943634317630866od_c_a @ X2 )
                      = ( produc4225943634317630866od_c_a @ Xa2 ) )
                    & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) )
                      = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xa2 ) ) )
                    & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) ) )
                      = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa2 ) ) ) ) )
                 => ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) ) )
                    = ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa2 ) ) ) ) ) ) ) ) ).

% observable.elims(3)
thf(fact_137_observable_Oelims_I3_J,axiom,
    ! [X: fsm_e_b_c] :
      ( ~ ( observable_e_b_c @ X )
     => ~ ! [X2: produc4050040609193146166od_c_e] :
            ( ( member6882148676089805663od_c_e @ X2 @ ( transitions_e_b_c @ X ) )
           => ! [Xa2: produc4050040609193146166od_c_e] :
                ( ( member6882148676089805663od_c_e @ Xa2 @ ( transitions_e_b_c @ X ) )
               => ( ( ( ( produc6751554238685325970od_c_e @ X2 )
                      = ( produc6751554238685325970od_c_e @ Xa2 ) )
                    & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ X2 ) )
                      = ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Xa2 ) ) )
                    & ( ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ X2 ) ) )
                      = ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ Xa2 ) ) ) ) )
                 => ( ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ X2 ) ) )
                    = ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ Xa2 ) ) ) ) ) ) ) ) ).

% observable.elims(3)
thf(fact_138_observable_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ( observable_a_b_c @ X )
     => ! [X4: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X4 @ ( transitions_a_b_c @ X ) )
         => ! [Xa3: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Xa3 @ ( transitions_a_b_c @ X ) )
             => ( ( ( ( produc4225943634317630866od_c_a @ X4 )
                    = ( produc4225943634317630866od_c_a @ Xa3 ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X4 ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xa3 ) ) )
                  & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X4 ) ) )
                    = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa3 ) ) ) ) )
               => ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X4 ) ) )
                  = ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa3 ) ) ) ) ) ) ) ) ).

% observable.elims(2)
thf(fact_139_observable_Oelims_I2_J,axiom,
    ! [X: fsm_e_b_c] :
      ( ( observable_e_b_c @ X )
     => ! [X4: produc4050040609193146166od_c_e] :
          ( ( member6882148676089805663od_c_e @ X4 @ ( transitions_e_b_c @ X ) )
         => ! [Xa3: produc4050040609193146166od_c_e] :
              ( ( member6882148676089805663od_c_e @ Xa3 @ ( transitions_e_b_c @ X ) )
             => ( ( ( ( produc6751554238685325970od_c_e @ X4 )
                    = ( produc6751554238685325970od_c_e @ Xa3 ) )
                  & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ X4 ) )
                    = ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Xa3 ) ) )
                  & ( ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ X4 ) ) )
                    = ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ Xa3 ) ) ) ) )
               => ( ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ X4 ) ) )
                  = ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ Xa3 ) ) ) ) ) ) ) ) ).

% observable.elims(2)
thf(fact_140_observable_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Y: $o] :
      ( ( ( observable_a_b_c @ X )
        = Y )
     => ( Y
        = ( ! [X3: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ X3 @ ( transitions_a_b_c @ X ) )
             => ! [Y3: produc2669932201312201782od_c_a] :
                  ( ( member5502040268208861279od_c_a @ Y3 @ ( transitions_a_b_c @ X ) )
                 => ( ( ( ( produc4225943634317630866od_c_a @ X3 )
                        = ( produc4225943634317630866od_c_a @ Y3 ) )
                      & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) )
                        = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Y3 ) ) )
                      & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) ) )
                        = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Y3 ) ) ) ) )
                   => ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) ) )
                      = ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Y3 ) ) ) ) ) ) ) ) ) ) ).

% observable.elims(1)
thf(fact_141_observable_Oelims_I1_J,axiom,
    ! [X: fsm_e_b_c,Y: $o] :
      ( ( ( observable_e_b_c @ X )
        = Y )
     => ( Y
        = ( ! [X3: produc4050040609193146166od_c_e] :
              ( ( member6882148676089805663od_c_e @ X3 @ ( transitions_e_b_c @ X ) )
             => ! [Y3: produc4050040609193146166od_c_e] :
                  ( ( member6882148676089805663od_c_e @ Y3 @ ( transitions_e_b_c @ X ) )
                 => ( ( ( ( produc6751554238685325970od_c_e @ X3 )
                        = ( produc6751554238685325970od_c_e @ Y3 ) )
                      & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ X3 ) )
                        = ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Y3 ) ) )
                      & ( ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ X3 ) ) )
                        = ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ Y3 ) ) ) ) )
                   => ( ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ X3 ) ) )
                      = ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ Y3 ) ) ) ) ) ) ) ) ) ) ).

% observable.elims(1)
thf(fact_142_observable_Osimps,axiom,
    ( observable_a_b_c
    = ( ^ [M2: fsm_a_b_c] :
        ! [X3: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X3 @ ( transitions_a_b_c @ M2 ) )
         => ! [Y3: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Y3 @ ( transitions_a_b_c @ M2 ) )
             => ( ( ( ( produc4225943634317630866od_c_a @ X3 )
                    = ( produc4225943634317630866od_c_a @ Y3 ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Y3 ) ) )
                  & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) ) )
                    = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Y3 ) ) ) ) )
               => ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) ) )
                  = ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Y3 ) ) ) ) ) ) ) ) ) ).

% observable.simps
thf(fact_143_observable_Osimps,axiom,
    ( observable_e_b_c
    = ( ^ [M2: fsm_e_b_c] :
        ! [X3: produc4050040609193146166od_c_e] :
          ( ( member6882148676089805663od_c_e @ X3 @ ( transitions_e_b_c @ M2 ) )
         => ! [Y3: produc4050040609193146166od_c_e] :
              ( ( member6882148676089805663od_c_e @ Y3 @ ( transitions_e_b_c @ M2 ) )
             => ( ( ( ( produc6751554238685325970od_c_e @ X3 )
                    = ( produc6751554238685325970od_c_e @ Y3 ) )
                  & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ X3 ) )
                    = ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Y3 ) ) )
                  & ( ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ X3 ) ) )
                    = ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ Y3 ) ) ) ) )
               => ( ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ X3 ) ) )
                  = ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ Y3 ) ) ) ) ) ) ) ) ) ).

% observable.simps
thf(fact_144_observable__alt__def,axiom,
    ( observable_a_b_c
    = ( ^ [M2: fsm_a_b_c] :
        ! [Q12: a,X3: b,Y3: c,Q13: a,Q14: a] :
          ( ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q12 @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ Q13 ) ) ) @ ( transitions_a_b_c @ M2 ) )
            & ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q12 @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ Q14 ) ) ) @ ( transitions_a_b_c @ M2 ) ) )
         => ( Q13 = Q14 ) ) ) ) ).

% observable_alt_def
thf(fact_145_observable__alt__def,axiom,
    ( observable_e_b_c
    = ( ^ [M2: fsm_e_b_c] :
        ! [Q12: e,X3: b,Y3: c,Q13: e,Q14: e] :
          ( ( ( member6882148676089805663od_c_e @ ( produc8288412161402371238od_c_e @ Q12 @ ( produc3440865931213796865od_c_e @ X3 @ ( product_Pair_c_e @ Y3 @ Q13 ) ) ) @ ( transitions_e_b_c @ M2 ) )
            & ( member6882148676089805663od_c_e @ ( produc8288412161402371238od_c_e @ Q12 @ ( produc3440865931213796865od_c_e @ X3 @ ( product_Pair_c_e @ Y3 @ Q14 ) ) ) @ ( transitions_e_b_c @ M2 ) ) )
         => ( Q13 = Q14 ) ) ) ) ).

% observable_alt_def
thf(fact_146_map__default_Osimps_I1_J,axiom,
    ! [K3: b,V3: c,F: c > c] :
      ( ( map_default_b_c @ K3 @ V3 @ F @ nil_Product_prod_b_c )
      = ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ K3 @ V3 ) @ nil_Product_prod_b_c ) ) ).

% map_default.simps(1)
thf(fact_147_update__with__aux_Osimps_I1_J,axiom,
    ! [V3: c,K3: b,F: c > c] :
      ( ( update_with_aux_c_b @ V3 @ K3 @ F @ nil_Product_prod_b_c )
      = ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ K3 @ ( F @ V3 ) ) @ nil_Product_prod_b_c ) ) ).

% update_with_aux.simps(1)
thf(fact_148_Util_Osuffixes_Osimps_I2_J,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( suffix2151784340763841114od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) )
      = ( append6992831555715836169od_b_c @ ( suffix2151784340763841114od_b_c @ Xs ) @ ( cons_l342771267123639716od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) @ nil_li8071162985807626740od_b_c ) ) ) ).

% Util.suffixes.simps(2)
thf(fact_149_Util_Osuffixes_Osimps_I1_J,axiom,
    ( ( suffix2151784340763841114od_b_c @ nil_Product_prod_b_c )
    = ( cons_l342771267123639716od_b_c @ nil_Product_prod_b_c @ nil_li8071162985807626740od_b_c ) ) ).

% Util.suffixes.simps(1)
thf(fact_150_exE__realizer_H,axiom,
    ! [P: d > prefix425356687782099470od_b_c > $o,P4: produc4534891791806675482_b_c_d] :
      ( ( P @ ( produc6779600879576379960_b_c_d @ P4 ) @ ( produc1447154562020694006_b_c_d @ P4 ) )
     => ~ ! [X2: prefix425356687782099470od_b_c,Y2: d] :
            ~ ( P @ Y2 @ X2 ) ) ).

% exE_realizer'
thf(fact_151_map__default_Osimps_I2_J,axiom,
    ! [P4: product_prod_b_c,K3: b,V3: c,F: c > c,Ps2: list_P903359562653991662od_b_c] :
      ( ( ( ( product_fst_b_c @ P4 )
          = K3 )
       => ( ( map_default_b_c @ K3 @ V3 @ F @ ( cons_P4529483553340347422od_b_c @ P4 @ Ps2 ) )
          = ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ K3 @ ( F @ ( product_snd_b_c @ P4 ) ) ) @ Ps2 ) ) )
      & ( ( ( product_fst_b_c @ P4 )
         != K3 )
       => ( ( map_default_b_c @ K3 @ V3 @ F @ ( cons_P4529483553340347422od_b_c @ P4 @ Ps2 ) )
          = ( cons_P4529483553340347422od_b_c @ P4 @ ( map_default_b_c @ K3 @ V3 @ F @ Ps2 ) ) ) ) ) ).

% map_default.simps(2)
thf(fact_152_map__default_Osimps_I2_J,axiom,
    ! [P4: produc4534891791806675482_b_c_d,K3: prefix425356687782099470od_b_c,V3: d,F: d > d,Ps2: list_P197655048861356576_b_c_d] :
      ( ( ( ( produc1447154562020694006_b_c_d @ P4 )
          = K3 )
       => ( ( map_de7650936251494337739_b_c_d @ K3 @ V3 @ F @ ( cons_P1373155234573727952_b_c_d @ P4 @ Ps2 ) )
          = ( cons_P1373155234573727952_b_c_d @ ( produc2511600812177743882_b_c_d @ K3 @ ( F @ ( produc6779600879576379960_b_c_d @ P4 ) ) ) @ Ps2 ) ) )
      & ( ( ( produc1447154562020694006_b_c_d @ P4 )
         != K3 )
       => ( ( map_de7650936251494337739_b_c_d @ K3 @ V3 @ F @ ( cons_P1373155234573727952_b_c_d @ P4 @ Ps2 ) )
          = ( cons_P1373155234573727952_b_c_d @ P4 @ ( map_de7650936251494337739_b_c_d @ K3 @ V3 @ F @ Ps2 ) ) ) ) ) ).

% map_default.simps(2)
thf(fact_153_map__entry_Osimps_I2_J,axiom,
    ! [P4: product_prod_b_c,K3: b,F: c > c,Ps2: list_P903359562653991662od_b_c] :
      ( ( ( ( product_fst_b_c @ P4 )
          = K3 )
       => ( ( map_entry_b_c @ K3 @ F @ ( cons_P4529483553340347422od_b_c @ P4 @ Ps2 ) )
          = ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ K3 @ ( F @ ( product_snd_b_c @ P4 ) ) ) @ Ps2 ) ) )
      & ( ( ( product_fst_b_c @ P4 )
         != K3 )
       => ( ( map_entry_b_c @ K3 @ F @ ( cons_P4529483553340347422od_b_c @ P4 @ Ps2 ) )
          = ( cons_P4529483553340347422od_b_c @ P4 @ ( map_entry_b_c @ K3 @ F @ Ps2 ) ) ) ) ) ).

% map_entry.simps(2)
thf(fact_154_map__entry_Osimps_I2_J,axiom,
    ! [P4: produc4534891791806675482_b_c_d,K3: prefix425356687782099470od_b_c,F: d > d,Ps2: list_P197655048861356576_b_c_d] :
      ( ( ( ( produc1447154562020694006_b_c_d @ P4 )
          = K3 )
       => ( ( map_en7111768261497259452_b_c_d @ K3 @ F @ ( cons_P1373155234573727952_b_c_d @ P4 @ Ps2 ) )
          = ( cons_P1373155234573727952_b_c_d @ ( produc2511600812177743882_b_c_d @ K3 @ ( F @ ( produc6779600879576379960_b_c_d @ P4 ) ) ) @ Ps2 ) ) )
      & ( ( ( produc1447154562020694006_b_c_d @ P4 )
         != K3 )
       => ( ( map_en7111768261497259452_b_c_d @ K3 @ F @ ( cons_P1373155234573727952_b_c_d @ P4 @ Ps2 ) )
          = ( cons_P1373155234573727952_b_c_d @ P4 @ ( map_en7111768261497259452_b_c_d @ K3 @ F @ Ps2 ) ) ) ) ) ).

% map_entry.simps(2)
thf(fact_155_set__Nil,axiom,
    ! [T3: prefix425356687782099470od_b_c] : ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ ( prefix9085958534787526401od_b_c @ T3 ) ) ).

% set_Nil
thf(fact_156_set__prefix,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,T: prefix425356687782099470od_b_c] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Xs @ Ys ) @ ( prefix9085958534787526401od_b_c @ T ) )
     => ( member6330420149250801815od_b_c @ Xs @ ( prefix9085958534787526401od_b_c @ T ) ) ) ).

% set_prefix
thf(fact_157_output__complete_Osimps,axiom,
    ( output3834324022317553264_a_b_c
    = ( ^ [M2: fsm_a_b_c] :
        ! [X3: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X3 @ ( transitions_a_b_c @ M2 ) )
         => ! [Y3: c] :
              ( ( member_c @ Y3 @ ( outputs_a_b_c @ M2 ) )
             => ? [Z2: produc2669932201312201782od_c_a] :
                  ( ( member5502040268208861279od_c_a @ Z2 @ ( transitions_a_b_c @ M2 ) )
                  & ( ( produc4225943634317630866od_c_a @ X3 )
                    = ( produc4225943634317630866od_c_a @ Z2 ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Z2 ) ) )
                  & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Z2 ) ) )
                    = Y3 ) ) ) ) ) ) ).

% output_complete.simps
thf(fact_158_output__complete_Osimps,axiom,
    ( output7772454409360524404_e_b_c
    = ( ^ [M2: fsm_e_b_c] :
        ! [X3: produc4050040609193146166od_c_e] :
          ( ( member6882148676089805663od_c_e @ X3 @ ( transitions_e_b_c @ M2 ) )
         => ! [Y3: c] :
              ( ( member_c @ Y3 @ ( outputs_e_b_c @ M2 ) )
             => ? [Z2: produc4050040609193146166od_c_e] :
                  ( ( member6882148676089805663od_c_e @ Z2 @ ( transitions_e_b_c @ M2 ) )
                  & ( ( produc6751554238685325970od_c_e @ X3 )
                    = ( produc6751554238685325970od_c_e @ Z2 ) )
                  & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ X3 ) )
                    = ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Z2 ) ) )
                  & ( ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ Z2 ) ) )
                    = Y3 ) ) ) ) ) ) ).

% output_complete.simps
thf(fact_159_output__complete_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Y: $o] :
      ( ( ( output3834324022317553264_a_b_c @ X )
        = Y )
     => ( Y
        = ( ! [X3: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ X3 @ ( transitions_a_b_c @ X ) )
             => ! [Y3: c] :
                  ( ( member_c @ Y3 @ ( outputs_a_b_c @ X ) )
                 => ? [Z2: produc2669932201312201782od_c_a] :
                      ( ( member5502040268208861279od_c_a @ Z2 @ ( transitions_a_b_c @ X ) )
                      & ( ( produc4225943634317630866od_c_a @ X3 )
                        = ( produc4225943634317630866od_c_a @ Z2 ) )
                      & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) )
                        = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Z2 ) ) )
                      & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Z2 ) ) )
                        = Y3 ) ) ) ) ) ) ) ).

% output_complete.elims(1)
thf(fact_160_output__complete_Oelims_I1_J,axiom,
    ! [X: fsm_e_b_c,Y: $o] :
      ( ( ( output7772454409360524404_e_b_c @ X )
        = Y )
     => ( Y
        = ( ! [X3: produc4050040609193146166od_c_e] :
              ( ( member6882148676089805663od_c_e @ X3 @ ( transitions_e_b_c @ X ) )
             => ! [Y3: c] :
                  ( ( member_c @ Y3 @ ( outputs_e_b_c @ X ) )
                 => ? [Z2: produc4050040609193146166od_c_e] :
                      ( ( member6882148676089805663od_c_e @ Z2 @ ( transitions_e_b_c @ X ) )
                      & ( ( produc6751554238685325970od_c_e @ X3 )
                        = ( produc6751554238685325970od_c_e @ Z2 ) )
                      & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ X3 ) )
                        = ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Z2 ) ) )
                      & ( ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ Z2 ) ) )
                        = Y3 ) ) ) ) ) ) ) ).

% output_complete.elims(1)
thf(fact_161_output__complete_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ( output3834324022317553264_a_b_c @ X )
     => ! [X4: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X4 @ ( transitions_a_b_c @ X ) )
         => ! [Xa3: c] :
              ( ( member_c @ Xa3 @ ( outputs_a_b_c @ X ) )
             => ? [Xb2: produc2669932201312201782od_c_a] :
                  ( ( member5502040268208861279od_c_a @ Xb2 @ ( transitions_a_b_c @ X ) )
                  & ( ( produc4225943634317630866od_c_a @ X4 )
                    = ( produc4225943634317630866od_c_a @ Xb2 ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X4 ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xb2 ) ) )
                  & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xb2 ) ) )
                    = Xa3 ) ) ) ) ) ).

% output_complete.elims(2)
thf(fact_162_output__complete_Oelims_I2_J,axiom,
    ! [X: fsm_e_b_c] :
      ( ( output7772454409360524404_e_b_c @ X )
     => ! [X4: produc4050040609193146166od_c_e] :
          ( ( member6882148676089805663od_c_e @ X4 @ ( transitions_e_b_c @ X ) )
         => ! [Xa3: c] :
              ( ( member_c @ Xa3 @ ( outputs_e_b_c @ X ) )
             => ? [Xb2: produc4050040609193146166od_c_e] :
                  ( ( member6882148676089805663od_c_e @ Xb2 @ ( transitions_e_b_c @ X ) )
                  & ( ( produc6751554238685325970od_c_e @ X4 )
                    = ( produc6751554238685325970od_c_e @ Xb2 ) )
                  & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ X4 ) )
                    = ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Xb2 ) ) )
                  & ( ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ Xb2 ) ) )
                    = Xa3 ) ) ) ) ) ).

% output_complete.elims(2)
thf(fact_163_output__complete_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ~ ( output3834324022317553264_a_b_c @ X )
     => ~ ! [X2: produc2669932201312201782od_c_a] :
            ( ( member5502040268208861279od_c_a @ X2 @ ( transitions_a_b_c @ X ) )
           => ! [Xa2: c] :
                ( ( member_c @ Xa2 @ ( outputs_a_b_c @ X ) )
               => ? [Xb3: produc2669932201312201782od_c_a] :
                    ( ( member5502040268208861279od_c_a @ Xb3 @ ( transitions_a_b_c @ X ) )
                    & ( ( produc4225943634317630866od_c_a @ X2 )
                      = ( produc4225943634317630866od_c_a @ Xb3 ) )
                    & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) )
                      = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xb3 ) ) )
                    & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xb3 ) ) )
                      = Xa2 ) ) ) ) ) ).

% output_complete.elims(3)
thf(fact_164_output__complete_Oelims_I3_J,axiom,
    ! [X: fsm_e_b_c] :
      ( ~ ( output7772454409360524404_e_b_c @ X )
     => ~ ! [X2: produc4050040609193146166od_c_e] :
            ( ( member6882148676089805663od_c_e @ X2 @ ( transitions_e_b_c @ X ) )
           => ! [Xa2: c] :
                ( ( member_c @ Xa2 @ ( outputs_e_b_c @ X ) )
               => ? [Xb3: produc4050040609193146166od_c_e] :
                    ( ( member6882148676089805663od_c_e @ Xb3 @ ( transitions_e_b_c @ X ) )
                    & ( ( produc6751554238685325970od_c_e @ X2 )
                      = ( produc6751554238685325970od_c_e @ Xb3 ) )
                    & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ X2 ) )
                      = ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Xb3 ) ) )
                    & ( ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ Xb3 ) ) )
                      = Xa2 ) ) ) ) ) ).

% output_complete.elims(3)
thf(fact_165_output__complete__alt__def,axiom,
    ( output3834324022317553264_a_b_c
    = ( ^ [M2: fsm_a_b_c] :
        ! [Q4: a,X3: b] :
          ( ? [Y3: c,Q5: a] : ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q4 @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ Q5 ) ) ) @ ( transitions_a_b_c @ M2 ) )
         => ! [Y3: c] :
              ( ( member_c @ Y3 @ ( outputs_a_b_c @ M2 ) )
             => ? [Q5: a] : ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q4 @ ( produc3440865914000881661od_c_a @ X3 @ ( product_Pair_c_a @ Y3 @ Q5 ) ) ) @ ( transitions_a_b_c @ M2 ) ) ) ) ) ) ).

% output_complete_alt_def
thf(fact_166_output__complete__alt__def,axiom,
    ( output7772454409360524404_e_b_c
    = ( ^ [M2: fsm_e_b_c] :
        ! [Q4: e,X3: b] :
          ( ? [Y3: c,Q5: e] : ( member6882148676089805663od_c_e @ ( produc8288412161402371238od_c_e @ Q4 @ ( produc3440865931213796865od_c_e @ X3 @ ( product_Pair_c_e @ Y3 @ Q5 ) ) ) @ ( transitions_e_b_c @ M2 ) )
         => ! [Y3: c] :
              ( ( member_c @ Y3 @ ( outputs_e_b_c @ M2 ) )
             => ? [Q5: e] : ( member6882148676089805663od_c_e @ ( produc8288412161402371238od_c_e @ Q4 @ ( produc3440865931213796865od_c_e @ X3 @ ( product_Pair_c_e @ Y3 @ Q5 ) ) ) @ ( transitions_e_b_c @ M2 ) ) ) ) ) ) ).

% output_complete_alt_def
thf(fact_167_longest__common__prefix_Ocases,axiom,
    ! [X: produc5878855887281848999od_b_c] :
      ( ! [X2: product_prod_b_c,Xs2: list_P903359562653991662od_b_c,Y2: product_prod_b_c,Ys2: list_P903359562653991662od_b_c] :
          ( X
         != ( produc3076307724246486423od_b_c @ ( cons_P4529483553340347422od_b_c @ X2 @ Xs2 ) @ ( cons_P4529483553340347422od_b_c @ Y2 @ Ys2 ) ) )
     => ( ! [Uv: list_P903359562653991662od_b_c] :
            ( X
           != ( produc3076307724246486423od_b_c @ nil_Product_prod_b_c @ Uv ) )
       => ~ ! [Uu: list_P903359562653991662od_b_c] :
              ( X
             != ( produc3076307724246486423od_b_c @ Uu @ nil_Product_prod_b_c ) ) ) ) ).

% longest_common_prefix.cases
thf(fact_168_after__transition__exhaust,axiom,
    ! [M: fsm_a_b_c,T3: produc2669932201312201782od_c_a] :
      ( ( observable_a_b_c @ M )
     => ( ( member5502040268208861279od_c_a @ T3 @ ( transitions_a_b_c @ M ) )
       => ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) )
          = ( after_a_b_c @ M @ ( produc4225943634317630866od_c_a @ T3 ) @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) ) ) @ nil_Product_prod_b_c ) ) ) ) ) ).

% after_transition_exhaust
thf(fact_169_after__transition__exhaust,axiom,
    ! [M: fsm_e_b_c,T3: produc4050040609193146166od_c_e] :
      ( ( observable_e_b_c @ M )
     => ( ( member6882148676089805663od_c_e @ T3 @ ( transitions_e_b_c @ M ) )
       => ( ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) )
          = ( after_e_b_c @ M @ ( produc6751554238685325970od_c_e @ T3 ) @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) @ ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) ) ) @ nil_Product_prod_b_c ) ) ) ) ) ).

% after_transition_exhaust
thf(fact_170_observable__language__transition__target,axiom,
    ! [M: fsm_a_b_c,T3: produc2669932201312201782od_c_a,Io: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member5502040268208861279od_c_a @ T3 @ ( transitions_a_b_c @ M ) )
       => ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) ) ) @ Io ) @ ( lS_a_b_c @ M @ ( produc4225943634317630866od_c_a @ T3 ) ) )
         => ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) ) ) ) ) ) ) ).

% observable_language_transition_target
thf(fact_171_observable__language__transition__target,axiom,
    ! [M: fsm_e_b_c,T3: produc4050040609193146166od_c_e,Io: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( member6882148676089805663od_c_e @ T3 @ ( transitions_e_b_c @ M ) )
       => ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) @ ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) ) ) @ Io ) @ ( lS_e_b_c @ M @ ( produc6751554238685325970od_c_e @ T3 ) ) )
         => ( member6330420149250801815od_b_c @ Io @ ( lS_e_b_c @ M @ ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) ) ) ) ) ) ) ).

% observable_language_transition_target
thf(fact_172_completely__specified__state_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c,Xa: a] :
      ( ~ ( comple2039557650379672579_a_b_c @ X @ Xa )
     => ~ ! [X2: b] :
            ( ( member_b @ X2 @ ( inputs_a_b_c @ X ) )
           => ? [Xa3: produc2669932201312201782od_c_a] :
                ( ( member5502040268208861279od_c_a @ Xa3 @ ( transitions_a_b_c @ X ) )
                & ( ( produc4225943634317630866od_c_a @ Xa3 )
                  = Xa )
                & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xa3 ) )
                  = X2 ) ) ) ) ).

% completely_specified_state.elims(3)
thf(fact_173_completely__specified__state_Oelims_I3_J,axiom,
    ! [X: fsm_e_b_c,Xa: e] :
      ( ~ ( comple5977688037422643719_e_b_c @ X @ Xa )
     => ~ ! [X2: b] :
            ( ( member_b @ X2 @ ( inputs_e_b_c @ X ) )
           => ? [Xa3: produc4050040609193146166od_c_e] :
                ( ( member6882148676089805663od_c_e @ Xa3 @ ( transitions_e_b_c @ X ) )
                & ( ( produc6751554238685325970od_c_e @ Xa3 )
                  = Xa )
                & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Xa3 ) )
                  = X2 ) ) ) ) ).

% completely_specified_state.elims(3)
thf(fact_174_completely__specified__state_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c,Xa: a] :
      ( ( comple2039557650379672579_a_b_c @ X @ Xa )
     => ! [X4: b] :
          ( ( member_b @ X4 @ ( inputs_a_b_c @ X ) )
         => ? [Xa2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Xa2 @ ( transitions_a_b_c @ X ) )
              & ( ( produc4225943634317630866od_c_a @ Xa2 )
                = Xa )
              & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xa2 ) )
                = X4 ) ) ) ) ).

% completely_specified_state.elims(2)
thf(fact_175_completely__specified__state_Oelims_I2_J,axiom,
    ! [X: fsm_e_b_c,Xa: e] :
      ( ( comple5977688037422643719_e_b_c @ X @ Xa )
     => ! [X4: b] :
          ( ( member_b @ X4 @ ( inputs_e_b_c @ X ) )
         => ? [Xa2: produc4050040609193146166od_c_e] :
              ( ( member6882148676089805663od_c_e @ Xa2 @ ( transitions_e_b_c @ X ) )
              & ( ( produc6751554238685325970od_c_e @ Xa2 )
                = Xa )
              & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Xa2 ) )
                = X4 ) ) ) ) ).

% completely_specified_state.elims(2)
thf(fact_176_completely__specified__state_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Xa: a,Y: $o] :
      ( ( ( comple2039557650379672579_a_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( ! [X3: b] :
              ( ( member_b @ X3 @ ( inputs_a_b_c @ X ) )
             => ? [Y3: produc2669932201312201782od_c_a] :
                  ( ( member5502040268208861279od_c_a @ Y3 @ ( transitions_a_b_c @ X ) )
                  & ( ( produc4225943634317630866od_c_a @ Y3 )
                    = Xa )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Y3 ) )
                    = X3 ) ) ) ) ) ) ).

% completely_specified_state.elims(1)
thf(fact_177_completely__specified__state_Oelims_I1_J,axiom,
    ! [X: fsm_e_b_c,Xa: e,Y: $o] :
      ( ( ( comple5977688037422643719_e_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( ! [X3: b] :
              ( ( member_b @ X3 @ ( inputs_e_b_c @ X ) )
             => ? [Y3: produc4050040609193146166od_c_e] :
                  ( ( member6882148676089805663od_c_e @ Y3 @ ( transitions_e_b_c @ X ) )
                  & ( ( produc6751554238685325970od_c_e @ Y3 )
                    = Xa )
                  & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Y3 ) )
                    = X3 ) ) ) ) ) ) ).

% completely_specified_state.elims(1)
thf(fact_178_completely__specified__state_Osimps,axiom,
    ( comple2039557650379672579_a_b_c
    = ( ^ [M2: fsm_a_b_c,Q4: a] :
        ! [X3: b] :
          ( ( member_b @ X3 @ ( inputs_a_b_c @ M2 ) )
         => ? [Y3: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Y3 @ ( transitions_a_b_c @ M2 ) )
              & ( ( produc4225943634317630866od_c_a @ Y3 )
                = Q4 )
              & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Y3 ) )
                = X3 ) ) ) ) ) ).

% completely_specified_state.simps
thf(fact_179_completely__specified__state_Osimps,axiom,
    ( comple5977688037422643719_e_b_c
    = ( ^ [M2: fsm_e_b_c,Q4: e] :
        ! [X3: b] :
          ( ( member_b @ X3 @ ( inputs_e_b_c @ M2 ) )
         => ? [Y3: produc4050040609193146166od_c_e] :
              ( ( member6882148676089805663od_c_e @ Y3 @ ( transitions_e_b_c @ M2 ) )
              & ( ( produc6751554238685325970od_c_e @ Y3 )
                = Q4 )
              & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Y3 ) )
                = X3 ) ) ) ) ) ).

% completely_specified_state.simps
thf(fact_180_LS__single__transition,axiom,
    ! [X: b,Y: c,M: fsm_a_b_c,Q: a] :
      ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) @ ( lS_a_b_c @ M @ Q ) )
      = ( ? [X3: produc2669932201312201782od_c_a] :
            ( ( member5502040268208861279od_c_a @ X3 @ ( transitions_a_b_c @ M ) )
            & ( ( produc4225943634317630866od_c_a @ X3 )
              = Q )
            & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) )
              = X )
            & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) ) )
              = Y ) ) ) ) ).

% LS_single_transition
thf(fact_181_LS__single__transition,axiom,
    ! [X: b,Y: c,M: fsm_e_b_c,Q: e] :
      ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) @ ( lS_e_b_c @ M @ Q ) )
      = ( ? [X3: produc4050040609193146166od_c_e] :
            ( ( member6882148676089805663od_c_e @ X3 @ ( transitions_e_b_c @ M ) )
            & ( ( produc6751554238685325970od_c_e @ X3 )
              = Q )
            & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ X3 ) )
              = X )
            & ( ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ X3 ) ) )
              = Y ) ) ) ) ).

% LS_single_transition
thf(fact_182_after__split,axiom,
    ! [M: fsm_a_b_c,Alpha2: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,Q: a] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) @ ( lS_a_b_c @ M @ Q ) )
       => ( ( after_a_b_c @ M @ ( after_a_b_c @ M @ Q @ Alpha2 ) @ Gamma )
          = ( after_a_b_c @ M @ Q @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) ) ) ) ) ).

% after_split
thf(fact_183_after__split,axiom,
    ! [M: fsm_e_b_c,Alpha2: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,Q: e] :
      ( ( observable_e_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) @ ( lS_e_b_c @ M @ Q ) )
       => ( ( after_e_b_c @ M @ ( after_e_b_c @ M @ Q @ Alpha2 ) @ Gamma )
          = ( after_e_b_c @ M @ Q @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) ) ) ) ) ).

% after_split
thf(fact_184_after__language__iff,axiom,
    ! [M: fsm_a_b_c,Alpha2: list_P903359562653991662od_b_c,Q: a,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Alpha2 @ ( lS_a_b_c @ M @ Q ) )
       => ( ( member6330420149250801815od_b_c @ Gamma @ ( lS_a_b_c @ M @ ( after_a_b_c @ M @ Q @ Alpha2 ) ) )
          = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ) ).

% after_language_iff
thf(fact_185_after__language__iff,axiom,
    ! [M: fsm_e_b_c,Alpha2: list_P903359562653991662od_b_c,Q: e,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Alpha2 @ ( lS_e_b_c @ M @ Q ) )
       => ( ( member6330420149250801815od_b_c @ Gamma @ ( lS_e_b_c @ M @ ( after_e_b_c @ M @ Q @ Alpha2 ) ) )
          = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) @ ( lS_e_b_c @ M @ Q ) ) ) ) ) ).

% after_language_iff
thf(fact_186_observable__after__eq,axiom,
    ! [M: fsm_a_b_c,Q: a,Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( ( after_a_b_c @ M @ Q @ Io1 )
          = ( after_a_b_c @ M @ Q @ Io2 ) )
       => ( ( member6330420149250801815od_b_c @ Io1 @ ( lS_a_b_c @ M @ Q ) )
         => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_a_b_c @ M @ Q ) )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io ) @ ( lS_a_b_c @ M @ Q ) )
              = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io2 @ Io ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ) ) ) ).

% observable_after_eq
thf(fact_187_observable__after__eq,axiom,
    ! [M: fsm_e_b_c,Q: e,Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( ( after_e_b_c @ M @ Q @ Io1 )
          = ( after_e_b_c @ M @ Q @ Io2 ) )
       => ( ( member6330420149250801815od_b_c @ Io1 @ ( lS_e_b_c @ M @ Q ) )
         => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_e_b_c @ M @ Q ) )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io ) @ ( lS_e_b_c @ M @ Q ) )
              = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io2 @ Io ) @ ( lS_e_b_c @ M @ Q ) ) ) ) ) ) ) ).

% observable_after_eq
thf(fact_188_observable__after__language__none,axiom,
    ! [M: fsm_a_b_c,Io1: list_P903359562653991662od_b_c,Q: a,Io2: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io1 @ ( lS_a_b_c @ M @ Q ) )
       => ( ~ ( member6330420149250801815od_b_c @ Io2 @ ( lS_a_b_c @ M @ ( after_a_b_c @ M @ Q @ Io1 ) ) )
         => ~ ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ) ).

% observable_after_language_none
thf(fact_189_observable__after__language__none,axiom,
    ! [M: fsm_e_b_c,Io1: list_P903359562653991662od_b_c,Q: e,Io2: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io1 @ ( lS_e_b_c @ M @ Q ) )
       => ( ~ ( member6330420149250801815od_b_c @ Io2 @ ( lS_e_b_c @ M @ ( after_e_b_c @ M @ Q @ Io1 ) ) )
         => ~ ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_e_b_c @ M @ Q ) ) ) ) ) ).

% observable_after_language_none
thf(fact_190_observable__after__language__append,axiom,
    ! [M: fsm_a_b_c,Io1: list_P903359562653991662od_b_c,Q: a,Io2: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io1 @ ( lS_a_b_c @ M @ Q ) )
       => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_a_b_c @ M @ ( after_a_b_c @ M @ Q @ Io1 ) ) )
         => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ) ).

% observable_after_language_append
thf(fact_191_observable__after__language__append,axiom,
    ! [M: fsm_e_b_c,Io1: list_P903359562653991662od_b_c,Q: e,Io2: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io1 @ ( lS_e_b_c @ M @ Q ) )
       => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_e_b_c @ M @ ( after_e_b_c @ M @ Q @ Io1 ) ) )
         => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_e_b_c @ M @ Q ) ) ) ) ) ).

% observable_after_language_append
thf(fact_192_after__reachable,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Io: list_P903359562653991662od_b_c,Q: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) )
       => ( ( member6330420149250801815od_b_c @ Q @ ( reacha8116992257183400179_c_b_c @ M ) )
         => ( member6330420149250801815od_b_c @ ( after_4052058690717316294_c_b_c @ M @ Q @ Io ) @ ( reacha8116992257183400179_c_b_c @ M ) ) ) ) ) ).

% after_reachable
thf(fact_193_after__reachable,axiom,
    ! [M: fsm_b_b_c,Io: list_P903359562653991662od_b_c,Q: b] :
      ( ( observable_b_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_b_b_c @ M @ Q ) )
       => ( ( member_b @ Q @ ( reacha7216524145940060804_b_b_c @ M ) )
         => ( member_b @ ( after_b_b_c @ M @ Q @ Io ) @ ( reacha7216524145940060804_b_b_c @ M ) ) ) ) ) ).

% after_reachable
thf(fact_194_after__reachable,axiom,
    ! [M: fsm_c_b_c,Io: list_P903359562653991662od_b_c,Q: c] :
      ( ( observable_c_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_c_b_c @ M @ Q ) )
       => ( ( member_c @ Q @ ( reacha3589370724273415685_c_b_c @ M ) )
         => ( member_c @ ( after_c_b_c @ M @ Q @ Io ) @ ( reacha3589370724273415685_c_b_c @ M ) ) ) ) ) ).

% after_reachable
thf(fact_195_after__reachable,axiom,
    ! [M: fsm_e_b_c,Io: list_P903359562653991662od_b_c,Q: e] :
      ( ( observable_e_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_e_b_c @ M @ Q ) )
       => ( ( member_e @ Q @ ( reacha5558435917794901255_e_b_c @ M ) )
         => ( member_e @ ( after_e_b_c @ M @ Q @ Io ) @ ( reacha5558435917794901255_e_b_c @ M ) ) ) ) ) ).

% after_reachable
thf(fact_196_after__reachable,axiom,
    ! [M: fsm_a_b_c,Io: list_P903359562653991662od_b_c,Q: a] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ Q ) )
       => ( ( member_a @ Q @ ( reacha1620305530751930115_a_b_c @ M ) )
         => ( member_a @ ( after_a_b_c @ M @ Q @ Io ) @ ( reacha1620305530751930115_a_b_c @ M ) ) ) ) ) ).

% after_reachable
thf(fact_197_language__prefix,axiom,
    ! [Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,M: fsm_a_b_c,Q: a] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_a_b_c @ M @ Q ) )
     => ( member6330420149250801815od_b_c @ Io1 @ ( lS_a_b_c @ M @ Q ) ) ) ).

% language_prefix
thf(fact_198_language__prefix,axiom,
    ! [Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,M: fsm_e_b_c,Q: e] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_e_b_c @ M @ Q ) )
     => ( member6330420149250801815od_b_c @ Io1 @ ( lS_e_b_c @ M @ Q ) ) ) ).

% language_prefix
thf(fact_199_after__transition,axiom,
    ! [M: fsm_a_b_c,Q: a,X: b,Y: c,Q6: a] :
      ( ( observable_a_b_c @ M )
     => ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q @ ( produc3440865914000881661od_c_a @ X @ ( product_Pair_c_a @ Y @ Q6 ) ) ) @ ( transitions_a_b_c @ M ) )
       => ( ( after_a_b_c @ M @ Q @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) )
          = Q6 ) ) ) ).

% after_transition
thf(fact_200_after__transition,axiom,
    ! [M: fsm_e_b_c,Q: e,X: b,Y: c,Q6: e] :
      ( ( observable_e_b_c @ M )
     => ( ( member6882148676089805663od_c_e @ ( produc8288412161402371238od_c_e @ Q @ ( produc3440865931213796865od_c_e @ X @ ( product_Pair_c_e @ Y @ Q6 ) ) ) @ ( transitions_e_b_c @ M ) )
       => ( ( after_e_b_c @ M @ Q @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) )
          = Q6 ) ) ) ).

% after_transition
thf(fact_201_observable__transition__target__language__eq,axiom,
    ! [M: fsm_a_b_c,T1: produc2669932201312201782od_c_a,T22: produc2669932201312201782od_c_a] :
      ( ( ( lS_a_b_c @ M @ ( produc4225943634317630866od_c_a @ T1 ) )
        = ( lS_a_b_c @ M @ ( produc4225943634317630866od_c_a @ T22 ) ) )
     => ( ( member5502040268208861279od_c_a @ T1 @ ( transitions_a_b_c @ M ) )
       => ( ( member5502040268208861279od_c_a @ T22 @ ( transitions_a_b_c @ M ) )
         => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T1 ) )
              = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T22 ) ) )
           => ( ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T1 ) ) )
                = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T22 ) ) ) )
             => ( ( observable_a_b_c @ M )
               => ( ( lS_a_b_c @ M @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T1 ) ) ) )
                  = ( lS_a_b_c @ M @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T22 ) ) ) ) ) ) ) ) ) ) ) ).

% observable_transition_target_language_eq
thf(fact_202_observable__transition__target__language__eq,axiom,
    ! [M: fsm_e_b_c,T1: produc4050040609193146166od_c_e,T22: produc4050040609193146166od_c_e] :
      ( ( ( lS_e_b_c @ M @ ( produc6751554238685325970od_c_e @ T1 ) )
        = ( lS_e_b_c @ M @ ( produc6751554238685325970od_c_e @ T22 ) ) )
     => ( ( member6882148676089805663od_c_e @ T1 @ ( transitions_e_b_c @ M ) )
       => ( ( member6882148676089805663od_c_e @ T22 @ ( transitions_e_b_c @ M ) )
         => ( ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T1 ) )
              = ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T22 ) ) )
           => ( ( ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T1 ) ) )
                = ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T22 ) ) ) )
             => ( ( observable_e_b_c @ M )
               => ( ( lS_e_b_c @ M @ ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T1 ) ) ) )
                  = ( lS_e_b_c @ M @ ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T22 ) ) ) ) ) ) ) ) ) ) ) ).

% observable_transition_target_language_eq
thf(fact_203_LS__prepend__transition,axiom,
    ! [T3: produc2669932201312201782od_c_a,M: fsm_a_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( member5502040268208861279od_c_a @ T3 @ ( transitions_a_b_c @ M ) )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) ) ) )
       => ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) ) ) @ Io ) @ ( lS_a_b_c @ M @ ( produc4225943634317630866od_c_a @ T3 ) ) ) ) ) ).

% LS_prepend_transition
thf(fact_204_LS__prepend__transition,axiom,
    ! [T3: produc4050040609193146166od_c_e,M: fsm_e_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( member6882148676089805663od_c_e @ T3 @ ( transitions_e_b_c @ M ) )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_e_b_c @ M @ ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) ) ) )
       => ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) @ ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) ) ) @ Io ) @ ( lS_e_b_c @ M @ ( produc6751554238685325970od_c_e @ T3 ) ) ) ) ) ).

% LS_prepend_transition
thf(fact_205_language__next__transition__ob,axiom,
    ! [X: b,Y: c,Ios: list_P903359562653991662od_b_c,M: fsm_a_b_c,Q: a] :
      ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ Ios ) @ ( lS_a_b_c @ M @ Q ) )
     => ~ ! [T4: produc2669932201312201782od_c_a] :
            ( ( ( produc4225943634317630866od_c_a @ T4 )
              = Q )
           => ( ( member5502040268208861279od_c_a @ T4 @ ( transitions_a_b_c @ M ) )
             => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) )
                  = X )
               => ( ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) )
                    = Y )
                 => ~ ( member6330420149250801815od_b_c @ Ios @ ( lS_a_b_c @ M @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) ) ) ) ) ) ) ) ).

% language_next_transition_ob
thf(fact_206_language__next__transition__ob,axiom,
    ! [X: b,Y: c,Ios: list_P903359562653991662od_b_c,M: fsm_e_b_c,Q: e] :
      ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ Ios ) @ ( lS_e_b_c @ M @ Q ) )
     => ~ ! [T4: produc4050040609193146166od_c_e] :
            ( ( ( produc6751554238685325970od_c_e @ T4 )
              = Q )
           => ( ( member6882148676089805663od_c_e @ T4 @ ( transitions_e_b_c @ M ) )
             => ( ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T4 ) )
                  = X )
               => ( ( ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T4 ) ) )
                    = Y )
                 => ~ ( member6330420149250801815od_b_c @ Ios @ ( lS_e_b_c @ M @ ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T4 ) ) ) ) ) ) ) ) ) ) ).

% language_next_transition_ob
thf(fact_207_a15,axiom,
    ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) ) @ ( prefix9085958534787526401od_b_c @ ( produc1447154562020694006_b_c_d @ ( f @ m1 @ v @ t @ g @ cg_insert @ cg_lookup @ q @ x @ y ) ) ) )
    = ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ m2 @ ( initial_e_b_c @ m2 ) ) @ ( prefix9085958534787526401od_b_c @ ( produc1447154562020694006_b_c_d @ ( f @ m1 @ v @ t @ g @ cg_insert @ cg_lookup @ q @ x @ y ) ) ) ) ) ).

% a15
thf(fact_208_observable__transition__target__language__subset,axiom,
    ! [M: fsm_a_b_c,T1: produc2669932201312201782od_c_a,T22: produc2669932201312201782od_c_a] :
      ( ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ M @ ( produc4225943634317630866od_c_a @ T1 ) ) @ ( lS_a_b_c @ M @ ( produc4225943634317630866od_c_a @ T22 ) ) )
     => ( ( member5502040268208861279od_c_a @ T1 @ ( transitions_a_b_c @ M ) )
       => ( ( member5502040268208861279od_c_a @ T22 @ ( transitions_a_b_c @ M ) )
         => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T1 ) )
              = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T22 ) ) )
           => ( ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T1 ) ) )
                = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T22 ) ) ) )
             => ( ( observable_a_b_c @ M )
               => ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ M @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T1 ) ) ) ) @ ( lS_a_b_c @ M @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T22 ) ) ) ) ) ) ) ) ) ) ) ).

% observable_transition_target_language_subset
thf(fact_209_observable__transition__target__language__subset,axiom,
    ! [M: fsm_e_b_c,T1: produc4050040609193146166od_c_e,T22: produc4050040609193146166od_c_e] :
      ( ( ord_le282488521294790766od_b_c @ ( lS_e_b_c @ M @ ( produc6751554238685325970od_c_e @ T1 ) ) @ ( lS_e_b_c @ M @ ( produc6751554238685325970od_c_e @ T22 ) ) )
     => ( ( member6882148676089805663od_c_e @ T1 @ ( transitions_e_b_c @ M ) )
       => ( ( member6882148676089805663od_c_e @ T22 @ ( transitions_e_b_c @ M ) )
         => ( ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T1 ) )
              = ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T22 ) ) )
           => ( ( ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T1 ) ) )
                = ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T22 ) ) ) )
             => ( ( observable_e_b_c @ M )
               => ( ord_le282488521294790766od_b_c @ ( lS_e_b_c @ M @ ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T1 ) ) ) ) @ ( lS_e_b_c @ M @ ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T22 ) ) ) ) ) ) ) ) ) ) ) ).

% observable_transition_target_language_subset
thf(fact_210_map__default_Opelims,axiom,
    ! [X: b,Xa: c,Xb: c > c,Xc: list_P903359562653991662od_b_c,Y: list_P903359562653991662od_b_c] :
      ( ( ( map_default_b_c @ X @ Xa @ Xb @ Xc )
        = Y )
     => ( ( accp_P2383248136236608210od_b_c @ map_default_rel_b_c @ ( produc1384939585547926677od_b_c @ X @ ( produc3590379597927054951od_b_c @ Xa @ ( produc1101678828523717360od_b_c @ Xb @ Xc ) ) ) )
       => ( ( ( Xc = nil_Product_prod_b_c )
           => ( ( Y
                = ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Xa ) @ nil_Product_prod_b_c ) )
             => ~ ( accp_P2383248136236608210od_b_c @ map_default_rel_b_c @ ( produc1384939585547926677od_b_c @ X @ ( produc3590379597927054951od_b_c @ Xa @ ( produc1101678828523717360od_b_c @ Xb @ nil_Product_prod_b_c ) ) ) ) ) )
         => ~ ! [P2: product_prod_b_c,Ps: list_P903359562653991662od_b_c] :
                ( ( Xc
                  = ( cons_P4529483553340347422od_b_c @ P2 @ Ps ) )
               => ( ( ( ( ( product_fst_b_c @ P2 )
                        = X )
                     => ( Y
                        = ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ ( Xb @ ( product_snd_b_c @ P2 ) ) ) @ Ps ) ) )
                    & ( ( ( product_fst_b_c @ P2 )
                       != X )
                     => ( Y
                        = ( cons_P4529483553340347422od_b_c @ P2 @ ( map_default_b_c @ X @ Xa @ Xb @ Ps ) ) ) ) )
                 => ~ ( accp_P2383248136236608210od_b_c @ map_default_rel_b_c @ ( produc1384939585547926677od_b_c @ X @ ( produc3590379597927054951od_b_c @ Xa @ ( produc1101678828523717360od_b_c @ Xb @ ( cons_P4529483553340347422od_b_c @ P2 @ Ps ) ) ) ) ) ) ) ) ) ) ).

% map_default.pelims
thf(fact_211_map__default_Opelims,axiom,
    ! [X: prefix425356687782099470od_b_c,Xa: d,Xb: d > d,Xc: list_P197655048861356576_b_c_d,Y: list_P197655048861356576_b_c_d] :
      ( ( ( map_de7650936251494337739_b_c_d @ X @ Xa @ Xb @ Xc )
        = Y )
     => ( ( accp_P6274674601512815188_b_c_d @ map_de4747112207106671252_b_c_d @ ( produc8293724434266651031_b_c_d @ X @ ( produc106980334620188890_b_c_d @ Xa @ ( produc2874902326144019298_b_c_d @ Xb @ Xc ) ) ) )
       => ( ( ( Xc = nil_Pr3869772434330527008_b_c_d )
           => ( ( Y
                = ( cons_P1373155234573727952_b_c_d @ ( produc2511600812177743882_b_c_d @ X @ Xa ) @ nil_Pr3869772434330527008_b_c_d ) )
             => ~ ( accp_P6274674601512815188_b_c_d @ map_de4747112207106671252_b_c_d @ ( produc8293724434266651031_b_c_d @ X @ ( produc106980334620188890_b_c_d @ Xa @ ( produc2874902326144019298_b_c_d @ Xb @ nil_Pr3869772434330527008_b_c_d ) ) ) ) ) )
         => ~ ! [P2: produc4534891791806675482_b_c_d,Ps: list_P197655048861356576_b_c_d] :
                ( ( Xc
                  = ( cons_P1373155234573727952_b_c_d @ P2 @ Ps ) )
               => ( ( ( ( ( produc1447154562020694006_b_c_d @ P2 )
                        = X )
                     => ( Y
                        = ( cons_P1373155234573727952_b_c_d @ ( produc2511600812177743882_b_c_d @ X @ ( Xb @ ( produc6779600879576379960_b_c_d @ P2 ) ) ) @ Ps ) ) )
                    & ( ( ( produc1447154562020694006_b_c_d @ P2 )
                       != X )
                     => ( Y
                        = ( cons_P1373155234573727952_b_c_d @ P2 @ ( map_de7650936251494337739_b_c_d @ X @ Xa @ Xb @ Ps ) ) ) ) )
                 => ~ ( accp_P6274674601512815188_b_c_d @ map_de4747112207106671252_b_c_d @ ( produc8293724434266651031_b_c_d @ X @ ( produc106980334620188890_b_c_d @ Xa @ ( produc2874902326144019298_b_c_d @ Xb @ ( cons_P1373155234573727952_b_c_d @ P2 @ Ps ) ) ) ) ) ) ) ) ) ) ).

% map_default.pelims
thf(fact_212_acyclic__induction,axiom,
    ! [M: fsm_a_b_c,P: a > $o] :
      ( ( acyclic_a_b_c @ M )
     => ( ! [Q7: a] :
            ( ( member_a @ Q7 @ ( reacha1620305530751930115_a_b_c @ M ) )
           => ( ! [T5: produc2669932201312201782od_c_a] :
                  ( ( member5502040268208861279od_c_a @ T5 @ ( transitions_a_b_c @ M ) )
                 => ( ( ( produc4225943634317630866od_c_a @ T5 )
                      = Q7 )
                   => ( P @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T5 ) ) ) ) ) )
             => ( P @ Q7 ) ) )
       => ! [X4: a] :
            ( ( member_a @ X4 @ ( reacha1620305530751930115_a_b_c @ M ) )
           => ( P @ X4 ) ) ) ) ).

% acyclic_induction
thf(fact_213_prefixes__snoc,axiom,
    ! [Xs: list_P903359562653991662od_b_c,X: product_prod_b_c] :
      ( ( prefix1131979855692807669od_b_c @ ( append2547753245680614915od_b_c @ Xs @ ( cons_P4529483553340347422od_b_c @ X @ nil_Product_prod_b_c ) ) )
      = ( append6992831555715836169od_b_c @ ( prefix1131979855692807669od_b_c @ Xs ) @ ( cons_l342771267123639716od_b_c @ ( append2547753245680614915od_b_c @ Xs @ ( cons_P4529483553340347422od_b_c @ X @ nil_Product_prod_b_c ) ) @ nil_li8071162985807626740od_b_c ) ) ) ).

% prefixes_snoc
thf(fact_214_transition__cover__def,axiom,
    ( transi1080538797461288133_e_b_c
    = ( ^ [M2: fsm_e_b_c,A5: set_li6436108459499378894od_b_c] :
        ! [X3: e] :
          ( ( member_e @ X3 @ ( reacha5558435917794901255_e_b_c @ M2 ) )
         => ! [Y3: b] :
              ( ( member_b @ Y3 @ ( inputs_e_b_c @ M2 ) )
             => ! [Z2: c] :
                  ( ( member_c @ Z2 @ ( outputs_e_b_c @ M2 ) )
                 => ? [Alpha3: list_P903359562653991662od_b_c] :
                      ( ( member6330420149250801815od_b_c @ Alpha3 @ A5 )
                      & ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha3 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ Y3 @ Z2 ) @ nil_Product_prod_b_c ) ) @ A5 )
                      & ( member6330420149250801815od_b_c @ Alpha3 @ ( lS_e_b_c @ M2 @ ( initial_e_b_c @ M2 ) ) )
                      & ( ( after_e_b_c @ M2 @ ( initial_e_b_c @ M2 ) @ Alpha3 )
                        = X3 ) ) ) ) ) ) ) ).

% transition_cover_def
thf(fact_215_transition__cover__def,axiom,
    ( transi6365780447273092801_a_b_c
    = ( ^ [M2: fsm_a_b_c,A5: set_li6436108459499378894od_b_c] :
        ! [X3: a] :
          ( ( member_a @ X3 @ ( reacha1620305530751930115_a_b_c @ M2 ) )
         => ! [Y3: b] :
              ( ( member_b @ Y3 @ ( inputs_a_b_c @ M2 ) )
             => ! [Z2: c] :
                  ( ( member_c @ Z2 @ ( outputs_a_b_c @ M2 ) )
                 => ? [Alpha3: list_P903359562653991662od_b_c] :
                      ( ( member6330420149250801815od_b_c @ Alpha3 @ A5 )
                      & ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha3 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ Y3 @ Z2 ) @ nil_Product_prod_b_c ) ) @ A5 )
                      & ( member6330420149250801815od_b_c @ Alpha3 @ ( lS_a_b_c @ M2 @ ( initial_a_b_c @ M2 ) ) )
                      & ( ( after_a_b_c @ M2 @ ( initial_a_b_c @ M2 ) @ Alpha3 )
                        = X3 ) ) ) ) ) ) ) ).

% transition_cover_def
thf(fact_216_a09,axiom,
    ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ m1 @ ( initial_a_b_c @ m1 ) ) @ ( image_8656872703560917237od_b_c @ v @ ( reacha1620305530751930115_a_b_c @ m1 ) ) )
    = ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ m2 @ ( initial_e_b_c @ m2 ) ) @ ( image_8656872703560917237od_b_c @ v @ ( reacha1620305530751930115_a_b_c @ m1 ) ) ) ) ).

% a09
thf(fact_217_reachable__states__initial,axiom,
    ! [M: fsm_e_b_c] : ( member_e @ ( initial_e_b_c @ M ) @ ( reacha5558435917794901255_e_b_c @ M ) ) ).

% reachable_states_initial
thf(fact_218_reachable__states__initial,axiom,
    ! [M: fsm_a_b_c] : ( member_a @ ( initial_a_b_c @ M ) @ ( reacha1620305530751930115_a_b_c @ M ) ) ).

% reachable_states_initial
thf(fact_219_language__contains__empty__sequence,axiom,
    ! [M: fsm_a_b_c] : ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ).

% language_contains_empty_sequence
thf(fact_220_language__contains__empty__sequence,axiom,
    ! [M: fsm_e_b_c] : ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) ) ).

% language_contains_empty_sequence
thf(fact_221_converge__refl,axiom,
    ! [Alpha2: list_P903359562653991662od_b_c,M: fsm_a_b_c] :
      ( ( member6330420149250801815od_b_c @ Alpha2 @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
     => ( converge_a_b_c @ M @ Alpha2 @ Alpha2 ) ) ).

% converge_refl
thf(fact_222_converge__refl,axiom,
    ! [Alpha2: list_P903359562653991662od_b_c,M: fsm_e_b_c] :
      ( ( member6330420149250801815od_b_c @ Alpha2 @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
     => ( converge_e_b_c @ M @ Alpha2 @ Alpha2 ) ) ).

% converge_refl
thf(fact_223_prefixes_Osimps_I1_J,axiom,
    ( ( prefix1131979855692807669od_b_c @ nil_Product_prod_b_c )
    = ( cons_l342771267123639716od_b_c @ nil_Product_prod_b_c @ nil_li8071162985807626740od_b_c ) ) ).

% prefixes.simps(1)
thf(fact_224_converge_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c] :
      ( ~ ( converge_a_b_c @ X @ Xa @ Xb )
     => ~ ( ( member6330420149250801815od_b_c @ Xa @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) )
          & ( member6330420149250801815od_b_c @ Xb @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) )
          & ( ( lS_a_b_c @ X @ ( after_a_b_c @ X @ ( initial_a_b_c @ X ) @ Xa ) )
            = ( lS_a_b_c @ X @ ( after_a_b_c @ X @ ( initial_a_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(3)
thf(fact_225_converge_Oelims_I3_J,axiom,
    ! [X: fsm_e_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c] :
      ( ~ ( converge_e_b_c @ X @ Xa @ Xb )
     => ~ ( ( member6330420149250801815od_b_c @ Xa @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) )
          & ( member6330420149250801815od_b_c @ Xb @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) )
          & ( ( lS_e_b_c @ X @ ( after_e_b_c @ X @ ( initial_e_b_c @ X ) @ Xa ) )
            = ( lS_e_b_c @ X @ ( after_e_b_c @ X @ ( initial_e_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(3)
thf(fact_226_converge_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c] :
      ( ( converge_a_b_c @ X @ Xa @ Xb )
     => ( ( member6330420149250801815od_b_c @ Xa @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) )
        & ( member6330420149250801815od_b_c @ Xb @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) )
        & ( ( lS_a_b_c @ X @ ( after_a_b_c @ X @ ( initial_a_b_c @ X ) @ Xa ) )
          = ( lS_a_b_c @ X @ ( after_a_b_c @ X @ ( initial_a_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(2)
thf(fact_227_converge_Oelims_I2_J,axiom,
    ! [X: fsm_e_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c] :
      ( ( converge_e_b_c @ X @ Xa @ Xb )
     => ( ( member6330420149250801815od_b_c @ Xa @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) )
        & ( member6330420149250801815od_b_c @ Xb @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) )
        & ( ( lS_e_b_c @ X @ ( after_e_b_c @ X @ ( initial_e_b_c @ X ) @ Xa ) )
          = ( lS_e_b_c @ X @ ( after_e_b_c @ X @ ( initial_e_b_c @ X ) @ Xb ) ) ) ) ) ).

% converge.elims(2)
thf(fact_228_converge_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c,Y: $o] :
      ( ( ( converge_a_b_c @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( ( member6330420149250801815od_b_c @ Xa @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) )
          & ( member6330420149250801815od_b_c @ Xb @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) )
          & ( ( lS_a_b_c @ X @ ( after_a_b_c @ X @ ( initial_a_b_c @ X ) @ Xa ) )
            = ( lS_a_b_c @ X @ ( after_a_b_c @ X @ ( initial_a_b_c @ X ) @ Xb ) ) ) ) ) ) ).

% converge.elims(1)
thf(fact_229_converge_Oelims_I1_J,axiom,
    ! [X: fsm_e_b_c,Xa: list_P903359562653991662od_b_c,Xb: list_P903359562653991662od_b_c,Y: $o] :
      ( ( ( converge_e_b_c @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( ( member6330420149250801815od_b_c @ Xa @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) )
          & ( member6330420149250801815od_b_c @ Xb @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) )
          & ( ( lS_e_b_c @ X @ ( after_e_b_c @ X @ ( initial_e_b_c @ X ) @ Xa ) )
            = ( lS_e_b_c @ X @ ( after_e_b_c @ X @ ( initial_e_b_c @ X ) @ Xb ) ) ) ) ) ) ).

% converge.elims(1)
thf(fact_230_converge_Osimps,axiom,
    ( converge_a_b_c
    = ( ^ [M2: fsm_a_b_c,Pi: list_P903359562653991662od_b_c,Tau: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ Pi @ ( lS_a_b_c @ M2 @ ( initial_a_b_c @ M2 ) ) )
          & ( member6330420149250801815od_b_c @ Tau @ ( lS_a_b_c @ M2 @ ( initial_a_b_c @ M2 ) ) )
          & ( ( lS_a_b_c @ M2 @ ( after_a_b_c @ M2 @ ( initial_a_b_c @ M2 ) @ Pi ) )
            = ( lS_a_b_c @ M2 @ ( after_a_b_c @ M2 @ ( initial_a_b_c @ M2 ) @ Tau ) ) ) ) ) ) ).

% converge.simps
thf(fact_231_converge_Osimps,axiom,
    ( converge_e_b_c
    = ( ^ [M2: fsm_e_b_c,Pi: list_P903359562653991662od_b_c,Tau: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ Pi @ ( lS_e_b_c @ M2 @ ( initial_e_b_c @ M2 ) ) )
          & ( member6330420149250801815od_b_c @ Tau @ ( lS_e_b_c @ M2 @ ( initial_e_b_c @ M2 ) ) )
          & ( ( lS_e_b_c @ M2 @ ( after_e_b_c @ M2 @ ( initial_e_b_c @ M2 ) @ Pi ) )
            = ( lS_e_b_c @ M2 @ ( after_e_b_c @ M2 @ ( initial_e_b_c @ M2 ) @ Tau ) ) ) ) ) ) ).

% converge.simps
thf(fact_232_is__state__cover__assignment__language,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,V: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,Q: list_P903359562653991662od_b_c] :
      ( ( state_2362830510734323903_c_b_c @ M @ V )
     => ( ( member6330420149250801815od_b_c @ Q @ ( reacha8116992257183400179_c_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( V @ Q ) @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) ) ) ) ).

% is_state_cover_assignment_language
thf(fact_233_is__state__cover__assignment__language,axiom,
    ! [M: fsm_b_b_c,V: b > list_P903359562653991662od_b_c,Q: b] :
      ( ( state_4045177151805148240_b_b_c @ M @ V )
     => ( ( member_b @ Q @ ( reacha7216524145940060804_b_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( V @ Q ) @ ( lS_b_b_c @ M @ ( initial_b_b_c @ M ) ) ) ) ) ).

% is_state_cover_assignment_language
thf(fact_234_is__state__cover__assignment__language,axiom,
    ! [M: fsm_c_b_c,V: c > list_P903359562653991662od_b_c,Q: c] :
      ( ( state_418023730138503121_c_b_c @ M @ V )
     => ( ( member_c @ Q @ ( reacha3589370724273415685_c_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( V @ Q ) @ ( lS_c_b_c @ M @ ( initial_c_b_c @ M ) ) ) ) ) ).

% is_state_cover_assignment_language
thf(fact_235_is__state__cover__assignment__language,axiom,
    ! [M: fsm_e_b_c,V: e > list_P903359562653991662od_b_c,Q: e] :
      ( ( state_2387088923659988691_e_b_c @ M @ V )
     => ( ( member_e @ Q @ ( reacha5558435917794901255_e_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( V @ Q ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) ) ) ) ).

% is_state_cover_assignment_language
thf(fact_236_is__state__cover__assignment__language,axiom,
    ! [M: fsm_a_b_c,V: a > list_P903359562653991662od_b_c,Q: a] :
      ( ( state_7672330573471793359_a_b_c @ M @ V )
     => ( ( member_a @ Q @ ( reacha1620305530751930115_a_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( V @ Q ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) ) ).

% is_state_cover_assignment_language
thf(fact_237_after__language__subset,axiom,
    ! [M: fsm_a_b_c,Alpha2: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
       => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) ) ) )
         => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Gamma @ Beta ) @ ( lS_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Alpha2 ) ) ) ) ) ) ).

% after_language_subset
thf(fact_238_after__language__subset,axiom,
    ! [M: fsm_e_b_c,Alpha2: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
       => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_e_b_c @ M @ ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) ) ) )
         => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Gamma @ Beta ) @ ( lS_e_b_c @ M @ ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ Alpha2 ) ) ) ) ) ) ).

% after_language_subset
thf(fact_239_after__language__append__iff,axiom,
    ! [M: fsm_a_b_c,Alpha2: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
       => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) ) ) )
          = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Gamma @ Beta ) @ ( lS_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Alpha2 ) ) ) ) ) ) ).

% after_language_append_iff
thf(fact_240_after__language__append__iff,axiom,
    ! [M: fsm_e_b_c,Alpha2: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
       => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_e_b_c @ M @ ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) ) ) )
          = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Gamma @ Beta ) @ ( lS_e_b_c @ M @ ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ Alpha2 ) ) ) ) ) ) ).

% after_language_append_iff
thf(fact_241_diverge__prefix,axiom,
    ! [M: fsm_a_b_c,Alpha2: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
         => ( ~ ( converge_a_b_c @ M @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) )
           => ~ ( converge_a_b_c @ M @ Alpha2 @ Beta ) ) ) ) ) ).

% diverge_prefix
thf(fact_242_diverge__prefix,axiom,
    ! [M: fsm_e_b_c,Alpha2: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
         => ( ~ ( converge_e_b_c @ M @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) )
           => ~ ( converge_e_b_c @ M @ Alpha2 @ Beta ) ) ) ) ) ).

% diverge_prefix
thf(fact_243_converge__append,axiom,
    ! [M: fsm_a_b_c,Alpha2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( converge_a_b_c @ M @ Alpha2 @ Beta )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
           => ( converge_a_b_c @ M @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) ) ) ) ) ) ).

% converge_append
thf(fact_244_converge__append,axiom,
    ! [M: fsm_e_b_c,Alpha2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( converge_e_b_c @ M @ Alpha2 @ Beta )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
           => ( converge_e_b_c @ M @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) ) ) ) ) ) ).

% converge_append
thf(fact_245_converge__extend,axiom,
    ! [M: fsm_a_b_c,Alpha2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( converge_a_b_c @ M @ Alpha2 @ Beta )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
           => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) ) ) ) ).

% converge_extend
thf(fact_246_converge__extend,axiom,
    ! [M: fsm_e_b_c,Alpha2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( converge_e_b_c @ M @ Alpha2 @ Beta )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
           => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) ) ) ) ) ) ).

% converge_extend
thf(fact_247_converge__append__language__iff,axiom,
    ! [M: fsm_a_b_c,Alpha2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( converge_a_b_c @ M @ Alpha2 @ Beta )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
          = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) ) ) ).

% converge_append_language_iff
thf(fact_248_converge__append__language__iff,axiom,
    ! [M: fsm_e_b_c,Alpha2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( converge_e_b_c @ M @ Alpha2 @ Beta )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
          = ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) ) ) ) ) ).

% converge_append_language_iff
thf(fact_249_after__reachable__initial,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) )
       => ( member6330420149250801815od_b_c @ ( after_4052058690717316294_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) @ Io ) @ ( reacha8116992257183400179_c_b_c @ M ) ) ) ) ).

% after_reachable_initial
thf(fact_250_after__reachable__initial,axiom,
    ! [M: fsm_b_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( observable_b_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_b_b_c @ M @ ( initial_b_b_c @ M ) ) )
       => ( member_b @ ( after_b_b_c @ M @ ( initial_b_b_c @ M ) @ Io ) @ ( reacha7216524145940060804_b_b_c @ M ) ) ) ) ).

% after_reachable_initial
thf(fact_251_after__reachable__initial,axiom,
    ! [M: fsm_c_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( observable_c_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_c_b_c @ M @ ( initial_c_b_c @ M ) ) )
       => ( member_c @ ( after_c_b_c @ M @ ( initial_c_b_c @ M ) @ Io ) @ ( reacha3589370724273415685_c_b_c @ M ) ) ) ) ).

% after_reachable_initial
thf(fact_252_after__reachable__initial,axiom,
    ! [M: fsm_e_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
       => ( member_e @ ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ Io ) @ ( reacha5558435917794901255_e_b_c @ M ) ) ) ) ).

% after_reachable_initial
thf(fact_253_after__reachable__initial,axiom,
    ! [M: fsm_a_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
       => ( member_a @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Io ) @ ( reacha1620305530751930115_a_b_c @ M ) ) ) ) ).

% after_reachable_initial
thf(fact_254_state__cover__assignment__after_I1_J,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,V: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,Q: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( state_2362830510734323903_c_b_c @ M @ V )
       => ( ( member6330420149250801815od_b_c @ Q @ ( reacha8116992257183400179_c_b_c @ M ) )
         => ( member6330420149250801815od_b_c @ ( V @ Q ) @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) ) ) ) ) ).

% state_cover_assignment_after(1)
thf(fact_255_state__cover__assignment__after_I1_J,axiom,
    ! [M: fsm_b_b_c,V: b > list_P903359562653991662od_b_c,Q: b] :
      ( ( observable_b_b_c @ M )
     => ( ( state_4045177151805148240_b_b_c @ M @ V )
       => ( ( member_b @ Q @ ( reacha7216524145940060804_b_b_c @ M ) )
         => ( member6330420149250801815od_b_c @ ( V @ Q ) @ ( lS_b_b_c @ M @ ( initial_b_b_c @ M ) ) ) ) ) ) ).

% state_cover_assignment_after(1)
thf(fact_256_state__cover__assignment__after_I1_J,axiom,
    ! [M: fsm_c_b_c,V: c > list_P903359562653991662od_b_c,Q: c] :
      ( ( observable_c_b_c @ M )
     => ( ( state_418023730138503121_c_b_c @ M @ V )
       => ( ( member_c @ Q @ ( reacha3589370724273415685_c_b_c @ M ) )
         => ( member6330420149250801815od_b_c @ ( V @ Q ) @ ( lS_c_b_c @ M @ ( initial_c_b_c @ M ) ) ) ) ) ) ).

% state_cover_assignment_after(1)
thf(fact_257_state__cover__assignment__after_I1_J,axiom,
    ! [M: fsm_e_b_c,V: e > list_P903359562653991662od_b_c,Q: e] :
      ( ( observable_e_b_c @ M )
     => ( ( state_2387088923659988691_e_b_c @ M @ V )
       => ( ( member_e @ Q @ ( reacha5558435917794901255_e_b_c @ M ) )
         => ( member6330420149250801815od_b_c @ ( V @ Q ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) ) ) ) ) ).

% state_cover_assignment_after(1)
thf(fact_258_state__cover__assignment__after_I1_J,axiom,
    ! [M: fsm_a_b_c,V: a > list_P903359562653991662od_b_c,Q: a] :
      ( ( observable_a_b_c @ M )
     => ( ( state_7672330573471793359_a_b_c @ M @ V )
       => ( ( member_a @ Q @ ( reacha1620305530751930115_a_b_c @ M ) )
         => ( member6330420149250801815od_b_c @ ( V @ Q ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) ) ) ).

% state_cover_assignment_after(1)
thf(fact_259_is__state__cover__assignment__observable__after,axiom,
    ! [M: fsm_e_b_c,V: e > list_P903359562653991662od_b_c,Q: e] :
      ( ( observable_e_b_c @ M )
     => ( ( state_2387088923659988691_e_b_c @ M @ V )
       => ( ( member_e @ Q @ ( reacha5558435917794901255_e_b_c @ M ) )
         => ( ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ ( V @ Q ) )
            = Q ) ) ) ) ).

% is_state_cover_assignment_observable_after
thf(fact_260_is__state__cover__assignment__observable__after,axiom,
    ! [M: fsm_a_b_c,V: a > list_P903359562653991662od_b_c,Q: a] :
      ( ( observable_a_b_c @ M )
     => ( ( state_7672330573471793359_a_b_c @ M @ V )
       => ( ( member_a @ Q @ ( reacha1620305530751930115_a_b_c @ M ) )
         => ( ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ ( V @ Q ) )
            = Q ) ) ) ) ).

% is_state_cover_assignment_observable_after
thf(fact_261_convergence__minimal,axiom,
    ! [M: fsm_a_b_c,Alpha2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( minimal_a_b_c @ M )
     => ( ( observable_a_b_c @ M )
       => ( ( member6330420149250801815od_b_c @ Alpha2 @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
           => ( ( converge_a_b_c @ M @ Alpha2 @ Beta )
              = ( ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Alpha2 )
                = ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Beta ) ) ) ) ) ) ) ).

% convergence_minimal
thf(fact_262_convergence__minimal,axiom,
    ! [M: fsm_e_b_c,Alpha2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( minimal_e_b_c @ M )
     => ( ( observable_e_b_c @ M )
       => ( ( member6330420149250801815od_b_c @ Alpha2 @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
           => ( ( converge_e_b_c @ M @ Alpha2 @ Beta )
              = ( ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ Alpha2 )
                = ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ Beta ) ) ) ) ) ) ) ).

% convergence_minimal
thf(fact_263_reachable__states__initial__or__target,axiom,
    ! [Q: e,M: fsm_e_b_c] :
      ( ( member_e @ Q @ ( reacha5558435917794901255_e_b_c @ M ) )
     => ( ( Q
          = ( initial_e_b_c @ M ) )
        | ? [X2: produc4050040609193146166od_c_e] :
            ( ( member6882148676089805663od_c_e @ X2 @ ( transitions_e_b_c @ M ) )
            & ( member_e @ ( produc6751554238685325970od_c_e @ X2 ) @ ( reacha5558435917794901255_e_b_c @ M ) )
            & ( ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ X2 ) ) )
              = Q ) ) ) ) ).

% reachable_states_initial_or_target
thf(fact_264_reachable__states__initial__or__target,axiom,
    ! [Q: a,M: fsm_a_b_c] :
      ( ( member_a @ Q @ ( reacha1620305530751930115_a_b_c @ M ) )
     => ( ( Q
          = ( initial_a_b_c @ M ) )
        | ? [X2: produc2669932201312201782od_c_a] :
            ( ( member5502040268208861279od_c_a @ X2 @ ( transitions_a_b_c @ M ) )
            & ( member_a @ ( produc4225943634317630866od_c_a @ X2 ) @ ( reacha1620305530751930115_a_b_c @ M ) )
            & ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) ) )
              = Q ) ) ) ) ).

% reachable_states_initial_or_target
thf(fact_265_reachable__states__induct,axiom,
    ! [Q: e,M: fsm_e_b_c,P: e > $o] :
      ( ( member_e @ Q @ ( reacha5558435917794901255_e_b_c @ M ) )
     => ( ( P @ ( initial_e_b_c @ M ) )
       => ( ! [T4: produc4050040609193146166od_c_e] :
              ( ( member6882148676089805663od_c_e @ T4 @ ( transitions_e_b_c @ M ) )
             => ( ( member_e @ ( produc6751554238685325970od_c_e @ T4 ) @ ( reacha5558435917794901255_e_b_c @ M ) )
               => ( ( P @ ( produc6751554238685325970od_c_e @ T4 ) )
                 => ( P @ ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T4 ) ) ) ) ) ) )
         => ( P @ Q ) ) ) ) ).

% reachable_states_induct
thf(fact_266_reachable__states__induct,axiom,
    ! [Q: a,M: fsm_a_b_c,P: a > $o] :
      ( ( member_a @ Q @ ( reacha1620305530751930115_a_b_c @ M ) )
     => ( ( P @ ( initial_a_b_c @ M ) )
       => ( ! [T4: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ T4 @ ( transitions_a_b_c @ M ) )
             => ( ( member_a @ ( produc4225943634317630866od_c_a @ T4 ) @ ( reacha1620305530751930115_a_b_c @ M ) )
               => ( ( P @ ( produc4225943634317630866od_c_a @ T4 ) )
                 => ( P @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) ) ) ) )
         => ( P @ Q ) ) ) ) ).

% reachable_states_induct
thf(fact_267_reachable__states__cases,axiom,
    ! [Q: e,M: fsm_e_b_c,P: e > $o] :
      ( ( member_e @ Q @ ( reacha5558435917794901255_e_b_c @ M ) )
     => ( ( P @ ( initial_e_b_c @ M ) )
       => ( ! [T4: produc4050040609193146166od_c_e] :
              ( ( member6882148676089805663od_c_e @ T4 @ ( transitions_e_b_c @ M ) )
             => ( ( member_e @ ( produc6751554238685325970od_c_e @ T4 ) @ ( reacha5558435917794901255_e_b_c @ M ) )
               => ( P @ ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T4 ) ) ) ) ) )
         => ( P @ Q ) ) ) ) ).

% reachable_states_cases
thf(fact_268_reachable__states__cases,axiom,
    ! [Q: a,M: fsm_a_b_c,P: a > $o] :
      ( ( member_a @ Q @ ( reacha1620305530751930115_a_b_c @ M ) )
     => ( ( P @ ( initial_a_b_c @ M ) )
       => ( ! [T4: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ T4 @ ( transitions_a_b_c @ M ) )
             => ( ( member_a @ ( produc4225943634317630866od_c_a @ T4 ) @ ( reacha1620305530751930115_a_b_c @ M ) )
               => ( P @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) ) ) )
         => ( P @ Q ) ) ) ) ).

% reachable_states_cases
thf(fact_269_prefixes__eq__snoc,axiom,
    ! [Ys: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c,X: list_P903359562653991662od_b_c] :
      ( ( ( prefix1131979855692807669od_b_c @ Ys )
        = ( append6992831555715836169od_b_c @ Xs @ ( cons_l342771267123639716od_b_c @ X @ nil_li8071162985807626740od_b_c ) ) )
      = ( ( ( ( Ys = nil_Product_prod_b_c )
            & ( Xs = nil_li8071162985807626740od_b_c ) )
          | ? [Z2: product_prod_b_c,Zs2: list_P903359562653991662od_b_c] :
              ( ( Ys
                = ( append2547753245680614915od_b_c @ Zs2 @ ( cons_P4529483553340347422od_b_c @ Z2 @ nil_Product_prod_b_c ) ) )
              & ( Xs
                = ( prefix1131979855692807669od_b_c @ Zs2 ) ) ) )
        & ( X = Ys ) ) ) ).

% prefixes_eq_snoc
thf(fact_270_acyclic__no__self__loop,axiom,
    ! [M: fsm_a_b_c,Q: a] :
      ( ( acyclic_a_b_c @ M )
     => ( ( member_a @ Q @ ( reacha1620305530751930115_a_b_c @ M ) )
       => ~ ? [X4: b,Y5: c] : ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q @ ( produc3440865914000881661od_c_a @ X4 @ ( product_Pair_c_a @ Y5 @ Q ) ) ) @ ( transitions_a_b_c @ M ) ) ) ) ).

% acyclic_no_self_loop
thf(fact_271_initialised__convergence__preserving__transition__cover__is__complete,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_a_b_c,T: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_a_b_c @ M1 )
         => ( ( minimal_a_b_c @ M22 )
           => ( ( ( inputs_a_b_c @ M22 )
                = ( inputs_a_b_c @ M1 ) )
             => ( ( ( outputs_a_b_c @ M22 )
                  = ( outputs_a_b_c @ M1 ) )
               => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ T )
                    = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ T ) )
                 => ( ( ord_le282488521294790766od_b_c @ A2 @ T )
                   => ( ( transi6365780447273092801_a_b_c @ M1 @ A2 )
                     => ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ A2 )
                       => ( ( preser1543909642583041678_b_c_a @ M1 @ M22 @ A2 )
                         => ( ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) )
                            = ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% initialised_convergence_preserving_transition_cover_is_complete
thf(fact_272_initialised__convergence__preserving__transition__cover__is__complete,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_e_b_c,T: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( observable_e_b_c @ M22 )
       => ( ( minimal_a_b_c @ M1 )
         => ( ( minimal_e_b_c @ M22 )
           => ( ( ( inputs_e_b_c @ M22 )
                = ( inputs_a_b_c @ M1 ) )
             => ( ( ( outputs_e_b_c @ M22 )
                  = ( outputs_a_b_c @ M1 ) )
               => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ T )
                    = ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M22 @ ( initial_e_b_c @ M22 ) ) @ T ) )
                 => ( ( ord_le282488521294790766od_b_c @ A2 @ T )
                   => ( ( transi6365780447273092801_a_b_c @ M1 @ A2 )
                     => ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ A2 )
                       => ( ( preser1543909642583041682_b_c_e @ M1 @ M22 @ A2 )
                         => ( ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) )
                            = ( lS_e_b_c @ M22 @ ( initial_e_b_c @ M22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% initialised_convergence_preserving_transition_cover_is_complete
thf(fact_273_initialised__convergence__preserving__transition__cover__is__complete,axiom,
    ! [M1: fsm_e_b_c,M22: fsm_a_b_c,T: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( observable_e_b_c @ M1 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_e_b_c @ M1 )
         => ( ( minimal_a_b_c @ M22 )
           => ( ( ( inputs_a_b_c @ M22 )
                = ( inputs_e_b_c @ M1 ) )
             => ( ( ( outputs_a_b_c @ M22 )
                  = ( outputs_e_b_c @ M1 ) )
               => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) @ T )
                    = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ T ) )
                 => ( ( ord_le282488521294790766od_b_c @ A2 @ T )
                   => ( ( transi1080538797461288133_e_b_c @ M1 @ A2 )
                     => ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ A2 )
                       => ( ( preser7495757791762235786_b_c_a @ M1 @ M22 @ A2 )
                         => ( ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) )
                            = ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% initialised_convergence_preserving_transition_cover_is_complete
thf(fact_274_initialised__convergence__preserving__transition__cover__is__complete,axiom,
    ! [M1: fsm_e_b_c,M22: fsm_e_b_c,T: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( observable_e_b_c @ M1 )
     => ( ( observable_e_b_c @ M22 )
       => ( ( minimal_e_b_c @ M1 )
         => ( ( minimal_e_b_c @ M22 )
           => ( ( ( inputs_e_b_c @ M22 )
                = ( inputs_e_b_c @ M1 ) )
             => ( ( ( outputs_e_b_c @ M22 )
                  = ( outputs_e_b_c @ M1 ) )
               => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) @ T )
                    = ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M22 @ ( initial_e_b_c @ M22 ) ) @ T ) )
                 => ( ( ord_le282488521294790766od_b_c @ A2 @ T )
                   => ( ( transi1080538797461288133_e_b_c @ M1 @ A2 )
                     => ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ A2 )
                       => ( ( preser7495757791762235790_b_c_e @ M1 @ M22 @ A2 )
                         => ( ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) )
                            = ( lS_e_b_c @ M22 @ ( initial_e_b_c @ M22 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% initialised_convergence_preserving_transition_cover_is_complete
thf(fact_275_pass__io__set__def,axiom,
    ( pass_io_set_a_b_c
    = ( ^ [M2: fsm_a_b_c,Ios2: set_li6436108459499378894od_b_c] :
        ! [Io3: list_P903359562653991662od_b_c,X3: b,Y3: c] :
          ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io3 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X3 @ Y3 ) @ nil_Product_prod_b_c ) ) @ Ios2 )
         => ! [Y6: c] :
              ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io3 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X3 @ Y6 ) @ nil_Product_prod_b_c ) ) @ ( lS_a_b_c @ M2 @ ( initial_a_b_c @ M2 ) ) )
             => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io3 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X3 @ Y6 ) @ nil_Product_prod_b_c ) ) @ Ios2 ) ) ) ) ) ).

% pass_io_set_def
thf(fact_276_pass__io__set__def,axiom,
    ( pass_io_set_e_b_c
    = ( ^ [M2: fsm_e_b_c,Ios2: set_li6436108459499378894od_b_c] :
        ! [Io3: list_P903359562653991662od_b_c,X3: b,Y3: c] :
          ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io3 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X3 @ Y3 ) @ nil_Product_prod_b_c ) ) @ Ios2 )
         => ! [Y6: c] :
              ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io3 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X3 @ Y6 ) @ nil_Product_prod_b_c ) ) @ ( lS_e_b_c @ M2 @ ( initial_e_b_c @ M2 ) ) )
             => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io3 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X3 @ Y6 ) @ nil_Product_prod_b_c ) ) @ Ios2 ) ) ) ) ) ).

% pass_io_set_def
thf(fact_277_pass__io__set__maximal__def,axiom,
    ( pass_i5868551379204665570_a_b_c
    = ( ^ [M2: fsm_a_b_c,Ios2: set_li6436108459499378894od_b_c] :
        ! [Io3: list_P903359562653991662od_b_c,X3: b,Y3: c,Io4: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io3 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X3 @ Y3 ) @ nil_Product_prod_b_c ) @ Io4 ) ) @ Ios2 )
         => ! [Y6: c] :
              ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io3 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X3 @ Y6 ) @ nil_Product_prod_b_c ) ) @ ( lS_a_b_c @ M2 @ ( initial_a_b_c @ M2 ) ) )
             => ? [Io5: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io3 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X3 @ Y6 ) @ nil_Product_prod_b_c ) @ Io5 ) ) @ Ios2 ) ) ) ) ) ).

% pass_io_set_maximal_def
thf(fact_278_pass__io__set__maximal__def,axiom,
    ( pass_i583309729392860902_e_b_c
    = ( ^ [M2: fsm_e_b_c,Ios2: set_li6436108459499378894od_b_c] :
        ! [Io3: list_P903359562653991662od_b_c,X3: b,Y3: c,Io4: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io3 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X3 @ Y3 ) @ nil_Product_prod_b_c ) @ Io4 ) ) @ Ios2 )
         => ! [Y6: c] :
              ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io3 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X3 @ Y6 ) @ nil_Product_prod_b_c ) ) @ ( lS_e_b_c @ M2 @ ( initial_e_b_c @ M2 ) ) )
             => ? [Io5: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io3 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X3 @ Y6 ) @ nil_Product_prod_b_c ) @ Io5 ) ) @ Ios2 ) ) ) ) ) ).

% pass_io_set_maximal_def
thf(fact_279_convergence__graph__insert__invar__def,axiom,
    ( conver9163591880137905914_c_e_d
    = ( ^ [M12: fsm_a_b_c,M23: fsm_e_b_c,Cg_lookup: d > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,Cg_insert: d > list_P903359562653991662od_b_c > d] :
        ! [G2: d,Gamma2: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ Gamma2 @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) )
         => ( ( member6330420149250801815od_b_c @ Gamma2 @ ( lS_e_b_c @ M23 @ ( initial_e_b_c @ M23 ) ) )
           => ( ( conver4302099639658809211_c_e_d @ M12 @ M23 @ Cg_lookup @ G2 )
             => ( conver4302099639658809211_c_e_d @ M12 @ M23 @ Cg_lookup @ ( Cg_insert @ G2 @ Gamma2 ) ) ) ) ) ) ) ).

% convergence_graph_insert_invar_def
thf(fact_280_observable__language__next,axiom,
    ! [Io: product_prod_b_c,Ios: list_P903359562653991662od_b_c,M: fsm_a_b_c,T3: produc2669932201312201782od_c_a] :
      ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ Io @ Ios ) @ ( lS_a_b_c @ M @ ( produc4225943634317630866od_c_a @ T3 ) ) )
     => ( ( observable_a_b_c @ M )
       => ( ( member5502040268208861279od_c_a @ T3 @ ( transitions_a_b_c @ M ) )
         => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) )
              = ( product_fst_b_c @ Io ) )
           => ( ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) )
                = ( product_snd_b_c @ Io ) )
             => ( member6330420149250801815od_b_c @ Ios @ ( lS_a_b_c @ ( from_FSM_a_b_c @ M @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) ) ) @ ( initial_a_b_c @ ( from_FSM_a_b_c @ M @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) ) ) ) ) ) ) ) ) ) ) ).

% observable_language_next
thf(fact_281_observable__language__next,axiom,
    ! [Io: product_prod_b_c,Ios: list_P903359562653991662od_b_c,M: fsm_e_b_c,T3: produc4050040609193146166od_c_e] :
      ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ Io @ Ios ) @ ( lS_e_b_c @ M @ ( produc6751554238685325970od_c_e @ T3 ) ) )
     => ( ( observable_e_b_c @ M )
       => ( ( member6882148676089805663od_c_e @ T3 @ ( transitions_e_b_c @ M ) )
         => ( ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) )
              = ( product_fst_b_c @ Io ) )
           => ( ( ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) )
                = ( product_snd_b_c @ Io ) )
             => ( member6330420149250801815od_b_c @ Ios @ ( lS_e_b_c @ ( from_FSM_e_b_c @ M @ ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) ) ) @ ( initial_e_b_c @ ( from_FSM_e_b_c @ M @ ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) ) ) ) ) ) ) ) ) ) ) ).

% observable_language_next
thf(fact_282_minimally__distinguishes__after__append__initial,axiom,
    ! [M: fsm_a_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( minimal_a_b_c @ M )
       => ( ( member6330420149250801815od_b_c @ U @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ V3 @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
           => ( ( minima243535863231358885_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ U ) @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ V3 ) @ ( append2547753245680614915od_b_c @ W @ W3 ) )
             => ( ( W3 != nil_Product_prod_b_c )
               => ( minima243535863231358885_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ ( append2547753245680614915od_b_c @ U @ W ) ) @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ ( append2547753245680614915od_b_c @ V3 @ W ) ) @ W3 ) ) ) ) ) ) ) ).

% minimally_distinguishes_after_append_initial
thf(fact_283_minimally__distinguishes__after__append__initial,axiom,
    ! [M: fsm_e_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( minimal_e_b_c @ M )
       => ( ( member6330420149250801815od_b_c @ U @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ V3 @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
           => ( ( minima4181666250274330025_e_b_c @ M @ ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ U ) @ ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ V3 ) @ ( append2547753245680614915od_b_c @ W @ W3 ) )
             => ( ( W3 != nil_Product_prod_b_c )
               => ( minima4181666250274330025_e_b_c @ M @ ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ ( append2547753245680614915od_b_c @ U @ W ) ) @ ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ ( append2547753245680614915od_b_c @ V3 @ W ) ) @ W3 ) ) ) ) ) ) ) ).

% minimally_distinguishes_after_append_initial
thf(fact_284_from__FSM__observable,axiom,
    ! [M: fsm_a_b_c,Q: a] :
      ( ( observable_a_b_c @ M )
     => ( observable_a_b_c @ ( from_FSM_a_b_c @ M @ Q ) ) ) ).

% from_FSM_observable
thf(fact_285_from__FSM__observable,axiom,
    ! [M: fsm_e_b_c,Q: e] :
      ( ( observable_e_b_c @ M )
     => ( observable_e_b_c @ ( from_FSM_e_b_c @ M @ Q ) ) ) ).

% from_FSM_observable
thf(fact_286_from__FSM__reachable__states,axiom,
    ! [Q: a,M: fsm_a_b_c] :
      ( ( member_a @ Q @ ( reacha1620305530751930115_a_b_c @ M ) )
     => ( ord_less_eq_set_a @ ( reacha1620305530751930115_a_b_c @ ( from_FSM_a_b_c @ M @ Q ) ) @ ( reacha1620305530751930115_a_b_c @ M ) ) ) ).

% from_FSM_reachable_states
thf(fact_287_from__FSM__acyclic,axiom,
    ! [Q: a,M: fsm_a_b_c] :
      ( ( member_a @ Q @ ( reacha1620305530751930115_a_b_c @ M ) )
     => ( ( acyclic_a_b_c @ M )
       => ( acyclic_a_b_c @ ( from_FSM_a_b_c @ M @ Q ) ) ) ) ).

% from_FSM_acyclic
thf(fact_288_state__cover__assignment__language,axiom,
    ! [M: fsm_e_b_c,V: e > list_P903359562653991662od_b_c] :
      ( ( state_2387088923659988691_e_b_c @ M @ V )
     => ( ord_le282488521294790766od_b_c @ ( image_5036025201050656753od_b_c @ V @ ( reacha5558435917794901255_e_b_c @ M ) ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) ) ) ).

% state_cover_assignment_language
thf(fact_289_state__cover__assignment__language,axiom,
    ! [M: fsm_a_b_c,V: a > list_P903359562653991662od_b_c] :
      ( ( state_7672330573471793359_a_b_c @ M @ V )
     => ( ord_le282488521294790766od_b_c @ ( image_8656872703560917237od_b_c @ V @ ( reacha1620305530751930115_a_b_c @ M ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) ).

% state_cover_assignment_language
thf(fact_290_preserves__convergence_Osimps,axiom,
    ( preser1543909642583041678_b_c_a
    = ( ^ [M12: fsm_a_b_c,M23: fsm_a_b_c,A5: set_li6436108459499378894od_b_c] :
        ! [X3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) @ A5 ) )
         => ! [Y3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Y3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) @ A5 ) )
             => ( ( converge_a_b_c @ M12 @ X3 @ Y3 )
               => ( converge_a_b_c @ M23 @ X3 @ Y3 ) ) ) ) ) ) ).

% preserves_convergence.simps
thf(fact_291_preserves__convergence_Osimps,axiom,
    ( preser1543909642583041682_b_c_e
    = ( ^ [M12: fsm_a_b_c,M23: fsm_e_b_c,A5: set_li6436108459499378894od_b_c] :
        ! [X3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) @ A5 ) )
         => ! [Y3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Y3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) @ A5 ) )
             => ( ( converge_a_b_c @ M12 @ X3 @ Y3 )
               => ( converge_e_b_c @ M23 @ X3 @ Y3 ) ) ) ) ) ) ).

% preserves_convergence.simps
thf(fact_292_preserves__convergence_Osimps,axiom,
    ( preser7495757791762235786_b_c_a
    = ( ^ [M12: fsm_e_b_c,M23: fsm_a_b_c,A5: set_li6436108459499378894od_b_c] :
        ! [X3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X3 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M12 @ ( initial_e_b_c @ M12 ) ) @ A5 ) )
         => ! [Y3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Y3 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M12 @ ( initial_e_b_c @ M12 ) ) @ A5 ) )
             => ( ( converge_e_b_c @ M12 @ X3 @ Y3 )
               => ( converge_a_b_c @ M23 @ X3 @ Y3 ) ) ) ) ) ) ).

% preserves_convergence.simps
thf(fact_293_preserves__convergence_Osimps,axiom,
    ( preser7495757791762235790_b_c_e
    = ( ^ [M12: fsm_e_b_c,M23: fsm_e_b_c,A5: set_li6436108459499378894od_b_c] :
        ! [X3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X3 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M12 @ ( initial_e_b_c @ M12 ) ) @ A5 ) )
         => ! [Y3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Y3 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M12 @ ( initial_e_b_c @ M12 ) ) @ A5 ) )
             => ( ( converge_e_b_c @ M12 @ X3 @ Y3 )
               => ( converge_e_b_c @ M23 @ X3 @ Y3 ) ) ) ) ) ) ).

% preserves_convergence.simps
thf(fact_294_preserves__convergence_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Xa: fsm_a_b_c,Xb: set_li6436108459499378894od_b_c,Y: $o] :
      ( ( ( preser1543909642583041678_b_c_a @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( ! [X3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
             => ! [Y3: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
                 => ( ( converge_a_b_c @ X @ X3 @ Y3 )
                   => ( converge_a_b_c @ Xa @ X3 @ Y3 ) ) ) ) ) ) ) ).

% preserves_convergence.elims(1)
thf(fact_295_preserves__convergence_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Xa: fsm_e_b_c,Xb: set_li6436108459499378894od_b_c,Y: $o] :
      ( ( ( preser1543909642583041682_b_c_e @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( ! [X3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
             => ! [Y3: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
                 => ( ( converge_a_b_c @ X @ X3 @ Y3 )
                   => ( converge_e_b_c @ Xa @ X3 @ Y3 ) ) ) ) ) ) ) ).

% preserves_convergence.elims(1)
thf(fact_296_preserves__convergence_Oelims_I1_J,axiom,
    ! [X: fsm_e_b_c,Xa: fsm_a_b_c,Xb: set_li6436108459499378894od_b_c,Y: $o] :
      ( ( ( preser7495757791762235786_b_c_a @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( ! [X3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X3 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
             => ! [Y3: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y3 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
                 => ( ( converge_e_b_c @ X @ X3 @ Y3 )
                   => ( converge_a_b_c @ Xa @ X3 @ Y3 ) ) ) ) ) ) ) ).

% preserves_convergence.elims(1)
thf(fact_297_preserves__convergence_Oelims_I1_J,axiom,
    ! [X: fsm_e_b_c,Xa: fsm_e_b_c,Xb: set_li6436108459499378894od_b_c,Y: $o] :
      ( ( ( preser7495757791762235790_b_c_e @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( ! [X3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X3 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
             => ! [Y3: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y3 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
                 => ( ( converge_e_b_c @ X @ X3 @ Y3 )
                   => ( converge_e_b_c @ Xa @ X3 @ Y3 ) ) ) ) ) ) ) ).

% preserves_convergence.elims(1)
thf(fact_298_preserves__convergence_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c,Xa: fsm_a_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ( preser1543909642583041678_b_c_a @ X @ Xa @ Xb )
     => ! [X4: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X4 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
         => ! [Xa3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Xa3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
             => ( ( converge_a_b_c @ X @ X4 @ Xa3 )
               => ( converge_a_b_c @ Xa @ X4 @ Xa3 ) ) ) ) ) ).

% preserves_convergence.elims(2)
thf(fact_299_preserves__convergence_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c,Xa: fsm_e_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ( preser1543909642583041682_b_c_e @ X @ Xa @ Xb )
     => ! [X4: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X4 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
         => ! [Xa3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Xa3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
             => ( ( converge_a_b_c @ X @ X4 @ Xa3 )
               => ( converge_e_b_c @ Xa @ X4 @ Xa3 ) ) ) ) ) ).

% preserves_convergence.elims(2)
thf(fact_300_preserves__convergence_Oelims_I2_J,axiom,
    ! [X: fsm_e_b_c,Xa: fsm_a_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ( preser7495757791762235786_b_c_a @ X @ Xa @ Xb )
     => ! [X4: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X4 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
         => ! [Xa3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Xa3 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
             => ( ( converge_e_b_c @ X @ X4 @ Xa3 )
               => ( converge_a_b_c @ Xa @ X4 @ Xa3 ) ) ) ) ) ).

% preserves_convergence.elims(2)
thf(fact_301_preserves__convergence_Oelims_I2_J,axiom,
    ! [X: fsm_e_b_c,Xa: fsm_e_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ( preser7495757791762235790_b_c_e @ X @ Xa @ Xb )
     => ! [X4: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X4 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
         => ! [Xa3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Xa3 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
             => ( ( converge_e_b_c @ X @ X4 @ Xa3 )
               => ( converge_e_b_c @ Xa @ X4 @ Xa3 ) ) ) ) ) ).

% preserves_convergence.elims(2)
thf(fact_302_preserves__convergence_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c,Xa: fsm_a_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ~ ( preser1543909642583041678_b_c_a @ X @ Xa @ Xb )
     => ~ ! [X2: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X2 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
           => ! [Xa2: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Xa2 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
               => ( ( converge_a_b_c @ X @ X2 @ Xa2 )
                 => ( converge_a_b_c @ Xa @ X2 @ Xa2 ) ) ) ) ) ).

% preserves_convergence.elims(3)
thf(fact_303_preserves__convergence_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c,Xa: fsm_e_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ~ ( preser1543909642583041682_b_c_e @ X @ Xa @ Xb )
     => ~ ! [X2: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X2 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
           => ! [Xa2: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Xa2 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
               => ( ( converge_a_b_c @ X @ X2 @ Xa2 )
                 => ( converge_e_b_c @ Xa @ X2 @ Xa2 ) ) ) ) ) ).

% preserves_convergence.elims(3)
thf(fact_304_preserves__convergence_Oelims_I3_J,axiom,
    ! [X: fsm_e_b_c,Xa: fsm_a_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ~ ( preser7495757791762235786_b_c_a @ X @ Xa @ Xb )
     => ~ ! [X2: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X2 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
           => ! [Xa2: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Xa2 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
               => ( ( converge_e_b_c @ X @ X2 @ Xa2 )
                 => ( converge_a_b_c @ Xa @ X2 @ Xa2 ) ) ) ) ) ).

% preserves_convergence.elims(3)
thf(fact_305_preserves__convergence_Oelims_I3_J,axiom,
    ! [X: fsm_e_b_c,Xa: fsm_e_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ~ ( preser7495757791762235790_b_c_e @ X @ Xa @ Xb )
     => ~ ! [X2: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X2 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
           => ! [Xa2: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Xa2 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
               => ( ( converge_e_b_c @ X @ X2 @ Xa2 )
                 => ( converge_e_b_c @ Xa @ X2 @ Xa2 ) ) ) ) ) ).

% preserves_convergence.elims(3)
thf(fact_306_convergence__graph__initial__invar__def,axiom,
    ( conver921086565505342681_c_e_d
    = ( ^ [M12: fsm_a_b_c,M23: fsm_e_b_c,Cg_lookup: d > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,Cg_initial: fsm_a_b_c > prefix425356687782099470od_b_c > d] :
        ! [T6: prefix425356687782099470od_b_c] :
          ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) @ ( prefix9085958534787526401od_b_c @ T6 ) )
            = ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M23 @ ( initial_e_b_c @ M23 ) ) @ ( prefix9085958534787526401od_b_c @ T6 ) ) )
         => ( ( prefix6767660319289835678od_b_c @ T6 )
           => ( conver4302099639658809211_c_e_d @ M12 @ M23 @ Cg_lookup @ ( Cg_initial @ M12 @ T6 ) ) ) ) ) ) ).

% convergence_graph_initial_invar_def
thf(fact_307_distinguish__converge__diverge,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_a_b_c,U3: list_P903359562653991662od_b_c,V5: list_P903359562653991662od_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_a_b_c @ M1 )
         => ( ( member6330420149250801815od_b_c @ U3 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
           => ( ( member6330420149250801815od_b_c @ V5 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
             => ( ( converge_a_b_c @ M1 @ U @ U3 )
               => ( ( converge_a_b_c @ M1 @ V3 @ V5 )
                 => ( ( converge_a_b_c @ M22 @ U @ U3 )
                   => ( ( converge_a_b_c @ M22 @ V3 @ V5 )
                     => ( ( distinguishes_a_b_c @ M1 @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ U ) @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ V3 ) @ Gamma )
                       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U3 @ Gamma ) @ T )
                         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V5 @ Gamma ) @ T )
                           => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ T )
                                = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ T ) )
                             => ~ ( converge_a_b_c @ M22 @ U @ V3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% distinguish_converge_diverge
thf(fact_308_distinguish__converge__diverge,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_e_b_c,U3: list_P903359562653991662od_b_c,V5: list_P903359562653991662od_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( observable_e_b_c @ M22 )
       => ( ( minimal_a_b_c @ M1 )
         => ( ( member6330420149250801815od_b_c @ U3 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
           => ( ( member6330420149250801815od_b_c @ V5 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
             => ( ( converge_a_b_c @ M1 @ U @ U3 )
               => ( ( converge_a_b_c @ M1 @ V3 @ V5 )
                 => ( ( converge_e_b_c @ M22 @ U @ U3 )
                   => ( ( converge_e_b_c @ M22 @ V3 @ V5 )
                     => ( ( distinguishes_a_b_c @ M1 @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ U ) @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ V3 ) @ Gamma )
                       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U3 @ Gamma ) @ T )
                         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V5 @ Gamma ) @ T )
                           => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ T )
                                = ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M22 @ ( initial_e_b_c @ M22 ) ) @ T ) )
                             => ~ ( converge_e_b_c @ M22 @ U @ V3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% distinguish_converge_diverge
thf(fact_309_distinguish__converge__diverge,axiom,
    ! [M1: fsm_e_b_c,M22: fsm_a_b_c,U3: list_P903359562653991662od_b_c,V5: list_P903359562653991662od_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T: set_li6436108459499378894od_b_c] :
      ( ( observable_e_b_c @ M1 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_e_b_c @ M1 )
         => ( ( member6330420149250801815od_b_c @ U3 @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) )
           => ( ( member6330420149250801815od_b_c @ V5 @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) )
             => ( ( converge_e_b_c @ M1 @ U @ U3 )
               => ( ( converge_e_b_c @ M1 @ V3 @ V5 )
                 => ( ( converge_a_b_c @ M22 @ U @ U3 )
                   => ( ( converge_a_b_c @ M22 @ V3 @ V5 )
                     => ( ( distinguishes_e_b_c @ M1 @ ( after_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) @ U ) @ ( after_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) @ V3 ) @ Gamma )
                       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U3 @ Gamma ) @ T )
                         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V5 @ Gamma ) @ T )
                           => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) @ T )
                                = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ T ) )
                             => ~ ( converge_a_b_c @ M22 @ U @ V3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% distinguish_converge_diverge
thf(fact_310_distinguish__converge__diverge,axiom,
    ! [M1: fsm_e_b_c,M22: fsm_e_b_c,U3: list_P903359562653991662od_b_c,V5: list_P903359562653991662od_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T: set_li6436108459499378894od_b_c] :
      ( ( observable_e_b_c @ M1 )
     => ( ( observable_e_b_c @ M22 )
       => ( ( minimal_e_b_c @ M1 )
         => ( ( member6330420149250801815od_b_c @ U3 @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) )
           => ( ( member6330420149250801815od_b_c @ V5 @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) )
             => ( ( converge_e_b_c @ M1 @ U @ U3 )
               => ( ( converge_e_b_c @ M1 @ V3 @ V5 )
                 => ( ( converge_e_b_c @ M22 @ U @ U3 )
                   => ( ( converge_e_b_c @ M22 @ V3 @ V5 )
                     => ( ( distinguishes_e_b_c @ M1 @ ( after_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) @ U ) @ ( after_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) @ V3 ) @ Gamma )
                       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U3 @ Gamma ) @ T )
                         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V5 @ Gamma ) @ T )
                           => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) @ T )
                                = ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M22 @ ( initial_e_b_c @ M22 ) ) @ T ) )
                             => ~ ( converge_e_b_c @ M22 @ U @ V3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

% distinguish_converge_diverge
thf(fact_311_LS__from__LS__acyclic,axiom,
    ! [M: fsm_a_b_c] :
      ( ( acyclic_a_b_c @ M )
     => ( ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) )
        = ( lS_acyclic_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) ).

% LS_from_LS_acyclic
thf(fact_312_LS__from__LS__acyclic,axiom,
    ! [M: fsm_e_b_c] :
      ( ( acyclic_e_b_c @ M )
     => ( ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) )
        = ( lS_acyclic_e_b_c @ M @ ( initial_e_b_c @ M ) ) ) ) ).

% LS_from_LS_acyclic
thf(fact_313_minimally__distinguishes__no__prefix,axiom,
    ! [M: fsm_a_b_c,U: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c,W4: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U @ W ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V3 @ W ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
         => ( ( minima243535863231358885_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ U ) @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ V3 ) @ ( append2547753245680614915od_b_c @ W @ ( append2547753245680614915od_b_c @ W3 @ W4 ) ) )
           => ( ( W3 != nil_Product_prod_b_c )
             => ~ ( distinguishes_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ ( append2547753245680614915od_b_c @ U @ W ) ) @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ ( append2547753245680614915od_b_c @ V3 @ W ) ) @ W4 ) ) ) ) ) ) ).

% minimally_distinguishes_no_prefix
thf(fact_314_minimally__distinguishes__no__prefix,axiom,
    ! [M: fsm_e_b_c,U: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c,W4: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U @ W ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V3 @ W ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
         => ( ( minima4181666250274330025_e_b_c @ M @ ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ U ) @ ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ V3 ) @ ( append2547753245680614915od_b_c @ W @ ( append2547753245680614915od_b_c @ W3 @ W4 ) ) )
           => ( ( W3 != nil_Product_prod_b_c )
             => ~ ( distinguishes_e_b_c @ M @ ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ ( append2547753245680614915od_b_c @ U @ W ) ) @ ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ ( append2547753245680614915od_b_c @ V3 @ W ) ) @ W4 ) ) ) ) ) ) ).

% minimally_distinguishes_no_prefix
thf(fact_315_distinguish__diverge,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_a_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( distinguishes_a_b_c @ M1 @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ U ) @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ V3 ) @ Gamma )
         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U @ Gamma ) @ T )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V3 @ Gamma ) @ T )
             => ( ( member6330420149250801815od_b_c @ U @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
               => ( ( member6330420149250801815od_b_c @ V3 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
                 => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ T )
                      = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ T ) )
                   => ~ ( converge_a_b_c @ M22 @ U @ V3 ) ) ) ) ) ) ) ) ) ).

% distinguish_diverge
thf(fact_316_distinguish__diverge,axiom,
    ! [M1: fsm_e_b_c,M22: fsm_a_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T: set_li6436108459499378894od_b_c] :
      ( ( observable_e_b_c @ M1 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( distinguishes_e_b_c @ M1 @ ( after_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) @ U ) @ ( after_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) @ V3 ) @ Gamma )
         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U @ Gamma ) @ T )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V3 @ Gamma ) @ T )
             => ( ( member6330420149250801815od_b_c @ U @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) )
               => ( ( member6330420149250801815od_b_c @ V3 @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) )
                 => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) @ T )
                      = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ T ) )
                   => ~ ( converge_a_b_c @ M22 @ U @ V3 ) ) ) ) ) ) ) ) ) ).

% distinguish_diverge
thf(fact_317_distinguish__diverge,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_e_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( observable_e_b_c @ M22 )
       => ( ( distinguishes_a_b_c @ M1 @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ U ) @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ V3 ) @ Gamma )
         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U @ Gamma ) @ T )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V3 @ Gamma ) @ T )
             => ( ( member6330420149250801815od_b_c @ U @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
               => ( ( member6330420149250801815od_b_c @ V3 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
                 => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ T )
                      = ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M22 @ ( initial_e_b_c @ M22 ) ) @ T ) )
                   => ~ ( converge_e_b_c @ M22 @ U @ V3 ) ) ) ) ) ) ) ) ) ).

% distinguish_diverge
thf(fact_318_distinguish__diverge,axiom,
    ! [M1: fsm_e_b_c,M22: fsm_e_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T: set_li6436108459499378894od_b_c] :
      ( ( observable_e_b_c @ M1 )
     => ( ( observable_e_b_c @ M22 )
       => ( ( distinguishes_e_b_c @ M1 @ ( after_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) @ U ) @ ( after_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) @ V3 ) @ Gamma )
         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ U @ Gamma ) @ T )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ V3 @ Gamma ) @ T )
             => ( ( member6330420149250801815od_b_c @ U @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) )
               => ( ( member6330420149250801815od_b_c @ V3 @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) )
                 => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) @ T )
                      = ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M22 @ ( initial_e_b_c @ M22 ) ) @ T ) )
                   => ~ ( converge_e_b_c @ M22 @ U @ V3 ) ) ) ) ) ) ) ) ) ).

% distinguish_diverge
thf(fact_319_preserves__divergence__converge__replace__iff,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_a_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,X5: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_a_b_c @ M1 )
         => ( ( minimal_a_b_c @ M22 )
           => ( ( converge_a_b_c @ M1 @ U @ V3 )
             => ( ( converge_a_b_c @ M22 @ U @ V3 )
               => ( ( preser261684820601417589_b_c_a @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ U @ X5 ) )
                  = ( preser261684820601417589_b_c_a @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ V3 @ X5 ) ) ) ) ) ) ) ) ) ).

% preserves_divergence_converge_replace_iff
thf(fact_320_preserves__divergence__converge__replace__iff,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_e_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,X5: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( observable_e_b_c @ M22 )
       => ( ( minimal_a_b_c @ M1 )
         => ( ( minimal_e_b_c @ M22 )
           => ( ( converge_a_b_c @ M1 @ U @ V3 )
             => ( ( converge_e_b_c @ M22 @ U @ V3 )
               => ( ( preser261684820601417593_b_c_e @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ U @ X5 ) )
                  = ( preser261684820601417593_b_c_e @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ V3 @ X5 ) ) ) ) ) ) ) ) ) ).

% preserves_divergence_converge_replace_iff
thf(fact_321_preserves__divergence__converge__replace__iff,axiom,
    ! [M1: fsm_e_b_c,M22: fsm_a_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,X5: set_li6436108459499378894od_b_c] :
      ( ( observable_e_b_c @ M1 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_e_b_c @ M1 )
         => ( ( minimal_a_b_c @ M22 )
           => ( ( converge_e_b_c @ M1 @ U @ V3 )
             => ( ( converge_a_b_c @ M22 @ U @ V3 )
               => ( ( preser6213532969780611697_b_c_a @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ U @ X5 ) )
                  = ( preser6213532969780611697_b_c_a @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ V3 @ X5 ) ) ) ) ) ) ) ) ) ).

% preserves_divergence_converge_replace_iff
thf(fact_322_preserves__divergence__converge__replace__iff,axiom,
    ! [M1: fsm_e_b_c,M22: fsm_e_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,X5: set_li6436108459499378894od_b_c] :
      ( ( observable_e_b_c @ M1 )
     => ( ( observable_e_b_c @ M22 )
       => ( ( minimal_e_b_c @ M1 )
         => ( ( minimal_e_b_c @ M22 )
           => ( ( converge_e_b_c @ M1 @ U @ V3 )
             => ( ( converge_e_b_c @ M22 @ U @ V3 )
               => ( ( preser6213532969780611701_b_c_e @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ U @ X5 ) )
                  = ( preser6213532969780611701_b_c_e @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ V3 @ X5 ) ) ) ) ) ) ) ) ) ).

% preserves_divergence_converge_replace_iff
thf(fact_323_preserves__divergence__converge__replace,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_a_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,X5: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_a_b_c @ M1 )
         => ( ( minimal_a_b_c @ M22 )
           => ( ( converge_a_b_c @ M1 @ U @ V3 )
             => ( ( converge_a_b_c @ M22 @ U @ V3 )
               => ( ( preser261684820601417589_b_c_a @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ U @ X5 ) )
                 => ( preser261684820601417589_b_c_a @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ V3 @ X5 ) ) ) ) ) ) ) ) ) ).

% preserves_divergence_converge_replace
thf(fact_324_preserves__divergence__converge__replace,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_e_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,X5: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( observable_e_b_c @ M22 )
       => ( ( minimal_a_b_c @ M1 )
         => ( ( minimal_e_b_c @ M22 )
           => ( ( converge_a_b_c @ M1 @ U @ V3 )
             => ( ( converge_e_b_c @ M22 @ U @ V3 )
               => ( ( preser261684820601417593_b_c_e @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ U @ X5 ) )
                 => ( preser261684820601417593_b_c_e @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ V3 @ X5 ) ) ) ) ) ) ) ) ) ).

% preserves_divergence_converge_replace
thf(fact_325_preserves__divergence__converge__replace,axiom,
    ! [M1: fsm_e_b_c,M22: fsm_a_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,X5: set_li6436108459499378894od_b_c] :
      ( ( observable_e_b_c @ M1 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_e_b_c @ M1 )
         => ( ( minimal_a_b_c @ M22 )
           => ( ( converge_e_b_c @ M1 @ U @ V3 )
             => ( ( converge_a_b_c @ M22 @ U @ V3 )
               => ( ( preser6213532969780611697_b_c_a @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ U @ X5 ) )
                 => ( preser6213532969780611697_b_c_a @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ V3 @ X5 ) ) ) ) ) ) ) ) ) ).

% preserves_divergence_converge_replace
thf(fact_326_preserves__divergence__converge__replace,axiom,
    ! [M1: fsm_e_b_c,M22: fsm_e_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,X5: set_li6436108459499378894od_b_c] :
      ( ( observable_e_b_c @ M1 )
     => ( ( observable_e_b_c @ M22 )
       => ( ( minimal_e_b_c @ M1 )
         => ( ( minimal_e_b_c @ M22 )
           => ( ( converge_e_b_c @ M1 @ U @ V3 )
             => ( ( converge_e_b_c @ M22 @ U @ V3 )
               => ( ( preser6213532969780611701_b_c_e @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ U @ X5 ) )
                 => ( preser6213532969780611701_b_c_e @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ V3 @ X5 ) ) ) ) ) ) ) ) ) ).

% preserves_divergence_converge_replace
thf(fact_327_preserves__divergence__converge__insert,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_a_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,X5: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_a_b_c @ M1 )
         => ( ( minimal_a_b_c @ M22 )
           => ( ( converge_a_b_c @ M1 @ U @ V3 )
             => ( ( converge_a_b_c @ M22 @ U @ V3 )
               => ( ( preser261684820601417589_b_c_a @ M1 @ M22 @ X5 )
                 => ( ( member6330420149250801815od_b_c @ U @ X5 )
                   => ( preser261684820601417589_b_c_a @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ V3 @ X5 ) ) ) ) ) ) ) ) ) ) ).

% preserves_divergence_converge_insert
thf(fact_328_preserves__divergence__converge__insert,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_e_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,X5: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( observable_e_b_c @ M22 )
       => ( ( minimal_a_b_c @ M1 )
         => ( ( minimal_e_b_c @ M22 )
           => ( ( converge_a_b_c @ M1 @ U @ V3 )
             => ( ( converge_e_b_c @ M22 @ U @ V3 )
               => ( ( preser261684820601417593_b_c_e @ M1 @ M22 @ X5 )
                 => ( ( member6330420149250801815od_b_c @ U @ X5 )
                   => ( preser261684820601417593_b_c_e @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ V3 @ X5 ) ) ) ) ) ) ) ) ) ) ).

% preserves_divergence_converge_insert
thf(fact_329_preserves__divergence__converge__insert,axiom,
    ! [M1: fsm_e_b_c,M22: fsm_a_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,X5: set_li6436108459499378894od_b_c] :
      ( ( observable_e_b_c @ M1 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_e_b_c @ M1 )
         => ( ( minimal_a_b_c @ M22 )
           => ( ( converge_e_b_c @ M1 @ U @ V3 )
             => ( ( converge_a_b_c @ M22 @ U @ V3 )
               => ( ( preser6213532969780611697_b_c_a @ M1 @ M22 @ X5 )
                 => ( ( member6330420149250801815od_b_c @ U @ X5 )
                   => ( preser6213532969780611697_b_c_a @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ V3 @ X5 ) ) ) ) ) ) ) ) ) ) ).

% preserves_divergence_converge_insert
thf(fact_330_preserves__divergence__converge__insert,axiom,
    ! [M1: fsm_e_b_c,M22: fsm_e_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,X5: set_li6436108459499378894od_b_c] :
      ( ( observable_e_b_c @ M1 )
     => ( ( observable_e_b_c @ M22 )
       => ( ( minimal_e_b_c @ M1 )
         => ( ( minimal_e_b_c @ M22 )
           => ( ( converge_e_b_c @ M1 @ U @ V3 )
             => ( ( converge_e_b_c @ M22 @ U @ V3 )
               => ( ( preser6213532969780611701_b_c_e @ M1 @ M22 @ X5 )
                 => ( ( member6330420149250801815od_b_c @ U @ X5 )
                   => ( preser6213532969780611701_b_c_e @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ V3 @ X5 ) ) ) ) ) ) ) ) ) ) ).

% preserves_divergence_converge_insert
thf(fact_331_language__empty__io,axiom,
    ! [M: fsm_a_b_c] :
      ( ( ( ( inputs_a_b_c @ M )
          = bot_bot_set_b )
        | ( ( outputs_a_b_c @ M )
          = bot_bot_set_c ) )
     => ( ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) )
        = ( insert6227932334100060350od_b_c @ nil_Product_prod_b_c @ bot_bo4166481423041325370od_b_c ) ) ) ).

% language_empty_io
thf(fact_332_language__empty__io,axiom,
    ! [M: fsm_e_b_c] :
      ( ( ( ( inputs_e_b_c @ M )
          = bot_bot_set_b )
        | ( ( outputs_e_b_c @ M )
          = bot_bot_set_c ) )
     => ( ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) )
        = ( insert6227932334100060350od_b_c @ nil_Product_prod_b_c @ bot_bo4166481423041325370od_b_c ) ) ) ).

% language_empty_io
thf(fact_333_preserves__divergence__insertI,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_a_b_c,X5: set_li6436108459499378894od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( preser261684820601417589_b_c_a @ M1 @ M22 @ X5 )
     => ( ! [Alpha: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ Alpha @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ X5 ) )
           => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
             => ( ~ ( converge_a_b_c @ M1 @ Alpha @ Beta )
               => ~ ( converge_a_b_c @ M22 @ Alpha @ Beta ) ) ) )
       => ( preser261684820601417589_b_c_a @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ Beta @ X5 ) ) ) ) ).

% preserves_divergence_insertI
thf(fact_334_preserves__divergence__insertI,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_e_b_c,X5: set_li6436108459499378894od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( preser261684820601417593_b_c_e @ M1 @ M22 @ X5 )
     => ( ! [Alpha: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ Alpha @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ X5 ) )
           => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
             => ( ~ ( converge_a_b_c @ M1 @ Alpha @ Beta )
               => ~ ( converge_e_b_c @ M22 @ Alpha @ Beta ) ) ) )
       => ( preser261684820601417593_b_c_e @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ Beta @ X5 ) ) ) ) ).

% preserves_divergence_insertI
thf(fact_335_preserves__divergence__insertI,axiom,
    ! [M1: fsm_e_b_c,M22: fsm_a_b_c,X5: set_li6436108459499378894od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( preser6213532969780611697_b_c_a @ M1 @ M22 @ X5 )
     => ( ! [Alpha: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ Alpha @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) @ X5 ) )
           => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) )
             => ( ~ ( converge_e_b_c @ M1 @ Alpha @ Beta )
               => ~ ( converge_a_b_c @ M22 @ Alpha @ Beta ) ) ) )
       => ( preser6213532969780611697_b_c_a @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ Beta @ X5 ) ) ) ) ).

% preserves_divergence_insertI
thf(fact_336_preserves__divergence__insertI,axiom,
    ! [M1: fsm_e_b_c,M22: fsm_e_b_c,X5: set_li6436108459499378894od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( preser6213532969780611701_b_c_e @ M1 @ M22 @ X5 )
     => ( ! [Alpha: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ Alpha @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) @ X5 ) )
           => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) )
             => ( ~ ( converge_e_b_c @ M1 @ Alpha @ Beta )
               => ~ ( converge_e_b_c @ M22 @ Alpha @ Beta ) ) ) )
       => ( preser6213532969780611701_b_c_e @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ Beta @ X5 ) ) ) ) ).

% preserves_divergence_insertI
thf(fact_337_preserves__divergence__insertE_I2_J,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_a_b_c,Beta: list_P903359562653991662od_b_c,X5: set_li6436108459499378894od_b_c,Alpha2: list_P903359562653991662od_b_c] :
      ( ( preser261684820601417589_b_c_a @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ Beta @ X5 ) )
     => ( ( member6330420149250801815od_b_c @ Alpha2 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ X5 ) )
       => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
         => ( ~ ( converge_a_b_c @ M1 @ Alpha2 @ Beta )
           => ~ ( converge_a_b_c @ M22 @ Alpha2 @ Beta ) ) ) ) ) ).

% preserves_divergence_insertE(2)
thf(fact_338_preserves__divergence__insertE_I2_J,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_e_b_c,Beta: list_P903359562653991662od_b_c,X5: set_li6436108459499378894od_b_c,Alpha2: list_P903359562653991662od_b_c] :
      ( ( preser261684820601417593_b_c_e @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ Beta @ X5 ) )
     => ( ( member6330420149250801815od_b_c @ Alpha2 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ X5 ) )
       => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
         => ( ~ ( converge_a_b_c @ M1 @ Alpha2 @ Beta )
           => ~ ( converge_e_b_c @ M22 @ Alpha2 @ Beta ) ) ) ) ) ).

% preserves_divergence_insertE(2)
thf(fact_339_preserves__divergence__insertE_I2_J,axiom,
    ! [M1: fsm_e_b_c,M22: fsm_a_b_c,Beta: list_P903359562653991662od_b_c,X5: set_li6436108459499378894od_b_c,Alpha2: list_P903359562653991662od_b_c] :
      ( ( preser6213532969780611697_b_c_a @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ Beta @ X5 ) )
     => ( ( member6330420149250801815od_b_c @ Alpha2 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) @ X5 ) )
       => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) )
         => ( ~ ( converge_e_b_c @ M1 @ Alpha2 @ Beta )
           => ~ ( converge_a_b_c @ M22 @ Alpha2 @ Beta ) ) ) ) ) ).

% preserves_divergence_insertE(2)
thf(fact_340_preserves__divergence__insertE_I2_J,axiom,
    ! [M1: fsm_e_b_c,M22: fsm_e_b_c,Beta: list_P903359562653991662od_b_c,X5: set_li6436108459499378894od_b_c,Alpha2: list_P903359562653991662od_b_c] :
      ( ( preser6213532969780611701_b_c_e @ M1 @ M22 @ ( insert6227932334100060350od_b_c @ Beta @ X5 ) )
     => ( ( member6330420149250801815od_b_c @ Alpha2 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) @ X5 ) )
       => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) )
         => ( ~ ( converge_e_b_c @ M1 @ Alpha2 @ Beta )
           => ~ ( converge_e_b_c @ M22 @ Alpha2 @ Beta ) ) ) ) ) ).

% preserves_divergence_insertE(2)
thf(fact_341_converge__distinguishable__helper,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_a_b_c,Pi2: list_P903359562653991662od_b_c,Alpha2: list_P903359562653991662od_b_c,Tau2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_a_b_c @ M1 )
         => ( ( minimal_a_b_c @ M22 )
           => ( ( converge_a_b_c @ M1 @ Pi2 @ Alpha2 )
             => ( ( converge_a_b_c @ M22 @ Pi2 @ Alpha2 )
               => ( ( converge_a_b_c @ M1 @ Tau2 @ Beta )
                 => ( ( converge_a_b_c @ M22 @ Tau2 @ Beta )
                   => ( ( distinguishes_a_b_c @ M22 @ ( after_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) @ Pi2 ) @ ( after_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) @ Tau2 ) @ V3 )
                     => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ ( insert6227932334100060350od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ V3 ) @ ( insert6227932334100060350od_b_c @ ( append2547753245680614915od_b_c @ Beta @ V3 ) @ bot_bo4166481423041325370od_b_c ) ) )
                          = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ ( insert6227932334100060350od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ V3 ) @ ( insert6227932334100060350od_b_c @ ( append2547753245680614915od_b_c @ Beta @ V3 ) @ bot_bo4166481423041325370od_b_c ) ) ) )
                       => ( ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ Pi2 )
                         != ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ Tau2 ) ) ) ) ) ) ) ) ) ) ) ) ).

% converge_distinguishable_helper
thf(fact_342_converge__distinguishable__helper,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_e_b_c,Pi2: list_P903359562653991662od_b_c,Alpha2: list_P903359562653991662od_b_c,Tau2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( observable_e_b_c @ M22 )
       => ( ( minimal_a_b_c @ M1 )
         => ( ( minimal_e_b_c @ M22 )
           => ( ( converge_a_b_c @ M1 @ Pi2 @ Alpha2 )
             => ( ( converge_e_b_c @ M22 @ Pi2 @ Alpha2 )
               => ( ( converge_a_b_c @ M1 @ Tau2 @ Beta )
                 => ( ( converge_e_b_c @ M22 @ Tau2 @ Beta )
                   => ( ( distinguishes_e_b_c @ M22 @ ( after_e_b_c @ M22 @ ( initial_e_b_c @ M22 ) @ Pi2 ) @ ( after_e_b_c @ M22 @ ( initial_e_b_c @ M22 ) @ Tau2 ) @ V3 )
                     => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ ( insert6227932334100060350od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ V3 ) @ ( insert6227932334100060350od_b_c @ ( append2547753245680614915od_b_c @ Beta @ V3 ) @ bot_bo4166481423041325370od_b_c ) ) )
                          = ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M22 @ ( initial_e_b_c @ M22 ) ) @ ( insert6227932334100060350od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ V3 ) @ ( insert6227932334100060350od_b_c @ ( append2547753245680614915od_b_c @ Beta @ V3 ) @ bot_bo4166481423041325370od_b_c ) ) ) )
                       => ( ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ Pi2 )
                         != ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ Tau2 ) ) ) ) ) ) ) ) ) ) ) ) ).

% converge_distinguishable_helper
thf(fact_343_converge__distinguishable__helper,axiom,
    ! [M1: fsm_e_b_c,M22: fsm_a_b_c,Pi2: list_P903359562653991662od_b_c,Alpha2: list_P903359562653991662od_b_c,Tau2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M1 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_e_b_c @ M1 )
         => ( ( minimal_a_b_c @ M22 )
           => ( ( converge_e_b_c @ M1 @ Pi2 @ Alpha2 )
             => ( ( converge_a_b_c @ M22 @ Pi2 @ Alpha2 )
               => ( ( converge_e_b_c @ M1 @ Tau2 @ Beta )
                 => ( ( converge_a_b_c @ M22 @ Tau2 @ Beta )
                   => ( ( distinguishes_a_b_c @ M22 @ ( after_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) @ Pi2 ) @ ( after_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) @ Tau2 ) @ V3 )
                     => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) @ ( insert6227932334100060350od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ V3 ) @ ( insert6227932334100060350od_b_c @ ( append2547753245680614915od_b_c @ Beta @ V3 ) @ bot_bo4166481423041325370od_b_c ) ) )
                          = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ ( insert6227932334100060350od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ V3 ) @ ( insert6227932334100060350od_b_c @ ( append2547753245680614915od_b_c @ Beta @ V3 ) @ bot_bo4166481423041325370od_b_c ) ) ) )
                       => ( ( after_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) @ Pi2 )
                         != ( after_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) @ Tau2 ) ) ) ) ) ) ) ) ) ) ) ) ).

% converge_distinguishable_helper
thf(fact_344_converge__distinguishable__helper,axiom,
    ! [M1: fsm_e_b_c,M22: fsm_e_b_c,Pi2: list_P903359562653991662od_b_c,Alpha2: list_P903359562653991662od_b_c,Tau2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M1 )
     => ( ( observable_e_b_c @ M22 )
       => ( ( minimal_e_b_c @ M1 )
         => ( ( minimal_e_b_c @ M22 )
           => ( ( converge_e_b_c @ M1 @ Pi2 @ Alpha2 )
             => ( ( converge_e_b_c @ M22 @ Pi2 @ Alpha2 )
               => ( ( converge_e_b_c @ M1 @ Tau2 @ Beta )
                 => ( ( converge_e_b_c @ M22 @ Tau2 @ Beta )
                   => ( ( distinguishes_e_b_c @ M22 @ ( after_e_b_c @ M22 @ ( initial_e_b_c @ M22 ) @ Pi2 ) @ ( after_e_b_c @ M22 @ ( initial_e_b_c @ M22 ) @ Tau2 ) @ V3 )
                     => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) @ ( insert6227932334100060350od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ V3 ) @ ( insert6227932334100060350od_b_c @ ( append2547753245680614915od_b_c @ Beta @ V3 ) @ bot_bo4166481423041325370od_b_c ) ) )
                          = ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M22 @ ( initial_e_b_c @ M22 ) ) @ ( insert6227932334100060350od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ V3 ) @ ( insert6227932334100060350od_b_c @ ( append2547753245680614915od_b_c @ Beta @ V3 ) @ bot_bo4166481423041325370od_b_c ) ) ) )
                       => ( ( after_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) @ Pi2 )
                         != ( after_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) @ Tau2 ) ) ) ) ) ) ) ) ) ) ) ) ).

% converge_distinguishable_helper
thf(fact_345_equivalence__preserves__divergence,axiom,
    ! [M: fsm_a_b_c,I: fsm_a_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( observable_a_b_c @ I )
       => ( ( ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) )
            = ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) )
         => ( preser261684820601417589_b_c_a @ M @ I @ A2 ) ) ) ) ).

% equivalence_preserves_divergence
thf(fact_346_equivalence__preserves__divergence,axiom,
    ! [M: fsm_a_b_c,I: fsm_e_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( observable_e_b_c @ I )
       => ( ( ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) )
            = ( lS_e_b_c @ I @ ( initial_e_b_c @ I ) ) )
         => ( preser261684820601417593_b_c_e @ M @ I @ A2 ) ) ) ) ).

% equivalence_preserves_divergence
thf(fact_347_equivalence__preserves__divergence,axiom,
    ! [M: fsm_e_b_c,I: fsm_a_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( observable_a_b_c @ I )
       => ( ( ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) )
            = ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) )
         => ( preser6213532969780611697_b_c_a @ M @ I @ A2 ) ) ) ) ).

% equivalence_preserves_divergence
thf(fact_348_equivalence__preserves__divergence,axiom,
    ! [M: fsm_e_b_c,I: fsm_e_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( observable_e_b_c @ I )
       => ( ( ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) )
            = ( lS_e_b_c @ I @ ( initial_e_b_c @ I ) ) )
         => ( preser6213532969780611701_b_c_e @ M @ I @ A2 ) ) ) ) ).

% equivalence_preserves_divergence
thf(fact_349_preserves__divergence_Osimps,axiom,
    ( preser261684820601417589_b_c_a
    = ( ^ [M12: fsm_a_b_c,M23: fsm_a_b_c,A5: set_li6436108459499378894od_b_c] :
        ! [X3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) @ A5 ) )
         => ! [Y3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Y3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) @ A5 ) )
             => ( ~ ( converge_a_b_c @ M12 @ X3 @ Y3 )
               => ~ ( converge_a_b_c @ M23 @ X3 @ Y3 ) ) ) ) ) ) ).

% preserves_divergence.simps
thf(fact_350_preserves__divergence_Osimps,axiom,
    ( preser261684820601417593_b_c_e
    = ( ^ [M12: fsm_a_b_c,M23: fsm_e_b_c,A5: set_li6436108459499378894od_b_c] :
        ! [X3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) @ A5 ) )
         => ! [Y3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Y3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) @ A5 ) )
             => ( ~ ( converge_a_b_c @ M12 @ X3 @ Y3 )
               => ~ ( converge_e_b_c @ M23 @ X3 @ Y3 ) ) ) ) ) ) ).

% preserves_divergence.simps
thf(fact_351_preserves__divergence_Osimps,axiom,
    ( preser6213532969780611697_b_c_a
    = ( ^ [M12: fsm_e_b_c,M23: fsm_a_b_c,A5: set_li6436108459499378894od_b_c] :
        ! [X3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X3 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M12 @ ( initial_e_b_c @ M12 ) ) @ A5 ) )
         => ! [Y3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Y3 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M12 @ ( initial_e_b_c @ M12 ) ) @ A5 ) )
             => ( ~ ( converge_e_b_c @ M12 @ X3 @ Y3 )
               => ~ ( converge_a_b_c @ M23 @ X3 @ Y3 ) ) ) ) ) ) ).

% preserves_divergence.simps
thf(fact_352_preserves__divergence_Osimps,axiom,
    ( preser6213532969780611701_b_c_e
    = ( ^ [M12: fsm_e_b_c,M23: fsm_e_b_c,A5: set_li6436108459499378894od_b_c] :
        ! [X3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X3 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M12 @ ( initial_e_b_c @ M12 ) ) @ A5 ) )
         => ! [Y3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Y3 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M12 @ ( initial_e_b_c @ M12 ) ) @ A5 ) )
             => ( ~ ( converge_e_b_c @ M12 @ X3 @ Y3 )
               => ~ ( converge_e_b_c @ M23 @ X3 @ Y3 ) ) ) ) ) ) ).

% preserves_divergence.simps
thf(fact_353_preserves__divergence_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Xa: fsm_a_b_c,Xb: set_li6436108459499378894od_b_c,Y: $o] :
      ( ( ( preser261684820601417589_b_c_a @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( ! [X3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
             => ! [Y3: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
                 => ( ~ ( converge_a_b_c @ X @ X3 @ Y3 )
                   => ~ ( converge_a_b_c @ Xa @ X3 @ Y3 ) ) ) ) ) ) ) ).

% preserves_divergence.elims(1)
thf(fact_354_preserves__divergence_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Xa: fsm_e_b_c,Xb: set_li6436108459499378894od_b_c,Y: $o] :
      ( ( ( preser261684820601417593_b_c_e @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( ! [X3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
             => ! [Y3: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
                 => ( ~ ( converge_a_b_c @ X @ X3 @ Y3 )
                   => ~ ( converge_e_b_c @ Xa @ X3 @ Y3 ) ) ) ) ) ) ) ).

% preserves_divergence.elims(1)
thf(fact_355_preserves__divergence_Oelims_I1_J,axiom,
    ! [X: fsm_e_b_c,Xa: fsm_a_b_c,Xb: set_li6436108459499378894od_b_c,Y: $o] :
      ( ( ( preser6213532969780611697_b_c_a @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( ! [X3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X3 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
             => ! [Y3: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y3 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
                 => ( ~ ( converge_e_b_c @ X @ X3 @ Y3 )
                   => ~ ( converge_a_b_c @ Xa @ X3 @ Y3 ) ) ) ) ) ) ) ).

% preserves_divergence.elims(1)
thf(fact_356_preserves__divergence_Oelims_I1_J,axiom,
    ! [X: fsm_e_b_c,Xa: fsm_e_b_c,Xb: set_li6436108459499378894od_b_c,Y: $o] :
      ( ( ( preser6213532969780611701_b_c_e @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( ! [X3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X3 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
             => ! [Y3: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y3 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
                 => ( ~ ( converge_e_b_c @ X @ X3 @ Y3 )
                   => ~ ( converge_e_b_c @ Xa @ X3 @ Y3 ) ) ) ) ) ) ) ).

% preserves_divergence.elims(1)
thf(fact_357_preserves__divergence_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c,Xa: fsm_a_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ( preser261684820601417589_b_c_a @ X @ Xa @ Xb )
     => ! [X4: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X4 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
         => ! [Xa3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Xa3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
             => ( ~ ( converge_a_b_c @ X @ X4 @ Xa3 )
               => ~ ( converge_a_b_c @ Xa @ X4 @ Xa3 ) ) ) ) ) ).

% preserves_divergence.elims(2)
thf(fact_358_preserves__divergence_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c,Xa: fsm_e_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ( preser261684820601417593_b_c_e @ X @ Xa @ Xb )
     => ! [X4: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X4 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
         => ! [Xa3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Xa3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
             => ( ~ ( converge_a_b_c @ X @ X4 @ Xa3 )
               => ~ ( converge_e_b_c @ Xa @ X4 @ Xa3 ) ) ) ) ) ).

% preserves_divergence.elims(2)
thf(fact_359_preserves__divergence_Oelims_I2_J,axiom,
    ! [X: fsm_e_b_c,Xa: fsm_a_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ( preser6213532969780611697_b_c_a @ X @ Xa @ Xb )
     => ! [X4: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X4 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
         => ! [Xa3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Xa3 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
             => ( ~ ( converge_e_b_c @ X @ X4 @ Xa3 )
               => ~ ( converge_a_b_c @ Xa @ X4 @ Xa3 ) ) ) ) ) ).

% preserves_divergence.elims(2)
thf(fact_360_preserves__divergence_Oelims_I2_J,axiom,
    ! [X: fsm_e_b_c,Xa: fsm_e_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ( preser6213532969780611701_b_c_e @ X @ Xa @ Xb )
     => ! [X4: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X4 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
         => ! [Xa3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Xa3 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
             => ( ~ ( converge_e_b_c @ X @ X4 @ Xa3 )
               => ~ ( converge_e_b_c @ Xa @ X4 @ Xa3 ) ) ) ) ) ).

% preserves_divergence.elims(2)
thf(fact_361_preserves__divergence_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c,Xa: fsm_a_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ~ ( preser261684820601417589_b_c_a @ X @ Xa @ Xb )
     => ~ ! [X2: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X2 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
           => ! [Xa2: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Xa2 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
               => ( ~ ( converge_a_b_c @ X @ X2 @ Xa2 )
                 => ~ ( converge_a_b_c @ Xa @ X2 @ Xa2 ) ) ) ) ) ).

% preserves_divergence.elims(3)
thf(fact_362_preserves__divergence_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c,Xa: fsm_e_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ~ ( preser261684820601417593_b_c_e @ X @ Xa @ Xb )
     => ~ ! [X2: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X2 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
           => ! [Xa2: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Xa2 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ X @ ( initial_a_b_c @ X ) ) @ Xb ) )
               => ( ~ ( converge_a_b_c @ X @ X2 @ Xa2 )
                 => ~ ( converge_e_b_c @ Xa @ X2 @ Xa2 ) ) ) ) ) ).

% preserves_divergence.elims(3)
thf(fact_363_preserves__divergence_Oelims_I3_J,axiom,
    ! [X: fsm_e_b_c,Xa: fsm_a_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ~ ( preser6213532969780611697_b_c_a @ X @ Xa @ Xb )
     => ~ ! [X2: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X2 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
           => ! [Xa2: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Xa2 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
               => ( ~ ( converge_e_b_c @ X @ X2 @ Xa2 )
                 => ~ ( converge_a_b_c @ Xa @ X2 @ Xa2 ) ) ) ) ) ).

% preserves_divergence.elims(3)
thf(fact_364_preserves__divergence_Oelims_I3_J,axiom,
    ! [X: fsm_e_b_c,Xa: fsm_e_b_c,Xb: set_li6436108459499378894od_b_c] :
      ( ~ ( preser6213532969780611701_b_c_e @ X @ Xa @ Xb )
     => ~ ! [X2: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X2 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
           => ! [Xa2: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Xa2 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ X @ ( initial_e_b_c @ X ) ) @ Xb ) )
               => ( ~ ( converge_e_b_c @ X @ X2 @ Xa2 )
                 => ~ ( converge_e_b_c @ Xa @ X2 @ Xa2 ) ) ) ) ) ).

% preserves_divergence.elims(3)
thf(fact_365_distinguish__prepend__initial,axiom,
    ! [M: fsm_a_b_c,Io1: list_P903359562653991662od_b_c,Io: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( distinguishes_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ ( append2547753245680614915od_b_c @ Io1 @ Io ) ) @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ ( append2547753245680614915od_b_c @ Io2 @ Io ) ) @ W )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io2 @ Io ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
           => ( distinguishes_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Io1 ) @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ Io2 ) @ ( append2547753245680614915od_b_c @ Io @ W ) ) ) ) ) ) ).

% distinguish_prepend_initial
thf(fact_366_distinguish__prepend__initial,axiom,
    ! [M: fsm_e_b_c,Io1: list_P903359562653991662od_b_c,Io: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( distinguishes_e_b_c @ M @ ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ ( append2547753245680614915od_b_c @ Io1 @ Io ) ) @ ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ ( append2547753245680614915od_b_c @ Io2 @ Io ) ) @ W )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io2 @ Io ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
           => ( distinguishes_e_b_c @ M @ ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ Io1 ) @ ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ Io2 ) @ ( append2547753245680614915od_b_c @ Io @ W ) ) ) ) ) ) ).

% distinguish_prepend_initial
thf(fact_367_after__distinguishes__language,axiom,
    ! [M1: fsm_a_b_c,Alpha2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( member6330420149250801815od_b_c @ Alpha2 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
       => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
         => ( ( distinguishes_a_b_c @ M1 @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ Alpha2 ) @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ Beta ) @ Gamma )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
             != ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) ) ) ) ) ) ) ).

% after_distinguishes_language
thf(fact_368_after__distinguishes__language,axiom,
    ! [M1: fsm_e_b_c,Alpha2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M1 )
     => ( ( member6330420149250801815od_b_c @ Alpha2 @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) )
       => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) )
         => ( ( distinguishes_e_b_c @ M1 @ ( after_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) @ Alpha2 ) @ ( after_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) @ Beta ) @ Gamma )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha2 @ Gamma ) @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) )
             != ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Beta @ Gamma ) @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) ) ) ) ) ) ) ).

% after_distinguishes_language
thf(fact_369_add__transition__with__components__simps_I3_J,axiom,
    ! [M: fsm_a_b_c,T3: produc2669932201312201782od_c_a] :
      ( ( outputs_a_b_c @ ( add_tr8224572408740125824_a_b_c @ M @ T3 ) )
      = ( insert_c @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) ) @ ( outputs_a_b_c @ M ) ) ) ).

% add_transition_with_components_simps(3)
thf(fact_370_add__transition__with__components__simps_I3_J,axiom,
    ! [M: fsm_e_b_c,T3: produc4050040609193146166od_c_e] :
      ( ( outputs_e_b_c @ ( add_tr2939330758928321156_e_b_c @ M @ T3 ) )
      = ( insert_c @ ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) ) @ ( outputs_e_b_c @ M ) ) ) ).

% add_transition_with_components_simps(3)
thf(fact_371_after__distinguishes__diverge,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_a_b_c,Alpha2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T12: prefix425356687782099470od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_a_b_c @ M1 )
         => ( ( minimal_a_b_c @ M22 )
           => ( ( member6330420149250801815od_b_c @ Alpha2 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
             => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
               => ( ( member6330420149250801815od_b_c @ Gamma @ ( inf_in4978071631833541052od_b_c @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T12 @ Alpha2 ) ) @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T12 @ Beta ) ) ) )
                 => ( ( distinguishes_a_b_c @ M1 @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ Alpha2 ) @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ Beta ) @ Gamma )
                   => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ ( prefix9085958534787526401od_b_c @ T12 ) )
                        = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ ( prefix9085958534787526401od_b_c @ T12 ) ) )
                     => ~ ( converge_a_b_c @ M22 @ Alpha2 @ Beta ) ) ) ) ) ) ) ) ) ) ).

% after_distinguishes_diverge
thf(fact_372_after__distinguishes__diverge,axiom,
    ! [M1: fsm_e_b_c,M22: fsm_a_b_c,Alpha2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T12: prefix425356687782099470od_b_c] :
      ( ( observable_e_b_c @ M1 )
     => ( ( observable_a_b_c @ M22 )
       => ( ( minimal_e_b_c @ M1 )
         => ( ( minimal_a_b_c @ M22 )
           => ( ( member6330420149250801815od_b_c @ Alpha2 @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) )
             => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) )
               => ( ( member6330420149250801815od_b_c @ Gamma @ ( inf_in4978071631833541052od_b_c @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T12 @ Alpha2 ) ) @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T12 @ Beta ) ) ) )
                 => ( ( distinguishes_e_b_c @ M1 @ ( after_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) @ Alpha2 ) @ ( after_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) @ Beta ) @ Gamma )
                   => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) @ ( prefix9085958534787526401od_b_c @ T12 ) )
                        = ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) @ ( prefix9085958534787526401od_b_c @ T12 ) ) )
                     => ~ ( converge_a_b_c @ M22 @ Alpha2 @ Beta ) ) ) ) ) ) ) ) ) ) ).

% after_distinguishes_diverge
thf(fact_373_after__distinguishes__diverge,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_e_b_c,Alpha2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T12: prefix425356687782099470od_b_c] :
      ( ( observable_a_b_c @ M1 )
     => ( ( observable_e_b_c @ M22 )
       => ( ( minimal_a_b_c @ M1 )
         => ( ( minimal_e_b_c @ M22 )
           => ( ( member6330420149250801815od_b_c @ Alpha2 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
             => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
               => ( ( member6330420149250801815od_b_c @ Gamma @ ( inf_in4978071631833541052od_b_c @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T12 @ Alpha2 ) ) @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T12 @ Beta ) ) ) )
                 => ( ( distinguishes_a_b_c @ M1 @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ Alpha2 ) @ ( after_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) @ Beta ) @ Gamma )
                   => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) @ ( prefix9085958534787526401od_b_c @ T12 ) )
                        = ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M22 @ ( initial_e_b_c @ M22 ) ) @ ( prefix9085958534787526401od_b_c @ T12 ) ) )
                     => ~ ( converge_e_b_c @ M22 @ Alpha2 @ Beta ) ) ) ) ) ) ) ) ) ) ).

% after_distinguishes_diverge
thf(fact_374_after__distinguishes__diverge,axiom,
    ! [M1: fsm_e_b_c,M22: fsm_e_b_c,Alpha2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c,Gamma: list_P903359562653991662od_b_c,T12: prefix425356687782099470od_b_c] :
      ( ( observable_e_b_c @ M1 )
     => ( ( observable_e_b_c @ M22 )
       => ( ( minimal_e_b_c @ M1 )
         => ( ( minimal_e_b_c @ M22 )
           => ( ( member6330420149250801815od_b_c @ Alpha2 @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) )
             => ( ( member6330420149250801815od_b_c @ Beta @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) )
               => ( ( member6330420149250801815od_b_c @ Gamma @ ( inf_in4978071631833541052od_b_c @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T12 @ Alpha2 ) ) @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T12 @ Beta ) ) ) )
                 => ( ( distinguishes_e_b_c @ M1 @ ( after_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) @ Alpha2 ) @ ( after_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) @ Beta ) @ Gamma )
                   => ( ( ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) ) @ ( prefix9085958534787526401od_b_c @ T12 ) )
                        = ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M22 @ ( initial_e_b_c @ M22 ) ) @ ( prefix9085958534787526401od_b_c @ T12 ) ) )
                     => ~ ( converge_e_b_c @ M22 @ Alpha2 @ Beta ) ) ) ) ) ) ) ) ) ) ).

% after_distinguishes_diverge
thf(fact_375_add__transition__with__components__simps_I2_J,axiom,
    ! [M: fsm_a_b_c,T3: produc2669932201312201782od_c_a] :
      ( ( inputs_a_b_c @ ( add_tr8224572408740125824_a_b_c @ M @ T3 ) )
      = ( insert_b @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) ) @ ( inputs_a_b_c @ M ) ) ) ).

% add_transition_with_components_simps(2)
thf(fact_376_add__transition__with__components__simps_I2_J,axiom,
    ! [M: fsm_e_b_c,T3: produc4050040609193146166od_c_e] :
      ( ( inputs_e_b_c @ ( add_tr2939330758928321156_e_b_c @ M @ T3 ) )
      = ( insert_b @ ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) @ ( inputs_e_b_c @ M ) ) ) ).

% add_transition_with_components_simps(2)
thf(fact_377_abstract__h__condition__soundness,axiom,
    ! [M: fsm_e_b_c,I: fsm_a_b_c,V: e > list_P903359562653991662od_b_c,M3: nat] :
      ( ( observable_e_b_c @ M )
     => ( ( observable_a_b_c @ I )
       => ( ( state_2387088923659988691_e_b_c @ M @ V )
         => ( ( ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) )
              = ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) )
           => ( h_sati5493416951118309199_b_c_a @ M @ I @ V @ M3 ) ) ) ) ) ).

% abstract_h_condition_soundness
thf(fact_378_abstract__h__condition__soundness,axiom,
    ! [M: fsm_e_b_c,I: fsm_e_b_c,V: e > list_P903359562653991662od_b_c,M3: nat] :
      ( ( observable_e_b_c @ M )
     => ( ( observable_e_b_c @ I )
       => ( ( state_2387088923659988691_e_b_c @ M @ V )
         => ( ( ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) )
              = ( lS_e_b_c @ I @ ( initial_e_b_c @ I ) ) )
           => ( h_sati5493416951118309203_b_c_e @ M @ I @ V @ M3 ) ) ) ) ) ).

% abstract_h_condition_soundness
thf(fact_379_abstract__h__condition__soundness,axiom,
    ! [M: fsm_a_b_c,I: fsm_a_b_c,V: a > list_P903359562653991662od_b_c,M3: nat] :
      ( ( observable_a_b_c @ M )
     => ( ( observable_a_b_c @ I )
       => ( ( state_7672330573471793359_a_b_c @ M @ V )
         => ( ( ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) )
              = ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) )
           => ( h_sati8764940838793890899_b_c_a @ M @ I @ V @ M3 ) ) ) ) ) ).

% abstract_h_condition_soundness
thf(fact_380_abstract__h__condition__soundness,axiom,
    ! [M: fsm_a_b_c,I: fsm_e_b_c,V: a > list_P903359562653991662od_b_c,M3: nat] :
      ( ( observable_a_b_c @ M )
     => ( ( observable_e_b_c @ I )
       => ( ( state_7672330573471793359_a_b_c @ M @ V )
         => ( ( ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) )
              = ( lS_e_b_c @ I @ ( initial_e_b_c @ I ) ) )
           => ( h_sati8764940838793890903_b_c_e @ M @ I @ V @ M3 ) ) ) ) ) ).

% abstract_h_condition_soundness
thf(fact_381_non__initialized__state__cover__assignment__diverges,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,F: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,SC: set_li6436108459499378894od_b_c,Q1: list_P903359562653991662od_b_c,Q2: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( minima1987601567150520449_c_b_c @ M )
       => ( ! [Q7: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ Q7 @ ( reacha8116992257183400179_c_b_c @ M ) )
             => ( member6330420149250801815od_b_c @ Q7 @ ( io_tar7088883562557314310_c_b_c @ M @ ( F @ Q7 ) @ ( initia3567573336347591134_c_b_c @ M ) ) ) )
         => ( ! [Q7: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Q7 @ ( reacha8116992257183400179_c_b_c @ M ) )
               => ( member6330420149250801815od_b_c @ ( F @ Q7 ) @ ( inf_in4978071631833541052od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) @ SC ) ) )
           => ( ( member6330420149250801815od_b_c @ Q1 @ ( reacha8116992257183400179_c_b_c @ M ) )
             => ( ( member6330420149250801815od_b_c @ Q2 @ ( reacha8116992257183400179_c_b_c @ M ) )
               => ( ( Q1 != Q2 )
                 => ~ ( conver6852411701971397450_c_b_c @ M @ ( F @ Q1 ) @ ( F @ Q2 ) ) ) ) ) ) ) ) ) ).

% non_initialized_state_cover_assignment_diverges
thf(fact_382_non__initialized__state__cover__assignment__diverges,axiom,
    ! [M: fsm_b_b_c,F: b > list_P903359562653991662od_b_c,SC: set_li6436108459499378894od_b_c,Q1: b,Q2: b] :
      ( ( observable_b_b_c @ M )
     => ( ( minimal_b_b_c @ M )
       => ( ! [Q7: b] :
              ( ( member_b @ Q7 @ ( reacha7216524145940060804_b_b_c @ M ) )
             => ( member_b @ Q7 @ ( io_targets_b_b_c @ M @ ( F @ Q7 ) @ ( initial_b_b_c @ M ) ) ) )
         => ( ! [Q7: b] :
                ( ( member_b @ Q7 @ ( reacha7216524145940060804_b_b_c @ M ) )
               => ( member6330420149250801815od_b_c @ ( F @ Q7 ) @ ( inf_in4978071631833541052od_b_c @ ( lS_b_b_c @ M @ ( initial_b_b_c @ M ) ) @ SC ) ) )
           => ( ( member_b @ Q1 @ ( reacha7216524145940060804_b_b_c @ M ) )
             => ( ( member_b @ Q2 @ ( reacha7216524145940060804_b_b_c @ M ) )
               => ( ( Q1 != Q2 )
                 => ~ ( converge_b_b_c @ M @ ( F @ Q1 ) @ ( F @ Q2 ) ) ) ) ) ) ) ) ) ).

% non_initialized_state_cover_assignment_diverges
thf(fact_383_non__initialized__state__cover__assignment__diverges,axiom,
    ! [M: fsm_c_b_c,F: c > list_P903359562653991662od_b_c,SC: set_li6436108459499378894od_b_c,Q1: c,Q2: c] :
      ( ( observable_c_b_c @ M )
     => ( ( minimal_c_b_c @ M )
       => ( ! [Q7: c] :
              ( ( member_c @ Q7 @ ( reacha3589370724273415685_c_b_c @ M ) )
             => ( member_c @ Q7 @ ( io_targets_c_b_c @ M @ ( F @ Q7 ) @ ( initial_c_b_c @ M ) ) ) )
         => ( ! [Q7: c] :
                ( ( member_c @ Q7 @ ( reacha3589370724273415685_c_b_c @ M ) )
               => ( member6330420149250801815od_b_c @ ( F @ Q7 ) @ ( inf_in4978071631833541052od_b_c @ ( lS_c_b_c @ M @ ( initial_c_b_c @ M ) ) @ SC ) ) )
           => ( ( member_c @ Q1 @ ( reacha3589370724273415685_c_b_c @ M ) )
             => ( ( member_c @ Q2 @ ( reacha3589370724273415685_c_b_c @ M ) )
               => ( ( Q1 != Q2 )
                 => ~ ( converge_c_b_c @ M @ ( F @ Q1 ) @ ( F @ Q2 ) ) ) ) ) ) ) ) ) ).

% non_initialized_state_cover_assignment_diverges
thf(fact_384_non__initialized__state__cover__assignment__diverges,axiom,
    ! [M: fsm_e_b_c,F: e > list_P903359562653991662od_b_c,SC: set_li6436108459499378894od_b_c,Q1: e,Q2: e] :
      ( ( observable_e_b_c @ M )
     => ( ( minimal_e_b_c @ M )
       => ( ! [Q7: e] :
              ( ( member_e @ Q7 @ ( reacha5558435917794901255_e_b_c @ M ) )
             => ( member_e @ Q7 @ ( io_targets_e_b_c @ M @ ( F @ Q7 ) @ ( initial_e_b_c @ M ) ) ) )
         => ( ! [Q7: e] :
                ( ( member_e @ Q7 @ ( reacha5558435917794901255_e_b_c @ M ) )
               => ( member6330420149250801815od_b_c @ ( F @ Q7 ) @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) @ SC ) ) )
           => ( ( member_e @ Q1 @ ( reacha5558435917794901255_e_b_c @ M ) )
             => ( ( member_e @ Q2 @ ( reacha5558435917794901255_e_b_c @ M ) )
               => ( ( Q1 != Q2 )
                 => ~ ( converge_e_b_c @ M @ ( F @ Q1 ) @ ( F @ Q2 ) ) ) ) ) ) ) ) ) ).

% non_initialized_state_cover_assignment_diverges
thf(fact_385_non__initialized__state__cover__assignment__diverges,axiom,
    ! [M: fsm_a_b_c,F: a > list_P903359562653991662od_b_c,SC: set_li6436108459499378894od_b_c,Q1: a,Q2: a] :
      ( ( observable_a_b_c @ M )
     => ( ( minimal_a_b_c @ M )
       => ( ! [Q7: a] :
              ( ( member_a @ Q7 @ ( reacha1620305530751930115_a_b_c @ M ) )
             => ( member_a @ Q7 @ ( io_targets_a_b_c @ M @ ( F @ Q7 ) @ ( initial_a_b_c @ M ) ) ) )
         => ( ! [Q7: a] :
                ( ( member_a @ Q7 @ ( reacha1620305530751930115_a_b_c @ M ) )
               => ( member6330420149250801815od_b_c @ ( F @ Q7 ) @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) @ SC ) ) )
           => ( ( member_a @ Q1 @ ( reacha1620305530751930115_a_b_c @ M ) )
             => ( ( member_a @ Q2 @ ( reacha1620305530751930115_a_b_c @ M ) )
               => ( ( Q1 != Q2 )
                 => ~ ( converge_a_b_c @ M @ ( F @ Q1 ) @ ( F @ Q2 ) ) ) ) ) ) ) ) ) ).

% non_initialized_state_cover_assignment_diverges
thf(fact_386_listset_Osimps_I1_J,axiom,
    ( ( listse5707276433534017357od_b_c @ nil_se6658356940551653326od_b_c )
    = ( insert6227932334100060350od_b_c @ nil_Product_prod_b_c @ bot_bo4166481423041325370od_b_c ) ) ).

% listset.simps(1)
thf(fact_387_add__transition__with__components__simps_I1_J,axiom,
    ! [M: fsm_a_b_c,T3: produc2669932201312201782od_c_a] :
      ( ( initial_a_b_c @ ( add_tr8224572408740125824_a_b_c @ M @ T3 ) )
      = ( initial_a_b_c @ M ) ) ).

% add_transition_with_components_simps(1)
thf(fact_388_add__transition__with__components__simps_I1_J,axiom,
    ! [M: fsm_e_b_c,T3: produc4050040609193146166od_c_e] :
      ( ( initial_e_b_c @ ( add_tr2939330758928321156_e_b_c @ M @ T3 ) )
      = ( initial_e_b_c @ M ) ) ).

% add_transition_with_components_simps(1)
thf(fact_389_io__targets__language,axiom,
    ! [Q6: e,M: fsm_e_b_c,Io: list_P903359562653991662od_b_c,Q: e] :
      ( ( member_e @ Q6 @ ( io_targets_e_b_c @ M @ Io @ Q ) )
     => ( member6330420149250801815od_b_c @ Io @ ( lS_e_b_c @ M @ Q ) ) ) ).

% io_targets_language
thf(fact_390_io__targets__language,axiom,
    ! [Q6: list_P903359562653991662od_b_c,M: fsm_li6801133765522507155_c_b_c,Io: list_P903359562653991662od_b_c,Q: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ Q6 @ ( io_tar7088883562557314310_c_b_c @ M @ Io @ Q ) )
     => ( member6330420149250801815od_b_c @ Io @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) ) ) ).

% io_targets_language
thf(fact_391_io__targets__language,axiom,
    ! [Q6: a,M: fsm_a_b_c,Io: list_P903359562653991662od_b_c,Q: a] :
      ( ( member_a @ Q6 @ ( io_targets_a_b_c @ M @ Io @ Q ) )
     => ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ Q ) ) ) ).

% io_targets_language
thf(fact_392_io__targets__language,axiom,
    ! [Q6: b,M: fsm_b_b_c,Io: list_P903359562653991662od_b_c,Q: b] :
      ( ( member_b @ Q6 @ ( io_targets_b_b_c @ M @ Io @ Q ) )
     => ( member6330420149250801815od_b_c @ Io @ ( lS_b_b_c @ M @ Q ) ) ) ).

% io_targets_language
thf(fact_393_io__targets__language,axiom,
    ! [Q6: c,M: fsm_c_b_c,Io: list_P903359562653991662od_b_c,Q: c] :
      ( ( member_c @ Q6 @ ( io_targets_c_b_c @ M @ Io @ Q ) )
     => ( member6330420149250801815od_b_c @ Io @ ( lS_c_b_c @ M @ Q ) ) ) ).

% io_targets_language
thf(fact_394_Prefix__Tree_Oafter_Osimps_I1_J,axiom,
    ! [T3: prefix425356687782099470od_b_c] :
      ( ( prefix8037181783833825927od_b_c @ T3 @ nil_Product_prod_b_c )
      = T3 ) ).

% Prefix_Tree.after.simps(1)
thf(fact_395_state__cover__assignment__card,axiom,
    ! [M: fsm_e_b_c,V: e > list_P903359562653991662od_b_c] :
      ( ( state_2387088923659988691_e_b_c @ M @ V )
     => ( ( observable_e_b_c @ M )
       => ( ( finite5583770498833199894od_b_c @ ( image_5036025201050656753od_b_c @ V @ ( reacha5558435917794901255_e_b_c @ M ) ) )
          = ( finite_card_e @ ( reacha5558435917794901255_e_b_c @ M ) ) ) ) ) ).

% state_cover_assignment_card
thf(fact_396_state__cover__assignment__card,axiom,
    ! [M: fsm_a_b_c,V: a > list_P903359562653991662od_b_c] :
      ( ( state_7672330573471793359_a_b_c @ M @ V )
     => ( ( observable_a_b_c @ M )
       => ( ( finite5583770498833199894od_b_c @ ( image_8656872703560917237od_b_c @ V @ ( reacha1620305530751930115_a_b_c @ M ) ) )
          = ( finite_card_a @ ( reacha1620305530751930115_a_b_c @ M ) ) ) ) ) ).

% state_cover_assignment_card
thf(fact_397_language__io__target__append,axiom,
    ! [Q6: e,M: fsm_e_b_c,Io1: list_P903359562653991662od_b_c,Q: e,Io2: list_P903359562653991662od_b_c] :
      ( ( member_e @ Q6 @ ( io_targets_e_b_c @ M @ Io1 @ Q ) )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_e_b_c @ M @ Q6 ) )
       => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_e_b_c @ M @ Q ) ) ) ) ).

% language_io_target_append
thf(fact_398_language__io__target__append,axiom,
    ! [Q6: list_P903359562653991662od_b_c,M: fsm_li6801133765522507155_c_b_c,Io1: list_P903359562653991662od_b_c,Q: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ Q6 @ ( io_tar7088883562557314310_c_b_c @ M @ Io1 @ Q ) )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_lis2930931384350476499_c_b_c @ M @ Q6 ) )
       => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) ) ) ) ).

% language_io_target_append
thf(fact_399_language__io__target__append,axiom,
    ! [Q6: a,M: fsm_a_b_c,Io1: list_P903359562653991662od_b_c,Q: a,Io2: list_P903359562653991662od_b_c] :
      ( ( member_a @ Q6 @ ( io_targets_a_b_c @ M @ Io1 @ Q ) )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_a_b_c @ M @ Q6 ) )
       => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ).

% language_io_target_append
thf(fact_400_language__io__target__append,axiom,
    ! [Q6: b,M: fsm_b_b_c,Io1: list_P903359562653991662od_b_c,Q: b,Io2: list_P903359562653991662od_b_c] :
      ( ( member_b @ Q6 @ ( io_targets_b_b_c @ M @ Io1 @ Q ) )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_b_b_c @ M @ Q6 ) )
       => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_b_b_c @ M @ Q ) ) ) ) ).

% language_io_target_append
thf(fact_401_language__io__target__append,axiom,
    ! [Q6: c,M: fsm_c_b_c,Io1: list_P903359562653991662od_b_c,Q: c,Io2: list_P903359562653991662od_b_c] :
      ( ( member_c @ Q6 @ ( io_targets_c_b_c @ M @ Io1 @ Q ) )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_c_b_c @ M @ Q6 ) )
       => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_c_b_c @ M @ Q ) ) ) ) ).

% language_io_target_append
thf(fact_402_io__targets__language__append,axiom,
    ! [Q1: e,M: fsm_e_b_c,Io1: list_P903359562653991662od_b_c,Q: e,Io2: list_P903359562653991662od_b_c] :
      ( ( member_e @ Q1 @ ( io_targets_e_b_c @ M @ Io1 @ Q ) )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_e_b_c @ M @ Q1 ) )
       => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_e_b_c @ M @ Q ) ) ) ) ).

% io_targets_language_append
thf(fact_403_io__targets__language__append,axiom,
    ! [Q1: list_P903359562653991662od_b_c,M: fsm_li6801133765522507155_c_b_c,Io1: list_P903359562653991662od_b_c,Q: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ Q1 @ ( io_tar7088883562557314310_c_b_c @ M @ Io1 @ Q ) )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_lis2930931384350476499_c_b_c @ M @ Q1 ) )
       => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) ) ) ) ).

% io_targets_language_append
thf(fact_404_io__targets__language__append,axiom,
    ! [Q1: a,M: fsm_a_b_c,Io1: list_P903359562653991662od_b_c,Q: a,Io2: list_P903359562653991662od_b_c] :
      ( ( member_a @ Q1 @ ( io_targets_a_b_c @ M @ Io1 @ Q ) )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_a_b_c @ M @ Q1 ) )
       => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ).

% io_targets_language_append
thf(fact_405_io__targets__language__append,axiom,
    ! [Q1: b,M: fsm_b_b_c,Io1: list_P903359562653991662od_b_c,Q: b,Io2: list_P903359562653991662od_b_c] :
      ( ( member_b @ Q1 @ ( io_targets_b_b_c @ M @ Io1 @ Q ) )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_b_b_c @ M @ Q1 ) )
       => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_b_b_c @ M @ Q ) ) ) ) ).

% io_targets_language_append
thf(fact_406_io__targets__language__append,axiom,
    ! [Q1: c,M: fsm_c_b_c,Io1: list_P903359562653991662od_b_c,Q: c,Io2: list_P903359562653991662od_b_c] :
      ( ( member_c @ Q1 @ ( io_targets_c_b_c @ M @ Io1 @ Q ) )
     => ( ( member6330420149250801815od_b_c @ Io2 @ ( lS_c_b_c @ M @ Q1 ) )
       => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_c_b_c @ M @ Q ) ) ) ) ).

% io_targets_language_append
thf(fact_407_abstract__h__condition__completeness,axiom,
    ! [M: fsm_e_b_c,I: fsm_a_b_c,M3: nat,V: e > list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( observable_a_b_c @ I )
       => ( ( minimal_e_b_c @ M )
         => ( ( ord_less_eq_nat @ ( size_a_b_c @ I ) @ M3 )
           => ( ( ord_less_eq_nat @ ( finite_card_e @ ( reacha5558435917794901255_e_b_c @ M ) ) @ M3 )
             => ( ( ( inputs_a_b_c @ I )
                  = ( inputs_e_b_c @ M ) )
               => ( ( ( outputs_a_b_c @ I )
                    = ( outputs_e_b_c @ M ) )
                 => ( ( state_2387088923659988691_e_b_c @ M @ V )
                   => ( ( h_sati5493416951118309199_b_c_a @ M @ I @ V @ M3 )
                      = ( ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) )
                        = ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) ) ) ) ) ) ) ) ) ) ) ).

% abstract_h_condition_completeness
thf(fact_408_abstract__h__condition__completeness,axiom,
    ! [M: fsm_e_b_c,I: fsm_e_b_c,M3: nat,V: e > list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( observable_e_b_c @ I )
       => ( ( minimal_e_b_c @ M )
         => ( ( ord_less_eq_nat @ ( size_e_b_c @ I ) @ M3 )
           => ( ( ord_less_eq_nat @ ( finite_card_e @ ( reacha5558435917794901255_e_b_c @ M ) ) @ M3 )
             => ( ( ( inputs_e_b_c @ I )
                  = ( inputs_e_b_c @ M ) )
               => ( ( ( outputs_e_b_c @ I )
                    = ( outputs_e_b_c @ M ) )
                 => ( ( state_2387088923659988691_e_b_c @ M @ V )
                   => ( ( h_sati5493416951118309203_b_c_e @ M @ I @ V @ M3 )
                      = ( ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) )
                        = ( lS_e_b_c @ I @ ( initial_e_b_c @ I ) ) ) ) ) ) ) ) ) ) ) ) ).

% abstract_h_condition_completeness
thf(fact_409_abstract__h__condition__completeness,axiom,
    ! [M: fsm_a_b_c,I: fsm_a_b_c,M3: nat,V: a > list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( observable_a_b_c @ I )
       => ( ( minimal_a_b_c @ M )
         => ( ( ord_less_eq_nat @ ( size_a_b_c @ I ) @ M3 )
           => ( ( ord_less_eq_nat @ ( finite_card_a @ ( reacha1620305530751930115_a_b_c @ M ) ) @ M3 )
             => ( ( ( inputs_a_b_c @ I )
                  = ( inputs_a_b_c @ M ) )
               => ( ( ( outputs_a_b_c @ I )
                    = ( outputs_a_b_c @ M ) )
                 => ( ( state_7672330573471793359_a_b_c @ M @ V )
                   => ( ( h_sati8764940838793890899_b_c_a @ M @ I @ V @ M3 )
                      = ( ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) )
                        = ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) ) ) ) ) ) ) ) ) ) ) ).

% abstract_h_condition_completeness
thf(fact_410_abstract__h__condition__completeness,axiom,
    ! [M: fsm_a_b_c,I: fsm_e_b_c,M3: nat,V: a > list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( observable_e_b_c @ I )
       => ( ( minimal_a_b_c @ M )
         => ( ( ord_less_eq_nat @ ( size_e_b_c @ I ) @ M3 )
           => ( ( ord_less_eq_nat @ ( finite_card_a @ ( reacha1620305530751930115_a_b_c @ M ) ) @ M3 )
             => ( ( ( inputs_e_b_c @ I )
                  = ( inputs_a_b_c @ M ) )
               => ( ( ( outputs_e_b_c @ I )
                    = ( outputs_a_b_c @ M ) )
                 => ( ( state_7672330573471793359_a_b_c @ M @ V )
                   => ( ( h_sati8764940838793890903_b_c_e @ M @ I @ V @ M3 )
                      = ( ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) )
                        = ( lS_e_b_c @ I @ ( initial_e_b_c @ I ) ) ) ) ) ) ) ) ) ) ) ) ).

% abstract_h_condition_completeness
thf(fact_411_abstract__h__condition__exhaustiveness,axiom,
    ! [M: fsm_e_b_c,I: fsm_a_b_c,M3: nat,V: e > list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( observable_a_b_c @ I )
       => ( ( minimal_e_b_c @ M )
         => ( ( ord_less_eq_nat @ ( size_a_b_c @ I ) @ M3 )
           => ( ( ord_less_eq_nat @ ( finite_card_e @ ( reacha5558435917794901255_e_b_c @ M ) ) @ M3 )
             => ( ( ( inputs_a_b_c @ I )
                  = ( inputs_e_b_c @ M ) )
               => ( ( ( outputs_a_b_c @ I )
                    = ( outputs_e_b_c @ M ) )
                 => ( ( state_2387088923659988691_e_b_c @ M @ V )
                   => ( ( h_sati5493416951118309199_b_c_a @ M @ I @ V @ M3 )
                     => ( ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) )
                        = ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) ) ) ) ) ) ) ) ) ) ) ).

% abstract_h_condition_exhaustiveness
thf(fact_412_abstract__h__condition__exhaustiveness,axiom,
    ! [M: fsm_e_b_c,I: fsm_e_b_c,M3: nat,V: e > list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( observable_e_b_c @ I )
       => ( ( minimal_e_b_c @ M )
         => ( ( ord_less_eq_nat @ ( size_e_b_c @ I ) @ M3 )
           => ( ( ord_less_eq_nat @ ( finite_card_e @ ( reacha5558435917794901255_e_b_c @ M ) ) @ M3 )
             => ( ( ( inputs_e_b_c @ I )
                  = ( inputs_e_b_c @ M ) )
               => ( ( ( outputs_e_b_c @ I )
                    = ( outputs_e_b_c @ M ) )
                 => ( ( state_2387088923659988691_e_b_c @ M @ V )
                   => ( ( h_sati5493416951118309203_b_c_e @ M @ I @ V @ M3 )
                     => ( ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) )
                        = ( lS_e_b_c @ I @ ( initial_e_b_c @ I ) ) ) ) ) ) ) ) ) ) ) ) ).

% abstract_h_condition_exhaustiveness
thf(fact_413_abstract__h__condition__exhaustiveness,axiom,
    ! [M: fsm_a_b_c,I: fsm_a_b_c,M3: nat,V: a > list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( observable_a_b_c @ I )
       => ( ( minimal_a_b_c @ M )
         => ( ( ord_less_eq_nat @ ( size_a_b_c @ I ) @ M3 )
           => ( ( ord_less_eq_nat @ ( finite_card_a @ ( reacha1620305530751930115_a_b_c @ M ) ) @ M3 )
             => ( ( ( inputs_a_b_c @ I )
                  = ( inputs_a_b_c @ M ) )
               => ( ( ( outputs_a_b_c @ I )
                    = ( outputs_a_b_c @ M ) )
                 => ( ( state_7672330573471793359_a_b_c @ M @ V )
                   => ( ( h_sati8764940838793890899_b_c_a @ M @ I @ V @ M3 )
                     => ( ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) )
                        = ( lS_a_b_c @ I @ ( initial_a_b_c @ I ) ) ) ) ) ) ) ) ) ) ) ) ).

% abstract_h_condition_exhaustiveness
thf(fact_414_abstract__h__condition__exhaustiveness,axiom,
    ! [M: fsm_a_b_c,I: fsm_e_b_c,M3: nat,V: a > list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( observable_e_b_c @ I )
       => ( ( minimal_a_b_c @ M )
         => ( ( ord_less_eq_nat @ ( size_e_b_c @ I ) @ M3 )
           => ( ( ord_less_eq_nat @ ( finite_card_a @ ( reacha1620305530751930115_a_b_c @ M ) ) @ M3 )
             => ( ( ( inputs_e_b_c @ I )
                  = ( inputs_a_b_c @ M ) )
               => ( ( ( outputs_e_b_c @ I )
                    = ( outputs_a_b_c @ M ) )
                 => ( ( state_7672330573471793359_a_b_c @ M @ V )
                   => ( ( h_sati8764940838793890903_b_c_e @ M @ I @ V @ M3 )
                     => ( ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) )
                        = ( lS_e_b_c @ I @ ( initial_e_b_c @ I ) ) ) ) ) ) ) ) ) ) ) ) ).

% abstract_h_condition_exhaustiveness
thf(fact_415_after__set__Cons,axiom,
    ! [Gamma: list_P903359562653991662od_b_c,T: prefix425356687782099470od_b_c,Alpha2: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ Gamma @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T @ Alpha2 ) ) )
     => ( ( Gamma != nil_Product_prod_b_c )
       => ( member6330420149250801815od_b_c @ Alpha2 @ ( prefix9085958534787526401od_b_c @ T ) ) ) ) ).

% after_set_Cons
thf(fact_416_subset__after__subset,axiom,
    ! [T23: prefix425356687782099470od_b_c,T12: prefix425356687782099470od_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ ( prefix9085958534787526401od_b_c @ T23 ) @ ( prefix9085958534787526401od_b_c @ T12 ) )
     => ( ord_le282488521294790766od_b_c @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T23 @ Xs ) ) @ ( prefix9085958534787526401od_b_c @ ( prefix8037181783833825927od_b_c @ T12 @ Xs ) ) ) ) ).

% subset_after_subset
thf(fact_417_observable__io__targets__language,axiom,
    ! [Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,M: fsm_li6801133765522507155_c_b_c,Q1: list_P903359562653991662od_b_c,Q2: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_lis2930931384350476499_c_b_c @ M @ Q1 ) )
     => ( ( observ6293852833591064631_c_b_c @ M )
       => ( ( member6330420149250801815od_b_c @ Q2 @ ( io_tar7088883562557314310_c_b_c @ M @ Io1 @ Q1 ) )
         => ( member6330420149250801815od_b_c @ Io2 @ ( lS_lis2930931384350476499_c_b_c @ M @ Q2 ) ) ) ) ) ).

% observable_io_targets_language
thf(fact_418_observable__io__targets__language,axiom,
    ! [Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,M: fsm_b_b_c,Q1: b,Q2: b] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_b_b_c @ M @ Q1 ) )
     => ( ( observable_b_b_c @ M )
       => ( ( member_b @ Q2 @ ( io_targets_b_b_c @ M @ Io1 @ Q1 ) )
         => ( member6330420149250801815od_b_c @ Io2 @ ( lS_b_b_c @ M @ Q2 ) ) ) ) ) ).

% observable_io_targets_language
thf(fact_419_observable__io__targets__language,axiom,
    ! [Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,M: fsm_c_b_c,Q1: c,Q2: c] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_c_b_c @ M @ Q1 ) )
     => ( ( observable_c_b_c @ M )
       => ( ( member_c @ Q2 @ ( io_targets_c_b_c @ M @ Io1 @ Q1 ) )
         => ( member6330420149250801815od_b_c @ Io2 @ ( lS_c_b_c @ M @ Q2 ) ) ) ) ) ).

% observable_io_targets_language
thf(fact_420_observable__io__targets__language,axiom,
    ! [Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,M: fsm_a_b_c,Q1: a,Q2: a] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_a_b_c @ M @ Q1 ) )
     => ( ( observable_a_b_c @ M )
       => ( ( member_a @ Q2 @ ( io_targets_a_b_c @ M @ Io1 @ Q1 ) )
         => ( member6330420149250801815od_b_c @ Io2 @ ( lS_a_b_c @ M @ Q2 ) ) ) ) ) ).

% observable_io_targets_language
thf(fact_421_observable__io__targets__language,axiom,
    ! [Io1: list_P903359562653991662od_b_c,Io2: list_P903359562653991662od_b_c,M: fsm_e_b_c,Q1: e,Q2: e] :
      ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io1 @ Io2 ) @ ( lS_e_b_c @ M @ Q1 ) )
     => ( ( observable_e_b_c @ M )
       => ( ( member_e @ Q2 @ ( io_targets_e_b_c @ M @ Io1 @ Q1 ) )
         => ( member6330420149250801815od_b_c @ Io2 @ ( lS_e_b_c @ M @ Q2 ) ) ) ) ) ).

% observable_io_targets_language
thf(fact_422_observable__io__targets,axiom,
    ! [M: fsm_a_b_c,Io: list_P903359562653991662od_b_c,Q: a] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ Q ) )
       => ~ ! [Q8: a] :
              ( ( io_targets_a_b_c @ M @ Io @ Q )
             != ( insert_a @ Q8 @ bot_bot_set_a ) ) ) ) ).

% observable_io_targets
thf(fact_423_observable__io__targets,axiom,
    ! [M: fsm_e_b_c,Io: list_P903359562653991662od_b_c,Q: e] :
      ( ( observable_e_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_e_b_c @ M @ Q ) )
       => ~ ! [Q8: e] :
              ( ( io_targets_e_b_c @ M @ Io @ Q )
             != ( insert_e @ Q8 @ bot_bot_set_e ) ) ) ) ).

% observable_io_targets
thf(fact_424_non__initialized__state__cover__assignment__from__non__initialized__state__cover,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,SC: set_li6436108459499378894od_b_c] :
      ( ! [Q7: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ Q7 @ ( reacha8116992257183400179_c_b_c @ M ) )
         => ? [X4: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X4 @ ( inf_in4978071631833541052od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) @ SC ) )
              & ( member6330420149250801815od_b_c @ Q7 @ ( io_tar7088883562557314310_c_b_c @ M @ X4 @ ( initia3567573336347591134_c_b_c @ M ) ) ) ) )
     => ~ ! [F2: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c] :
            ( ! [Q9: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Q9 @ ( reacha8116992257183400179_c_b_c @ M ) )
               => ( member6330420149250801815od_b_c @ Q9 @ ( io_tar7088883562557314310_c_b_c @ M @ ( F2 @ Q9 ) @ ( initia3567573336347591134_c_b_c @ M ) ) ) )
           => ~ ! [Q9: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Q9 @ ( reacha8116992257183400179_c_b_c @ M ) )
                 => ( member6330420149250801815od_b_c @ ( F2 @ Q9 ) @ ( inf_in4978071631833541052od_b_c @ ( lS_lis2930931384350476499_c_b_c @ M @ ( initia3567573336347591134_c_b_c @ M ) ) @ SC ) ) ) ) ) ).

% non_initialized_state_cover_assignment_from_non_initialized_state_cover
thf(fact_425_non__initialized__state__cover__assignment__from__non__initialized__state__cover,axiom,
    ! [M: fsm_b_b_c,SC: set_li6436108459499378894od_b_c] :
      ( ! [Q7: b] :
          ( ( member_b @ Q7 @ ( reacha7216524145940060804_b_b_c @ M ) )
         => ? [X4: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X4 @ ( inf_in4978071631833541052od_b_c @ ( lS_b_b_c @ M @ ( initial_b_b_c @ M ) ) @ SC ) )
              & ( member_b @ Q7 @ ( io_targets_b_b_c @ M @ X4 @ ( initial_b_b_c @ M ) ) ) ) )
     => ~ ! [F2: b > list_P903359562653991662od_b_c] :
            ( ! [Q9: b] :
                ( ( member_b @ Q9 @ ( reacha7216524145940060804_b_b_c @ M ) )
               => ( member_b @ Q9 @ ( io_targets_b_b_c @ M @ ( F2 @ Q9 ) @ ( initial_b_b_c @ M ) ) ) )
           => ~ ! [Q9: b] :
                  ( ( member_b @ Q9 @ ( reacha7216524145940060804_b_b_c @ M ) )
                 => ( member6330420149250801815od_b_c @ ( F2 @ Q9 ) @ ( inf_in4978071631833541052od_b_c @ ( lS_b_b_c @ M @ ( initial_b_b_c @ M ) ) @ SC ) ) ) ) ) ).

% non_initialized_state_cover_assignment_from_non_initialized_state_cover
thf(fact_426_non__initialized__state__cover__assignment__from__non__initialized__state__cover,axiom,
    ! [M: fsm_c_b_c,SC: set_li6436108459499378894od_b_c] :
      ( ! [Q7: c] :
          ( ( member_c @ Q7 @ ( reacha3589370724273415685_c_b_c @ M ) )
         => ? [X4: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X4 @ ( inf_in4978071631833541052od_b_c @ ( lS_c_b_c @ M @ ( initial_c_b_c @ M ) ) @ SC ) )
              & ( member_c @ Q7 @ ( io_targets_c_b_c @ M @ X4 @ ( initial_c_b_c @ M ) ) ) ) )
     => ~ ! [F2: c > list_P903359562653991662od_b_c] :
            ( ! [Q9: c] :
                ( ( member_c @ Q9 @ ( reacha3589370724273415685_c_b_c @ M ) )
               => ( member_c @ Q9 @ ( io_targets_c_b_c @ M @ ( F2 @ Q9 ) @ ( initial_c_b_c @ M ) ) ) )
           => ~ ! [Q9: c] :
                  ( ( member_c @ Q9 @ ( reacha3589370724273415685_c_b_c @ M ) )
                 => ( member6330420149250801815od_b_c @ ( F2 @ Q9 ) @ ( inf_in4978071631833541052od_b_c @ ( lS_c_b_c @ M @ ( initial_c_b_c @ M ) ) @ SC ) ) ) ) ) ).

% non_initialized_state_cover_assignment_from_non_initialized_state_cover
thf(fact_427_non__initialized__state__cover__assignment__from__non__initialized__state__cover,axiom,
    ! [M: fsm_e_b_c,SC: set_li6436108459499378894od_b_c] :
      ( ! [Q7: e] :
          ( ( member_e @ Q7 @ ( reacha5558435917794901255_e_b_c @ M ) )
         => ? [X4: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X4 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) @ SC ) )
              & ( member_e @ Q7 @ ( io_targets_e_b_c @ M @ X4 @ ( initial_e_b_c @ M ) ) ) ) )
     => ~ ! [F2: e > list_P903359562653991662od_b_c] :
            ( ! [Q9: e] :
                ( ( member_e @ Q9 @ ( reacha5558435917794901255_e_b_c @ M ) )
               => ( member_e @ Q9 @ ( io_targets_e_b_c @ M @ ( F2 @ Q9 ) @ ( initial_e_b_c @ M ) ) ) )
           => ~ ! [Q9: e] :
                  ( ( member_e @ Q9 @ ( reacha5558435917794901255_e_b_c @ M ) )
                 => ( member6330420149250801815od_b_c @ ( F2 @ Q9 ) @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) @ SC ) ) ) ) ) ).

% non_initialized_state_cover_assignment_from_non_initialized_state_cover
thf(fact_428_non__initialized__state__cover__assignment__from__non__initialized__state__cover,axiom,
    ! [M: fsm_a_b_c,SC: set_li6436108459499378894od_b_c] :
      ( ! [Q7: a] :
          ( ( member_a @ Q7 @ ( reacha1620305530751930115_a_b_c @ M ) )
         => ? [X4: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X4 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) @ SC ) )
              & ( member_a @ Q7 @ ( io_targets_a_b_c @ M @ X4 @ ( initial_a_b_c @ M ) ) ) ) )
     => ~ ! [F2: a > list_P903359562653991662od_b_c] :
            ( ! [Q9: a] :
                ( ( member_a @ Q9 @ ( reacha1620305530751930115_a_b_c @ M ) )
               => ( member_a @ Q9 @ ( io_targets_a_b_c @ M @ ( F2 @ Q9 ) @ ( initial_a_b_c @ M ) ) ) )
           => ~ ! [Q9: a] :
                  ( ( member_a @ Q9 @ ( reacha1620305530751930115_a_b_c @ M ) )
                 => ( member6330420149250801815od_b_c @ ( F2 @ Q9 ) @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) @ SC ) ) ) ) ) ).

% non_initialized_state_cover_assignment_from_non_initialized_state_cover
thf(fact_429_observable__language__target__failure,axiom,
    ! [M: fsm_b_b_c,Q: b,Io1: list_P903359562653991662od_b_c,T3: a,T: fsm_a_b_c] :
      ( ( observable_b_b_c @ M )
     => ( ( member_b @ Q @ ( io_targets_b_b_c @ M @ Io1 @ ( initial_b_b_c @ M ) ) )
       => ( ( member_a @ T3 @ ( io_targets_a_b_c @ T @ Io1 @ ( initial_a_b_c @ T ) ) )
         => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ T3 ) @ ( lS_b_b_c @ M @ Q ) )
           => ~ ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ ( initial_a_b_c @ T ) ) @ ( lS_b_b_c @ M @ ( initial_b_b_c @ M ) ) ) ) ) ) ) ).

% observable_language_target_failure
thf(fact_430_observable__language__target__failure,axiom,
    ! [M: fsm_c_b_c,Q: c,Io1: list_P903359562653991662od_b_c,T3: a,T: fsm_a_b_c] :
      ( ( observable_c_b_c @ M )
     => ( ( member_c @ Q @ ( io_targets_c_b_c @ M @ Io1 @ ( initial_c_b_c @ M ) ) )
       => ( ( member_a @ T3 @ ( io_targets_a_b_c @ T @ Io1 @ ( initial_a_b_c @ T ) ) )
         => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ T3 ) @ ( lS_c_b_c @ M @ Q ) )
           => ~ ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ ( initial_a_b_c @ T ) ) @ ( lS_c_b_c @ M @ ( initial_c_b_c @ M ) ) ) ) ) ) ) ).

% observable_language_target_failure
thf(fact_431_observable__language__target__failure,axiom,
    ! [M: fsm_b_b_c,Q: b,Io1: list_P903359562653991662od_b_c,T3: e,T: fsm_e_b_c] :
      ( ( observable_b_b_c @ M )
     => ( ( member_b @ Q @ ( io_targets_b_b_c @ M @ Io1 @ ( initial_b_b_c @ M ) ) )
       => ( ( member_e @ T3 @ ( io_targets_e_b_c @ T @ Io1 @ ( initial_e_b_c @ T ) ) )
         => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_e_b_c @ T @ T3 ) @ ( lS_b_b_c @ M @ Q ) )
           => ~ ( ord_le282488521294790766od_b_c @ ( lS_e_b_c @ T @ ( initial_e_b_c @ T ) ) @ ( lS_b_b_c @ M @ ( initial_b_b_c @ M ) ) ) ) ) ) ) ).

% observable_language_target_failure
thf(fact_432_observable__language__target__failure,axiom,
    ! [M: fsm_c_b_c,Q: c,Io1: list_P903359562653991662od_b_c,T3: e,T: fsm_e_b_c] :
      ( ( observable_c_b_c @ M )
     => ( ( member_c @ Q @ ( io_targets_c_b_c @ M @ Io1 @ ( initial_c_b_c @ M ) ) )
       => ( ( member_e @ T3 @ ( io_targets_e_b_c @ T @ Io1 @ ( initial_e_b_c @ T ) ) )
         => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_e_b_c @ T @ T3 ) @ ( lS_c_b_c @ M @ Q ) )
           => ~ ( ord_le282488521294790766od_b_c @ ( lS_e_b_c @ T @ ( initial_e_b_c @ T ) ) @ ( lS_c_b_c @ M @ ( initial_c_b_c @ M ) ) ) ) ) ) ) ).

% observable_language_target_failure
thf(fact_433_observable__language__target__failure,axiom,
    ! [M: fsm_a_b_c,Q: a,Io1: list_P903359562653991662od_b_c,T3: b,T: fsm_b_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member_a @ Q @ ( io_targets_a_b_c @ M @ Io1 @ ( initial_a_b_c @ M ) ) )
       => ( ( member_b @ T3 @ ( io_targets_b_b_c @ T @ Io1 @ ( initial_b_b_c @ T ) ) )
         => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_b_b_c @ T @ T3 ) @ ( lS_a_b_c @ M @ Q ) )
           => ~ ( ord_le282488521294790766od_b_c @ ( lS_b_b_c @ T @ ( initial_b_b_c @ T ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) ) ) ) ).

% observable_language_target_failure
thf(fact_434_observable__language__target__failure,axiom,
    ! [M: fsm_a_b_c,Q: a,Io1: list_P903359562653991662od_b_c,T3: c,T: fsm_c_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member_a @ Q @ ( io_targets_a_b_c @ M @ Io1 @ ( initial_a_b_c @ M ) ) )
       => ( ( member_c @ T3 @ ( io_targets_c_b_c @ T @ Io1 @ ( initial_c_b_c @ T ) ) )
         => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_c_b_c @ T @ T3 ) @ ( lS_a_b_c @ M @ Q ) )
           => ~ ( ord_le282488521294790766od_b_c @ ( lS_c_b_c @ T @ ( initial_c_b_c @ T ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) ) ) ) ).

% observable_language_target_failure
thf(fact_435_observable__language__target__failure,axiom,
    ! [M: fsm_a_b_c,Q: a,Io1: list_P903359562653991662od_b_c,T3: a,T: fsm_a_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member_a @ Q @ ( io_targets_a_b_c @ M @ Io1 @ ( initial_a_b_c @ M ) ) )
       => ( ( member_a @ T3 @ ( io_targets_a_b_c @ T @ Io1 @ ( initial_a_b_c @ T ) ) )
         => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ T3 ) @ ( lS_a_b_c @ M @ Q ) )
           => ~ ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ ( initial_a_b_c @ T ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) ) ) ) ).

% observable_language_target_failure
thf(fact_436_observable__language__target__failure,axiom,
    ! [M: fsm_a_b_c,Q: a,Io1: list_P903359562653991662od_b_c,T3: e,T: fsm_e_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member_a @ Q @ ( io_targets_a_b_c @ M @ Io1 @ ( initial_a_b_c @ M ) ) )
       => ( ( member_e @ T3 @ ( io_targets_e_b_c @ T @ Io1 @ ( initial_e_b_c @ T ) ) )
         => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_e_b_c @ T @ T3 ) @ ( lS_a_b_c @ M @ Q ) )
           => ~ ( ord_le282488521294790766od_b_c @ ( lS_e_b_c @ T @ ( initial_e_b_c @ T ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) ) ) ) ).

% observable_language_target_failure
thf(fact_437_observable__language__target__failure,axiom,
    ! [M: fsm_e_b_c,Q: e,Io1: list_P903359562653991662od_b_c,T3: b,T: fsm_b_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( member_e @ Q @ ( io_targets_e_b_c @ M @ Io1 @ ( initial_e_b_c @ M ) ) )
       => ( ( member_b @ T3 @ ( io_targets_b_b_c @ T @ Io1 @ ( initial_b_b_c @ T ) ) )
         => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_b_b_c @ T @ T3 ) @ ( lS_e_b_c @ M @ Q ) )
           => ~ ( ord_le282488521294790766od_b_c @ ( lS_b_b_c @ T @ ( initial_b_b_c @ T ) ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) ) ) ) ) ) ).

% observable_language_target_failure
thf(fact_438_observable__language__target__failure,axiom,
    ! [M: fsm_e_b_c,Q: e,Io1: list_P903359562653991662od_b_c,T3: c,T: fsm_c_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( member_e @ Q @ ( io_targets_e_b_c @ M @ Io1 @ ( initial_e_b_c @ M ) ) )
       => ( ( member_c @ T3 @ ( io_targets_c_b_c @ T @ Io1 @ ( initial_c_b_c @ T ) ) )
         => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_c_b_c @ T @ T3 ) @ ( lS_e_b_c @ M @ Q ) )
           => ~ ( ord_le282488521294790766od_b_c @ ( lS_c_b_c @ T @ ( initial_c_b_c @ T ) ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) ) ) ) ) ) ).

% observable_language_target_failure
thf(fact_439_observable__language__target,axiom,
    ! [M: fsm_b_b_c,Q: b,Io1: list_P903359562653991662od_b_c,T3: a,T: fsm_a_b_c] :
      ( ( observable_b_b_c @ M )
     => ( ( member_b @ Q @ ( io_targets_b_b_c @ M @ Io1 @ ( initial_b_b_c @ M ) ) )
       => ( ( member_a @ T3 @ ( io_targets_a_b_c @ T @ Io1 @ ( initial_a_b_c @ T ) ) )
         => ( ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ ( initial_a_b_c @ T ) ) @ ( lS_b_b_c @ M @ ( initial_b_b_c @ M ) ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ T3 ) @ ( lS_b_b_c @ M @ Q ) ) ) ) ) ) ).

% observable_language_target
thf(fact_440_observable__language__target,axiom,
    ! [M: fsm_c_b_c,Q: c,Io1: list_P903359562653991662od_b_c,T3: a,T: fsm_a_b_c] :
      ( ( observable_c_b_c @ M )
     => ( ( member_c @ Q @ ( io_targets_c_b_c @ M @ Io1 @ ( initial_c_b_c @ M ) ) )
       => ( ( member_a @ T3 @ ( io_targets_a_b_c @ T @ Io1 @ ( initial_a_b_c @ T ) ) )
         => ( ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ ( initial_a_b_c @ T ) ) @ ( lS_c_b_c @ M @ ( initial_c_b_c @ M ) ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ T3 ) @ ( lS_c_b_c @ M @ Q ) ) ) ) ) ) ).

% observable_language_target
thf(fact_441_observable__language__target,axiom,
    ! [M: fsm_b_b_c,Q: b,Io1: list_P903359562653991662od_b_c,T3: e,T: fsm_e_b_c] :
      ( ( observable_b_b_c @ M )
     => ( ( member_b @ Q @ ( io_targets_b_b_c @ M @ Io1 @ ( initial_b_b_c @ M ) ) )
       => ( ( member_e @ T3 @ ( io_targets_e_b_c @ T @ Io1 @ ( initial_e_b_c @ T ) ) )
         => ( ( ord_le282488521294790766od_b_c @ ( lS_e_b_c @ T @ ( initial_e_b_c @ T ) ) @ ( lS_b_b_c @ M @ ( initial_b_b_c @ M ) ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_e_b_c @ T @ T3 ) @ ( lS_b_b_c @ M @ Q ) ) ) ) ) ) ).

% observable_language_target
thf(fact_442_observable__language__target,axiom,
    ! [M: fsm_c_b_c,Q: c,Io1: list_P903359562653991662od_b_c,T3: e,T: fsm_e_b_c] :
      ( ( observable_c_b_c @ M )
     => ( ( member_c @ Q @ ( io_targets_c_b_c @ M @ Io1 @ ( initial_c_b_c @ M ) ) )
       => ( ( member_e @ T3 @ ( io_targets_e_b_c @ T @ Io1 @ ( initial_e_b_c @ T ) ) )
         => ( ( ord_le282488521294790766od_b_c @ ( lS_e_b_c @ T @ ( initial_e_b_c @ T ) ) @ ( lS_c_b_c @ M @ ( initial_c_b_c @ M ) ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_e_b_c @ T @ T3 ) @ ( lS_c_b_c @ M @ Q ) ) ) ) ) ) ).

% observable_language_target
thf(fact_443_observable__language__target,axiom,
    ! [M: fsm_a_b_c,Q: a,Io1: list_P903359562653991662od_b_c,T3: b,T: fsm_b_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member_a @ Q @ ( io_targets_a_b_c @ M @ Io1 @ ( initial_a_b_c @ M ) ) )
       => ( ( member_b @ T3 @ ( io_targets_b_b_c @ T @ Io1 @ ( initial_b_b_c @ T ) ) )
         => ( ( ord_le282488521294790766od_b_c @ ( lS_b_b_c @ T @ ( initial_b_b_c @ T ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_b_b_c @ T @ T3 ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ) ) ).

% observable_language_target
thf(fact_444_observable__language__target,axiom,
    ! [M: fsm_a_b_c,Q: a,Io1: list_P903359562653991662od_b_c,T3: c,T: fsm_c_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member_a @ Q @ ( io_targets_a_b_c @ M @ Io1 @ ( initial_a_b_c @ M ) ) )
       => ( ( member_c @ T3 @ ( io_targets_c_b_c @ T @ Io1 @ ( initial_c_b_c @ T ) ) )
         => ( ( ord_le282488521294790766od_b_c @ ( lS_c_b_c @ T @ ( initial_c_b_c @ T ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_c_b_c @ T @ T3 ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ) ) ).

% observable_language_target
thf(fact_445_observable__language__target,axiom,
    ! [M: fsm_a_b_c,Q: a,Io1: list_P903359562653991662od_b_c,T3: a,T: fsm_a_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member_a @ Q @ ( io_targets_a_b_c @ M @ Io1 @ ( initial_a_b_c @ M ) ) )
       => ( ( member_a @ T3 @ ( io_targets_a_b_c @ T @ Io1 @ ( initial_a_b_c @ T ) ) )
         => ( ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ ( initial_a_b_c @ T ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ T @ T3 ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ) ) ).

% observable_language_target
thf(fact_446_observable__language__target,axiom,
    ! [M: fsm_a_b_c,Q: a,Io1: list_P903359562653991662od_b_c,T3: e,T: fsm_e_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member_a @ Q @ ( io_targets_a_b_c @ M @ Io1 @ ( initial_a_b_c @ M ) ) )
       => ( ( member_e @ T3 @ ( io_targets_e_b_c @ T @ Io1 @ ( initial_e_b_c @ T ) ) )
         => ( ( ord_le282488521294790766od_b_c @ ( lS_e_b_c @ T @ ( initial_e_b_c @ T ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_e_b_c @ T @ T3 ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ) ) ).

% observable_language_target
thf(fact_447_observable__language__target,axiom,
    ! [M: fsm_e_b_c,Q: e,Io1: list_P903359562653991662od_b_c,T3: b,T: fsm_b_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( member_e @ Q @ ( io_targets_e_b_c @ M @ Io1 @ ( initial_e_b_c @ M ) ) )
       => ( ( member_b @ T3 @ ( io_targets_b_b_c @ T @ Io1 @ ( initial_b_b_c @ T ) ) )
         => ( ( ord_le282488521294790766od_b_c @ ( lS_b_b_c @ T @ ( initial_b_b_c @ T ) ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_b_b_c @ T @ T3 ) @ ( lS_e_b_c @ M @ Q ) ) ) ) ) ) ).

% observable_language_target
thf(fact_448_observable__language__target,axiom,
    ! [M: fsm_e_b_c,Q: e,Io1: list_P903359562653991662od_b_c,T3: c,T: fsm_c_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( member_e @ Q @ ( io_targets_e_b_c @ M @ Io1 @ ( initial_e_b_c @ M ) ) )
       => ( ( member_c @ T3 @ ( io_targets_c_b_c @ T @ Io1 @ ( initial_c_b_c @ T ) ) )
         => ( ( ord_le282488521294790766od_b_c @ ( lS_c_b_c @ T @ ( initial_c_b_c @ T ) ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
           => ( ord_le282488521294790766od_b_c @ ( lS_c_b_c @ T @ T3 ) @ ( lS_e_b_c @ M @ Q ) ) ) ) ) ) ).

% observable_language_target
thf(fact_449_is__state__cover__assignment_Oelims_I3_J,axiom,
    ! [X: fsm_li6801133765522507155_c_b_c,Xa: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c] :
      ( ~ ( state_2362830510734323903_c_b_c @ X @ Xa )
     => ~ ( ( ( Xa @ ( initia3567573336347591134_c_b_c @ X ) )
            = nil_Product_prod_b_c )
          & ! [X2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X2 @ ( reacha8116992257183400179_c_b_c @ X ) )
             => ( member6330420149250801815od_b_c @ X2 @ ( io_tar7088883562557314310_c_b_c @ X @ ( Xa @ X2 ) @ ( initia3567573336347591134_c_b_c @ X ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(3)
thf(fact_450_is__state__cover__assignment_Oelims_I3_J,axiom,
    ! [X: fsm_b_b_c,Xa: b > list_P903359562653991662od_b_c] :
      ( ~ ( state_4045177151805148240_b_b_c @ X @ Xa )
     => ~ ( ( ( Xa @ ( initial_b_b_c @ X ) )
            = nil_Product_prod_b_c )
          & ! [X2: b] :
              ( ( member_b @ X2 @ ( reacha7216524145940060804_b_b_c @ X ) )
             => ( member_b @ X2 @ ( io_targets_b_b_c @ X @ ( Xa @ X2 ) @ ( initial_b_b_c @ X ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(3)
thf(fact_451_is__state__cover__assignment_Oelims_I3_J,axiom,
    ! [X: fsm_c_b_c,Xa: c > list_P903359562653991662od_b_c] :
      ( ~ ( state_418023730138503121_c_b_c @ X @ Xa )
     => ~ ( ( ( Xa @ ( initial_c_b_c @ X ) )
            = nil_Product_prod_b_c )
          & ! [X2: c] :
              ( ( member_c @ X2 @ ( reacha3589370724273415685_c_b_c @ X ) )
             => ( member_c @ X2 @ ( io_targets_c_b_c @ X @ ( Xa @ X2 ) @ ( initial_c_b_c @ X ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(3)
thf(fact_452_is__state__cover__assignment_Oelims_I3_J,axiom,
    ! [X: fsm_e_b_c,Xa: e > list_P903359562653991662od_b_c] :
      ( ~ ( state_2387088923659988691_e_b_c @ X @ Xa )
     => ~ ( ( ( Xa @ ( initial_e_b_c @ X ) )
            = nil_Product_prod_b_c )
          & ! [X2: e] :
              ( ( member_e @ X2 @ ( reacha5558435917794901255_e_b_c @ X ) )
             => ( member_e @ X2 @ ( io_targets_e_b_c @ X @ ( Xa @ X2 ) @ ( initial_e_b_c @ X ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(3)
thf(fact_453_is__state__cover__assignment_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c,Xa: a > list_P903359562653991662od_b_c] :
      ( ~ ( state_7672330573471793359_a_b_c @ X @ Xa )
     => ~ ( ( ( Xa @ ( initial_a_b_c @ X ) )
            = nil_Product_prod_b_c )
          & ! [X2: a] :
              ( ( member_a @ X2 @ ( reacha1620305530751930115_a_b_c @ X ) )
             => ( member_a @ X2 @ ( io_targets_a_b_c @ X @ ( Xa @ X2 ) @ ( initial_a_b_c @ X ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(3)
thf(fact_454_is__state__cover__assignment_Oelims_I2_J,axiom,
    ! [X: fsm_li6801133765522507155_c_b_c,Xa: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c] :
      ( ( state_2362830510734323903_c_b_c @ X @ Xa )
     => ( ( ( Xa @ ( initia3567573336347591134_c_b_c @ X ) )
          = nil_Product_prod_b_c )
        & ! [X4: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X4 @ ( reacha8116992257183400179_c_b_c @ X ) )
           => ( member6330420149250801815od_b_c @ X4 @ ( io_tar7088883562557314310_c_b_c @ X @ ( Xa @ X4 ) @ ( initia3567573336347591134_c_b_c @ X ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(2)
thf(fact_455_is__state__cover__assignment_Oelims_I2_J,axiom,
    ! [X: fsm_b_b_c,Xa: b > list_P903359562653991662od_b_c] :
      ( ( state_4045177151805148240_b_b_c @ X @ Xa )
     => ( ( ( Xa @ ( initial_b_b_c @ X ) )
          = nil_Product_prod_b_c )
        & ! [X4: b] :
            ( ( member_b @ X4 @ ( reacha7216524145940060804_b_b_c @ X ) )
           => ( member_b @ X4 @ ( io_targets_b_b_c @ X @ ( Xa @ X4 ) @ ( initial_b_b_c @ X ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(2)
thf(fact_456_is__state__cover__assignment_Oelims_I2_J,axiom,
    ! [X: fsm_c_b_c,Xa: c > list_P903359562653991662od_b_c] :
      ( ( state_418023730138503121_c_b_c @ X @ Xa )
     => ( ( ( Xa @ ( initial_c_b_c @ X ) )
          = nil_Product_prod_b_c )
        & ! [X4: c] :
            ( ( member_c @ X4 @ ( reacha3589370724273415685_c_b_c @ X ) )
           => ( member_c @ X4 @ ( io_targets_c_b_c @ X @ ( Xa @ X4 ) @ ( initial_c_b_c @ X ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(2)
thf(fact_457_is__state__cover__assignment_Oelims_I2_J,axiom,
    ! [X: fsm_e_b_c,Xa: e > list_P903359562653991662od_b_c] :
      ( ( state_2387088923659988691_e_b_c @ X @ Xa )
     => ( ( ( Xa @ ( initial_e_b_c @ X ) )
          = nil_Product_prod_b_c )
        & ! [X4: e] :
            ( ( member_e @ X4 @ ( reacha5558435917794901255_e_b_c @ X ) )
           => ( member_e @ X4 @ ( io_targets_e_b_c @ X @ ( Xa @ X4 ) @ ( initial_e_b_c @ X ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(2)
thf(fact_458_is__state__cover__assignment_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c,Xa: a > list_P903359562653991662od_b_c] :
      ( ( state_7672330573471793359_a_b_c @ X @ Xa )
     => ( ( ( Xa @ ( initial_a_b_c @ X ) )
          = nil_Product_prod_b_c )
        & ! [X4: a] :
            ( ( member_a @ X4 @ ( reacha1620305530751930115_a_b_c @ X ) )
           => ( member_a @ X4 @ ( io_targets_a_b_c @ X @ ( Xa @ X4 ) @ ( initial_a_b_c @ X ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(2)
thf(fact_459_is__state__cover__assignment_Oelims_I1_J,axiom,
    ! [X: fsm_li6801133765522507155_c_b_c,Xa: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c,Y: $o] :
      ( ( ( state_2362830510734323903_c_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( ( ( Xa @ ( initia3567573336347591134_c_b_c @ X ) )
            = nil_Product_prod_b_c )
          & ! [X3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X3 @ ( reacha8116992257183400179_c_b_c @ X ) )
             => ( member6330420149250801815od_b_c @ X3 @ ( io_tar7088883562557314310_c_b_c @ X @ ( Xa @ X3 ) @ ( initia3567573336347591134_c_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(1)
thf(fact_460_is__state__cover__assignment_Oelims_I1_J,axiom,
    ! [X: fsm_b_b_c,Xa: b > list_P903359562653991662od_b_c,Y: $o] :
      ( ( ( state_4045177151805148240_b_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( ( ( Xa @ ( initial_b_b_c @ X ) )
            = nil_Product_prod_b_c )
          & ! [X3: b] :
              ( ( member_b @ X3 @ ( reacha7216524145940060804_b_b_c @ X ) )
             => ( member_b @ X3 @ ( io_targets_b_b_c @ X @ ( Xa @ X3 ) @ ( initial_b_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(1)
thf(fact_461_is__state__cover__assignment_Oelims_I1_J,axiom,
    ! [X: fsm_c_b_c,Xa: c > list_P903359562653991662od_b_c,Y: $o] :
      ( ( ( state_418023730138503121_c_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( ( ( Xa @ ( initial_c_b_c @ X ) )
            = nil_Product_prod_b_c )
          & ! [X3: c] :
              ( ( member_c @ X3 @ ( reacha3589370724273415685_c_b_c @ X ) )
             => ( member_c @ X3 @ ( io_targets_c_b_c @ X @ ( Xa @ X3 ) @ ( initial_c_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(1)
thf(fact_462_is__state__cover__assignment_Oelims_I1_J,axiom,
    ! [X: fsm_e_b_c,Xa: e > list_P903359562653991662od_b_c,Y: $o] :
      ( ( ( state_2387088923659988691_e_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( ( ( Xa @ ( initial_e_b_c @ X ) )
            = nil_Product_prod_b_c )
          & ! [X3: e] :
              ( ( member_e @ X3 @ ( reacha5558435917794901255_e_b_c @ X ) )
             => ( member_e @ X3 @ ( io_targets_e_b_c @ X @ ( Xa @ X3 ) @ ( initial_e_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(1)
thf(fact_463_is__state__cover__assignment_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Xa: a > list_P903359562653991662od_b_c,Y: $o] :
      ( ( ( state_7672330573471793359_a_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( ( ( Xa @ ( initial_a_b_c @ X ) )
            = nil_Product_prod_b_c )
          & ! [X3: a] :
              ( ( member_a @ X3 @ ( reacha1620305530751930115_a_b_c @ X ) )
             => ( member_a @ X3 @ ( io_targets_a_b_c @ X @ ( Xa @ X3 ) @ ( initial_a_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover_assignment.elims(1)
thf(fact_464_is__state__cover__assignment_Osimps,axiom,
    ( state_2362830510734323903_c_b_c
    = ( ^ [M2: fsm_li6801133765522507155_c_b_c,F3: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c] :
          ( ( ( F3 @ ( initia3567573336347591134_c_b_c @ M2 ) )
            = nil_Product_prod_b_c )
          & ! [X3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X3 @ ( reacha8116992257183400179_c_b_c @ M2 ) )
             => ( member6330420149250801815od_b_c @ X3 @ ( io_tar7088883562557314310_c_b_c @ M2 @ ( F3 @ X3 ) @ ( initia3567573336347591134_c_b_c @ M2 ) ) ) ) ) ) ) ).

% is_state_cover_assignment.simps
thf(fact_465_is__state__cover__assignment_Osimps,axiom,
    ( state_4045177151805148240_b_b_c
    = ( ^ [M2: fsm_b_b_c,F3: b > list_P903359562653991662od_b_c] :
          ( ( ( F3 @ ( initial_b_b_c @ M2 ) )
            = nil_Product_prod_b_c )
          & ! [X3: b] :
              ( ( member_b @ X3 @ ( reacha7216524145940060804_b_b_c @ M2 ) )
             => ( member_b @ X3 @ ( io_targets_b_b_c @ M2 @ ( F3 @ X3 ) @ ( initial_b_b_c @ M2 ) ) ) ) ) ) ) ).

% is_state_cover_assignment.simps
thf(fact_466_is__state__cover__assignment_Osimps,axiom,
    ( state_418023730138503121_c_b_c
    = ( ^ [M2: fsm_c_b_c,F3: c > list_P903359562653991662od_b_c] :
          ( ( ( F3 @ ( initial_c_b_c @ M2 ) )
            = nil_Product_prod_b_c )
          & ! [X3: c] :
              ( ( member_c @ X3 @ ( reacha3589370724273415685_c_b_c @ M2 ) )
             => ( member_c @ X3 @ ( io_targets_c_b_c @ M2 @ ( F3 @ X3 ) @ ( initial_c_b_c @ M2 ) ) ) ) ) ) ) ).

% is_state_cover_assignment.simps
thf(fact_467_is__state__cover__assignment_Osimps,axiom,
    ( state_2387088923659988691_e_b_c
    = ( ^ [M2: fsm_e_b_c,F3: e > list_P903359562653991662od_b_c] :
          ( ( ( F3 @ ( initial_e_b_c @ M2 ) )
            = nil_Product_prod_b_c )
          & ! [X3: e] :
              ( ( member_e @ X3 @ ( reacha5558435917794901255_e_b_c @ M2 ) )
             => ( member_e @ X3 @ ( io_targets_e_b_c @ M2 @ ( F3 @ X3 ) @ ( initial_e_b_c @ M2 ) ) ) ) ) ) ) ).

% is_state_cover_assignment.simps
thf(fact_468_is__state__cover__assignment_Osimps,axiom,
    ( state_7672330573471793359_a_b_c
    = ( ^ [M2: fsm_a_b_c,F3: a > list_P903359562653991662od_b_c] :
          ( ( ( F3 @ ( initial_a_b_c @ M2 ) )
            = nil_Product_prod_b_c )
          & ! [X3: a] :
              ( ( member_a @ X3 @ ( reacha1620305530751930115_a_b_c @ M2 ) )
             => ( member_a @ X3 @ ( io_targets_a_b_c @ M2 @ ( F3 @ X3 ) @ ( initial_a_b_c @ M2 ) ) ) ) ) ) ) ).

% is_state_cover_assignment.simps
thf(fact_469_minimal__equivalence__size__r,axiom,
    ! [M1: fsm_e_b_c,M22: fsm_e_b_c] :
      ( ( minimal_e_b_c @ M1 )
     => ( ( minimal_e_b_c @ M22 )
       => ( ( observable_e_b_c @ M1 )
         => ( ( observable_e_b_c @ M22 )
           => ( ( ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) )
                = ( lS_e_b_c @ M22 @ ( initial_e_b_c @ M22 ) ) )
             => ( ( finite_card_e @ ( reacha5558435917794901255_e_b_c @ M1 ) )
                = ( finite_card_e @ ( reacha5558435917794901255_e_b_c @ M22 ) ) ) ) ) ) ) ) ).

% minimal_equivalence_size_r
thf(fact_470_minimal__equivalence__size__r,axiom,
    ! [M1: fsm_e_b_c,M22: fsm_a_b_c] :
      ( ( minimal_e_b_c @ M1 )
     => ( ( minimal_a_b_c @ M22 )
       => ( ( observable_e_b_c @ M1 )
         => ( ( observable_a_b_c @ M22 )
           => ( ( ( lS_e_b_c @ M1 @ ( initial_e_b_c @ M1 ) )
                = ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) )
             => ( ( finite_card_e @ ( reacha5558435917794901255_e_b_c @ M1 ) )
                = ( finite_card_a @ ( reacha1620305530751930115_a_b_c @ M22 ) ) ) ) ) ) ) ) ).

% minimal_equivalence_size_r
thf(fact_471_minimal__equivalence__size__r,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_e_b_c] :
      ( ( minimal_a_b_c @ M1 )
     => ( ( minimal_e_b_c @ M22 )
       => ( ( observable_a_b_c @ M1 )
         => ( ( observable_e_b_c @ M22 )
           => ( ( ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) )
                = ( lS_e_b_c @ M22 @ ( initial_e_b_c @ M22 ) ) )
             => ( ( finite_card_a @ ( reacha1620305530751930115_a_b_c @ M1 ) )
                = ( finite_card_e @ ( reacha5558435917794901255_e_b_c @ M22 ) ) ) ) ) ) ) ) ).

% minimal_equivalence_size_r
thf(fact_472_minimal__equivalence__size__r,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_a_b_c] :
      ( ( minimal_a_b_c @ M1 )
     => ( ( minimal_a_b_c @ M22 )
       => ( ( observable_a_b_c @ M1 )
         => ( ( observable_a_b_c @ M22 )
           => ( ( ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) )
                = ( lS_a_b_c @ M22 @ ( initial_a_b_c @ M22 ) ) )
             => ( ( finite_card_a @ ( reacha1620305530751930115_a_b_c @ M1 ) )
                = ( finite_card_a @ ( reacha1620305530751930115_a_b_c @ M22 ) ) ) ) ) ) ) ) ).

% minimal_equivalence_size_r
thf(fact_473_completely__specified__io__targets,axiom,
    ! [M: fsm_a_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( comple6900478119722646120_a_b_c @ M )
     => ! [X4: a] :
          ( ( member_a @ X4 @ ( io_targets_a_b_c @ M @ Io @ ( initial_a_b_c @ M ) ) )
         => ! [Xa3: b] :
              ( ( member_b @ Xa3 @ ( inputs_a_b_c @ M ) )
             => ? [Xb2: produc2669932201312201782od_c_a] :
                  ( ( member5502040268208861279od_c_a @ Xb2 @ ( transitions_a_b_c @ M ) )
                  & ( ( produc4225943634317630866od_c_a @ Xb2 )
                    = X4 )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xb2 ) )
                    = Xa3 ) ) ) ) ) ).

% completely_specified_io_targets
thf(fact_474_completely__specified__io__targets,axiom,
    ! [M: fsm_e_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( comple1615236469910841452_e_b_c @ M )
     => ! [X4: e] :
          ( ( member_e @ X4 @ ( io_targets_e_b_c @ M @ Io @ ( initial_e_b_c @ M ) ) )
         => ! [Xa3: b] :
              ( ( member_b @ Xa3 @ ( inputs_e_b_c @ M ) )
             => ? [Xb2: produc4050040609193146166od_c_e] :
                  ( ( member6882148676089805663od_c_e @ Xb2 @ ( transitions_e_b_c @ M ) )
                  & ( ( produc6751554238685325970od_c_e @ Xb2 )
                    = X4 )
                  & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Xb2 ) )
                    = Xa3 ) ) ) ) ) ).

% completely_specified_io_targets
thf(fact_475_distinguishes__diverge__prefix,axiom,
    ! [M: fsm_a_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( distinguishes_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ U ) @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ V3 ) @ W )
       => ( ( member6330420149250801815od_b_c @ U @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ V3 @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
           => ( ( member6330420149250801815od_b_c @ W3 @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ W ) ) )
             => ( ( member6330420149250801815od_b_c @ W3 @ ( lS_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ U ) ) )
               => ( ( member6330420149250801815od_b_c @ W3 @ ( lS_a_b_c @ M @ ( after_a_b_c @ M @ ( initial_a_b_c @ M ) @ V3 ) ) )
                 => ~ ( converge_a_b_c @ M @ ( append2547753245680614915od_b_c @ U @ W3 ) @ ( append2547753245680614915od_b_c @ V3 @ W3 ) ) ) ) ) ) ) ) ) ).

% distinguishes_diverge_prefix
thf(fact_476_distinguishes__diverge__prefix,axiom,
    ! [M: fsm_e_b_c,U: list_P903359562653991662od_b_c,V3: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( distinguishes_e_b_c @ M @ ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ U ) @ ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ V3 ) @ W )
       => ( ( member6330420149250801815od_b_c @ U @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
         => ( ( member6330420149250801815od_b_c @ V3 @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
           => ( ( member6330420149250801815od_b_c @ W3 @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ W ) ) )
             => ( ( member6330420149250801815od_b_c @ W3 @ ( lS_e_b_c @ M @ ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ U ) ) )
               => ( ( member6330420149250801815od_b_c @ W3 @ ( lS_e_b_c @ M @ ( after_e_b_c @ M @ ( initial_e_b_c @ M ) @ V3 ) ) )
                 => ~ ( converge_e_b_c @ M @ ( append2547753245680614915od_b_c @ U @ W3 ) @ ( append2547753245680614915od_b_c @ V3 @ W3 ) ) ) ) ) ) ) ) ) ).

% distinguishes_diverge_prefix
thf(fact_477_is__state__cover_Oelims_I3_J,axiom,
    ! [X: fsm_li6801133765522507155_c_b_c,Xa: set_li6436108459499378894od_b_c] :
      ( ~ ( state_6970031540555430092_c_b_c @ X @ Xa )
     => ~ ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
          & ! [X2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X2 @ ( reacha8116992257183400179_c_b_c @ X ) )
             => ? [Xa3: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Xa3 @ Xa )
                  & ( member6330420149250801815od_b_c @ X2 @ ( io_tar7088883562557314310_c_b_c @ X @ Xa3 @ ( initia3567573336347591134_c_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover.elims(3)
thf(fact_478_is__state__cover_Oelims_I3_J,axiom,
    ! [X: fsm_b_b_c,Xa: set_li6436108459499378894od_b_c] :
      ( ~ ( state_8391474831432717277_b_b_c @ X @ Xa )
     => ~ ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
          & ! [X2: b] :
              ( ( member_b @ X2 @ ( reacha7216524145940060804_b_b_c @ X ) )
             => ? [Xa3: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Xa3 @ Xa )
                  & ( member_b @ X2 @ ( io_targets_b_b_c @ X @ Xa3 @ ( initial_b_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover.elims(3)
thf(fact_479_is__state__cover_Oelims_I3_J,axiom,
    ! [X: fsm_c_b_c,Xa: set_li6436108459499378894od_b_c] :
      ( ~ ( state_4764321409766072158_c_b_c @ X @ Xa )
     => ~ ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
          & ! [X2: c] :
              ( ( member_c @ X2 @ ( reacha3589370724273415685_c_b_c @ X ) )
             => ? [Xa3: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Xa3 @ Xa )
                  & ( member_c @ X2 @ ( io_targets_c_b_c @ X @ Xa3 @ ( initial_c_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover.elims(3)
thf(fact_480_is__state__cover_Oelims_I3_J,axiom,
    ! [X: fsm_e_b_c,Xa: set_li6436108459499378894od_b_c] :
      ( ~ ( state_6733386603287557728_e_b_c @ X @ Xa )
     => ~ ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
          & ! [X2: e] :
              ( ( member_e @ X2 @ ( reacha5558435917794901255_e_b_c @ X ) )
             => ? [Xa3: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Xa3 @ Xa )
                  & ( member_e @ X2 @ ( io_targets_e_b_c @ X @ Xa3 @ ( initial_e_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover.elims(3)
thf(fact_481_is__state__cover_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c,Xa: set_li6436108459499378894od_b_c] :
      ( ~ ( state_2795256216244586588_a_b_c @ X @ Xa )
     => ~ ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
          & ! [X2: a] :
              ( ( member_a @ X2 @ ( reacha1620305530751930115_a_b_c @ X ) )
             => ? [Xa3: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Xa3 @ Xa )
                  & ( member_a @ X2 @ ( io_targets_a_b_c @ X @ Xa3 @ ( initial_a_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover.elims(3)
thf(fact_482_fsm__initial,axiom,
    ! [M: fsm_a_b_c] : ( member_a @ ( initial_a_b_c @ M ) @ ( states_a_b_c @ M ) ) ).

% fsm_initial
thf(fact_483_fsm__initial,axiom,
    ! [M: fsm_e_b_c] : ( member_e @ ( initial_e_b_c @ M ) @ ( states_e_b_c @ M ) ) ).

% fsm_initial
thf(fact_484_set__empty2,axiom,
    ! [Xs: list_P903359562653991662od_b_c] :
      ( ( bot_bo2863795366942399540od_b_c
        = ( set_Product_prod_b_c2 @ Xs ) )
      = ( Xs = nil_Product_prod_b_c ) ) ).

% set_empty2
thf(fact_485_List_Oset__empty,axiom,
    ! [Xs: list_P903359562653991662od_b_c] :
      ( ( ( set_Product_prod_b_c2 @ Xs )
        = bot_bo2863795366942399540od_b_c )
      = ( Xs = nil_Product_prod_b_c ) ) ).

% List.set_empty
thf(fact_486_list_Osimps_I15_J,axiom,
    ! [X21: product_prod_b_c,X22: list_P903359562653991662od_b_c] :
      ( ( set_Product_prod_b_c2 @ ( cons_P4529483553340347422od_b_c @ X21 @ X22 ) )
      = ( insert1747480808674937912od_b_c @ X21 @ ( set_Product_prod_b_c2 @ X22 ) ) ) ).

% list.simps(15)
thf(fact_487_from__FSM__simps_I1_J,axiom,
    ! [Q: a,M: fsm_a_b_c] :
      ( ( member_a @ Q @ ( states_a_b_c @ M ) )
     => ( ( initial_a_b_c @ ( from_FSM_a_b_c @ M @ Q ) )
        = Q ) ) ).

% from_FSM_simps(1)
thf(fact_488_from__FSM__simps_I1_J,axiom,
    ! [Q: e,M: fsm_e_b_c] :
      ( ( member_e @ Q @ ( states_e_b_c @ M ) )
     => ( ( initial_e_b_c @ ( from_FSM_e_b_c @ M @ Q ) )
        = Q ) ) ).

% from_FSM_simps(1)
thf(fact_489_from__FSM__simps_I2_J,axiom,
    ! [Q: e,M: fsm_e_b_c] :
      ( ( member_e @ Q @ ( states_e_b_c @ M ) )
     => ( ( inputs_e_b_c @ ( from_FSM_e_b_c @ M @ Q ) )
        = ( inputs_e_b_c @ M ) ) ) ).

% from_FSM_simps(2)
thf(fact_490_from__FSM__simps_I2_J,axiom,
    ! [Q: a,M: fsm_a_b_c] :
      ( ( member_a @ Q @ ( states_a_b_c @ M ) )
     => ( ( inputs_a_b_c @ ( from_FSM_a_b_c @ M @ Q ) )
        = ( inputs_a_b_c @ M ) ) ) ).

% from_FSM_simps(2)
thf(fact_491_from__FSM__simps_I3_J,axiom,
    ! [Q: a,M: fsm_a_b_c] :
      ( ( member_a @ Q @ ( states_a_b_c @ M ) )
     => ( ( outputs_a_b_c @ ( from_FSM_a_b_c @ M @ Q ) )
        = ( outputs_a_b_c @ M ) ) ) ).

% from_FSM_simps(3)
thf(fact_492_from__FSM__simps_I3_J,axiom,
    ! [Q: e,M: fsm_e_b_c] :
      ( ( member_e @ Q @ ( states_e_b_c @ M ) )
     => ( ( outputs_e_b_c @ ( from_FSM_e_b_c @ M @ Q ) )
        = ( outputs_e_b_c @ M ) ) ) ).

% from_FSM_simps(3)
thf(fact_493_list_Oset__intros_I2_J,axiom,
    ! [Y: list_P903359562653991662od_b_c,X22: list_l8907847357763382004od_b_c,X21: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ Y @ ( set_li4480668622519654659od_b_c @ X22 ) )
     => ( member6330420149250801815od_b_c @ Y @ ( set_li4480668622519654659od_b_c @ ( cons_l342771267123639716od_b_c @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_494_list_Oset__intros_I2_J,axiom,
    ! [Y: a,X22: list_a,X21: a] :
      ( ( member_a @ Y @ ( set_a2 @ X22 ) )
     => ( member_a @ Y @ ( set_a2 @ ( cons_a @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_495_list_Oset__intros_I2_J,axiom,
    ! [Y: b,X22: list_b,X21: b] :
      ( ( member_b @ Y @ ( set_b2 @ X22 ) )
     => ( member_b @ Y @ ( set_b2 @ ( cons_b @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_496_list_Oset__intros_I2_J,axiom,
    ! [Y: c,X22: list_c,X21: c] :
      ( ( member_c @ Y @ ( set_c2 @ X22 ) )
     => ( member_c @ Y @ ( set_c2 @ ( cons_c @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_497_list_Oset__intros_I2_J,axiom,
    ! [Y: product_prod_b_c,X22: list_P903359562653991662od_b_c,X21: product_prod_b_c] :
      ( ( member7862447941013992593od_b_c @ Y @ ( set_Product_prod_b_c2 @ X22 ) )
     => ( member7862447941013992593od_b_c @ Y @ ( set_Product_prod_b_c2 @ ( cons_P4529483553340347422od_b_c @ X21 @ X22 ) ) ) ) ).

% list.set_intros(2)
thf(fact_498_list_Oset__intros_I1_J,axiom,
    ! [X21: list_P903359562653991662od_b_c,X22: list_l8907847357763382004od_b_c] : ( member6330420149250801815od_b_c @ X21 @ ( set_li4480668622519654659od_b_c @ ( cons_l342771267123639716od_b_c @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_499_list_Oset__intros_I1_J,axiom,
    ! [X21: a,X22: list_a] : ( member_a @ X21 @ ( set_a2 @ ( cons_a @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_500_list_Oset__intros_I1_J,axiom,
    ! [X21: b,X22: list_b] : ( member_b @ X21 @ ( set_b2 @ ( cons_b @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_501_list_Oset__intros_I1_J,axiom,
    ! [X21: c,X22: list_c] : ( member_c @ X21 @ ( set_c2 @ ( cons_c @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_502_list_Oset__intros_I1_J,axiom,
    ! [X21: product_prod_b_c,X22: list_P903359562653991662od_b_c] : ( member7862447941013992593od_b_c @ X21 @ ( set_Product_prod_b_c2 @ ( cons_P4529483553340347422od_b_c @ X21 @ X22 ) ) ) ).

% list.set_intros(1)
thf(fact_503_list_Oset__cases,axiom,
    ! [E: list_P903359562653991662od_b_c,A: list_l8907847357763382004od_b_c] :
      ( ( member6330420149250801815od_b_c @ E @ ( set_li4480668622519654659od_b_c @ A ) )
     => ( ! [Z22: list_l8907847357763382004od_b_c] :
            ( A
           != ( cons_l342771267123639716od_b_c @ E @ Z22 ) )
       => ~ ! [Z1: list_P903359562653991662od_b_c,Z22: list_l8907847357763382004od_b_c] :
              ( ( A
                = ( cons_l342771267123639716od_b_c @ Z1 @ Z22 ) )
             => ~ ( member6330420149250801815od_b_c @ E @ ( set_li4480668622519654659od_b_c @ Z22 ) ) ) ) ) ).

% list.set_cases
thf(fact_504_list_Oset__cases,axiom,
    ! [E: a,A: list_a] :
      ( ( member_a @ E @ ( set_a2 @ A ) )
     => ( ! [Z22: list_a] :
            ( A
           != ( cons_a @ E @ Z22 ) )
       => ~ ! [Z1: a,Z22: list_a] :
              ( ( A
                = ( cons_a @ Z1 @ Z22 ) )
             => ~ ( member_a @ E @ ( set_a2 @ Z22 ) ) ) ) ) ).

% list.set_cases
thf(fact_505_list_Oset__cases,axiom,
    ! [E: b,A: list_b] :
      ( ( member_b @ E @ ( set_b2 @ A ) )
     => ( ! [Z22: list_b] :
            ( A
           != ( cons_b @ E @ Z22 ) )
       => ~ ! [Z1: b,Z22: list_b] :
              ( ( A
                = ( cons_b @ Z1 @ Z22 ) )
             => ~ ( member_b @ E @ ( set_b2 @ Z22 ) ) ) ) ) ).

% list.set_cases
thf(fact_506_list_Oset__cases,axiom,
    ! [E: c,A: list_c] :
      ( ( member_c @ E @ ( set_c2 @ A ) )
     => ( ! [Z22: list_c] :
            ( A
           != ( cons_c @ E @ Z22 ) )
       => ~ ! [Z1: c,Z22: list_c] :
              ( ( A
                = ( cons_c @ Z1 @ Z22 ) )
             => ~ ( member_c @ E @ ( set_c2 @ Z22 ) ) ) ) ) ).

% list.set_cases
thf(fact_507_list_Oset__cases,axiom,
    ! [E: product_prod_b_c,A: list_P903359562653991662od_b_c] :
      ( ( member7862447941013992593od_b_c @ E @ ( set_Product_prod_b_c2 @ A ) )
     => ( ! [Z22: list_P903359562653991662od_b_c] :
            ( A
           != ( cons_P4529483553340347422od_b_c @ E @ Z22 ) )
       => ~ ! [Z1: product_prod_b_c,Z22: list_P903359562653991662od_b_c] :
              ( ( A
                = ( cons_P4529483553340347422od_b_c @ Z1 @ Z22 ) )
             => ~ ( member7862447941013992593od_b_c @ E @ ( set_Product_prod_b_c2 @ Z22 ) ) ) ) ) ).

% list.set_cases
thf(fact_508_set__ConsD,axiom,
    ! [Y: list_P903359562653991662od_b_c,X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c] :
      ( ( member6330420149250801815od_b_c @ Y @ ( set_li4480668622519654659od_b_c @ ( cons_l342771267123639716od_b_c @ X @ Xs ) ) )
     => ( ( Y = X )
        | ( member6330420149250801815od_b_c @ Y @ ( set_li4480668622519654659od_b_c @ Xs ) ) ) ) ).

% set_ConsD
thf(fact_509_set__ConsD,axiom,
    ! [Y: a,X: a,Xs: list_a] :
      ( ( member_a @ Y @ ( set_a2 @ ( cons_a @ X @ Xs ) ) )
     => ( ( Y = X )
        | ( member_a @ Y @ ( set_a2 @ Xs ) ) ) ) ).

% set_ConsD
thf(fact_510_set__ConsD,axiom,
    ! [Y: b,X: b,Xs: list_b] :
      ( ( member_b @ Y @ ( set_b2 @ ( cons_b @ X @ Xs ) ) )
     => ( ( Y = X )
        | ( member_b @ Y @ ( set_b2 @ Xs ) ) ) ) ).

% set_ConsD
thf(fact_511_set__ConsD,axiom,
    ! [Y: c,X: c,Xs: list_c] :
      ( ( member_c @ Y @ ( set_c2 @ ( cons_c @ X @ Xs ) ) )
     => ( ( Y = X )
        | ( member_c @ Y @ ( set_c2 @ Xs ) ) ) ) ).

% set_ConsD
thf(fact_512_set__ConsD,axiom,
    ! [Y: product_prod_b_c,X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( member7862447941013992593od_b_c @ Y @ ( set_Product_prod_b_c2 @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) ) )
     => ( ( Y = X )
        | ( member7862447941013992593od_b_c @ Y @ ( set_Product_prod_b_c2 @ Xs ) ) ) ) ).

% set_ConsD
thf(fact_513_subset__code_I1_J,axiom,
    ! [Xs: list_l8907847357763382004od_b_c,B4: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ ( set_li4480668622519654659od_b_c @ Xs ) @ B4 )
      = ( ! [X3: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X3 @ ( set_li4480668622519654659od_b_c @ Xs ) )
           => ( member6330420149250801815od_b_c @ X3 @ B4 ) ) ) ) ).

% subset_code(1)
thf(fact_514_subset__code_I1_J,axiom,
    ! [Xs: list_a,B4: set_a] :
      ( ( ord_less_eq_set_a @ ( set_a2 @ Xs ) @ B4 )
      = ( ! [X3: a] :
            ( ( member_a @ X3 @ ( set_a2 @ Xs ) )
           => ( member_a @ X3 @ B4 ) ) ) ) ).

% subset_code(1)
thf(fact_515_subset__code_I1_J,axiom,
    ! [Xs: list_b,B4: set_b] :
      ( ( ord_less_eq_set_b @ ( set_b2 @ Xs ) @ B4 )
      = ( ! [X3: b] :
            ( ( member_b @ X3 @ ( set_b2 @ Xs ) )
           => ( member_b @ X3 @ B4 ) ) ) ) ).

% subset_code(1)
thf(fact_516_subset__code_I1_J,axiom,
    ! [Xs: list_c,B4: set_c] :
      ( ( ord_less_eq_set_c @ ( set_c2 @ Xs ) @ B4 )
      = ( ! [X3: c] :
            ( ( member_c @ X3 @ ( set_c2 @ Xs ) )
           => ( member_c @ X3 @ B4 ) ) ) ) ).

% subset_code(1)
thf(fact_517_list__set__sym,axiom,
    ! [X: list_P903359562653991662od_b_c,Y: list_P903359562653991662od_b_c] :
      ( ( set_Product_prod_b_c2 @ ( append2547753245680614915od_b_c @ X @ Y ) )
      = ( set_Product_prod_b_c2 @ ( append2547753245680614915od_b_c @ Y @ X ) ) ) ).

% list_set_sym
thf(fact_518_list__prefix__elem,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c,Ys: list_l8907847357763382004od_b_c] :
      ( ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ ( append6992831555715836169od_b_c @ Xs @ Ys ) ) )
     => ( ~ ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Ys ) )
       => ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) ) ) ) ).

% list_prefix_elem
thf(fact_519_list__prefix__elem,axiom,
    ! [X: a,Xs: list_a,Ys: list_a] :
      ( ( member_a @ X @ ( set_a2 @ ( append_a @ Xs @ Ys ) ) )
     => ( ~ ( member_a @ X @ ( set_a2 @ Ys ) )
       => ( member_a @ X @ ( set_a2 @ Xs ) ) ) ) ).

% list_prefix_elem
thf(fact_520_list__prefix__elem,axiom,
    ! [X: b,Xs: list_b,Ys: list_b] :
      ( ( member_b @ X @ ( set_b2 @ ( append_b @ Xs @ Ys ) ) )
     => ( ~ ( member_b @ X @ ( set_b2 @ Ys ) )
       => ( member_b @ X @ ( set_b2 @ Xs ) ) ) ) ).

% list_prefix_elem
thf(fact_521_list__prefix__elem,axiom,
    ! [X: c,Xs: list_c,Ys: list_c] :
      ( ( member_c @ X @ ( set_c2 @ ( append_c @ Xs @ Ys ) ) )
     => ( ~ ( member_c @ X @ ( set_c2 @ Ys ) )
       => ( member_c @ X @ ( set_c2 @ Xs ) ) ) ) ).

% list_prefix_elem
thf(fact_522_list__prefix__elem,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ ( append2547753245680614915od_b_c @ Xs @ Ys ) ) )
     => ( ~ ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Ys ) )
       => ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Xs ) ) ) ) ).

% list_prefix_elem
thf(fact_523_list__concat__non__elem,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c,Ys: list_l8907847357763382004od_b_c] :
      ( ~ ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) )
     => ( ~ ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Ys ) )
       => ~ ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ ( append6992831555715836169od_b_c @ Xs @ Ys ) ) ) ) ) ).

% list_concat_non_elem
thf(fact_524_list__concat__non__elem,axiom,
    ! [X: a,Xs: list_a,Ys: list_a] :
      ( ~ ( member_a @ X @ ( set_a2 @ Xs ) )
     => ( ~ ( member_a @ X @ ( set_a2 @ Ys ) )
       => ~ ( member_a @ X @ ( set_a2 @ ( append_a @ Xs @ Ys ) ) ) ) ) ).

% list_concat_non_elem
thf(fact_525_list__concat__non__elem,axiom,
    ! [X: b,Xs: list_b,Ys: list_b] :
      ( ~ ( member_b @ X @ ( set_b2 @ Xs ) )
     => ( ~ ( member_b @ X @ ( set_b2 @ Ys ) )
       => ~ ( member_b @ X @ ( set_b2 @ ( append_b @ Xs @ Ys ) ) ) ) ) ).

% list_concat_non_elem
thf(fact_526_list__concat__non__elem,axiom,
    ! [X: c,Xs: list_c,Ys: list_c] :
      ( ~ ( member_c @ X @ ( set_c2 @ Xs ) )
     => ( ~ ( member_c @ X @ ( set_c2 @ Ys ) )
       => ~ ( member_c @ X @ ( set_c2 @ ( append_c @ Xs @ Ys ) ) ) ) ) ).

% list_concat_non_elem
thf(fact_527_list__concat__non__elem,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ~ ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Xs ) )
     => ( ~ ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Ys ) )
       => ~ ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ ( append2547753245680614915od_b_c @ Xs @ Ys ) ) ) ) ) ).

% list_concat_non_elem
thf(fact_528_reachable__state__is__state,axiom,
    ! [Q: a,M: fsm_a_b_c] :
      ( ( member_a @ Q @ ( reacha1620305530751930115_a_b_c @ M ) )
     => ( member_a @ Q @ ( states_a_b_c @ M ) ) ) ).

% reachable_state_is_state
thf(fact_529_prefixes__prefixes,axiom,
    ! [Ys: list_P903359562653991662od_b_c,Xs: list_P903359562653991662od_b_c,Zs: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ Ys @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Xs ) ) )
     => ( ( member6330420149250801815od_b_c @ Zs @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Xs ) ) )
       => ( ( member6330420149250801815od_b_c @ Ys @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Zs ) ) )
          | ( member6330420149250801815od_b_c @ Zs @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Ys ) ) ) ) ) ) ).

% prefixes_prefixes
thf(fact_530_empty__set,axiom,
    ( bot_bo2863795366942399540od_b_c
    = ( set_Product_prod_b_c2 @ nil_Product_prod_b_c ) ) ).

% empty_set
thf(fact_531_set__subset__Cons,axiom,
    ! [Xs: list_P903359562653991662od_b_c,X: product_prod_b_c] : ( ord_le253122037897321832od_b_c @ ( set_Product_prod_b_c2 @ Xs ) @ ( set_Product_prod_b_c2 @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) ) ) ).

% set_subset_Cons
thf(fact_532_split__list,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c] :
      ( ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) )
     => ? [Ys2: list_l8907847357763382004od_b_c,Zs3: list_l8907847357763382004od_b_c] :
          ( Xs
          = ( append6992831555715836169od_b_c @ Ys2 @ ( cons_l342771267123639716od_b_c @ X @ Zs3 ) ) ) ) ).

% split_list
thf(fact_533_split__list,axiom,
    ! [X: a,Xs: list_a] :
      ( ( member_a @ X @ ( set_a2 @ Xs ) )
     => ? [Ys2: list_a,Zs3: list_a] :
          ( Xs
          = ( append_a @ Ys2 @ ( cons_a @ X @ Zs3 ) ) ) ) ).

% split_list
thf(fact_534_split__list,axiom,
    ! [X: b,Xs: list_b] :
      ( ( member_b @ X @ ( set_b2 @ Xs ) )
     => ? [Ys2: list_b,Zs3: list_b] :
          ( Xs
          = ( append_b @ Ys2 @ ( cons_b @ X @ Zs3 ) ) ) ) ).

% split_list
thf(fact_535_split__list,axiom,
    ! [X: c,Xs: list_c] :
      ( ( member_c @ X @ ( set_c2 @ Xs ) )
     => ? [Ys2: list_c,Zs3: list_c] :
          ( Xs
          = ( append_c @ Ys2 @ ( cons_c @ X @ Zs3 ) ) ) ) ).

% split_list
thf(fact_536_split__list,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Xs ) )
     => ? [Ys2: list_P903359562653991662od_b_c,Zs3: list_P903359562653991662od_b_c] :
          ( Xs
          = ( append2547753245680614915od_b_c @ Ys2 @ ( cons_P4529483553340347422od_b_c @ X @ Zs3 ) ) ) ) ).

% split_list
thf(fact_537_split__list__last,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c] :
      ( ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) )
     => ? [Ys2: list_l8907847357763382004od_b_c,Zs3: list_l8907847357763382004od_b_c] :
          ( ( Xs
            = ( append6992831555715836169od_b_c @ Ys2 @ ( cons_l342771267123639716od_b_c @ X @ Zs3 ) ) )
          & ~ ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Zs3 ) ) ) ) ).

% split_list_last
thf(fact_538_split__list__last,axiom,
    ! [X: a,Xs: list_a] :
      ( ( member_a @ X @ ( set_a2 @ Xs ) )
     => ? [Ys2: list_a,Zs3: list_a] :
          ( ( Xs
            = ( append_a @ Ys2 @ ( cons_a @ X @ Zs3 ) ) )
          & ~ ( member_a @ X @ ( set_a2 @ Zs3 ) ) ) ) ).

% split_list_last
thf(fact_539_split__list__last,axiom,
    ! [X: b,Xs: list_b] :
      ( ( member_b @ X @ ( set_b2 @ Xs ) )
     => ? [Ys2: list_b,Zs3: list_b] :
          ( ( Xs
            = ( append_b @ Ys2 @ ( cons_b @ X @ Zs3 ) ) )
          & ~ ( member_b @ X @ ( set_b2 @ Zs3 ) ) ) ) ).

% split_list_last
thf(fact_540_split__list__last,axiom,
    ! [X: c,Xs: list_c] :
      ( ( member_c @ X @ ( set_c2 @ Xs ) )
     => ? [Ys2: list_c,Zs3: list_c] :
          ( ( Xs
            = ( append_c @ Ys2 @ ( cons_c @ X @ Zs3 ) ) )
          & ~ ( member_c @ X @ ( set_c2 @ Zs3 ) ) ) ) ).

% split_list_last
thf(fact_541_split__list__last,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Xs ) )
     => ? [Ys2: list_P903359562653991662od_b_c,Zs3: list_P903359562653991662od_b_c] :
          ( ( Xs
            = ( append2547753245680614915od_b_c @ Ys2 @ ( cons_P4529483553340347422od_b_c @ X @ Zs3 ) ) )
          & ~ ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Zs3 ) ) ) ) ).

% split_list_last
thf(fact_542_split__list__prop,axiom,
    ! [Xs: list_P903359562653991662od_b_c,P: product_prod_b_c > $o] :
      ( ? [X4: product_prod_b_c] :
          ( ( member7862447941013992593od_b_c @ X4 @ ( set_Product_prod_b_c2 @ Xs ) )
          & ( P @ X4 ) )
     => ? [Ys2: list_P903359562653991662od_b_c,X2: product_prod_b_c] :
          ( ? [Zs3: list_P903359562653991662od_b_c] :
              ( Xs
              = ( append2547753245680614915od_b_c @ Ys2 @ ( cons_P4529483553340347422od_b_c @ X2 @ Zs3 ) ) )
          & ( P @ X2 ) ) ) ).

% split_list_prop
thf(fact_543_split__list__first,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c] :
      ( ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) )
     => ? [Ys2: list_l8907847357763382004od_b_c,Zs3: list_l8907847357763382004od_b_c] :
          ( ( Xs
            = ( append6992831555715836169od_b_c @ Ys2 @ ( cons_l342771267123639716od_b_c @ X @ Zs3 ) ) )
          & ~ ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Ys2 ) ) ) ) ).

% split_list_first
thf(fact_544_split__list__first,axiom,
    ! [X: a,Xs: list_a] :
      ( ( member_a @ X @ ( set_a2 @ Xs ) )
     => ? [Ys2: list_a,Zs3: list_a] :
          ( ( Xs
            = ( append_a @ Ys2 @ ( cons_a @ X @ Zs3 ) ) )
          & ~ ( member_a @ X @ ( set_a2 @ Ys2 ) ) ) ) ).

% split_list_first
thf(fact_545_split__list__first,axiom,
    ! [X: b,Xs: list_b] :
      ( ( member_b @ X @ ( set_b2 @ Xs ) )
     => ? [Ys2: list_b,Zs3: list_b] :
          ( ( Xs
            = ( append_b @ Ys2 @ ( cons_b @ X @ Zs3 ) ) )
          & ~ ( member_b @ X @ ( set_b2 @ Ys2 ) ) ) ) ).

% split_list_first
thf(fact_546_split__list__first,axiom,
    ! [X: c,Xs: list_c] :
      ( ( member_c @ X @ ( set_c2 @ Xs ) )
     => ? [Ys2: list_c,Zs3: list_c] :
          ( ( Xs
            = ( append_c @ Ys2 @ ( cons_c @ X @ Zs3 ) ) )
          & ~ ( member_c @ X @ ( set_c2 @ Ys2 ) ) ) ) ).

% split_list_first
thf(fact_547_split__list__first,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Xs ) )
     => ? [Ys2: list_P903359562653991662od_b_c,Zs3: list_P903359562653991662od_b_c] :
          ( ( Xs
            = ( append2547753245680614915od_b_c @ Ys2 @ ( cons_P4529483553340347422od_b_c @ X @ Zs3 ) ) )
          & ~ ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Ys2 ) ) ) ) ).

% split_list_first
thf(fact_548_split__list__propE,axiom,
    ! [Xs: list_P903359562653991662od_b_c,P: product_prod_b_c > $o] :
      ( ? [X4: product_prod_b_c] :
          ( ( member7862447941013992593od_b_c @ X4 @ ( set_Product_prod_b_c2 @ Xs ) )
          & ( P @ X4 ) )
     => ~ ! [Ys2: list_P903359562653991662od_b_c,X2: product_prod_b_c] :
            ( ? [Zs3: list_P903359562653991662od_b_c] :
                ( Xs
                = ( append2547753245680614915od_b_c @ Ys2 @ ( cons_P4529483553340347422od_b_c @ X2 @ Zs3 ) ) )
           => ~ ( P @ X2 ) ) ) ).

% split_list_propE
thf(fact_549_append__Cons__eq__iff,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c,Ys: list_l8907847357763382004od_b_c,Xs3: list_l8907847357763382004od_b_c,Ys5: list_l8907847357763382004od_b_c] :
      ( ~ ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) )
     => ( ~ ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Ys ) )
       => ( ( ( append6992831555715836169od_b_c @ Xs @ ( cons_l342771267123639716od_b_c @ X @ Ys ) )
            = ( append6992831555715836169od_b_c @ Xs3 @ ( cons_l342771267123639716od_b_c @ X @ Ys5 ) ) )
          = ( ( Xs = Xs3 )
            & ( Ys = Ys5 ) ) ) ) ) ).

% append_Cons_eq_iff
thf(fact_550_append__Cons__eq__iff,axiom,
    ! [X: a,Xs: list_a,Ys: list_a,Xs3: list_a,Ys5: list_a] :
      ( ~ ( member_a @ X @ ( set_a2 @ Xs ) )
     => ( ~ ( member_a @ X @ ( set_a2 @ Ys ) )
       => ( ( ( append_a @ Xs @ ( cons_a @ X @ Ys ) )
            = ( append_a @ Xs3 @ ( cons_a @ X @ Ys5 ) ) )
          = ( ( Xs = Xs3 )
            & ( Ys = Ys5 ) ) ) ) ) ).

% append_Cons_eq_iff
thf(fact_551_append__Cons__eq__iff,axiom,
    ! [X: b,Xs: list_b,Ys: list_b,Xs3: list_b,Ys5: list_b] :
      ( ~ ( member_b @ X @ ( set_b2 @ Xs ) )
     => ( ~ ( member_b @ X @ ( set_b2 @ Ys ) )
       => ( ( ( append_b @ Xs @ ( cons_b @ X @ Ys ) )
            = ( append_b @ Xs3 @ ( cons_b @ X @ Ys5 ) ) )
          = ( ( Xs = Xs3 )
            & ( Ys = Ys5 ) ) ) ) ) ).

% append_Cons_eq_iff
thf(fact_552_append__Cons__eq__iff,axiom,
    ! [X: c,Xs: list_c,Ys: list_c,Xs3: list_c,Ys5: list_c] :
      ( ~ ( member_c @ X @ ( set_c2 @ Xs ) )
     => ( ~ ( member_c @ X @ ( set_c2 @ Ys ) )
       => ( ( ( append_c @ Xs @ ( cons_c @ X @ Ys ) )
            = ( append_c @ Xs3 @ ( cons_c @ X @ Ys5 ) ) )
          = ( ( Xs = Xs3 )
            & ( Ys = Ys5 ) ) ) ) ) ).

% append_Cons_eq_iff
thf(fact_553_append__Cons__eq__iff,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c,Xs3: list_P903359562653991662od_b_c,Ys5: list_P903359562653991662od_b_c] :
      ( ~ ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Xs ) )
     => ( ~ ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Ys ) )
       => ( ( ( append2547753245680614915od_b_c @ Xs @ ( cons_P4529483553340347422od_b_c @ X @ Ys ) )
            = ( append2547753245680614915od_b_c @ Xs3 @ ( cons_P4529483553340347422od_b_c @ X @ Ys5 ) ) )
          = ( ( Xs = Xs3 )
            & ( Ys = Ys5 ) ) ) ) ) ).

% append_Cons_eq_iff
thf(fact_554_in__set__conv__decomp,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c] :
      ( ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) )
      = ( ? [Ys3: list_l8907847357763382004od_b_c,Zs2: list_l8907847357763382004od_b_c] :
            ( Xs
            = ( append6992831555715836169od_b_c @ Ys3 @ ( cons_l342771267123639716od_b_c @ X @ Zs2 ) ) ) ) ) ).

% in_set_conv_decomp
thf(fact_555_in__set__conv__decomp,axiom,
    ! [X: a,Xs: list_a] :
      ( ( member_a @ X @ ( set_a2 @ Xs ) )
      = ( ? [Ys3: list_a,Zs2: list_a] :
            ( Xs
            = ( append_a @ Ys3 @ ( cons_a @ X @ Zs2 ) ) ) ) ) ).

% in_set_conv_decomp
thf(fact_556_in__set__conv__decomp,axiom,
    ! [X: b,Xs: list_b] :
      ( ( member_b @ X @ ( set_b2 @ Xs ) )
      = ( ? [Ys3: list_b,Zs2: list_b] :
            ( Xs
            = ( append_b @ Ys3 @ ( cons_b @ X @ Zs2 ) ) ) ) ) ).

% in_set_conv_decomp
thf(fact_557_in__set__conv__decomp,axiom,
    ! [X: c,Xs: list_c] :
      ( ( member_c @ X @ ( set_c2 @ Xs ) )
      = ( ? [Ys3: list_c,Zs2: list_c] :
            ( Xs
            = ( append_c @ Ys3 @ ( cons_c @ X @ Zs2 ) ) ) ) ) ).

% in_set_conv_decomp
thf(fact_558_in__set__conv__decomp,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Xs ) )
      = ( ? [Ys3: list_P903359562653991662od_b_c,Zs2: list_P903359562653991662od_b_c] :
            ( Xs
            = ( append2547753245680614915od_b_c @ Ys3 @ ( cons_P4529483553340347422od_b_c @ X @ Zs2 ) ) ) ) ) ).

% in_set_conv_decomp
thf(fact_559_split__list__last__prop,axiom,
    ! [Xs: list_P903359562653991662od_b_c,P: product_prod_b_c > $o] :
      ( ? [X4: product_prod_b_c] :
          ( ( member7862447941013992593od_b_c @ X4 @ ( set_Product_prod_b_c2 @ Xs ) )
          & ( P @ X4 ) )
     => ? [Ys2: list_P903359562653991662od_b_c,X2: product_prod_b_c,Zs3: list_P903359562653991662od_b_c] :
          ( ( Xs
            = ( append2547753245680614915od_b_c @ Ys2 @ ( cons_P4529483553340347422od_b_c @ X2 @ Zs3 ) ) )
          & ( P @ X2 )
          & ! [Xa3: product_prod_b_c] :
              ( ( member7862447941013992593od_b_c @ Xa3 @ ( set_Product_prod_b_c2 @ Zs3 ) )
             => ~ ( P @ Xa3 ) ) ) ) ).

% split_list_last_prop
thf(fact_560_split__list__first__prop,axiom,
    ! [Xs: list_P903359562653991662od_b_c,P: product_prod_b_c > $o] :
      ( ? [X4: product_prod_b_c] :
          ( ( member7862447941013992593od_b_c @ X4 @ ( set_Product_prod_b_c2 @ Xs ) )
          & ( P @ X4 ) )
     => ? [Ys2: list_P903359562653991662od_b_c,X2: product_prod_b_c] :
          ( ? [Zs3: list_P903359562653991662od_b_c] :
              ( Xs
              = ( append2547753245680614915od_b_c @ Ys2 @ ( cons_P4529483553340347422od_b_c @ X2 @ Zs3 ) ) )
          & ( P @ X2 )
          & ! [Xa3: product_prod_b_c] :
              ( ( member7862447941013992593od_b_c @ Xa3 @ ( set_Product_prod_b_c2 @ Ys2 ) )
             => ~ ( P @ Xa3 ) ) ) ) ).

% split_list_first_prop
thf(fact_561_split__list__last__propE,axiom,
    ! [Xs: list_P903359562653991662od_b_c,P: product_prod_b_c > $o] :
      ( ? [X4: product_prod_b_c] :
          ( ( member7862447941013992593od_b_c @ X4 @ ( set_Product_prod_b_c2 @ Xs ) )
          & ( P @ X4 ) )
     => ~ ! [Ys2: list_P903359562653991662od_b_c,X2: product_prod_b_c,Zs3: list_P903359562653991662od_b_c] :
            ( ( Xs
              = ( append2547753245680614915od_b_c @ Ys2 @ ( cons_P4529483553340347422od_b_c @ X2 @ Zs3 ) ) )
           => ( ( P @ X2 )
             => ~ ! [Xa3: product_prod_b_c] :
                    ( ( member7862447941013992593od_b_c @ Xa3 @ ( set_Product_prod_b_c2 @ Zs3 ) )
                   => ~ ( P @ Xa3 ) ) ) ) ) ).

% split_list_last_propE
thf(fact_562_split__list__first__propE,axiom,
    ! [Xs: list_P903359562653991662od_b_c,P: product_prod_b_c > $o] :
      ( ? [X4: product_prod_b_c] :
          ( ( member7862447941013992593od_b_c @ X4 @ ( set_Product_prod_b_c2 @ Xs ) )
          & ( P @ X4 ) )
     => ~ ! [Ys2: list_P903359562653991662od_b_c,X2: product_prod_b_c] :
            ( ? [Zs3: list_P903359562653991662od_b_c] :
                ( Xs
                = ( append2547753245680614915od_b_c @ Ys2 @ ( cons_P4529483553340347422od_b_c @ X2 @ Zs3 ) ) )
           => ( ( P @ X2 )
             => ~ ! [Xa3: product_prod_b_c] :
                    ( ( member7862447941013992593od_b_c @ Xa3 @ ( set_Product_prod_b_c2 @ Ys2 ) )
                   => ~ ( P @ Xa3 ) ) ) ) ) ).

% split_list_first_propE
thf(fact_563_in__set__conv__decomp__last,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c] :
      ( ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) )
      = ( ? [Ys3: list_l8907847357763382004od_b_c,Zs2: list_l8907847357763382004od_b_c] :
            ( ( Xs
              = ( append6992831555715836169od_b_c @ Ys3 @ ( cons_l342771267123639716od_b_c @ X @ Zs2 ) ) )
            & ~ ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Zs2 ) ) ) ) ) ).

% in_set_conv_decomp_last
thf(fact_564_in__set__conv__decomp__last,axiom,
    ! [X: a,Xs: list_a] :
      ( ( member_a @ X @ ( set_a2 @ Xs ) )
      = ( ? [Ys3: list_a,Zs2: list_a] :
            ( ( Xs
              = ( append_a @ Ys3 @ ( cons_a @ X @ Zs2 ) ) )
            & ~ ( member_a @ X @ ( set_a2 @ Zs2 ) ) ) ) ) ).

% in_set_conv_decomp_last
thf(fact_565_in__set__conv__decomp__last,axiom,
    ! [X: b,Xs: list_b] :
      ( ( member_b @ X @ ( set_b2 @ Xs ) )
      = ( ? [Ys3: list_b,Zs2: list_b] :
            ( ( Xs
              = ( append_b @ Ys3 @ ( cons_b @ X @ Zs2 ) ) )
            & ~ ( member_b @ X @ ( set_b2 @ Zs2 ) ) ) ) ) ).

% in_set_conv_decomp_last
thf(fact_566_in__set__conv__decomp__last,axiom,
    ! [X: c,Xs: list_c] :
      ( ( member_c @ X @ ( set_c2 @ Xs ) )
      = ( ? [Ys3: list_c,Zs2: list_c] :
            ( ( Xs
              = ( append_c @ Ys3 @ ( cons_c @ X @ Zs2 ) ) )
            & ~ ( member_c @ X @ ( set_c2 @ Zs2 ) ) ) ) ) ).

% in_set_conv_decomp_last
thf(fact_567_in__set__conv__decomp__last,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Xs ) )
      = ( ? [Ys3: list_P903359562653991662od_b_c,Zs2: list_P903359562653991662od_b_c] :
            ( ( Xs
              = ( append2547753245680614915od_b_c @ Ys3 @ ( cons_P4529483553340347422od_b_c @ X @ Zs2 ) ) )
            & ~ ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Zs2 ) ) ) ) ) ).

% in_set_conv_decomp_last
thf(fact_568_in__set__conv__decomp__first,axiom,
    ! [X: list_P903359562653991662od_b_c,Xs: list_l8907847357763382004od_b_c] :
      ( ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Xs ) )
      = ( ? [Ys3: list_l8907847357763382004od_b_c,Zs2: list_l8907847357763382004od_b_c] :
            ( ( Xs
              = ( append6992831555715836169od_b_c @ Ys3 @ ( cons_l342771267123639716od_b_c @ X @ Zs2 ) ) )
            & ~ ( member6330420149250801815od_b_c @ X @ ( set_li4480668622519654659od_b_c @ Ys3 ) ) ) ) ) ).

% in_set_conv_decomp_first
thf(fact_569_in__set__conv__decomp__first,axiom,
    ! [X: a,Xs: list_a] :
      ( ( member_a @ X @ ( set_a2 @ Xs ) )
      = ( ? [Ys3: list_a,Zs2: list_a] :
            ( ( Xs
              = ( append_a @ Ys3 @ ( cons_a @ X @ Zs2 ) ) )
            & ~ ( member_a @ X @ ( set_a2 @ Ys3 ) ) ) ) ) ).

% in_set_conv_decomp_first
thf(fact_570_in__set__conv__decomp__first,axiom,
    ! [X: b,Xs: list_b] :
      ( ( member_b @ X @ ( set_b2 @ Xs ) )
      = ( ? [Ys3: list_b,Zs2: list_b] :
            ( ( Xs
              = ( append_b @ Ys3 @ ( cons_b @ X @ Zs2 ) ) )
            & ~ ( member_b @ X @ ( set_b2 @ Ys3 ) ) ) ) ) ).

% in_set_conv_decomp_first
thf(fact_571_in__set__conv__decomp__first,axiom,
    ! [X: c,Xs: list_c] :
      ( ( member_c @ X @ ( set_c2 @ Xs ) )
      = ( ? [Ys3: list_c,Zs2: list_c] :
            ( ( Xs
              = ( append_c @ Ys3 @ ( cons_c @ X @ Zs2 ) ) )
            & ~ ( member_c @ X @ ( set_c2 @ Ys3 ) ) ) ) ) ).

% in_set_conv_decomp_first
thf(fact_572_in__set__conv__decomp__first,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Xs ) )
      = ( ? [Ys3: list_P903359562653991662od_b_c,Zs2: list_P903359562653991662od_b_c] :
            ( ( Xs
              = ( append2547753245680614915od_b_c @ Ys3 @ ( cons_P4529483553340347422od_b_c @ X @ Zs2 ) ) )
            & ~ ( member7862447941013992593od_b_c @ X @ ( set_Product_prod_b_c2 @ Ys3 ) ) ) ) ) ).

% in_set_conv_decomp_first
thf(fact_573_split__list__last__prop__iff,axiom,
    ! [Xs: list_P903359562653991662od_b_c,P: product_prod_b_c > $o] :
      ( ( ? [X3: product_prod_b_c] :
            ( ( member7862447941013992593od_b_c @ X3 @ ( set_Product_prod_b_c2 @ Xs ) )
            & ( P @ X3 ) ) )
      = ( ? [Ys3: list_P903359562653991662od_b_c,X3: product_prod_b_c,Zs2: list_P903359562653991662od_b_c] :
            ( ( Xs
              = ( append2547753245680614915od_b_c @ Ys3 @ ( cons_P4529483553340347422od_b_c @ X3 @ Zs2 ) ) )
            & ( P @ X3 )
            & ! [Y3: product_prod_b_c] :
                ( ( member7862447941013992593od_b_c @ Y3 @ ( set_Product_prod_b_c2 @ Zs2 ) )
               => ~ ( P @ Y3 ) ) ) ) ) ).

% split_list_last_prop_iff
thf(fact_574_split__list__first__prop__iff,axiom,
    ! [Xs: list_P903359562653991662od_b_c,P: product_prod_b_c > $o] :
      ( ( ? [X3: product_prod_b_c] :
            ( ( member7862447941013992593od_b_c @ X3 @ ( set_Product_prod_b_c2 @ Xs ) )
            & ( P @ X3 ) ) )
      = ( ? [Ys3: list_P903359562653991662od_b_c,X3: product_prod_b_c] :
            ( ? [Zs2: list_P903359562653991662od_b_c] :
                ( Xs
                = ( append2547753245680614915od_b_c @ Ys3 @ ( cons_P4529483553340347422od_b_c @ X3 @ Zs2 ) ) )
            & ( P @ X3 )
            & ! [Y3: product_prod_b_c] :
                ( ( member7862447941013992593od_b_c @ Y3 @ ( set_Product_prod_b_c2 @ Ys3 ) )
               => ~ ( P @ Y3 ) ) ) ) ) ).

% split_list_first_prop_iff
thf(fact_575_list__append__subset3,axiom,
    ! [Xs1: list_P903359562653991662od_b_c,Ys1: list_P903359562653991662od_b_c,Xs22: list_P903359562653991662od_b_c,Ys22: list_P903359562653991662od_b_c,Xs32: list_P903359562653991662od_b_c,Ys32: list_P903359562653991662od_b_c] :
      ( ( ord_le253122037897321832od_b_c @ ( set_Product_prod_b_c2 @ Xs1 ) @ ( set_Product_prod_b_c2 @ Ys1 ) )
     => ( ( ord_le253122037897321832od_b_c @ ( set_Product_prod_b_c2 @ Xs22 ) @ ( set_Product_prod_b_c2 @ Ys22 ) )
       => ( ( ord_le253122037897321832od_b_c @ ( set_Product_prod_b_c2 @ Xs32 ) @ ( set_Product_prod_b_c2 @ Ys32 ) )
         => ( ord_le253122037897321832od_b_c @ ( set_Product_prod_b_c2 @ ( append2547753245680614915od_b_c @ Xs1 @ ( append2547753245680614915od_b_c @ Xs22 @ Xs32 ) ) ) @ ( set_Product_prod_b_c2 @ ( append2547753245680614915od_b_c @ Ys1 @ ( append2547753245680614915od_b_c @ Ys22 @ Ys32 ) ) ) ) ) ) ) ).

% list_append_subset3
thf(fact_576_list__prefix__subset,axiom,
    ! [Ts: list_P903359562653991662od_b_c,Xs: list_P903359562653991662od_b_c] :
      ( ? [Ys6: list_P903359562653991662od_b_c] :
          ( Ts
          = ( append2547753245680614915od_b_c @ Xs @ Ys6 ) )
     => ( ord_le253122037897321832od_b_c @ ( set_Product_prod_b_c2 @ Xs ) @ ( set_Product_prod_b_c2 @ Ts ) ) ) ).

% list_prefix_subset
thf(fact_577_prefixes__Cons_I2_J,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,Y: product_prod_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ ( cons_P4529483553340347422od_b_c @ Y @ Ys ) ) ) )
     => ( member6330420149250801815od_b_c @ Xs @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Ys ) ) ) ) ).

% prefixes_Cons(2)
thf(fact_578_prefixes__Cons_I1_J,axiom,
    ! [X: product_prod_b_c,Xs: list_P903359562653991662od_b_c,Y: product_prod_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ ( cons_P4529483553340347422od_b_c @ X @ Xs ) @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ ( cons_P4529483553340347422od_b_c @ Y @ Ys ) ) ) )
     => ( X = Y ) ) ).

% prefixes_Cons(1)
thf(fact_579_minimal__alt__def,axiom,
    ( minimal_a_b_c
    = ( ^ [M2: fsm_a_b_c] :
        ! [Q4: a,Q5: a] :
          ( ( member_a @ Q4 @ ( states_a_b_c @ M2 ) )
         => ( ( member_a @ Q5 @ ( states_a_b_c @ M2 ) )
           => ( ( ( lS_a_b_c @ M2 @ Q4 )
                = ( lS_a_b_c @ M2 @ Q5 ) )
             => ( Q4 = Q5 ) ) ) ) ) ) ).

% minimal_alt_def
thf(fact_580_minimal__alt__def,axiom,
    ( minimal_e_b_c
    = ( ^ [M2: fsm_e_b_c] :
        ! [Q4: e,Q5: e] :
          ( ( member_e @ Q4 @ ( states_e_b_c @ M2 ) )
         => ( ( member_e @ Q5 @ ( states_e_b_c @ M2 ) )
           => ( ( ( lS_e_b_c @ M2 @ Q4 )
                = ( lS_e_b_c @ M2 @ Q5 ) )
             => ( Q4 = Q5 ) ) ) ) ) ) ).

% minimal_alt_def
thf(fact_581_minimal_Osimps,axiom,
    ( minimal_a_b_c
    = ( ^ [M2: fsm_a_b_c] :
        ! [X3: a] :
          ( ( member_a @ X3 @ ( states_a_b_c @ M2 ) )
         => ! [Y3: a] :
              ( ( member_a @ Y3 @ ( states_a_b_c @ M2 ) )
             => ( ( X3 != Y3 )
               => ( ( lS_a_b_c @ M2 @ X3 )
                 != ( lS_a_b_c @ M2 @ Y3 ) ) ) ) ) ) ) ).

% minimal.simps
thf(fact_582_minimal_Osimps,axiom,
    ( minimal_e_b_c
    = ( ^ [M2: fsm_e_b_c] :
        ! [X3: e] :
          ( ( member_e @ X3 @ ( states_e_b_c @ M2 ) )
         => ! [Y3: e] :
              ( ( member_e @ Y3 @ ( states_e_b_c @ M2 ) )
             => ( ( X3 != Y3 )
               => ( ( lS_e_b_c @ M2 @ X3 )
                 != ( lS_e_b_c @ M2 @ Y3 ) ) ) ) ) ) ) ).

% minimal.simps
thf(fact_583_minimal_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Y: $o] :
      ( ( ( minimal_a_b_c @ X )
        = Y )
     => ( Y
        = ( ! [X3: a] :
              ( ( member_a @ X3 @ ( states_a_b_c @ X ) )
             => ! [Y3: a] :
                  ( ( member_a @ Y3 @ ( states_a_b_c @ X ) )
                 => ( ( X3 != Y3 )
                   => ( ( lS_a_b_c @ X @ X3 )
                     != ( lS_a_b_c @ X @ Y3 ) ) ) ) ) ) ) ) ).

% minimal.elims(1)
thf(fact_584_minimal_Oelims_I1_J,axiom,
    ! [X: fsm_e_b_c,Y: $o] :
      ( ( ( minimal_e_b_c @ X )
        = Y )
     => ( Y
        = ( ! [X3: e] :
              ( ( member_e @ X3 @ ( states_e_b_c @ X ) )
             => ! [Y3: e] :
                  ( ( member_e @ Y3 @ ( states_e_b_c @ X ) )
                 => ( ( X3 != Y3 )
                   => ( ( lS_e_b_c @ X @ X3 )
                     != ( lS_e_b_c @ X @ Y3 ) ) ) ) ) ) ) ) ).

% minimal.elims(1)
thf(fact_585_minimal_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ( minimal_a_b_c @ X )
     => ! [X4: a] :
          ( ( member_a @ X4 @ ( states_a_b_c @ X ) )
         => ! [Xa3: a] :
              ( ( member_a @ Xa3 @ ( states_a_b_c @ X ) )
             => ( ( X4 != Xa3 )
               => ( ( lS_a_b_c @ X @ X4 )
                 != ( lS_a_b_c @ X @ Xa3 ) ) ) ) ) ) ).

% minimal.elims(2)
thf(fact_586_minimal_Oelims_I2_J,axiom,
    ! [X: fsm_e_b_c] :
      ( ( minimal_e_b_c @ X )
     => ! [X4: e] :
          ( ( member_e @ X4 @ ( states_e_b_c @ X ) )
         => ! [Xa3: e] :
              ( ( member_e @ Xa3 @ ( states_e_b_c @ X ) )
             => ( ( X4 != Xa3 )
               => ( ( lS_e_b_c @ X @ X4 )
                 != ( lS_e_b_c @ X @ Xa3 ) ) ) ) ) ) ).

% minimal.elims(2)
thf(fact_587_minimal_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ~ ( minimal_a_b_c @ X )
     => ~ ! [X2: a] :
            ( ( member_a @ X2 @ ( states_a_b_c @ X ) )
           => ! [Xa2: a] :
                ( ( member_a @ Xa2 @ ( states_a_b_c @ X ) )
               => ( ( X2 != Xa2 )
                 => ( ( lS_a_b_c @ X @ X2 )
                   != ( lS_a_b_c @ X @ Xa2 ) ) ) ) ) ) ).

% minimal.elims(3)
thf(fact_588_minimal_Oelims_I3_J,axiom,
    ! [X: fsm_e_b_c] :
      ( ~ ( minimal_e_b_c @ X )
     => ~ ! [X2: e] :
            ( ( member_e @ X2 @ ( states_e_b_c @ X ) )
           => ! [Xa2: e] :
                ( ( member_e @ Xa2 @ ( states_e_b_c @ X ) )
               => ( ( X2 != Xa2 )
                 => ( ( lS_e_b_c @ X @ X2 )
                   != ( lS_e_b_c @ X @ Xa2 ) ) ) ) ) ) ).

% minimal.elims(3)
thf(fact_589_prefixes__set__Nil,axiom,
    ! [Xs: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Xs ) ) ) ).

% prefixes_set_Nil
thf(fact_590_prefixes__set__ob,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Xss2: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ Xs @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Xss2 ) ) )
     => ~ ! [Xs4: list_P903359562653991662od_b_c] :
            ( Xss2
           != ( append2547753245680614915od_b_c @ Xs @ Xs4 ) ) ) ).

% prefixes_set_ob
thf(fact_591_prefixes__prepend,axiom,
    ! [Xs3: list_P903359562653991662od_b_c,Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ Xs3 @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Xs ) ) )
     => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Ys @ Xs3 ) @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ ( append2547753245680614915od_b_c @ Ys @ Xs ) ) ) ) ) ).

% prefixes_prepend
thf(fact_592_distinguishes__not__Nil,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Q1: list_P903359562653991662od_b_c,Q2: list_P903359562653991662od_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( distin2804555989863659119_c_b_c @ M @ Q1 @ Q2 @ Io )
     => ( ( member6330420149250801815od_b_c @ Q1 @ ( states7681702920031268536_c_b_c @ M ) )
       => ( ( member6330420149250801815od_b_c @ Q2 @ ( states7681702920031268536_c_b_c @ M ) )
         => ( Io != nil_Product_prod_b_c ) ) ) ) ).

% distinguishes_not_Nil
thf(fact_593_distinguishes__not__Nil,axiom,
    ! [M: fsm_a_b_c,Q1: a,Q2: a,Io: list_P903359562653991662od_b_c] :
      ( ( distinguishes_a_b_c @ M @ Q1 @ Q2 @ Io )
     => ( ( member_a @ Q1 @ ( states_a_b_c @ M ) )
       => ( ( member_a @ Q2 @ ( states_a_b_c @ M ) )
         => ( Io != nil_Product_prod_b_c ) ) ) ) ).

% distinguishes_not_Nil
thf(fact_594_distinguishes__not__Nil,axiom,
    ! [M: fsm_b_b_c,Q1: b,Q2: b,Io: list_P903359562653991662od_b_c] :
      ( ( distinguishes_b_b_c @ M @ Q1 @ Q2 @ Io )
     => ( ( member_b @ Q1 @ ( states_b_b_c @ M ) )
       => ( ( member_b @ Q2 @ ( states_b_b_c @ M ) )
         => ( Io != nil_Product_prod_b_c ) ) ) ) ).

% distinguishes_not_Nil
thf(fact_595_distinguishes__not__Nil,axiom,
    ! [M: fsm_c_b_c,Q1: c,Q2: c,Io: list_P903359562653991662od_b_c] :
      ( ( distinguishes_c_b_c @ M @ Q1 @ Q2 @ Io )
     => ( ( member_c @ Q1 @ ( states_c_b_c @ M ) )
       => ( ( member_c @ Q2 @ ( states_c_b_c @ M ) )
         => ( Io != nil_Product_prod_b_c ) ) ) ) ).

% distinguishes_not_Nil
thf(fact_596_prefixes__prefix__subset,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ Xs @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Ys ) ) )
     => ( ord_le282488521294790766od_b_c @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Xs ) ) @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Ys ) ) ) ) ).

% prefixes_prefix_subset
thf(fact_597_minimally__distinguishes__ex,axiom,
    ! [Q1: e,M: fsm_e_b_c,Q2: e] :
      ( ( member_e @ Q1 @ ( states_e_b_c @ M ) )
     => ( ( member_e @ Q2 @ ( states_e_b_c @ M ) )
       => ( ( ( lS_e_b_c @ M @ Q1 )
           != ( lS_e_b_c @ M @ Q2 ) )
         => ~ ! [V2: list_P903359562653991662od_b_c] :
                ~ ( minima4181666250274330025_e_b_c @ M @ Q1 @ Q2 @ V2 ) ) ) ) ).

% minimally_distinguishes_ex
thf(fact_598_minimally__distinguishes__ex,axiom,
    ! [Q1: a,M: fsm_a_b_c,Q2: a] :
      ( ( member_a @ Q1 @ ( states_a_b_c @ M ) )
     => ( ( member_a @ Q2 @ ( states_a_b_c @ M ) )
       => ( ( ( lS_a_b_c @ M @ Q1 )
           != ( lS_a_b_c @ M @ Q2 ) )
         => ~ ! [V2: list_P903359562653991662od_b_c] :
                ~ ( minima243535863231358885_a_b_c @ M @ Q1 @ Q2 @ V2 ) ) ) ) ).

% minimally_distinguishes_ex
thf(fact_599_completely__specified__alt__def,axiom,
    ( comple6900478119722646120_a_b_c
    = ( ^ [M2: fsm_a_b_c] :
        ! [X3: a] :
          ( ( member_a @ X3 @ ( states_a_b_c @ M2 ) )
         => ! [Y3: b] :
              ( ( member_b @ Y3 @ ( inputs_a_b_c @ M2 ) )
             => ? [Q5: a,Z2: c] : ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ X3 @ ( produc3440865914000881661od_c_a @ Y3 @ ( product_Pair_c_a @ Z2 @ Q5 ) ) ) @ ( transitions_a_b_c @ M2 ) ) ) ) ) ) ).

% completely_specified_alt_def
thf(fact_600_completely__specified__alt__def,axiom,
    ( comple1615236469910841452_e_b_c
    = ( ^ [M2: fsm_e_b_c] :
        ! [X3: e] :
          ( ( member_e @ X3 @ ( states_e_b_c @ M2 ) )
         => ! [Y3: b] :
              ( ( member_b @ Y3 @ ( inputs_e_b_c @ M2 ) )
             => ? [Q5: e,Z2: c] : ( member6882148676089805663od_c_e @ ( produc8288412161402371238od_c_e @ X3 @ ( produc3440865931213796865od_c_e @ Y3 @ ( product_Pair_c_e @ Z2 @ Q5 ) ) ) @ ( transitions_e_b_c @ M2 ) ) ) ) ) ) ).

% completely_specified_alt_def
thf(fact_601_completely__specified_Osimps,axiom,
    ( comple6900478119722646120_a_b_c
    = ( ^ [M2: fsm_a_b_c] :
        ! [X3: a] :
          ( ( member_a @ X3 @ ( states_a_b_c @ M2 ) )
         => ! [Y3: b] :
              ( ( member_b @ Y3 @ ( inputs_a_b_c @ M2 ) )
             => ? [Z2: produc2669932201312201782od_c_a] :
                  ( ( member5502040268208861279od_c_a @ Z2 @ ( transitions_a_b_c @ M2 ) )
                  & ( ( produc4225943634317630866od_c_a @ Z2 )
                    = X3 )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Z2 ) )
                    = Y3 ) ) ) ) ) ) ).

% completely_specified.simps
thf(fact_602_completely__specified_Osimps,axiom,
    ( comple1615236469910841452_e_b_c
    = ( ^ [M2: fsm_e_b_c] :
        ! [X3: e] :
          ( ( member_e @ X3 @ ( states_e_b_c @ M2 ) )
         => ! [Y3: b] :
              ( ( member_b @ Y3 @ ( inputs_e_b_c @ M2 ) )
             => ? [Z2: produc4050040609193146166od_c_e] :
                  ( ( member6882148676089805663od_c_e @ Z2 @ ( transitions_e_b_c @ M2 ) )
                  & ( ( produc6751554238685325970od_c_e @ Z2 )
                    = X3 )
                  & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Z2 ) )
                    = Y3 ) ) ) ) ) ) ).

% completely_specified.simps
thf(fact_603_completely__specified_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Y: $o] :
      ( ( ( comple6900478119722646120_a_b_c @ X )
        = Y )
     => ( Y
        = ( ! [X3: a] :
              ( ( member_a @ X3 @ ( states_a_b_c @ X ) )
             => ! [Y3: b] :
                  ( ( member_b @ Y3 @ ( inputs_a_b_c @ X ) )
                 => ? [Z2: produc2669932201312201782od_c_a] :
                      ( ( member5502040268208861279od_c_a @ Z2 @ ( transitions_a_b_c @ X ) )
                      & ( ( produc4225943634317630866od_c_a @ Z2 )
                        = X3 )
                      & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Z2 ) )
                        = Y3 ) ) ) ) ) ) ) ).

% completely_specified.elims(1)
thf(fact_604_completely__specified_Oelims_I1_J,axiom,
    ! [X: fsm_e_b_c,Y: $o] :
      ( ( ( comple1615236469910841452_e_b_c @ X )
        = Y )
     => ( Y
        = ( ! [X3: e] :
              ( ( member_e @ X3 @ ( states_e_b_c @ X ) )
             => ! [Y3: b] :
                  ( ( member_b @ Y3 @ ( inputs_e_b_c @ X ) )
                 => ? [Z2: produc4050040609193146166od_c_e] :
                      ( ( member6882148676089805663od_c_e @ Z2 @ ( transitions_e_b_c @ X ) )
                      & ( ( produc6751554238685325970od_c_e @ Z2 )
                        = X3 )
                      & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Z2 ) )
                        = Y3 ) ) ) ) ) ) ) ).

% completely_specified.elims(1)
thf(fact_605_completely__specified_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ( comple6900478119722646120_a_b_c @ X )
     => ! [X4: a] :
          ( ( member_a @ X4 @ ( states_a_b_c @ X ) )
         => ! [Xa3: b] :
              ( ( member_b @ Xa3 @ ( inputs_a_b_c @ X ) )
             => ? [Xb2: produc2669932201312201782od_c_a] :
                  ( ( member5502040268208861279od_c_a @ Xb2 @ ( transitions_a_b_c @ X ) )
                  & ( ( produc4225943634317630866od_c_a @ Xb2 )
                    = X4 )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xb2 ) )
                    = Xa3 ) ) ) ) ) ).

% completely_specified.elims(2)
thf(fact_606_completely__specified_Oelims_I2_J,axiom,
    ! [X: fsm_e_b_c] :
      ( ( comple1615236469910841452_e_b_c @ X )
     => ! [X4: e] :
          ( ( member_e @ X4 @ ( states_e_b_c @ X ) )
         => ! [Xa3: b] :
              ( ( member_b @ Xa3 @ ( inputs_e_b_c @ X ) )
             => ? [Xb2: produc4050040609193146166od_c_e] :
                  ( ( member6882148676089805663od_c_e @ Xb2 @ ( transitions_e_b_c @ X ) )
                  & ( ( produc6751554238685325970od_c_e @ Xb2 )
                    = X4 )
                  & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Xb2 ) )
                    = Xa3 ) ) ) ) ) ).

% completely_specified.elims(2)
thf(fact_607_completely__specified_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ~ ( comple6900478119722646120_a_b_c @ X )
     => ~ ! [X2: a] :
            ( ( member_a @ X2 @ ( states_a_b_c @ X ) )
           => ! [Xa2: b] :
                ( ( member_b @ Xa2 @ ( inputs_a_b_c @ X ) )
               => ? [Xb3: produc2669932201312201782od_c_a] :
                    ( ( member5502040268208861279od_c_a @ Xb3 @ ( transitions_a_b_c @ X ) )
                    & ( ( produc4225943634317630866od_c_a @ Xb3 )
                      = X2 )
                    & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xb3 ) )
                      = Xa2 ) ) ) ) ) ).

% completely_specified.elims(3)
thf(fact_608_completely__specified_Oelims_I3_J,axiom,
    ! [X: fsm_e_b_c] :
      ( ~ ( comple1615236469910841452_e_b_c @ X )
     => ~ ! [X2: e] :
            ( ( member_e @ X2 @ ( states_e_b_c @ X ) )
           => ! [Xa2: b] :
                ( ( member_b @ Xa2 @ ( inputs_e_b_c @ X ) )
               => ? [Xb3: produc4050040609193146166od_c_e] :
                    ( ( member6882148676089805663od_c_e @ Xb3 @ ( transitions_e_b_c @ X ) )
                    & ( ( produc6751554238685325970od_c_e @ Xb3 )
                      = X2 )
                    & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Xb3 ) )
                      = Xa2 ) ) ) ) ) ).

% completely_specified.elims(3)
thf(fact_609_language__io_I1_J,axiom,
    ! [Io: list_P903359562653991662od_b_c,M: fsm_a_b_c,Q: a,X: b,Y: c] :
      ( ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ Q ) )
     => ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X @ Y ) @ ( set_Product_prod_b_c2 @ Io ) )
       => ( member_b @ X @ ( inputs_a_b_c @ M ) ) ) ) ).

% language_io(1)
thf(fact_610_language__io_I1_J,axiom,
    ! [Io: list_P903359562653991662od_b_c,M: fsm_e_b_c,Q: e,X: b,Y: c] :
      ( ( member6330420149250801815od_b_c @ Io @ ( lS_e_b_c @ M @ Q ) )
     => ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X @ Y ) @ ( set_Product_prod_b_c2 @ Io ) )
       => ( member_b @ X @ ( inputs_e_b_c @ M ) ) ) ) ).

% language_io(1)
thf(fact_611_language__io_I2_J,axiom,
    ! [Io: list_P903359562653991662od_b_c,M: fsm_a_b_c,Q: a,X: b,Y: c] :
      ( ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ Q ) )
     => ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X @ Y ) @ ( set_Product_prod_b_c2 @ Io ) )
       => ( member_c @ Y @ ( outputs_a_b_c @ M ) ) ) ) ).

% language_io(2)
thf(fact_612_language__io_I2_J,axiom,
    ! [Io: list_P903359562653991662od_b_c,M: fsm_e_b_c,Q: e,X: b,Y: c] :
      ( ( member6330420149250801815od_b_c @ Io @ ( lS_e_b_c @ M @ Q ) )
     => ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X @ Y ) @ ( set_Product_prod_b_c2 @ Io ) )
       => ( member_c @ Y @ ( outputs_e_b_c @ M ) ) ) ) ).

% language_io(2)
thf(fact_613_prefixes__prefix__suffix__ob,axiom,
    ! [A: list_P903359562653991662od_b_c,B: list_P903359562653991662od_b_c,C: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ A @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ ( append2547753245680614915od_b_c @ B @ C ) ) ) )
     => ( ~ ( member6330420149250801815od_b_c @ A @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ B ) ) )
       => ~ ! [C2: list_P903359562653991662od_b_c] :
              ( ? [C3: list_P903359562653991662od_b_c] :
                  ( C
                  = ( append2547753245680614915od_b_c @ C2 @ C3 ) )
             => ( ( A
                  = ( append2547753245680614915od_b_c @ B @ C2 ) )
               => ( C2 = nil_Product_prod_b_c ) ) ) ) ) ).

% prefixes_prefix_suffix_ob
thf(fact_614_after__is__state,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Io: list_P903359562653991662od_b_c,Q: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) )
       => ( member6330420149250801815od_b_c @ ( after_4052058690717316294_c_b_c @ M @ Q @ Io ) @ ( states7681702920031268536_c_b_c @ M ) ) ) ) ).

% after_is_state
thf(fact_615_after__is__state,axiom,
    ! [M: fsm_b_b_c,Io: list_P903359562653991662od_b_c,Q: b] :
      ( ( observable_b_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_b_b_c @ M @ Q ) )
       => ( member_b @ ( after_b_b_c @ M @ Q @ Io ) @ ( states_b_b_c @ M ) ) ) ) ).

% after_is_state
thf(fact_616_after__is__state,axiom,
    ! [M: fsm_c_b_c,Io: list_P903359562653991662od_b_c,Q: c] :
      ( ( observable_c_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_c_b_c @ M @ Q ) )
       => ( member_c @ ( after_c_b_c @ M @ Q @ Io ) @ ( states_c_b_c @ M ) ) ) ) ).

% after_is_state
thf(fact_617_after__is__state,axiom,
    ! [M: fsm_a_b_c,Io: list_P903359562653991662od_b_c,Q: a] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ Q ) )
       => ( member_a @ ( after_a_b_c @ M @ Q @ Io ) @ ( states_a_b_c @ M ) ) ) ) ).

% after_is_state
thf(fact_618_after__is__state,axiom,
    ! [M: fsm_e_b_c,Io: list_P903359562653991662od_b_c,Q: e] :
      ( ( observable_e_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io @ ( lS_e_b_c @ M @ Q ) )
       => ( member_e @ ( after_e_b_c @ M @ Q @ Io ) @ ( states_e_b_c @ M ) ) ) ) ).

% after_is_state
thf(fact_619_from__FSM__language,axiom,
    ! [Q: a,M: fsm_a_b_c] :
      ( ( member_a @ Q @ ( states_a_b_c @ M ) )
     => ( ( lS_a_b_c @ ( from_FSM_a_b_c @ M @ Q ) @ ( initial_a_b_c @ ( from_FSM_a_b_c @ M @ Q ) ) )
        = ( lS_a_b_c @ M @ Q ) ) ) ).

% from_FSM_language
thf(fact_620_from__FSM__language,axiom,
    ! [Q: e,M: fsm_e_b_c] :
      ( ( member_e @ Q @ ( states_e_b_c @ M ) )
     => ( ( lS_e_b_c @ ( from_FSM_e_b_c @ M @ Q ) @ ( initial_e_b_c @ ( from_FSM_e_b_c @ M @ Q ) ) )
        = ( lS_e_b_c @ M @ Q ) ) ) ).

% from_FSM_language
thf(fact_621_prefixes__set__subset,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] : ( ord_le282488521294790766od_b_c @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Xs ) ) @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ ( append2547753245680614915od_b_c @ Xs @ Ys ) ) ) ) ).

% prefixes_set_subset
thf(fact_622_completely__specified__language__extension,axiom,
    ! [M: fsm_e_b_c,Q: e,Io: list_P903359562653991662od_b_c,X: b] :
      ( ( comple1615236469910841452_e_b_c @ M )
     => ( ( member_e @ Q @ ( states_e_b_c @ M ) )
       => ( ( member6330420149250801815od_b_c @ Io @ ( lS_e_b_c @ M @ Q ) )
         => ( ( member_b @ X @ ( inputs_e_b_c @ M ) )
           => ~ ! [Y2: c] :
                  ~ ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y2 ) @ nil_Product_prod_b_c ) ) @ ( lS_e_b_c @ M @ Q ) ) ) ) ) ) ).

% completely_specified_language_extension
thf(fact_623_completely__specified__language__extension,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Q: list_P903359562653991662od_b_c,Io: list_P903359562653991662od_b_c,X: b] :
      ( ( comple7395250079248894168_c_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Q @ ( states7681702920031268536_c_b_c @ M ) )
       => ( ( member6330420149250801815od_b_c @ Io @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) )
         => ( ( member_b @ X @ ( inputs3199863676006542481_c_b_c @ M ) )
           => ~ ! [Y2: c] :
                  ~ ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y2 ) @ nil_Product_prod_b_c ) ) @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) ) ) ) ) ) ).

% completely_specified_language_extension
thf(fact_624_completely__specified__language__extension,axiom,
    ! [M: fsm_a_b_c,Q: a,Io: list_P903359562653991662od_b_c,X: b] :
      ( ( comple6900478119722646120_a_b_c @ M )
     => ( ( member_a @ Q @ ( states_a_b_c @ M ) )
       => ( ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ Q ) )
         => ( ( member_b @ X @ ( inputs_a_b_c @ M ) )
           => ~ ! [Y2: c] :
                  ~ ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y2 ) @ nil_Product_prod_b_c ) ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ) ) ).

% completely_specified_language_extension
thf(fact_625_completely__specified__language__extension,axiom,
    ! [M: fsm_b_b_c,Q: b,Io: list_P903359562653991662od_b_c,X: b] :
      ( ( comple3273324698056001001_b_b_c @ M )
     => ( ( member_b @ Q @ ( states_b_b_c @ M ) )
       => ( ( member6330420149250801815od_b_c @ Io @ ( lS_b_b_c @ M @ Q ) )
         => ( ( member_b @ X @ ( inputs_b_b_c @ M ) )
           => ~ ! [Y2: c] :
                  ~ ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y2 ) @ nil_Product_prod_b_c ) ) @ ( lS_b_b_c @ M @ Q ) ) ) ) ) ) ).

% completely_specified_language_extension
thf(fact_626_completely__specified__language__extension,axiom,
    ! [M: fsm_c_b_c,Q: c,Io: list_P903359562653991662od_b_c,X: b] :
      ( ( comple8869543313244131690_c_b_c @ M )
     => ( ( member_c @ Q @ ( states_c_b_c @ M ) )
       => ( ( member6330420149250801815od_b_c @ Io @ ( lS_c_b_c @ M @ Q ) )
         => ( ( member_b @ X @ ( inputs_c_b_c @ M ) )
           => ~ ! [Y2: c] :
                  ~ ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y2 ) @ nil_Product_prod_b_c ) ) @ ( lS_c_b_c @ M @ Q ) ) ) ) ) ) ).

% completely_specified_language_extension
thf(fact_627_minimally__distinguishes__proper__prefix__in__language,axiom,
    ! [M: fsm_a_b_c,Q1: a,Q2: a,Io: list_P903359562653991662od_b_c,Io6: list_P903359562653991662od_b_c] :
      ( ( minima243535863231358885_a_b_c @ M @ Q1 @ Q2 @ Io )
     => ( ( member6330420149250801815od_b_c @ Io6 @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Io ) ) )
       => ( ( Io6 != Io )
         => ( member6330420149250801815od_b_c @ Io6 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M @ Q1 ) @ ( lS_a_b_c @ M @ Q2 ) ) ) ) ) ) ).

% minimally_distinguishes_proper_prefix_in_language
thf(fact_628_minimally__distinguishes__proper__prefix__in__language,axiom,
    ! [M: fsm_e_b_c,Q1: e,Q2: e,Io: list_P903359562653991662od_b_c,Io6: list_P903359562653991662od_b_c] :
      ( ( minima4181666250274330025_e_b_c @ M @ Q1 @ Q2 @ Io )
     => ( ( member6330420149250801815od_b_c @ Io6 @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Io ) ) )
       => ( ( Io6 != Io )
         => ( member6330420149250801815od_b_c @ Io6 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M @ Q1 ) @ ( lS_e_b_c @ M @ Q2 ) ) ) ) ) ) ).

% minimally_distinguishes_proper_prefix_in_language
thf(fact_629_state__cover__assignment__from__state__cover,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,SC: set_li6436108459499378894od_b_c] :
      ( ( state_6970031540555430092_c_b_c @ M @ SC )
     => ~ ! [F2: list_P903359562653991662od_b_c > list_P903359562653991662od_b_c] :
            ( ( state_2362830510734323903_c_b_c @ M @ F2 )
           => ~ ! [Q9: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Q9 @ ( reacha8116992257183400179_c_b_c @ M ) )
                 => ( member6330420149250801815od_b_c @ ( F2 @ Q9 ) @ SC ) ) ) ) ).

% state_cover_assignment_from_state_cover
thf(fact_630_state__cover__assignment__from__state__cover,axiom,
    ! [M: fsm_b_b_c,SC: set_li6436108459499378894od_b_c] :
      ( ( state_8391474831432717277_b_b_c @ M @ SC )
     => ~ ! [F2: b > list_P903359562653991662od_b_c] :
            ( ( state_4045177151805148240_b_b_c @ M @ F2 )
           => ~ ! [Q9: b] :
                  ( ( member_b @ Q9 @ ( reacha7216524145940060804_b_b_c @ M ) )
                 => ( member6330420149250801815od_b_c @ ( F2 @ Q9 ) @ SC ) ) ) ) ).

% state_cover_assignment_from_state_cover
thf(fact_631_state__cover__assignment__from__state__cover,axiom,
    ! [M: fsm_c_b_c,SC: set_li6436108459499378894od_b_c] :
      ( ( state_4764321409766072158_c_b_c @ M @ SC )
     => ~ ! [F2: c > list_P903359562653991662od_b_c] :
            ( ( state_418023730138503121_c_b_c @ M @ F2 )
           => ~ ! [Q9: c] :
                  ( ( member_c @ Q9 @ ( reacha3589370724273415685_c_b_c @ M ) )
                 => ( member6330420149250801815od_b_c @ ( F2 @ Q9 ) @ SC ) ) ) ) ).

% state_cover_assignment_from_state_cover
thf(fact_632_state__cover__assignment__from__state__cover,axiom,
    ! [M: fsm_a_b_c,SC: set_li6436108459499378894od_b_c] :
      ( ( state_2795256216244586588_a_b_c @ M @ SC )
     => ~ ! [F2: a > list_P903359562653991662od_b_c] :
            ( ( state_7672330573471793359_a_b_c @ M @ F2 )
           => ~ ! [Q9: a] :
                  ( ( member_a @ Q9 @ ( reacha1620305530751930115_a_b_c @ M ) )
                 => ( member6330420149250801815od_b_c @ ( F2 @ Q9 ) @ SC ) ) ) ) ).

% state_cover_assignment_from_state_cover
thf(fact_633_convergence__graph__lookup__invar__simp_I2_J,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_e_b_c,Cg_lookup2: d > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,G: d,Alpha2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( conver4302099639658809211_c_e_d @ M1 @ M22 @ Cg_lookup2 @ G )
     => ( ( member6330420149250801815od_b_c @ Alpha2 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
       => ( ( member6330420149250801815od_b_c @ Alpha2 @ ( lS_e_b_c @ M22 @ ( initial_e_b_c @ M22 ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( set_li4480668622519654659od_b_c @ ( Cg_lookup2 @ G @ Alpha2 ) ) )
           => ( converge_e_b_c @ M22 @ Alpha2 @ Beta ) ) ) ) ) ).

% convergence_graph_lookup_invar_simp(2)
thf(fact_634_convergence__graph__lookup__invar__simp_I1_J,axiom,
    ! [M1: fsm_a_b_c,M22: fsm_e_b_c,Cg_lookup2: d > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,G: d,Alpha2: list_P903359562653991662od_b_c,Beta: list_P903359562653991662od_b_c] :
      ( ( conver4302099639658809211_c_e_d @ M1 @ M22 @ Cg_lookup2 @ G )
     => ( ( member6330420149250801815od_b_c @ Alpha2 @ ( lS_a_b_c @ M1 @ ( initial_a_b_c @ M1 ) ) )
       => ( ( member6330420149250801815od_b_c @ Alpha2 @ ( lS_e_b_c @ M22 @ ( initial_e_b_c @ M22 ) ) )
         => ( ( member6330420149250801815od_b_c @ Beta @ ( set_li4480668622519654659od_b_c @ ( Cg_lookup2 @ G @ Alpha2 ) ) )
           => ( converge_a_b_c @ M1 @ Alpha2 @ Beta ) ) ) ) ) ).

% convergence_graph_lookup_invar_simp(1)
thf(fact_635_convergence__graph__lookup__invar__def,axiom,
    ( conver4302099639658809211_c_e_d
    = ( ^ [M12: fsm_a_b_c,M23: fsm_e_b_c,Cg_lookup: d > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,G2: d] :
        ! [Alpha3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ Alpha3 @ ( lS_a_b_c @ M12 @ ( initial_a_b_c @ M12 ) ) )
         => ( ( member6330420149250801815od_b_c @ Alpha3 @ ( lS_e_b_c @ M23 @ ( initial_e_b_c @ M23 ) ) )
           => ( ( member6330420149250801815od_b_c @ Alpha3 @ ( set_li4480668622519654659od_b_c @ ( Cg_lookup @ G2 @ Alpha3 ) ) )
              & ! [Beta2: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Beta2 @ ( set_li4480668622519654659od_b_c @ ( Cg_lookup @ G2 @ Alpha3 ) ) )
                 => ( ( converge_a_b_c @ M12 @ Alpha3 @ Beta2 )
                    & ( converge_e_b_c @ M23 @ Alpha3 @ Beta2 ) ) ) ) ) ) ) ) ).

% convergence_graph_lookup_invar_def
thf(fact_636_prefixes__set__Cons__insert,axiom,
    ! [W3: list_P903359562653991662od_b_c,Xy: product_prod_b_c] :
      ( ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ ( append2547753245680614915od_b_c @ W3 @ ( cons_P4529483553340347422od_b_c @ Xy @ nil_Product_prod_b_c ) ) ) )
      = ( insert6227932334100060350od_b_c @ ( append2547753245680614915od_b_c @ W3 @ ( cons_P4529483553340347422od_b_c @ Xy @ nil_Product_prod_b_c ) ) @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ W3 ) ) ) ) ).

% prefixes_set_Cons_insert
thf(fact_637_distinguish__prepend,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Q1: list_P903359562653991662od_b_c,Io: list_P903359562653991662od_b_c,Q2: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( distin2804555989863659119_c_b_c @ M @ ( after_4052058690717316294_c_b_c @ M @ Q1 @ Io ) @ ( after_4052058690717316294_c_b_c @ M @ Q2 @ Io ) @ W )
       => ( ( member6330420149250801815od_b_c @ Q1 @ ( states7681702920031268536_c_b_c @ M ) )
         => ( ( member6330420149250801815od_b_c @ Q2 @ ( states7681702920031268536_c_b_c @ M ) )
           => ( ( member6330420149250801815od_b_c @ Io @ ( lS_lis2930931384350476499_c_b_c @ M @ Q1 ) )
             => ( ( member6330420149250801815od_b_c @ Io @ ( lS_lis2930931384350476499_c_b_c @ M @ Q2 ) )
               => ( distin2804555989863659119_c_b_c @ M @ Q1 @ Q2 @ ( append2547753245680614915od_b_c @ Io @ W ) ) ) ) ) ) ) ) ).

% distinguish_prepend
thf(fact_638_distinguish__prepend,axiom,
    ! [M: fsm_b_b_c,Q1: b,Io: list_P903359562653991662od_b_c,Q2: b,W: list_P903359562653991662od_b_c] :
      ( ( observable_b_b_c @ M )
     => ( ( distinguishes_b_b_c @ M @ ( after_b_b_c @ M @ Q1 @ Io ) @ ( after_b_b_c @ M @ Q2 @ Io ) @ W )
       => ( ( member_b @ Q1 @ ( states_b_b_c @ M ) )
         => ( ( member_b @ Q2 @ ( states_b_b_c @ M ) )
           => ( ( member6330420149250801815od_b_c @ Io @ ( lS_b_b_c @ M @ Q1 ) )
             => ( ( member6330420149250801815od_b_c @ Io @ ( lS_b_b_c @ M @ Q2 ) )
               => ( distinguishes_b_b_c @ M @ Q1 @ Q2 @ ( append2547753245680614915od_b_c @ Io @ W ) ) ) ) ) ) ) ) ).

% distinguish_prepend
thf(fact_639_distinguish__prepend,axiom,
    ! [M: fsm_c_b_c,Q1: c,Io: list_P903359562653991662od_b_c,Q2: c,W: list_P903359562653991662od_b_c] :
      ( ( observable_c_b_c @ M )
     => ( ( distinguishes_c_b_c @ M @ ( after_c_b_c @ M @ Q1 @ Io ) @ ( after_c_b_c @ M @ Q2 @ Io ) @ W )
       => ( ( member_c @ Q1 @ ( states_c_b_c @ M ) )
         => ( ( member_c @ Q2 @ ( states_c_b_c @ M ) )
           => ( ( member6330420149250801815od_b_c @ Io @ ( lS_c_b_c @ M @ Q1 ) )
             => ( ( member6330420149250801815od_b_c @ Io @ ( lS_c_b_c @ M @ Q2 ) )
               => ( distinguishes_c_b_c @ M @ Q1 @ Q2 @ ( append2547753245680614915od_b_c @ Io @ W ) ) ) ) ) ) ) ) ).

% distinguish_prepend
thf(fact_640_distinguish__prepend,axiom,
    ! [M: fsm_a_b_c,Q1: a,Io: list_P903359562653991662od_b_c,Q2: a,W: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( distinguishes_a_b_c @ M @ ( after_a_b_c @ M @ Q1 @ Io ) @ ( after_a_b_c @ M @ Q2 @ Io ) @ W )
       => ( ( member_a @ Q1 @ ( states_a_b_c @ M ) )
         => ( ( member_a @ Q2 @ ( states_a_b_c @ M ) )
           => ( ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ Q1 ) )
             => ( ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ Q2 ) )
               => ( distinguishes_a_b_c @ M @ Q1 @ Q2 @ ( append2547753245680614915od_b_c @ Io @ W ) ) ) ) ) ) ) ) ).

% distinguish_prepend
thf(fact_641_distinguish__prepend,axiom,
    ! [M: fsm_e_b_c,Q1: e,Io: list_P903359562653991662od_b_c,Q2: e,W: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( distinguishes_e_b_c @ M @ ( after_e_b_c @ M @ Q1 @ Io ) @ ( after_e_b_c @ M @ Q2 @ Io ) @ W )
       => ( ( member_e @ Q1 @ ( states_e_b_c @ M ) )
         => ( ( member_e @ Q2 @ ( states_e_b_c @ M ) )
           => ( ( member6330420149250801815od_b_c @ Io @ ( lS_e_b_c @ M @ Q1 ) )
             => ( ( member6330420149250801815od_b_c @ Io @ ( lS_e_b_c @ M @ Q2 ) )
               => ( distinguishes_e_b_c @ M @ Q1 @ Q2 @ ( append2547753245680614915od_b_c @ Io @ W ) ) ) ) ) ) ) ) ).

% distinguish_prepend
thf(fact_642_language__maximal__contained__prefix__ob,axiom,
    ! [Io: list_P903359562653991662od_b_c,M: fsm_li6801133765522507155_c_b_c,Q: list_P903359562653991662od_b_c] :
      ( ~ ( member6330420149250801815od_b_c @ Io @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) )
     => ( ( member6330420149250801815od_b_c @ Q @ ( states7681702920031268536_c_b_c @ M ) )
       => ( ( observ6293852833591064631_c_b_c @ M )
         => ~ ! [Io7: list_P903359562653991662od_b_c,X2: b,Y2: c] :
                ( ? [Io8: list_P903359562653991662od_b_c] :
                    ( Io
                    = ( append2547753245680614915od_b_c @ Io7 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ nil_Product_prod_b_c ) @ Io8 ) ) )
               => ( ( member6330420149250801815od_b_c @ Io7 @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) )
                 => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io7 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ nil_Product_prod_b_c ) ) @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_643_language__maximal__contained__prefix__ob,axiom,
    ! [Io: list_P903359562653991662od_b_c,M: fsm_b_b_c,Q: b] :
      ( ~ ( member6330420149250801815od_b_c @ Io @ ( lS_b_b_c @ M @ Q ) )
     => ( ( member_b @ Q @ ( states_b_b_c @ M ) )
       => ( ( observable_b_b_c @ M )
         => ~ ! [Io7: list_P903359562653991662od_b_c,X2: b,Y2: c] :
                ( ? [Io8: list_P903359562653991662od_b_c] :
                    ( Io
                    = ( append2547753245680614915od_b_c @ Io7 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ nil_Product_prod_b_c ) @ Io8 ) ) )
               => ( ( member6330420149250801815od_b_c @ Io7 @ ( lS_b_b_c @ M @ Q ) )
                 => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io7 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ nil_Product_prod_b_c ) ) @ ( lS_b_b_c @ M @ Q ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_644_language__maximal__contained__prefix__ob,axiom,
    ! [Io: list_P903359562653991662od_b_c,M: fsm_c_b_c,Q: c] :
      ( ~ ( member6330420149250801815od_b_c @ Io @ ( lS_c_b_c @ M @ Q ) )
     => ( ( member_c @ Q @ ( states_c_b_c @ M ) )
       => ( ( observable_c_b_c @ M )
         => ~ ! [Io7: list_P903359562653991662od_b_c,X2: b,Y2: c] :
                ( ? [Io8: list_P903359562653991662od_b_c] :
                    ( Io
                    = ( append2547753245680614915od_b_c @ Io7 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ nil_Product_prod_b_c ) @ Io8 ) ) )
               => ( ( member6330420149250801815od_b_c @ Io7 @ ( lS_c_b_c @ M @ Q ) )
                 => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io7 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ nil_Product_prod_b_c ) ) @ ( lS_c_b_c @ M @ Q ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_645_language__maximal__contained__prefix__ob,axiom,
    ! [Io: list_P903359562653991662od_b_c,M: fsm_a_b_c,Q: a] :
      ( ~ ( member6330420149250801815od_b_c @ Io @ ( lS_a_b_c @ M @ Q ) )
     => ( ( member_a @ Q @ ( states_a_b_c @ M ) )
       => ( ( observable_a_b_c @ M )
         => ~ ! [Io7: list_P903359562653991662od_b_c,X2: b,Y2: c] :
                ( ? [Io8: list_P903359562653991662od_b_c] :
                    ( Io
                    = ( append2547753245680614915od_b_c @ Io7 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ nil_Product_prod_b_c ) @ Io8 ) ) )
               => ( ( member6330420149250801815od_b_c @ Io7 @ ( lS_a_b_c @ M @ Q ) )
                 => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io7 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ nil_Product_prod_b_c ) ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_646_language__maximal__contained__prefix__ob,axiom,
    ! [Io: list_P903359562653991662od_b_c,M: fsm_e_b_c,Q: e] :
      ( ~ ( member6330420149250801815od_b_c @ Io @ ( lS_e_b_c @ M @ Q ) )
     => ( ( member_e @ Q @ ( states_e_b_c @ M ) )
       => ( ( observable_e_b_c @ M )
         => ~ ! [Io7: list_P903359562653991662od_b_c,X2: b,Y2: c] :
                ( ? [Io8: list_P903359562653991662od_b_c] :
                    ( Io
                    = ( append2547753245680614915od_b_c @ Io7 @ ( append2547753245680614915od_b_c @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ nil_Product_prod_b_c ) @ Io8 ) ) )
               => ( ( member6330420149250801815od_b_c @ Io7 @ ( lS_e_b_c @ M @ Q ) )
                 => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io7 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ nil_Product_prod_b_c ) ) @ ( lS_e_b_c @ M @ Q ) ) ) ) ) ) ) ).

% language_maximal_contained_prefix_ob
thf(fact_647_convergence__graph__merge__invar__def,axiom,
    ( conver4668632057843472301_c_e_d
    = ( ^ [M12: fsm_a_b_c,M23: fsm_e_b_c,Cg_lookup: d > list_P903359562653991662od_b_c > list_l8907847357763382004od_b_c,Cg_merge: d > list_P903359562653991662od_b_c > list_P903359562653991662od_b_c > d] :
        ! [G2: d,Gamma2: list_P903359562653991662od_b_c,Gamma3: list_P903359562653991662od_b_c] :
          ( ( converge_a_b_c @ M12 @ Gamma2 @ Gamma3 )
         => ( ( converge_e_b_c @ M23 @ Gamma2 @ Gamma3 )
           => ( ( conver4302099639658809211_c_e_d @ M12 @ M23 @ Cg_lookup @ G2 )
             => ( conver4302099639658809211_c_e_d @ M12 @ M23 @ Cg_lookup @ ( Cg_merge @ G2 @ Gamma2 @ Gamma3 ) ) ) ) ) ) ) ).

% convergence_graph_merge_invar_def
thf(fact_648_minimally__distinguishes__after__append,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Q1: list_P903359562653991662od_b_c,Q2: list_P903359562653991662od_b_c,W: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( minima1987601567150520449_c_b_c @ M )
       => ( ( member6330420149250801815od_b_c @ Q1 @ ( states7681702920031268536_c_b_c @ M ) )
         => ( ( member6330420149250801815od_b_c @ Q2 @ ( states7681702920031268536_c_b_c @ M ) )
           => ( ( minima9089413714839006869_c_b_c @ M @ Q1 @ Q2 @ ( append2547753245680614915od_b_c @ W @ W3 ) )
             => ( ( W3 != nil_Product_prod_b_c )
               => ( minima9089413714839006869_c_b_c @ M @ ( after_4052058690717316294_c_b_c @ M @ Q1 @ W ) @ ( after_4052058690717316294_c_b_c @ M @ Q2 @ W ) @ W3 ) ) ) ) ) ) ) ).

% minimally_distinguishes_after_append
thf(fact_649_minimally__distinguishes__after__append,axiom,
    ! [M: fsm_b_b_c,Q1: b,Q2: b,W: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c] :
      ( ( observable_b_b_c @ M )
     => ( ( minimal_b_b_c @ M )
       => ( ( member_b @ Q1 @ ( states_b_b_c @ M ) )
         => ( ( member_b @ Q2 @ ( states_b_b_c @ M ) )
           => ( ( minima5839754478419489574_b_b_c @ M @ Q1 @ Q2 @ ( append2547753245680614915od_b_c @ W @ W3 ) )
             => ( ( W3 != nil_Product_prod_b_c )
               => ( minima5839754478419489574_b_b_c @ M @ ( after_b_b_c @ M @ Q1 @ W ) @ ( after_b_b_c @ M @ Q2 @ W ) @ W3 ) ) ) ) ) ) ) ).

% minimally_distinguishes_after_append
thf(fact_650_minimally__distinguishes__after__append,axiom,
    ! [M: fsm_c_b_c,Q1: c,Q2: c,W: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c] :
      ( ( observable_c_b_c @ M )
     => ( ( minimal_c_b_c @ M )
       => ( ( member_c @ Q1 @ ( states_c_b_c @ M ) )
         => ( ( member_c @ Q2 @ ( states_c_b_c @ M ) )
           => ( ( minima2212601056752844455_c_b_c @ M @ Q1 @ Q2 @ ( append2547753245680614915od_b_c @ W @ W3 ) )
             => ( ( W3 != nil_Product_prod_b_c )
               => ( minima2212601056752844455_c_b_c @ M @ ( after_c_b_c @ M @ Q1 @ W ) @ ( after_c_b_c @ M @ Q2 @ W ) @ W3 ) ) ) ) ) ) ) ).

% minimally_distinguishes_after_append
thf(fact_651_minimally__distinguishes__after__append,axiom,
    ! [M: fsm_a_b_c,Q1: a,Q2: a,W: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( minimal_a_b_c @ M )
       => ( ( member_a @ Q1 @ ( states_a_b_c @ M ) )
         => ( ( member_a @ Q2 @ ( states_a_b_c @ M ) )
           => ( ( minima243535863231358885_a_b_c @ M @ Q1 @ Q2 @ ( append2547753245680614915od_b_c @ W @ W3 ) )
             => ( ( W3 != nil_Product_prod_b_c )
               => ( minima243535863231358885_a_b_c @ M @ ( after_a_b_c @ M @ Q1 @ W ) @ ( after_a_b_c @ M @ Q2 @ W ) @ W3 ) ) ) ) ) ) ) ).

% minimally_distinguishes_after_append
thf(fact_652_minimally__distinguishes__after__append,axiom,
    ! [M: fsm_e_b_c,Q1: e,Q2: e,W: list_P903359562653991662od_b_c,W3: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( minimal_e_b_c @ M )
       => ( ( member_e @ Q1 @ ( states_e_b_c @ M ) )
         => ( ( member_e @ Q2 @ ( states_e_b_c @ M ) )
           => ( ( minima4181666250274330025_e_b_c @ M @ Q1 @ Q2 @ ( append2547753245680614915od_b_c @ W @ W3 ) )
             => ( ( W3 != nil_Product_prod_b_c )
               => ( minima4181666250274330025_e_b_c @ M @ ( after_e_b_c @ M @ Q1 @ W ) @ ( after_e_b_c @ M @ Q2 @ W ) @ W3 ) ) ) ) ) ) ) ).

% minimally_distinguishes_after_append
thf(fact_653_is__state__cover_Osimps,axiom,
    ( state_6970031540555430092_c_b_c
    = ( ^ [M2: fsm_li6801133765522507155_c_b_c,SC2: set_li6436108459499378894od_b_c] :
          ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ SC2 )
          & ! [X3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X3 @ ( reacha8116992257183400179_c_b_c @ M2 ) )
             => ? [Y3: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y3 @ SC2 )
                  & ( member6330420149250801815od_b_c @ X3 @ ( io_tar7088883562557314310_c_b_c @ M2 @ Y3 @ ( initia3567573336347591134_c_b_c @ M2 ) ) ) ) ) ) ) ) ).

% is_state_cover.simps
thf(fact_654_is__state__cover_Osimps,axiom,
    ( state_8391474831432717277_b_b_c
    = ( ^ [M2: fsm_b_b_c,SC2: set_li6436108459499378894od_b_c] :
          ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ SC2 )
          & ! [X3: b] :
              ( ( member_b @ X3 @ ( reacha7216524145940060804_b_b_c @ M2 ) )
             => ? [Y3: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y3 @ SC2 )
                  & ( member_b @ X3 @ ( io_targets_b_b_c @ M2 @ Y3 @ ( initial_b_b_c @ M2 ) ) ) ) ) ) ) ) ).

% is_state_cover.simps
thf(fact_655_is__state__cover_Osimps,axiom,
    ( state_4764321409766072158_c_b_c
    = ( ^ [M2: fsm_c_b_c,SC2: set_li6436108459499378894od_b_c] :
          ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ SC2 )
          & ! [X3: c] :
              ( ( member_c @ X3 @ ( reacha3589370724273415685_c_b_c @ M2 ) )
             => ? [Y3: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y3 @ SC2 )
                  & ( member_c @ X3 @ ( io_targets_c_b_c @ M2 @ Y3 @ ( initial_c_b_c @ M2 ) ) ) ) ) ) ) ) ).

% is_state_cover.simps
thf(fact_656_is__state__cover_Osimps,axiom,
    ( state_6733386603287557728_e_b_c
    = ( ^ [M2: fsm_e_b_c,SC2: set_li6436108459499378894od_b_c] :
          ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ SC2 )
          & ! [X3: e] :
              ( ( member_e @ X3 @ ( reacha5558435917794901255_e_b_c @ M2 ) )
             => ? [Y3: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y3 @ SC2 )
                  & ( member_e @ X3 @ ( io_targets_e_b_c @ M2 @ Y3 @ ( initial_e_b_c @ M2 ) ) ) ) ) ) ) ) ).

% is_state_cover.simps
thf(fact_657_is__state__cover_Osimps,axiom,
    ( state_2795256216244586588_a_b_c
    = ( ^ [M2: fsm_a_b_c,SC2: set_li6436108459499378894od_b_c] :
          ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ SC2 )
          & ! [X3: a] :
              ( ( member_a @ X3 @ ( reacha1620305530751930115_a_b_c @ M2 ) )
             => ? [Y3: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y3 @ SC2 )
                  & ( member_a @ X3 @ ( io_targets_a_b_c @ M2 @ Y3 @ ( initial_a_b_c @ M2 ) ) ) ) ) ) ) ) ).

% is_state_cover.simps
thf(fact_658_is__state__cover_Oelims_I1_J,axiom,
    ! [X: fsm_li6801133765522507155_c_b_c,Xa: set_li6436108459499378894od_b_c,Y: $o] :
      ( ( ( state_6970031540555430092_c_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
          & ! [X3: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X3 @ ( reacha8116992257183400179_c_b_c @ X ) )
             => ? [Y3: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y3 @ Xa )
                  & ( member6330420149250801815od_b_c @ X3 @ ( io_tar7088883562557314310_c_b_c @ X @ Y3 @ ( initia3567573336347591134_c_b_c @ X ) ) ) ) ) ) ) ) ).

% is_state_cover.elims(1)
thf(fact_659_is__state__cover_Oelims_I1_J,axiom,
    ! [X: fsm_b_b_c,Xa: set_li6436108459499378894od_b_c,Y: $o] :
      ( ( ( state_8391474831432717277_b_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
          & ! [X3: b] :
              ( ( member_b @ X3 @ ( reacha7216524145940060804_b_b_c @ X ) )
             => ? [Y3: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y3 @ Xa )
                  & ( member_b @ X3 @ ( io_targets_b_b_c @ X @ Y3 @ ( initial_b_b_c @ X ) ) ) ) ) ) ) ) ).

% is_state_cover.elims(1)
thf(fact_660_is__state__cover_Oelims_I1_J,axiom,
    ! [X: fsm_c_b_c,Xa: set_li6436108459499378894od_b_c,Y: $o] :
      ( ( ( state_4764321409766072158_c_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
          & ! [X3: c] :
              ( ( member_c @ X3 @ ( reacha3589370724273415685_c_b_c @ X ) )
             => ? [Y3: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y3 @ Xa )
                  & ( member_c @ X3 @ ( io_targets_c_b_c @ X @ Y3 @ ( initial_c_b_c @ X ) ) ) ) ) ) ) ) ).

% is_state_cover.elims(1)
thf(fact_661_is__state__cover_Oelims_I1_J,axiom,
    ! [X: fsm_e_b_c,Xa: set_li6436108459499378894od_b_c,Y: $o] :
      ( ( ( state_6733386603287557728_e_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
          & ! [X3: e] :
              ( ( member_e @ X3 @ ( reacha5558435917794901255_e_b_c @ X ) )
             => ? [Y3: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y3 @ Xa )
                  & ( member_e @ X3 @ ( io_targets_e_b_c @ X @ Y3 @ ( initial_e_b_c @ X ) ) ) ) ) ) ) ) ).

% is_state_cover.elims(1)
thf(fact_662_is__state__cover_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Xa: set_li6436108459499378894od_b_c,Y: $o] :
      ( ( ( state_2795256216244586588_a_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
          & ! [X3: a] :
              ( ( member_a @ X3 @ ( reacha1620305530751930115_a_b_c @ X ) )
             => ? [Y3: list_P903359562653991662od_b_c] :
                  ( ( member6330420149250801815od_b_c @ Y3 @ Xa )
                  & ( member_a @ X3 @ ( io_targets_a_b_c @ X @ Y3 @ ( initial_a_b_c @ X ) ) ) ) ) ) ) ) ).

% is_state_cover.elims(1)
thf(fact_663_is__state__cover_Oelims_I2_J,axiom,
    ! [X: fsm_li6801133765522507155_c_b_c,Xa: set_li6436108459499378894od_b_c] :
      ( ( state_6970031540555430092_c_b_c @ X @ Xa )
     => ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
        & ! [X4: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X4 @ ( reacha8116992257183400179_c_b_c @ X ) )
           => ? [Xa2: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Xa2 @ Xa )
                & ( member6330420149250801815od_b_c @ X4 @ ( io_tar7088883562557314310_c_b_c @ X @ Xa2 @ ( initia3567573336347591134_c_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover.elims(2)
thf(fact_664_is__state__cover_Oelims_I2_J,axiom,
    ! [X: fsm_b_b_c,Xa: set_li6436108459499378894od_b_c] :
      ( ( state_8391474831432717277_b_b_c @ X @ Xa )
     => ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
        & ! [X4: b] :
            ( ( member_b @ X4 @ ( reacha7216524145940060804_b_b_c @ X ) )
           => ? [Xa2: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Xa2 @ Xa )
                & ( member_b @ X4 @ ( io_targets_b_b_c @ X @ Xa2 @ ( initial_b_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover.elims(2)
thf(fact_665_is__state__cover_Oelims_I2_J,axiom,
    ! [X: fsm_c_b_c,Xa: set_li6436108459499378894od_b_c] :
      ( ( state_4764321409766072158_c_b_c @ X @ Xa )
     => ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
        & ! [X4: c] :
            ( ( member_c @ X4 @ ( reacha3589370724273415685_c_b_c @ X ) )
           => ? [Xa2: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Xa2 @ Xa )
                & ( member_c @ X4 @ ( io_targets_c_b_c @ X @ Xa2 @ ( initial_c_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover.elims(2)
thf(fact_666_is__state__cover_Oelims_I2_J,axiom,
    ! [X: fsm_e_b_c,Xa: set_li6436108459499378894od_b_c] :
      ( ( state_6733386603287557728_e_b_c @ X @ Xa )
     => ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
        & ! [X4: e] :
            ( ( member_e @ X4 @ ( reacha5558435917794901255_e_b_c @ X ) )
           => ? [Xa2: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Xa2 @ Xa )
                & ( member_e @ X4 @ ( io_targets_e_b_c @ X @ Xa2 @ ( initial_e_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover.elims(2)
thf(fact_667_is__state__cover_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c,Xa: set_li6436108459499378894od_b_c] :
      ( ( state_2795256216244586588_a_b_c @ X @ Xa )
     => ( ( member6330420149250801815od_b_c @ nil_Product_prod_b_c @ Xa )
        & ! [X4: a] :
            ( ( member_a @ X4 @ ( reacha1620305530751930115_a_b_c @ X ) )
           => ? [Xa2: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ Xa2 @ Xa )
                & ( member_a @ X4 @ ( io_targets_a_b_c @ X @ Xa2 @ ( initial_a_b_c @ X ) ) ) ) ) ) ) ).

% is_state_cover.elims(2)
thf(fact_668_add__transition__simps_I4_J,axiom,
    ! [T3: produc7928013997122480633od_a_a,M: fsm_a_a_a] :
      ( ( member_a @ ( produc6136681935859420373od_a_a @ T3 ) @ ( states_a_a_a @ M ) )
     => ( ( member_a @ ( produc6516300539023753772od_a_a @ ( produc775496654069540887od_a_a @ T3 ) ) @ ( inputs_a_a_a @ M ) )
       => ( ( member_a @ ( product_fst_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T3 ) ) ) @ ( outputs_a_a_a @ M ) )
         => ( ( member_a @ ( product_snd_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T3 ) ) ) @ ( states_a_a_a @ M ) )
           => ( ( transitions_a_a_a @ ( add_transition_a_a_a @ M @ T3 ) )
              = ( insert4139916166978504649od_a_a @ T3 @ ( transitions_a_a_a @ M ) ) ) ) ) ) ) ).

% add_transition_simps(4)
thf(fact_669_add__transition__simps_I4_J,axiom,
    ! [T3: produc1355312390766300472od_b_a,M: fsm_a_a_b] :
      ( ( member_a @ ( produc5501032935254433684od_b_a @ T3 ) @ ( states_a_a_b @ M ) )
     => ( ( member_a @ ( produc3728844957051077739od_b_a @ ( produc139847653464554198od_b_a @ T3 ) ) @ ( inputs_a_a_b @ M ) )
       => ( ( member_b @ ( product_fst_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T3 ) ) ) @ ( outputs_a_a_b @ M ) )
         => ( ( member_a @ ( product_snd_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T3 ) ) ) @ ( states_a_a_b @ M ) )
           => ( ( transitions_a_a_b @ ( add_transition_a_a_b @ M @ T3 ) )
              = ( insert6790586597477100296od_b_a @ T3 @ ( transitions_a_a_b @ M ) ) ) ) ) ) ) ).

% add_transition_simps(4)
thf(fact_670_add__transition__simps_I4_J,axiom,
    ! [T3: produc4005982821264896119od_c_a,M: fsm_a_a_c] :
      ( ( member_a @ ( produc4865383934649446995od_c_a @ T3 ) @ ( states_a_a_c @ M ) )
     => ( ( member_a @ ( produc941389375078401706od_c_a @ ( produc8727570689714343317od_c_a @ T3 ) ) @ ( inputs_a_a_c @ M ) )
       => ( ( member_c @ ( product_fst_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T3 ) ) ) @ ( outputs_a_a_c @ M ) )
         => ( ( member_a @ ( product_snd_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T3 ) ) ) @ ( states_a_a_c @ M ) )
           => ( ( transitions_a_a_c @ ( add_transition_a_a_c @ M @ T3 ) )
              = ( insert217884991120920135od_c_a @ T3 @ ( transitions_a_a_c @ M ) ) ) ) ) ) ) ).

% add_transition_simps(4)
thf(fact_671_add__transition__simps_I4_J,axiom,
    ! [T3: produc6591963377169786296od_a_a,M: fsm_a_b_a] :
      ( ( member_a @ ( produc5497241635527604244od_a_a @ T3 ) @ ( states_a_b_a @ M ) )
     => ( ( member_b @ ( produc5876860238691937643od_a_a @ ( produc136056353737724758od_a_a @ T3 ) ) @ ( inputs_a_b_a @ M ) )
       => ( ( member_a @ ( product_fst_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T3 ) ) ) @ ( outputs_a_b_a @ M ) )
         => ( ( member_a @ ( product_snd_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T3 ) ) ) @ ( states_a_b_a @ M ) )
           => ( ( transitions_a_b_a @ ( add_transition_a_b_a @ M @ T3 ) )
              = ( insert2803865547025810312od_a_a @ T3 @ ( transitions_a_b_a @ M ) ) ) ) ) ) ) ).

% add_transition_simps(4)
thf(fact_672_add__transition__simps_I4_J,axiom,
    ! [T3: produc19261770813606135od_b_a,M: fsm_a_b_b] :
      ( ( member_a @ ( produc4861592634922617555od_b_a @ T3 ) @ ( states_a_b_b @ M ) )
     => ( ( member_b @ ( produc3089404656719261610od_b_a @ ( produc8723779389987513877od_b_a @ T3 ) ) @ ( inputs_a_b_b @ M ) )
       => ( ( member_b @ ( product_fst_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T3 ) ) ) @ ( outputs_a_b_b @ M ) )
         => ( ( member_a @ ( product_snd_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T3 ) ) ) @ ( states_a_b_b @ M ) )
           => ( ( transitions_a_b_b @ ( add_transition_a_b_b @ M @ T3 ) )
              = ( insert5454535977524405959od_b_a @ T3 @ ( transitions_a_b_b @ M ) ) ) ) ) ) ) ).

% add_transition_simps(4)
thf(fact_673_add__transition__simps_I4_J,axiom,
    ! [T3: produc5255912757217091959od_a_a,M: fsm_a_c_a] :
      ( ( member_a @ ( produc4857801335195788115od_a_a @ T3 ) @ ( states_a_c_a @ M ) )
     => ( ( member_c @ ( produc5237419938360121514od_a_a @ ( produc8719988090260684437od_a_a @ T3 ) ) @ ( inputs_a_c_a @ M ) )
       => ( ( member_a @ ( product_fst_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T3 ) ) ) @ ( outputs_a_c_a @ M ) )
         => ( ( member_a @ ( product_snd_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T3 ) ) ) @ ( states_a_c_a @ M ) )
           => ( ( transitions_a_c_a @ ( add_transition_a_c_a @ M @ T3 ) )
              = ( insert1467814927073115975od_a_a @ T3 @ ( transitions_a_c_a @ M ) ) ) ) ) ) ) ).

% add_transition_simps(4)
thf(fact_674_add__transition__simps_I4_J,axiom,
    ! [T3: produc7906583187715687606od_b_a,M: fsm_a_c_b] :
      ( ( member_a @ ( produc4222152334590801426od_b_a @ T3 ) @ ( states_a_c_b @ M ) )
     => ( ( member_c @ ( produc2449964356387445481od_b_a @ ( produc8084339089655697748od_b_a @ T3 ) ) @ ( inputs_a_c_b @ M ) )
       => ( ( member_b @ ( product_fst_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T3 ) ) ) @ ( outputs_a_c_b @ M ) )
         => ( ( member_a @ ( product_snd_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T3 ) ) ) @ ( states_a_c_b @ M ) )
           => ( ( transitions_a_c_b @ ( add_transition_a_c_b @ M @ T3 ) )
              = ( insert4118485357571711622od_b_a @ T3 @ ( transitions_a_c_b @ M ) ) ) ) ) ) ) ).

% add_transition_simps(4)
thf(fact_675_add__transition__simps_I4_J,axiom,
    ! [T3: produc1333881581359507445od_c_a,M: fsm_a_c_c] :
      ( ( member_a @ ( produc3586503333985814737od_c_a @ T3 ) @ ( states_a_c_c @ M ) )
     => ( ( member_c @ ( produc8885880811269545256od_c_a @ ( produc7448690089050711059od_c_a @ T3 ) ) @ ( inputs_a_c_c @ M ) )
       => ( ( member_c @ ( product_fst_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T3 ) ) ) @ ( outputs_a_c_c @ M ) )
         => ( ( member_a @ ( product_snd_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T3 ) ) ) @ ( states_a_c_c @ M ) )
           => ( ( transitions_a_c_c @ ( add_transition_a_c_c @ M @ T3 ) )
              = ( insert6769155788070307269od_c_a @ T3 @ ( transitions_a_c_c @ M ) ) ) ) ) ) ) ).

% add_transition_simps(4)
thf(fact_676_add__transition__simps_I4_J,axiom,
    ! [T3: produc1355512071451634873od_a_b,M: fsm_b_a_a] :
      ( ( member_b @ ( produc2156398568523956245od_a_b @ T3 ) @ ( states_b_a_a @ M ) )
     => ( ( member_a @ ( produc6516300543326982573od_a_b @ ( produc6018585323588852567od_a_b @ T3 ) ) @ ( inputs_b_a_a @ M ) )
       => ( ( member_a @ ( product_fst_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T3 ) ) ) @ ( outputs_b_a_a @ M ) )
         => ( ( member_b @ ( product_snd_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T3 ) ) ) @ ( states_b_a_a @ M ) )
           => ( ( transitions_b_a_a @ ( add_transition_b_a_a @ M @ T3 ) )
              = ( insert6790786278162434697od_a_b @ T3 @ ( transitions_b_a_a @ M ) ) ) ) ) ) ) ).

% add_transition_simps(4)
thf(fact_677_add__transition__simps_I4_J,axiom,
    ! [T3: produc4006182501950230520od_b_b,M: fsm_b_a_b] :
      ( ( member_b @ ( produc1520749567918969556od_b_b @ T3 ) @ ( states_b_a_b @ M ) )
     => ( ( member_a @ ( produc3728844961354306540od_b_b @ ( produc5382936322983865878od_b_b @ T3 ) ) @ ( inputs_b_a_b @ M ) )
       => ( ( member_b @ ( product_fst_b_b @ ( produc8648342210768306478od_b_b @ ( produc5382936322983865878od_b_b @ T3 ) ) ) @ ( outputs_b_a_b @ M ) )
         => ( ( member_b @ ( product_snd_b_b @ ( produc8648342210768306478od_b_b @ ( produc5382936322983865878od_b_b @ T3 ) ) ) @ ( states_b_a_b @ M ) )
           => ( ( transitions_b_a_b @ ( add_transition_b_a_b @ M @ T3 ) )
              = ( insert218084671806254536od_b_b @ T3 @ ( transitions_b_a_b @ M ) ) ) ) ) ) ) ).

% add_transition_simps(4)
thf(fact_678_add__transition__simps_I1_J,axiom,
    ! [T3: produc7928013997122480633od_a_a,M: fsm_a_a_a] :
      ( ( member_a @ ( produc6136681935859420373od_a_a @ T3 ) @ ( states_a_a_a @ M ) )
     => ( ( member_a @ ( produc6516300539023753772od_a_a @ ( produc775496654069540887od_a_a @ T3 ) ) @ ( inputs_a_a_a @ M ) )
       => ( ( member_a @ ( product_fst_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T3 ) ) ) @ ( outputs_a_a_a @ M ) )
         => ( ( member_a @ ( product_snd_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T3 ) ) ) @ ( states_a_a_a @ M ) )
           => ( ( initial_a_a_a @ ( add_transition_a_a_a @ M @ T3 ) )
              = ( initial_a_a_a @ M ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_679_add__transition__simps_I1_J,axiom,
    ! [T3: produc1355312390766300472od_b_a,M: fsm_a_a_b] :
      ( ( member_a @ ( produc5501032935254433684od_b_a @ T3 ) @ ( states_a_a_b @ M ) )
     => ( ( member_a @ ( produc3728844957051077739od_b_a @ ( produc139847653464554198od_b_a @ T3 ) ) @ ( inputs_a_a_b @ M ) )
       => ( ( member_b @ ( product_fst_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T3 ) ) ) @ ( outputs_a_a_b @ M ) )
         => ( ( member_a @ ( product_snd_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T3 ) ) ) @ ( states_a_a_b @ M ) )
           => ( ( initial_a_a_b @ ( add_transition_a_a_b @ M @ T3 ) )
              = ( initial_a_a_b @ M ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_680_add__transition__simps_I1_J,axiom,
    ! [T3: produc4005982821264896119od_c_a,M: fsm_a_a_c] :
      ( ( member_a @ ( produc4865383934649446995od_c_a @ T3 ) @ ( states_a_a_c @ M ) )
     => ( ( member_a @ ( produc941389375078401706od_c_a @ ( produc8727570689714343317od_c_a @ T3 ) ) @ ( inputs_a_a_c @ M ) )
       => ( ( member_c @ ( product_fst_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T3 ) ) ) @ ( outputs_a_a_c @ M ) )
         => ( ( member_a @ ( product_snd_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T3 ) ) ) @ ( states_a_a_c @ M ) )
           => ( ( initial_a_a_c @ ( add_transition_a_a_c @ M @ T3 ) )
              = ( initial_a_a_c @ M ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_681_add__transition__simps_I1_J,axiom,
    ! [T3: produc6591963377169786296od_a_a,M: fsm_a_b_a] :
      ( ( member_a @ ( produc5497241635527604244od_a_a @ T3 ) @ ( states_a_b_a @ M ) )
     => ( ( member_b @ ( produc5876860238691937643od_a_a @ ( produc136056353737724758od_a_a @ T3 ) ) @ ( inputs_a_b_a @ M ) )
       => ( ( member_a @ ( product_fst_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T3 ) ) ) @ ( outputs_a_b_a @ M ) )
         => ( ( member_a @ ( product_snd_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T3 ) ) ) @ ( states_a_b_a @ M ) )
           => ( ( initial_a_b_a @ ( add_transition_a_b_a @ M @ T3 ) )
              = ( initial_a_b_a @ M ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_682_add__transition__simps_I1_J,axiom,
    ! [T3: produc19261770813606135od_b_a,M: fsm_a_b_b] :
      ( ( member_a @ ( produc4861592634922617555od_b_a @ T3 ) @ ( states_a_b_b @ M ) )
     => ( ( member_b @ ( produc3089404656719261610od_b_a @ ( produc8723779389987513877od_b_a @ T3 ) ) @ ( inputs_a_b_b @ M ) )
       => ( ( member_b @ ( product_fst_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T3 ) ) ) @ ( outputs_a_b_b @ M ) )
         => ( ( member_a @ ( product_snd_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T3 ) ) ) @ ( states_a_b_b @ M ) )
           => ( ( initial_a_b_b @ ( add_transition_a_b_b @ M @ T3 ) )
              = ( initial_a_b_b @ M ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_683_add__transition__simps_I1_J,axiom,
    ! [T3: produc5255912757217091959od_a_a,M: fsm_a_c_a] :
      ( ( member_a @ ( produc4857801335195788115od_a_a @ T3 ) @ ( states_a_c_a @ M ) )
     => ( ( member_c @ ( produc5237419938360121514od_a_a @ ( produc8719988090260684437od_a_a @ T3 ) ) @ ( inputs_a_c_a @ M ) )
       => ( ( member_a @ ( product_fst_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T3 ) ) ) @ ( outputs_a_c_a @ M ) )
         => ( ( member_a @ ( product_snd_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T3 ) ) ) @ ( states_a_c_a @ M ) )
           => ( ( initial_a_c_a @ ( add_transition_a_c_a @ M @ T3 ) )
              = ( initial_a_c_a @ M ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_684_add__transition__simps_I1_J,axiom,
    ! [T3: produc7906583187715687606od_b_a,M: fsm_a_c_b] :
      ( ( member_a @ ( produc4222152334590801426od_b_a @ T3 ) @ ( states_a_c_b @ M ) )
     => ( ( member_c @ ( produc2449964356387445481od_b_a @ ( produc8084339089655697748od_b_a @ T3 ) ) @ ( inputs_a_c_b @ M ) )
       => ( ( member_b @ ( product_fst_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T3 ) ) ) @ ( outputs_a_c_b @ M ) )
         => ( ( member_a @ ( product_snd_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T3 ) ) ) @ ( states_a_c_b @ M ) )
           => ( ( initial_a_c_b @ ( add_transition_a_c_b @ M @ T3 ) )
              = ( initial_a_c_b @ M ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_685_add__transition__simps_I1_J,axiom,
    ! [T3: produc1333881581359507445od_c_a,M: fsm_a_c_c] :
      ( ( member_a @ ( produc3586503333985814737od_c_a @ T3 ) @ ( states_a_c_c @ M ) )
     => ( ( member_c @ ( produc8885880811269545256od_c_a @ ( produc7448690089050711059od_c_a @ T3 ) ) @ ( inputs_a_c_c @ M ) )
       => ( ( member_c @ ( product_fst_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T3 ) ) ) @ ( outputs_a_c_c @ M ) )
         => ( ( member_a @ ( product_snd_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T3 ) ) ) @ ( states_a_c_c @ M ) )
           => ( ( initial_a_c_c @ ( add_transition_a_c_c @ M @ T3 ) )
              = ( initial_a_c_c @ M ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_686_add__transition__simps_I1_J,axiom,
    ! [T3: produc1355512071451634873od_a_b,M: fsm_b_a_a] :
      ( ( member_b @ ( produc2156398568523956245od_a_b @ T3 ) @ ( states_b_a_a @ M ) )
     => ( ( member_a @ ( produc6516300543326982573od_a_b @ ( produc6018585323588852567od_a_b @ T3 ) ) @ ( inputs_b_a_a @ M ) )
       => ( ( member_a @ ( product_fst_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T3 ) ) ) @ ( outputs_b_a_a @ M ) )
         => ( ( member_b @ ( product_snd_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T3 ) ) ) @ ( states_b_a_a @ M ) )
           => ( ( initial_b_a_a @ ( add_transition_b_a_a @ M @ T3 ) )
              = ( initial_b_a_a @ M ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_687_add__transition__simps_I1_J,axiom,
    ! [T3: produc4006182501950230520od_b_b,M: fsm_b_a_b] :
      ( ( member_b @ ( produc1520749567918969556od_b_b @ T3 ) @ ( states_b_a_b @ M ) )
     => ( ( member_a @ ( produc3728844961354306540od_b_b @ ( produc5382936322983865878od_b_b @ T3 ) ) @ ( inputs_b_a_b @ M ) )
       => ( ( member_b @ ( product_fst_b_b @ ( produc8648342210768306478od_b_b @ ( produc5382936322983865878od_b_b @ T3 ) ) ) @ ( outputs_b_a_b @ M ) )
         => ( ( member_b @ ( product_snd_b_b @ ( produc8648342210768306478od_b_b @ ( produc5382936322983865878od_b_b @ T3 ) ) ) @ ( states_b_a_b @ M ) )
           => ( ( initial_b_a_b @ ( add_transition_b_a_b @ M @ T3 ) )
              = ( initial_b_a_b @ M ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_688_add__transition__simps_I2_J,axiom,
    ! [T3: produc7928013997122480633od_a_a,M: fsm_a_a_a] :
      ( ( member_a @ ( produc6136681935859420373od_a_a @ T3 ) @ ( states_a_a_a @ M ) )
     => ( ( member_a @ ( produc6516300539023753772od_a_a @ ( produc775496654069540887od_a_a @ T3 ) ) @ ( inputs_a_a_a @ M ) )
       => ( ( member_a @ ( product_fst_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T3 ) ) ) @ ( outputs_a_a_a @ M ) )
         => ( ( member_a @ ( product_snd_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T3 ) ) ) @ ( states_a_a_a @ M ) )
           => ( ( inputs_a_a_a @ ( add_transition_a_a_a @ M @ T3 ) )
              = ( inputs_a_a_a @ M ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_689_add__transition__simps_I2_J,axiom,
    ! [T3: produc1355312390766300472od_b_a,M: fsm_a_a_b] :
      ( ( member_a @ ( produc5501032935254433684od_b_a @ T3 ) @ ( states_a_a_b @ M ) )
     => ( ( member_a @ ( produc3728844957051077739od_b_a @ ( produc139847653464554198od_b_a @ T3 ) ) @ ( inputs_a_a_b @ M ) )
       => ( ( member_b @ ( product_fst_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T3 ) ) ) @ ( outputs_a_a_b @ M ) )
         => ( ( member_a @ ( product_snd_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T3 ) ) ) @ ( states_a_a_b @ M ) )
           => ( ( inputs_a_a_b @ ( add_transition_a_a_b @ M @ T3 ) )
              = ( inputs_a_a_b @ M ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_690_add__transition__simps_I2_J,axiom,
    ! [T3: produc4005982821264896119od_c_a,M: fsm_a_a_c] :
      ( ( member_a @ ( produc4865383934649446995od_c_a @ T3 ) @ ( states_a_a_c @ M ) )
     => ( ( member_a @ ( produc941389375078401706od_c_a @ ( produc8727570689714343317od_c_a @ T3 ) ) @ ( inputs_a_a_c @ M ) )
       => ( ( member_c @ ( product_fst_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T3 ) ) ) @ ( outputs_a_a_c @ M ) )
         => ( ( member_a @ ( product_snd_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T3 ) ) ) @ ( states_a_a_c @ M ) )
           => ( ( inputs_a_a_c @ ( add_transition_a_a_c @ M @ T3 ) )
              = ( inputs_a_a_c @ M ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_691_add__transition__simps_I2_J,axiom,
    ! [T3: produc6591963377169786296od_a_a,M: fsm_a_b_a] :
      ( ( member_a @ ( produc5497241635527604244od_a_a @ T3 ) @ ( states_a_b_a @ M ) )
     => ( ( member_b @ ( produc5876860238691937643od_a_a @ ( produc136056353737724758od_a_a @ T3 ) ) @ ( inputs_a_b_a @ M ) )
       => ( ( member_a @ ( product_fst_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T3 ) ) ) @ ( outputs_a_b_a @ M ) )
         => ( ( member_a @ ( product_snd_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T3 ) ) ) @ ( states_a_b_a @ M ) )
           => ( ( inputs_a_b_a @ ( add_transition_a_b_a @ M @ T3 ) )
              = ( inputs_a_b_a @ M ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_692_add__transition__simps_I2_J,axiom,
    ! [T3: produc19261770813606135od_b_a,M: fsm_a_b_b] :
      ( ( member_a @ ( produc4861592634922617555od_b_a @ T3 ) @ ( states_a_b_b @ M ) )
     => ( ( member_b @ ( produc3089404656719261610od_b_a @ ( produc8723779389987513877od_b_a @ T3 ) ) @ ( inputs_a_b_b @ M ) )
       => ( ( member_b @ ( product_fst_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T3 ) ) ) @ ( outputs_a_b_b @ M ) )
         => ( ( member_a @ ( product_snd_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T3 ) ) ) @ ( states_a_b_b @ M ) )
           => ( ( inputs_a_b_b @ ( add_transition_a_b_b @ M @ T3 ) )
              = ( inputs_a_b_b @ M ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_693_add__transition__simps_I2_J,axiom,
    ! [T3: produc5255912757217091959od_a_a,M: fsm_a_c_a] :
      ( ( member_a @ ( produc4857801335195788115od_a_a @ T3 ) @ ( states_a_c_a @ M ) )
     => ( ( member_c @ ( produc5237419938360121514od_a_a @ ( produc8719988090260684437od_a_a @ T3 ) ) @ ( inputs_a_c_a @ M ) )
       => ( ( member_a @ ( product_fst_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T3 ) ) ) @ ( outputs_a_c_a @ M ) )
         => ( ( member_a @ ( product_snd_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T3 ) ) ) @ ( states_a_c_a @ M ) )
           => ( ( inputs_a_c_a @ ( add_transition_a_c_a @ M @ T3 ) )
              = ( inputs_a_c_a @ M ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_694_add__transition__simps_I2_J,axiom,
    ! [T3: produc7906583187715687606od_b_a,M: fsm_a_c_b] :
      ( ( member_a @ ( produc4222152334590801426od_b_a @ T3 ) @ ( states_a_c_b @ M ) )
     => ( ( member_c @ ( produc2449964356387445481od_b_a @ ( produc8084339089655697748od_b_a @ T3 ) ) @ ( inputs_a_c_b @ M ) )
       => ( ( member_b @ ( product_fst_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T3 ) ) ) @ ( outputs_a_c_b @ M ) )
         => ( ( member_a @ ( product_snd_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T3 ) ) ) @ ( states_a_c_b @ M ) )
           => ( ( inputs_a_c_b @ ( add_transition_a_c_b @ M @ T3 ) )
              = ( inputs_a_c_b @ M ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_695_add__transition__simps_I2_J,axiom,
    ! [T3: produc1333881581359507445od_c_a,M: fsm_a_c_c] :
      ( ( member_a @ ( produc3586503333985814737od_c_a @ T3 ) @ ( states_a_c_c @ M ) )
     => ( ( member_c @ ( produc8885880811269545256od_c_a @ ( produc7448690089050711059od_c_a @ T3 ) ) @ ( inputs_a_c_c @ M ) )
       => ( ( member_c @ ( product_fst_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T3 ) ) ) @ ( outputs_a_c_c @ M ) )
         => ( ( member_a @ ( product_snd_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T3 ) ) ) @ ( states_a_c_c @ M ) )
           => ( ( inputs_a_c_c @ ( add_transition_a_c_c @ M @ T3 ) )
              = ( inputs_a_c_c @ M ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_696_add__transition__simps_I2_J,axiom,
    ! [T3: produc1355512071451634873od_a_b,M: fsm_b_a_a] :
      ( ( member_b @ ( produc2156398568523956245od_a_b @ T3 ) @ ( states_b_a_a @ M ) )
     => ( ( member_a @ ( produc6516300543326982573od_a_b @ ( produc6018585323588852567od_a_b @ T3 ) ) @ ( inputs_b_a_a @ M ) )
       => ( ( member_a @ ( product_fst_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T3 ) ) ) @ ( outputs_b_a_a @ M ) )
         => ( ( member_b @ ( product_snd_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T3 ) ) ) @ ( states_b_a_a @ M ) )
           => ( ( inputs_b_a_a @ ( add_transition_b_a_a @ M @ T3 ) )
              = ( inputs_b_a_a @ M ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_697_add__transition__simps_I2_J,axiom,
    ! [T3: produc4006182501950230520od_b_b,M: fsm_b_a_b] :
      ( ( member_b @ ( produc1520749567918969556od_b_b @ T3 ) @ ( states_b_a_b @ M ) )
     => ( ( member_a @ ( produc3728844961354306540od_b_b @ ( produc5382936322983865878od_b_b @ T3 ) ) @ ( inputs_b_a_b @ M ) )
       => ( ( member_b @ ( product_fst_b_b @ ( produc8648342210768306478od_b_b @ ( produc5382936322983865878od_b_b @ T3 ) ) ) @ ( outputs_b_a_b @ M ) )
         => ( ( member_b @ ( product_snd_b_b @ ( produc8648342210768306478od_b_b @ ( produc5382936322983865878od_b_b @ T3 ) ) ) @ ( states_b_a_b @ M ) )
           => ( ( inputs_b_a_b @ ( add_transition_b_a_b @ M @ T3 ) )
              = ( inputs_b_a_b @ M ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_698_add__transition__simps_I3_J,axiom,
    ! [T3: produc7928013997122480633od_a_a,M: fsm_a_a_a] :
      ( ( member_a @ ( produc6136681935859420373od_a_a @ T3 ) @ ( states_a_a_a @ M ) )
     => ( ( member_a @ ( produc6516300539023753772od_a_a @ ( produc775496654069540887od_a_a @ T3 ) ) @ ( inputs_a_a_a @ M ) )
       => ( ( member_a @ ( product_fst_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T3 ) ) ) @ ( outputs_a_a_a @ M ) )
         => ( ( member_a @ ( product_snd_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T3 ) ) ) @ ( states_a_a_a @ M ) )
           => ( ( outputs_a_a_a @ ( add_transition_a_a_a @ M @ T3 ) )
              = ( outputs_a_a_a @ M ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_699_add__transition__simps_I3_J,axiom,
    ! [T3: produc1355312390766300472od_b_a,M: fsm_a_a_b] :
      ( ( member_a @ ( produc5501032935254433684od_b_a @ T3 ) @ ( states_a_a_b @ M ) )
     => ( ( member_a @ ( produc3728844957051077739od_b_a @ ( produc139847653464554198od_b_a @ T3 ) ) @ ( inputs_a_a_b @ M ) )
       => ( ( member_b @ ( product_fst_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T3 ) ) ) @ ( outputs_a_a_b @ M ) )
         => ( ( member_a @ ( product_snd_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T3 ) ) ) @ ( states_a_a_b @ M ) )
           => ( ( outputs_a_a_b @ ( add_transition_a_a_b @ M @ T3 ) )
              = ( outputs_a_a_b @ M ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_700_add__transition__simps_I3_J,axiom,
    ! [T3: produc4005982821264896119od_c_a,M: fsm_a_a_c] :
      ( ( member_a @ ( produc4865383934649446995od_c_a @ T3 ) @ ( states_a_a_c @ M ) )
     => ( ( member_a @ ( produc941389375078401706od_c_a @ ( produc8727570689714343317od_c_a @ T3 ) ) @ ( inputs_a_a_c @ M ) )
       => ( ( member_c @ ( product_fst_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T3 ) ) ) @ ( outputs_a_a_c @ M ) )
         => ( ( member_a @ ( product_snd_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T3 ) ) ) @ ( states_a_a_c @ M ) )
           => ( ( outputs_a_a_c @ ( add_transition_a_a_c @ M @ T3 ) )
              = ( outputs_a_a_c @ M ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_701_add__transition__simps_I3_J,axiom,
    ! [T3: produc6591963377169786296od_a_a,M: fsm_a_b_a] :
      ( ( member_a @ ( produc5497241635527604244od_a_a @ T3 ) @ ( states_a_b_a @ M ) )
     => ( ( member_b @ ( produc5876860238691937643od_a_a @ ( produc136056353737724758od_a_a @ T3 ) ) @ ( inputs_a_b_a @ M ) )
       => ( ( member_a @ ( product_fst_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T3 ) ) ) @ ( outputs_a_b_a @ M ) )
         => ( ( member_a @ ( product_snd_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T3 ) ) ) @ ( states_a_b_a @ M ) )
           => ( ( outputs_a_b_a @ ( add_transition_a_b_a @ M @ T3 ) )
              = ( outputs_a_b_a @ M ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_702_add__transition__simps_I3_J,axiom,
    ! [T3: produc19261770813606135od_b_a,M: fsm_a_b_b] :
      ( ( member_a @ ( produc4861592634922617555od_b_a @ T3 ) @ ( states_a_b_b @ M ) )
     => ( ( member_b @ ( produc3089404656719261610od_b_a @ ( produc8723779389987513877od_b_a @ T3 ) ) @ ( inputs_a_b_b @ M ) )
       => ( ( member_b @ ( product_fst_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T3 ) ) ) @ ( outputs_a_b_b @ M ) )
         => ( ( member_a @ ( product_snd_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T3 ) ) ) @ ( states_a_b_b @ M ) )
           => ( ( outputs_a_b_b @ ( add_transition_a_b_b @ M @ T3 ) )
              = ( outputs_a_b_b @ M ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_703_add__transition__simps_I3_J,axiom,
    ! [T3: produc5255912757217091959od_a_a,M: fsm_a_c_a] :
      ( ( member_a @ ( produc4857801335195788115od_a_a @ T3 ) @ ( states_a_c_a @ M ) )
     => ( ( member_c @ ( produc5237419938360121514od_a_a @ ( produc8719988090260684437od_a_a @ T3 ) ) @ ( inputs_a_c_a @ M ) )
       => ( ( member_a @ ( product_fst_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T3 ) ) ) @ ( outputs_a_c_a @ M ) )
         => ( ( member_a @ ( product_snd_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T3 ) ) ) @ ( states_a_c_a @ M ) )
           => ( ( outputs_a_c_a @ ( add_transition_a_c_a @ M @ T3 ) )
              = ( outputs_a_c_a @ M ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_704_add__transition__simps_I3_J,axiom,
    ! [T3: produc7906583187715687606od_b_a,M: fsm_a_c_b] :
      ( ( member_a @ ( produc4222152334590801426od_b_a @ T3 ) @ ( states_a_c_b @ M ) )
     => ( ( member_c @ ( produc2449964356387445481od_b_a @ ( produc8084339089655697748od_b_a @ T3 ) ) @ ( inputs_a_c_b @ M ) )
       => ( ( member_b @ ( product_fst_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T3 ) ) ) @ ( outputs_a_c_b @ M ) )
         => ( ( member_a @ ( product_snd_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T3 ) ) ) @ ( states_a_c_b @ M ) )
           => ( ( outputs_a_c_b @ ( add_transition_a_c_b @ M @ T3 ) )
              = ( outputs_a_c_b @ M ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_705_add__transition__simps_I3_J,axiom,
    ! [T3: produc1333881581359507445od_c_a,M: fsm_a_c_c] :
      ( ( member_a @ ( produc3586503333985814737od_c_a @ T3 ) @ ( states_a_c_c @ M ) )
     => ( ( member_c @ ( produc8885880811269545256od_c_a @ ( produc7448690089050711059od_c_a @ T3 ) ) @ ( inputs_a_c_c @ M ) )
       => ( ( member_c @ ( product_fst_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T3 ) ) ) @ ( outputs_a_c_c @ M ) )
         => ( ( member_a @ ( product_snd_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T3 ) ) ) @ ( states_a_c_c @ M ) )
           => ( ( outputs_a_c_c @ ( add_transition_a_c_c @ M @ T3 ) )
              = ( outputs_a_c_c @ M ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_706_add__transition__simps_I3_J,axiom,
    ! [T3: produc1355512071451634873od_a_b,M: fsm_b_a_a] :
      ( ( member_b @ ( produc2156398568523956245od_a_b @ T3 ) @ ( states_b_a_a @ M ) )
     => ( ( member_a @ ( produc6516300543326982573od_a_b @ ( produc6018585323588852567od_a_b @ T3 ) ) @ ( inputs_b_a_a @ M ) )
       => ( ( member_a @ ( product_fst_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T3 ) ) ) @ ( outputs_b_a_a @ M ) )
         => ( ( member_b @ ( product_snd_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T3 ) ) ) @ ( states_b_a_a @ M ) )
           => ( ( outputs_b_a_a @ ( add_transition_b_a_a @ M @ T3 ) )
              = ( outputs_b_a_a @ M ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_707_add__transition__simps_I3_J,axiom,
    ! [T3: produc4006182501950230520od_b_b,M: fsm_b_a_b] :
      ( ( member_b @ ( produc1520749567918969556od_b_b @ T3 ) @ ( states_b_a_b @ M ) )
     => ( ( member_a @ ( produc3728844961354306540od_b_b @ ( produc5382936322983865878od_b_b @ T3 ) ) @ ( inputs_b_a_b @ M ) )
       => ( ( member_b @ ( product_fst_b_b @ ( produc8648342210768306478od_b_b @ ( produc5382936322983865878od_b_b @ T3 ) ) ) @ ( outputs_b_a_b @ M ) )
         => ( ( member_b @ ( product_snd_b_b @ ( produc8648342210768306478od_b_b @ ( produc5382936322983865878od_b_b @ T3 ) ) ) @ ( states_b_a_b @ M ) )
           => ( ( outputs_b_a_b @ ( add_transition_b_a_b @ M @ T3 ) )
              = ( outputs_b_a_b @ M ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_708_add__transition__simps_I5_J,axiom,
    ! [T3: produc7928013997122480633od_a_a,M: fsm_a_a_a] :
      ( ( member_a @ ( produc6136681935859420373od_a_a @ T3 ) @ ( states_a_a_a @ M ) )
     => ( ( member_a @ ( produc6516300539023753772od_a_a @ ( produc775496654069540887od_a_a @ T3 ) ) @ ( inputs_a_a_a @ M ) )
       => ( ( member_a @ ( product_fst_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T3 ) ) ) @ ( outputs_a_a_a @ M ) )
         => ( ( member_a @ ( product_snd_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T3 ) ) ) @ ( states_a_a_a @ M ) )
           => ( ( states_a_a_a @ ( add_transition_a_a_a @ M @ T3 ) )
              = ( states_a_a_a @ M ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_709_add__transition__simps_I5_J,axiom,
    ! [T3: produc1355312390766300472od_b_a,M: fsm_a_a_b] :
      ( ( member_a @ ( produc5501032935254433684od_b_a @ T3 ) @ ( states_a_a_b @ M ) )
     => ( ( member_a @ ( produc3728844957051077739od_b_a @ ( produc139847653464554198od_b_a @ T3 ) ) @ ( inputs_a_a_b @ M ) )
       => ( ( member_b @ ( product_fst_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T3 ) ) ) @ ( outputs_a_a_b @ M ) )
         => ( ( member_a @ ( product_snd_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T3 ) ) ) @ ( states_a_a_b @ M ) )
           => ( ( states_a_a_b @ ( add_transition_a_a_b @ M @ T3 ) )
              = ( states_a_a_b @ M ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_710_add__transition__simps_I5_J,axiom,
    ! [T3: produc4005982821264896119od_c_a,M: fsm_a_a_c] :
      ( ( member_a @ ( produc4865383934649446995od_c_a @ T3 ) @ ( states_a_a_c @ M ) )
     => ( ( member_a @ ( produc941389375078401706od_c_a @ ( produc8727570689714343317od_c_a @ T3 ) ) @ ( inputs_a_a_c @ M ) )
       => ( ( member_c @ ( product_fst_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T3 ) ) ) @ ( outputs_a_a_c @ M ) )
         => ( ( member_a @ ( product_snd_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T3 ) ) ) @ ( states_a_a_c @ M ) )
           => ( ( states_a_a_c @ ( add_transition_a_a_c @ M @ T3 ) )
              = ( states_a_a_c @ M ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_711_add__transition__simps_I5_J,axiom,
    ! [T3: produc6591963377169786296od_a_a,M: fsm_a_b_a] :
      ( ( member_a @ ( produc5497241635527604244od_a_a @ T3 ) @ ( states_a_b_a @ M ) )
     => ( ( member_b @ ( produc5876860238691937643od_a_a @ ( produc136056353737724758od_a_a @ T3 ) ) @ ( inputs_a_b_a @ M ) )
       => ( ( member_a @ ( product_fst_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T3 ) ) ) @ ( outputs_a_b_a @ M ) )
         => ( ( member_a @ ( product_snd_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T3 ) ) ) @ ( states_a_b_a @ M ) )
           => ( ( states_a_b_a @ ( add_transition_a_b_a @ M @ T3 ) )
              = ( states_a_b_a @ M ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_712_add__transition__simps_I5_J,axiom,
    ! [T3: produc19261770813606135od_b_a,M: fsm_a_b_b] :
      ( ( member_a @ ( produc4861592634922617555od_b_a @ T3 ) @ ( states_a_b_b @ M ) )
     => ( ( member_b @ ( produc3089404656719261610od_b_a @ ( produc8723779389987513877od_b_a @ T3 ) ) @ ( inputs_a_b_b @ M ) )
       => ( ( member_b @ ( product_fst_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T3 ) ) ) @ ( outputs_a_b_b @ M ) )
         => ( ( member_a @ ( product_snd_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T3 ) ) ) @ ( states_a_b_b @ M ) )
           => ( ( states_a_b_b @ ( add_transition_a_b_b @ M @ T3 ) )
              = ( states_a_b_b @ M ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_713_add__transition__simps_I5_J,axiom,
    ! [T3: produc5255912757217091959od_a_a,M: fsm_a_c_a] :
      ( ( member_a @ ( produc4857801335195788115od_a_a @ T3 ) @ ( states_a_c_a @ M ) )
     => ( ( member_c @ ( produc5237419938360121514od_a_a @ ( produc8719988090260684437od_a_a @ T3 ) ) @ ( inputs_a_c_a @ M ) )
       => ( ( member_a @ ( product_fst_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T3 ) ) ) @ ( outputs_a_c_a @ M ) )
         => ( ( member_a @ ( product_snd_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T3 ) ) ) @ ( states_a_c_a @ M ) )
           => ( ( states_a_c_a @ ( add_transition_a_c_a @ M @ T3 ) )
              = ( states_a_c_a @ M ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_714_add__transition__simps_I5_J,axiom,
    ! [T3: produc7906583187715687606od_b_a,M: fsm_a_c_b] :
      ( ( member_a @ ( produc4222152334590801426od_b_a @ T3 ) @ ( states_a_c_b @ M ) )
     => ( ( member_c @ ( produc2449964356387445481od_b_a @ ( produc8084339089655697748od_b_a @ T3 ) ) @ ( inputs_a_c_b @ M ) )
       => ( ( member_b @ ( product_fst_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T3 ) ) ) @ ( outputs_a_c_b @ M ) )
         => ( ( member_a @ ( product_snd_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T3 ) ) ) @ ( states_a_c_b @ M ) )
           => ( ( states_a_c_b @ ( add_transition_a_c_b @ M @ T3 ) )
              = ( states_a_c_b @ M ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_715_add__transition__simps_I5_J,axiom,
    ! [T3: produc1333881581359507445od_c_a,M: fsm_a_c_c] :
      ( ( member_a @ ( produc3586503333985814737od_c_a @ T3 ) @ ( states_a_c_c @ M ) )
     => ( ( member_c @ ( produc8885880811269545256od_c_a @ ( produc7448690089050711059od_c_a @ T3 ) ) @ ( inputs_a_c_c @ M ) )
       => ( ( member_c @ ( product_fst_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T3 ) ) ) @ ( outputs_a_c_c @ M ) )
         => ( ( member_a @ ( product_snd_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T3 ) ) ) @ ( states_a_c_c @ M ) )
           => ( ( states_a_c_c @ ( add_transition_a_c_c @ M @ T3 ) )
              = ( states_a_c_c @ M ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_716_add__transition__simps_I5_J,axiom,
    ! [T3: produc1355512071451634873od_a_b,M: fsm_b_a_a] :
      ( ( member_b @ ( produc2156398568523956245od_a_b @ T3 ) @ ( states_b_a_a @ M ) )
     => ( ( member_a @ ( produc6516300543326982573od_a_b @ ( produc6018585323588852567od_a_b @ T3 ) ) @ ( inputs_b_a_a @ M ) )
       => ( ( member_a @ ( product_fst_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T3 ) ) ) @ ( outputs_b_a_a @ M ) )
         => ( ( member_b @ ( product_snd_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T3 ) ) ) @ ( states_b_a_a @ M ) )
           => ( ( states_b_a_a @ ( add_transition_b_a_a @ M @ T3 ) )
              = ( states_b_a_a @ M ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_717_add__transition__simps_I5_J,axiom,
    ! [T3: produc4006182501950230520od_b_b,M: fsm_b_a_b] :
      ( ( member_b @ ( produc1520749567918969556od_b_b @ T3 ) @ ( states_b_a_b @ M ) )
     => ( ( member_a @ ( produc3728844961354306540od_b_b @ ( produc5382936322983865878od_b_b @ T3 ) ) @ ( inputs_b_a_b @ M ) )
       => ( ( member_b @ ( product_fst_b_b @ ( produc8648342210768306478od_b_b @ ( produc5382936322983865878od_b_b @ T3 ) ) ) @ ( outputs_b_a_b @ M ) )
         => ( ( member_b @ ( product_snd_b_b @ ( produc8648342210768306478od_b_b @ ( produc5382936322983865878od_b_b @ T3 ) ) ) @ ( states_b_a_b @ M ) )
           => ( ( states_b_a_b @ ( add_transition_b_a_b @ M @ T3 ) )
              = ( states_b_a_b @ M ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_718_add__transitions__simps_I1_J,axiom,
    ! [Ts: set_Pr625025929086095065od_a_a,M: fsm_a_a_a] :
      ( ! [T4: produc7928013997122480633od_a_a] :
          ( ( member1536750027164364322od_a_a @ T4 @ Ts )
         => ( ( member_a @ ( produc6136681935859420373od_a_a @ T4 ) @ ( states_a_a_a @ M ) )
            & ( member_a @ ( produc6516300539023753772od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) @ ( inputs_a_a_a @ M ) )
            & ( member_a @ ( product_fst_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) ) @ ( outputs_a_a_a @ M ) )
            & ( member_a @ ( product_snd_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) ) @ ( states_a_a_a @ M ) ) ) )
     => ( ( initial_a_a_a @ ( add_tr3755657074655224972_a_a_a @ M @ Ts ) )
        = ( initial_a_a_a @ M ) ) ) ).

% add_transitions_simps(1)
thf(fact_719_add__transitions__simps_I1_J,axiom,
    ! [Ts: set_Pr172305270015935128od_b_a,M: fsm_a_a_b] :
      ( ! [T4: produc1355312390766300472od_b_a] :
          ( ( member4187420457662959969od_b_a @ T4 @ Ts )
         => ( ( member_a @ ( produc5501032935254433684od_b_a @ T4 ) @ ( states_a_a_b @ M ) )
            & ( member_a @ ( produc3728844957051077739od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) @ ( inputs_a_a_b @ M ) )
            & ( member_b @ ( product_fst_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) ) @ ( outputs_a_a_b @ M ) )
            & ( member_a @ ( product_snd_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) ) @ ( states_a_a_b @ M ) ) ) )
     => ( ( initial_a_a_b @ ( add_tr3755657074655224973_a_a_b @ M @ Ts ) )
        = ( initial_a_a_b @ M ) ) ) ).

% add_transitions_simps(1)
thf(fact_720_add__transitions__simps_I1_J,axiom,
    ! [Ts: set_Pr8942956647800550999od_c_a,M: fsm_a_a_c] :
      ( ! [T4: produc4005982821264896119od_c_a] :
          ( ( member6838090888161555616od_c_a @ T4 @ Ts )
         => ( ( member_a @ ( produc4865383934649446995od_c_a @ T4 ) @ ( states_a_a_c @ M ) )
            & ( member_a @ ( produc941389375078401706od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) @ ( inputs_a_a_c @ M ) )
            & ( member_c @ ( product_fst_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) ) @ ( outputs_a_a_c @ M ) )
            & ( member_a @ ( product_snd_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) ) @ ( states_a_a_c @ M ) ) ) )
     => ( ( initial_a_a_c @ ( add_tr3755657074655224974_a_a_c @ M @ Ts ) )
        = ( initial_a_a_c @ M ) ) ) ).

% add_transitions_simps(1)
thf(fact_721_add__transitions__simps_I1_J,axiom,
    ! [Ts: set_Pr39693332076387096od_a_a,M: fsm_a_b_a] :
      ( ! [T4: produc6591963377169786296od_a_a] :
          ( ( member200699407211669985od_a_a @ T4 @ Ts )
         => ( ( member_a @ ( produc5497241635527604244od_a_a @ T4 ) @ ( states_a_b_a @ M ) )
            & ( member_b @ ( produc5876860238691937643od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) @ ( inputs_a_b_a @ M ) )
            & ( member_a @ ( product_fst_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) ) @ ( outputs_a_b_a @ M ) )
            & ( member_a @ ( product_snd_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) ) @ ( states_a_b_a @ M ) ) ) )
     => ( ( initial_a_b_a @ ( add_tr968201492682548939_a_b_a @ M @ Ts ) )
        = ( initial_a_b_a @ M ) ) ) ).

% add_transitions_simps(1)
thf(fact_722_add__transitions__simps_I1_J,axiom,
    ! [Ts: set_Pr8810344709861002967od_b_a,M: fsm_a_b_b] :
      ( ! [T4: produc19261770813606135od_b_a] :
          ( ( member2851369837710265632od_b_a @ T4 @ Ts )
         => ( ( member_a @ ( produc4861592634922617555od_b_a @ T4 ) @ ( states_a_b_b @ M ) )
            & ( member_b @ ( produc3089404656719261610od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) @ ( inputs_a_b_b @ M ) )
            & ( member_b @ ( product_fst_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) ) @ ( outputs_a_b_b @ M ) )
            & ( member_a @ ( product_snd_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) ) @ ( states_a_b_b @ M ) ) ) )
     => ( ( initial_a_b_b @ ( add_tr968201492682548940_a_b_b @ M @ Ts ) )
        = ( initial_a_b_b @ M ) ) ) ).

% add_transitions_simps(1)
thf(fact_723_add__transitions__simps_I1_J,axiom,
    ! [Ts: set_Pr8677732771921454935od_a_a,M: fsm_a_c_a] :
      ( ! [T4: produc5255912757217091959od_a_a] :
          ( ( member8088020824113751456od_a_a @ T4 @ Ts )
         => ( ( member_a @ ( produc4857801335195788115od_a_a @ T4 ) @ ( states_a_c_a @ M ) )
            & ( member_c @ ( produc5237419938360121514od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) @ ( inputs_a_c_a @ M ) )
            & ( member_a @ ( product_fst_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) ) @ ( outputs_a_c_a @ M ) )
            & ( member_a @ ( product_snd_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) ) @ ( states_a_c_a @ M ) ) ) )
     => ( ( initial_a_c_a @ ( add_tr7404117947564648714_a_c_a @ M @ Ts ) )
        = ( initial_a_c_a @ M ) ) ) ).

% add_transitions_simps(1)
thf(fact_724_add__transitions__simps_I1_J,axiom,
    ! [Ts: set_Pr8225012112851294998od_b_a,M: fsm_a_c_b] :
      ( ! [T4: produc7906583187715687606od_b_a] :
          ( ( member1515319217757571295od_b_a @ T4 @ Ts )
         => ( ( member_a @ ( produc4222152334590801426od_b_a @ T4 ) @ ( states_a_c_b @ M ) )
            & ( member_c @ ( produc2449964356387445481od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) @ ( inputs_a_c_b @ M ) )
            & ( member_b @ ( product_fst_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) ) @ ( outputs_a_c_b @ M ) )
            & ( member_a @ ( product_snd_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) ) @ ( states_a_c_b @ M ) ) ) )
     => ( ( initial_a_c_b @ ( add_tr7404117947564648715_a_c_b @ M @ Ts ) )
        = ( initial_a_c_b @ M ) ) ) ).

% add_transitions_simps(1)
thf(fact_725_add__transitions__simps_I1_J,axiom,
    ! [Ts: set_Pr7772291453781135061od_c_a,M: fsm_a_c_c] :
      ( ! [T4: produc1333881581359507445od_c_a] :
          ( ( member4165989648256166942od_c_a @ T4 @ Ts )
         => ( ( member_a @ ( produc3586503333985814737od_c_a @ T4 ) @ ( states_a_c_c @ M ) )
            & ( member_c @ ( produc8885880811269545256od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) @ ( inputs_a_c_c @ M ) )
            & ( member_c @ ( product_fst_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) ) @ ( outputs_a_c_c @ M ) )
            & ( member_a @ ( product_snd_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) ) @ ( states_a_c_c @ M ) ) ) )
     => ( ( initial_a_c_c @ ( add_tr7404117947564648716_a_c_c @ M @ Ts ) )
        = ( initial_a_c_c @ M ) ) ) ).

% add_transitions_simps(1)
thf(fact_726_add__transitions__simps_I1_J,axiom,
    ! [Ts: set_Pr4062742218091393433od_a_b,M: fsm_b_a_a] :
      ( ! [T4: produc1355512071451634873od_a_b] :
          ( ( member4187620138348294370od_a_b @ T4 @ Ts )
         => ( ( member_b @ ( produc2156398568523956245od_a_b @ T4 ) @ ( states_b_a_a @ M ) )
            & ( member_a @ ( produc6516300543326982573od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) @ ( inputs_b_a_a @ M ) )
            & ( member_a @ ( product_fst_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) ) @ ( outputs_b_a_a @ M ) )
            & ( member_b @ ( product_snd_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) ) @ ( states_b_a_a @ M ) ) ) )
     => ( ( initial_b_a_a @ ( add_tr128503652988579853_b_a_a @ M @ Ts ) )
        = ( initial_b_a_a @ M ) ) ) ).

% add_transitions_simps(1)
thf(fact_727_add__transitions__simps_I1_J,axiom,
    ! [Ts: set_Pr3610021559021233496od_b_b,M: fsm_b_a_b] :
      ( ! [T4: produc4006182501950230520od_b_b] :
          ( ( member6838290568846890017od_b_b @ T4 @ Ts )
         => ( ( member_b @ ( produc1520749567918969556od_b_b @ T4 ) @ ( states_b_a_b @ M ) )
            & ( member_a @ ( produc3728844961354306540od_b_b @ ( produc5382936322983865878od_b_b @ T4 ) ) @ ( inputs_b_a_b @ M ) )
            & ( member_b @ ( product_fst_b_b @ ( produc8648342210768306478od_b_b @ ( produc5382936322983865878od_b_b @ T4 ) ) ) @ ( outputs_b_a_b @ M ) )
            & ( member_b @ ( product_snd_b_b @ ( produc8648342210768306478od_b_b @ ( produc5382936322983865878od_b_b @ T4 ) ) ) @ ( states_b_a_b @ M ) ) ) )
     => ( ( initial_b_a_b @ ( add_tr128503652988579854_b_a_b @ M @ Ts ) )
        = ( initial_b_a_b @ M ) ) ) ).

% add_transitions_simps(1)
thf(fact_728_add__transitions__simps_I4_J,axiom,
    ! [Ts: set_Pr625025929086095065od_a_a,M: fsm_a_a_a] :
      ( ! [T4: produc7928013997122480633od_a_a] :
          ( ( member1536750027164364322od_a_a @ T4 @ Ts )
         => ( ( member_a @ ( produc6136681935859420373od_a_a @ T4 ) @ ( states_a_a_a @ M ) )
            & ( member_a @ ( produc6516300539023753772od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) @ ( inputs_a_a_a @ M ) )
            & ( member_a @ ( product_fst_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) ) @ ( outputs_a_a_a @ M ) )
            & ( member_a @ ( product_snd_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) ) @ ( states_a_a_a @ M ) ) ) )
     => ( ( outputs_a_a_a @ ( add_tr3755657074655224972_a_a_a @ M @ Ts ) )
        = ( outputs_a_a_a @ M ) ) ) ).

% add_transitions_simps(4)
thf(fact_729_add__transitions__simps_I4_J,axiom,
    ! [Ts: set_Pr172305270015935128od_b_a,M: fsm_a_a_b] :
      ( ! [T4: produc1355312390766300472od_b_a] :
          ( ( member4187420457662959969od_b_a @ T4 @ Ts )
         => ( ( member_a @ ( produc5501032935254433684od_b_a @ T4 ) @ ( states_a_a_b @ M ) )
            & ( member_a @ ( produc3728844957051077739od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) @ ( inputs_a_a_b @ M ) )
            & ( member_b @ ( product_fst_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) ) @ ( outputs_a_a_b @ M ) )
            & ( member_a @ ( product_snd_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) ) @ ( states_a_a_b @ M ) ) ) )
     => ( ( outputs_a_a_b @ ( add_tr3755657074655224973_a_a_b @ M @ Ts ) )
        = ( outputs_a_a_b @ M ) ) ) ).

% add_transitions_simps(4)
thf(fact_730_add__transitions__simps_I4_J,axiom,
    ! [Ts: set_Pr8942956647800550999od_c_a,M: fsm_a_a_c] :
      ( ! [T4: produc4005982821264896119od_c_a] :
          ( ( member6838090888161555616od_c_a @ T4 @ Ts )
         => ( ( member_a @ ( produc4865383934649446995od_c_a @ T4 ) @ ( states_a_a_c @ M ) )
            & ( member_a @ ( produc941389375078401706od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) @ ( inputs_a_a_c @ M ) )
            & ( member_c @ ( product_fst_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) ) @ ( outputs_a_a_c @ M ) )
            & ( member_a @ ( product_snd_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) ) @ ( states_a_a_c @ M ) ) ) )
     => ( ( outputs_a_a_c @ ( add_tr3755657074655224974_a_a_c @ M @ Ts ) )
        = ( outputs_a_a_c @ M ) ) ) ).

% add_transitions_simps(4)
thf(fact_731_add__transitions__simps_I4_J,axiom,
    ! [Ts: set_Pr39693332076387096od_a_a,M: fsm_a_b_a] :
      ( ! [T4: produc6591963377169786296od_a_a] :
          ( ( member200699407211669985od_a_a @ T4 @ Ts )
         => ( ( member_a @ ( produc5497241635527604244od_a_a @ T4 ) @ ( states_a_b_a @ M ) )
            & ( member_b @ ( produc5876860238691937643od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) @ ( inputs_a_b_a @ M ) )
            & ( member_a @ ( product_fst_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) ) @ ( outputs_a_b_a @ M ) )
            & ( member_a @ ( product_snd_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) ) @ ( states_a_b_a @ M ) ) ) )
     => ( ( outputs_a_b_a @ ( add_tr968201492682548939_a_b_a @ M @ Ts ) )
        = ( outputs_a_b_a @ M ) ) ) ).

% add_transitions_simps(4)
thf(fact_732_add__transitions__simps_I4_J,axiom,
    ! [Ts: set_Pr8810344709861002967od_b_a,M: fsm_a_b_b] :
      ( ! [T4: produc19261770813606135od_b_a] :
          ( ( member2851369837710265632od_b_a @ T4 @ Ts )
         => ( ( member_a @ ( produc4861592634922617555od_b_a @ T4 ) @ ( states_a_b_b @ M ) )
            & ( member_b @ ( produc3089404656719261610od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) @ ( inputs_a_b_b @ M ) )
            & ( member_b @ ( product_fst_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) ) @ ( outputs_a_b_b @ M ) )
            & ( member_a @ ( product_snd_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) ) @ ( states_a_b_b @ M ) ) ) )
     => ( ( outputs_a_b_b @ ( add_tr968201492682548940_a_b_b @ M @ Ts ) )
        = ( outputs_a_b_b @ M ) ) ) ).

% add_transitions_simps(4)
thf(fact_733_add__transitions__simps_I4_J,axiom,
    ! [Ts: set_Pr8677732771921454935od_a_a,M: fsm_a_c_a] :
      ( ! [T4: produc5255912757217091959od_a_a] :
          ( ( member8088020824113751456od_a_a @ T4 @ Ts )
         => ( ( member_a @ ( produc4857801335195788115od_a_a @ T4 ) @ ( states_a_c_a @ M ) )
            & ( member_c @ ( produc5237419938360121514od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) @ ( inputs_a_c_a @ M ) )
            & ( member_a @ ( product_fst_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) ) @ ( outputs_a_c_a @ M ) )
            & ( member_a @ ( product_snd_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) ) @ ( states_a_c_a @ M ) ) ) )
     => ( ( outputs_a_c_a @ ( add_tr7404117947564648714_a_c_a @ M @ Ts ) )
        = ( outputs_a_c_a @ M ) ) ) ).

% add_transitions_simps(4)
thf(fact_734_add__transitions__simps_I4_J,axiom,
    ! [Ts: set_Pr8225012112851294998od_b_a,M: fsm_a_c_b] :
      ( ! [T4: produc7906583187715687606od_b_a] :
          ( ( member1515319217757571295od_b_a @ T4 @ Ts )
         => ( ( member_a @ ( produc4222152334590801426od_b_a @ T4 ) @ ( states_a_c_b @ M ) )
            & ( member_c @ ( produc2449964356387445481od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) @ ( inputs_a_c_b @ M ) )
            & ( member_b @ ( product_fst_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) ) @ ( outputs_a_c_b @ M ) )
            & ( member_a @ ( product_snd_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) ) @ ( states_a_c_b @ M ) ) ) )
     => ( ( outputs_a_c_b @ ( add_tr7404117947564648715_a_c_b @ M @ Ts ) )
        = ( outputs_a_c_b @ M ) ) ) ).

% add_transitions_simps(4)
thf(fact_735_add__transitions__simps_I4_J,axiom,
    ! [Ts: set_Pr7772291453781135061od_c_a,M: fsm_a_c_c] :
      ( ! [T4: produc1333881581359507445od_c_a] :
          ( ( member4165989648256166942od_c_a @ T4 @ Ts )
         => ( ( member_a @ ( produc3586503333985814737od_c_a @ T4 ) @ ( states_a_c_c @ M ) )
            & ( member_c @ ( produc8885880811269545256od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) @ ( inputs_a_c_c @ M ) )
            & ( member_c @ ( product_fst_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) ) @ ( outputs_a_c_c @ M ) )
            & ( member_a @ ( product_snd_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) ) @ ( states_a_c_c @ M ) ) ) )
     => ( ( outputs_a_c_c @ ( add_tr7404117947564648716_a_c_c @ M @ Ts ) )
        = ( outputs_a_c_c @ M ) ) ) ).

% add_transitions_simps(4)
thf(fact_736_add__transitions__simps_I4_J,axiom,
    ! [Ts: set_Pr4062742218091393433od_a_b,M: fsm_b_a_a] :
      ( ! [T4: produc1355512071451634873od_a_b] :
          ( ( member4187620138348294370od_a_b @ T4 @ Ts )
         => ( ( member_b @ ( produc2156398568523956245od_a_b @ T4 ) @ ( states_b_a_a @ M ) )
            & ( member_a @ ( produc6516300543326982573od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) @ ( inputs_b_a_a @ M ) )
            & ( member_a @ ( product_fst_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) ) @ ( outputs_b_a_a @ M ) )
            & ( member_b @ ( product_snd_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) ) @ ( states_b_a_a @ M ) ) ) )
     => ( ( outputs_b_a_a @ ( add_tr128503652988579853_b_a_a @ M @ Ts ) )
        = ( outputs_b_a_a @ M ) ) ) ).

% add_transitions_simps(4)
thf(fact_737_add__transitions__simps_I4_J,axiom,
    ! [Ts: set_Pr3610021559021233496od_b_b,M: fsm_b_a_b] :
      ( ! [T4: produc4006182501950230520od_b_b] :
          ( ( member6838290568846890017od_b_b @ T4 @ Ts )
         => ( ( member_b @ ( produc1520749567918969556od_b_b @ T4 ) @ ( states_b_a_b @ M ) )
            & ( member_a @ ( produc3728844961354306540od_b_b @ ( produc5382936322983865878od_b_b @ T4 ) ) @ ( inputs_b_a_b @ M ) )
            & ( member_b @ ( product_fst_b_b @ ( produc8648342210768306478od_b_b @ ( produc5382936322983865878od_b_b @ T4 ) ) ) @ ( outputs_b_a_b @ M ) )
            & ( member_b @ ( product_snd_b_b @ ( produc8648342210768306478od_b_b @ ( produc5382936322983865878od_b_b @ T4 ) ) ) @ ( states_b_a_b @ M ) ) ) )
     => ( ( outputs_b_a_b @ ( add_tr128503652988579854_b_a_b @ M @ Ts ) )
        = ( outputs_b_a_b @ M ) ) ) ).

% add_transitions_simps(4)
thf(fact_738_add__transitions__simps_I3_J,axiom,
    ! [Ts: set_Pr625025929086095065od_a_a,M: fsm_a_a_a] :
      ( ! [T4: produc7928013997122480633od_a_a] :
          ( ( member1536750027164364322od_a_a @ T4 @ Ts )
         => ( ( member_a @ ( produc6136681935859420373od_a_a @ T4 ) @ ( states_a_a_a @ M ) )
            & ( member_a @ ( produc6516300539023753772od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) @ ( inputs_a_a_a @ M ) )
            & ( member_a @ ( product_fst_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) ) @ ( outputs_a_a_a @ M ) )
            & ( member_a @ ( product_snd_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) ) @ ( states_a_a_a @ M ) ) ) )
     => ( ( inputs_a_a_a @ ( add_tr3755657074655224972_a_a_a @ M @ Ts ) )
        = ( inputs_a_a_a @ M ) ) ) ).

% add_transitions_simps(3)
thf(fact_739_add__transitions__simps_I3_J,axiom,
    ! [Ts: set_Pr172305270015935128od_b_a,M: fsm_a_a_b] :
      ( ! [T4: produc1355312390766300472od_b_a] :
          ( ( member4187420457662959969od_b_a @ T4 @ Ts )
         => ( ( member_a @ ( produc5501032935254433684od_b_a @ T4 ) @ ( states_a_a_b @ M ) )
            & ( member_a @ ( produc3728844957051077739od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) @ ( inputs_a_a_b @ M ) )
            & ( member_b @ ( product_fst_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) ) @ ( outputs_a_a_b @ M ) )
            & ( member_a @ ( product_snd_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) ) @ ( states_a_a_b @ M ) ) ) )
     => ( ( inputs_a_a_b @ ( add_tr3755657074655224973_a_a_b @ M @ Ts ) )
        = ( inputs_a_a_b @ M ) ) ) ).

% add_transitions_simps(3)
thf(fact_740_add__transitions__simps_I3_J,axiom,
    ! [Ts: set_Pr8942956647800550999od_c_a,M: fsm_a_a_c] :
      ( ! [T4: produc4005982821264896119od_c_a] :
          ( ( member6838090888161555616od_c_a @ T4 @ Ts )
         => ( ( member_a @ ( produc4865383934649446995od_c_a @ T4 ) @ ( states_a_a_c @ M ) )
            & ( member_a @ ( produc941389375078401706od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) @ ( inputs_a_a_c @ M ) )
            & ( member_c @ ( product_fst_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) ) @ ( outputs_a_a_c @ M ) )
            & ( member_a @ ( product_snd_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) ) @ ( states_a_a_c @ M ) ) ) )
     => ( ( inputs_a_a_c @ ( add_tr3755657074655224974_a_a_c @ M @ Ts ) )
        = ( inputs_a_a_c @ M ) ) ) ).

% add_transitions_simps(3)
thf(fact_741_add__transitions__simps_I3_J,axiom,
    ! [Ts: set_Pr39693332076387096od_a_a,M: fsm_a_b_a] :
      ( ! [T4: produc6591963377169786296od_a_a] :
          ( ( member200699407211669985od_a_a @ T4 @ Ts )
         => ( ( member_a @ ( produc5497241635527604244od_a_a @ T4 ) @ ( states_a_b_a @ M ) )
            & ( member_b @ ( produc5876860238691937643od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) @ ( inputs_a_b_a @ M ) )
            & ( member_a @ ( product_fst_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) ) @ ( outputs_a_b_a @ M ) )
            & ( member_a @ ( product_snd_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) ) @ ( states_a_b_a @ M ) ) ) )
     => ( ( inputs_a_b_a @ ( add_tr968201492682548939_a_b_a @ M @ Ts ) )
        = ( inputs_a_b_a @ M ) ) ) ).

% add_transitions_simps(3)
thf(fact_742_add__transitions__simps_I3_J,axiom,
    ! [Ts: set_Pr8810344709861002967od_b_a,M: fsm_a_b_b] :
      ( ! [T4: produc19261770813606135od_b_a] :
          ( ( member2851369837710265632od_b_a @ T4 @ Ts )
         => ( ( member_a @ ( produc4861592634922617555od_b_a @ T4 ) @ ( states_a_b_b @ M ) )
            & ( member_b @ ( produc3089404656719261610od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) @ ( inputs_a_b_b @ M ) )
            & ( member_b @ ( product_fst_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) ) @ ( outputs_a_b_b @ M ) )
            & ( member_a @ ( product_snd_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) ) @ ( states_a_b_b @ M ) ) ) )
     => ( ( inputs_a_b_b @ ( add_tr968201492682548940_a_b_b @ M @ Ts ) )
        = ( inputs_a_b_b @ M ) ) ) ).

% add_transitions_simps(3)
thf(fact_743_add__transitions__simps_I3_J,axiom,
    ! [Ts: set_Pr8677732771921454935od_a_a,M: fsm_a_c_a] :
      ( ! [T4: produc5255912757217091959od_a_a] :
          ( ( member8088020824113751456od_a_a @ T4 @ Ts )
         => ( ( member_a @ ( produc4857801335195788115od_a_a @ T4 ) @ ( states_a_c_a @ M ) )
            & ( member_c @ ( produc5237419938360121514od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) @ ( inputs_a_c_a @ M ) )
            & ( member_a @ ( product_fst_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) ) @ ( outputs_a_c_a @ M ) )
            & ( member_a @ ( product_snd_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) ) @ ( states_a_c_a @ M ) ) ) )
     => ( ( inputs_a_c_a @ ( add_tr7404117947564648714_a_c_a @ M @ Ts ) )
        = ( inputs_a_c_a @ M ) ) ) ).

% add_transitions_simps(3)
thf(fact_744_add__transitions__simps_I3_J,axiom,
    ! [Ts: set_Pr8225012112851294998od_b_a,M: fsm_a_c_b] :
      ( ! [T4: produc7906583187715687606od_b_a] :
          ( ( member1515319217757571295od_b_a @ T4 @ Ts )
         => ( ( member_a @ ( produc4222152334590801426od_b_a @ T4 ) @ ( states_a_c_b @ M ) )
            & ( member_c @ ( produc2449964356387445481od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) @ ( inputs_a_c_b @ M ) )
            & ( member_b @ ( product_fst_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) ) @ ( outputs_a_c_b @ M ) )
            & ( member_a @ ( product_snd_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) ) @ ( states_a_c_b @ M ) ) ) )
     => ( ( inputs_a_c_b @ ( add_tr7404117947564648715_a_c_b @ M @ Ts ) )
        = ( inputs_a_c_b @ M ) ) ) ).

% add_transitions_simps(3)
thf(fact_745_add__transitions__simps_I3_J,axiom,
    ! [Ts: set_Pr7772291453781135061od_c_a,M: fsm_a_c_c] :
      ( ! [T4: produc1333881581359507445od_c_a] :
          ( ( member4165989648256166942od_c_a @ T4 @ Ts )
         => ( ( member_a @ ( produc3586503333985814737od_c_a @ T4 ) @ ( states_a_c_c @ M ) )
            & ( member_c @ ( produc8885880811269545256od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) @ ( inputs_a_c_c @ M ) )
            & ( member_c @ ( product_fst_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) ) @ ( outputs_a_c_c @ M ) )
            & ( member_a @ ( product_snd_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) ) @ ( states_a_c_c @ M ) ) ) )
     => ( ( inputs_a_c_c @ ( add_tr7404117947564648716_a_c_c @ M @ Ts ) )
        = ( inputs_a_c_c @ M ) ) ) ).

% add_transitions_simps(3)
thf(fact_746_add__transitions__simps_I3_J,axiom,
    ! [Ts: set_Pr4062742218091393433od_a_b,M: fsm_b_a_a] :
      ( ! [T4: produc1355512071451634873od_a_b] :
          ( ( member4187620138348294370od_a_b @ T4 @ Ts )
         => ( ( member_b @ ( produc2156398568523956245od_a_b @ T4 ) @ ( states_b_a_a @ M ) )
            & ( member_a @ ( produc6516300543326982573od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) @ ( inputs_b_a_a @ M ) )
            & ( member_a @ ( product_fst_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) ) @ ( outputs_b_a_a @ M ) )
            & ( member_b @ ( product_snd_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) ) @ ( states_b_a_a @ M ) ) ) )
     => ( ( inputs_b_a_a @ ( add_tr128503652988579853_b_a_a @ M @ Ts ) )
        = ( inputs_b_a_a @ M ) ) ) ).

% add_transitions_simps(3)
thf(fact_747_add__transitions__simps_I3_J,axiom,
    ! [Ts: set_Pr3610021559021233496od_b_b,M: fsm_b_a_b] :
      ( ! [T4: produc4006182501950230520od_b_b] :
          ( ( member6838290568846890017od_b_b @ T4 @ Ts )
         => ( ( member_b @ ( produc1520749567918969556od_b_b @ T4 ) @ ( states_b_a_b @ M ) )
            & ( member_a @ ( produc3728844961354306540od_b_b @ ( produc5382936322983865878od_b_b @ T4 ) ) @ ( inputs_b_a_b @ M ) )
            & ( member_b @ ( product_fst_b_b @ ( produc8648342210768306478od_b_b @ ( produc5382936322983865878od_b_b @ T4 ) ) ) @ ( outputs_b_a_b @ M ) )
            & ( member_b @ ( product_snd_b_b @ ( produc8648342210768306478od_b_b @ ( produc5382936322983865878od_b_b @ T4 ) ) ) @ ( states_b_a_b @ M ) ) ) )
     => ( ( inputs_b_a_b @ ( add_tr128503652988579854_b_a_b @ M @ Ts ) )
        = ( inputs_b_a_b @ M ) ) ) ).

% add_transitions_simps(3)
thf(fact_748_add__transitions__simps_I2_J,axiom,
    ! [Ts: set_Pr625025929086095065od_a_a,M: fsm_a_a_a] :
      ( ! [T4: produc7928013997122480633od_a_a] :
          ( ( member1536750027164364322od_a_a @ T4 @ Ts )
         => ( ( member_a @ ( produc6136681935859420373od_a_a @ T4 ) @ ( states_a_a_a @ M ) )
            & ( member_a @ ( produc6516300539023753772od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) @ ( inputs_a_a_a @ M ) )
            & ( member_a @ ( product_fst_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) ) @ ( outputs_a_a_a @ M ) )
            & ( member_a @ ( product_snd_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) ) @ ( states_a_a_a @ M ) ) ) )
     => ( ( states_a_a_a @ ( add_tr3755657074655224972_a_a_a @ M @ Ts ) )
        = ( states_a_a_a @ M ) ) ) ).

% add_transitions_simps(2)
thf(fact_749_add__transitions__simps_I2_J,axiom,
    ! [Ts: set_Pr172305270015935128od_b_a,M: fsm_a_a_b] :
      ( ! [T4: produc1355312390766300472od_b_a] :
          ( ( member4187420457662959969od_b_a @ T4 @ Ts )
         => ( ( member_a @ ( produc5501032935254433684od_b_a @ T4 ) @ ( states_a_a_b @ M ) )
            & ( member_a @ ( produc3728844957051077739od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) @ ( inputs_a_a_b @ M ) )
            & ( member_b @ ( product_fst_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) ) @ ( outputs_a_a_b @ M ) )
            & ( member_a @ ( product_snd_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) ) @ ( states_a_a_b @ M ) ) ) )
     => ( ( states_a_a_b @ ( add_tr3755657074655224973_a_a_b @ M @ Ts ) )
        = ( states_a_a_b @ M ) ) ) ).

% add_transitions_simps(2)
thf(fact_750_add__transitions__simps_I2_J,axiom,
    ! [Ts: set_Pr8942956647800550999od_c_a,M: fsm_a_a_c] :
      ( ! [T4: produc4005982821264896119od_c_a] :
          ( ( member6838090888161555616od_c_a @ T4 @ Ts )
         => ( ( member_a @ ( produc4865383934649446995od_c_a @ T4 ) @ ( states_a_a_c @ M ) )
            & ( member_a @ ( produc941389375078401706od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) @ ( inputs_a_a_c @ M ) )
            & ( member_c @ ( product_fst_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) ) @ ( outputs_a_a_c @ M ) )
            & ( member_a @ ( product_snd_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) ) @ ( states_a_a_c @ M ) ) ) )
     => ( ( states_a_a_c @ ( add_tr3755657074655224974_a_a_c @ M @ Ts ) )
        = ( states_a_a_c @ M ) ) ) ).

% add_transitions_simps(2)
thf(fact_751_add__transitions__simps_I2_J,axiom,
    ! [Ts: set_Pr39693332076387096od_a_a,M: fsm_a_b_a] :
      ( ! [T4: produc6591963377169786296od_a_a] :
          ( ( member200699407211669985od_a_a @ T4 @ Ts )
         => ( ( member_a @ ( produc5497241635527604244od_a_a @ T4 ) @ ( states_a_b_a @ M ) )
            & ( member_b @ ( produc5876860238691937643od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) @ ( inputs_a_b_a @ M ) )
            & ( member_a @ ( product_fst_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) ) @ ( outputs_a_b_a @ M ) )
            & ( member_a @ ( product_snd_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) ) @ ( states_a_b_a @ M ) ) ) )
     => ( ( states_a_b_a @ ( add_tr968201492682548939_a_b_a @ M @ Ts ) )
        = ( states_a_b_a @ M ) ) ) ).

% add_transitions_simps(2)
thf(fact_752_add__transitions__simps_I2_J,axiom,
    ! [Ts: set_Pr8810344709861002967od_b_a,M: fsm_a_b_b] :
      ( ! [T4: produc19261770813606135od_b_a] :
          ( ( member2851369837710265632od_b_a @ T4 @ Ts )
         => ( ( member_a @ ( produc4861592634922617555od_b_a @ T4 ) @ ( states_a_b_b @ M ) )
            & ( member_b @ ( produc3089404656719261610od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) @ ( inputs_a_b_b @ M ) )
            & ( member_b @ ( product_fst_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) ) @ ( outputs_a_b_b @ M ) )
            & ( member_a @ ( product_snd_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) ) @ ( states_a_b_b @ M ) ) ) )
     => ( ( states_a_b_b @ ( add_tr968201492682548940_a_b_b @ M @ Ts ) )
        = ( states_a_b_b @ M ) ) ) ).

% add_transitions_simps(2)
thf(fact_753_add__transitions__simps_I2_J,axiom,
    ! [Ts: set_Pr8677732771921454935od_a_a,M: fsm_a_c_a] :
      ( ! [T4: produc5255912757217091959od_a_a] :
          ( ( member8088020824113751456od_a_a @ T4 @ Ts )
         => ( ( member_a @ ( produc4857801335195788115od_a_a @ T4 ) @ ( states_a_c_a @ M ) )
            & ( member_c @ ( produc5237419938360121514od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) @ ( inputs_a_c_a @ M ) )
            & ( member_a @ ( product_fst_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) ) @ ( outputs_a_c_a @ M ) )
            & ( member_a @ ( product_snd_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) ) @ ( states_a_c_a @ M ) ) ) )
     => ( ( states_a_c_a @ ( add_tr7404117947564648714_a_c_a @ M @ Ts ) )
        = ( states_a_c_a @ M ) ) ) ).

% add_transitions_simps(2)
thf(fact_754_add__transitions__simps_I2_J,axiom,
    ! [Ts: set_Pr8225012112851294998od_b_a,M: fsm_a_c_b] :
      ( ! [T4: produc7906583187715687606od_b_a] :
          ( ( member1515319217757571295od_b_a @ T4 @ Ts )
         => ( ( member_a @ ( produc4222152334590801426od_b_a @ T4 ) @ ( states_a_c_b @ M ) )
            & ( member_c @ ( produc2449964356387445481od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) @ ( inputs_a_c_b @ M ) )
            & ( member_b @ ( product_fst_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) ) @ ( outputs_a_c_b @ M ) )
            & ( member_a @ ( product_snd_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) ) @ ( states_a_c_b @ M ) ) ) )
     => ( ( states_a_c_b @ ( add_tr7404117947564648715_a_c_b @ M @ Ts ) )
        = ( states_a_c_b @ M ) ) ) ).

% add_transitions_simps(2)
thf(fact_755_add__transitions__simps_I2_J,axiom,
    ! [Ts: set_Pr7772291453781135061od_c_a,M: fsm_a_c_c] :
      ( ! [T4: produc1333881581359507445od_c_a] :
          ( ( member4165989648256166942od_c_a @ T4 @ Ts )
         => ( ( member_a @ ( produc3586503333985814737od_c_a @ T4 ) @ ( states_a_c_c @ M ) )
            & ( member_c @ ( produc8885880811269545256od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) @ ( inputs_a_c_c @ M ) )
            & ( member_c @ ( product_fst_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) ) @ ( outputs_a_c_c @ M ) )
            & ( member_a @ ( product_snd_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) ) @ ( states_a_c_c @ M ) ) ) )
     => ( ( states_a_c_c @ ( add_tr7404117947564648716_a_c_c @ M @ Ts ) )
        = ( states_a_c_c @ M ) ) ) ).

% add_transitions_simps(2)
thf(fact_756_add__transitions__simps_I2_J,axiom,
    ! [Ts: set_Pr4062742218091393433od_a_b,M: fsm_b_a_a] :
      ( ! [T4: produc1355512071451634873od_a_b] :
          ( ( member4187620138348294370od_a_b @ T4 @ Ts )
         => ( ( member_b @ ( produc2156398568523956245od_a_b @ T4 ) @ ( states_b_a_a @ M ) )
            & ( member_a @ ( produc6516300543326982573od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) @ ( inputs_b_a_a @ M ) )
            & ( member_a @ ( product_fst_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) ) @ ( outputs_b_a_a @ M ) )
            & ( member_b @ ( product_snd_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) ) @ ( states_b_a_a @ M ) ) ) )
     => ( ( states_b_a_a @ ( add_tr128503652988579853_b_a_a @ M @ Ts ) )
        = ( states_b_a_a @ M ) ) ) ).

% add_transitions_simps(2)
thf(fact_757_add__transitions__simps_I2_J,axiom,
    ! [Ts: set_Pr3610021559021233496od_b_b,M: fsm_b_a_b] :
      ( ! [T4: produc4006182501950230520od_b_b] :
          ( ( member6838290568846890017od_b_b @ T4 @ Ts )
         => ( ( member_b @ ( produc1520749567918969556od_b_b @ T4 ) @ ( states_b_a_b @ M ) )
            & ( member_a @ ( produc3728844961354306540od_b_b @ ( produc5382936322983865878od_b_b @ T4 ) ) @ ( inputs_b_a_b @ M ) )
            & ( member_b @ ( product_fst_b_b @ ( produc8648342210768306478od_b_b @ ( produc5382936322983865878od_b_b @ T4 ) ) ) @ ( outputs_b_a_b @ M ) )
            & ( member_b @ ( product_snd_b_b @ ( produc8648342210768306478od_b_b @ ( produc5382936322983865878od_b_b @ T4 ) ) ) @ ( states_b_a_b @ M ) ) ) )
     => ( ( states_b_a_b @ ( add_tr128503652988579854_b_a_b @ M @ Ts ) )
        = ( states_b_a_b @ M ) ) ) ).

% add_transitions_simps(2)
thf(fact_758_add__transitions__simps_I5_J,axiom,
    ! [Ts: set_Pr625025929086095065od_a_a,M: fsm_a_a_a] :
      ( ! [T4: produc7928013997122480633od_a_a] :
          ( ( member1536750027164364322od_a_a @ T4 @ Ts )
         => ( ( member_a @ ( produc6136681935859420373od_a_a @ T4 ) @ ( states_a_a_a @ M ) )
            & ( member_a @ ( produc6516300539023753772od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) @ ( inputs_a_a_a @ M ) )
            & ( member_a @ ( product_fst_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) ) @ ( outputs_a_a_a @ M ) )
            & ( member_a @ ( product_snd_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) ) @ ( states_a_a_a @ M ) ) ) )
     => ( ( transitions_a_a_a @ ( add_tr3755657074655224972_a_a_a @ M @ Ts ) )
        = ( sup_su218285043347849389od_a_a @ ( transitions_a_a_a @ M ) @ Ts ) ) ) ).

% add_transitions_simps(5)
thf(fact_759_add__transitions__simps_I5_J,axiom,
    ! [Ts: set_Pr172305270015935128od_b_a,M: fsm_a_a_b] :
      ( ! [T4: produc1355312390766300472od_b_a] :
          ( ( member4187420457662959969od_b_a @ T4 @ Ts )
         => ( ( member_a @ ( produc5501032935254433684od_b_a @ T4 ) @ ( states_a_a_b @ M ) )
            & ( member_a @ ( produc3728844957051077739od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) @ ( inputs_a_a_b @ M ) )
            & ( member_b @ ( product_fst_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) ) @ ( outputs_a_a_b @ M ) )
            & ( member_a @ ( product_snd_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) ) @ ( states_a_a_b @ M ) ) ) )
     => ( ( transitions_a_a_b @ ( add_tr3755657074655224973_a_a_b @ M @ Ts ) )
        = ( sup_su8988936421132465260od_b_a @ ( transitions_a_a_b @ M ) @ Ts ) ) ) ).

% add_transitions_simps(5)
thf(fact_760_add__transitions__simps_I5_J,axiom,
    ! [Ts: set_Pr8942956647800550999od_c_a,M: fsm_a_a_c] :
      ( ! [T4: produc4005982821264896119od_c_a] :
          ( ( member6838090888161555616od_c_a @ T4 @ Ts )
         => ( ( member_a @ ( produc4865383934649446995od_c_a @ T4 ) @ ( states_a_a_c @ M ) )
            & ( member_a @ ( produc941389375078401706od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) @ ( inputs_a_a_c @ M ) )
            & ( member_c @ ( product_fst_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) ) @ ( outputs_a_a_c @ M ) )
            & ( member_a @ ( product_snd_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) ) @ ( states_a_a_c @ M ) ) ) )
     => ( ( transitions_a_a_c @ ( add_tr3755657074655224974_a_a_c @ M @ Ts ) )
        = ( sup_su8536215762062305323od_c_a @ ( transitions_a_a_c @ M ) @ Ts ) ) ) ).

% add_transitions_simps(5)
thf(fact_761_add__transitions__simps_I5_J,axiom,
    ! [Ts: set_Pr39693332076387096od_a_a,M: fsm_a_b_a] :
      ( ! [T4: produc6591963377169786296od_a_a] :
          ( ( member200699407211669985od_a_a @ T4 @ Ts )
         => ( ( member_a @ ( produc5497241635527604244od_a_a @ T4 ) @ ( states_a_b_a @ M ) )
            & ( member_b @ ( produc5876860238691937643od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) @ ( inputs_a_b_a @ M ) )
            & ( member_a @ ( product_fst_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) ) @ ( outputs_a_b_a @ M ) )
            & ( member_a @ ( product_snd_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) ) @ ( states_a_b_a @ M ) ) ) )
     => ( ( transitions_a_b_a @ ( add_tr968201492682548939_a_b_a @ M @ Ts ) )
        = ( sup_su8856324483192917228od_a_a @ ( transitions_a_b_a @ M ) @ Ts ) ) ) ).

% add_transitions_simps(5)
thf(fact_762_add__transitions__simps_I5_J,axiom,
    ! [Ts: set_Pr8810344709861002967od_b_a,M: fsm_a_b_b] :
      ( ! [T4: produc19261770813606135od_b_a] :
          ( ( member2851369837710265632od_b_a @ T4 @ Ts )
         => ( ( member_a @ ( produc4861592634922617555od_b_a @ T4 ) @ ( states_a_b_b @ M ) )
            & ( member_b @ ( produc3089404656719261610od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) @ ( inputs_a_b_b @ M ) )
            & ( member_b @ ( product_fst_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) ) @ ( outputs_a_b_b @ M ) )
            & ( member_a @ ( product_snd_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) ) @ ( states_a_b_b @ M ) ) ) )
     => ( ( transitions_a_b_b @ ( add_tr968201492682548940_a_b_b @ M @ Ts ) )
        = ( sup_su8403603824122757291od_b_a @ ( transitions_a_b_b @ M ) @ Ts ) ) ) ).

% add_transitions_simps(5)
thf(fact_763_add__transitions__simps_I5_J,axiom,
    ! [Ts: set_Pr8677732771921454935od_a_a,M: fsm_a_c_a] :
      ( ! [T4: produc5255912757217091959od_a_a] :
          ( ( member8088020824113751456od_a_a @ T4 @ Ts )
         => ( ( member_a @ ( produc4857801335195788115od_a_a @ T4 ) @ ( states_a_c_a @ M ) )
            & ( member_c @ ( produc5237419938360121514od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) @ ( inputs_a_c_a @ M ) )
            & ( member_a @ ( product_fst_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) ) @ ( outputs_a_c_a @ M ) )
            & ( member_a @ ( product_snd_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) ) @ ( states_a_c_a @ M ) ) ) )
     => ( ( transitions_a_c_a @ ( add_tr7404117947564648714_a_c_a @ M @ Ts ) )
        = ( sup_su8270991886183209259od_a_a @ ( transitions_a_c_a @ M ) @ Ts ) ) ) ).

% add_transitions_simps(5)
thf(fact_764_add__transitions__simps_I5_J,axiom,
    ! [Ts: set_Pr8225012112851294998od_b_a,M: fsm_a_c_b] :
      ( ! [T4: produc7906583187715687606od_b_a] :
          ( ( member1515319217757571295od_b_a @ T4 @ Ts )
         => ( ( member_a @ ( produc4222152334590801426od_b_a @ T4 ) @ ( states_a_c_b @ M ) )
            & ( member_c @ ( produc2449964356387445481od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) @ ( inputs_a_c_b @ M ) )
            & ( member_b @ ( product_fst_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) ) @ ( outputs_a_c_b @ M ) )
            & ( member_a @ ( product_snd_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) ) @ ( states_a_c_b @ M ) ) ) )
     => ( ( transitions_a_c_b @ ( add_tr7404117947564648715_a_c_b @ M @ Ts ) )
        = ( sup_su7818271227113049322od_b_a @ ( transitions_a_c_b @ M ) @ Ts ) ) ) ).

% add_transitions_simps(5)
thf(fact_765_add__transitions__simps_I5_J,axiom,
    ! [Ts: set_Pr7772291453781135061od_c_a,M: fsm_a_c_c] :
      ( ! [T4: produc1333881581359507445od_c_a] :
          ( ( member4165989648256166942od_c_a @ T4 @ Ts )
         => ( ( member_a @ ( produc3586503333985814737od_c_a @ T4 ) @ ( states_a_c_c @ M ) )
            & ( member_c @ ( produc8885880811269545256od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) @ ( inputs_a_c_c @ M ) )
            & ( member_c @ ( product_fst_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) ) @ ( outputs_a_c_c @ M ) )
            & ( member_a @ ( product_snd_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) ) @ ( states_a_c_c @ M ) ) ) )
     => ( ( transitions_a_c_c @ ( add_tr7404117947564648716_a_c_c @ M @ Ts ) )
        = ( sup_su7365550568042889385od_c_a @ ( transitions_a_c_c @ M ) @ Ts ) ) ) ).

% add_transitions_simps(5)
thf(fact_766_add__transitions__simps_I5_J,axiom,
    ! [Ts: set_Pr4062742218091393433od_a_b,M: fsm_b_a_a] :
      ( ! [T4: produc1355512071451634873od_a_b] :
          ( ( member4187620138348294370od_a_b @ T4 @ Ts )
         => ( ( member_b @ ( produc2156398568523956245od_a_b @ T4 ) @ ( states_b_a_a @ M ) )
            & ( member_a @ ( produc6516300543326982573od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) @ ( inputs_b_a_a @ M ) )
            & ( member_a @ ( product_fst_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) ) @ ( outputs_b_a_a @ M ) )
            & ( member_b @ ( product_snd_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) ) @ ( states_b_a_a @ M ) ) ) )
     => ( ( transitions_b_a_a @ ( add_tr128503652988579853_b_a_a @ M @ Ts ) )
        = ( sup_su3656001332353147757od_a_b @ ( transitions_b_a_a @ M ) @ Ts ) ) ) ).

% add_transitions_simps(5)
thf(fact_767_add__transitions__simps_I5_J,axiom,
    ! [Ts: set_Pr3610021559021233496od_b_b,M: fsm_b_a_b] :
      ( ! [T4: produc4006182501950230520od_b_b] :
          ( ( member6838290568846890017od_b_b @ T4 @ Ts )
         => ( ( member_b @ ( produc1520749567918969556od_b_b @ T4 ) @ ( states_b_a_b @ M ) )
            & ( member_a @ ( produc3728844961354306540od_b_b @ ( produc5382936322983865878od_b_b @ T4 ) ) @ ( inputs_b_a_b @ M ) )
            & ( member_b @ ( product_fst_b_b @ ( produc8648342210768306478od_b_b @ ( produc5382936322983865878od_b_b @ T4 ) ) ) @ ( outputs_b_a_b @ M ) )
            & ( member_b @ ( product_snd_b_b @ ( produc8648342210768306478od_b_b @ ( produc5382936322983865878od_b_b @ T4 ) ) ) @ ( states_b_a_b @ M ) ) ) )
     => ( ( transitions_b_a_b @ ( add_tr128503652988579854_b_a_b @ M @ Ts ) )
        = ( sup_su3203280673282987820od_b_b @ ( transitions_b_a_b @ M ) @ Ts ) ) ) ).

% add_transitions_simps(5)
thf(fact_768_create__fsm__from__self,axiom,
    ! [M3: fsm_a_b_c] :
      ( M3
      = ( create3933655864275538163_a_b_c @ ( initial_a_b_c @ M3 ) @ ( states_a_b_c @ M3 ) @ ( inputs_a_b_c @ M3 ) @ ( outputs_a_b_c @ M3 ) @ ( transitions_a_b_c @ M3 ) ) ) ).

% create_fsm_from_self
thf(fact_769_create__fsm__from__self,axiom,
    ! [M3: fsm_e_b_c] :
      ( M3
      = ( create7871786251318509303_e_b_c @ ( initial_e_b_c @ M3 ) @ ( states_e_b_c @ M3 ) @ ( inputs_e_b_c @ M3 ) @ ( outputs_e_b_c @ M3 ) @ ( transitions_e_b_c @ M3 ) ) ) ).

% create_fsm_from_self
thf(fact_770_maximal__prefix__in__language__properties_I2_J,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Q: list_P903359562653991662od_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Q @ ( states7681702920031268536_c_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( maxima8146652644187019584_c_b_c @ M @ Q @ Io ) @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Io ) ) ) ) ) ).

% maximal_prefix_in_language_properties(2)
thf(fact_771_maximal__prefix__in__language__properties_I2_J,axiom,
    ! [M: fsm_b_b_c,Q: b,Io: list_P903359562653991662od_b_c] :
      ( ( observable_b_b_c @ M )
     => ( ( member_b @ Q @ ( states_b_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( maxima7155769175971615313_b_b_c @ M @ Q @ Io ) @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Io ) ) ) ) ) ).

% maximal_prefix_in_language_properties(2)
thf(fact_772_maximal__prefix__in__language__properties_I2_J,axiom,
    ! [M: fsm_c_b_c,Q: c,Io: list_P903359562653991662od_b_c] :
      ( ( observable_c_b_c @ M )
     => ( ( member_c @ Q @ ( states_c_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( maxima3528615754304970194_c_b_c @ M @ Q @ Io ) @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Io ) ) ) ) ) ).

% maximal_prefix_in_language_properties(2)
thf(fact_773_maximal__prefix__in__language__properties_I2_J,axiom,
    ! [M: fsm_a_b_c,Q: a,Io: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member_a @ Q @ ( states_a_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( maxima1559550560783484624_a_b_c @ M @ Q @ Io ) @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Io ) ) ) ) ) ).

% maximal_prefix_in_language_properties(2)
thf(fact_774_maximal__prefix__in__language__properties_I2_J,axiom,
    ! [M: fsm_e_b_c,Q: e,Io: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( member_e @ Q @ ( states_e_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( maxima5497680947826455764_e_b_c @ M @ Q @ Io ) @ ( set_li4480668622519654659od_b_c @ ( prefix1131979855692807669od_b_c @ Io ) ) ) ) ) ).

% maximal_prefix_in_language_properties(2)
thf(fact_775_is__submachine_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c,Xa: fsm_a_b_c] :
      ( ~ ( is_submachine_a_b_c @ X @ Xa )
     => ~ ( ( ( initial_a_b_c @ X )
            = ( initial_a_b_c @ Xa ) )
          & ( ord_le3226338165915859510od_c_a @ ( transitions_a_b_c @ X ) @ ( transitions_a_b_c @ Xa ) )
          & ( ( inputs_a_b_c @ X )
            = ( inputs_a_b_c @ Xa ) )
          & ( ( outputs_a_b_c @ X )
            = ( outputs_a_b_c @ Xa ) )
          & ( ord_less_eq_set_a @ ( states_a_b_c @ X ) @ ( states_a_b_c @ Xa ) ) ) ) ).

% is_submachine.elims(3)
thf(fact_776_is__submachine_Oelims_I3_J,axiom,
    ! [X: fsm_e_b_c,Xa: fsm_e_b_c] :
      ( ~ ( is_submachine_e_b_c @ X @ Xa )
     => ~ ( ( ( initial_e_b_c @ X )
            = ( initial_e_b_c @ Xa ) )
          & ( ord_le7753831285082277174od_c_e @ ( transitions_e_b_c @ X ) @ ( transitions_e_b_c @ Xa ) )
          & ( ( inputs_e_b_c @ X )
            = ( inputs_e_b_c @ Xa ) )
          & ( ( outputs_e_b_c @ X )
            = ( outputs_e_b_c @ Xa ) )
          & ( ord_less_eq_set_e @ ( states_e_b_c @ X ) @ ( states_e_b_c @ Xa ) ) ) ) ).

% is_submachine.elims(3)
thf(fact_777_is__submachine_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c,Xa: fsm_a_b_c] :
      ( ( is_submachine_a_b_c @ X @ Xa )
     => ( ( ( initial_a_b_c @ X )
          = ( initial_a_b_c @ Xa ) )
        & ( ord_le3226338165915859510od_c_a @ ( transitions_a_b_c @ X ) @ ( transitions_a_b_c @ Xa ) )
        & ( ( inputs_a_b_c @ X )
          = ( inputs_a_b_c @ Xa ) )
        & ( ( outputs_a_b_c @ X )
          = ( outputs_a_b_c @ Xa ) )
        & ( ord_less_eq_set_a @ ( states_a_b_c @ X ) @ ( states_a_b_c @ Xa ) ) ) ) ).

% is_submachine.elims(2)
thf(fact_778_is__submachine_Oelims_I2_J,axiom,
    ! [X: fsm_e_b_c,Xa: fsm_e_b_c] :
      ( ( is_submachine_e_b_c @ X @ Xa )
     => ( ( ( initial_e_b_c @ X )
          = ( initial_e_b_c @ Xa ) )
        & ( ord_le7753831285082277174od_c_e @ ( transitions_e_b_c @ X ) @ ( transitions_e_b_c @ Xa ) )
        & ( ( inputs_e_b_c @ X )
          = ( inputs_e_b_c @ Xa ) )
        & ( ( outputs_e_b_c @ X )
          = ( outputs_e_b_c @ Xa ) )
        & ( ord_less_eq_set_e @ ( states_e_b_c @ X ) @ ( states_e_b_c @ Xa ) ) ) ) ).

% is_submachine.elims(2)
thf(fact_779_set__append,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( set_Product_prod_b_c2 @ ( append2547753245680614915od_b_c @ Xs @ Ys ) )
      = ( sup_su2554677861087362972od_b_c @ ( set_Product_prod_b_c2 @ Xs ) @ ( set_Product_prod_b_c2 @ Ys ) ) ) ).

% set_append
thf(fact_780_submachine__simps_I1_J,axiom,
    ! [A2: fsm_a_b_c,B4: fsm_a_b_c] :
      ( ( is_submachine_a_b_c @ A2 @ B4 )
     => ( ( initial_a_b_c @ A2 )
        = ( initial_a_b_c @ B4 ) ) ) ).

% submachine_simps(1)
thf(fact_781_submachine__simps_I1_J,axiom,
    ! [A2: fsm_e_b_c,B4: fsm_e_b_c] :
      ( ( is_submachine_e_b_c @ A2 @ B4 )
     => ( ( initial_e_b_c @ A2 )
        = ( initial_e_b_c @ B4 ) ) ) ).

% submachine_simps(1)
thf(fact_782_submachine__observable,axiom,
    ! [S2: fsm_a_b_c,M: fsm_a_b_c] :
      ( ( is_submachine_a_b_c @ S2 @ M )
     => ( ( observable_a_b_c @ M )
       => ( observable_a_b_c @ S2 ) ) ) ).

% submachine_observable
thf(fact_783_submachine__observable,axiom,
    ! [S2: fsm_e_b_c,M: fsm_e_b_c] :
      ( ( is_submachine_e_b_c @ S2 @ M )
     => ( ( observable_e_b_c @ M )
       => ( observable_e_b_c @ S2 ) ) ) ).

% submachine_observable
thf(fact_784_submachine__simps_I3_J,axiom,
    ! [A2: fsm_a_b_c,B4: fsm_a_b_c] :
      ( ( is_submachine_a_b_c @ A2 @ B4 )
     => ( ( inputs_a_b_c @ A2 )
        = ( inputs_a_b_c @ B4 ) ) ) ).

% submachine_simps(3)
thf(fact_785_submachine__simps_I3_J,axiom,
    ! [A2: fsm_e_b_c,B4: fsm_e_b_c] :
      ( ( is_submachine_e_b_c @ A2 @ B4 )
     => ( ( inputs_e_b_c @ A2 )
        = ( inputs_e_b_c @ B4 ) ) ) ).

% submachine_simps(3)
thf(fact_786_submachine__simps_I4_J,axiom,
    ! [A2: fsm_a_b_c,B4: fsm_a_b_c] :
      ( ( is_submachine_a_b_c @ A2 @ B4 )
     => ( ( outputs_a_b_c @ A2 )
        = ( outputs_a_b_c @ B4 ) ) ) ).

% submachine_simps(4)
thf(fact_787_submachine__simps_I4_J,axiom,
    ! [A2: fsm_e_b_c,B4: fsm_e_b_c] :
      ( ( is_submachine_e_b_c @ A2 @ B4 )
     => ( ( outputs_e_b_c @ A2 )
        = ( outputs_e_b_c @ B4 ) ) ) ).

% submachine_simps(4)
thf(fact_788_submachine__reachable__subset,axiom,
    ! [A2: fsm_a_b_c,B4: fsm_a_b_c] :
      ( ( is_submachine_a_b_c @ A2 @ B4 )
     => ( ord_less_eq_set_a @ ( reacha1620305530751930115_a_b_c @ A2 ) @ ( reacha1620305530751930115_a_b_c @ B4 ) ) ) ).

% submachine_reachable_subset
thf(fact_789_submachine__language,axiom,
    ! [S2: fsm_a_b_c,M: fsm_a_b_c] :
      ( ( is_submachine_a_b_c @ S2 @ M )
     => ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ S2 @ ( initial_a_b_c @ S2 ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) ).

% submachine_language
thf(fact_790_submachine__language,axiom,
    ! [S2: fsm_e_b_c,M: fsm_e_b_c] :
      ( ( is_submachine_e_b_c @ S2 @ M )
     => ( ord_le282488521294790766od_b_c @ ( lS_e_b_c @ S2 @ ( initial_e_b_c @ S2 ) ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) ) ) ).

% submachine_language
thf(fact_791_complete__submachine__initial,axiom,
    ! [A2: fsm_a_b_c,B4: fsm_a_b_c] :
      ( ( is_submachine_a_b_c @ A2 @ B4 )
     => ( ( comple6900478119722646120_a_b_c @ A2 )
       => ( comple2039557650379672579_a_b_c @ B4 @ ( initial_a_b_c @ B4 ) ) ) ) ).

% complete_submachine_initial
thf(fact_792_complete__submachine__initial,axiom,
    ! [A2: fsm_e_b_c,B4: fsm_e_b_c] :
      ( ( is_submachine_e_b_c @ A2 @ B4 )
     => ( ( comple1615236469910841452_e_b_c @ A2 )
       => ( comple5977688037422643719_e_b_c @ B4 @ ( initial_e_b_c @ B4 ) ) ) ) ).

% complete_submachine_initial
thf(fact_793_maximal__prefix__in__language__properties_I1_J,axiom,
    ! [M: fsm_li6801133765522507155_c_b_c,Q: list_P903359562653991662od_b_c,Io: list_P903359562653991662od_b_c] :
      ( ( observ6293852833591064631_c_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Q @ ( states7681702920031268536_c_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( maxima8146652644187019584_c_b_c @ M @ Q @ Io ) @ ( lS_lis2930931384350476499_c_b_c @ M @ Q ) ) ) ) ).

% maximal_prefix_in_language_properties(1)
thf(fact_794_maximal__prefix__in__language__properties_I1_J,axiom,
    ! [M: fsm_b_b_c,Q: b,Io: list_P903359562653991662od_b_c] :
      ( ( observable_b_b_c @ M )
     => ( ( member_b @ Q @ ( states_b_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( maxima7155769175971615313_b_b_c @ M @ Q @ Io ) @ ( lS_b_b_c @ M @ Q ) ) ) ) ).

% maximal_prefix_in_language_properties(1)
thf(fact_795_maximal__prefix__in__language__properties_I1_J,axiom,
    ! [M: fsm_c_b_c,Q: c,Io: list_P903359562653991662od_b_c] :
      ( ( observable_c_b_c @ M )
     => ( ( member_c @ Q @ ( states_c_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( maxima3528615754304970194_c_b_c @ M @ Q @ Io ) @ ( lS_c_b_c @ M @ Q ) ) ) ) ).

% maximal_prefix_in_language_properties(1)
thf(fact_796_maximal__prefix__in__language__properties_I1_J,axiom,
    ! [M: fsm_a_b_c,Q: a,Io: list_P903359562653991662od_b_c] :
      ( ( observable_a_b_c @ M )
     => ( ( member_a @ Q @ ( states_a_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( maxima1559550560783484624_a_b_c @ M @ Q @ Io ) @ ( lS_a_b_c @ M @ Q ) ) ) ) ).

% maximal_prefix_in_language_properties(1)
thf(fact_797_maximal__prefix__in__language__properties_I1_J,axiom,
    ! [M: fsm_e_b_c,Q: e,Io: list_P903359562653991662od_b_c] :
      ( ( observable_e_b_c @ M )
     => ( ( member_e @ Q @ ( states_e_b_c @ M ) )
       => ( member6330420149250801815od_b_c @ ( maxima5497680947826455764_e_b_c @ M @ Q @ Io ) @ ( lS_e_b_c @ M @ Q ) ) ) ) ).

% maximal_prefix_in_language_properties(1)
thf(fact_798_is__submachine_Osimps,axiom,
    ( is_submachine_a_b_c
    = ( ^ [A5: fsm_a_b_c,B5: fsm_a_b_c] :
          ( ( ( initial_a_b_c @ A5 )
            = ( initial_a_b_c @ B5 ) )
          & ( ord_le3226338165915859510od_c_a @ ( transitions_a_b_c @ A5 ) @ ( transitions_a_b_c @ B5 ) )
          & ( ( inputs_a_b_c @ A5 )
            = ( inputs_a_b_c @ B5 ) )
          & ( ( outputs_a_b_c @ A5 )
            = ( outputs_a_b_c @ B5 ) )
          & ( ord_less_eq_set_a @ ( states_a_b_c @ A5 ) @ ( states_a_b_c @ B5 ) ) ) ) ) ).

% is_submachine.simps
thf(fact_799_is__submachine_Osimps,axiom,
    ( is_submachine_e_b_c
    = ( ^ [A5: fsm_e_b_c,B5: fsm_e_b_c] :
          ( ( ( initial_e_b_c @ A5 )
            = ( initial_e_b_c @ B5 ) )
          & ( ord_le7753831285082277174od_c_e @ ( transitions_e_b_c @ A5 ) @ ( transitions_e_b_c @ B5 ) )
          & ( ( inputs_e_b_c @ A5 )
            = ( inputs_e_b_c @ B5 ) )
          & ( ( outputs_e_b_c @ A5 )
            = ( outputs_e_b_c @ B5 ) )
          & ( ord_less_eq_set_e @ ( states_e_b_c @ A5 ) @ ( states_e_b_c @ B5 ) ) ) ) ) ).

% is_submachine.simps
thf(fact_800_is__submachine_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Xa: fsm_a_b_c,Y: $o] :
      ( ( ( is_submachine_a_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( ( ( initial_a_b_c @ X )
            = ( initial_a_b_c @ Xa ) )
          & ( ord_le3226338165915859510od_c_a @ ( transitions_a_b_c @ X ) @ ( transitions_a_b_c @ Xa ) )
          & ( ( inputs_a_b_c @ X )
            = ( inputs_a_b_c @ Xa ) )
          & ( ( outputs_a_b_c @ X )
            = ( outputs_a_b_c @ Xa ) )
          & ( ord_less_eq_set_a @ ( states_a_b_c @ X ) @ ( states_a_b_c @ Xa ) ) ) ) ) ).

% is_submachine.elims(1)
thf(fact_801_is__submachine_Oelims_I1_J,axiom,
    ! [X: fsm_e_b_c,Xa: fsm_e_b_c,Y: $o] :
      ( ( ( is_submachine_e_b_c @ X @ Xa )
        = Y )
     => ( Y
        = ( ( ( initial_e_b_c @ X )
            = ( initial_e_b_c @ Xa ) )
          & ( ord_le7753831285082277174od_c_e @ ( transitions_e_b_c @ X ) @ ( transitions_e_b_c @ Xa ) )
          & ( ( inputs_e_b_c @ X )
            = ( inputs_e_b_c @ Xa ) )
          & ( ( outputs_e_b_c @ X )
            = ( outputs_e_b_c @ Xa ) )
          & ( ord_less_eq_set_e @ ( states_e_b_c @ X ) @ ( states_e_b_c @ Xa ) ) ) ) ) ).

% is_submachine.elims(1)
thf(fact_802_create__fsm__from__sets__simps_I4_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_a,Outs: set_a,Ts: set_Pr625025929086095065od_a_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_a @ Ins )
         => ( ( finite_finite_a @ Outs )
           => ( ! [T4: produc7928013997122480633od_a_a] :
                  ( ( member1536750027164364322od_a_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc6136681935859420373od_a_a @ T4 ) @ Qs )
                    & ( member_a @ ( produc6516300539023753772od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) @ Ins )
                    & ( member_a @ ( product_fst_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( outputs_a_a_a @ ( create6721111446248214194_a_a_a @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Outs ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(4)
thf(fact_803_create__fsm__from__sets__simps_I4_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_a,Outs: set_b,Ts: set_Pr172305270015935128od_b_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_a @ Ins )
         => ( ( finite_finite_b @ Outs )
           => ( ! [T4: produc1355312390766300472od_b_a] :
                  ( ( member4187420457662959969od_b_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc5501032935254433684od_b_a @ T4 ) @ Qs )
                    & ( member_a @ ( produc3728844957051077739od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) @ Ins )
                    & ( member_b @ ( product_fst_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( outputs_a_a_b @ ( create6721111446248214195_a_a_b @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Outs ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(4)
thf(fact_804_create__fsm__from__sets__simps_I4_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_a,Outs: set_c,Ts: set_Pr8942956647800550999od_c_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_a @ Ins )
         => ( ( finite_finite_c @ Outs )
           => ( ! [T4: produc4005982821264896119od_c_a] :
                  ( ( member6838090888161555616od_c_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc4865383934649446995od_c_a @ T4 ) @ Qs )
                    & ( member_a @ ( produc941389375078401706od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) @ Ins )
                    & ( member_c @ ( product_fst_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( outputs_a_a_c @ ( create6721111446248214196_a_a_c @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Outs ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(4)
thf(fact_805_create__fsm__from__sets__simps_I4_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_b,Outs: set_a,Ts: set_Pr39693332076387096od_a_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_b @ Ins )
         => ( ( finite_finite_a @ Outs )
           => ( ! [T4: produc6591963377169786296od_a_a] :
                  ( ( member200699407211669985od_a_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc5497241635527604244od_a_a @ T4 ) @ Qs )
                    & ( member_b @ ( produc5876860238691937643od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) @ Ins )
                    & ( member_a @ ( product_fst_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( outputs_a_b_a @ ( create3933655864275538161_a_b_a @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Outs ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(4)
thf(fact_806_create__fsm__from__sets__simps_I4_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_b,Outs: set_b,Ts: set_Pr8810344709861002967od_b_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_b @ Ins )
         => ( ( finite_finite_b @ Outs )
           => ( ! [T4: produc19261770813606135od_b_a] :
                  ( ( member2851369837710265632od_b_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc4861592634922617555od_b_a @ T4 ) @ Qs )
                    & ( member_b @ ( produc3089404656719261610od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) @ Ins )
                    & ( member_b @ ( product_fst_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( outputs_a_b_b @ ( create3933655864275538162_a_b_b @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Outs ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(4)
thf(fact_807_create__fsm__from__sets__simps_I4_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_c,Outs: set_a,Ts: set_Pr8677732771921454935od_a_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_c @ Ins )
         => ( ( finite_finite_a @ Outs )
           => ( ! [T4: produc5255912757217091959od_a_a] :
                  ( ( member8088020824113751456od_a_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc4857801335195788115od_a_a @ T4 ) @ Qs )
                    & ( member_c @ ( produc5237419938360121514od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) @ Ins )
                    & ( member_a @ ( product_fst_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( outputs_a_c_a @ ( create1146200282302862128_a_c_a @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Outs ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(4)
thf(fact_808_create__fsm__from__sets__simps_I4_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_c,Outs: set_b,Ts: set_Pr8225012112851294998od_b_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_c @ Ins )
         => ( ( finite_finite_b @ Outs )
           => ( ! [T4: produc7906583187715687606od_b_a] :
                  ( ( member1515319217757571295od_b_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc4222152334590801426od_b_a @ T4 ) @ Qs )
                    & ( member_c @ ( produc2449964356387445481od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) @ Ins )
                    & ( member_b @ ( product_fst_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( outputs_a_c_b @ ( create1146200282302862129_a_c_b @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Outs ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(4)
thf(fact_809_create__fsm__from__sets__simps_I4_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_c,Outs: set_c,Ts: set_Pr7772291453781135061od_c_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_c @ Ins )
         => ( ( finite_finite_c @ Outs )
           => ( ! [T4: produc1333881581359507445od_c_a] :
                  ( ( member4165989648256166942od_c_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc3586503333985814737od_c_a @ T4 ) @ Qs )
                    & ( member_c @ ( produc8885880811269545256od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) @ Ins )
                    & ( member_c @ ( product_fst_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( outputs_a_c_c @ ( create1146200282302862130_a_c_c @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Outs ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(4)
thf(fact_810_create__fsm__from__sets__simps_I4_J,axiom,
    ! [Q: b,Qs: set_b,Ins: set_a,Outs: set_a,Ts: set_Pr4062742218091393433od_a_b] :
      ( ( member_b @ Q @ Qs )
     => ( ( finite_finite_b @ Qs )
       => ( ( finite_finite_a @ Ins )
         => ( ( finite_finite_a @ Outs )
           => ( ! [T4: produc1355512071451634873od_a_b] :
                  ( ( member4187620138348294370od_a_b @ T4 @ Ts )
                 => ( ( member_b @ ( produc2156398568523956245od_a_b @ T4 ) @ Qs )
                    & ( member_a @ ( produc6516300543326982573od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) @ Ins )
                    & ( member_a @ ( product_fst_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) ) @ Outs )
                    & ( member_b @ ( product_snd_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) ) @ Qs ) ) )
             => ( ( outputs_b_a_a @ ( create3093958024581569075_b_a_a @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Outs ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(4)
thf(fact_811_create__fsm__from__sets__simps_I4_J,axiom,
    ! [Q: b,Qs: set_b,Ins: set_a,Outs: set_b,Ts: set_Pr3610021559021233496od_b_b] :
      ( ( member_b @ Q @ Qs )
     => ( ( finite_finite_b @ Qs )
       => ( ( finite_finite_a @ Ins )
         => ( ( finite_finite_b @ Outs )
           => ( ! [T4: produc4006182501950230520od_b_b] :
                  ( ( member6838290568846890017od_b_b @ T4 @ Ts )
                 => ( ( member_b @ ( produc1520749567918969556od_b_b @ T4 ) @ Qs )
                    & ( member_a @ ( produc3728844961354306540od_b_b @ ( produc5382936322983865878od_b_b @ T4 ) ) @ Ins )
                    & ( member_b @ ( product_fst_b_b @ ( produc8648342210768306478od_b_b @ ( produc5382936322983865878od_b_b @ T4 ) ) ) @ Outs )
                    & ( member_b @ ( product_snd_b_b @ ( produc8648342210768306478od_b_b @ ( produc5382936322983865878od_b_b @ T4 ) ) ) @ Qs ) ) )
             => ( ( outputs_b_a_b @ ( create3093958024581569076_b_a_b @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Outs ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(4)
thf(fact_812_create__fsm__from__sets__simps_I3_J,axiom,
    ! [Q: e,Qs: set_e,Ins: set_b,Outs: set_c,Ts: set_Pr3661745133102484886od_c_e] :
      ( ( member_e @ Q @ Qs )
     => ( ( finite_finite_e @ Qs )
       => ( ( finite_finite_b @ Ins )
         => ( ( finite_finite_c @ Outs )
           => ( ! [T4: produc4050040609193146166od_c_e] :
                  ( ( member6882148676089805663od_c_e @ T4 @ Ts )
                 => ( ( member_e @ ( produc6751554238685325970od_c_e @ T4 ) @ Qs )
                    & ( member_b @ ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T4 ) ) @ Ins )
                    & ( member_c @ ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T4 ) ) ) @ Outs )
                    & ( member_e @ ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T4 ) ) ) @ Qs ) ) )
             => ( ( inputs_e_b_c @ ( create7871786251318509303_e_b_c @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Ins ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(3)
thf(fact_813_create__fsm__from__sets__simps_I3_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_a,Outs: set_a,Ts: set_Pr625025929086095065od_a_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_a @ Ins )
         => ( ( finite_finite_a @ Outs )
           => ( ! [T4: produc7928013997122480633od_a_a] :
                  ( ( member1536750027164364322od_a_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc6136681935859420373od_a_a @ T4 ) @ Qs )
                    & ( member_a @ ( produc6516300539023753772od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) @ Ins )
                    & ( member_a @ ( product_fst_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( inputs_a_a_a @ ( create6721111446248214194_a_a_a @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Ins ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(3)
thf(fact_814_create__fsm__from__sets__simps_I3_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_a,Outs: set_b,Ts: set_Pr172305270015935128od_b_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_a @ Ins )
         => ( ( finite_finite_b @ Outs )
           => ( ! [T4: produc1355312390766300472od_b_a] :
                  ( ( member4187420457662959969od_b_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc5501032935254433684od_b_a @ T4 ) @ Qs )
                    & ( member_a @ ( produc3728844957051077739od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) @ Ins )
                    & ( member_b @ ( product_fst_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( inputs_a_a_b @ ( create6721111446248214195_a_a_b @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Ins ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(3)
thf(fact_815_create__fsm__from__sets__simps_I3_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_a,Outs: set_c,Ts: set_Pr8942956647800550999od_c_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_a @ Ins )
         => ( ( finite_finite_c @ Outs )
           => ( ! [T4: produc4005982821264896119od_c_a] :
                  ( ( member6838090888161555616od_c_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc4865383934649446995od_c_a @ T4 ) @ Qs )
                    & ( member_a @ ( produc941389375078401706od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) @ Ins )
                    & ( member_c @ ( product_fst_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( inputs_a_a_c @ ( create6721111446248214196_a_a_c @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Ins ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(3)
thf(fact_816_create__fsm__from__sets__simps_I3_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_b,Outs: set_a,Ts: set_Pr39693332076387096od_a_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_b @ Ins )
         => ( ( finite_finite_a @ Outs )
           => ( ! [T4: produc6591963377169786296od_a_a] :
                  ( ( member200699407211669985od_a_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc5497241635527604244od_a_a @ T4 ) @ Qs )
                    & ( member_b @ ( produc5876860238691937643od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) @ Ins )
                    & ( member_a @ ( product_fst_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( inputs_a_b_a @ ( create3933655864275538161_a_b_a @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Ins ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(3)
thf(fact_817_create__fsm__from__sets__simps_I3_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_b,Outs: set_b,Ts: set_Pr8810344709861002967od_b_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_b @ Ins )
         => ( ( finite_finite_b @ Outs )
           => ( ! [T4: produc19261770813606135od_b_a] :
                  ( ( member2851369837710265632od_b_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc4861592634922617555od_b_a @ T4 ) @ Qs )
                    & ( member_b @ ( produc3089404656719261610od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) @ Ins )
                    & ( member_b @ ( product_fst_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( inputs_a_b_b @ ( create3933655864275538162_a_b_b @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Ins ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(3)
thf(fact_818_create__fsm__from__sets__simps_I3_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_b,Outs: set_c,Ts: set_Pr8357624050790843030od_c_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_b @ Ins )
         => ( ( finite_finite_c @ Outs )
           => ( ! [T4: produc2669932201312201782od_c_a] :
                  ( ( member5502040268208861279od_c_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc4225943634317630866od_c_a @ T4 ) @ Qs )
                    & ( member_b @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ Ins )
                    & ( member_c @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( inputs_a_b_c @ ( create3933655864275538163_a_b_c @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Ins ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(3)
thf(fact_819_create__fsm__from__sets__simps_I3_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_c,Outs: set_a,Ts: set_Pr8677732771921454935od_a_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_c @ Ins )
         => ( ( finite_finite_a @ Outs )
           => ( ! [T4: produc5255912757217091959od_a_a] :
                  ( ( member8088020824113751456od_a_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc4857801335195788115od_a_a @ T4 ) @ Qs )
                    & ( member_c @ ( produc5237419938360121514od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) @ Ins )
                    & ( member_a @ ( product_fst_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( inputs_a_c_a @ ( create1146200282302862128_a_c_a @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Ins ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(3)
thf(fact_820_create__fsm__from__sets__simps_I3_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_c,Outs: set_b,Ts: set_Pr8225012112851294998od_b_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_c @ Ins )
         => ( ( finite_finite_b @ Outs )
           => ( ! [T4: produc7906583187715687606od_b_a] :
                  ( ( member1515319217757571295od_b_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc4222152334590801426od_b_a @ T4 ) @ Qs )
                    & ( member_c @ ( produc2449964356387445481od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) @ Ins )
                    & ( member_b @ ( product_fst_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( inputs_a_c_b @ ( create1146200282302862129_a_c_b @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Ins ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(3)
thf(fact_821_create__fsm__from__sets__simps_I3_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_c,Outs: set_c,Ts: set_Pr7772291453781135061od_c_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_c @ Ins )
         => ( ( finite_finite_c @ Outs )
           => ( ! [T4: produc1333881581359507445od_c_a] :
                  ( ( member4165989648256166942od_c_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc3586503333985814737od_c_a @ T4 ) @ Qs )
                    & ( member_c @ ( produc8885880811269545256od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) @ Ins )
                    & ( member_c @ ( product_fst_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( inputs_a_c_c @ ( create1146200282302862130_a_c_c @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Ins ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(3)
thf(fact_822_create__fsm__from__sets__simps_I5_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_a,Outs: set_a,Ts: set_Pr625025929086095065od_a_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_a @ Ins )
         => ( ( finite_finite_a @ Outs )
           => ( ! [T4: produc7928013997122480633od_a_a] :
                  ( ( member1536750027164364322od_a_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc6136681935859420373od_a_a @ T4 ) @ Qs )
                    & ( member_a @ ( produc6516300539023753772od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) @ Ins )
                    & ( member_a @ ( product_fst_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( transitions_a_a_a @ ( create6721111446248214194_a_a_a @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Ts ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(5)
thf(fact_823_create__fsm__from__sets__simps_I5_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_a,Outs: set_b,Ts: set_Pr172305270015935128od_b_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_a @ Ins )
         => ( ( finite_finite_b @ Outs )
           => ( ! [T4: produc1355312390766300472od_b_a] :
                  ( ( member4187420457662959969od_b_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc5501032935254433684od_b_a @ T4 ) @ Qs )
                    & ( member_a @ ( produc3728844957051077739od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) @ Ins )
                    & ( member_b @ ( product_fst_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( transitions_a_a_b @ ( create6721111446248214195_a_a_b @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Ts ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(5)
thf(fact_824_create__fsm__from__sets__simps_I5_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_a,Outs: set_c,Ts: set_Pr8942956647800550999od_c_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_a @ Ins )
         => ( ( finite_finite_c @ Outs )
           => ( ! [T4: produc4005982821264896119od_c_a] :
                  ( ( member6838090888161555616od_c_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc4865383934649446995od_c_a @ T4 ) @ Qs )
                    & ( member_a @ ( produc941389375078401706od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) @ Ins )
                    & ( member_c @ ( product_fst_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( transitions_a_a_c @ ( create6721111446248214196_a_a_c @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Ts ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(5)
thf(fact_825_create__fsm__from__sets__simps_I5_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_b,Outs: set_a,Ts: set_Pr39693332076387096od_a_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_b @ Ins )
         => ( ( finite_finite_a @ Outs )
           => ( ! [T4: produc6591963377169786296od_a_a] :
                  ( ( member200699407211669985od_a_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc5497241635527604244od_a_a @ T4 ) @ Qs )
                    & ( member_b @ ( produc5876860238691937643od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) @ Ins )
                    & ( member_a @ ( product_fst_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( transitions_a_b_a @ ( create3933655864275538161_a_b_a @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Ts ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(5)
thf(fact_826_create__fsm__from__sets__simps_I5_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_b,Outs: set_b,Ts: set_Pr8810344709861002967od_b_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_b @ Ins )
         => ( ( finite_finite_b @ Outs )
           => ( ! [T4: produc19261770813606135od_b_a] :
                  ( ( member2851369837710265632od_b_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc4861592634922617555od_b_a @ T4 ) @ Qs )
                    & ( member_b @ ( produc3089404656719261610od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) @ Ins )
                    & ( member_b @ ( product_fst_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( transitions_a_b_b @ ( create3933655864275538162_a_b_b @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Ts ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(5)
thf(fact_827_create__fsm__from__sets__simps_I5_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_b,Outs: set_c,Ts: set_Pr8357624050790843030od_c_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_b @ Ins )
         => ( ( finite_finite_c @ Outs )
           => ( ! [T4: produc2669932201312201782od_c_a] :
                  ( ( member5502040268208861279od_c_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc4225943634317630866od_c_a @ T4 ) @ Qs )
                    & ( member_b @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ Ins )
                    & ( member_c @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( transitions_a_b_c @ ( create3933655864275538163_a_b_c @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Ts ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(5)
thf(fact_828_create__fsm__from__sets__simps_I5_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_c,Outs: set_a,Ts: set_Pr8677732771921454935od_a_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_c @ Ins )
         => ( ( finite_finite_a @ Outs )
           => ( ! [T4: produc5255912757217091959od_a_a] :
                  ( ( member8088020824113751456od_a_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc4857801335195788115od_a_a @ T4 ) @ Qs )
                    & ( member_c @ ( produc5237419938360121514od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) @ Ins )
                    & ( member_a @ ( product_fst_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( transitions_a_c_a @ ( create1146200282302862128_a_c_a @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Ts ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(5)
thf(fact_829_create__fsm__from__sets__simps_I5_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_c,Outs: set_b,Ts: set_Pr8225012112851294998od_b_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_c @ Ins )
         => ( ( finite_finite_b @ Outs )
           => ( ! [T4: produc7906583187715687606od_b_a] :
                  ( ( member1515319217757571295od_b_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc4222152334590801426od_b_a @ T4 ) @ Qs )
                    & ( member_c @ ( produc2449964356387445481od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) @ Ins )
                    & ( member_b @ ( product_fst_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( transitions_a_c_b @ ( create1146200282302862129_a_c_b @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Ts ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(5)
thf(fact_830_create__fsm__from__sets__simps_I5_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_c,Outs: set_c,Ts: set_Pr7772291453781135061od_c_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_c @ Ins )
         => ( ( finite_finite_c @ Outs )
           => ( ! [T4: produc1333881581359507445od_c_a] :
                  ( ( member4165989648256166942od_c_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc3586503333985814737od_c_a @ T4 ) @ Qs )
                    & ( member_c @ ( produc8885880811269545256od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) @ Ins )
                    & ( member_c @ ( product_fst_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( transitions_a_c_c @ ( create1146200282302862130_a_c_c @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Ts ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(5)
thf(fact_831_create__fsm__from__sets__simps_I5_J,axiom,
    ! [Q: b,Qs: set_b,Ins: set_a,Outs: set_a,Ts: set_Pr4062742218091393433od_a_b] :
      ( ( member_b @ Q @ Qs )
     => ( ( finite_finite_b @ Qs )
       => ( ( finite_finite_a @ Ins )
         => ( ( finite_finite_a @ Outs )
           => ( ! [T4: produc1355512071451634873od_a_b] :
                  ( ( member4187620138348294370od_a_b @ T4 @ Ts )
                 => ( ( member_b @ ( produc2156398568523956245od_a_b @ T4 ) @ Qs )
                    & ( member_a @ ( produc6516300543326982573od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) @ Ins )
                    & ( member_a @ ( product_fst_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) ) @ Outs )
                    & ( member_b @ ( product_snd_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) ) @ Qs ) ) )
             => ( ( transitions_b_a_a @ ( create3093958024581569075_b_a_a @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Ts ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(5)
thf(fact_832_create__fsm__from__sets__simps_I2_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_a,Outs: set_a,Ts: set_Pr625025929086095065od_a_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_a @ Ins )
         => ( ( finite_finite_a @ Outs )
           => ( ! [T4: produc7928013997122480633od_a_a] :
                  ( ( member1536750027164364322od_a_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc6136681935859420373od_a_a @ T4 ) @ Qs )
                    & ( member_a @ ( produc6516300539023753772od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) @ Ins )
                    & ( member_a @ ( product_fst_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_a_a @ ( produc2212425751582977902od_a_a @ ( produc775496654069540887od_a_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( states_a_a_a @ ( create6721111446248214194_a_a_a @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Qs ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(2)
thf(fact_833_create__fsm__from__sets__simps_I2_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_a,Outs: set_b,Ts: set_Pr172305270015935128od_b_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_a @ Ins )
         => ( ( finite_finite_b @ Outs )
           => ( ! [T4: produc1355312390766300472od_b_a] :
                  ( ( member4187420457662959969od_b_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc5501032935254433684od_b_a @ T4 ) @ Qs )
                    & ( member_a @ ( produc3728844957051077739od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) @ Ins )
                    & ( member_b @ ( product_fst_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_b_a @ ( produc8648342206465077677od_b_a @ ( produc139847653464554198od_b_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( states_a_a_b @ ( create6721111446248214195_a_a_b @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Qs ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(2)
thf(fact_834_create__fsm__from__sets__simps_I2_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_a,Outs: set_c,Ts: set_Pr8942956647800550999od_c_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_a @ Ins )
         => ( ( finite_finite_c @ Outs )
           => ( ! [T4: produc4005982821264896119od_c_a] :
                  ( ( member6838090888161555616od_c_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc4865383934649446995od_c_a @ T4 ) @ Qs )
                    & ( member_a @ ( produc941389375078401706od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) @ Ins )
                    & ( member_c @ ( product_fst_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_c_a @ ( produc5860886624492401644od_c_a @ ( produc8727570689714343317od_c_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( states_a_a_c @ ( create6721111446248214196_a_a_c @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Qs ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(2)
thf(fact_835_create__fsm__from__sets__simps_I2_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_b,Outs: set_a,Ts: set_Pr39693332076387096od_a_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_b @ Ins )
         => ( ( finite_finite_a @ Outs )
           => ( ! [T4: produc6591963377169786296od_a_a] :
                  ( ( member200699407211669985od_a_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc5497241635527604244od_a_a @ T4 ) @ Qs )
                    & ( member_b @ ( produc5876860238691937643od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) @ Ins )
                    & ( member_a @ ( product_fst_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_a_a @ ( produc1572985451251161773od_a_a @ ( produc136056353737724758od_a_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( states_a_b_a @ ( create3933655864275538161_a_b_a @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Qs ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(2)
thf(fact_836_create__fsm__from__sets__simps_I2_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_b,Outs: set_b,Ts: set_Pr8810344709861002967od_b_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_b @ Ins )
         => ( ( finite_finite_b @ Outs )
           => ( ! [T4: produc19261770813606135od_b_a] :
                  ( ( member2851369837710265632od_b_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc4861592634922617555od_b_a @ T4 ) @ Qs )
                    & ( member_b @ ( produc3089404656719261610od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) @ Ins )
                    & ( member_b @ ( product_fst_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_b_a @ ( produc8008901906133261548od_b_a @ ( produc8723779389987513877od_b_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( states_a_b_b @ ( create3933655864275538162_a_b_b @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Qs ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(2)
thf(fact_837_create__fsm__from__sets__simps_I2_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_b,Outs: set_c,Ts: set_Pr8357624050790843030od_c_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_b @ Ins )
         => ( ( finite_finite_c @ Outs )
           => ( ! [T4: produc2669932201312201782od_c_a] :
                  ( ( member5502040268208861279od_c_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc4225943634317630866od_c_a @ T4 ) @ Qs )
                    & ( member_b @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) @ Ins )
                    & ( member_c @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( states_a_b_c @ ( create3933655864275538163_a_b_c @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Qs ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(2)
thf(fact_838_create__fsm__from__sets__simps_I2_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_c,Outs: set_a,Ts: set_Pr8677732771921454935od_a_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_c @ Ins )
         => ( ( finite_finite_a @ Outs )
           => ( ! [T4: produc5255912757217091959od_a_a] :
                  ( ( member8088020824113751456od_a_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc4857801335195788115od_a_a @ T4 ) @ Qs )
                    & ( member_c @ ( produc5237419938360121514od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) @ Ins )
                    & ( member_a @ ( product_fst_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_a_a @ ( produc933545150919345644od_a_a @ ( produc8719988090260684437od_a_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( states_a_c_a @ ( create1146200282302862128_a_c_a @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Qs ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(2)
thf(fact_839_create__fsm__from__sets__simps_I2_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_c,Outs: set_b,Ts: set_Pr8225012112851294998od_b_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_c @ Ins )
         => ( ( finite_finite_b @ Outs )
           => ( ! [T4: produc7906583187715687606od_b_a] :
                  ( ( member1515319217757571295od_b_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc4222152334590801426od_b_a @ T4 ) @ Qs )
                    & ( member_c @ ( produc2449964356387445481od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) @ Ins )
                    & ( member_b @ ( product_fst_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_b_a @ ( produc7369461605801445419od_b_a @ ( produc8084339089655697748od_b_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( states_a_c_b @ ( create1146200282302862129_a_c_b @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Qs ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(2)
thf(fact_840_create__fsm__from__sets__simps_I2_J,axiom,
    ! [Q: a,Qs: set_a,Ins: set_c,Outs: set_c,Ts: set_Pr7772291453781135061od_c_a] :
      ( ( member_a @ Q @ Qs )
     => ( ( finite_finite_a @ Qs )
       => ( ( finite_finite_c @ Ins )
         => ( ( finite_finite_c @ Outs )
           => ( ! [T4: produc1333881581359507445od_c_a] :
                  ( ( member4165989648256166942od_c_a @ T4 @ Ts )
                 => ( ( member_a @ ( produc3586503333985814737od_c_a @ T4 ) @ Qs )
                    & ( member_c @ ( produc8885880811269545256od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) @ Ins )
                    & ( member_c @ ( product_fst_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) ) @ Outs )
                    & ( member_a @ ( product_snd_c_a @ ( produc4582006023828769386od_c_a @ ( produc7448690089050711059od_c_a @ T4 ) ) ) @ Qs ) ) )
             => ( ( states_a_c_c @ ( create1146200282302862130_a_c_c @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Qs ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(2)
thf(fact_841_create__fsm__from__sets__simps_I2_J,axiom,
    ! [Q: b,Qs: set_b,Ins: set_a,Outs: set_a,Ts: set_Pr4062742218091393433od_a_b] :
      ( ( member_b @ Q @ Qs )
     => ( ( finite_finite_b @ Qs )
       => ( ( finite_finite_a @ Ins )
         => ( ( finite_finite_a @ Outs )
           => ( ! [T4: produc1355512071451634873od_a_b] :
                  ( ( member4187620138348294370od_a_b @ T4 @ Ts )
                 => ( ( member_b @ ( produc2156398568523956245od_a_b @ T4 ) @ Qs )
                    & ( member_a @ ( produc6516300543326982573od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) @ Ins )
                    & ( member_a @ ( product_fst_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) ) @ Outs )
                    & ( member_b @ ( product_snd_a_b @ ( produc2212425755886206703od_a_b @ ( produc6018585323588852567od_a_b @ T4 ) ) ) @ Qs ) ) )
             => ( ( states_b_a_a @ ( create3093958024581569075_b_a_a @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Qs ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(2)
thf(fact_842_finite__set__min__param__ex,axiom,
    ! [XS: set_li6436108459499378894od_b_c,P: list_P903359562653991662od_b_c > nat > $o] :
      ( ( finite3074115686814133143od_b_c @ XS )
     => ( ! [X2: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X2 @ XS )
           => ? [K4: nat] :
              ! [K2: nat] :
                ( ( ord_less_eq_nat @ K4 @ K2 )
               => ( P @ X2 @ K2 ) ) )
       => ? [K: nat] :
          ! [X4: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X4 @ XS )
           => ( P @ X4 @ K ) ) ) ) ).

% finite_set_min_param_ex
thf(fact_843_finite__set__min__param__ex,axiom,
    ! [XS: set_a,P: a > nat > $o] :
      ( ( finite_finite_a @ XS )
     => ( ! [X2: a] :
            ( ( member_a @ X2 @ XS )
           => ? [K4: nat] :
              ! [K2: nat] :
                ( ( ord_less_eq_nat @ K4 @ K2 )
               => ( P @ X2 @ K2 ) ) )
       => ? [K: nat] :
          ! [X4: a] :
            ( ( member_a @ X4 @ XS )
           => ( P @ X4 @ K ) ) ) ) ).

% finite_set_min_param_ex
thf(fact_844_finite__set__min__param__ex,axiom,
    ! [XS: set_b,P: b > nat > $o] :
      ( ( finite_finite_b @ XS )
     => ( ! [X2: b] :
            ( ( member_b @ X2 @ XS )
           => ? [K4: nat] :
              ! [K2: nat] :
                ( ( ord_less_eq_nat @ K4 @ K2 )
               => ( P @ X2 @ K2 ) ) )
       => ? [K: nat] :
          ! [X4: b] :
            ( ( member_b @ X4 @ XS )
           => ( P @ X4 @ K ) ) ) ) ).

% finite_set_min_param_ex
thf(fact_845_finite__set__min__param__ex,axiom,
    ! [XS: set_c,P: c > nat > $o] :
      ( ( finite_finite_c @ XS )
     => ( ! [X2: c] :
            ( ( member_c @ X2 @ XS )
           => ? [K4: nat] :
              ! [K2: nat] :
                ( ( ord_less_eq_nat @ K4 @ K2 )
               => ( P @ X2 @ K2 ) ) )
       => ? [K: nat] :
          ! [X4: c] :
            ( ( member_c @ X4 @ XS )
           => ( P @ X4 @ K ) ) ) ) ).

% finite_set_min_param_ex
thf(fact_846_reachable__states__finite,axiom,
    ! [M: fsm_a_b_c] : ( finite_finite_a @ ( reacha1620305530751930115_a_b_c @ M ) ) ).

% reachable_states_finite
thf(fact_847_fsm__inputs__finite,axiom,
    ! [M: fsm_a_b_c] : ( finite_finite_b @ ( inputs_a_b_c @ M ) ) ).

% fsm_inputs_finite
thf(fact_848_fsm__inputs__finite,axiom,
    ! [M: fsm_e_b_c] : ( finite_finite_b @ ( inputs_e_b_c @ M ) ) ).

% fsm_inputs_finite
thf(fact_849_fsm__outputs__finite,axiom,
    ! [M: fsm_a_b_c] : ( finite_finite_c @ ( outputs_a_b_c @ M ) ) ).

% fsm_outputs_finite
thf(fact_850_fsm__outputs__finite,axiom,
    ! [M: fsm_e_b_c] : ( finite_finite_c @ ( outputs_e_b_c @ M ) ) ).

% fsm_outputs_finite
thf(fact_851_finite__set__elem__maximal__extension__ex,axiom,
    ! [Xs: list_P903359562653991662od_b_c,S2: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ Xs @ S2 )
     => ( ( finite3074115686814133143od_b_c @ S2 )
       => ? [Ys2: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Xs @ Ys2 ) @ S2 )
            & ~ ? [Zs4: list_P903359562653991662od_b_c] :
                  ( ( Zs4 != nil_Product_prod_b_c )
                  & ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Xs @ ( append2547753245680614915od_b_c @ Ys2 @ Zs4 ) ) @ S2 ) ) ) ) ) ).

% finite_set_elem_maximal_extension_ex
thf(fact_852_prefix__free__set__maximal__list__ob,axiom,
    ! [Xs: set_li6436108459499378894od_b_c,X: list_P903359562653991662od_b_c] :
      ( ( finite3074115686814133143od_b_c @ Xs )
     => ( ( member6330420149250801815od_b_c @ X @ Xs )
       => ~ ! [X6: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ X @ X6 ) @ Xs )
             => ? [Y7: list_P903359562653991662od_b_c] :
                  ( ( Y7 != nil_Product_prod_b_c )
                  & ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ ( append2547753245680614915od_b_c @ X @ X6 ) @ Y7 ) @ Xs ) ) ) ) ) ).

% prefix_free_set_maximal_list_ob
thf(fact_853_image__inj__card__helper,axiom,
    ! [X5: set_a,F: a > list_P903359562653991662od_b_c] :
      ( ( finite_finite_a @ X5 )
     => ( ! [A4: a,B3: a] :
            ( ( member_a @ A4 @ X5 )
           => ( ( member_a @ B3 @ X5 )
             => ( ( A4 != B3 )
               => ( ( F @ A4 )
                 != ( F @ B3 ) ) ) ) )
       => ( ( finite5583770498833199894od_b_c @ ( image_8656872703560917237od_b_c @ F @ X5 ) )
          = ( finite_card_a @ X5 ) ) ) ) ).

% image_inj_card_helper
thf(fact_854_finite__tree__iff,axiom,
    ( prefix6767660319289835678od_b_c
    = ( ^ [T2: prefix425356687782099470od_b_c] : ( finite3074115686814133143od_b_c @ ( prefix9085958534787526401od_b_c @ T2 ) ) ) ) ).

% finite_tree_iff
thf(fact_855_distinguishes__def,axiom,
    ( distinguishes_a_b_c
    = ( ^ [M2: fsm_a_b_c,Q12: a,Q22: a,Io3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ Io3 @ ( sup_su3823046536922626210od_b_c @ ( lS_a_b_c @ M2 @ Q12 ) @ ( lS_a_b_c @ M2 @ Q22 ) ) )
          & ~ ( member6330420149250801815od_b_c @ Io3 @ ( inf_in4978071631833541052od_b_c @ ( lS_a_b_c @ M2 @ Q12 ) @ ( lS_a_b_c @ M2 @ Q22 ) ) ) ) ) ) ).

% distinguishes_def
thf(fact_856_distinguishes__def,axiom,
    ( distinguishes_e_b_c
    = ( ^ [M2: fsm_e_b_c,Q12: e,Q22: e,Io3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ Io3 @ ( sup_su3823046536922626210od_b_c @ ( lS_e_b_c @ M2 @ Q12 ) @ ( lS_e_b_c @ M2 @ Q22 ) ) )
          & ~ ( member6330420149250801815od_b_c @ Io3 @ ( inf_in4978071631833541052od_b_c @ ( lS_e_b_c @ M2 @ Q12 ) @ ( lS_e_b_c @ M2 @ Q22 ) ) ) ) ) ) ).

% distinguishes_def
thf(fact_857_acyclic__alt__def,axiom,
    ( acyclic_a_b_c
    = ( ^ [M2: fsm_a_b_c] : ( finite3074115686814133143od_b_c @ ( lS_a_b_c @ M2 @ ( initial_a_b_c @ M2 ) ) ) ) ) ).

% acyclic_alt_def
thf(fact_858_acyclic__alt__def,axiom,
    ( acyclic_e_b_c
    = ( ^ [M2: fsm_e_b_c] : ( finite3074115686814133143od_b_c @ ( lS_e_b_c @ M2 @ ( initial_e_b_c @ M2 ) ) ) ) ) ).

% acyclic_alt_def
thf(fact_859_create__fsm__from__sets__simps_I1_J,axiom,
    ! [Q: b,Qs: set_b,Ins: set_b,Outs: set_a,Ts: set_Pr3477409621081685464od_a_b] :
      ( ( member_b @ Q @ Qs )
     => ( ( finite_finite_b @ Qs )
       => ( ( finite_finite_b @ Ins )
         => ( ( finite_finite_a @ Outs )
           => ( ! [T4: produc19461451498940536od_a_b] :
                  ( ( member2851569518395600033od_a_b @ T4 @ Ts )
                 => ( ( member_b @ ( produc1516958268192140116od_a_b @ T4 ) @ Qs )
                    & ( member_b @ ( produc5876860242995166444od_a_b @ ( produc5379145023257036438od_a_b @ T4 ) ) @ Ins )
                    & ( member_a @ ( product_fst_a_b @ ( produc1572985455554390574od_a_b @ ( produc5379145023257036438od_a_b @ T4 ) ) ) @ Outs )
                    & ( member_b @ ( product_snd_a_b @ ( produc1572985455554390574od_a_b @ ( produc5379145023257036438od_a_b @ T4 ) ) ) @ Qs ) ) )
             => ( ( initial_b_b_a @ ( create306502442608893042_b_b_a @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Q ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(1)
thf(fact_860_create__fsm__from__sets__simps_I1_J,axiom,
    ! [Q: b,Qs: set_b,Ins: set_b,Outs: set_b,Ts: set_Pr3024688962011525527od_b_b] :
      ( ( member_b @ Q @ Qs )
     => ( ( finite_finite_b @ Qs )
       => ( ( finite_finite_b @ Ins )
         => ( ( finite_finite_b @ Outs )
           => ( ! [T4: produc2670131881997536183od_b_b] :
                  ( ( member5502239948894195680od_b_b @ T4 @ Ts )
                 => ( ( member_b @ ( produc881309267587153427od_b_b @ T4 ) @ Qs )
                    & ( member_b @ ( produc3089404661022490411od_b_b @ ( produc4743496022652049749od_b_b @ T4 ) ) @ Ins )
                    & ( member_b @ ( product_fst_b_b @ ( produc8008901910436490349od_b_b @ ( produc4743496022652049749od_b_b @ T4 ) ) ) @ Outs )
                    & ( member_b @ ( product_snd_b_b @ ( produc8008901910436490349od_b_b @ ( produc4743496022652049749od_b_b @ T4 ) ) ) @ Qs ) ) )
             => ( ( initial_b_b_b @ ( create306502442608893043_b_b_b @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Q ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(1)
thf(fact_861_create__fsm__from__sets__simps_I1_J,axiom,
    ! [Q: b,Qs: set_b,Ins: set_b,Outs: set_c,Ts: set_Pr2571968302941365590od_c_b] :
      ( ( member_b @ Q @ Qs )
     => ( ( finite_finite_b @ Qs )
       => ( ( finite_finite_b @ Ins )
         => ( ( finite_finite_c @ Outs )
           => ( ! [T4: produc5320802312496131830od_c_b] :
                  ( ( member8152910379392791327od_c_b @ T4 @ Ts )
                 => ( ( member_b @ ( produc245660266982166738od_c_b @ T4 ) @ Qs )
                    & ( member_b @ ( produc301949079049814378od_c_b @ ( produc4107847022047063060od_c_b @ T4 ) ) @ Ins )
                    & ( member_c @ ( product_fst_c_b @ ( produc5221446328463814316od_c_b @ ( produc4107847022047063060od_c_b @ T4 ) ) ) @ Outs )
                    & ( member_b @ ( product_snd_c_b @ ( produc5221446328463814316od_c_b @ ( produc4107847022047063060od_c_b @ T4 ) ) ) @ Qs ) ) )
             => ( ( initial_b_b_c @ ( create306502442608893044_b_b_c @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Q ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(1)
thf(fact_862_create__fsm__from__sets__simps_I1_J,axiom,
    ! [Q: b,Qs: set_b,Ins: set_c,Outs: set_a,Ts: set_Pr2892077024071977495od_a_b] :
      ( ( member_b @ Q @ Qs )
     => ( ( finite_finite_b @ Qs )
       => ( ( finite_finite_c @ Ins )
         => ( ( finite_finite_a @ Outs )
           => ( ! [T4: produc7906782868401022007od_a_b] :
                  ( ( member1515518898442905696od_a_b @ T4 @ Ts )
                 => ( ( member_b @ ( produc877517967860323987od_a_b @ T4 ) @ Qs )
                    & ( member_c @ ( produc5237419942663350315od_a_b @ ( produc4739704722925220309od_a_b @ T4 ) ) @ Ins )
                    & ( member_a @ ( product_fst_a_b @ ( produc933545155222574445od_a_b @ ( produc4739704722925220309od_a_b @ T4 ) ) ) @ Outs )
                    & ( member_b @ ( product_snd_a_b @ ( produc933545155222574445od_a_b @ ( produc4739704722925220309od_a_b @ T4 ) ) ) @ Qs ) ) )
             => ( ( initial_b_c_a @ ( create6742418897490992817_b_c_a @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Q ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(1)
thf(fact_863_create__fsm__from__sets__simps_I1_J,axiom,
    ! [Q: b,Qs: set_b,Ins: set_c,Outs: set_b,Ts: set_Pr2439356365001817558od_b_b] :
      ( ( member_b @ Q @ Qs )
     => ( ( finite_finite_b @ Qs )
       => ( ( finite_finite_c @ Ins )
         => ( ( finite_finite_b @ Outs )
           => ( ! [T4: produc1334081262044841846od_b_b] :
                  ( ( member4166189328941501343od_b_b @ T4 @ Ts )
                 => ( ( member_b @ ( produc241868967255337298od_b_b @ T4 ) @ Qs )
                    & ( member_c @ ( produc2449964360690674282od_b_b @ ( produc4104055722320233620od_b_b @ T4 ) ) @ Ins )
                    & ( member_b @ ( product_fst_b_b @ ( produc7369461610104674220od_b_b @ ( produc4104055722320233620od_b_b @ T4 ) ) ) @ Outs )
                    & ( member_b @ ( product_snd_b_b @ ( produc7369461610104674220od_b_b @ ( produc4104055722320233620od_b_b @ T4 ) ) ) @ Qs ) ) )
             => ( ( initial_b_c_b @ ( create6742418897490992818_b_c_b @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Q ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(1)
thf(fact_864_create__fsm__from__sets__simps_I1_J,axiom,
    ! [Q: b,Qs: set_b,Ins: set_c,Outs: set_c,Ts: set_Pr1986635705931657621od_c_b] :
      ( ( member_b @ Q @ Qs )
     => ( ( finite_finite_b @ Qs )
       => ( ( finite_finite_c @ Ins )
         => ( ( finite_finite_c @ Outs )
           => ( ! [T4: produc3984751692543437493od_c_b] :
                  ( ( member6816859759440096990od_c_b @ T4 @ Ts )
                 => ( ( member_b @ ( produc8829592003505126417od_c_b @ T4 ) @ Qs )
                    & ( member_c @ ( produc8885880815572774057od_c_b @ ( produc3468406721715246931od_c_b @ T4 ) ) @ Ins )
                    & ( member_c @ ( product_fst_c_b @ ( produc4582006028131998187od_c_b @ ( produc3468406721715246931od_c_b @ T4 ) ) ) @ Outs )
                    & ( member_b @ ( product_snd_c_b @ ( produc4582006028131998187od_c_b @ ( produc3468406721715246931od_c_b @ T4 ) ) ) @ Qs ) ) )
             => ( ( initial_b_c_c @ ( create6742418897490992819_b_c_c @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Q ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(1)
thf(fact_865_create__fsm__from__sets__simps_I1_J,axiom,
    ! [Q: c,Qs: set_c,Ins: set_a,Outs: set_a,Ts: set_Pr7500458507096691801od_a_c] :
      ( ( member_c @ Q @ Qs )
     => ( ( finite_finite_c @ Qs )
       => ( ( finite_finite_a @ Ins )
         => ( ( finite_finite_a @ Outs )
           => ( ! [T4: produc4006382182635564921od_a_c] :
                  ( ( member6838490249532224418od_a_c @ T4 @ Ts )
                 => ( ( member_c @ ( produc7399487238043267925od_a_c @ T4 ) @ Qs )
                    & ( member_a @ ( produc6516300547630211374od_a_c @ ( produc2038301956253388439od_a_c @ T4 ) ) @ Ins )
                    & ( member_a @ ( product_fst_a_c @ ( produc2212425760189435504od_a_c @ ( produc2038301956253388439od_a_c @ T4 ) ) ) @ Outs )
                    & ( member_c @ ( product_snd_a_c @ ( produc2212425760189435504od_a_c @ ( produc2038301956253388439od_a_c @ T4 ) ) ) @ Qs ) ) )
             => ( ( initial_c_a_a @ ( create8690176639769699764_c_a_a @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Q ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(1)
thf(fact_866_create__fsm__from__sets__simps_I1_J,axiom,
    ! [Q: c,Qs: set_c,Ins: set_a,Outs: set_b,Ts: set_Pr7047737848026531864od_b_c] :
      ( ( member_c @ Q @ Qs )
     => ( ( finite_finite_c @ Qs )
       => ( ( finite_finite_a @ Ins )
         => ( ( finite_finite_b @ Outs )
           => ( ! [T4: produc6657052613134160568od_b_c] :
                  ( ( member265788643176044257od_b_c @ T4 @ Ts )
                 => ( ( member_c @ ( produc6763838237438281236od_b_c @ T4 ) @ Qs )
                    & ( member_a @ ( produc3728844965657535341od_b_c @ ( produc1402652955648401750od_b_c @ T4 ) ) @ Ins )
                    & ( member_b @ ( product_fst_b_c @ ( produc8648342215071535279od_b_c @ ( produc1402652955648401750od_b_c @ T4 ) ) ) @ Outs )
                    & ( member_c @ ( product_snd_b_c @ ( produc8648342215071535279od_b_c @ ( produc1402652955648401750od_b_c @ T4 ) ) ) @ Qs ) ) )
             => ( ( initial_c_a_b @ ( create8690176639769699765_c_a_b @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Q ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(1)
thf(fact_867_create__fsm__from__sets__simps_I1_J,axiom,
    ! [Q: c,Qs: set_c,Ins: set_a,Outs: set_c,Ts: set_Pr6595017188956371927od_c_c] :
      ( ( member_c @ Q @ Qs )
     => ( ( finite_finite_c @ Qs )
       => ( ( finite_finite_a @ Ins )
         => ( ( finite_finite_c @ Outs )
           => ( ! [T4: produc84351006777980407od_c_c] :
                  ( ( member2916459073674639904od_c_c @ T4 @ Ts )
                 => ( ( member_c @ ( produc6128189236833294547od_c_c @ T4 ) @ Qs )
                    & ( member_a @ ( produc941389383684859308od_c_c @ ( produc767003955043415061od_c_c @ T4 ) ) @ Ins )
                    & ( member_c @ ( product_fst_c_c @ ( produc5860886633098859246od_c_c @ ( produc767003955043415061od_c_c @ T4 ) ) ) @ Outs )
                    & ( member_c @ ( product_snd_c_c @ ( produc5860886633098859246od_c_c @ ( produc767003955043415061od_c_c @ T4 ) ) ) @ Qs ) ) )
             => ( ( initial_c_a_c @ ( create8690176639769699766_c_a_c @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Q ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(1)
thf(fact_868_create__fsm__from__sets__simps_I1_J,axiom,
    ! [Q: c,Qs: set_c,Ins: set_b,Outs: set_a,Ts: set_Pr6915125910086983832od_a_c] :
      ( ( member_c @ Q @ Qs )
     => ( ( finite_finite_c @ Qs )
       => ( ( finite_finite_b @ Ins )
         => ( ( finite_finite_a @ Outs )
           => ( ! [T4: produc2670331562682870584od_a_c] :
                  ( ( member5502439629579530081od_a_c @ T4 @ Ts )
                 => ( ( member_c @ ( produc6760046937711451796od_a_c @ T4 ) @ Qs )
                    & ( member_b @ ( produc5876860247298395245od_a_c @ ( produc1398861655921572310od_a_c @ T4 ) ) @ Ins )
                    & ( member_a @ ( product_fst_a_c @ ( produc1572985459857619375od_a_c @ ( produc1398861655921572310od_a_c @ T4 ) ) ) @ Outs )
                    & ( member_c @ ( product_snd_a_c @ ( produc1572985459857619375od_a_c @ ( produc1398861655921572310od_a_c @ T4 ) ) ) @ Qs ) ) )
             => ( ( initial_c_b_a @ ( create5902721057797023731_c_b_a @ Q @ Qs @ Ins @ Outs @ Ts ) )
                = Q ) ) ) ) ) ) ).

% create_fsm_from_sets_simps(1)
thf(fact_869_recursion__renaming__helper,axiom,
    ! [F1: nat > nat,P: nat > $o,F22: nat > nat,K3: nat] :
      ( ( F1
        = ( ^ [X3: nat] : ( if_nat @ ( P @ X3 ) @ X3 @ ( F1 @ ( suc @ X3 ) ) ) ) )
     => ( ( F22
          = ( ^ [X3: nat] : ( if_nat @ ( P @ X3 ) @ X3 @ ( F22 @ ( suc @ X3 ) ) ) ) )
       => ( ! [X2: nat] :
              ( ( ord_less_eq_nat @ K3 @ X2 )
             => ( P @ X2 ) )
         => ( F1 = F22 ) ) ) ) ).

% recursion_renaming_helper
thf(fact_870_minimal__fixpoint__helper_I1_J,axiom,
    ! [F: nat > nat,P: nat > $o,K3: nat,X: nat] :
      ( ( F
        = ( ^ [X3: nat] : ( if_nat @ ( P @ X3 ) @ X3 @ ( F @ ( suc @ X3 ) ) ) ) )
     => ( ! [X2: nat] :
            ( ( ord_less_eq_nat @ K3 @ X2 )
           => ( P @ X2 ) )
       => ( P @ ( F @ X ) ) ) ) ).

% minimal_fixpoint_helper(1)
thf(fact_871_minimal__fixpoint__helper_I2_J,axiom,
    ! [F: nat > nat,P: nat > $o,K3: nat,X: nat,X7: nat] :
      ( ( F
        = ( ^ [X3: nat] : ( if_nat @ ( P @ X3 ) @ X3 @ ( F @ ( suc @ X3 ) ) ) ) )
     => ( ! [X2: nat] :
            ( ( ord_less_eq_nat @ K3 @ X2 )
           => ( P @ X2 ) )
       => ( ( ord_less_eq_nat @ X @ X7 )
         => ( ( ord_less_nat @ X7 @ ( F @ X ) )
           => ~ ( P @ X7 ) ) ) ) ) ).

% minimal_fixpoint_helper(2)
thf(fact_872_monotone__function__with__limit__witness__helper,axiom,
    ! [F: nat > nat,K3: nat] :
      ( ! [I2: nat,J: nat] :
          ( ( ord_less_eq_nat @ I2 @ J )
         => ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) )
     => ( ! [I2: nat,J: nat] :
            ( ( ord_less_nat @ I2 @ J )
           => ( ( ( F @ I2 )
                = ( F @ J ) )
             => ! [M4: nat] :
                  ( ( ord_less_eq_nat @ J @ M4 )
                 => ( ( F @ I2 )
                    = ( F @ M4 ) ) ) ) )
       => ( ! [I2: nat] : ( ord_less_eq_nat @ ( F @ I2 ) @ K3 )
         => ~ ! [X2: nat] :
                ( ( ( F @ ( suc @ X2 ) )
                  = ( F @ X2 ) )
               => ~ ( ord_less_eq_nat @ X2 @ ( minus_minus_nat @ K3 @ ( F @ zero_zero_nat ) ) ) ) ) ) ) ).

% monotone_function_with_limit_witness_helper

% Helper facts (3)
thf(help_If_3_1_If_001t__Nat__Onat_T,axiom,
    ! [P: $o] :
      ( ( P = $true )
      | ( P = $false ) ) ).

thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
    ! [X: nat,Y: nat] :
      ( ( if_nat @ $false @ X @ Y )
      = Y ) ).

thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
    ! [X: nat,Y: nat] :
      ( ( if_nat @ $true @ X @ Y )
      = X ) ).

% Conjectures (2)
thf(conj_0,hypothesis,
    ! [Alpha4: list_P903359562653991662od_b_c] :
      ( ( converge_a_b_c @ m1 @ Alpha4 @ ( v @ q ) )
     => ( ( converge_e_b_c @ m2 @ Alpha4 @ ( v @ q ) )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Alpha4 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ x @ y ) @ nil_Product_prod_b_c ) ) @ ( prefix9085958534787526401od_b_c @ ( produc1447154562020694006_b_c_d @ ( f @ m1 @ v @ t @ g @ cg_insert @ cg_lookup @ q @ x @ y ) ) ) )
         => thesis ) ) ) ).

thf(conj_1,conjecture,
    thesis ).

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