TPTP Problem File: SLH0993^1.p

%------------------------------------------------------------------------------
% 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/0049_Test_Suite/prob_02802_134421__20163872_1 [Des23]

% Status   : Theorem
% Rating   : ? v8.2.0
% Syntax   : Number of formulae    : 1913 ( 627 unt; 633 typ;   0 def)
%            Number of atoms       : 4035 (1715 equ;   0 cnn)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives : 13447 ( 319   ~;  56   |; 524   &;11036   @)
%                                         (   0 <=>;1512  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (   6 avg)
%            Number of types       :  123 ( 122 usr)
%            Number of type conns  : 1056 (1056   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  513 ( 511 usr;  52 con; 0-7 aty)
%            Number of variables   : 3493 ( 503   ^;2877   !; 113   ?;3493   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2023-01-19 11:28:58.349
%------------------------------------------------------------------------------
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thf(sy_c_member_001t__Product____Type__Oprod_Itf__e_Mt__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_Itf__e_Mtf__e_J_J_J,type,
    member2960117500232221149od_e_e: produc128009433335561652od_e_e > set_Pr2756303814962165012od_e_e > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__e_Mt__Product____Type__Oprod_Itf__e_Mt__Product____Type__Oprod_Itf__a_Mtf__e_J_J_J,type,
    member6796027992089307166od_a_e: produc3963919925192647669od_a_e > set_Pr2811188660213680853od_a_e > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__e_Mt__Product____Type__Oprod_Itf__e_Mt__Product____Type__Oprod_Itf__b_Mtf__e_J_J_J,type,
    member223326385733127005od_b_e: produc6614590355691243316od_b_e > set_Pr2358468001143520916od_b_e > $o ).

thf(sy_c_member_001t__Product____Type__Oprod_Itf__e_Mt__Product____Type__Oprod_Itf__e_Mt__Product____Type__Oprod_Itf__e_Mtf__e_J_J_J,type,
    member8175337677228913946od_e_e: produc5343229610332254449od_e_e > set_Pr1000306023933041105od_e_e > $o ).

thf(sy_c_member_001tf__a,type,
    member_a: a > set_a > $o ).

thf(sy_c_member_001tf__b,type,
    member_b: b > set_b > $o ).

thf(sy_c_member_001tf__c,type,
    member_c: c > set_c > $o ).

thf(sy_c_member_001tf__e,type,
    member_e: e > set_e > $o ).

thf(sy_v_M,type,
    m: fsm_a_b_c ).

thf(sy_v_M_H,type,
    m2: fsm_e_b_c ).

thf(sy_v_P____,type,
    p: fsm_a_b_c ).

thf(sy_v_dM____,type,
    dM: produc1703568184450464039_set_a ).

thf(sy_v_f____,type,
    f: a > list_P6327159017948738492od_c_a ).

thf(sy_v_ioEx____,type,
    ioEx: list_P903359562653991662od_b_c ).

thf(sy_v_ioX____,type,
    ioX: list_P903359562653991662od_b_c ).

thf(sy_v_io____,type,
    io: list_P903359562653991662od_b_c ).

thf(sy_v_m,type,
    m3: nat ).

thf(sy_v_pM____,type,
    pM: list_P6327159017948738492od_c_a ).

thf(sy_v_pP____,type,
    pP: list_P6327159017948738492od_c_a ).

thf(sy_v_prs,type,
    prs: set_Pr2640454425625433516_a_b_c ).

thf(sy_v_q_H____,type,
    q: a ).

thf(sy_v_q____,type,
    q2: a ).

thf(sy_v_rd__targets,type,
    rd_targets: produc3220416805844688357od_c_a > set_a ).

thf(sy_v_repetition__sets____,type,
    repetition_sets: list_P3660316430366008877_set_a ).

thf(sy_v_separators,type,
    separators: product_prod_a_a > set_Pr9130538228769002824od_d_d ).

thf(sy_v_thesis____,type,
    thesis: $o ).

thf(sy_v_thesisa____,type,
    thesisa: $o ).

thf(sy_v_tps,type,
    tps: a > set_li1159382662694783132od_c_a ).

% Relevant facts (1272)
thf(fact_0_assms_I7_J,axiom,
    comple6900478119722646120_a_b_c @ m ).

% assms(7)
thf(fact_1_assms_I8_J,axiom,
    comple1615236469910841452_e_b_c @ m2 ).

% assms(8)
thf(fact_2__092_060open_062RP_AM_Aq_Aq_H_ApP_ApM_Aprs_AM_H_A_092_060noteq_062_AR_AM_Aq_Aq_H_ApP_ApM_092_060close_062,axiom,
    ( ( test_RP_a_b_c_e @ m @ q2 @ q @ pP @ pM @ prs @ m2 )
   != ( test_R_a_b_c @ m @ q2 @ q @ pP @ pM ) ) ).

% \<open>RP M q q' pP pM prs M' \<noteq> R M q q' pP pM\<close>
thf(fact_3_assms_I3_J,axiom,
    observable_a_b_c @ m ).

% assms(3)
thf(fact_4_assms_I4_J,axiom,
    observable_e_b_c @ m2 ).

% assms(4)
thf(fact_5__092_060open_062q_A_092_060in_062_AFSM_Ostates_AM_092_060close_062,axiom,
    member_a @ q2 @ ( states_a_b_c @ m ) ).

% \<open>q \<in> FSM.states M\<close>
thf(fact_6_that,axiom,
    ! [X: list_P6327159017948738492od_c_a] :
      ( ( ( test_RP_a_b_c_e @ m @ q2 @ q @ pP @ pM @ prs @ m2 )
        = ( insert4789241225314331020od_c_a @ X @ ( test_R_a_b_c @ m @ q2 @ q @ pP @ pM ) ) )
     => thesisa ) ).

% that
thf(fact_7__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062pP_Aio_O_Aminimal__sequence__to__failure__extending__preamble__path_AM_AM_H_Aprs_ApP_Aio_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
    ~ ! [PP: list_P6327159017948738492od_c_a,Io: list_P903359562653991662od_b_c] :
        ~ ( state_7720781447231630558_b_c_e @ m @ m2 @ prs @ PP @ Io ) ).

% \<open>\<And>thesis. (\<And>pP io. minimal_sequence_to_failure_extending_preamble_path M M' prs pP io \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_8__092_060open_062minimal__sequence__to__failure__extending__preamble__path_AM_AM_H_Aprs_ApP_Aio_092_060close_062,axiom,
    state_7720781447231630558_b_c_e @ m @ m2 @ prs @ pP @ io ).

% \<open>minimal_sequence_to_failure_extending_preamble_path M M' prs pP io\<close>
thf(fact_9__092_060open_062path_AM_Aq_ApM_092_060close_062,axiom,
    path_a_b_c @ m @ q2 @ pM ).

% \<open>path M q pM\<close>
thf(fact_10__092_060open_062_092_060And_062f_O_A_I_092_060And_062q_H_O_Aq_H_A_092_060in_062_Asnd_AdM_A_092_060Longrightarrow_062_ARP_AM_Aq_Aq_H_ApP_ApM_Aprs_AM_H_A_061_Ainsert_A_If_Aq_H_J_A_IR_AM_Aq_Aq_H_ApP_ApM_J_A_092_060and_062_Af_Aq_H_A_092_060notin_062_AR_AM_Aq_Aq_H_ApP_ApM_J_A_092_060Longrightarrow_062_Athesis_____092_060close_062,axiom,
    ! [F: a > list_P6327159017948738492od_c_a] :
      ( ! [Q: a] :
          ( ( member_a @ Q @ ( produc1983107199584856133_set_a @ dM ) )
         => ( ( ( test_RP_a_b_c_e @ m @ q2 @ Q @ pP @ pM @ prs @ m2 )
              = ( insert4789241225314331020od_c_a @ ( F @ Q ) @ ( test_R_a_b_c @ m @ q2 @ Q @ pP @ pM ) ) )
            & ~ ( member7410604586820865893od_c_a @ ( F @ Q ) @ ( test_R_a_b_c @ m @ q2 @ Q @ pP @ pM ) ) ) )
     => thesis ) ).

% \<open>\<And>f. (\<And>q'. q' \<in> snd dM \<Longrightarrow> RP M q q' pP pM prs M' = insert (f q') (R M q q' pP pM) \<and> f q' \<notin> R M q q' pP pM) \<Longrightarrow> thesis__\<close>
thf(fact_11_insertCI,axiom,
    ! [A: list_P903359562653991662od_b_c,B: set_li6436108459499378894od_b_c,B2: list_P903359562653991662od_b_c] :
      ( ( ~ ( member6330420149250801815od_b_c @ A @ B )
       => ( A = B2 ) )
     => ( member6330420149250801815od_b_c @ A @ ( insert6227932334100060350od_b_c @ B2 @ B ) ) ) ).

% insertCI
thf(fact_12_insertCI,axiom,
    ! [A: list_P6327159017948738492od_c_a,B: set_li1159382662694783132od_c_a,B2: list_P6327159017948738492od_c_a] :
      ( ( ~ ( member7410604586820865893od_c_a @ A @ B )
       => ( A = B2 ) )
     => ( member7410604586820865893od_c_a @ A @ ( insert4789241225314331020od_c_a @ B2 @ B ) ) ) ).

% insertCI
thf(fact_13_insertCI,axiom,
    ! [A: e,B: set_e,B2: e] :
      ( ( ~ ( member_e @ A @ B )
       => ( A = B2 ) )
     => ( member_e @ A @ ( insert_e @ B2 @ B ) ) ) ).

% insertCI
thf(fact_14_insertCI,axiom,
    ! [A: b,B: set_b,B2: b] :
      ( ( ~ ( member_b @ A @ B )
       => ( A = B2 ) )
     => ( member_b @ A @ ( insert_b @ B2 @ B ) ) ) ).

% insertCI
thf(fact_15_insertCI,axiom,
    ! [A: a,B: set_a,B2: a] :
      ( ( ~ ( member_a @ A @ B )
       => ( A = B2 ) )
     => ( member_a @ A @ ( insert_a @ B2 @ B ) ) ) ).

% insertCI
thf(fact_16_insert__iff,axiom,
    ! [A: list_P903359562653991662od_b_c,B2: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ A @ ( insert6227932334100060350od_b_c @ B2 @ A2 ) )
      = ( ( A = B2 )
        | ( member6330420149250801815od_b_c @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_17_insert__iff,axiom,
    ! [A: list_P6327159017948738492od_c_a,B2: list_P6327159017948738492od_c_a,A2: set_li1159382662694783132od_c_a] :
      ( ( member7410604586820865893od_c_a @ A @ ( insert4789241225314331020od_c_a @ B2 @ A2 ) )
      = ( ( A = B2 )
        | ( member7410604586820865893od_c_a @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_18_insert__iff,axiom,
    ! [A: e,B2: e,A2: set_e] :
      ( ( member_e @ A @ ( insert_e @ B2 @ A2 ) )
      = ( ( A = B2 )
        | ( member_e @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_19_insert__iff,axiom,
    ! [A: b,B2: b,A2: set_b] :
      ( ( member_b @ A @ ( insert_b @ B2 @ A2 ) )
      = ( ( A = B2 )
        | ( member_b @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_20_insert__iff,axiom,
    ! [A: a,B2: a,A2: set_a] :
      ( ( member_a @ A @ ( insert_a @ B2 @ A2 ) )
      = ( ( A = B2 )
        | ( member_a @ A @ A2 ) ) ) ).

% insert_iff
thf(fact_21_insert__absorb2,axiom,
    ! [X: list_P6327159017948738492od_c_a,A2: set_li1159382662694783132od_c_a] :
      ( ( insert4789241225314331020od_c_a @ X @ ( insert4789241225314331020od_c_a @ X @ A2 ) )
      = ( insert4789241225314331020od_c_a @ X @ A2 ) ) ).

% insert_absorb2
thf(fact_22_insert__absorb2,axiom,
    ! [X: e,A2: set_e] :
      ( ( insert_e @ X @ ( insert_e @ X @ A2 ) )
      = ( insert_e @ X @ A2 ) ) ).

% insert_absorb2
thf(fact_23__092_060open_062_Iq_M_AP_J_A_092_060in_062_Aprs_092_060close_062,axiom,
    member997585926662434933_a_b_c @ ( produc2795441082327197628_a_b_c @ q2 @ p ) @ prs ).

% \<open>(q, P) \<in> prs\<close>
thf(fact_24__092_060open_062sequence__to__failure__extending__preamble__path_AM_AM_H_Aprs_ApP_Aio_092_060close_062,axiom,
    state_5244820657802497663_b_c_e @ m @ m2 @ prs @ pP @ io ).

% \<open>sequence_to_failure_extending_preamble_path M M' prs pP io\<close>
thf(fact_25_f__def,axiom,
    ( f
    = ( ^ [Q2: a] :
          ( fChoic6541264315744621840od_c_a
          @ ^ [P: list_P6327159017948738492od_c_a] :
              ( ( ( test_RP_a_b_c_e @ m @ q2 @ Q2 @ pP @ pM @ prs @ m2 )
                = ( insert4789241225314331020od_c_a @ P @ ( test_R_a_b_c @ m @ q2 @ Q2 @ pP @ pM ) ) )
              & ~ ( member7410604586820865893od_c_a @ P @ ( test_R_a_b_c @ m @ q2 @ Q2 @ pP @ pM ) ) ) ) ) ) ).

% f_def
thf(fact_26__092_060open_062is__preamble_AP_AM_Aq_092_060close_062,axiom,
    state_3011419026027373943_a_b_c @ p @ m @ q2 ).

% \<open>is_preamble P M q\<close>
thf(fact_27_assms_I5_J,axiom,
    ( ( inputs_e_b_c @ m2 )
    = ( inputs_a_b_c @ m ) ) ).

% assms(5)
thf(fact_28__092_060open_062q_H_A_092_060in_062_Asnd_AdM_092_060close_062,axiom,
    member_a @ q @ ( produc1983107199584856133_set_a @ dM ) ).

% \<open>q' \<in> snd dM\<close>
thf(fact_29_t2,axiom,
    ! [Q3: a,P2: fsm_a_b_c] :
      ( ( member997585926662434933_a_b_c @ ( produc2795441082327197628_a_b_c @ Q3 @ P2 ) @ prs )
     => ( state_3011419026027373943_a_b_c @ P2 @ m @ Q3 ) ) ).

% t2
thf(fact_30_assms_I6_J,axiom,
    ( ( inputs_a_b_c @ m )
   != bot_bot_set_b ) ).

% assms(6)
thf(fact_31__092_060open_062path_AP_A_IFSM_Oinitial_AP_J_ApP_092_060close_062,axiom,
    path_a_b_c @ p @ ( initial_a_b_c @ p ) @ pP ).

% \<open>path P (FSM.initial P) pP\<close>
thf(fact_32_insert__compr,axiom,
    ( insert6227932334100060350od_b_c
    = ( ^ [A3: list_P903359562653991662od_b_c,B3: set_li6436108459499378894od_b_c] :
          ( collec2280997390073109977od_b_c
          @ ^ [X2: list_P903359562653991662od_b_c] :
              ( ( X2 = A3 )
              | ( member6330420149250801815od_b_c @ X2 @ B3 ) ) ) ) ) ).

% insert_compr
thf(fact_33_insert__compr,axiom,
    ( insert_e
    = ( ^ [A3: e,B3: set_e] :
          ( collect_e
          @ ^ [X2: e] :
              ( ( X2 = A3 )
              | ( member_e @ X2 @ B3 ) ) ) ) ) ).

% insert_compr
thf(fact_34_insert__compr,axiom,
    ( insert_b
    = ( ^ [A3: b,B3: set_b] :
          ( collect_b
          @ ^ [X2: b] :
              ( ( X2 = A3 )
              | ( member_b @ X2 @ B3 ) ) ) ) ) ).

% insert_compr
thf(fact_35_insert__compr,axiom,
    ( insert_a
    = ( ^ [A3: a,B3: set_a] :
          ( collect_a
          @ ^ [X2: a] :
              ( ( X2 = A3 )
              | ( member_a @ X2 @ B3 ) ) ) ) ) ).

% insert_compr
thf(fact_36_insert__compr,axiom,
    ( insert4789241225314331020od_c_a
    = ( ^ [A3: list_P6327159017948738492od_c_a,B3: set_li1159382662694783132od_c_a] :
          ( collec6273869032445462695od_c_a
          @ ^ [X2: list_P6327159017948738492od_c_a] :
              ( ( X2 = A3 )
              | ( member7410604586820865893od_c_a @ X2 @ B3 ) ) ) ) ) ).

% insert_compr
thf(fact_37_insert__Collect,axiom,
    ! [A: e,P2: e > $o] :
      ( ( insert_e @ A @ ( collect_e @ P2 ) )
      = ( collect_e
        @ ^ [U: e] :
            ( ( U != A )
           => ( P2 @ U ) ) ) ) ).

% insert_Collect
thf(fact_38_insert__Collect,axiom,
    ! [A: list_P6327159017948738492od_c_a,P2: list_P6327159017948738492od_c_a > $o] :
      ( ( insert4789241225314331020od_c_a @ A @ ( collec6273869032445462695od_c_a @ P2 ) )
      = ( collec6273869032445462695od_c_a
        @ ^ [U: list_P6327159017948738492od_c_a] :
            ( ( U != A )
           => ( P2 @ U ) ) ) ) ).

% insert_Collect
thf(fact_39_mk__disjoint__insert,axiom,
    ! [A: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ A @ A2 )
     => ? [B4: set_li6436108459499378894od_b_c] :
          ( ( A2
            = ( insert6227932334100060350od_b_c @ A @ B4 ) )
          & ~ ( member6330420149250801815od_b_c @ A @ B4 ) ) ) ).

% mk_disjoint_insert
thf(fact_40_mk__disjoint__insert,axiom,
    ! [A: list_P6327159017948738492od_c_a,A2: set_li1159382662694783132od_c_a] :
      ( ( member7410604586820865893od_c_a @ A @ A2 )
     => ? [B4: set_li1159382662694783132od_c_a] :
          ( ( A2
            = ( insert4789241225314331020od_c_a @ A @ B4 ) )
          & ~ ( member7410604586820865893od_c_a @ A @ B4 ) ) ) ).

% mk_disjoint_insert
thf(fact_41_mk__disjoint__insert,axiom,
    ! [A: e,A2: set_e] :
      ( ( member_e @ A @ A2 )
     => ? [B4: set_e] :
          ( ( A2
            = ( insert_e @ A @ B4 ) )
          & ~ ( member_e @ A @ B4 ) ) ) ).

% mk_disjoint_insert
thf(fact_42_mk__disjoint__insert,axiom,
    ! [A: b,A2: set_b] :
      ( ( member_b @ A @ A2 )
     => ? [B4: set_b] :
          ( ( A2
            = ( insert_b @ A @ B4 ) )
          & ~ ( member_b @ A @ B4 ) ) ) ).

% mk_disjoint_insert
thf(fact_43_mk__disjoint__insert,axiom,
    ! [A: a,A2: set_a] :
      ( ( member_a @ A @ A2 )
     => ? [B4: set_a] :
          ( ( A2
            = ( insert_a @ A @ B4 ) )
          & ~ ( member_a @ A @ B4 ) ) ) ).

% mk_disjoint_insert
thf(fact_44_insert__commute,axiom,
    ! [X: list_P6327159017948738492od_c_a,Y: list_P6327159017948738492od_c_a,A2: set_li1159382662694783132od_c_a] :
      ( ( insert4789241225314331020od_c_a @ X @ ( insert4789241225314331020od_c_a @ Y @ A2 ) )
      = ( insert4789241225314331020od_c_a @ Y @ ( insert4789241225314331020od_c_a @ X @ A2 ) ) ) ).

% insert_commute
thf(fact_45_insert__commute,axiom,
    ! [X: e,Y: e,A2: set_e] :
      ( ( insert_e @ X @ ( insert_e @ Y @ A2 ) )
      = ( insert_e @ Y @ ( insert_e @ X @ A2 ) ) ) ).

% insert_commute
thf(fact_46_insert__eq__iff,axiom,
    ! [A: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c,B2: list_P903359562653991662od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ~ ( member6330420149250801815od_b_c @ A @ A2 )
     => ( ~ ( member6330420149250801815od_b_c @ B2 @ B )
       => ( ( ( insert6227932334100060350od_b_c @ A @ A2 )
            = ( insert6227932334100060350od_b_c @ B2 @ B ) )
          = ( ( ( A = B2 )
             => ( A2 = B ) )
            & ( ( A != B2 )
             => ? [C: set_li6436108459499378894od_b_c] :
                  ( ( A2
                    = ( insert6227932334100060350od_b_c @ B2 @ C ) )
                  & ~ ( member6330420149250801815od_b_c @ B2 @ C )
                  & ( B
                    = ( insert6227932334100060350od_b_c @ A @ C ) )
                  & ~ ( member6330420149250801815od_b_c @ A @ C ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_47_insert__eq__iff,axiom,
    ! [A: list_P6327159017948738492od_c_a,A2: set_li1159382662694783132od_c_a,B2: list_P6327159017948738492od_c_a,B: set_li1159382662694783132od_c_a] :
      ( ~ ( member7410604586820865893od_c_a @ A @ A2 )
     => ( ~ ( member7410604586820865893od_c_a @ B2 @ B )
       => ( ( ( insert4789241225314331020od_c_a @ A @ A2 )
            = ( insert4789241225314331020od_c_a @ B2 @ B ) )
          = ( ( ( A = B2 )
             => ( A2 = B ) )
            & ( ( A != B2 )
             => ? [C: set_li1159382662694783132od_c_a] :
                  ( ( A2
                    = ( insert4789241225314331020od_c_a @ B2 @ C ) )
                  & ~ ( member7410604586820865893od_c_a @ B2 @ C )
                  & ( B
                    = ( insert4789241225314331020od_c_a @ A @ C ) )
                  & ~ ( member7410604586820865893od_c_a @ A @ C ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_48_insert__eq__iff,axiom,
    ! [A: e,A2: set_e,B2: e,B: set_e] :
      ( ~ ( member_e @ A @ A2 )
     => ( ~ ( member_e @ B2 @ B )
       => ( ( ( insert_e @ A @ A2 )
            = ( insert_e @ B2 @ B ) )
          = ( ( ( A = B2 )
             => ( A2 = B ) )
            & ( ( A != B2 )
             => ? [C: set_e] :
                  ( ( A2
                    = ( insert_e @ B2 @ C ) )
                  & ~ ( member_e @ B2 @ C )
                  & ( B
                    = ( insert_e @ A @ C ) )
                  & ~ ( member_e @ A @ C ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_49_insert__eq__iff,axiom,
    ! [A: b,A2: set_b,B2: b,B: set_b] :
      ( ~ ( member_b @ A @ A2 )
     => ( ~ ( member_b @ B2 @ B )
       => ( ( ( insert_b @ A @ A2 )
            = ( insert_b @ B2 @ B ) )
          = ( ( ( A = B2 )
             => ( A2 = B ) )
            & ( ( A != B2 )
             => ? [C: set_b] :
                  ( ( A2
                    = ( insert_b @ B2 @ C ) )
                  & ~ ( member_b @ B2 @ C )
                  & ( B
                    = ( insert_b @ A @ C ) )
                  & ~ ( member_b @ A @ C ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_50_insert__eq__iff,axiom,
    ! [A: a,A2: set_a,B2: a,B: set_a] :
      ( ~ ( member_a @ A @ A2 )
     => ( ~ ( member_a @ B2 @ B )
       => ( ( ( insert_a @ A @ A2 )
            = ( insert_a @ B2 @ B ) )
          = ( ( ( A = B2 )
             => ( A2 = B ) )
            & ( ( A != B2 )
             => ? [C: set_a] :
                  ( ( A2
                    = ( insert_a @ B2 @ C ) )
                  & ~ ( member_a @ B2 @ C )
                  & ( B
                    = ( insert_a @ A @ C ) )
                  & ~ ( member_a @ A @ C ) ) ) ) ) ) ) ).

% insert_eq_iff
thf(fact_51_insert__absorb,axiom,
    ! [A: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ A @ A2 )
     => ( ( insert6227932334100060350od_b_c @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_52_insert__absorb,axiom,
    ! [A: list_P6327159017948738492od_c_a,A2: set_li1159382662694783132od_c_a] :
      ( ( member7410604586820865893od_c_a @ A @ A2 )
     => ( ( insert4789241225314331020od_c_a @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_53_insert__absorb,axiom,
    ! [A: e,A2: set_e] :
      ( ( member_e @ A @ A2 )
     => ( ( insert_e @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_54_insert__absorb,axiom,
    ! [A: b,A2: set_b] :
      ( ( member_b @ A @ A2 )
     => ( ( insert_b @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_55_insert__absorb,axiom,
    ! [A: a,A2: set_a] :
      ( ( member_a @ A @ A2 )
     => ( ( insert_a @ A @ A2 )
        = A2 ) ) ).

% insert_absorb
thf(fact_56_insert__ident,axiom,
    ! [X: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ~ ( member6330420149250801815od_b_c @ X @ A2 )
     => ( ~ ( member6330420149250801815od_b_c @ X @ B )
       => ( ( ( insert6227932334100060350od_b_c @ X @ A2 )
            = ( insert6227932334100060350od_b_c @ X @ B ) )
          = ( A2 = B ) ) ) ) ).

% insert_ident
thf(fact_57_insert__ident,axiom,
    ! [X: list_P6327159017948738492od_c_a,A2: set_li1159382662694783132od_c_a,B: set_li1159382662694783132od_c_a] :
      ( ~ ( member7410604586820865893od_c_a @ X @ A2 )
     => ( ~ ( member7410604586820865893od_c_a @ X @ B )
       => ( ( ( insert4789241225314331020od_c_a @ X @ A2 )
            = ( insert4789241225314331020od_c_a @ X @ B ) )
          = ( A2 = B ) ) ) ) ).

% insert_ident
thf(fact_58_insert__ident,axiom,
    ! [X: e,A2: set_e,B: set_e] :
      ( ~ ( member_e @ X @ A2 )
     => ( ~ ( member_e @ X @ B )
       => ( ( ( insert_e @ X @ A2 )
            = ( insert_e @ X @ B ) )
          = ( A2 = B ) ) ) ) ).

% insert_ident
thf(fact_59_insert__ident,axiom,
    ! [X: b,A2: set_b,B: set_b] :
      ( ~ ( member_b @ X @ A2 )
     => ( ~ ( member_b @ X @ B )
       => ( ( ( insert_b @ X @ A2 )
            = ( insert_b @ X @ B ) )
          = ( A2 = B ) ) ) ) ).

% insert_ident
thf(fact_60_insert__ident,axiom,
    ! [X: a,A2: set_a,B: set_a] :
      ( ~ ( member_a @ X @ A2 )
     => ( ~ ( member_a @ X @ B )
       => ( ( ( insert_a @ X @ A2 )
            = ( insert_a @ X @ B ) )
          = ( A2 = B ) ) ) ) ).

% insert_ident
thf(fact_61_Set_Oset__insert,axiom,
    ! [X: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ X @ A2 )
     => ~ ! [B4: set_li6436108459499378894od_b_c] :
            ( ( A2
              = ( insert6227932334100060350od_b_c @ X @ B4 ) )
           => ( member6330420149250801815od_b_c @ X @ B4 ) ) ) ).

% Set.set_insert
thf(fact_62_Set_Oset__insert,axiom,
    ! [X: list_P6327159017948738492od_c_a,A2: set_li1159382662694783132od_c_a] :
      ( ( member7410604586820865893od_c_a @ X @ A2 )
     => ~ ! [B4: set_li1159382662694783132od_c_a] :
            ( ( A2
              = ( insert4789241225314331020od_c_a @ X @ B4 ) )
           => ( member7410604586820865893od_c_a @ X @ B4 ) ) ) ).

% Set.set_insert
thf(fact_63_Set_Oset__insert,axiom,
    ! [X: e,A2: set_e] :
      ( ( member_e @ X @ A2 )
     => ~ ! [B4: set_e] :
            ( ( A2
              = ( insert_e @ X @ B4 ) )
           => ( member_e @ X @ B4 ) ) ) ).

% Set.set_insert
thf(fact_64_Set_Oset__insert,axiom,
    ! [X: b,A2: set_b] :
      ( ( member_b @ X @ A2 )
     => ~ ! [B4: set_b] :
            ( ( A2
              = ( insert_b @ X @ B4 ) )
           => ( member_b @ X @ B4 ) ) ) ).

% Set.set_insert
thf(fact_65_Set_Oset__insert,axiom,
    ! [X: a,A2: set_a] :
      ( ( member_a @ X @ A2 )
     => ~ ! [B4: set_a] :
            ( ( A2
              = ( insert_a @ X @ B4 ) )
           => ( member_a @ X @ B4 ) ) ) ).

% Set.set_insert
thf(fact_66_insertI2,axiom,
    ! [A: list_P903359562653991662od_b_c,B: set_li6436108459499378894od_b_c,B2: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ A @ B )
     => ( member6330420149250801815od_b_c @ A @ ( insert6227932334100060350od_b_c @ B2 @ B ) ) ) ).

% insertI2
thf(fact_67_insertI2,axiom,
    ! [A: list_P6327159017948738492od_c_a,B: set_li1159382662694783132od_c_a,B2: list_P6327159017948738492od_c_a] :
      ( ( member7410604586820865893od_c_a @ A @ B )
     => ( member7410604586820865893od_c_a @ A @ ( insert4789241225314331020od_c_a @ B2 @ B ) ) ) ).

% insertI2
thf(fact_68_insertI2,axiom,
    ! [A: e,B: set_e,B2: e] :
      ( ( member_e @ A @ B )
     => ( member_e @ A @ ( insert_e @ B2 @ B ) ) ) ).

% insertI2
thf(fact_69_insertI2,axiom,
    ! [A: b,B: set_b,B2: b] :
      ( ( member_b @ A @ B )
     => ( member_b @ A @ ( insert_b @ B2 @ B ) ) ) ).

% insertI2
thf(fact_70_insertI2,axiom,
    ! [A: a,B: set_a,B2: a] :
      ( ( member_a @ A @ B )
     => ( member_a @ A @ ( insert_a @ B2 @ B ) ) ) ).

% insertI2
thf(fact_71_insertI1,axiom,
    ! [A: list_P903359562653991662od_b_c,B: set_li6436108459499378894od_b_c] : ( member6330420149250801815od_b_c @ A @ ( insert6227932334100060350od_b_c @ A @ B ) ) ).

% insertI1
thf(fact_72_insertI1,axiom,
    ! [A: list_P6327159017948738492od_c_a,B: set_li1159382662694783132od_c_a] : ( member7410604586820865893od_c_a @ A @ ( insert4789241225314331020od_c_a @ A @ B ) ) ).

% insertI1
thf(fact_73_insertI1,axiom,
    ! [A: e,B: set_e] : ( member_e @ A @ ( insert_e @ A @ B ) ) ).

% insertI1
thf(fact_74_insertI1,axiom,
    ! [A: b,B: set_b] : ( member_b @ A @ ( insert_b @ A @ B ) ) ).

% insertI1
thf(fact_75_insertI1,axiom,
    ! [A: a,B: set_a] : ( member_a @ A @ ( insert_a @ A @ B ) ) ).

% insertI1
thf(fact_76_insertE,axiom,
    ! [A: list_P903359562653991662od_b_c,B2: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ A @ ( insert6227932334100060350od_b_c @ B2 @ A2 ) )
     => ( ( A != B2 )
       => ( member6330420149250801815od_b_c @ A @ A2 ) ) ) ).

% insertE
thf(fact_77_insertE,axiom,
    ! [A: list_P6327159017948738492od_c_a,B2: list_P6327159017948738492od_c_a,A2: set_li1159382662694783132od_c_a] :
      ( ( member7410604586820865893od_c_a @ A @ ( insert4789241225314331020od_c_a @ B2 @ A2 ) )
     => ( ( A != B2 )
       => ( member7410604586820865893od_c_a @ A @ A2 ) ) ) ).

% insertE
thf(fact_78_insertE,axiom,
    ! [A: e,B2: e,A2: set_e] :
      ( ( member_e @ A @ ( insert_e @ B2 @ A2 ) )
     => ( ( A != B2 )
       => ( member_e @ A @ A2 ) ) ) ).

% insertE
thf(fact_79_insertE,axiom,
    ! [A: b,B2: b,A2: set_b] :
      ( ( member_b @ A @ ( insert_b @ B2 @ A2 ) )
     => ( ( A != B2 )
       => ( member_b @ A @ A2 ) ) ) ).

% insertE
thf(fact_80_insertE,axiom,
    ! [A: a,B2: a,A2: set_a] :
      ( ( member_a @ A @ ( insert_a @ B2 @ A2 ) )
     => ( ( A != B2 )
       => ( member_a @ A @ A2 ) ) ) ).

% insertE
thf(fact_81_some__equality,axiom,
    ! [P2: list_P6327159017948738492od_c_a > $o,A: list_P6327159017948738492od_c_a] :
      ( ( P2 @ A )
     => ( ! [X3: list_P6327159017948738492od_c_a] :
            ( ( P2 @ X3 )
           => ( X3 = A ) )
       => ( ( fChoic6541264315744621840od_c_a @ P2 )
          = A ) ) ) ).

% some_equality
thf(fact_82_some__eq__trivial,axiom,
    ! [X: list_P6327159017948738492od_c_a] :
      ( ( fChoic6541264315744621840od_c_a
        @ ^ [Y2: list_P6327159017948738492od_c_a] : ( Y2 = X ) )
      = X ) ).

% some_eq_trivial
thf(fact_83_some__sym__eq__trivial,axiom,
    ! [X: list_P6327159017948738492od_c_a] :
      ( ( fChoic6541264315744621840od_c_a
        @ ( ^ [Y3: list_P6327159017948738492od_c_a,Z: list_P6327159017948738492od_c_a] : ( Y3 = Z )
          @ X ) )
      = X ) ).

% some_sym_eq_trivial
thf(fact_84__092_060open_062path_AM_A_IFSM_Oinitial_AM_J_ApP_092_060close_062,axiom,
    path_a_b_c @ m @ ( initial_a_b_c @ m ) @ pP ).

% \<open>path M (FSM.initial M) pP\<close>
thf(fact_85__092_060open_062FSM_Oinitial_AP_A_061_AFSM_Oinitial_AM_092_060close_062,axiom,
    ( ( initial_a_b_c @ p )
    = ( initial_a_b_c @ m ) ) ).

% \<open>FSM.initial P = FSM.initial M\<close>
thf(fact_86_prod_Oinject,axiom,
    ! [X1: d,X22: d,Y1: d,Y22: d] :
      ( ( ( product_Pair_d_d @ X1 @ X22 )
        = ( product_Pair_d_d @ Y1 @ Y22 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y22 ) ) ) ).

% prod.inject
thf(fact_87_prod_Oinject,axiom,
    ! [X1: b,X22: c,Y1: b,Y22: c] :
      ( ( ( product_Pair_b_c @ X1 @ X22 )
        = ( product_Pair_b_c @ Y1 @ Y22 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y22 ) ) ) ).

% prod.inject
thf(fact_88_prod_Oinject,axiom,
    ! [X1: a,X22: list_P6327159017948738492od_c_a,Y1: a,Y22: list_P6327159017948738492od_c_a] :
      ( ( ( produc3580641852002036821od_c_a @ X1 @ X22 )
        = ( produc3580641852002036821od_c_a @ Y1 @ Y22 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y22 ) ) ) ).

% prod.inject
thf(fact_89_prod_Oinject,axiom,
    ! [X1: a,X22: fsm_a_b_c,Y1: a,Y22: fsm_a_b_c] :
      ( ( ( produc2795441082327197628_a_b_c @ X1 @ X22 )
        = ( produc2795441082327197628_a_b_c @ Y1 @ Y22 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y22 ) ) ) ).

% prod.inject
thf(fact_90_prod_Oinject,axiom,
    ! [X1: a,X22: a,Y1: a,Y22: a] :
      ( ( ( product_Pair_a_a @ X1 @ X22 )
        = ( product_Pair_a_a @ Y1 @ Y22 ) )
      = ( ( X1 = Y1 )
        & ( X22 = Y22 ) ) ) ).

% prod.inject
thf(fact_91_old_Oprod_Oinject,axiom,
    ! [A: d,B2: d,A4: d,B5: d] :
      ( ( ( product_Pair_d_d @ A @ B2 )
        = ( product_Pair_d_d @ A4 @ B5 ) )
      = ( ( A = A4 )
        & ( B2 = B5 ) ) ) ).

% old.prod.inject
thf(fact_92_old_Oprod_Oinject,axiom,
    ! [A: b,B2: c,A4: b,B5: c] :
      ( ( ( product_Pair_b_c @ A @ B2 )
        = ( product_Pair_b_c @ A4 @ B5 ) )
      = ( ( A = A4 )
        & ( B2 = B5 ) ) ) ).

% old.prod.inject
thf(fact_93_old_Oprod_Oinject,axiom,
    ! [A: a,B2: list_P6327159017948738492od_c_a,A4: a,B5: list_P6327159017948738492od_c_a] :
      ( ( ( produc3580641852002036821od_c_a @ A @ B2 )
        = ( produc3580641852002036821od_c_a @ A4 @ B5 ) )
      = ( ( A = A4 )
        & ( B2 = B5 ) ) ) ).

% old.prod.inject
thf(fact_94_old_Oprod_Oinject,axiom,
    ! [A: a,B2: fsm_a_b_c,A4: a,B5: fsm_a_b_c] :
      ( ( ( produc2795441082327197628_a_b_c @ A @ B2 )
        = ( produc2795441082327197628_a_b_c @ A4 @ B5 ) )
      = ( ( A = A4 )
        & ( B2 = B5 ) ) ) ).

% old.prod.inject
thf(fact_95_old_Oprod_Oinject,axiom,
    ! [A: a,B2: a,A4: a,B5: a] :
      ( ( ( product_Pair_a_a @ A @ B2 )
        = ( product_Pair_a_a @ A4 @ B5 ) )
      = ( ( A = A4 )
        & ( B2 = B5 ) ) ) ).

% old.prod.inject
thf(fact_96__092_060open_062_092_060And_062io_H_O_Asequence__to__failure__extending__preamble__path_AM_AM_H_Aprs_ApP_Aio_H_A_092_060Longrightarrow_062_Alength_Aio_A_092_060le_062_Alength_Aio_H_092_060close_062,axiom,
    ! [Io2: list_P903359562653991662od_b_c] :
      ( ( state_5244820657802497663_b_c_e @ m @ m2 @ prs @ pP @ Io2 )
     => ( ord_less_eq_nat @ ( size_s3392097710323735898od_b_c @ io ) @ ( size_s3392097710323735898od_b_c @ Io2 ) ) ) ).

% \<open>\<And>io'. sequence_to_failure_extending_preamble_path M M' prs pP io' \<Longrightarrow> length io \<le> length io'\<close>
thf(fact_97_is__preamble__is__state,axiom,
    ! [P2: fsm_a_b_c,M: fsm_a_b_c,Q3: a] :
      ( ( state_3011419026027373943_a_b_c @ P2 @ M @ Q3 )
     => ( member_a @ Q3 @ ( states_a_b_c @ M ) ) ) ).

% is_preamble_is_state
thf(fact_98_path__begin__state,axiom,
    ! [M: fsm_a_b_c,Q3: a,P3: list_P6327159017948738492od_c_a] :
      ( ( path_a_b_c @ M @ Q3 @ P3 )
     => ( member_a @ Q3 @ ( states_a_b_c @ M ) ) ) ).

% path_begin_state
thf(fact_99__092_060open_062target_A_IFSM_Oinitial_AP_J_ApP_A_061_Aq_092_060close_062,axiom,
    ( ( target_a_b_c @ ( initial_a_b_c @ p ) @ pP )
    = q2 ) ).

% \<open>target (FSM.initial P) pP = q\<close>
thf(fact_100_mem__Collect__eq,axiom,
    ! [A: list_P903359562653991662od_b_c,P2: list_P903359562653991662od_b_c > $o] :
      ( ( member6330420149250801815od_b_c @ A @ ( collec2280997390073109977od_b_c @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_101_mem__Collect__eq,axiom,
    ! [A: e,P2: e > $o] :
      ( ( member_e @ A @ ( collect_e @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_102_mem__Collect__eq,axiom,
    ! [A: b,P2: b > $o] :
      ( ( member_b @ A @ ( collect_b @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_103_mem__Collect__eq,axiom,
    ! [A: a,P2: a > $o] :
      ( ( member_a @ A @ ( collect_a @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_104_mem__Collect__eq,axiom,
    ! [A: list_P6327159017948738492od_c_a,P2: list_P6327159017948738492od_c_a > $o] :
      ( ( member7410604586820865893od_c_a @ A @ ( collec6273869032445462695od_c_a @ P2 ) )
      = ( P2 @ A ) ) ).

% mem_Collect_eq
thf(fact_105_Collect__mem__eq,axiom,
    ! [A2: set_li6436108459499378894od_b_c] :
      ( ( collec2280997390073109977od_b_c
        @ ^ [X2: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ X2 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_106_Collect__mem__eq,axiom,
    ! [A2: set_e] :
      ( ( collect_e
        @ ^ [X2: e] : ( member_e @ X2 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_107_Collect__mem__eq,axiom,
    ! [A2: set_b] :
      ( ( collect_b
        @ ^ [X2: b] : ( member_b @ X2 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_108_Collect__mem__eq,axiom,
    ! [A2: set_a] :
      ( ( collect_a
        @ ^ [X2: a] : ( member_a @ X2 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_109_Collect__mem__eq,axiom,
    ! [A2: set_li1159382662694783132od_c_a] :
      ( ( collec6273869032445462695od_c_a
        @ ^ [X2: list_P6327159017948738492od_c_a] : ( member7410604586820865893od_c_a @ X2 @ A2 ) )
      = A2 ) ).

% Collect_mem_eq
thf(fact_110_Collect__cong,axiom,
    ! [P2: list_P6327159017948738492od_c_a > $o,Q4: list_P6327159017948738492od_c_a > $o] :
      ( ! [X3: list_P6327159017948738492od_c_a] :
          ( ( P2 @ X3 )
          = ( Q4 @ X3 ) )
     => ( ( collec6273869032445462695od_c_a @ P2 )
        = ( collec6273869032445462695od_c_a @ Q4 ) ) ) ).

% Collect_cong
thf(fact_111_sndI,axiom,
    ! [X: product_prod_d_d,Y: d,Z2: d] :
      ( ( X
        = ( product_Pair_d_d @ Y @ Z2 ) )
     => ( ( product_snd_d_d @ X )
        = Z2 ) ) ).

% sndI
thf(fact_112_sndI,axiom,
    ! [X: produc3220416805844688357od_c_a,Y: a,Z2: list_P6327159017948738492od_c_a] :
      ( ( X
        = ( produc3580641852002036821od_c_a @ Y @ Z2 ) )
     => ( ( produc5527568727691618435od_c_a @ X )
        = Z2 ) ) ).

% sndI
thf(fact_113_sndI,axiom,
    ! [X: produc8838969699183119820_a_b_c,Y: a,Z2: fsm_a_b_c] :
      ( ( X
        = ( produc2795441082327197628_a_b_c @ Y @ Z2 ) )
     => ( ( produc4728557313310798826_a_b_c @ X )
        = Z2 ) ) ).

% sndI
thf(fact_114_sndI,axiom,
    ! [X: product_prod_a_a,Y: a,Z2: a] :
      ( ( X
        = ( product_Pair_a_a @ Y @ Z2 ) )
     => ( ( product_snd_a_a @ X )
        = Z2 ) ) ).

% sndI
thf(fact_115_sndI,axiom,
    ! [X: produc1703568184450464039_set_a,Y: set_a,Z2: set_a] :
      ( ( X
        = ( produc9088192753505129239_set_a @ Y @ Z2 ) )
     => ( ( produc1983107199584856133_set_a @ X )
        = Z2 ) ) ).

% sndI
thf(fact_116_sndI,axiom,
    ! [X: produc2669932201312201782od_c_a,Y: a,Z2: produc2133359284458116493od_c_a] :
      ( ( X
        = ( produc5762801557034676134od_c_a @ Y @ Z2 ) )
     => ( ( produc8088130389382527188od_c_a @ X )
        = Z2 ) ) ).

% sndI
thf(fact_117_sndI,axiom,
    ! [X: produc2133359284458116493od_c_a,Y: b,Z2: product_prod_c_a] :
      ( ( X
        = ( produc3440865914000881661od_c_a @ Y @ Z2 ) )
     => ( ( produc5221446324160585515od_c_a @ X )
        = Z2 ) ) ).

% sndI
thf(fact_118_sndI,axiom,
    ! [X: product_prod_b_c,Y: b,Z2: c] :
      ( ( X
        = ( product_Pair_b_c @ Y @ Z2 ) )
     => ( ( product_snd_b_c @ X )
        = Z2 ) ) ).

% sndI
thf(fact_119_empty__iff,axiom,
    ! [C2: list_P903359562653991662od_b_c] :
      ~ ( member6330420149250801815od_b_c @ C2 @ bot_bo4166481423041325370od_b_c ) ).

% empty_iff
thf(fact_120_empty__iff,axiom,
    ! [C2: list_P6327159017948738492od_c_a] :
      ~ ( member7410604586820865893od_c_a @ C2 @ bot_bo6236370880139903240od_c_a ) ).

% empty_iff
thf(fact_121_empty__iff,axiom,
    ! [C2: a] :
      ~ ( member_a @ C2 @ bot_bot_set_a ) ).

% empty_iff
thf(fact_122_empty__iff,axiom,
    ! [C2: b] :
      ~ ( member_b @ C2 @ bot_bot_set_b ) ).

% empty_iff
thf(fact_123_empty__iff,axiom,
    ! [C2: produc4859908366599477352od_d_d] :
      ~ ( member73601632213084689od_d_d @ C2 @ bot_bo7612717905841165748od_d_d ) ).

% empty_iff
thf(fact_124_empty__iff,axiom,
    ! [C2: e] :
      ~ ( member_e @ C2 @ bot_bot_set_e ) ).

% empty_iff
thf(fact_125_all__not__in__conv,axiom,
    ! [A2: set_li6436108459499378894od_b_c] :
      ( ( ! [X2: list_P903359562653991662od_b_c] :
            ~ ( member6330420149250801815od_b_c @ X2 @ A2 ) )
      = ( A2 = bot_bo4166481423041325370od_b_c ) ) ).

% all_not_in_conv
thf(fact_126_all__not__in__conv,axiom,
    ! [A2: set_li1159382662694783132od_c_a] :
      ( ( ! [X2: list_P6327159017948738492od_c_a] :
            ~ ( member7410604586820865893od_c_a @ X2 @ A2 ) )
      = ( A2 = bot_bo6236370880139903240od_c_a ) ) ).

% all_not_in_conv
thf(fact_127_all__not__in__conv,axiom,
    ! [A2: set_a] :
      ( ( ! [X2: a] :
            ~ ( member_a @ X2 @ A2 ) )
      = ( A2 = bot_bot_set_a ) ) ).

% all_not_in_conv
thf(fact_128_all__not__in__conv,axiom,
    ! [A2: set_b] :
      ( ( ! [X2: b] :
            ~ ( member_b @ X2 @ A2 ) )
      = ( A2 = bot_bot_set_b ) ) ).

% all_not_in_conv
thf(fact_129_all__not__in__conv,axiom,
    ! [A2: set_Pr9130538228769002824od_d_d] :
      ( ( ! [X2: produc4859908366599477352od_d_d] :
            ~ ( member73601632213084689od_d_d @ X2 @ A2 ) )
      = ( A2 = bot_bo7612717905841165748od_d_d ) ) ).

% all_not_in_conv
thf(fact_130_all__not__in__conv,axiom,
    ! [A2: set_e] :
      ( ( ! [X2: e] :
            ~ ( member_e @ X2 @ A2 ) )
      = ( A2 = bot_bot_set_e ) ) ).

% all_not_in_conv
thf(fact_131_Collect__empty__eq,axiom,
    ! [P2: list_P6327159017948738492od_c_a > $o] :
      ( ( ( collec6273869032445462695od_c_a @ P2 )
        = bot_bo6236370880139903240od_c_a )
      = ( ! [X2: list_P6327159017948738492od_c_a] :
            ~ ( P2 @ X2 ) ) ) ).

% Collect_empty_eq
thf(fact_132_Collect__empty__eq,axiom,
    ! [P2: b > $o] :
      ( ( ( collect_b @ P2 )
        = bot_bot_set_b )
      = ( ! [X2: b] :
            ~ ( P2 @ X2 ) ) ) ).

% Collect_empty_eq
thf(fact_133_Collect__empty__eq,axiom,
    ! [P2: produc4859908366599477352od_d_d > $o] :
      ( ( ( collec5362705567740981075od_d_d @ P2 )
        = bot_bo7612717905841165748od_d_d )
      = ( ! [X2: produc4859908366599477352od_d_d] :
            ~ ( P2 @ X2 ) ) ) ).

% Collect_empty_eq
thf(fact_134_Collect__empty__eq,axiom,
    ! [P2: e > $o] :
      ( ( ( collect_e @ P2 )
        = bot_bot_set_e )
      = ( ! [X2: e] :
            ~ ( P2 @ X2 ) ) ) ).

% Collect_empty_eq
thf(fact_135_empty__Collect__eq,axiom,
    ! [P2: list_P6327159017948738492od_c_a > $o] :
      ( ( bot_bo6236370880139903240od_c_a
        = ( collec6273869032445462695od_c_a @ P2 ) )
      = ( ! [X2: list_P6327159017948738492od_c_a] :
            ~ ( P2 @ X2 ) ) ) ).

% empty_Collect_eq
thf(fact_136_empty__Collect__eq,axiom,
    ! [P2: b > $o] :
      ( ( bot_bot_set_b
        = ( collect_b @ P2 ) )
      = ( ! [X2: b] :
            ~ ( P2 @ X2 ) ) ) ).

% empty_Collect_eq
thf(fact_137_empty__Collect__eq,axiom,
    ! [P2: produc4859908366599477352od_d_d > $o] :
      ( ( bot_bo7612717905841165748od_d_d
        = ( collec5362705567740981075od_d_d @ P2 ) )
      = ( ! [X2: produc4859908366599477352od_d_d] :
            ~ ( P2 @ X2 ) ) ) ).

% empty_Collect_eq
thf(fact_138_empty__Collect__eq,axiom,
    ! [P2: e > $o] :
      ( ( bot_bot_set_e
        = ( collect_e @ P2 ) )
      = ( ! [X2: e] :
            ~ ( P2 @ X2 ) ) ) ).

% empty_Collect_eq
thf(fact_139__092_060open_062target_A_IFSM_Oinitial_AM_J_ApP_A_061_Aq_092_060close_062,axiom,
    ( ( target_a_b_c @ ( initial_a_b_c @ m ) @ pP )
    = q2 ) ).

% \<open>target (FSM.initial M) pP = q\<close>
thf(fact_140_singletonI,axiom,
    ! [A: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ A @ ( insert6227932334100060350od_b_c @ A @ bot_bo4166481423041325370od_b_c ) ) ).

% singletonI
thf(fact_141_singletonI,axiom,
    ! [A: list_P6327159017948738492od_c_a] : ( member7410604586820865893od_c_a @ A @ ( insert4789241225314331020od_c_a @ A @ bot_bo6236370880139903240od_c_a ) ) ).

% singletonI
thf(fact_142_singletonI,axiom,
    ! [A: a] : ( member_a @ A @ ( insert_a @ A @ bot_bot_set_a ) ) ).

% singletonI
thf(fact_143_singletonI,axiom,
    ! [A: b] : ( member_b @ A @ ( insert_b @ A @ bot_bot_set_b ) ) ).

% singletonI
thf(fact_144_singletonI,axiom,
    ! [A: produc4859908366599477352od_d_d] : ( member73601632213084689od_d_d @ A @ ( insert4898623881593564728od_d_d @ A @ bot_bo7612717905841165748od_d_d ) ) ).

% singletonI
thf(fact_145_singletonI,axiom,
    ! [A: e] : ( member_e @ A @ ( insert_e @ A @ bot_bot_set_e ) ) ).

% singletonI
thf(fact_146_fsm__initial,axiom,
    ! [M: fsm_a_b_c] : ( member_a @ ( initial_a_b_c @ M ) @ ( states_a_b_c @ M ) ) ).

% fsm_initial
thf(fact_147_fsm__initial,axiom,
    ! [M: fsm_e_b_c] : ( member_e @ ( initial_e_b_c @ M ) @ ( states_e_b_c @ M ) ) ).

% fsm_initial
thf(fact_148__092_060open_062path_AM_A_Itarget_A_IFSM_Oinitial_AM_J_ApP_J_ApM_092_060close_062,axiom,
    path_a_b_c @ m @ ( target_a_b_c @ ( initial_a_b_c @ m ) @ pP ) @ pM ).

% \<open>path M (target (FSM.initial M) pP) pM\<close>
thf(fact_149_singleton__conv2,axiom,
    ! [A: list_P6327159017948738492od_c_a] :
      ( ( collec6273869032445462695od_c_a
        @ ( ^ [Y3: list_P6327159017948738492od_c_a,Z: list_P6327159017948738492od_c_a] : ( Y3 = Z )
          @ A ) )
      = ( insert4789241225314331020od_c_a @ A @ bot_bo6236370880139903240od_c_a ) ) ).

% singleton_conv2
thf(fact_150_singleton__conv2,axiom,
    ! [A: b] :
      ( ( collect_b
        @ ( ^ [Y3: b,Z: b] : ( Y3 = Z )
          @ A ) )
      = ( insert_b @ A @ bot_bot_set_b ) ) ).

% singleton_conv2
thf(fact_151_singleton__conv2,axiom,
    ! [A: produc4859908366599477352od_d_d] :
      ( ( collec5362705567740981075od_d_d
        @ ( ^ [Y3: produc4859908366599477352od_d_d,Z: produc4859908366599477352od_d_d] : ( Y3 = Z )
          @ A ) )
      = ( insert4898623881593564728od_d_d @ A @ bot_bo7612717905841165748od_d_d ) ) ).

% singleton_conv2
thf(fact_152_singleton__conv2,axiom,
    ! [A: e] :
      ( ( collect_e
        @ ( ^ [Y3: e,Z: e] : ( Y3 = Z )
          @ A ) )
      = ( insert_e @ A @ bot_bot_set_e ) ) ).

% singleton_conv2
thf(fact_153_singleton__conv,axiom,
    ! [A: list_P6327159017948738492od_c_a] :
      ( ( collec6273869032445462695od_c_a
        @ ^ [X2: list_P6327159017948738492od_c_a] : ( X2 = A ) )
      = ( insert4789241225314331020od_c_a @ A @ bot_bo6236370880139903240od_c_a ) ) ).

% singleton_conv
thf(fact_154_singleton__conv,axiom,
    ! [A: b] :
      ( ( collect_b
        @ ^ [X2: b] : ( X2 = A ) )
      = ( insert_b @ A @ bot_bot_set_b ) ) ).

% singleton_conv
thf(fact_155_singleton__conv,axiom,
    ! [A: produc4859908366599477352od_d_d] :
      ( ( collec5362705567740981075od_d_d
        @ ^ [X2: produc4859908366599477352od_d_d] : ( X2 = A ) )
      = ( insert4898623881593564728od_d_d @ A @ bot_bo7612717905841165748od_d_d ) ) ).

% singleton_conv
thf(fact_156_singleton__conv,axiom,
    ! [A: e] :
      ( ( collect_e
        @ ^ [X2: e] : ( X2 = A ) )
      = ( insert_e @ A @ bot_bot_set_e ) ) ).

% singleton_conv
thf(fact_157_emptyE,axiom,
    ! [A: list_P903359562653991662od_b_c] :
      ~ ( member6330420149250801815od_b_c @ A @ bot_bo4166481423041325370od_b_c ) ).

% emptyE
thf(fact_158_emptyE,axiom,
    ! [A: list_P6327159017948738492od_c_a] :
      ~ ( member7410604586820865893od_c_a @ A @ bot_bo6236370880139903240od_c_a ) ).

% emptyE
thf(fact_159_emptyE,axiom,
    ! [A: a] :
      ~ ( member_a @ A @ bot_bot_set_a ) ).

% emptyE
thf(fact_160_emptyE,axiom,
    ! [A: b] :
      ~ ( member_b @ A @ bot_bot_set_b ) ).

% emptyE
thf(fact_161_emptyE,axiom,
    ! [A: produc4859908366599477352od_d_d] :
      ~ ( member73601632213084689od_d_d @ A @ bot_bo7612717905841165748od_d_d ) ).

% emptyE
thf(fact_162_emptyE,axiom,
    ! [A: e] :
      ~ ( member_e @ A @ bot_bot_set_e ) ).

% emptyE
thf(fact_163_equals0D,axiom,
    ! [A2: set_li6436108459499378894od_b_c,A: list_P903359562653991662od_b_c] :
      ( ( A2 = bot_bo4166481423041325370od_b_c )
     => ~ ( member6330420149250801815od_b_c @ A @ A2 ) ) ).

% equals0D
thf(fact_164_equals0D,axiom,
    ! [A2: set_li1159382662694783132od_c_a,A: list_P6327159017948738492od_c_a] :
      ( ( A2 = bot_bo6236370880139903240od_c_a )
     => ~ ( member7410604586820865893od_c_a @ A @ A2 ) ) ).

% equals0D
thf(fact_165_equals0D,axiom,
    ! [A2: set_a,A: a] :
      ( ( A2 = bot_bot_set_a )
     => ~ ( member_a @ A @ A2 ) ) ).

% equals0D
thf(fact_166_equals0D,axiom,
    ! [A2: set_b,A: b] :
      ( ( A2 = bot_bot_set_b )
     => ~ ( member_b @ A @ A2 ) ) ).

% equals0D
thf(fact_167_equals0D,axiom,
    ! [A2: set_Pr9130538228769002824od_d_d,A: produc4859908366599477352od_d_d] :
      ( ( A2 = bot_bo7612717905841165748od_d_d )
     => ~ ( member73601632213084689od_d_d @ A @ A2 ) ) ).

% equals0D
thf(fact_168_equals0D,axiom,
    ! [A2: set_e,A: e] :
      ( ( A2 = bot_bot_set_e )
     => ~ ( member_e @ A @ A2 ) ) ).

% equals0D
thf(fact_169_equals0I,axiom,
    ! [A2: set_li6436108459499378894od_b_c] :
      ( ! [Y4: list_P903359562653991662od_b_c] :
          ~ ( member6330420149250801815od_b_c @ Y4 @ A2 )
     => ( A2 = bot_bo4166481423041325370od_b_c ) ) ).

% equals0I
thf(fact_170_equals0I,axiom,
    ! [A2: set_li1159382662694783132od_c_a] :
      ( ! [Y4: list_P6327159017948738492od_c_a] :
          ~ ( member7410604586820865893od_c_a @ Y4 @ A2 )
     => ( A2 = bot_bo6236370880139903240od_c_a ) ) ).

% equals0I
thf(fact_171_equals0I,axiom,
    ! [A2: set_a] :
      ( ! [Y4: a] :
          ~ ( member_a @ Y4 @ A2 )
     => ( A2 = bot_bot_set_a ) ) ).

% equals0I
thf(fact_172_equals0I,axiom,
    ! [A2: set_b] :
      ( ! [Y4: b] :
          ~ ( member_b @ Y4 @ A2 )
     => ( A2 = bot_bot_set_b ) ) ).

% equals0I
thf(fact_173_equals0I,axiom,
    ! [A2: set_Pr9130538228769002824od_d_d] :
      ( ! [Y4: produc4859908366599477352od_d_d] :
          ~ ( member73601632213084689od_d_d @ Y4 @ A2 )
     => ( A2 = bot_bo7612717905841165748od_d_d ) ) ).

% equals0I
thf(fact_174_equals0I,axiom,
    ! [A2: set_e] :
      ( ! [Y4: e] :
          ~ ( member_e @ Y4 @ A2 )
     => ( A2 = bot_bot_set_e ) ) ).

% equals0I
thf(fact_175_ex__in__conv,axiom,
    ! [A2: set_li6436108459499378894od_b_c] :
      ( ( ? [X2: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ X2 @ A2 ) )
      = ( A2 != bot_bo4166481423041325370od_b_c ) ) ).

% ex_in_conv
thf(fact_176_ex__in__conv,axiom,
    ! [A2: set_li1159382662694783132od_c_a] :
      ( ( ? [X2: list_P6327159017948738492od_c_a] : ( member7410604586820865893od_c_a @ X2 @ A2 ) )
      = ( A2 != bot_bo6236370880139903240od_c_a ) ) ).

% ex_in_conv
thf(fact_177_ex__in__conv,axiom,
    ! [A2: set_a] :
      ( ( ? [X2: a] : ( member_a @ X2 @ A2 ) )
      = ( A2 != bot_bot_set_a ) ) ).

% ex_in_conv
thf(fact_178_ex__in__conv,axiom,
    ! [A2: set_b] :
      ( ( ? [X2: b] : ( member_b @ X2 @ A2 ) )
      = ( A2 != bot_bot_set_b ) ) ).

% ex_in_conv
thf(fact_179_ex__in__conv,axiom,
    ! [A2: set_Pr9130538228769002824od_d_d] :
      ( ( ? [X2: produc4859908366599477352od_d_d] : ( member73601632213084689od_d_d @ X2 @ A2 ) )
      = ( A2 != bot_bo7612717905841165748od_d_d ) ) ).

% ex_in_conv
thf(fact_180_ex__in__conv,axiom,
    ! [A2: set_e] :
      ( ( ? [X2: e] : ( member_e @ X2 @ A2 ) )
      = ( A2 != bot_bot_set_e ) ) ).

% ex_in_conv
thf(fact_181_Set_Oempty__def,axiom,
    ( bot_bo6236370880139903240od_c_a
    = ( collec6273869032445462695od_c_a
      @ ^ [X2: list_P6327159017948738492od_c_a] : $false ) ) ).

% Set.empty_def
thf(fact_182_Set_Oempty__def,axiom,
    ( bot_bot_set_b
    = ( collect_b
      @ ^ [X2: b] : $false ) ) ).

% Set.empty_def
thf(fact_183_Set_Oempty__def,axiom,
    ( bot_bo7612717905841165748od_d_d
    = ( collec5362705567740981075od_d_d
      @ ^ [X2: produc4859908366599477352od_d_d] : $false ) ) ).

% Set.empty_def
thf(fact_184_Set_Oempty__def,axiom,
    ( bot_bot_set_e
    = ( collect_e
      @ ^ [X2: e] : $false ) ) ).

% Set.empty_def
thf(fact_185_some__in__eq,axiom,
    ! [A2: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c
        @ ( fChoic3287323656706165826od_b_c
          @ ^ [X2: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ X2 @ A2 ) )
        @ A2 )
      = ( A2 != bot_bo4166481423041325370od_b_c ) ) ).

% some_in_eq
thf(fact_186_some__in__eq,axiom,
    ! [A2: set_a] :
      ( ( member_a
        @ ( fChoice_a
          @ ^ [X2: a] : ( member_a @ X2 @ A2 ) )
        @ A2 )
      = ( A2 != bot_bot_set_a ) ) ).

% some_in_eq
thf(fact_187_some__in__eq,axiom,
    ! [A2: set_li1159382662694783132od_c_a] :
      ( ( member7410604586820865893od_c_a
        @ ( fChoic6541264315744621840od_c_a
          @ ^ [X2: list_P6327159017948738492od_c_a] : ( member7410604586820865893od_c_a @ X2 @ A2 ) )
        @ A2 )
      = ( A2 != bot_bo6236370880139903240od_c_a ) ) ).

% some_in_eq
thf(fact_188_some__in__eq,axiom,
    ! [A2: set_b] :
      ( ( member_b
        @ ( fChoice_b
          @ ^ [X2: b] : ( member_b @ X2 @ A2 ) )
        @ A2 )
      = ( A2 != bot_bot_set_b ) ) ).

% some_in_eq
thf(fact_189_some__in__eq,axiom,
    ! [A2: set_Pr9130538228769002824od_d_d] :
      ( ( member73601632213084689od_d_d
        @ ( fChoic8563934328396083644od_d_d
          @ ^ [X2: produc4859908366599477352od_d_d] : ( member73601632213084689od_d_d @ X2 @ A2 ) )
        @ A2 )
      = ( A2 != bot_bo7612717905841165748od_d_d ) ) ).

% some_in_eq
thf(fact_190_some__in__eq,axiom,
    ! [A2: set_e] :
      ( ( member_e
        @ ( fChoice_e
          @ ^ [X2: e] : ( member_e @ X2 @ A2 ) )
        @ A2 )
      = ( A2 != bot_bot_set_e ) ) ).

% some_in_eq
thf(fact_191_minimal__sequence__to__failure__extending__preamble__path__def,axiom,
    ( state_7720781447231630558_b_c_e
    = ( ^ [M2: fsm_a_b_c,M3: fsm_e_b_c,PS: set_Pr2640454425625433516_a_b_c,P: list_P6327159017948738492od_c_a,Io3: list_P903359562653991662od_b_c] :
          ( ( state_5244820657802497663_b_c_e @ M2 @ M3 @ PS @ P @ Io3 )
          & ! [P4: list_P6327159017948738492od_c_a,Io4: list_P903359562653991662od_b_c] :
              ( ( state_5244820657802497663_b_c_e @ M2 @ M3 @ PS @ P4 @ Io4 )
             => ( ord_less_eq_nat @ ( size_s3392097710323735898od_b_c @ Io3 ) @ ( size_s3392097710323735898od_b_c @ Io4 ) ) ) ) ) ) ).

% minimal_sequence_to_failure_extending_preamble_path_def
thf(fact_192_singletonD,axiom,
    ! [B2: list_P903359562653991662od_b_c,A: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ B2 @ ( insert6227932334100060350od_b_c @ A @ bot_bo4166481423041325370od_b_c ) )
     => ( B2 = A ) ) ).

% singletonD
thf(fact_193_singletonD,axiom,
    ! [B2: list_P6327159017948738492od_c_a,A: list_P6327159017948738492od_c_a] :
      ( ( member7410604586820865893od_c_a @ B2 @ ( insert4789241225314331020od_c_a @ A @ bot_bo6236370880139903240od_c_a ) )
     => ( B2 = A ) ) ).

% singletonD
thf(fact_194_singletonD,axiom,
    ! [B2: a,A: a] :
      ( ( member_a @ B2 @ ( insert_a @ A @ bot_bot_set_a ) )
     => ( B2 = A ) ) ).

% singletonD
thf(fact_195_singletonD,axiom,
    ! [B2: b,A: b] :
      ( ( member_b @ B2 @ ( insert_b @ A @ bot_bot_set_b ) )
     => ( B2 = A ) ) ).

% singletonD
thf(fact_196_singletonD,axiom,
    ! [B2: produc4859908366599477352od_d_d,A: produc4859908366599477352od_d_d] :
      ( ( member73601632213084689od_d_d @ B2 @ ( insert4898623881593564728od_d_d @ A @ bot_bo7612717905841165748od_d_d ) )
     => ( B2 = A ) ) ).

% singletonD
thf(fact_197_singletonD,axiom,
    ! [B2: e,A: e] :
      ( ( member_e @ B2 @ ( insert_e @ A @ bot_bot_set_e ) )
     => ( B2 = A ) ) ).

% singletonD
thf(fact_198_singleton__iff,axiom,
    ! [B2: list_P903359562653991662od_b_c,A: list_P903359562653991662od_b_c] :
      ( ( member6330420149250801815od_b_c @ B2 @ ( insert6227932334100060350od_b_c @ A @ bot_bo4166481423041325370od_b_c ) )
      = ( B2 = A ) ) ).

% singleton_iff
thf(fact_199_singleton__iff,axiom,
    ! [B2: list_P6327159017948738492od_c_a,A: list_P6327159017948738492od_c_a] :
      ( ( member7410604586820865893od_c_a @ B2 @ ( insert4789241225314331020od_c_a @ A @ bot_bo6236370880139903240od_c_a ) )
      = ( B2 = A ) ) ).

% singleton_iff
thf(fact_200_singleton__iff,axiom,
    ! [B2: a,A: a] :
      ( ( member_a @ B2 @ ( insert_a @ A @ bot_bot_set_a ) )
      = ( B2 = A ) ) ).

% singleton_iff
thf(fact_201_singleton__iff,axiom,
    ! [B2: b,A: b] :
      ( ( member_b @ B2 @ ( insert_b @ A @ bot_bot_set_b ) )
      = ( B2 = A ) ) ).

% singleton_iff
thf(fact_202_singleton__iff,axiom,
    ! [B2: produc4859908366599477352od_d_d,A: produc4859908366599477352od_d_d] :
      ( ( member73601632213084689od_d_d @ B2 @ ( insert4898623881593564728od_d_d @ A @ bot_bo7612717905841165748od_d_d ) )
      = ( B2 = A ) ) ).

% singleton_iff
thf(fact_203_singleton__iff,axiom,
    ! [B2: e,A: e] :
      ( ( member_e @ B2 @ ( insert_e @ A @ bot_bot_set_e ) )
      = ( B2 = A ) ) ).

% singleton_iff
thf(fact_204_doubleton__eq__iff,axiom,
    ! [A: list_P6327159017948738492od_c_a,B2: list_P6327159017948738492od_c_a,C2: list_P6327159017948738492od_c_a,D: list_P6327159017948738492od_c_a] :
      ( ( ( insert4789241225314331020od_c_a @ A @ ( insert4789241225314331020od_c_a @ B2 @ bot_bo6236370880139903240od_c_a ) )
        = ( insert4789241225314331020od_c_a @ C2 @ ( insert4789241225314331020od_c_a @ D @ bot_bo6236370880139903240od_c_a ) ) )
      = ( ( ( A = C2 )
          & ( B2 = D ) )
        | ( ( A = D )
          & ( B2 = C2 ) ) ) ) ).

% doubleton_eq_iff
thf(fact_205_doubleton__eq__iff,axiom,
    ! [A: b,B2: b,C2: b,D: b] :
      ( ( ( insert_b @ A @ ( insert_b @ B2 @ bot_bot_set_b ) )
        = ( insert_b @ C2 @ ( insert_b @ D @ bot_bot_set_b ) ) )
      = ( ( ( A = C2 )
          & ( B2 = D ) )
        | ( ( A = D )
          & ( B2 = C2 ) ) ) ) ).

% doubleton_eq_iff
thf(fact_206_doubleton__eq__iff,axiom,
    ! [A: produc4859908366599477352od_d_d,B2: produc4859908366599477352od_d_d,C2: produc4859908366599477352od_d_d,D: produc4859908366599477352od_d_d] :
      ( ( ( insert4898623881593564728od_d_d @ A @ ( insert4898623881593564728od_d_d @ B2 @ bot_bo7612717905841165748od_d_d ) )
        = ( insert4898623881593564728od_d_d @ C2 @ ( insert4898623881593564728od_d_d @ D @ bot_bo7612717905841165748od_d_d ) ) )
      = ( ( ( A = C2 )
          & ( B2 = D ) )
        | ( ( A = D )
          & ( B2 = C2 ) ) ) ) ).

% doubleton_eq_iff
thf(fact_207_doubleton__eq__iff,axiom,
    ! [A: e,B2: e,C2: e,D: e] :
      ( ( ( insert_e @ A @ ( insert_e @ B2 @ bot_bot_set_e ) )
        = ( insert_e @ C2 @ ( insert_e @ D @ bot_bot_set_e ) ) )
      = ( ( ( A = C2 )
          & ( B2 = D ) )
        | ( ( A = D )
          & ( B2 = C2 ) ) ) ) ).

% doubleton_eq_iff
thf(fact_208_insert__not__empty,axiom,
    ! [A: list_P6327159017948738492od_c_a,A2: set_li1159382662694783132od_c_a] :
      ( ( insert4789241225314331020od_c_a @ A @ A2 )
     != bot_bo6236370880139903240od_c_a ) ).

% insert_not_empty
thf(fact_209_insert__not__empty,axiom,
    ! [A: b,A2: set_b] :
      ( ( insert_b @ A @ A2 )
     != bot_bot_set_b ) ).

% insert_not_empty
thf(fact_210_insert__not__empty,axiom,
    ! [A: produc4859908366599477352od_d_d,A2: set_Pr9130538228769002824od_d_d] :
      ( ( insert4898623881593564728od_d_d @ A @ A2 )
     != bot_bo7612717905841165748od_d_d ) ).

% insert_not_empty
thf(fact_211_insert__not__empty,axiom,
    ! [A: e,A2: set_e] :
      ( ( insert_e @ A @ A2 )
     != bot_bot_set_e ) ).

% insert_not_empty
thf(fact_212_singleton__inject,axiom,
    ! [A: list_P6327159017948738492od_c_a,B2: list_P6327159017948738492od_c_a] :
      ( ( ( insert4789241225314331020od_c_a @ A @ bot_bo6236370880139903240od_c_a )
        = ( insert4789241225314331020od_c_a @ B2 @ bot_bo6236370880139903240od_c_a ) )
     => ( A = B2 ) ) ).

% singleton_inject
thf(fact_213_singleton__inject,axiom,
    ! [A: b,B2: b] :
      ( ( ( insert_b @ A @ bot_bot_set_b )
        = ( insert_b @ B2 @ bot_bot_set_b ) )
     => ( A = B2 ) ) ).

% singleton_inject
thf(fact_214_singleton__inject,axiom,
    ! [A: produc4859908366599477352od_d_d,B2: produc4859908366599477352od_d_d] :
      ( ( ( insert4898623881593564728od_d_d @ A @ bot_bo7612717905841165748od_d_d )
        = ( insert4898623881593564728od_d_d @ B2 @ bot_bo7612717905841165748od_d_d ) )
     => ( A = B2 ) ) ).

% singleton_inject
thf(fact_215_singleton__inject,axiom,
    ! [A: e,B2: e] :
      ( ( ( insert_e @ A @ bot_bot_set_e )
        = ( insert_e @ B2 @ bot_bot_set_e ) )
     => ( A = B2 ) ) ).

% singleton_inject
thf(fact_216_path__target__is__state,axiom,
    ! [M: fsm_a_b_c,Q3: a,P3: list_P6327159017948738492od_c_a] :
      ( ( path_a_b_c @ M @ Q3 @ P3 )
     => ( member_a @ ( target_a_b_c @ Q3 @ P3 ) @ ( states_a_b_c @ M ) ) ) ).

% path_target_is_state
thf(fact_217_Collect__conv__if2,axiom,
    ! [P2: list_P6327159017948738492od_c_a > $o,A: list_P6327159017948738492od_c_a] :
      ( ( ( P2 @ A )
       => ( ( collec6273869032445462695od_c_a
            @ ^ [X2: list_P6327159017948738492od_c_a] :
                ( ( A = X2 )
                & ( P2 @ X2 ) ) )
          = ( insert4789241225314331020od_c_a @ A @ bot_bo6236370880139903240od_c_a ) ) )
      & ( ~ ( P2 @ A )
       => ( ( collec6273869032445462695od_c_a
            @ ^ [X2: list_P6327159017948738492od_c_a] :
                ( ( A = X2 )
                & ( P2 @ X2 ) ) )
          = bot_bo6236370880139903240od_c_a ) ) ) ).

% Collect_conv_if2
thf(fact_218_Collect__conv__if2,axiom,
    ! [P2: b > $o,A: b] :
      ( ( ( P2 @ A )
       => ( ( collect_b
            @ ^ [X2: b] :
                ( ( A = X2 )
                & ( P2 @ X2 ) ) )
          = ( insert_b @ A @ bot_bot_set_b ) ) )
      & ( ~ ( P2 @ A )
       => ( ( collect_b
            @ ^ [X2: b] :
                ( ( A = X2 )
                & ( P2 @ X2 ) ) )
          = bot_bot_set_b ) ) ) ).

% Collect_conv_if2
thf(fact_219_Collect__conv__if2,axiom,
    ! [P2: produc4859908366599477352od_d_d > $o,A: produc4859908366599477352od_d_d] :
      ( ( ( P2 @ A )
       => ( ( collec5362705567740981075od_d_d
            @ ^ [X2: produc4859908366599477352od_d_d] :
                ( ( A = X2 )
                & ( P2 @ X2 ) ) )
          = ( insert4898623881593564728od_d_d @ A @ bot_bo7612717905841165748od_d_d ) ) )
      & ( ~ ( P2 @ A )
       => ( ( collec5362705567740981075od_d_d
            @ ^ [X2: produc4859908366599477352od_d_d] :
                ( ( A = X2 )
                & ( P2 @ X2 ) ) )
          = bot_bo7612717905841165748od_d_d ) ) ) ).

% Collect_conv_if2
thf(fact_220_Collect__conv__if2,axiom,
    ! [P2: e > $o,A: e] :
      ( ( ( P2 @ A )
       => ( ( collect_e
            @ ^ [X2: e] :
                ( ( A = X2 )
                & ( P2 @ X2 ) ) )
          = ( insert_e @ A @ bot_bot_set_e ) ) )
      & ( ~ ( P2 @ A )
       => ( ( collect_e
            @ ^ [X2: e] :
                ( ( A = X2 )
                & ( P2 @ X2 ) ) )
          = bot_bot_set_e ) ) ) ).

% Collect_conv_if2
thf(fact_221_Collect__conv__if,axiom,
    ! [P2: list_P6327159017948738492od_c_a > $o,A: list_P6327159017948738492od_c_a] :
      ( ( ( P2 @ A )
       => ( ( collec6273869032445462695od_c_a
            @ ^ [X2: list_P6327159017948738492od_c_a] :
                ( ( X2 = A )
                & ( P2 @ X2 ) ) )
          = ( insert4789241225314331020od_c_a @ A @ bot_bo6236370880139903240od_c_a ) ) )
      & ( ~ ( P2 @ A )
       => ( ( collec6273869032445462695od_c_a
            @ ^ [X2: list_P6327159017948738492od_c_a] :
                ( ( X2 = A )
                & ( P2 @ X2 ) ) )
          = bot_bo6236370880139903240od_c_a ) ) ) ).

% Collect_conv_if
thf(fact_222_Collect__conv__if,axiom,
    ! [P2: b > $o,A: b] :
      ( ( ( P2 @ A )
       => ( ( collect_b
            @ ^ [X2: b] :
                ( ( X2 = A )
                & ( P2 @ X2 ) ) )
          = ( insert_b @ A @ bot_bot_set_b ) ) )
      & ( ~ ( P2 @ A )
       => ( ( collect_b
            @ ^ [X2: b] :
                ( ( X2 = A )
                & ( P2 @ X2 ) ) )
          = bot_bot_set_b ) ) ) ).

% Collect_conv_if
thf(fact_223_Collect__conv__if,axiom,
    ! [P2: produc4859908366599477352od_d_d > $o,A: produc4859908366599477352od_d_d] :
      ( ( ( P2 @ A )
       => ( ( collec5362705567740981075od_d_d
            @ ^ [X2: produc4859908366599477352od_d_d] :
                ( ( X2 = A )
                & ( P2 @ X2 ) ) )
          = ( insert4898623881593564728od_d_d @ A @ bot_bo7612717905841165748od_d_d ) ) )
      & ( ~ ( P2 @ A )
       => ( ( collec5362705567740981075od_d_d
            @ ^ [X2: produc4859908366599477352od_d_d] :
                ( ( X2 = A )
                & ( P2 @ X2 ) ) )
          = bot_bo7612717905841165748od_d_d ) ) ) ).

% Collect_conv_if
thf(fact_224_Collect__conv__if,axiom,
    ! [P2: e > $o,A: e] :
      ( ( ( P2 @ A )
       => ( ( collect_e
            @ ^ [X2: e] :
                ( ( X2 = A )
                & ( P2 @ X2 ) ) )
          = ( insert_e @ A @ bot_bot_set_e ) ) )
      & ( ~ ( P2 @ A )
       => ( ( collect_e
            @ ^ [X2: e] :
                ( ( X2 = A )
                & ( P2 @ X2 ) ) )
          = bot_bot_set_e ) ) ) ).

% Collect_conv_if
thf(fact_225_Pair__inject,axiom,
    ! [A: d,B2: d,A4: d,B5: d] :
      ( ( ( product_Pair_d_d @ A @ B2 )
        = ( product_Pair_d_d @ A4 @ B5 ) )
     => ~ ( ( A = A4 )
         => ( B2 != B5 ) ) ) ).

% Pair_inject
thf(fact_226_Pair__inject,axiom,
    ! [A: b,B2: c,A4: b,B5: c] :
      ( ( ( product_Pair_b_c @ A @ B2 )
        = ( product_Pair_b_c @ A4 @ B5 ) )
     => ~ ( ( A = A4 )
         => ( B2 != B5 ) ) ) ).

% Pair_inject
thf(fact_227_Pair__inject,axiom,
    ! [A: a,B2: list_P6327159017948738492od_c_a,A4: a,B5: list_P6327159017948738492od_c_a] :
      ( ( ( produc3580641852002036821od_c_a @ A @ B2 )
        = ( produc3580641852002036821od_c_a @ A4 @ B5 ) )
     => ~ ( ( A = A4 )
         => ( B2 != B5 ) ) ) ).

% Pair_inject
thf(fact_228_Pair__inject,axiom,
    ! [A: a,B2: fsm_a_b_c,A4: a,B5: fsm_a_b_c] :
      ( ( ( produc2795441082327197628_a_b_c @ A @ B2 )
        = ( produc2795441082327197628_a_b_c @ A4 @ B5 ) )
     => ~ ( ( A = A4 )
         => ( B2 != B5 ) ) ) ).

% Pair_inject
thf(fact_229_Pair__inject,axiom,
    ! [A: a,B2: a,A4: a,B5: a] :
      ( ( ( product_Pair_a_a @ A @ B2 )
        = ( product_Pair_a_a @ A4 @ B5 ) )
     => ~ ( ( A = A4 )
         => ( B2 != B5 ) ) ) ).

% Pair_inject
thf(fact_230_prod__cases,axiom,
    ! [P2: product_prod_d_d > $o,P3: product_prod_d_d] :
      ( ! [A5: d,B6: d] : ( P2 @ ( product_Pair_d_d @ A5 @ B6 ) )
     => ( P2 @ P3 ) ) ).

% prod_cases
thf(fact_231_prod__cases,axiom,
    ! [P2: product_prod_b_c > $o,P3: product_prod_b_c] :
      ( ! [A5: b,B6: c] : ( P2 @ ( product_Pair_b_c @ A5 @ B6 ) )
     => ( P2 @ P3 ) ) ).

% prod_cases
thf(fact_232_prod__cases,axiom,
    ! [P2: produc3220416805844688357od_c_a > $o,P3: produc3220416805844688357od_c_a] :
      ( ! [A5: a,B6: list_P6327159017948738492od_c_a] : ( P2 @ ( produc3580641852002036821od_c_a @ A5 @ B6 ) )
     => ( P2 @ P3 ) ) ).

% prod_cases
thf(fact_233_prod__cases,axiom,
    ! [P2: produc8838969699183119820_a_b_c > $o,P3: produc8838969699183119820_a_b_c] :
      ( ! [A5: a,B6: fsm_a_b_c] : ( P2 @ ( produc2795441082327197628_a_b_c @ A5 @ B6 ) )
     => ( P2 @ P3 ) ) ).

% prod_cases
thf(fact_234_prod__cases,axiom,
    ! [P2: product_prod_a_a > $o,P3: product_prod_a_a] :
      ( ! [A5: a,B6: a] : ( P2 @ ( product_Pair_a_a @ A5 @ B6 ) )
     => ( P2 @ P3 ) ) ).

% prod_cases
thf(fact_235_surj__pair,axiom,
    ! [P3: product_prod_d_d] :
    ? [X3: d,Y4: d] :
      ( P3
      = ( product_Pair_d_d @ X3 @ Y4 ) ) ).

% surj_pair
thf(fact_236_surj__pair,axiom,
    ! [P3: product_prod_b_c] :
    ? [X3: b,Y4: c] :
      ( P3
      = ( product_Pair_b_c @ X3 @ Y4 ) ) ).

% surj_pair
thf(fact_237_surj__pair,axiom,
    ! [P3: produc3220416805844688357od_c_a] :
    ? [X3: a,Y4: list_P6327159017948738492od_c_a] :
      ( P3
      = ( produc3580641852002036821od_c_a @ X3 @ Y4 ) ) ).

% surj_pair
thf(fact_238_surj__pair,axiom,
    ! [P3: produc8838969699183119820_a_b_c] :
    ? [X3: a,Y4: fsm_a_b_c] :
      ( P3
      = ( produc2795441082327197628_a_b_c @ X3 @ Y4 ) ) ).

% surj_pair
thf(fact_239_surj__pair,axiom,
    ! [P3: product_prod_a_a] :
    ? [X3: a,Y4: a] :
      ( P3
      = ( product_Pair_a_a @ X3 @ Y4 ) ) ).

% surj_pair
thf(fact_240_old_Oprod_Oexhaust,axiom,
    ! [Y: product_prod_d_d] :
      ~ ! [A5: d,B6: d] :
          ( Y
         != ( product_Pair_d_d @ A5 @ B6 ) ) ).

% old.prod.exhaust
thf(fact_241_old_Oprod_Oexhaust,axiom,
    ! [Y: product_prod_b_c] :
      ~ ! [A5: b,B6: c] :
          ( Y
         != ( product_Pair_b_c @ A5 @ B6 ) ) ).

% old.prod.exhaust
thf(fact_242_old_Oprod_Oexhaust,axiom,
    ! [Y: produc3220416805844688357od_c_a] :
      ~ ! [A5: a,B6: list_P6327159017948738492od_c_a] :
          ( Y
         != ( produc3580641852002036821od_c_a @ A5 @ B6 ) ) ).

% old.prod.exhaust
thf(fact_243_old_Oprod_Oexhaust,axiom,
    ! [Y: produc8838969699183119820_a_b_c] :
      ~ ! [A5: a,B6: fsm_a_b_c] :
          ( Y
         != ( produc2795441082327197628_a_b_c @ A5 @ B6 ) ) ).

% old.prod.exhaust
thf(fact_244_old_Oprod_Oexhaust,axiom,
    ! [Y: product_prod_a_a] :
      ~ ! [A5: a,B6: a] :
          ( Y
         != ( product_Pair_a_a @ A5 @ B6 ) ) ).

% old.prod.exhaust
thf(fact_245_some__eq__imp,axiom,
    ! [P2: list_P6327159017948738492od_c_a > $o,A: list_P6327159017948738492od_c_a,B2: list_P6327159017948738492od_c_a] :
      ( ( ( fChoic6541264315744621840od_c_a @ P2 )
        = A )
     => ( ( P2 @ B2 )
       => ( P2 @ A ) ) ) ).

% some_eq_imp
thf(fact_246_tfl__some,axiom,
    ! [P5: list_P6327159017948738492od_c_a > $o,X4: list_P6327159017948738492od_c_a] :
      ( ( P5 @ X4 )
     => ( P5 @ ( fChoic6541264315744621840od_c_a @ P5 ) ) ) ).

% tfl_some
thf(fact_247_Eps__cong,axiom,
    ! [P2: list_P6327159017948738492od_c_a > $o,Q4: list_P6327159017948738492od_c_a > $o] :
      ( ! [X3: list_P6327159017948738492od_c_a] :
          ( ( P2 @ X3 )
          = ( Q4 @ X3 ) )
     => ( ( fChoic6541264315744621840od_c_a @ P2 )
        = ( fChoic6541264315744621840od_c_a @ Q4 ) ) ) ).

% Eps_cong
thf(fact_248_someI,axiom,
    ! [P2: list_P6327159017948738492od_c_a > $o,X: list_P6327159017948738492od_c_a] :
      ( ( P2 @ X )
     => ( P2 @ ( fChoic6541264315744621840od_c_a @ P2 ) ) ) ).

% someI
thf(fact_249_some1__equality,axiom,
    ! [P2: list_P6327159017948738492od_c_a > $o,A: list_P6327159017948738492od_c_a] :
      ( ? [X4: list_P6327159017948738492od_c_a] :
          ( ( P2 @ X4 )
          & ! [Y4: list_P6327159017948738492od_c_a] :
              ( ( P2 @ Y4 )
             => ( Y4 = X4 ) ) )
     => ( ( P2 @ A )
       => ( ( fChoic6541264315744621840od_c_a @ P2 )
          = A ) ) ) ).

% some1_equality
thf(fact_250_some__eq__ex,axiom,
    ! [P2: list_P6327159017948738492od_c_a > $o] :
      ( ( P2 @ ( fChoic6541264315744621840od_c_a @ P2 ) )
      = ( ? [X5: list_P6327159017948738492od_c_a] : ( P2 @ X5 ) ) ) ).

% some_eq_ex
thf(fact_251_someI2__bex,axiom,
    ! [A2: set_li6436108459499378894od_b_c,P2: list_P903359562653991662od_b_c > $o,Q4: list_P903359562653991662od_b_c > $o] :
      ( ? [X4: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X4 @ A2 )
          & ( P2 @ X4 ) )
     => ( ! [X3: list_P903359562653991662od_b_c] :
            ( ( ( member6330420149250801815od_b_c @ X3 @ A2 )
              & ( P2 @ X3 ) )
           => ( Q4 @ X3 ) )
       => ( Q4
          @ ( fChoic3287323656706165826od_b_c
            @ ^ [X2: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ X2 @ A2 )
                & ( P2 @ X2 ) ) ) ) ) ) ).

% someI2_bex
thf(fact_252_someI2__bex,axiom,
    ! [A2: set_e,P2: e > $o,Q4: e > $o] :
      ( ? [X4: e] :
          ( ( member_e @ X4 @ A2 )
          & ( P2 @ X4 ) )
     => ( ! [X3: e] :
            ( ( ( member_e @ X3 @ A2 )
              & ( P2 @ X3 ) )
           => ( Q4 @ X3 ) )
       => ( Q4
          @ ( fChoice_e
            @ ^ [X2: e] :
                ( ( member_e @ X2 @ A2 )
                & ( P2 @ X2 ) ) ) ) ) ) ).

% someI2_bex
thf(fact_253_someI2__bex,axiom,
    ! [A2: set_b,P2: b > $o,Q4: b > $o] :
      ( ? [X4: b] :
          ( ( member_b @ X4 @ A2 )
          & ( P2 @ X4 ) )
     => ( ! [X3: b] :
            ( ( ( member_b @ X3 @ A2 )
              & ( P2 @ X3 ) )
           => ( Q4 @ X3 ) )
       => ( Q4
          @ ( fChoice_b
            @ ^ [X2: b] :
                ( ( member_b @ X2 @ A2 )
                & ( P2 @ X2 ) ) ) ) ) ) ).

% someI2_bex
thf(fact_254_someI2__bex,axiom,
    ! [A2: set_a,P2: a > $o,Q4: a > $o] :
      ( ? [X4: a] :
          ( ( member_a @ X4 @ A2 )
          & ( P2 @ X4 ) )
     => ( ! [X3: a] :
            ( ( ( member_a @ X3 @ A2 )
              & ( P2 @ X3 ) )
           => ( Q4 @ X3 ) )
       => ( Q4
          @ ( fChoice_a
            @ ^ [X2: a] :
                ( ( member_a @ X2 @ A2 )
                & ( P2 @ X2 ) ) ) ) ) ) ).

% someI2_bex
thf(fact_255_someI2__bex,axiom,
    ! [A2: set_li1159382662694783132od_c_a,P2: list_P6327159017948738492od_c_a > $o,Q4: list_P6327159017948738492od_c_a > $o] :
      ( ? [X4: list_P6327159017948738492od_c_a] :
          ( ( member7410604586820865893od_c_a @ X4 @ A2 )
          & ( P2 @ X4 ) )
     => ( ! [X3: list_P6327159017948738492od_c_a] :
            ( ( ( member7410604586820865893od_c_a @ X3 @ A2 )
              & ( P2 @ X3 ) )
           => ( Q4 @ X3 ) )
       => ( Q4
          @ ( fChoic6541264315744621840od_c_a
            @ ^ [X2: list_P6327159017948738492od_c_a] :
                ( ( member7410604586820865893od_c_a @ X2 @ A2 )
                & ( P2 @ X2 ) ) ) ) ) ) ).

% someI2_bex
thf(fact_256_someI2__ex,axiom,
    ! [P2: list_P6327159017948738492od_c_a > $o,Q4: list_P6327159017948738492od_c_a > $o] :
      ( ? [X_1: list_P6327159017948738492od_c_a] : ( P2 @ X_1 )
     => ( ! [X3: list_P6327159017948738492od_c_a] :
            ( ( P2 @ X3 )
           => ( Q4 @ X3 ) )
       => ( Q4 @ ( fChoic6541264315744621840od_c_a @ P2 ) ) ) ) ).

% someI2_ex
thf(fact_257_someI__ex,axiom,
    ! [P2: list_P6327159017948738492od_c_a > $o] :
      ( ? [X_1: list_P6327159017948738492od_c_a] : ( P2 @ X_1 )
     => ( P2 @ ( fChoic6541264315744621840od_c_a @ P2 ) ) ) ).

% someI_ex
thf(fact_258_someI2,axiom,
    ! [P2: list_P6327159017948738492od_c_a > $o,A: list_P6327159017948738492od_c_a,Q4: list_P6327159017948738492od_c_a > $o] :
      ( ( P2 @ A )
     => ( ! [X3: list_P6327159017948738492od_c_a] :
            ( ( P2 @ X3 )
           => ( Q4 @ X3 ) )
       => ( Q4 @ ( fChoic6541264315744621840od_c_a @ P2 ) ) ) ) ).

% someI2
thf(fact_259_snd__conv,axiom,
    ! [X1: d,X22: d] :
      ( ( product_snd_d_d @ ( product_Pair_d_d @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_260_snd__conv,axiom,
    ! [X1: a,X22: list_P6327159017948738492od_c_a] :
      ( ( produc5527568727691618435od_c_a @ ( produc3580641852002036821od_c_a @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_261_snd__conv,axiom,
    ! [X1: a,X22: fsm_a_b_c] :
      ( ( produc4728557313310798826_a_b_c @ ( produc2795441082327197628_a_b_c @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_262_snd__conv,axiom,
    ! [X1: a,X22: a] :
      ( ( product_snd_a_a @ ( product_Pair_a_a @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_263_snd__conv,axiom,
    ! [X1: set_a,X22: set_a] :
      ( ( produc1983107199584856133_set_a @ ( produc9088192753505129239_set_a @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_264_snd__conv,axiom,
    ! [X1: a,X22: produc2133359284458116493od_c_a] :
      ( ( produc8088130389382527188od_c_a @ ( produc5762801557034676134od_c_a @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_265_snd__conv,axiom,
    ! [X1: b,X22: product_prod_c_a] :
      ( ( produc5221446324160585515od_c_a @ ( produc3440865914000881661od_c_a @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_266_snd__conv,axiom,
    ! [X1: b,X22: c] :
      ( ( product_snd_b_c @ ( product_Pair_b_c @ X1 @ X22 ) )
      = X22 ) ).

% snd_conv
thf(fact_267_snd__eqD,axiom,
    ! [X: d,Y: d,A: d] :
      ( ( ( product_snd_d_d @ ( product_Pair_d_d @ X @ Y ) )
        = A )
     => ( Y = A ) ) ).

% snd_eqD
thf(fact_268_snd__eqD,axiom,
    ! [X: a,Y: list_P6327159017948738492od_c_a,A: list_P6327159017948738492od_c_a] :
      ( ( ( produc5527568727691618435od_c_a @ ( produc3580641852002036821od_c_a @ X @ Y ) )
        = A )
     => ( Y = A ) ) ).

% snd_eqD
thf(fact_269_snd__eqD,axiom,
    ! [X: a,Y: fsm_a_b_c,A: fsm_a_b_c] :
      ( ( ( produc4728557313310798826_a_b_c @ ( produc2795441082327197628_a_b_c @ X @ Y ) )
        = A )
     => ( Y = A ) ) ).

% snd_eqD
thf(fact_270_snd__eqD,axiom,
    ! [X: a,Y: a,A: a] :
      ( ( ( product_snd_a_a @ ( product_Pair_a_a @ X @ Y ) )
        = A )
     => ( Y = A ) ) ).

% snd_eqD
thf(fact_271_snd__eqD,axiom,
    ! [X: set_a,Y: set_a,A: set_a] :
      ( ( ( produc1983107199584856133_set_a @ ( produc9088192753505129239_set_a @ X @ Y ) )
        = A )
     => ( Y = A ) ) ).

% snd_eqD
thf(fact_272_snd__eqD,axiom,
    ! [X: a,Y: produc2133359284458116493od_c_a,A: produc2133359284458116493od_c_a] :
      ( ( ( produc8088130389382527188od_c_a @ ( produc5762801557034676134od_c_a @ X @ Y ) )
        = A )
     => ( Y = A ) ) ).

% snd_eqD
thf(fact_273_snd__eqD,axiom,
    ! [X: b,Y: product_prod_c_a,A: product_prod_c_a] :
      ( ( ( produc5221446324160585515od_c_a @ ( produc3440865914000881661od_c_a @ X @ Y ) )
        = A )
     => ( Y = A ) ) ).

% snd_eqD
thf(fact_274_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_275_t1,axiom,
    member997585926662434933_a_b_c @ ( produc2795441082327197628_a_b_c @ ( initial_a_b_c @ m ) @ ( state_4132440018836379711_a_b_c @ m ) ) @ prs ).

% t1
thf(fact_276_reachable__def,axiom,
    ( reachable_a_b_c
    = ( ^ [M2: fsm_a_b_c,Q5: a] :
        ? [P: list_P6327159017948738492od_c_a] :
          ( ( path_a_b_c @ M2 @ ( initial_a_b_c @ M2 ) @ P )
          & ( ( target_a_b_c @ ( initial_a_b_c @ M2 ) @ P )
            = Q5 ) ) ) ) ).

% reachable_def
thf(fact_277_reachable__def,axiom,
    ( reachable_e_b_c
    = ( ^ [M2: fsm_e_b_c,Q5: e] :
        ? [P: list_P1631280100260380348od_c_e] :
          ( ( path_e_b_c @ M2 @ ( initial_e_b_c @ M2 ) @ P )
          & ( ( target_e_b_c @ ( initial_e_b_c @ M2 ) @ P )
            = Q5 ) ) ) ) ).

% reachable_def
thf(fact_278_dual__order_Orefl,axiom,
    ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).

% dual_order.refl
thf(fact_279_dual__order_Orefl,axiom,
    ! [A: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ A @ A ) ).

% dual_order.refl
thf(fact_280_dual__order_Orefl,axiom,
    ! [A: set_a] : ( ord_less_eq_set_a @ A @ A ) ).

% dual_order.refl
thf(fact_281_dual__order_Orefl,axiom,
    ! [A: set_li1159382662694783132od_c_a] : ( ord_le2998388488506175548od_c_a @ A @ A ) ).

% dual_order.refl
thf(fact_282_order__refl,axiom,
    ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).

% order_refl
thf(fact_283_order__refl,axiom,
    ! [X: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ X @ X ) ).

% order_refl
thf(fact_284_order__refl,axiom,
    ! [X: set_a] : ( ord_less_eq_set_a @ X @ X ) ).

% order_refl
thf(fact_285_order__refl,axiom,
    ! [X: set_li1159382662694783132od_c_a] : ( ord_le2998388488506175548od_c_a @ X @ X ) ).

% order_refl
thf(fact_286_is__singletonI,axiom,
    ! [X: list_P6327159017948738492od_c_a] : ( is_sin490879544914702512od_c_a @ ( insert4789241225314331020od_c_a @ X @ bot_bo6236370880139903240od_c_a ) ) ).

% is_singletonI
thf(fact_287_is__singletonI,axiom,
    ! [X: b] : ( is_singleton_b @ ( insert_b @ X @ bot_bot_set_b ) ) ).

% is_singletonI
thf(fact_288_is__singletonI,axiom,
    ! [X: produc4859908366599477352od_d_d] : ( is_sin881476898019872092od_d_d @ ( insert4898623881593564728od_d_d @ X @ bot_bo7612717905841165748od_d_d ) ) ).

% is_singletonI
thf(fact_289_is__singletonI,axiom,
    ! [X: e] : ( is_singleton_e @ ( insert_e @ X @ bot_bot_set_e ) ) ).

% is_singletonI
thf(fact_290_initial__preamble__simps_I2_J,axiom,
    ! [M: fsm_e_b_c] :
      ( ( states_e_b_c @ ( state_8070570405879350851_e_b_c @ M ) )
      = ( insert_e @ ( initial_e_b_c @ M ) @ bot_bot_set_e ) ) ).

% initial_preamble_simps(2)
thf(fact_291_initial__preamble__simps_I2_J,axiom,
    ! [M: fsm_a_b_c] :
      ( ( states_a_b_c @ ( state_4132440018836379711_a_b_c @ M ) )
      = ( insert_a @ ( initial_a_b_c @ M ) @ bot_bot_set_a ) ) ).

% initial_preamble_simps(2)
thf(fact_292_bot_Oextremum__uniqueI,axiom,
    ! [A: set_b] :
      ( ( ord_less_eq_set_b @ A @ bot_bot_set_b )
     => ( A = bot_bot_set_b ) ) ).

% bot.extremum_uniqueI
thf(fact_293_bot_Oextremum__uniqueI,axiom,
    ! [A: set_Pr9130538228769002824od_d_d] :
      ( ( ord_le7464911323401878760od_d_d @ A @ bot_bo7612717905841165748od_d_d )
     => ( A = bot_bo7612717905841165748od_d_d ) ) ).

% bot.extremum_uniqueI
thf(fact_294_bot_Oextremum__uniqueI,axiom,
    ! [A: set_e] :
      ( ( ord_less_eq_set_e @ A @ bot_bot_set_e )
     => ( A = bot_bot_set_e ) ) ).

% bot.extremum_uniqueI
thf(fact_295_bot_Oextremum__uniqueI,axiom,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ A @ bot_bot_nat )
     => ( A = bot_bot_nat ) ) ).

% bot.extremum_uniqueI
thf(fact_296_bot_Oextremum__uniqueI,axiom,
    ! [A: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ bot_bo4166481423041325370od_b_c )
     => ( A = bot_bo4166481423041325370od_b_c ) ) ).

% bot.extremum_uniqueI
thf(fact_297_bot_Oextremum__uniqueI,axiom,
    ! [A: set_a] :
      ( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
     => ( A = bot_bot_set_a ) ) ).

% bot.extremum_uniqueI
thf(fact_298_bot_Oextremum__uniqueI,axiom,
    ! [A: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ A @ bot_bo6236370880139903240od_c_a )
     => ( A = bot_bo6236370880139903240od_c_a ) ) ).

% bot.extremum_uniqueI
thf(fact_299_bot_Oextremum__unique,axiom,
    ! [A: set_b] :
      ( ( ord_less_eq_set_b @ A @ bot_bot_set_b )
      = ( A = bot_bot_set_b ) ) ).

% bot.extremum_unique
thf(fact_300_bot_Oextremum__unique,axiom,
    ! [A: set_Pr9130538228769002824od_d_d] :
      ( ( ord_le7464911323401878760od_d_d @ A @ bot_bo7612717905841165748od_d_d )
      = ( A = bot_bo7612717905841165748od_d_d ) ) ).

% bot.extremum_unique
thf(fact_301_bot_Oextremum__unique,axiom,
    ! [A: set_e] :
      ( ( ord_less_eq_set_e @ A @ bot_bot_set_e )
      = ( A = bot_bot_set_e ) ) ).

% bot.extremum_unique
thf(fact_302_bot_Oextremum__unique,axiom,
    ! [A: nat] :
      ( ( ord_less_eq_nat @ A @ bot_bot_nat )
      = ( A = bot_bot_nat ) ) ).

% bot.extremum_unique
thf(fact_303_bot_Oextremum__unique,axiom,
    ! [A: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ bot_bo4166481423041325370od_b_c )
      = ( A = bot_bo4166481423041325370od_b_c ) ) ).

% bot.extremum_unique
thf(fact_304_bot_Oextremum__unique,axiom,
    ! [A: set_a] :
      ( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
      = ( A = bot_bot_set_a ) ) ).

% bot.extremum_unique
thf(fact_305_bot_Oextremum__unique,axiom,
    ! [A: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ A @ bot_bo6236370880139903240od_c_a )
      = ( A = bot_bo6236370880139903240od_c_a ) ) ).

% bot.extremum_unique
thf(fact_306_bot_Oextremum,axiom,
    ! [A: set_b] : ( ord_less_eq_set_b @ bot_bot_set_b @ A ) ).

% bot.extremum
thf(fact_307_bot_Oextremum,axiom,
    ! [A: set_Pr9130538228769002824od_d_d] : ( ord_le7464911323401878760od_d_d @ bot_bo7612717905841165748od_d_d @ A ) ).

% bot.extremum
thf(fact_308_bot_Oextremum,axiom,
    ! [A: set_e] : ( ord_less_eq_set_e @ bot_bot_set_e @ A ) ).

% bot.extremum
thf(fact_309_bot_Oextremum,axiom,
    ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).

% bot.extremum
thf(fact_310_bot_Oextremum,axiom,
    ! [A: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ bot_bo4166481423041325370od_b_c @ A ) ).

% bot.extremum
thf(fact_311_bot_Oextremum,axiom,
    ! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ) ).

% bot.extremum
thf(fact_312_bot_Oextremum,axiom,
    ! [A: set_li1159382662694783132od_c_a] : ( ord_le2998388488506175548od_c_a @ bot_bo6236370880139903240od_c_a @ A ) ).

% bot.extremum
thf(fact_313_empty__subsetI,axiom,
    ! [A2: set_b] : ( ord_less_eq_set_b @ bot_bot_set_b @ A2 ) ).

% empty_subsetI
thf(fact_314_empty__subsetI,axiom,
    ! [A2: set_Pr9130538228769002824od_d_d] : ( ord_le7464911323401878760od_d_d @ bot_bo7612717905841165748od_d_d @ A2 ) ).

% empty_subsetI
thf(fact_315_empty__subsetI,axiom,
    ! [A2: set_e] : ( ord_less_eq_set_e @ bot_bot_set_e @ A2 ) ).

% empty_subsetI
thf(fact_316_empty__subsetI,axiom,
    ! [A2: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ bot_bo4166481423041325370od_b_c @ A2 ) ).

% empty_subsetI
thf(fact_317_empty__subsetI,axiom,
    ! [A2: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A2 ) ).

% empty_subsetI
thf(fact_318_empty__subsetI,axiom,
    ! [A2: set_li1159382662694783132od_c_a] : ( ord_le2998388488506175548od_c_a @ bot_bo6236370880139903240od_c_a @ A2 ) ).

% empty_subsetI
thf(fact_319_subset__empty,axiom,
    ! [A2: set_b] :
      ( ( ord_less_eq_set_b @ A2 @ bot_bot_set_b )
      = ( A2 = bot_bot_set_b ) ) ).

% subset_empty
thf(fact_320_subset__empty,axiom,
    ! [A2: set_Pr9130538228769002824od_d_d] :
      ( ( ord_le7464911323401878760od_d_d @ A2 @ bot_bo7612717905841165748od_d_d )
      = ( A2 = bot_bo7612717905841165748od_d_d ) ) ).

% subset_empty
thf(fact_321_subset__empty,axiom,
    ! [A2: set_e] :
      ( ( ord_less_eq_set_e @ A2 @ bot_bot_set_e )
      = ( A2 = bot_bot_set_e ) ) ).

% subset_empty
thf(fact_322_subset__empty,axiom,
    ! [A2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A2 @ bot_bo4166481423041325370od_b_c )
      = ( A2 = bot_bo4166481423041325370od_b_c ) ) ).

% subset_empty
thf(fact_323_subset__empty,axiom,
    ! [A2: set_a] :
      ( ( ord_less_eq_set_a @ A2 @ bot_bot_set_a )
      = ( A2 = bot_bot_set_a ) ) ).

% subset_empty
thf(fact_324_subset__empty,axiom,
    ! [A2: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ A2 @ bot_bo6236370880139903240od_c_a )
      = ( A2 = bot_bo6236370880139903240od_c_a ) ) ).

% subset_empty
thf(fact_325_insert__subset,axiom,
    ! [X: e,A2: set_e,B: set_e] :
      ( ( ord_less_eq_set_e @ ( insert_e @ X @ A2 ) @ B )
      = ( ( member_e @ X @ B )
        & ( ord_less_eq_set_e @ A2 @ B ) ) ) ).

% insert_subset
thf(fact_326_insert__subset,axiom,
    ! [X: b,A2: set_b,B: set_b] :
      ( ( ord_less_eq_set_b @ ( insert_b @ X @ A2 ) @ B )
      = ( ( member_b @ X @ B )
        & ( ord_less_eq_set_b @ A2 @ B ) ) ) ).

% insert_subset
thf(fact_327_insert__subset,axiom,
    ! [X: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ ( insert6227932334100060350od_b_c @ X @ A2 ) @ B )
      = ( ( member6330420149250801815od_b_c @ X @ B )
        & ( ord_le282488521294790766od_b_c @ A2 @ B ) ) ) ).

% insert_subset
thf(fact_328_insert__subset,axiom,
    ! [X: a,A2: set_a,B: set_a] :
      ( ( ord_less_eq_set_a @ ( insert_a @ X @ A2 ) @ B )
      = ( ( member_a @ X @ B )
        & ( ord_less_eq_set_a @ A2 @ B ) ) ) ).

% insert_subset
thf(fact_329_insert__subset,axiom,
    ! [X: list_P6327159017948738492od_c_a,A2: set_li1159382662694783132od_c_a,B: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ ( insert4789241225314331020od_c_a @ X @ A2 ) @ B )
      = ( ( member7410604586820865893od_c_a @ X @ B )
        & ( ord_le2998388488506175548od_c_a @ A2 @ B ) ) ) ).

% insert_subset
thf(fact_330_singleton__insert__inj__eq,axiom,
    ! [B2: b,A: b,A2: set_b] :
      ( ( ( insert_b @ B2 @ bot_bot_set_b )
        = ( insert_b @ A @ A2 ) )
      = ( ( A = B2 )
        & ( ord_less_eq_set_b @ A2 @ ( insert_b @ B2 @ bot_bot_set_b ) ) ) ) ).

% singleton_insert_inj_eq
thf(fact_331_singleton__insert__inj__eq,axiom,
    ! [B2: produc4859908366599477352od_d_d,A: produc4859908366599477352od_d_d,A2: set_Pr9130538228769002824od_d_d] :
      ( ( ( insert4898623881593564728od_d_d @ B2 @ bot_bo7612717905841165748od_d_d )
        = ( insert4898623881593564728od_d_d @ A @ A2 ) )
      = ( ( A = B2 )
        & ( ord_le7464911323401878760od_d_d @ A2 @ ( insert4898623881593564728od_d_d @ B2 @ bot_bo7612717905841165748od_d_d ) ) ) ) ).

% singleton_insert_inj_eq
thf(fact_332_singleton__insert__inj__eq,axiom,
    ! [B2: e,A: e,A2: set_e] :
      ( ( ( insert_e @ B2 @ bot_bot_set_e )
        = ( insert_e @ A @ A2 ) )
      = ( ( A = B2 )
        & ( ord_less_eq_set_e @ A2 @ ( insert_e @ B2 @ bot_bot_set_e ) ) ) ) ).

% singleton_insert_inj_eq
thf(fact_333_singleton__insert__inj__eq,axiom,
    ! [B2: list_P903359562653991662od_b_c,A: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( ( insert6227932334100060350od_b_c @ B2 @ bot_bo4166481423041325370od_b_c )
        = ( insert6227932334100060350od_b_c @ A @ A2 ) )
      = ( ( A = B2 )
        & ( ord_le282488521294790766od_b_c @ A2 @ ( insert6227932334100060350od_b_c @ B2 @ bot_bo4166481423041325370od_b_c ) ) ) ) ).

% singleton_insert_inj_eq
thf(fact_334_singleton__insert__inj__eq,axiom,
    ! [B2: a,A: a,A2: set_a] :
      ( ( ( insert_a @ B2 @ bot_bot_set_a )
        = ( insert_a @ A @ A2 ) )
      = ( ( A = B2 )
        & ( ord_less_eq_set_a @ A2 @ ( insert_a @ B2 @ bot_bot_set_a ) ) ) ) ).

% singleton_insert_inj_eq
thf(fact_335_singleton__insert__inj__eq,axiom,
    ! [B2: list_P6327159017948738492od_c_a,A: list_P6327159017948738492od_c_a,A2: set_li1159382662694783132od_c_a] :
      ( ( ( insert4789241225314331020od_c_a @ B2 @ bot_bo6236370880139903240od_c_a )
        = ( insert4789241225314331020od_c_a @ A @ A2 ) )
      = ( ( A = B2 )
        & ( ord_le2998388488506175548od_c_a @ A2 @ ( insert4789241225314331020od_c_a @ B2 @ bot_bo6236370880139903240od_c_a ) ) ) ) ).

% singleton_insert_inj_eq
thf(fact_336_singleton__insert__inj__eq_H,axiom,
    ! [A: b,A2: set_b,B2: b] :
      ( ( ( insert_b @ A @ A2 )
        = ( insert_b @ B2 @ bot_bot_set_b ) )
      = ( ( A = B2 )
        & ( ord_less_eq_set_b @ A2 @ ( insert_b @ B2 @ bot_bot_set_b ) ) ) ) ).

% singleton_insert_inj_eq'
thf(fact_337_singleton__insert__inj__eq_H,axiom,
    ! [A: produc4859908366599477352od_d_d,A2: set_Pr9130538228769002824od_d_d,B2: produc4859908366599477352od_d_d] :
      ( ( ( insert4898623881593564728od_d_d @ A @ A2 )
        = ( insert4898623881593564728od_d_d @ B2 @ bot_bo7612717905841165748od_d_d ) )
      = ( ( A = B2 )
        & ( ord_le7464911323401878760od_d_d @ A2 @ ( insert4898623881593564728od_d_d @ B2 @ bot_bo7612717905841165748od_d_d ) ) ) ) ).

% singleton_insert_inj_eq'
thf(fact_338_singleton__insert__inj__eq_H,axiom,
    ! [A: e,A2: set_e,B2: e] :
      ( ( ( insert_e @ A @ A2 )
        = ( insert_e @ B2 @ bot_bot_set_e ) )
      = ( ( A = B2 )
        & ( ord_less_eq_set_e @ A2 @ ( insert_e @ B2 @ bot_bot_set_e ) ) ) ) ).

% singleton_insert_inj_eq'
thf(fact_339_singleton__insert__inj__eq_H,axiom,
    ! [A: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c,B2: list_P903359562653991662od_b_c] :
      ( ( ( insert6227932334100060350od_b_c @ A @ A2 )
        = ( insert6227932334100060350od_b_c @ B2 @ bot_bo4166481423041325370od_b_c ) )
      = ( ( A = B2 )
        & ( ord_le282488521294790766od_b_c @ A2 @ ( insert6227932334100060350od_b_c @ B2 @ bot_bo4166481423041325370od_b_c ) ) ) ) ).

% singleton_insert_inj_eq'
thf(fact_340_singleton__insert__inj__eq_H,axiom,
    ! [A: a,A2: set_a,B2: a] :
      ( ( ( insert_a @ A @ A2 )
        = ( insert_a @ B2 @ bot_bot_set_a ) )
      = ( ( A = B2 )
        & ( ord_less_eq_set_a @ A2 @ ( insert_a @ B2 @ bot_bot_set_a ) ) ) ) ).

% singleton_insert_inj_eq'
thf(fact_341_singleton__insert__inj__eq_H,axiom,
    ! [A: list_P6327159017948738492od_c_a,A2: set_li1159382662694783132od_c_a,B2: list_P6327159017948738492od_c_a] :
      ( ( ( insert4789241225314331020od_c_a @ A @ A2 )
        = ( insert4789241225314331020od_c_a @ B2 @ bot_bo6236370880139903240od_c_a ) )
      = ( ( A = B2 )
        & ( ord_le2998388488506175548od_c_a @ A2 @ ( insert4789241225314331020od_c_a @ B2 @ bot_bo6236370880139903240od_c_a ) ) ) ) ).

% singleton_insert_inj_eq'
thf(fact_342_initial__preamble__simps_I1_J,axiom,
    ! [M: fsm_e_b_c] :
      ( ( initial_e_b_c @ ( state_8070570405879350851_e_b_c @ M ) )
      = ( initial_e_b_c @ M ) ) ).

% initial_preamble_simps(1)
thf(fact_343_initial__preamble__simps_I1_J,axiom,
    ! [M: fsm_a_b_c] :
      ( ( initial_a_b_c @ ( state_4132440018836379711_a_b_c @ M ) )
      = ( initial_a_b_c @ M ) ) ).

% initial_preamble_simps(1)
thf(fact_344_initial__preamble__simps_I3_J,axiom,
    ! [M: fsm_e_b_c] :
      ( ( inputs_e_b_c @ ( state_8070570405879350851_e_b_c @ M ) )
      = ( inputs_e_b_c @ M ) ) ).

% initial_preamble_simps(3)
thf(fact_345_initial__preamble__simps_I3_J,axiom,
    ! [M: fsm_a_b_c] :
      ( ( inputs_a_b_c @ ( state_4132440018836379711_a_b_c @ M ) )
      = ( inputs_a_b_c @ M ) ) ).

% initial_preamble_simps(3)
thf(fact_346_bot__set__def,axiom,
    ( bot_bo6236370880139903240od_c_a
    = ( collec6273869032445462695od_c_a @ bot_bo4941546593110769109_c_a_o ) ) ).

% bot_set_def
thf(fact_347_bot__set__def,axiom,
    ( bot_bot_set_b
    = ( collect_b @ bot_bot_b_o ) ) ).

% bot_set_def
thf(fact_348_bot__set__def,axiom,
    ( bot_bo7612717905841165748od_d_d
    = ( collec5362705567740981075od_d_d @ bot_bo8796992887960848425_d_d_o ) ) ).

% bot_set_def
thf(fact_349_bot__set__def,axiom,
    ( bot_bot_set_e
    = ( collect_e @ bot_bot_e_o ) ) ).

% bot_set_def
thf(fact_350_subset__insertI2,axiom,
    ! [A2: set_e,B: set_e,B2: e] :
      ( ( ord_less_eq_set_e @ A2 @ B )
     => ( ord_less_eq_set_e @ A2 @ ( insert_e @ B2 @ B ) ) ) ).

% subset_insertI2
thf(fact_351_subset__insertI2,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c,B2: list_P903359562653991662od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A2 @ B )
     => ( ord_le282488521294790766od_b_c @ A2 @ ( insert6227932334100060350od_b_c @ B2 @ B ) ) ) ).

% subset_insertI2
thf(fact_352_subset__insertI2,axiom,
    ! [A2: set_a,B: set_a,B2: a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ord_less_eq_set_a @ A2 @ ( insert_a @ B2 @ B ) ) ) ).

% subset_insertI2
thf(fact_353_subset__insertI2,axiom,
    ! [A2: set_li1159382662694783132od_c_a,B: set_li1159382662694783132od_c_a,B2: list_P6327159017948738492od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ A2 @ B )
     => ( ord_le2998388488506175548od_c_a @ A2 @ ( insert4789241225314331020od_c_a @ B2 @ B ) ) ) ).

% subset_insertI2
thf(fact_354_subset__insertI,axiom,
    ! [B: set_e,A: e] : ( ord_less_eq_set_e @ B @ ( insert_e @ A @ B ) ) ).

% subset_insertI
thf(fact_355_subset__insertI,axiom,
    ! [B: set_li6436108459499378894od_b_c,A: list_P903359562653991662od_b_c] : ( ord_le282488521294790766od_b_c @ B @ ( insert6227932334100060350od_b_c @ A @ B ) ) ).

% subset_insertI
thf(fact_356_subset__insertI,axiom,
    ! [B: set_a,A: a] : ( ord_less_eq_set_a @ B @ ( insert_a @ A @ B ) ) ).

% subset_insertI
thf(fact_357_subset__insertI,axiom,
    ! [B: set_li1159382662694783132od_c_a,A: list_P6327159017948738492od_c_a] : ( ord_le2998388488506175548od_c_a @ B @ ( insert4789241225314331020od_c_a @ A @ B ) ) ).

% subset_insertI
thf(fact_358_subset__insert,axiom,
    ! [X: e,A2: set_e,B: set_e] :
      ( ~ ( member_e @ X @ A2 )
     => ( ( ord_less_eq_set_e @ A2 @ ( insert_e @ X @ B ) )
        = ( ord_less_eq_set_e @ A2 @ B ) ) ) ).

% subset_insert
thf(fact_359_subset__insert,axiom,
    ! [X: b,A2: set_b,B: set_b] :
      ( ~ ( member_b @ X @ A2 )
     => ( ( ord_less_eq_set_b @ A2 @ ( insert_b @ X @ B ) )
        = ( ord_less_eq_set_b @ A2 @ B ) ) ) ).

% subset_insert
thf(fact_360_subset__insert,axiom,
    ! [X: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ~ ( member6330420149250801815od_b_c @ X @ A2 )
     => ( ( ord_le282488521294790766od_b_c @ A2 @ ( insert6227932334100060350od_b_c @ X @ B ) )
        = ( ord_le282488521294790766od_b_c @ A2 @ B ) ) ) ).

% subset_insert
thf(fact_361_subset__insert,axiom,
    ! [X: a,A2: set_a,B: set_a] :
      ( ~ ( member_a @ X @ A2 )
     => ( ( ord_less_eq_set_a @ A2 @ ( insert_a @ X @ B ) )
        = ( ord_less_eq_set_a @ A2 @ B ) ) ) ).

% subset_insert
thf(fact_362_subset__insert,axiom,
    ! [X: list_P6327159017948738492od_c_a,A2: set_li1159382662694783132od_c_a,B: set_li1159382662694783132od_c_a] :
      ( ~ ( member7410604586820865893od_c_a @ X @ A2 )
     => ( ( ord_le2998388488506175548od_c_a @ A2 @ ( insert4789241225314331020od_c_a @ X @ B ) )
        = ( ord_le2998388488506175548od_c_a @ A2 @ B ) ) ) ).

% subset_insert
thf(fact_363_insert__mono,axiom,
    ! [C3: set_e,D2: set_e,A: e] :
      ( ( ord_less_eq_set_e @ C3 @ D2 )
     => ( ord_less_eq_set_e @ ( insert_e @ A @ C3 ) @ ( insert_e @ A @ D2 ) ) ) ).

% insert_mono
thf(fact_364_insert__mono,axiom,
    ! [C3: set_li6436108459499378894od_b_c,D2: set_li6436108459499378894od_b_c,A: list_P903359562653991662od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ C3 @ D2 )
     => ( ord_le282488521294790766od_b_c @ ( insert6227932334100060350od_b_c @ A @ C3 ) @ ( insert6227932334100060350od_b_c @ A @ D2 ) ) ) ).

% insert_mono
thf(fact_365_insert__mono,axiom,
    ! [C3: set_a,D2: set_a,A: a] :
      ( ( ord_less_eq_set_a @ C3 @ D2 )
     => ( ord_less_eq_set_a @ ( insert_a @ A @ C3 ) @ ( insert_a @ A @ D2 ) ) ) ).

% insert_mono
thf(fact_366_insert__mono,axiom,
    ! [C3: set_li1159382662694783132od_c_a,D2: set_li1159382662694783132od_c_a,A: list_P6327159017948738492od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ C3 @ D2 )
     => ( ord_le2998388488506175548od_c_a @ ( insert4789241225314331020od_c_a @ A @ C3 ) @ ( insert4789241225314331020od_c_a @ A @ D2 ) ) ) ).

% insert_mono
thf(fact_367_subset__singletonD,axiom,
    ! [A2: set_b,X: b] :
      ( ( ord_less_eq_set_b @ A2 @ ( insert_b @ X @ bot_bot_set_b ) )
     => ( ( A2 = bot_bot_set_b )
        | ( A2
          = ( insert_b @ X @ bot_bot_set_b ) ) ) ) ).

% subset_singletonD
thf(fact_368_subset__singletonD,axiom,
    ! [A2: set_Pr9130538228769002824od_d_d,X: produc4859908366599477352od_d_d] :
      ( ( ord_le7464911323401878760od_d_d @ A2 @ ( insert4898623881593564728od_d_d @ X @ bot_bo7612717905841165748od_d_d ) )
     => ( ( A2 = bot_bo7612717905841165748od_d_d )
        | ( A2
          = ( insert4898623881593564728od_d_d @ X @ bot_bo7612717905841165748od_d_d ) ) ) ) ).

% subset_singletonD
thf(fact_369_subset__singletonD,axiom,
    ! [A2: set_e,X: e] :
      ( ( ord_less_eq_set_e @ A2 @ ( insert_e @ X @ bot_bot_set_e ) )
     => ( ( A2 = bot_bot_set_e )
        | ( A2
          = ( insert_e @ X @ bot_bot_set_e ) ) ) ) ).

% subset_singletonD
thf(fact_370_subset__singletonD,axiom,
    ! [A2: set_li6436108459499378894od_b_c,X: list_P903359562653991662od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A2 @ ( insert6227932334100060350od_b_c @ X @ bot_bo4166481423041325370od_b_c ) )
     => ( ( A2 = bot_bo4166481423041325370od_b_c )
        | ( A2
          = ( insert6227932334100060350od_b_c @ X @ bot_bo4166481423041325370od_b_c ) ) ) ) ).

% subset_singletonD
thf(fact_371_subset__singletonD,axiom,
    ! [A2: set_a,X: a] :
      ( ( ord_less_eq_set_a @ A2 @ ( insert_a @ X @ bot_bot_set_a ) )
     => ( ( A2 = bot_bot_set_a )
        | ( A2
          = ( insert_a @ X @ bot_bot_set_a ) ) ) ) ).

% subset_singletonD
thf(fact_372_subset__singletonD,axiom,
    ! [A2: set_li1159382662694783132od_c_a,X: list_P6327159017948738492od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ A2 @ ( insert4789241225314331020od_c_a @ X @ bot_bo6236370880139903240od_c_a ) )
     => ( ( A2 = bot_bo6236370880139903240od_c_a )
        | ( A2
          = ( insert4789241225314331020od_c_a @ X @ bot_bo6236370880139903240od_c_a ) ) ) ) ).

% subset_singletonD
thf(fact_373_subset__singleton__iff,axiom,
    ! [X6: set_b,A: b] :
      ( ( ord_less_eq_set_b @ X6 @ ( insert_b @ A @ bot_bot_set_b ) )
      = ( ( X6 = bot_bot_set_b )
        | ( X6
          = ( insert_b @ A @ bot_bot_set_b ) ) ) ) ).

% subset_singleton_iff
thf(fact_374_subset__singleton__iff,axiom,
    ! [X6: set_Pr9130538228769002824od_d_d,A: produc4859908366599477352od_d_d] :
      ( ( ord_le7464911323401878760od_d_d @ X6 @ ( insert4898623881593564728od_d_d @ A @ bot_bo7612717905841165748od_d_d ) )
      = ( ( X6 = bot_bo7612717905841165748od_d_d )
        | ( X6
          = ( insert4898623881593564728od_d_d @ A @ bot_bo7612717905841165748od_d_d ) ) ) ) ).

% subset_singleton_iff
thf(fact_375_subset__singleton__iff,axiom,
    ! [X6: set_e,A: e] :
      ( ( ord_less_eq_set_e @ X6 @ ( insert_e @ A @ bot_bot_set_e ) )
      = ( ( X6 = bot_bot_set_e )
        | ( X6
          = ( insert_e @ A @ bot_bot_set_e ) ) ) ) ).

% subset_singleton_iff
thf(fact_376_subset__singleton__iff,axiom,
    ! [X6: set_li6436108459499378894od_b_c,A: list_P903359562653991662od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ X6 @ ( insert6227932334100060350od_b_c @ A @ bot_bo4166481423041325370od_b_c ) )
      = ( ( X6 = bot_bo4166481423041325370od_b_c )
        | ( X6
          = ( insert6227932334100060350od_b_c @ A @ bot_bo4166481423041325370od_b_c ) ) ) ) ).

% subset_singleton_iff
thf(fact_377_subset__singleton__iff,axiom,
    ! [X6: set_a,A: a] :
      ( ( ord_less_eq_set_a @ X6 @ ( insert_a @ A @ bot_bot_set_a ) )
      = ( ( X6 = bot_bot_set_a )
        | ( X6
          = ( insert_a @ A @ bot_bot_set_a ) ) ) ) ).

% subset_singleton_iff
thf(fact_378_subset__singleton__iff,axiom,
    ! [X6: set_li1159382662694783132od_c_a,A: list_P6327159017948738492od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ X6 @ ( insert4789241225314331020od_c_a @ A @ bot_bo6236370880139903240od_c_a ) )
      = ( ( X6 = bot_bo6236370880139903240od_c_a )
        | ( X6
          = ( insert4789241225314331020od_c_a @ A @ bot_bo6236370880139903240od_c_a ) ) ) ) ).

% subset_singleton_iff
thf(fact_379_is__singletonI_H,axiom,
    ! [A2: set_li6436108459499378894od_b_c] :
      ( ( A2 != bot_bo4166481423041325370od_b_c )
     => ( ! [X3: list_P903359562653991662od_b_c,Y4: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X3 @ A2 )
           => ( ( member6330420149250801815od_b_c @ Y4 @ A2 )
             => ( X3 = Y4 ) ) )
       => ( is_sin2898727439159961570od_b_c @ A2 ) ) ) ).

% is_singletonI'
thf(fact_380_is__singletonI_H,axiom,
    ! [A2: set_li1159382662694783132od_c_a] :
      ( ( A2 != bot_bo6236370880139903240od_c_a )
     => ( ! [X3: list_P6327159017948738492od_c_a,Y4: list_P6327159017948738492od_c_a] :
            ( ( member7410604586820865893od_c_a @ X3 @ A2 )
           => ( ( member7410604586820865893od_c_a @ Y4 @ A2 )
             => ( X3 = Y4 ) ) )
       => ( is_sin490879544914702512od_c_a @ A2 ) ) ) ).

% is_singletonI'
thf(fact_381_is__singletonI_H,axiom,
    ! [A2: set_a] :
      ( ( A2 != bot_bot_set_a )
     => ( ! [X3: a,Y4: a] :
            ( ( member_a @ X3 @ A2 )
           => ( ( member_a @ Y4 @ A2 )
             => ( X3 = Y4 ) ) )
       => ( is_singleton_a @ A2 ) ) ) ).

% is_singletonI'
thf(fact_382_is__singletonI_H,axiom,
    ! [A2: set_b] :
      ( ( A2 != bot_bot_set_b )
     => ( ! [X3: b,Y4: b] :
            ( ( member_b @ X3 @ A2 )
           => ( ( member_b @ Y4 @ A2 )
             => ( X3 = Y4 ) ) )
       => ( is_singleton_b @ A2 ) ) ) ).

% is_singletonI'
thf(fact_383_is__singletonI_H,axiom,
    ! [A2: set_Pr9130538228769002824od_d_d] :
      ( ( A2 != bot_bo7612717905841165748od_d_d )
     => ( ! [X3: produc4859908366599477352od_d_d,Y4: produc4859908366599477352od_d_d] :
            ( ( member73601632213084689od_d_d @ X3 @ A2 )
           => ( ( member73601632213084689od_d_d @ Y4 @ A2 )
             => ( X3 = Y4 ) ) )
       => ( is_sin881476898019872092od_d_d @ A2 ) ) ) ).

% is_singletonI'
thf(fact_384_is__singletonI_H,axiom,
    ! [A2: set_e] :
      ( ( A2 != bot_bot_set_e )
     => ( ! [X3: e,Y4: e] :
            ( ( member_e @ X3 @ A2 )
           => ( ( member_e @ Y4 @ A2 )
             => ( X3 = Y4 ) ) )
       => ( is_singleton_e @ A2 ) ) ) ).

% is_singletonI'
thf(fact_385_is__preamble__initial,axiom,
    ! [M: fsm_e_b_c] : ( state_6949549413070345083_e_b_c @ ( state_8070570405879350851_e_b_c @ M ) @ M @ ( initial_e_b_c @ M ) ) ).

% is_preamble_initial
thf(fact_386_is__preamble__initial,axiom,
    ! [M: fsm_a_b_c] : ( state_3011419026027373943_a_b_c @ ( state_4132440018836379711_a_b_c @ M ) @ M @ ( initial_a_b_c @ M ) ) ).

% is_preamble_initial
thf(fact_387_nle__le,axiom,
    ! [A: nat,B2: nat] :
      ( ( ~ ( ord_less_eq_nat @ A @ B2 ) )
      = ( ( ord_less_eq_nat @ B2 @ A )
        & ( B2 != A ) ) ) ).

% nle_le
thf(fact_388_le__cases3,axiom,
    ! [X: nat,Y: nat,Z2: nat] :
      ( ( ( ord_less_eq_nat @ X @ Y )
       => ~ ( ord_less_eq_nat @ Y @ Z2 ) )
     => ( ( ( ord_less_eq_nat @ Y @ X )
         => ~ ( ord_less_eq_nat @ X @ Z2 ) )
       => ( ( ( ord_less_eq_nat @ X @ Z2 )
           => ~ ( ord_less_eq_nat @ Z2 @ Y ) )
         => ( ( ( ord_less_eq_nat @ Z2 @ Y )
             => ~ ( ord_less_eq_nat @ Y @ X ) )
           => ( ( ( ord_less_eq_nat @ Y @ Z2 )
               => ~ ( ord_less_eq_nat @ Z2 @ X ) )
             => ~ ( ( ord_less_eq_nat @ Z2 @ X )
                 => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).

% le_cases3
thf(fact_389_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
    = ( ^ [X2: nat,Y2: nat] :
          ( ( ord_less_eq_nat @ X2 @ Y2 )
          & ( ord_less_eq_nat @ Y2 @ X2 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_390_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: set_li6436108459499378894od_b_c,Z: set_li6436108459499378894od_b_c] : ( Y3 = Z ) )
    = ( ^ [X2: set_li6436108459499378894od_b_c,Y2: set_li6436108459499378894od_b_c] :
          ( ( ord_le282488521294790766od_b_c @ X2 @ Y2 )
          & ( ord_le282488521294790766od_b_c @ Y2 @ X2 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_391_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: set_a,Z: set_a] : ( Y3 = Z ) )
    = ( ^ [X2: set_a,Y2: set_a] :
          ( ( ord_less_eq_set_a @ X2 @ Y2 )
          & ( ord_less_eq_set_a @ Y2 @ X2 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_392_order__class_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: set_li1159382662694783132od_c_a,Z: set_li1159382662694783132od_c_a] : ( Y3 = Z ) )
    = ( ^ [X2: set_li1159382662694783132od_c_a,Y2: set_li1159382662694783132od_c_a] :
          ( ( ord_le2998388488506175548od_c_a @ X2 @ Y2 )
          & ( ord_le2998388488506175548od_c_a @ Y2 @ X2 ) ) ) ) ).

% order_class.order_eq_iff
thf(fact_393_ord__eq__le__trans,axiom,
    ! [A: nat,B2: nat,C2: nat] :
      ( ( A = B2 )
     => ( ( ord_less_eq_nat @ B2 @ C2 )
       => ( ord_less_eq_nat @ A @ C2 ) ) ) ).

% ord_eq_le_trans
thf(fact_394_ord__eq__le__trans,axiom,
    ! [A: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c,C2: set_li6436108459499378894od_b_c] :
      ( ( A = B2 )
     => ( ( ord_le282488521294790766od_b_c @ B2 @ C2 )
       => ( ord_le282488521294790766od_b_c @ A @ C2 ) ) ) ).

% ord_eq_le_trans
thf(fact_395_ord__eq__le__trans,axiom,
    ! [A: set_a,B2: set_a,C2: set_a] :
      ( ( A = B2 )
     => ( ( ord_less_eq_set_a @ B2 @ C2 )
       => ( ord_less_eq_set_a @ A @ C2 ) ) ) ).

% ord_eq_le_trans
thf(fact_396_ord__eq__le__trans,axiom,
    ! [A: set_li1159382662694783132od_c_a,B2: set_li1159382662694783132od_c_a,C2: set_li1159382662694783132od_c_a] :
      ( ( A = B2 )
     => ( ( ord_le2998388488506175548od_c_a @ B2 @ C2 )
       => ( ord_le2998388488506175548od_c_a @ A @ C2 ) ) ) ).

% ord_eq_le_trans
thf(fact_397_ord__le__eq__trans,axiom,
    ! [A: nat,B2: nat,C2: nat] :
      ( ( ord_less_eq_nat @ A @ B2 )
     => ( ( B2 = C2 )
       => ( ord_less_eq_nat @ A @ C2 ) ) ) ).

% ord_le_eq_trans
thf(fact_398_ord__le__eq__trans,axiom,
    ! [A: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c,C2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ B2 )
     => ( ( B2 = C2 )
       => ( ord_le282488521294790766od_b_c @ A @ C2 ) ) ) ).

% ord_le_eq_trans
thf(fact_399_ord__le__eq__trans,axiom,
    ! [A: set_a,B2: set_a,C2: set_a] :
      ( ( ord_less_eq_set_a @ A @ B2 )
     => ( ( B2 = C2 )
       => ( ord_less_eq_set_a @ A @ C2 ) ) ) ).

% ord_le_eq_trans
thf(fact_400_ord__le__eq__trans,axiom,
    ! [A: set_li1159382662694783132od_c_a,B2: set_li1159382662694783132od_c_a,C2: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ A @ B2 )
     => ( ( B2 = C2 )
       => ( ord_le2998388488506175548od_c_a @ A @ C2 ) ) ) ).

% ord_le_eq_trans
thf(fact_401_order__antisym,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_eq_nat @ X @ Y )
     => ( ( ord_less_eq_nat @ Y @ X )
       => ( X = Y ) ) ) ).

% order_antisym
thf(fact_402_order__antisym,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ X @ Y )
     => ( ( ord_le282488521294790766od_b_c @ Y @ X )
       => ( X = Y ) ) ) ).

% order_antisym
thf(fact_403_order__antisym,axiom,
    ! [X: set_a,Y: set_a] :
      ( ( ord_less_eq_set_a @ X @ Y )
     => ( ( ord_less_eq_set_a @ Y @ X )
       => ( X = Y ) ) ) ).

% order_antisym
thf(fact_404_order__antisym,axiom,
    ! [X: set_li1159382662694783132od_c_a,Y: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ X @ Y )
     => ( ( ord_le2998388488506175548od_c_a @ Y @ X )
       => ( X = Y ) ) ) ).

% order_antisym
thf(fact_405_order_Otrans,axiom,
    ! [A: nat,B2: nat,C2: nat] :
      ( ( ord_less_eq_nat @ A @ B2 )
     => ( ( ord_less_eq_nat @ B2 @ C2 )
       => ( ord_less_eq_nat @ A @ C2 ) ) ) ).

% order.trans
thf(fact_406_order_Otrans,axiom,
    ! [A: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c,C2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ B2 )
     => ( ( ord_le282488521294790766od_b_c @ B2 @ C2 )
       => ( ord_le282488521294790766od_b_c @ A @ C2 ) ) ) ).

% order.trans
thf(fact_407_order_Otrans,axiom,
    ! [A: set_a,B2: set_a,C2: set_a] :
      ( ( ord_less_eq_set_a @ A @ B2 )
     => ( ( ord_less_eq_set_a @ B2 @ C2 )
       => ( ord_less_eq_set_a @ A @ C2 ) ) ) ).

% order.trans
thf(fact_408_order_Otrans,axiom,
    ! [A: set_li1159382662694783132od_c_a,B2: set_li1159382662694783132od_c_a,C2: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ A @ B2 )
     => ( ( ord_le2998388488506175548od_c_a @ B2 @ C2 )
       => ( ord_le2998388488506175548od_c_a @ A @ C2 ) ) ) ).

% order.trans
thf(fact_409_order__trans,axiom,
    ! [X: nat,Y: nat,Z2: nat] :
      ( ( ord_less_eq_nat @ X @ Y )
     => ( ( ord_less_eq_nat @ Y @ Z2 )
       => ( ord_less_eq_nat @ X @ Z2 ) ) ) ).

% order_trans
thf(fact_410_order__trans,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c,Z2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ X @ Y )
     => ( ( ord_le282488521294790766od_b_c @ Y @ Z2 )
       => ( ord_le282488521294790766od_b_c @ X @ Z2 ) ) ) ).

% order_trans
thf(fact_411_order__trans,axiom,
    ! [X: set_a,Y: set_a,Z2: set_a] :
      ( ( ord_less_eq_set_a @ X @ Y )
     => ( ( ord_less_eq_set_a @ Y @ Z2 )
       => ( ord_less_eq_set_a @ X @ Z2 ) ) ) ).

% order_trans
thf(fact_412_order__trans,axiom,
    ! [X: set_li1159382662694783132od_c_a,Y: set_li1159382662694783132od_c_a,Z2: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ X @ Y )
     => ( ( ord_le2998388488506175548od_c_a @ Y @ Z2 )
       => ( ord_le2998388488506175548od_c_a @ X @ Z2 ) ) ) ).

% order_trans
thf(fact_413_linorder__wlog,axiom,
    ! [P2: nat > nat > $o,A: nat,B2: nat] :
      ( ! [A5: nat,B6: nat] :
          ( ( ord_less_eq_nat @ A5 @ B6 )
         => ( P2 @ A5 @ B6 ) )
     => ( ! [A5: nat,B6: nat] :
            ( ( P2 @ B6 @ A5 )
           => ( P2 @ A5 @ B6 ) )
       => ( P2 @ A @ B2 ) ) ) ).

% linorder_wlog
thf(fact_414_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
    = ( ^ [A3: nat,B7: nat] :
          ( ( ord_less_eq_nat @ B7 @ A3 )
          & ( ord_less_eq_nat @ A3 @ B7 ) ) ) ) ).

% dual_order.eq_iff
thf(fact_415_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y3: set_li6436108459499378894od_b_c,Z: set_li6436108459499378894od_b_c] : ( Y3 = Z ) )
    = ( ^ [A3: set_li6436108459499378894od_b_c,B7: set_li6436108459499378894od_b_c] :
          ( ( ord_le282488521294790766od_b_c @ B7 @ A3 )
          & ( ord_le282488521294790766od_b_c @ A3 @ B7 ) ) ) ) ).

% dual_order.eq_iff
thf(fact_416_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y3: set_a,Z: set_a] : ( Y3 = Z ) )
    = ( ^ [A3: set_a,B7: set_a] :
          ( ( ord_less_eq_set_a @ B7 @ A3 )
          & ( ord_less_eq_set_a @ A3 @ B7 ) ) ) ) ).

% dual_order.eq_iff
thf(fact_417_dual__order_Oeq__iff,axiom,
    ( ( ^ [Y3: set_li1159382662694783132od_c_a,Z: set_li1159382662694783132od_c_a] : ( Y3 = Z ) )
    = ( ^ [A3: set_li1159382662694783132od_c_a,B7: set_li1159382662694783132od_c_a] :
          ( ( ord_le2998388488506175548od_c_a @ B7 @ A3 )
          & ( ord_le2998388488506175548od_c_a @ A3 @ B7 ) ) ) ) ).

% dual_order.eq_iff
thf(fact_418_dual__order_Oantisym,axiom,
    ! [B2: nat,A: nat] :
      ( ( ord_less_eq_nat @ B2 @ A )
     => ( ( ord_less_eq_nat @ A @ B2 )
       => ( A = B2 ) ) ) ).

% dual_order.antisym
thf(fact_419_dual__order_Oantisym,axiom,
    ! [B2: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ B2 @ A )
     => ( ( ord_le282488521294790766od_b_c @ A @ B2 )
       => ( A = B2 ) ) ) ).

% dual_order.antisym
thf(fact_420_dual__order_Oantisym,axiom,
    ! [B2: set_a,A: set_a] :
      ( ( ord_less_eq_set_a @ B2 @ A )
     => ( ( ord_less_eq_set_a @ A @ B2 )
       => ( A = B2 ) ) ) ).

% dual_order.antisym
thf(fact_421_dual__order_Oantisym,axiom,
    ! [B2: set_li1159382662694783132od_c_a,A: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ B2 @ A )
     => ( ( ord_le2998388488506175548od_c_a @ A @ B2 )
       => ( A = B2 ) ) ) ).

% dual_order.antisym
thf(fact_422_dual__order_Otrans,axiom,
    ! [B2: nat,A: nat,C2: nat] :
      ( ( ord_less_eq_nat @ B2 @ A )
     => ( ( ord_less_eq_nat @ C2 @ B2 )
       => ( ord_less_eq_nat @ C2 @ A ) ) ) ).

% dual_order.trans
thf(fact_423_dual__order_Otrans,axiom,
    ! [B2: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c,C2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ B2 @ A )
     => ( ( ord_le282488521294790766od_b_c @ C2 @ B2 )
       => ( ord_le282488521294790766od_b_c @ C2 @ A ) ) ) ).

% dual_order.trans
thf(fact_424_dual__order_Otrans,axiom,
    ! [B2: set_a,A: set_a,C2: set_a] :
      ( ( ord_less_eq_set_a @ B2 @ A )
     => ( ( ord_less_eq_set_a @ C2 @ B2 )
       => ( ord_less_eq_set_a @ C2 @ A ) ) ) ).

% dual_order.trans
thf(fact_425_dual__order_Otrans,axiom,
    ! [B2: set_li1159382662694783132od_c_a,A: set_li1159382662694783132od_c_a,C2: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ B2 @ A )
     => ( ( ord_le2998388488506175548od_c_a @ C2 @ B2 )
       => ( ord_le2998388488506175548od_c_a @ C2 @ A ) ) ) ).

% dual_order.trans
thf(fact_426_antisym,axiom,
    ! [A: nat,B2: nat] :
      ( ( ord_less_eq_nat @ A @ B2 )
     => ( ( ord_less_eq_nat @ B2 @ A )
       => ( A = B2 ) ) ) ).

% antisym
thf(fact_427_antisym,axiom,
    ! [A: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ B2 )
     => ( ( ord_le282488521294790766od_b_c @ B2 @ A )
       => ( A = B2 ) ) ) ).

% antisym
thf(fact_428_antisym,axiom,
    ! [A: set_a,B2: set_a] :
      ( ( ord_less_eq_set_a @ A @ B2 )
     => ( ( ord_less_eq_set_a @ B2 @ A )
       => ( A = B2 ) ) ) ).

% antisym
thf(fact_429_antisym,axiom,
    ! [A: set_li1159382662694783132od_c_a,B2: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ A @ B2 )
     => ( ( ord_le2998388488506175548od_c_a @ B2 @ A )
       => ( A = B2 ) ) ) ).

% antisym
thf(fact_430_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: nat,Z: nat] : ( Y3 = Z ) )
    = ( ^ [A3: nat,B7: nat] :
          ( ( ord_less_eq_nat @ A3 @ B7 )
          & ( ord_less_eq_nat @ B7 @ A3 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_431_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: set_li6436108459499378894od_b_c,Z: set_li6436108459499378894od_b_c] : ( Y3 = Z ) )
    = ( ^ [A3: set_li6436108459499378894od_b_c,B7: set_li6436108459499378894od_b_c] :
          ( ( ord_le282488521294790766od_b_c @ A3 @ B7 )
          & ( ord_le282488521294790766od_b_c @ B7 @ A3 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_432_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: set_a,Z: set_a] : ( Y3 = Z ) )
    = ( ^ [A3: set_a,B7: set_a] :
          ( ( ord_less_eq_set_a @ A3 @ B7 )
          & ( ord_less_eq_set_a @ B7 @ A3 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_433_Orderings_Oorder__eq__iff,axiom,
    ( ( ^ [Y3: set_li1159382662694783132od_c_a,Z: set_li1159382662694783132od_c_a] : ( Y3 = Z ) )
    = ( ^ [A3: set_li1159382662694783132od_c_a,B7: set_li1159382662694783132od_c_a] :
          ( ( ord_le2998388488506175548od_c_a @ A3 @ B7 )
          & ( ord_le2998388488506175548od_c_a @ B7 @ A3 ) ) ) ) ).

% Orderings.order_eq_iff
thf(fact_434_order__subst1,axiom,
    ! [A: nat,F: nat > nat,B2: nat,C2: nat] :
      ( ( ord_less_eq_nat @ A @ ( F @ B2 ) )
     => ( ( ord_less_eq_nat @ B2 @ C2 )
       => ( ! [X3: nat,Y4: nat] :
              ( ( ord_less_eq_nat @ X3 @ Y4 )
             => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).

% order_subst1
thf(fact_435_order__subst1,axiom,
    ! [A: nat,F: set_a > nat,B2: set_a,C2: set_a] :
      ( ( ord_less_eq_nat @ A @ ( F @ B2 ) )
     => ( ( ord_less_eq_set_a @ B2 @ C2 )
       => ( ! [X3: set_a,Y4: set_a] :
              ( ( ord_less_eq_set_a @ X3 @ Y4 )
             => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).

% order_subst1
thf(fact_436_order__subst1,axiom,
    ! [A: set_a,F: nat > set_a,B2: nat,C2: nat] :
      ( ( ord_less_eq_set_a @ A @ ( F @ B2 ) )
     => ( ( ord_less_eq_nat @ B2 @ C2 )
       => ( ! [X3: nat,Y4: nat] :
              ( ( ord_less_eq_nat @ X3 @ Y4 )
             => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_set_a @ A @ ( F @ C2 ) ) ) ) ) ).

% order_subst1
thf(fact_437_order__subst1,axiom,
    ! [A: set_a,F: set_a > set_a,B2: set_a,C2: set_a] :
      ( ( ord_less_eq_set_a @ A @ ( F @ B2 ) )
     => ( ( ord_less_eq_set_a @ B2 @ C2 )
       => ( ! [X3: set_a,Y4: set_a] :
              ( ( ord_less_eq_set_a @ X3 @ Y4 )
             => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_set_a @ A @ ( F @ C2 ) ) ) ) ) ).

% order_subst1
thf(fact_438_order__subst1,axiom,
    ! [A: nat,F: set_li6436108459499378894od_b_c > nat,B2: set_li6436108459499378894od_b_c,C2: set_li6436108459499378894od_b_c] :
      ( ( ord_less_eq_nat @ A @ ( F @ B2 ) )
     => ( ( ord_le282488521294790766od_b_c @ B2 @ C2 )
       => ( ! [X3: set_li6436108459499378894od_b_c,Y4: set_li6436108459499378894od_b_c] :
              ( ( ord_le282488521294790766od_b_c @ X3 @ Y4 )
             => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).

% order_subst1
thf(fact_439_order__subst1,axiom,
    ! [A: set_li6436108459499378894od_b_c,F: nat > set_li6436108459499378894od_b_c,B2: nat,C2: nat] :
      ( ( ord_le282488521294790766od_b_c @ A @ ( F @ B2 ) )
     => ( ( ord_less_eq_nat @ B2 @ C2 )
       => ( ! [X3: nat,Y4: nat] :
              ( ( ord_less_eq_nat @ X3 @ Y4 )
             => ( ord_le282488521294790766od_b_c @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_le282488521294790766od_b_c @ A @ ( F @ C2 ) ) ) ) ) ).

% order_subst1
thf(fact_440_order__subst1,axiom,
    ! [A: set_li6436108459499378894od_b_c,F: set_a > set_li6436108459499378894od_b_c,B2: set_a,C2: set_a] :
      ( ( ord_le282488521294790766od_b_c @ A @ ( F @ B2 ) )
     => ( ( ord_less_eq_set_a @ B2 @ C2 )
       => ( ! [X3: set_a,Y4: set_a] :
              ( ( ord_less_eq_set_a @ X3 @ Y4 )
             => ( ord_le282488521294790766od_b_c @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_le282488521294790766od_b_c @ A @ ( F @ C2 ) ) ) ) ) ).

% order_subst1
thf(fact_441_order__subst1,axiom,
    ! [A: set_a,F: set_li6436108459499378894od_b_c > set_a,B2: set_li6436108459499378894od_b_c,C2: set_li6436108459499378894od_b_c] :
      ( ( ord_less_eq_set_a @ A @ ( F @ B2 ) )
     => ( ( ord_le282488521294790766od_b_c @ B2 @ C2 )
       => ( ! [X3: set_li6436108459499378894od_b_c,Y4: set_li6436108459499378894od_b_c] :
              ( ( ord_le282488521294790766od_b_c @ X3 @ Y4 )
             => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_set_a @ A @ ( F @ C2 ) ) ) ) ) ).

% order_subst1
thf(fact_442_order__subst1,axiom,
    ! [A: nat,F: set_li1159382662694783132od_c_a > nat,B2: set_li1159382662694783132od_c_a,C2: set_li1159382662694783132od_c_a] :
      ( ( ord_less_eq_nat @ A @ ( F @ B2 ) )
     => ( ( ord_le2998388488506175548od_c_a @ B2 @ C2 )
       => ( ! [X3: set_li1159382662694783132od_c_a,Y4: set_li1159382662694783132od_c_a] :
              ( ( ord_le2998388488506175548od_c_a @ X3 @ Y4 )
             => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).

% order_subst1
thf(fact_443_order__subst1,axiom,
    ! [A: set_li6436108459499378894od_b_c,F: set_li6436108459499378894od_b_c > set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c,C2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ ( F @ B2 ) )
     => ( ( ord_le282488521294790766od_b_c @ B2 @ C2 )
       => ( ! [X3: set_li6436108459499378894od_b_c,Y4: set_li6436108459499378894od_b_c] :
              ( ( ord_le282488521294790766od_b_c @ X3 @ Y4 )
             => ( ord_le282488521294790766od_b_c @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_le282488521294790766od_b_c @ A @ ( F @ C2 ) ) ) ) ) ).

% order_subst1
thf(fact_444_order__subst2,axiom,
    ! [A: nat,B2: nat,F: nat > nat,C2: nat] :
      ( ( ord_less_eq_nat @ A @ B2 )
     => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C2 )
       => ( ! [X3: nat,Y4: nat] :
              ( ( ord_less_eq_nat @ X3 @ Y4 )
             => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).

% order_subst2
thf(fact_445_order__subst2,axiom,
    ! [A: nat,B2: nat,F: nat > set_a,C2: set_a] :
      ( ( ord_less_eq_nat @ A @ B2 )
     => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C2 )
       => ( ! [X3: nat,Y4: nat] :
              ( ( ord_less_eq_nat @ X3 @ Y4 )
             => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_set_a @ ( F @ A ) @ C2 ) ) ) ) ).

% order_subst2
thf(fact_446_order__subst2,axiom,
    ! [A: set_a,B2: set_a,F: set_a > nat,C2: nat] :
      ( ( ord_less_eq_set_a @ A @ B2 )
     => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C2 )
       => ( ! [X3: set_a,Y4: set_a] :
              ( ( ord_less_eq_set_a @ X3 @ Y4 )
             => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).

% order_subst2
thf(fact_447_order__subst2,axiom,
    ! [A: set_a,B2: set_a,F: set_a > set_a,C2: set_a] :
      ( ( ord_less_eq_set_a @ A @ B2 )
     => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C2 )
       => ( ! [X3: set_a,Y4: set_a] :
              ( ( ord_less_eq_set_a @ X3 @ Y4 )
             => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_set_a @ ( F @ A ) @ C2 ) ) ) ) ).

% order_subst2
thf(fact_448_order__subst2,axiom,
    ! [A: nat,B2: nat,F: nat > set_li6436108459499378894od_b_c,C2: set_li6436108459499378894od_b_c] :
      ( ( ord_less_eq_nat @ A @ B2 )
     => ( ( ord_le282488521294790766od_b_c @ ( F @ B2 ) @ C2 )
       => ( ! [X3: nat,Y4: nat] :
              ( ( ord_less_eq_nat @ X3 @ Y4 )
             => ( ord_le282488521294790766od_b_c @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_le282488521294790766od_b_c @ ( F @ A ) @ C2 ) ) ) ) ).

% order_subst2
thf(fact_449_order__subst2,axiom,
    ! [A: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c,F: set_li6436108459499378894od_b_c > nat,C2: nat] :
      ( ( ord_le282488521294790766od_b_c @ A @ B2 )
     => ( ( ord_less_eq_nat @ ( F @ B2 ) @ C2 )
       => ( ! [X3: set_li6436108459499378894od_b_c,Y4: set_li6436108459499378894od_b_c] :
              ( ( ord_le282488521294790766od_b_c @ X3 @ Y4 )
             => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).

% order_subst2
thf(fact_450_order__subst2,axiom,
    ! [A: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c,F: set_li6436108459499378894od_b_c > set_a,C2: set_a] :
      ( ( ord_le282488521294790766od_b_c @ A @ B2 )
     => ( ( ord_less_eq_set_a @ ( F @ B2 ) @ C2 )
       => ( ! [X3: set_li6436108459499378894od_b_c,Y4: set_li6436108459499378894od_b_c] :
              ( ( ord_le282488521294790766od_b_c @ X3 @ Y4 )
             => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_set_a @ ( F @ A ) @ C2 ) ) ) ) ).

% order_subst2
thf(fact_451_order__subst2,axiom,
    ! [A: set_a,B2: set_a,F: set_a > set_li6436108459499378894od_b_c,C2: set_li6436108459499378894od_b_c] :
      ( ( ord_less_eq_set_a @ A @ B2 )
     => ( ( ord_le282488521294790766od_b_c @ ( F @ B2 ) @ C2 )
       => ( ! [X3: set_a,Y4: set_a] :
              ( ( ord_less_eq_set_a @ X3 @ Y4 )
             => ( ord_le282488521294790766od_b_c @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_le282488521294790766od_b_c @ ( F @ A ) @ C2 ) ) ) ) ).

% order_subst2
thf(fact_452_order__subst2,axiom,
    ! [A: nat,B2: nat,F: nat > set_li1159382662694783132od_c_a,C2: set_li1159382662694783132od_c_a] :
      ( ( ord_less_eq_nat @ A @ B2 )
     => ( ( ord_le2998388488506175548od_c_a @ ( F @ B2 ) @ C2 )
       => ( ! [X3: nat,Y4: nat] :
              ( ( ord_less_eq_nat @ X3 @ Y4 )
             => ( ord_le2998388488506175548od_c_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_le2998388488506175548od_c_a @ ( F @ A ) @ C2 ) ) ) ) ).

% order_subst2
thf(fact_453_order__subst2,axiom,
    ! [A: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c,F: set_li6436108459499378894od_b_c > set_li6436108459499378894od_b_c,C2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ B2 )
     => ( ( ord_le282488521294790766od_b_c @ ( F @ B2 ) @ C2 )
       => ( ! [X3: set_li6436108459499378894od_b_c,Y4: set_li6436108459499378894od_b_c] :
              ( ( ord_le282488521294790766od_b_c @ X3 @ Y4 )
             => ( ord_le282488521294790766od_b_c @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_le282488521294790766od_b_c @ ( F @ A ) @ C2 ) ) ) ) ).

% order_subst2
thf(fact_454_order__eq__refl,axiom,
    ! [X: nat,Y: nat] :
      ( ( X = Y )
     => ( ord_less_eq_nat @ X @ Y ) ) ).

% order_eq_refl
thf(fact_455_order__eq__refl,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c] :
      ( ( X = Y )
     => ( ord_le282488521294790766od_b_c @ X @ Y ) ) ).

% order_eq_refl
thf(fact_456_order__eq__refl,axiom,
    ! [X: set_a,Y: set_a] :
      ( ( X = Y )
     => ( ord_less_eq_set_a @ X @ Y ) ) ).

% order_eq_refl
thf(fact_457_order__eq__refl,axiom,
    ! [X: set_li1159382662694783132od_c_a,Y: set_li1159382662694783132od_c_a] :
      ( ( X = Y )
     => ( ord_le2998388488506175548od_c_a @ X @ Y ) ) ).

% order_eq_refl
thf(fact_458_linorder__linear,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_eq_nat @ X @ Y )
      | ( ord_less_eq_nat @ Y @ X ) ) ).

% linorder_linear
thf(fact_459_ord__eq__le__subst,axiom,
    ! [A: nat,F: nat > nat,B2: nat,C2: nat] :
      ( ( A
        = ( F @ B2 ) )
     => ( ( ord_less_eq_nat @ B2 @ C2 )
       => ( ! [X3: nat,Y4: nat] :
              ( ( ord_less_eq_nat @ X3 @ Y4 )
             => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_460_ord__eq__le__subst,axiom,
    ! [A: set_a,F: nat > set_a,B2: nat,C2: nat] :
      ( ( A
        = ( F @ B2 ) )
     => ( ( ord_less_eq_nat @ B2 @ C2 )
       => ( ! [X3: nat,Y4: nat] :
              ( ( ord_less_eq_nat @ X3 @ Y4 )
             => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_set_a @ A @ ( F @ C2 ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_461_ord__eq__le__subst,axiom,
    ! [A: nat,F: set_a > nat,B2: set_a,C2: set_a] :
      ( ( A
        = ( F @ B2 ) )
     => ( ( ord_less_eq_set_a @ B2 @ C2 )
       => ( ! [X3: set_a,Y4: set_a] :
              ( ( ord_less_eq_set_a @ X3 @ Y4 )
             => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_462_ord__eq__le__subst,axiom,
    ! [A: set_a,F: set_a > set_a,B2: set_a,C2: set_a] :
      ( ( A
        = ( F @ B2 ) )
     => ( ( ord_less_eq_set_a @ B2 @ C2 )
       => ( ! [X3: set_a,Y4: set_a] :
              ( ( ord_less_eq_set_a @ X3 @ Y4 )
             => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_set_a @ A @ ( F @ C2 ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_463_ord__eq__le__subst,axiom,
    ! [A: set_li6436108459499378894od_b_c,F: nat > set_li6436108459499378894od_b_c,B2: nat,C2: nat] :
      ( ( A
        = ( F @ B2 ) )
     => ( ( ord_less_eq_nat @ B2 @ C2 )
       => ( ! [X3: nat,Y4: nat] :
              ( ( ord_less_eq_nat @ X3 @ Y4 )
             => ( ord_le282488521294790766od_b_c @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_le282488521294790766od_b_c @ A @ ( F @ C2 ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_464_ord__eq__le__subst,axiom,
    ! [A: nat,F: set_li6436108459499378894od_b_c > nat,B2: set_li6436108459499378894od_b_c,C2: set_li6436108459499378894od_b_c] :
      ( ( A
        = ( F @ B2 ) )
     => ( ( ord_le282488521294790766od_b_c @ B2 @ C2 )
       => ( ! [X3: set_li6436108459499378894od_b_c,Y4: set_li6436108459499378894od_b_c] :
              ( ( ord_le282488521294790766od_b_c @ X3 @ Y4 )
             => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_nat @ A @ ( F @ C2 ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_465_ord__eq__le__subst,axiom,
    ! [A: set_a,F: set_li6436108459499378894od_b_c > set_a,B2: set_li6436108459499378894od_b_c,C2: set_li6436108459499378894od_b_c] :
      ( ( A
        = ( F @ B2 ) )
     => ( ( ord_le282488521294790766od_b_c @ B2 @ C2 )
       => ( ! [X3: set_li6436108459499378894od_b_c,Y4: set_li6436108459499378894od_b_c] :
              ( ( ord_le282488521294790766od_b_c @ X3 @ Y4 )
             => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_set_a @ A @ ( F @ C2 ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_466_ord__eq__le__subst,axiom,
    ! [A: set_li6436108459499378894od_b_c,F: set_a > set_li6436108459499378894od_b_c,B2: set_a,C2: set_a] :
      ( ( A
        = ( F @ B2 ) )
     => ( ( ord_less_eq_set_a @ B2 @ C2 )
       => ( ! [X3: set_a,Y4: set_a] :
              ( ( ord_less_eq_set_a @ X3 @ Y4 )
             => ( ord_le282488521294790766od_b_c @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_le282488521294790766od_b_c @ A @ ( F @ C2 ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_467_ord__eq__le__subst,axiom,
    ! [A: set_li1159382662694783132od_c_a,F: nat > set_li1159382662694783132od_c_a,B2: nat,C2: nat] :
      ( ( A
        = ( F @ B2 ) )
     => ( ( ord_less_eq_nat @ B2 @ C2 )
       => ( ! [X3: nat,Y4: nat] :
              ( ( ord_less_eq_nat @ X3 @ Y4 )
             => ( ord_le2998388488506175548od_c_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_le2998388488506175548od_c_a @ A @ ( F @ C2 ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_468_ord__eq__le__subst,axiom,
    ! [A: set_li6436108459499378894od_b_c,F: set_li6436108459499378894od_b_c > set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c,C2: set_li6436108459499378894od_b_c] :
      ( ( A
        = ( F @ B2 ) )
     => ( ( ord_le282488521294790766od_b_c @ B2 @ C2 )
       => ( ! [X3: set_li6436108459499378894od_b_c,Y4: set_li6436108459499378894od_b_c] :
              ( ( ord_le282488521294790766od_b_c @ X3 @ Y4 )
             => ( ord_le282488521294790766od_b_c @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_le282488521294790766od_b_c @ A @ ( F @ C2 ) ) ) ) ) ).

% ord_eq_le_subst
thf(fact_469_ord__le__eq__subst,axiom,
    ! [A: nat,B2: nat,F: nat > nat,C2: nat] :
      ( ( ord_less_eq_nat @ A @ B2 )
     => ( ( ( F @ B2 )
          = C2 )
       => ( ! [X3: nat,Y4: nat] :
              ( ( ord_less_eq_nat @ X3 @ Y4 )
             => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).

% ord_le_eq_subst
thf(fact_470_ord__le__eq__subst,axiom,
    ! [A: nat,B2: nat,F: nat > set_a,C2: set_a] :
      ( ( ord_less_eq_nat @ A @ B2 )
     => ( ( ( F @ B2 )
          = C2 )
       => ( ! [X3: nat,Y4: nat] :
              ( ( ord_less_eq_nat @ X3 @ Y4 )
             => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_set_a @ ( F @ A ) @ C2 ) ) ) ) ).

% ord_le_eq_subst
thf(fact_471_ord__le__eq__subst,axiom,
    ! [A: set_a,B2: set_a,F: set_a > nat,C2: nat] :
      ( ( ord_less_eq_set_a @ A @ B2 )
     => ( ( ( F @ B2 )
          = C2 )
       => ( ! [X3: set_a,Y4: set_a] :
              ( ( ord_less_eq_set_a @ X3 @ Y4 )
             => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).

% ord_le_eq_subst
thf(fact_472_ord__le__eq__subst,axiom,
    ! [A: set_a,B2: set_a,F: set_a > set_a,C2: set_a] :
      ( ( ord_less_eq_set_a @ A @ B2 )
     => ( ( ( F @ B2 )
          = C2 )
       => ( ! [X3: set_a,Y4: set_a] :
              ( ( ord_less_eq_set_a @ X3 @ Y4 )
             => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_set_a @ ( F @ A ) @ C2 ) ) ) ) ).

% ord_le_eq_subst
thf(fact_473_ord__le__eq__subst,axiom,
    ! [A: nat,B2: nat,F: nat > set_li6436108459499378894od_b_c,C2: set_li6436108459499378894od_b_c] :
      ( ( ord_less_eq_nat @ A @ B2 )
     => ( ( ( F @ B2 )
          = C2 )
       => ( ! [X3: nat,Y4: nat] :
              ( ( ord_less_eq_nat @ X3 @ Y4 )
             => ( ord_le282488521294790766od_b_c @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_le282488521294790766od_b_c @ ( F @ A ) @ C2 ) ) ) ) ).

% ord_le_eq_subst
thf(fact_474_ord__le__eq__subst,axiom,
    ! [A: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c,F: set_li6436108459499378894od_b_c > nat,C2: nat] :
      ( ( ord_le282488521294790766od_b_c @ A @ B2 )
     => ( ( ( F @ B2 )
          = C2 )
       => ( ! [X3: set_li6436108459499378894od_b_c,Y4: set_li6436108459499378894od_b_c] :
              ( ( ord_le282488521294790766od_b_c @ X3 @ Y4 )
             => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_nat @ ( F @ A ) @ C2 ) ) ) ) ).

% ord_le_eq_subst
thf(fact_475_ord__le__eq__subst,axiom,
    ! [A: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c,F: set_li6436108459499378894od_b_c > set_a,C2: set_a] :
      ( ( ord_le282488521294790766od_b_c @ A @ B2 )
     => ( ( ( F @ B2 )
          = C2 )
       => ( ! [X3: set_li6436108459499378894od_b_c,Y4: set_li6436108459499378894od_b_c] :
              ( ( ord_le282488521294790766od_b_c @ X3 @ Y4 )
             => ( ord_less_eq_set_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_less_eq_set_a @ ( F @ A ) @ C2 ) ) ) ) ).

% ord_le_eq_subst
thf(fact_476_ord__le__eq__subst,axiom,
    ! [A: set_a,B2: set_a,F: set_a > set_li6436108459499378894od_b_c,C2: set_li6436108459499378894od_b_c] :
      ( ( ord_less_eq_set_a @ A @ B2 )
     => ( ( ( F @ B2 )
          = C2 )
       => ( ! [X3: set_a,Y4: set_a] :
              ( ( ord_less_eq_set_a @ X3 @ Y4 )
             => ( ord_le282488521294790766od_b_c @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_le282488521294790766od_b_c @ ( F @ A ) @ C2 ) ) ) ) ).

% ord_le_eq_subst
thf(fact_477_ord__le__eq__subst,axiom,
    ! [A: nat,B2: nat,F: nat > set_li1159382662694783132od_c_a,C2: set_li1159382662694783132od_c_a] :
      ( ( ord_less_eq_nat @ A @ B2 )
     => ( ( ( F @ B2 )
          = C2 )
       => ( ! [X3: nat,Y4: nat] :
              ( ( ord_less_eq_nat @ X3 @ Y4 )
             => ( ord_le2998388488506175548od_c_a @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_le2998388488506175548od_c_a @ ( F @ A ) @ C2 ) ) ) ) ).

% ord_le_eq_subst
thf(fact_478_ord__le__eq__subst,axiom,
    ! [A: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c,F: set_li6436108459499378894od_b_c > set_li6436108459499378894od_b_c,C2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ B2 )
     => ( ( ( F @ B2 )
          = C2 )
       => ( ! [X3: set_li6436108459499378894od_b_c,Y4: set_li6436108459499378894od_b_c] :
              ( ( ord_le282488521294790766od_b_c @ X3 @ Y4 )
             => ( ord_le282488521294790766od_b_c @ ( F @ X3 ) @ ( F @ Y4 ) ) )
         => ( ord_le282488521294790766od_b_c @ ( F @ A ) @ C2 ) ) ) ) ).

% ord_le_eq_subst
thf(fact_479_linorder__le__cases,axiom,
    ! [X: nat,Y: nat] :
      ( ~ ( ord_less_eq_nat @ X @ Y )
     => ( ord_less_eq_nat @ Y @ X ) ) ).

% linorder_le_cases
thf(fact_480_order__antisym__conv,axiom,
    ! [Y: nat,X: nat] :
      ( ( ord_less_eq_nat @ Y @ X )
     => ( ( ord_less_eq_nat @ X @ Y )
        = ( X = Y ) ) ) ).

% order_antisym_conv
thf(fact_481_order__antisym__conv,axiom,
    ! [Y: set_li6436108459499378894od_b_c,X: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ Y @ X )
     => ( ( ord_le282488521294790766od_b_c @ X @ Y )
        = ( X = Y ) ) ) ).

% order_antisym_conv
thf(fact_482_order__antisym__conv,axiom,
    ! [Y: set_a,X: set_a] :
      ( ( ord_less_eq_set_a @ Y @ X )
     => ( ( ord_less_eq_set_a @ X @ Y )
        = ( X = Y ) ) ) ).

% order_antisym_conv
thf(fact_483_order__antisym__conv,axiom,
    ! [Y: set_li1159382662694783132od_c_a,X: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ Y @ X )
     => ( ( ord_le2998388488506175548od_c_a @ X @ Y )
        = ( X = Y ) ) ) ).

% order_antisym_conv
thf(fact_484_is__singleton__def,axiom,
    ( is_sin490879544914702512od_c_a
    = ( ^ [A6: set_li1159382662694783132od_c_a] :
        ? [X2: list_P6327159017948738492od_c_a] :
          ( A6
          = ( insert4789241225314331020od_c_a @ X2 @ bot_bo6236370880139903240od_c_a ) ) ) ) ).

% is_singleton_def
thf(fact_485_is__singleton__def,axiom,
    ( is_singleton_b
    = ( ^ [A6: set_b] :
        ? [X2: b] :
          ( A6
          = ( insert_b @ X2 @ bot_bot_set_b ) ) ) ) ).

% is_singleton_def
thf(fact_486_is__singleton__def,axiom,
    ( is_sin881476898019872092od_d_d
    = ( ^ [A6: set_Pr9130538228769002824od_d_d] :
        ? [X2: produc4859908366599477352od_d_d] :
          ( A6
          = ( insert4898623881593564728od_d_d @ X2 @ bot_bo7612717905841165748od_d_d ) ) ) ) ).

% is_singleton_def
thf(fact_487_is__singleton__def,axiom,
    ( is_singleton_e
    = ( ^ [A6: set_e] :
        ? [X2: e] :
          ( A6
          = ( insert_e @ X2 @ bot_bot_set_e ) ) ) ) ).

% is_singleton_def
thf(fact_488_is__singletonE,axiom,
    ! [A2: set_li1159382662694783132od_c_a] :
      ( ( is_sin490879544914702512od_c_a @ A2 )
     => ~ ! [X3: list_P6327159017948738492od_c_a] :
            ( A2
           != ( insert4789241225314331020od_c_a @ X3 @ bot_bo6236370880139903240od_c_a ) ) ) ).

% is_singletonE
thf(fact_489_is__singletonE,axiom,
    ! [A2: set_b] :
      ( ( is_singleton_b @ A2 )
     => ~ ! [X3: b] :
            ( A2
           != ( insert_b @ X3 @ bot_bot_set_b ) ) ) ).

% is_singletonE
thf(fact_490_is__singletonE,axiom,
    ! [A2: set_Pr9130538228769002824od_d_d] :
      ( ( is_sin881476898019872092od_d_d @ A2 )
     => ~ ! [X3: produc4859908366599477352od_d_d] :
            ( A2
           != ( insert4898623881593564728od_d_d @ X3 @ bot_bo7612717905841165748od_d_d ) ) ) ).

% is_singletonE
thf(fact_491_is__singletonE,axiom,
    ! [A2: set_e] :
      ( ( is_singleton_e @ A2 )
     => ~ ! [X3: e] :
            ( A2
           != ( insert_e @ X3 @ bot_bot_set_e ) ) ) ).

% is_singletonE
thf(fact_492_path__of__length__ex,axiom,
    ! [M: fsm_a_b_c,Q3: a,K: nat] :
      ( ( comple6900478119722646120_a_b_c @ M )
     => ( ( member_a @ Q3 @ ( states_a_b_c @ M ) )
       => ( ( ( inputs_a_b_c @ M )
           != bot_bot_set_b )
         => ? [P6: list_P6327159017948738492od_c_a] :
              ( ( path_a_b_c @ M @ Q3 @ P6 )
              & ( ( size_s3386368156187063848od_c_a @ P6 )
                = K ) ) ) ) ) ).

% path_of_length_ex
thf(fact_493_path__of__length__ex,axiom,
    ! [M: fsm_e_b_c,Q3: e,K: nat] :
      ( ( comple1615236469910841452_e_b_c @ M )
     => ( ( member_e @ Q3 @ ( states_e_b_c @ M ) )
       => ( ( ( inputs_e_b_c @ M )
           != bot_bot_set_b )
         => ? [P6: list_P1631280100260380348od_c_e] :
              ( ( path_e_b_c @ M @ Q3 @ P6 )
              & ( ( size_s7913861275353481512od_c_e @ P6 )
                = K ) ) ) ) ) ).

% path_of_length_ex
thf(fact_494_paths__up__to__length__set,axiom,
    ! [Q3: a,M: fsm_a_b_c,K: nat] :
      ( ( member_a @ Q3 @ ( states_a_b_c @ M ) )
     => ( ( paths_5655032219139660648_a_b_c @ M @ Q3 @ K )
        = ( collec6273869032445462695od_c_a
          @ ^ [P: list_P6327159017948738492od_c_a] :
              ( ( path_a_b_c @ M @ Q3 @ P )
              & ( ord_less_eq_nat @ ( size_s3386368156187063848od_c_a @ P ) @ K ) ) ) ) ) ).

% paths_up_to_length_set
thf(fact_495_bot__prod__def,axiom,
    ( bot_bo7528007385491256659_set_b
    = ( produc1352782758248380759_set_b @ bot_bot_set_b @ bot_bot_set_b ) ) ).

% bot_prod_def
thf(fact_496_bot__prod__def,axiom,
    ( bot_bo3024046383501997244od_d_d
    = ( produc5044851488359005888od_d_d @ bot_bot_set_b @ bot_bo7612717905841165748od_d_d ) ) ).

% bot_prod_def
thf(fact_497_bot__prod__def,axiom,
    ( bot_bo7741109505630294614_set_e
    = ( produc1352782771158067162_set_e @ bot_bot_set_b @ bot_bot_set_e ) ) ).

% bot_prod_def
thf(fact_498_bot__prod__def,axiom,
    ( bot_bo5900522890569837738_set_b
    = ( produc8111279789426023470_set_b @ bot_bo7612717905841165748od_d_d @ bot_bot_set_b ) ) ).

% bot_prod_def
thf(fact_499_bot__prod__def,axiom,
    ( bot_bo7438930390146683283od_d_d
    = ( produc674974495270471447od_d_d @ bot_bo7612717905841165748od_d_d @ bot_bo7612717905841165748od_d_d ) ) ).

% bot_prod_def
thf(fact_500_bot__prod__def,axiom,
    ( bot_bo6113625010708875693_set_e
    = ( produc8111279802335709873_set_e @ bot_bo7612717905841165748od_d_d @ bot_bot_set_e ) ) ).

% bot_prod_def
thf(fact_501_bot__prod__def,axiom,
    ( bot_bo2768521460520876432_set_b
    = ( produc5816668870132776340_set_b @ bot_bot_set_e @ bot_bot_set_b ) ) ).

% bot_prod_def
thf(fact_502_bot__prod__def,axiom,
    ( bot_bo8527920200830965113od_d_d
    = ( produc1325353268833197949od_d_d @ bot_bot_set_e @ bot_bo7612717905841165748od_d_d ) ) ).

% bot_prod_def
thf(fact_503_bot__prod__def,axiom,
    ( bot_bo2981623580659914387_set_e
    = ( produc5816668883042462743_set_e @ bot_bot_set_e @ bot_bot_set_e ) ) ).

% bot_prod_def
thf(fact_504_eq__snd__iff,axiom,
    ! [B2: d,P3: product_prod_d_d] :
      ( ( B2
        = ( product_snd_d_d @ P3 ) )
      = ( ? [A3: d] :
            ( P3
            = ( product_Pair_d_d @ A3 @ B2 ) ) ) ) ).

% eq_snd_iff
thf(fact_505_eq__snd__iff,axiom,
    ! [B2: list_P6327159017948738492od_c_a,P3: produc3220416805844688357od_c_a] :
      ( ( B2
        = ( produc5527568727691618435od_c_a @ P3 ) )
      = ( ? [A3: a] :
            ( P3
            = ( produc3580641852002036821od_c_a @ A3 @ B2 ) ) ) ) ).

% eq_snd_iff
thf(fact_506_eq__snd__iff,axiom,
    ! [B2: fsm_a_b_c,P3: produc8838969699183119820_a_b_c] :
      ( ( B2
        = ( produc4728557313310798826_a_b_c @ P3 ) )
      = ( ? [A3: a] :
            ( P3
            = ( produc2795441082327197628_a_b_c @ A3 @ B2 ) ) ) ) ).

% eq_snd_iff
thf(fact_507_eq__snd__iff,axiom,
    ! [B2: a,P3: product_prod_a_a] :
      ( ( B2
        = ( product_snd_a_a @ P3 ) )
      = ( ? [A3: a] :
            ( P3
            = ( product_Pair_a_a @ A3 @ B2 ) ) ) ) ).

% eq_snd_iff
thf(fact_508_eq__snd__iff,axiom,
    ! [B2: set_a,P3: produc1703568184450464039_set_a] :
      ( ( B2
        = ( produc1983107199584856133_set_a @ P3 ) )
      = ( ? [A3: set_a] :
            ( P3
            = ( produc9088192753505129239_set_a @ A3 @ B2 ) ) ) ) ).

% eq_snd_iff
thf(fact_509_eq__snd__iff,axiom,
    ! [B2: produc2133359284458116493od_c_a,P3: produc2669932201312201782od_c_a] :
      ( ( B2
        = ( produc8088130389382527188od_c_a @ P3 ) )
      = ( ? [A3: a] :
            ( P3
            = ( produc5762801557034676134od_c_a @ A3 @ B2 ) ) ) ) ).

% eq_snd_iff
thf(fact_510_eq__snd__iff,axiom,
    ! [B2: product_prod_c_a,P3: produc2133359284458116493od_c_a] :
      ( ( B2
        = ( produc5221446324160585515od_c_a @ P3 ) )
      = ( ? [A3: b] :
            ( P3
            = ( produc3440865914000881661od_c_a @ A3 @ B2 ) ) ) ) ).

% eq_snd_iff
thf(fact_511_eq__snd__iff,axiom,
    ! [B2: c,P3: product_prod_b_c] :
      ( ( B2
        = ( product_snd_b_c @ P3 ) )
      = ( ? [A3: b] :
            ( P3
            = ( product_Pair_b_c @ A3 @ B2 ) ) ) ) ).

% eq_snd_iff
thf(fact_512__092_060open_062io_A_092_060noteq_062_A_091_093_092_060close_062,axiom,
    io != nil_Product_prod_b_c ).

% \<open>io \<noteq> []\<close>
thf(fact_513_completely__specified__alt__def,axiom,
    ( comple6900478119722646120_a_b_c
    = ( ^ [M2: fsm_a_b_c] :
        ! [X2: a] :
          ( ( member_a @ X2 @ ( states_a_b_c @ M2 ) )
         => ! [Y2: b] :
              ( ( member_b @ Y2 @ ( inputs_a_b_c @ M2 ) )
             => ? [Q2: a,Z3: c] : ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ X2 @ ( produc3440865914000881661od_c_a @ Y2 @ ( product_Pair_c_a @ Z3 @ Q2 ) ) ) @ ( transitions_a_b_c @ M2 ) ) ) ) ) ) ).

% completely_specified_alt_def
thf(fact_514_completely__specified__alt__def,axiom,
    ( comple1615236469910841452_e_b_c
    = ( ^ [M2: fsm_e_b_c] :
        ! [X2: e] :
          ( ( member_e @ X2 @ ( states_e_b_c @ M2 ) )
         => ! [Y2: b] :
              ( ( member_b @ Y2 @ ( inputs_e_b_c @ M2 ) )
             => ? [Q2: e,Z3: c] : ( member6882148676089805663od_c_e @ ( produc8288412161402371238od_c_e @ X2 @ ( produc3440865931213796865od_c_e @ Y2 @ ( product_Pair_c_e @ Z3 @ Q2 ) ) ) @ ( transitions_e_b_c @ M2 ) ) ) ) ) ) ).

% completely_specified_alt_def
thf(fact_515_add__input__simps_I2_J,axiom,
    ! [M: fsm_e_b_c,X: b] :
      ( ( inputs_e_b_c @ ( add_input_e_b_c @ M @ X ) )
      = ( insert_b @ X @ ( inputs_e_b_c @ M ) ) ) ).

% add_input_simps(2)
thf(fact_516_add__input__simps_I2_J,axiom,
    ! [M: fsm_a_b_c,X: b] :
      ( ( inputs_a_b_c @ ( add_input_a_b_c @ M @ X ) )
      = ( insert_b @ X @ ( inputs_a_b_c @ M ) ) ) ).

% add_input_simps(2)
thf(fact_517__092_060open_062ioEx_A_092_060noteq_062_A_091_093_092_060close_062,axiom,
    ioEx != nil_Product_prod_b_c ).

% \<open>ioEx \<noteq> []\<close>
thf(fact_518_subsetI,axiom,
    ! [A2: set_e,B: set_e] :
      ( ! [X3: e] :
          ( ( member_e @ X3 @ A2 )
         => ( member_e @ X3 @ B ) )
     => ( ord_less_eq_set_e @ A2 @ B ) ) ).

% subsetI
thf(fact_519_subsetI,axiom,
    ! [A2: set_b,B: set_b] :
      ( ! [X3: b] :
          ( ( member_b @ X3 @ A2 )
         => ( member_b @ X3 @ B ) )
     => ( ord_less_eq_set_b @ A2 @ B ) ) ).

% subsetI
thf(fact_520_subsetI,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ! [X3: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X3 @ A2 )
         => ( member6330420149250801815od_b_c @ X3 @ B ) )
     => ( ord_le282488521294790766od_b_c @ A2 @ B ) ) ).

% subsetI
thf(fact_521_subsetI,axiom,
    ! [A2: set_a,B: set_a] :
      ( ! [X3: a] :
          ( ( member_a @ X3 @ A2 )
         => ( member_a @ X3 @ B ) )
     => ( ord_less_eq_set_a @ A2 @ B ) ) ).

% subsetI
thf(fact_522_subsetI,axiom,
    ! [A2: set_li1159382662694783132od_c_a,B: set_li1159382662694783132od_c_a] :
      ( ! [X3: list_P6327159017948738492od_c_a] :
          ( ( member7410604586820865893od_c_a @ X3 @ A2 )
         => ( member7410604586820865893od_c_a @ X3 @ B ) )
     => ( ord_le2998388488506175548od_c_a @ A2 @ B ) ) ).

% subsetI
thf(fact_523_subset__antisym,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A2 @ B )
     => ( ( ord_le282488521294790766od_b_c @ B @ A2 )
       => ( A2 = B ) ) ) ).

% subset_antisym
thf(fact_524_subset__antisym,axiom,
    ! [A2: set_a,B: set_a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ( ord_less_eq_set_a @ B @ A2 )
       => ( A2 = B ) ) ) ).

% subset_antisym
thf(fact_525_subset__antisym,axiom,
    ! [A2: set_li1159382662694783132od_c_a,B: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ A2 @ B )
     => ( ( ord_le2998388488506175548od_c_a @ B @ A2 )
       => ( A2 = B ) ) ) ).

% subset_antisym
thf(fact_526_initial__preamble__simps_I5_J,axiom,
    ! [M: fsm_a_b_c] :
      ( ( transitions_a_b_c @ ( state_4132440018836379711_a_b_c @ M ) )
      = bot_bo267491471446728962od_c_a ) ).

% initial_preamble_simps(5)
thf(fact_527_add__input__simps_I1_J,axiom,
    ! [M: fsm_a_b_c,X: b] :
      ( ( initial_a_b_c @ ( add_input_a_b_c @ M @ X ) )
      = ( initial_a_b_c @ M ) ) ).

% add_input_simps(1)
thf(fact_528_add__input__simps_I1_J,axiom,
    ! [M: fsm_e_b_c,X: b] :
      ( ( initial_e_b_c @ ( add_input_e_b_c @ M @ X ) )
      = ( initial_e_b_c @ M ) ) ).

% add_input_simps(1)
thf(fact_529_add__input__simps_I5_J,axiom,
    ! [M: fsm_a_b_c,X: b] :
      ( ( states_a_b_c @ ( add_input_a_b_c @ M @ X ) )
      = ( states_a_b_c @ M ) ) ).

% add_input_simps(5)
thf(fact_530_fsm__transition__target,axiom,
    ! [T: produc2669932201312201782od_c_a,M: fsm_a_b_c] :
      ( ( member5502040268208861279od_c_a @ T @ ( transitions_a_b_c @ M ) )
     => ( member_a @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) @ ( states_a_b_c @ M ) ) ) ).

% fsm_transition_target
thf(fact_531_fsm__transition__target,axiom,
    ! [T: produc3205353004677322104od_c_a,M: fsm_Pr1886043760914421514_a_a_b] :
      ( ( member6508725278956418977od_c_a @ T @ ( transi2941759273464634107_a_a_b @ M ) )
     => ( member5074992350434858958od_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) @ ( states367398909958982703_a_a_b @ M ) ) ) ).

% fsm_transition_target
thf(fact_532_in__mono,axiom,
    ! [A2: set_e,B: set_e,X: e] :
      ( ( ord_less_eq_set_e @ A2 @ B )
     => ( ( member_e @ X @ A2 )
       => ( member_e @ X @ B ) ) ) ).

% in_mono
thf(fact_533_in__mono,axiom,
    ! [A2: set_b,B: set_b,X: b] :
      ( ( ord_less_eq_set_b @ A2 @ B )
     => ( ( member_b @ X @ A2 )
       => ( member_b @ X @ B ) ) ) ).

% in_mono
thf(fact_534_in__mono,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c,X: list_P903359562653991662od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A2 @ B )
     => ( ( member6330420149250801815od_b_c @ X @ A2 )
       => ( member6330420149250801815od_b_c @ X @ B ) ) ) ).

% in_mono
thf(fact_535_in__mono,axiom,
    ! [A2: set_a,B: set_a,X: a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ( member_a @ X @ A2 )
       => ( member_a @ X @ B ) ) ) ).

% in_mono
thf(fact_536_in__mono,axiom,
    ! [A2: set_li1159382662694783132od_c_a,B: set_li1159382662694783132od_c_a,X: list_P6327159017948738492od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ A2 @ B )
     => ( ( member7410604586820865893od_c_a @ X @ A2 )
       => ( member7410604586820865893od_c_a @ X @ B ) ) ) ).

% in_mono
thf(fact_537_subsetD,axiom,
    ! [A2: set_e,B: set_e,C2: e] :
      ( ( ord_less_eq_set_e @ A2 @ B )
     => ( ( member_e @ C2 @ A2 )
       => ( member_e @ C2 @ B ) ) ) ).

% subsetD
thf(fact_538_subsetD,axiom,
    ! [A2: set_b,B: set_b,C2: b] :
      ( ( ord_less_eq_set_b @ A2 @ B )
     => ( ( member_b @ C2 @ A2 )
       => ( member_b @ C2 @ B ) ) ) ).

% subsetD
thf(fact_539_subsetD,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c,C2: list_P903359562653991662od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A2 @ B )
     => ( ( member6330420149250801815od_b_c @ C2 @ A2 )
       => ( member6330420149250801815od_b_c @ C2 @ B ) ) ) ).

% subsetD
thf(fact_540_subsetD,axiom,
    ! [A2: set_a,B: set_a,C2: a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ( member_a @ C2 @ A2 )
       => ( member_a @ C2 @ B ) ) ) ).

% subsetD
thf(fact_541_subsetD,axiom,
    ! [A2: set_li1159382662694783132od_c_a,B: set_li1159382662694783132od_c_a,C2: list_P6327159017948738492od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ A2 @ B )
     => ( ( member7410604586820865893od_c_a @ C2 @ A2 )
       => ( member7410604586820865893od_c_a @ C2 @ B ) ) ) ).

% subsetD
thf(fact_542_equalityE,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( A2 = B )
     => ~ ( ( ord_le282488521294790766od_b_c @ A2 @ B )
         => ~ ( ord_le282488521294790766od_b_c @ B @ A2 ) ) ) ).

% equalityE
thf(fact_543_equalityE,axiom,
    ! [A2: set_a,B: set_a] :
      ( ( A2 = B )
     => ~ ( ( ord_less_eq_set_a @ A2 @ B )
         => ~ ( ord_less_eq_set_a @ B @ A2 ) ) ) ).

% equalityE
thf(fact_544_equalityE,axiom,
    ! [A2: set_li1159382662694783132od_c_a,B: set_li1159382662694783132od_c_a] :
      ( ( A2 = B )
     => ~ ( ( ord_le2998388488506175548od_c_a @ A2 @ B )
         => ~ ( ord_le2998388488506175548od_c_a @ B @ A2 ) ) ) ).

% equalityE
thf(fact_545_subset__eq,axiom,
    ( ord_less_eq_set_e
    = ( ^ [A6: set_e,B3: set_e] :
        ! [X2: e] :
          ( ( member_e @ X2 @ A6 )
         => ( member_e @ X2 @ B3 ) ) ) ) ).

% subset_eq
thf(fact_546_subset__eq,axiom,
    ( ord_less_eq_set_b
    = ( ^ [A6: set_b,B3: set_b] :
        ! [X2: b] :
          ( ( member_b @ X2 @ A6 )
         => ( member_b @ X2 @ B3 ) ) ) ) ).

% subset_eq
thf(fact_547_subset__eq,axiom,
    ( ord_le282488521294790766od_b_c
    = ( ^ [A6: set_li6436108459499378894od_b_c,B3: set_li6436108459499378894od_b_c] :
        ! [X2: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ X2 @ A6 )
         => ( member6330420149250801815od_b_c @ X2 @ B3 ) ) ) ) ).

% subset_eq
thf(fact_548_subset__eq,axiom,
    ( ord_less_eq_set_a
    = ( ^ [A6: set_a,B3: set_a] :
        ! [X2: a] :
          ( ( member_a @ X2 @ A6 )
         => ( member_a @ X2 @ B3 ) ) ) ) ).

% subset_eq
thf(fact_549_subset__eq,axiom,
    ( ord_le2998388488506175548od_c_a
    = ( ^ [A6: set_li1159382662694783132od_c_a,B3: set_li1159382662694783132od_c_a] :
        ! [X2: list_P6327159017948738492od_c_a] :
          ( ( member7410604586820865893od_c_a @ X2 @ A6 )
         => ( member7410604586820865893od_c_a @ X2 @ B3 ) ) ) ) ).

% subset_eq
thf(fact_550_equalityD1,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( A2 = B )
     => ( ord_le282488521294790766od_b_c @ A2 @ B ) ) ).

% equalityD1
thf(fact_551_equalityD1,axiom,
    ! [A2: set_a,B: set_a] :
      ( ( A2 = B )
     => ( ord_less_eq_set_a @ A2 @ B ) ) ).

% equalityD1
thf(fact_552_equalityD1,axiom,
    ! [A2: set_li1159382662694783132od_c_a,B: set_li1159382662694783132od_c_a] :
      ( ( A2 = B )
     => ( ord_le2998388488506175548od_c_a @ A2 @ B ) ) ).

% equalityD1
thf(fact_553_equalityD2,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( A2 = B )
     => ( ord_le282488521294790766od_b_c @ B @ A2 ) ) ).

% equalityD2
thf(fact_554_equalityD2,axiom,
    ! [A2: set_a,B: set_a] :
      ( ( A2 = B )
     => ( ord_less_eq_set_a @ B @ A2 ) ) ).

% equalityD2
thf(fact_555_equalityD2,axiom,
    ! [A2: set_li1159382662694783132od_c_a,B: set_li1159382662694783132od_c_a] :
      ( ( A2 = B )
     => ( ord_le2998388488506175548od_c_a @ B @ A2 ) ) ).

% equalityD2
thf(fact_556_subset__iff,axiom,
    ( ord_less_eq_set_e
    = ( ^ [A6: set_e,B3: set_e] :
        ! [T2: e] :
          ( ( member_e @ T2 @ A6 )
         => ( member_e @ T2 @ B3 ) ) ) ) ).

% subset_iff
thf(fact_557_subset__iff,axiom,
    ( ord_less_eq_set_b
    = ( ^ [A6: set_b,B3: set_b] :
        ! [T2: b] :
          ( ( member_b @ T2 @ A6 )
         => ( member_b @ T2 @ B3 ) ) ) ) ).

% subset_iff
thf(fact_558_subset__iff,axiom,
    ( ord_le282488521294790766od_b_c
    = ( ^ [A6: set_li6436108459499378894od_b_c,B3: set_li6436108459499378894od_b_c] :
        ! [T2: list_P903359562653991662od_b_c] :
          ( ( member6330420149250801815od_b_c @ T2 @ A6 )
         => ( member6330420149250801815od_b_c @ T2 @ B3 ) ) ) ) ).

% subset_iff
thf(fact_559_subset__iff,axiom,
    ( ord_less_eq_set_a
    = ( ^ [A6: set_a,B3: set_a] :
        ! [T2: a] :
          ( ( member_a @ T2 @ A6 )
         => ( member_a @ T2 @ B3 ) ) ) ) ).

% subset_iff
thf(fact_560_subset__iff,axiom,
    ( ord_le2998388488506175548od_c_a
    = ( ^ [A6: set_li1159382662694783132od_c_a,B3: set_li1159382662694783132od_c_a] :
        ! [T2: list_P6327159017948738492od_c_a] :
          ( ( member7410604586820865893od_c_a @ T2 @ A6 )
         => ( member7410604586820865893od_c_a @ T2 @ B3 ) ) ) ) ).

% subset_iff
thf(fact_561_subset__refl,axiom,
    ! [A2: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ A2 @ A2 ) ).

% subset_refl
thf(fact_562_subset__refl,axiom,
    ! [A2: set_a] : ( ord_less_eq_set_a @ A2 @ A2 ) ).

% subset_refl
thf(fact_563_subset__refl,axiom,
    ! [A2: set_li1159382662694783132od_c_a] : ( ord_le2998388488506175548od_c_a @ A2 @ A2 ) ).

% subset_refl
thf(fact_564_Collect__mono,axiom,
    ! [P2: list_P903359562653991662od_b_c > $o,Q4: list_P903359562653991662od_b_c > $o] :
      ( ! [X3: list_P903359562653991662od_b_c] :
          ( ( P2 @ X3 )
         => ( Q4 @ X3 ) )
     => ( ord_le282488521294790766od_b_c @ ( collec2280997390073109977od_b_c @ P2 ) @ ( collec2280997390073109977od_b_c @ Q4 ) ) ) ).

% Collect_mono
thf(fact_565_Collect__mono,axiom,
    ! [P2: a > $o,Q4: a > $o] :
      ( ! [X3: a] :
          ( ( P2 @ X3 )
         => ( Q4 @ X3 ) )
     => ( ord_less_eq_set_a @ ( collect_a @ P2 ) @ ( collect_a @ Q4 ) ) ) ).

% Collect_mono
thf(fact_566_Collect__mono,axiom,
    ! [P2: list_P6327159017948738492od_c_a > $o,Q4: list_P6327159017948738492od_c_a > $o] :
      ( ! [X3: list_P6327159017948738492od_c_a] :
          ( ( P2 @ X3 )
         => ( Q4 @ X3 ) )
     => ( ord_le2998388488506175548od_c_a @ ( collec6273869032445462695od_c_a @ P2 ) @ ( collec6273869032445462695od_c_a @ Q4 ) ) ) ).

% Collect_mono
thf(fact_567_subset__trans,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c,C3: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A2 @ B )
     => ( ( ord_le282488521294790766od_b_c @ B @ C3 )
       => ( ord_le282488521294790766od_b_c @ A2 @ C3 ) ) ) ).

% subset_trans
thf(fact_568_subset__trans,axiom,
    ! [A2: set_a,B: set_a,C3: set_a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ( ord_less_eq_set_a @ B @ C3 )
       => ( ord_less_eq_set_a @ A2 @ C3 ) ) ) ).

% subset_trans
thf(fact_569_subset__trans,axiom,
    ! [A2: set_li1159382662694783132od_c_a,B: set_li1159382662694783132od_c_a,C3: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ A2 @ B )
     => ( ( ord_le2998388488506175548od_c_a @ B @ C3 )
       => ( ord_le2998388488506175548od_c_a @ A2 @ C3 ) ) ) ).

% subset_trans
thf(fact_570_set__eq__subset,axiom,
    ( ( ^ [Y3: set_li6436108459499378894od_b_c,Z: set_li6436108459499378894od_b_c] : ( Y3 = Z ) )
    = ( ^ [A6: set_li6436108459499378894od_b_c,B3: set_li6436108459499378894od_b_c] :
          ( ( ord_le282488521294790766od_b_c @ A6 @ B3 )
          & ( ord_le282488521294790766od_b_c @ B3 @ A6 ) ) ) ) ).

% set_eq_subset
thf(fact_571_set__eq__subset,axiom,
    ( ( ^ [Y3: set_a,Z: set_a] : ( Y3 = Z ) )
    = ( ^ [A6: set_a,B3: set_a] :
          ( ( ord_less_eq_set_a @ A6 @ B3 )
          & ( ord_less_eq_set_a @ B3 @ A6 ) ) ) ) ).

% set_eq_subset
thf(fact_572_set__eq__subset,axiom,
    ( ( ^ [Y3: set_li1159382662694783132od_c_a,Z: set_li1159382662694783132od_c_a] : ( Y3 = Z ) )
    = ( ^ [A6: set_li1159382662694783132od_c_a,B3: set_li1159382662694783132od_c_a] :
          ( ( ord_le2998388488506175548od_c_a @ A6 @ B3 )
          & ( ord_le2998388488506175548od_c_a @ B3 @ A6 ) ) ) ) ).

% set_eq_subset
thf(fact_573_less__eq__set__def,axiom,
    ( ord_less_eq_set_e
    = ( ^ [A6: set_e,B3: set_e] :
          ( ord_less_eq_e_o
          @ ^ [X2: e] : ( member_e @ X2 @ A6 )
          @ ^ [X2: e] : ( member_e @ X2 @ B3 ) ) ) ) ).

% less_eq_set_def
thf(fact_574_less__eq__set__def,axiom,
    ( ord_less_eq_set_b
    = ( ^ [A6: set_b,B3: set_b] :
          ( ord_less_eq_b_o
          @ ^ [X2: b] : ( member_b @ X2 @ A6 )
          @ ^ [X2: b] : ( member_b @ X2 @ B3 ) ) ) ) ).

% less_eq_set_def
thf(fact_575_less__eq__set__def,axiom,
    ( ord_le282488521294790766od_b_c
    = ( ^ [A6: set_li6436108459499378894od_b_c,B3: set_li6436108459499378894od_b_c] :
          ( ord_le1261880702084804079_b_c_o
          @ ^ [X2: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ X2 @ A6 )
          @ ^ [X2: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ X2 @ B3 ) ) ) ) ).

% less_eq_set_def
thf(fact_576_less__eq__set__def,axiom,
    ( ord_less_eq_set_a
    = ( ^ [A6: set_a,B3: set_a] :
          ( ord_less_eq_a_o
          @ ^ [X2: a] : ( member_a @ X2 @ A6 )
          @ ^ [X2: a] : ( member_a @ X2 @ B3 ) ) ) ) ).

% less_eq_set_def
thf(fact_577_less__eq__set__def,axiom,
    ( ord_le2998388488506175548od_c_a
    = ( ^ [A6: set_li1159382662694783132od_c_a,B3: set_li1159382662694783132od_c_a] :
          ( ord_le2170622466739808161_c_a_o
          @ ^ [X2: list_P6327159017948738492od_c_a] : ( member7410604586820865893od_c_a @ X2 @ A6 )
          @ ^ [X2: list_P6327159017948738492od_c_a] : ( member7410604586820865893od_c_a @ X2 @ B3 ) ) ) ) ).

% less_eq_set_def
thf(fact_578_Collect__mono__iff,axiom,
    ! [P2: list_P903359562653991662od_b_c > $o,Q4: list_P903359562653991662od_b_c > $o] :
      ( ( ord_le282488521294790766od_b_c @ ( collec2280997390073109977od_b_c @ P2 ) @ ( collec2280997390073109977od_b_c @ Q4 ) )
      = ( ! [X2: list_P903359562653991662od_b_c] :
            ( ( P2 @ X2 )
           => ( Q4 @ X2 ) ) ) ) ).

% Collect_mono_iff
thf(fact_579_Collect__mono__iff,axiom,
    ! [P2: a > $o,Q4: a > $o] :
      ( ( ord_less_eq_set_a @ ( collect_a @ P2 ) @ ( collect_a @ Q4 ) )
      = ( ! [X2: a] :
            ( ( P2 @ X2 )
           => ( Q4 @ X2 ) ) ) ) ).

% Collect_mono_iff
thf(fact_580_Collect__mono__iff,axiom,
    ! [P2: list_P6327159017948738492od_c_a > $o,Q4: list_P6327159017948738492od_c_a > $o] :
      ( ( ord_le2998388488506175548od_c_a @ ( collec6273869032445462695od_c_a @ P2 ) @ ( collec6273869032445462695od_c_a @ Q4 ) )
      = ( ! [X2: list_P6327159017948738492od_c_a] :
            ( ( P2 @ X2 )
           => ( Q4 @ X2 ) ) ) ) ).

% Collect_mono_iff
thf(fact_581_Collect__subset,axiom,
    ! [A2: set_e,P2: e > $o] :
      ( ord_less_eq_set_e
      @ ( collect_e
        @ ^ [X2: e] :
            ( ( member_e @ X2 @ A2 )
            & ( P2 @ X2 ) ) )
      @ A2 ) ).

% Collect_subset
thf(fact_582_Collect__subset,axiom,
    ! [A2: set_b,P2: b > $o] :
      ( ord_less_eq_set_b
      @ ( collect_b
        @ ^ [X2: b] :
            ( ( member_b @ X2 @ A2 )
            & ( P2 @ X2 ) ) )
      @ A2 ) ).

% Collect_subset
thf(fact_583_Collect__subset,axiom,
    ! [A2: set_li6436108459499378894od_b_c,P2: list_P903359562653991662od_b_c > $o] :
      ( ord_le282488521294790766od_b_c
      @ ( collec2280997390073109977od_b_c
        @ ^ [X2: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X2 @ A2 )
            & ( P2 @ X2 ) ) )
      @ A2 ) ).

% Collect_subset
thf(fact_584_Collect__subset,axiom,
    ! [A2: set_a,P2: a > $o] :
      ( ord_less_eq_set_a
      @ ( collect_a
        @ ^ [X2: a] :
            ( ( member_a @ X2 @ A2 )
            & ( P2 @ X2 ) ) )
      @ A2 ) ).

% Collect_subset
thf(fact_585_Collect__subset,axiom,
    ! [A2: set_li1159382662694783132od_c_a,P2: list_P6327159017948738492od_c_a > $o] :
      ( ord_le2998388488506175548od_c_a
      @ ( collec6273869032445462695od_c_a
        @ ^ [X2: list_P6327159017948738492od_c_a] :
            ( ( member7410604586820865893od_c_a @ X2 @ A2 )
            & ( P2 @ X2 ) ) )
      @ A2 ) ).

% Collect_subset
thf(fact_586_transition__subset__path,axiom,
    ! [A2: fsm_a_b_c,B: fsm_a_b_c,Q3: a,P3: list_P6327159017948738492od_c_a] :
      ( ( ord_le3226338165915859510od_c_a @ ( transitions_a_b_c @ A2 ) @ ( transitions_a_b_c @ B ) )
     => ( ( path_a_b_c @ A2 @ Q3 @ P3 )
       => ( ( member_a @ Q3 @ ( states_a_b_c @ B ) )
         => ( path_a_b_c @ B @ Q3 @ P3 ) ) ) ) ).

% transition_subset_path
thf(fact_587_observable__alt__def,axiom,
    ( observable_a_b_c
    = ( ^ [M2: fsm_a_b_c] :
        ! [Q1: a,X2: b,Y2: c,Q12: a,Q13: a] :
          ( ( ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q1 @ ( produc3440865914000881661od_c_a @ X2 @ ( product_Pair_c_a @ Y2 @ Q12 ) ) ) @ ( transitions_a_b_c @ M2 ) )
            & ( member5502040268208861279od_c_a @ ( produc5762801557034676134od_c_a @ Q1 @ ( produc3440865914000881661od_c_a @ X2 @ ( product_Pair_c_a @ Y2 @ Q13 ) ) ) @ ( transitions_a_b_c @ M2 ) ) )
         => ( Q12 = Q13 ) ) ) ) ).

% observable_alt_def
thf(fact_588_observable__alt__def,axiom,
    ( observable_e_b_c
    = ( ^ [M2: fsm_e_b_c] :
        ! [Q1: e,X2: b,Y2: c,Q12: e,Q13: e] :
          ( ( ( member6882148676089805663od_c_e @ ( produc8288412161402371238od_c_e @ Q1 @ ( produc3440865931213796865od_c_e @ X2 @ ( product_Pair_c_e @ Y2 @ Q12 ) ) ) @ ( transitions_e_b_c @ M2 ) )
            & ( member6882148676089805663od_c_e @ ( produc8288412161402371238od_c_e @ Q1 @ ( produc3440865931213796865od_c_e @ X2 @ ( product_Pair_c_e @ Y2 @ Q13 ) ) ) @ ( transitions_e_b_c @ M2 ) ) )
         => ( Q12 = Q13 ) ) ) ) ).

% observable_alt_def
thf(fact_589_Collect__empty__eq__bot,axiom,
    ! [P2: list_P6327159017948738492od_c_a > $o] :
      ( ( ( collec6273869032445462695od_c_a @ P2 )
        = bot_bo6236370880139903240od_c_a )
      = ( P2 = bot_bo4941546593110769109_c_a_o ) ) ).

% Collect_empty_eq_bot
thf(fact_590_Collect__empty__eq__bot,axiom,
    ! [P2: b > $o] :
      ( ( ( collect_b @ P2 )
        = bot_bot_set_b )
      = ( P2 = bot_bot_b_o ) ) ).

% Collect_empty_eq_bot
thf(fact_591_Collect__empty__eq__bot,axiom,
    ! [P2: produc4859908366599477352od_d_d > $o] :
      ( ( ( collec5362705567740981075od_d_d @ P2 )
        = bot_bo7612717905841165748od_d_d )
      = ( P2 = bot_bo8796992887960848425_d_d_o ) ) ).

% Collect_empty_eq_bot
thf(fact_592_Collect__empty__eq__bot,axiom,
    ! [P2: e > $o] :
      ( ( ( collect_e @ P2 )
        = bot_bot_set_e )
      = ( P2 = bot_bot_e_o ) ) ).

% Collect_empty_eq_bot
thf(fact_593_bot__empty__eq,axiom,
    ( bot_bo5496101219168594979_b_c_o
    = ( ^ [X2: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ X2 @ bot_bo4166481423041325370od_b_c ) ) ) ).

% bot_empty_eq
thf(fact_594_bot__empty__eq,axiom,
    ( bot_bo4941546593110769109_c_a_o
    = ( ^ [X2: list_P6327159017948738492od_c_a] : ( member7410604586820865893od_c_a @ X2 @ bot_bo6236370880139903240od_c_a ) ) ) ).

% bot_empty_eq
thf(fact_595_bot__empty__eq,axiom,
    ( bot_bot_a_o
    = ( ^ [X2: a] : ( member_a @ X2 @ bot_bot_set_a ) ) ) ).

% bot_empty_eq
thf(fact_596_bot__empty__eq,axiom,
    ( bot_bot_b_o
    = ( ^ [X2: b] : ( member_b @ X2 @ bot_bot_set_b ) ) ) ).

% bot_empty_eq
thf(fact_597_bot__empty__eq,axiom,
    ( bot_bo8796992887960848425_d_d_o
    = ( ^ [X2: produc4859908366599477352od_d_d] : ( member73601632213084689od_d_d @ X2 @ bot_bo7612717905841165748od_d_d ) ) ) ).

% bot_empty_eq
thf(fact_598_bot__empty__eq,axiom,
    ( bot_bot_e_o
    = ( ^ [X2: e] : ( member_e @ X2 @ bot_bot_set_e ) ) ) ).

% bot_empty_eq
thf(fact_599_insert__subsetI,axiom,
    ! [X: e,A2: set_e,X6: set_e] :
      ( ( member_e @ X @ A2 )
     => ( ( ord_less_eq_set_e @ X6 @ A2 )
       => ( ord_less_eq_set_e @ ( insert_e @ X @ X6 ) @ A2 ) ) ) ).

% insert_subsetI
thf(fact_600_insert__subsetI,axiom,
    ! [X: b,A2: set_b,X6: set_b] :
      ( ( member_b @ X @ A2 )
     => ( ( ord_less_eq_set_b @ X6 @ A2 )
       => ( ord_less_eq_set_b @ ( insert_b @ X @ X6 ) @ A2 ) ) ) ).

% insert_subsetI
thf(fact_601_insert__subsetI,axiom,
    ! [X: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c,X6: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ X @ A2 )
     => ( ( ord_le282488521294790766od_b_c @ X6 @ A2 )
       => ( ord_le282488521294790766od_b_c @ ( insert6227932334100060350od_b_c @ X @ X6 ) @ A2 ) ) ) ).

% insert_subsetI
thf(fact_602_insert__subsetI,axiom,
    ! [X: a,A2: set_a,X6: set_a] :
      ( ( member_a @ X @ A2 )
     => ( ( ord_less_eq_set_a @ X6 @ A2 )
       => ( ord_less_eq_set_a @ ( insert_a @ X @ X6 ) @ A2 ) ) ) ).

% insert_subsetI
thf(fact_603_insert__subsetI,axiom,
    ! [X: list_P6327159017948738492od_c_a,A2: set_li1159382662694783132od_c_a,X6: set_li1159382662694783132od_c_a] :
      ( ( member7410604586820865893od_c_a @ X @ A2 )
     => ( ( ord_le2998388488506175548od_c_a @ X6 @ A2 )
       => ( ord_le2998388488506175548od_c_a @ ( insert4789241225314331020od_c_a @ X @ X6 ) @ A2 ) ) ) ).

% insert_subsetI
thf(fact_604_subset__emptyI,axiom,
    ! [A2: set_b] :
      ( ! [X3: b] :
          ~ ( member_b @ X3 @ A2 )
     => ( ord_less_eq_set_b @ A2 @ bot_bot_set_b ) ) ).

% subset_emptyI
thf(fact_605_subset__emptyI,axiom,
    ! [A2: set_Pr9130538228769002824od_d_d] :
      ( ! [X3: produc4859908366599477352od_d_d] :
          ~ ( member73601632213084689od_d_d @ X3 @ A2 )
     => ( ord_le7464911323401878760od_d_d @ A2 @ bot_bo7612717905841165748od_d_d ) ) ).

% subset_emptyI
thf(fact_606_subset__emptyI,axiom,
    ! [A2: set_e] :
      ( ! [X3: e] :
          ~ ( member_e @ X3 @ A2 )
     => ( ord_less_eq_set_e @ A2 @ bot_bot_set_e ) ) ).

% subset_emptyI
thf(fact_607_subset__emptyI,axiom,
    ! [A2: set_li6436108459499378894od_b_c] :
      ( ! [X3: list_P903359562653991662od_b_c] :
          ~ ( member6330420149250801815od_b_c @ X3 @ A2 )
     => ( ord_le282488521294790766od_b_c @ A2 @ bot_bo4166481423041325370od_b_c ) ) ).

% subset_emptyI
thf(fact_608_subset__emptyI,axiom,
    ! [A2: set_a] :
      ( ! [X3: a] :
          ~ ( member_a @ X3 @ A2 )
     => ( ord_less_eq_set_a @ A2 @ bot_bot_set_a ) ) ).

% subset_emptyI
thf(fact_609_subset__emptyI,axiom,
    ! [A2: set_li1159382662694783132od_c_a] :
      ( ! [X3: list_P6327159017948738492od_c_a] :
          ~ ( member7410604586820865893od_c_a @ X3 @ A2 )
     => ( ord_le2998388488506175548od_c_a @ A2 @ bot_bo6236370880139903240od_c_a ) ) ).

% subset_emptyI
thf(fact_610_add__state__simps_I5_J,axiom,
    ! [M: fsm_a_b_c,Q3: a] :
      ( ( states_a_b_c @ ( add_state_a_b_c @ M @ Q3 ) )
      = ( insert_a @ Q3 @ ( states_a_b_c @ M ) ) ) ).

% add_state_simps(5)
thf(fact_611_assms_I9_J,axiom,
    ord_less_eq_nat @ ( size_e_b_c @ m2 ) @ m3 ).

% assms(9)
thf(fact_612_add__state__simps_I1_J,axiom,
    ! [M: fsm_a_b_c,Q3: a] :
      ( ( initial_a_b_c @ ( add_state_a_b_c @ M @ Q3 ) )
      = ( initial_a_b_c @ M ) ) ).

% add_state_simps(1)
thf(fact_613_add__state__simps_I1_J,axiom,
    ! [M: fsm_e_b_c,Q3: e] :
      ( ( initial_e_b_c @ ( add_state_e_b_c @ M @ Q3 ) )
      = ( initial_e_b_c @ M ) ) ).

% add_state_simps(1)
thf(fact_614_add__state__simps_I2_J,axiom,
    ! [M: fsm_e_b_c,Q3: e] :
      ( ( inputs_e_b_c @ ( add_state_e_b_c @ M @ Q3 ) )
      = ( inputs_e_b_c @ M ) ) ).

% add_state_simps(2)
thf(fact_615_add__state__simps_I2_J,axiom,
    ! [M: fsm_a_b_c,Q3: a] :
      ( ( inputs_a_b_c @ ( add_state_a_b_c @ M @ Q3 ) )
      = ( inputs_a_b_c @ M ) ) ).

% add_state_simps(2)
thf(fact_616_subrelI,axiom,
    ! [R: set_Product_prod_d_d,S: set_Product_prod_d_d] :
      ( ! [X3: d,Y4: d] :
          ( ( member2287536781371869328od_d_d @ ( product_Pair_d_d @ X3 @ Y4 ) @ R )
         => ( member2287536781371869328od_d_d @ ( product_Pair_d_d @ X3 @ Y4 ) @ S ) )
     => ( ord_le8276230113588470247od_d_d @ R @ S ) ) ).

% subrelI
thf(fact_617_subrelI,axiom,
    ! [R: set_Product_prod_b_c,S: set_Product_prod_b_c] :
      ( ! [X3: b,Y4: c] :
          ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X3 @ Y4 ) @ R )
         => ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X3 @ Y4 ) @ S ) )
     => ( ord_le253122037897321832od_b_c @ R @ S ) ) ).

% subrelI
thf(fact_618_subrelI,axiom,
    ! [R: set_Pr5230154892316275013od_c_a,S: set_Pr5230154892316275013od_c_a] :
      ( ! [X3: a,Y4: list_P6327159017948738492od_c_a] :
          ( ( member3484049051949443214od_c_a @ ( produc3580641852002036821od_c_a @ X3 @ Y4 ) @ R )
         => ( member3484049051949443214od_c_a @ ( produc3580641852002036821od_c_a @ X3 @ Y4 ) @ S ) )
     => ( ord_le1109660078794635493od_c_a @ R @ S ) ) ).

% subrelI
thf(fact_619_subrelI,axiom,
    ! [R: set_Pr2640454425625433516_a_b_c,S: set_Pr2640454425625433516_a_b_c] :
      ( ! [X3: a,Y4: fsm_a_b_c] :
          ( ( member997585926662434933_a_b_c @ ( produc2795441082327197628_a_b_c @ X3 @ Y4 ) @ R )
         => ( member997585926662434933_a_b_c @ ( produc2795441082327197628_a_b_c @ X3 @ Y4 ) @ S ) )
     => ( ord_le6086132928344890700_a_b_c @ R @ S ) ) ).

% subrelI
thf(fact_620_subrelI,axiom,
    ! [R: set_Product_prod_a_a,S: set_Product_prod_a_a] :
      ( ! [X3: a,Y4: a] :
          ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X3 @ Y4 ) @ R )
         => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X3 @ Y4 ) @ S ) )
     => ( ord_le746702958409616551od_a_a @ R @ S ) ) ).

% subrelI
thf(fact_621_ssubst__Pair__rhs,axiom,
    ! [R: d,S: d,R2: set_Product_prod_d_d,S2: d] :
      ( ( member2287536781371869328od_d_d @ ( product_Pair_d_d @ R @ S ) @ R2 )
     => ( ( S2 = S )
       => ( member2287536781371869328od_d_d @ ( product_Pair_d_d @ R @ S2 ) @ R2 ) ) ) ).

% ssubst_Pair_rhs
thf(fact_622_ssubst__Pair__rhs,axiom,
    ! [R: b,S: c,R2: set_Product_prod_b_c,S2: c] :
      ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ R @ S ) @ R2 )
     => ( ( S2 = S )
       => ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ R @ S2 ) @ R2 ) ) ) ).

% ssubst_Pair_rhs
thf(fact_623_ssubst__Pair__rhs,axiom,
    ! [R: a,S: list_P6327159017948738492od_c_a,R2: set_Pr5230154892316275013od_c_a,S2: list_P6327159017948738492od_c_a] :
      ( ( member3484049051949443214od_c_a @ ( produc3580641852002036821od_c_a @ R @ S ) @ R2 )
     => ( ( S2 = S )
       => ( member3484049051949443214od_c_a @ ( produc3580641852002036821od_c_a @ R @ S2 ) @ R2 ) ) ) ).

% ssubst_Pair_rhs
thf(fact_624_ssubst__Pair__rhs,axiom,
    ! [R: a,S: fsm_a_b_c,R2: set_Pr2640454425625433516_a_b_c,S2: fsm_a_b_c] :
      ( ( member997585926662434933_a_b_c @ ( produc2795441082327197628_a_b_c @ R @ S ) @ R2 )
     => ( ( S2 = S )
       => ( member997585926662434933_a_b_c @ ( produc2795441082327197628_a_b_c @ R @ S2 ) @ R2 ) ) ) ).

% ssubst_Pair_rhs
thf(fact_625_ssubst__Pair__rhs,axiom,
    ! [R: a,S: a,R2: set_Product_prod_a_a,S2: a] :
      ( ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ R @ S ) @ R2 )
     => ( ( S2 = S )
       => ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ R @ S2 ) @ R2 ) ) ) ).

% ssubst_Pair_rhs
thf(fact_626_bot__empty__eq2,axiom,
    ( bot_bot_d_d_o
    = ( ^ [X2: d,Y2: d] : ( member2287536781371869328od_d_d @ ( product_Pair_d_d @ X2 @ Y2 ) @ bot_bo1663531405778772147od_d_d ) ) ) ).

% bot_empty_eq2
thf(fact_627_bot__empty__eq2,axiom,
    ( bot_bot_b_c_o
    = ( ^ [X2: b,Y2: c] : ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ bot_bo2863795366942399540od_b_c ) ) ) ).

% bot_empty_eq2
thf(fact_628_bot__empty__eq2,axiom,
    ( bot_bo3521679593239096604_c_a_o
    = ( ^ [X2: a,Y2: list_P6327159017948738492od_c_a] : ( member3484049051949443214od_c_a @ ( produc3580641852002036821od_c_a @ X2 @ Y2 ) @ bot_bo8583553918513061297od_c_a ) ) ) ).

% bot_empty_eq2
thf(fact_629_bot__empty__eq2,axiom,
    ( bot_bo1622131512164620661_b_c_o
    = ( ^ [X2: a,Y2: fsm_a_b_c] : ( member997585926662434933_a_b_c @ ( produc2795441082327197628_a_b_c @ X2 @ Y2 ) @ bot_bo7091552727507591704_a_b_c ) ) ) ).

% bot_empty_eq2
thf(fact_630_bot__empty__eq2,axiom,
    ( bot_bot_a_a_o
    = ( ^ [X2: a,Y2: a] : ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X2 @ Y2 ) @ bot_bo3357376287454694259od_a_a ) ) ) ).

% bot_empty_eq2
thf(fact_631_bot__empty__eq2,axiom,
    ( bot_bo246499355471594329_d_d_o
    = ( ^ [X2: fsm_d_b_c,Y2: product_prod_d_d] : ( member73601632213084689od_d_d @ ( produc3676634857637483352od_d_d @ X2 @ Y2 ) @ bot_bo7612717905841165748od_d_d ) ) ) ).

% bot_empty_eq2
thf(fact_632_pred__subset__eq2,axiom,
    ! [R2: set_Product_prod_d_d,S3: set_Product_prod_d_d] :
      ( ( ord_less_eq_d_d_o
        @ ^ [X2: d,Y2: d] : ( member2287536781371869328od_d_d @ ( product_Pair_d_d @ X2 @ Y2 ) @ R2 )
        @ ^ [X2: d,Y2: d] : ( member2287536781371869328od_d_d @ ( product_Pair_d_d @ X2 @ Y2 ) @ S3 ) )
      = ( ord_le8276230113588470247od_d_d @ R2 @ S3 ) ) ).

% pred_subset_eq2
thf(fact_633_pred__subset__eq2,axiom,
    ! [R2: set_Product_prod_b_c,S3: set_Product_prod_b_c] :
      ( ( ord_less_eq_b_c_o
        @ ^ [X2: b,Y2: c] : ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ R2 )
        @ ^ [X2: b,Y2: c] : ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ S3 ) )
      = ( ord_le253122037897321832od_b_c @ R2 @ S3 ) ) ).

% pred_subset_eq2
thf(fact_634_pred__subset__eq2,axiom,
    ! [R2: set_Pr5230154892316275013od_c_a,S3: set_Pr5230154892316275013od_c_a] :
      ( ( ord_le2733832144826581072_c_a_o
        @ ^ [X2: a,Y2: list_P6327159017948738492od_c_a] : ( member3484049051949443214od_c_a @ ( produc3580641852002036821od_c_a @ X2 @ Y2 ) @ R2 )
        @ ^ [X2: a,Y2: list_P6327159017948738492od_c_a] : ( member3484049051949443214od_c_a @ ( produc3580641852002036821od_c_a @ X2 @ Y2 ) @ S3 ) )
      = ( ord_le1109660078794635493od_c_a @ R2 @ S3 ) ) ).

% pred_subset_eq2
thf(fact_635_pred__subset__eq2,axiom,
    ! [R2: set_Pr2640454425625433516_a_b_c,S3: set_Pr2640454425625433516_a_b_c] :
      ( ( ord_le2277051310423379113_b_c_o
        @ ^ [X2: a,Y2: fsm_a_b_c] : ( member997585926662434933_a_b_c @ ( produc2795441082327197628_a_b_c @ X2 @ Y2 ) @ R2 )
        @ ^ [X2: a,Y2: fsm_a_b_c] : ( member997585926662434933_a_b_c @ ( produc2795441082327197628_a_b_c @ X2 @ Y2 ) @ S3 ) )
      = ( ord_le6086132928344890700_a_b_c @ R2 @ S3 ) ) ).

% pred_subset_eq2
thf(fact_636_pred__subset__eq2,axiom,
    ! [R2: set_Product_prod_a_a,S3: set_Product_prod_a_a] :
      ( ( ord_less_eq_a_a_o
        @ ^ [X2: a,Y2: a] : ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X2 @ Y2 ) @ R2 )
        @ ^ [X2: a,Y2: a] : ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X2 @ Y2 ) @ S3 ) )
      = ( ord_le746702958409616551od_a_a @ R2 @ S3 ) ) ).

% pred_subset_eq2
thf(fact_637_pred__equals__eq2,axiom,
    ! [R2: set_Product_prod_d_d,S3: set_Product_prod_d_d] :
      ( ( ( ^ [X2: d,Y2: d] : ( member2287536781371869328od_d_d @ ( product_Pair_d_d @ X2 @ Y2 ) @ R2 ) )
        = ( ^ [X2: d,Y2: d] : ( member2287536781371869328od_d_d @ ( product_Pair_d_d @ X2 @ Y2 ) @ S3 ) ) )
      = ( R2 = S3 ) ) ).

% pred_equals_eq2
thf(fact_638_pred__equals__eq2,axiom,
    ! [R2: set_Product_prod_b_c,S3: set_Product_prod_b_c] :
      ( ( ( ^ [X2: b,Y2: c] : ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ R2 ) )
        = ( ^ [X2: b,Y2: c] : ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ S3 ) ) )
      = ( R2 = S3 ) ) ).

% pred_equals_eq2
thf(fact_639_pred__equals__eq2,axiom,
    ! [R2: set_Pr5230154892316275013od_c_a,S3: set_Pr5230154892316275013od_c_a] :
      ( ( ( ^ [X2: a,Y2: list_P6327159017948738492od_c_a] : ( member3484049051949443214od_c_a @ ( produc3580641852002036821od_c_a @ X2 @ Y2 ) @ R2 ) )
        = ( ^ [X2: a,Y2: list_P6327159017948738492od_c_a] : ( member3484049051949443214od_c_a @ ( produc3580641852002036821od_c_a @ X2 @ Y2 ) @ S3 ) ) )
      = ( R2 = S3 ) ) ).

% pred_equals_eq2
thf(fact_640_pred__equals__eq2,axiom,
    ! [R2: set_Pr2640454425625433516_a_b_c,S3: set_Pr2640454425625433516_a_b_c] :
      ( ( ( ^ [X2: a,Y2: fsm_a_b_c] : ( member997585926662434933_a_b_c @ ( produc2795441082327197628_a_b_c @ X2 @ Y2 ) @ R2 ) )
        = ( ^ [X2: a,Y2: fsm_a_b_c] : ( member997585926662434933_a_b_c @ ( produc2795441082327197628_a_b_c @ X2 @ Y2 ) @ S3 ) ) )
      = ( R2 = S3 ) ) ).

% pred_equals_eq2
thf(fact_641_pred__equals__eq2,axiom,
    ! [R2: set_Product_prod_a_a,S3: set_Product_prod_a_a] :
      ( ( ( ^ [X2: a,Y2: a] : ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X2 @ Y2 ) @ R2 ) )
        = ( ^ [X2: a,Y2: a] : ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X2 @ Y2 ) @ S3 ) ) )
      = ( R2 = S3 ) ) ).

% pred_equals_eq2
thf(fact_642_Collect__restrict,axiom,
    ! [X6: set_e,P2: e > $o] :
      ( ord_less_eq_set_e
      @ ( collect_e
        @ ^ [X2: e] :
            ( ( member_e @ X2 @ X6 )
            & ( P2 @ X2 ) ) )
      @ X6 ) ).

% Collect_restrict
thf(fact_643_Collect__restrict,axiom,
    ! [X6: set_b,P2: b > $o] :
      ( ord_less_eq_set_b
      @ ( collect_b
        @ ^ [X2: b] :
            ( ( member_b @ X2 @ X6 )
            & ( P2 @ X2 ) ) )
      @ X6 ) ).

% Collect_restrict
thf(fact_644_Collect__restrict,axiom,
    ! [X6: set_li6436108459499378894od_b_c,P2: list_P903359562653991662od_b_c > $o] :
      ( ord_le282488521294790766od_b_c
      @ ( collec2280997390073109977od_b_c
        @ ^ [X2: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X2 @ X6 )
            & ( P2 @ X2 ) ) )
      @ X6 ) ).

% Collect_restrict
thf(fact_645_Collect__restrict,axiom,
    ! [X6: set_a,P2: a > $o] :
      ( ord_less_eq_set_a
      @ ( collect_a
        @ ^ [X2: a] :
            ( ( member_a @ X2 @ X6 )
            & ( P2 @ X2 ) ) )
      @ X6 ) ).

% Collect_restrict
thf(fact_646_Collect__restrict,axiom,
    ! [X6: set_li1159382662694783132od_c_a,P2: list_P6327159017948738492od_c_a > $o] :
      ( ord_le2998388488506175548od_c_a
      @ ( collec6273869032445462695od_c_a
        @ ^ [X2: list_P6327159017948738492od_c_a] :
            ( ( member7410604586820865893od_c_a @ X2 @ X6 )
            & ( P2 @ X2 ) ) )
      @ X6 ) ).

% Collect_restrict
thf(fact_647_prop__restrict,axiom,
    ! [X: e,Z4: set_e,X6: set_e,P2: e > $o] :
      ( ( member_e @ X @ Z4 )
     => ( ( ord_less_eq_set_e @ Z4
          @ ( collect_e
            @ ^ [X2: e] :
                ( ( member_e @ X2 @ X6 )
                & ( P2 @ X2 ) ) ) )
       => ( P2 @ X ) ) ) ).

% prop_restrict
thf(fact_648_prop__restrict,axiom,
    ! [X: b,Z4: set_b,X6: set_b,P2: b > $o] :
      ( ( member_b @ X @ Z4 )
     => ( ( ord_less_eq_set_b @ Z4
          @ ( collect_b
            @ ^ [X2: b] :
                ( ( member_b @ X2 @ X6 )
                & ( P2 @ X2 ) ) ) )
       => ( P2 @ X ) ) ) ).

% prop_restrict
thf(fact_649_prop__restrict,axiom,
    ! [X: list_P903359562653991662od_b_c,Z4: set_li6436108459499378894od_b_c,X6: set_li6436108459499378894od_b_c,P2: list_P903359562653991662od_b_c > $o] :
      ( ( member6330420149250801815od_b_c @ X @ Z4 )
     => ( ( ord_le282488521294790766od_b_c @ Z4
          @ ( collec2280997390073109977od_b_c
            @ ^ [X2: list_P903359562653991662od_b_c] :
                ( ( member6330420149250801815od_b_c @ X2 @ X6 )
                & ( P2 @ X2 ) ) ) )
       => ( P2 @ X ) ) ) ).

% prop_restrict
thf(fact_650_prop__restrict,axiom,
    ! [X: a,Z4: set_a,X6: set_a,P2: a > $o] :
      ( ( member_a @ X @ Z4 )
     => ( ( ord_less_eq_set_a @ Z4
          @ ( collect_a
            @ ^ [X2: a] :
                ( ( member_a @ X2 @ X6 )
                & ( P2 @ X2 ) ) ) )
       => ( P2 @ X ) ) ) ).

% prop_restrict
thf(fact_651_prop__restrict,axiom,
    ! [X: list_P6327159017948738492od_c_a,Z4: set_li1159382662694783132od_c_a,X6: set_li1159382662694783132od_c_a,P2: list_P6327159017948738492od_c_a > $o] :
      ( ( member7410604586820865893od_c_a @ X @ Z4 )
     => ( ( ord_le2998388488506175548od_c_a @ Z4
          @ ( collec6273869032445462695od_c_a
            @ ^ [X2: list_P6327159017948738492od_c_a] :
                ( ( member7410604586820865893od_c_a @ X2 @ X6 )
                & ( P2 @ X2 ) ) ) )
       => ( P2 @ X ) ) ) ).

% prop_restrict
thf(fact_652_pred__subset__eq,axiom,
    ! [R2: set_e,S3: set_e] :
      ( ( ord_less_eq_e_o
        @ ^ [X2: e] : ( member_e @ X2 @ R2 )
        @ ^ [X2: e] : ( member_e @ X2 @ S3 ) )
      = ( ord_less_eq_set_e @ R2 @ S3 ) ) ).

% pred_subset_eq
thf(fact_653_pred__subset__eq,axiom,
    ! [R2: set_b,S3: set_b] :
      ( ( ord_less_eq_b_o
        @ ^ [X2: b] : ( member_b @ X2 @ R2 )
        @ ^ [X2: b] : ( member_b @ X2 @ S3 ) )
      = ( ord_less_eq_set_b @ R2 @ S3 ) ) ).

% pred_subset_eq
thf(fact_654_pred__subset__eq,axiom,
    ! [R2: set_li6436108459499378894od_b_c,S3: set_li6436108459499378894od_b_c] :
      ( ( ord_le1261880702084804079_b_c_o
        @ ^ [X2: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ X2 @ R2 )
        @ ^ [X2: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ X2 @ S3 ) )
      = ( ord_le282488521294790766od_b_c @ R2 @ S3 ) ) ).

% pred_subset_eq
thf(fact_655_pred__subset__eq,axiom,
    ! [R2: set_a,S3: set_a] :
      ( ( ord_less_eq_a_o
        @ ^ [X2: a] : ( member_a @ X2 @ R2 )
        @ ^ [X2: a] : ( member_a @ X2 @ S3 ) )
      = ( ord_less_eq_set_a @ R2 @ S3 ) ) ).

% pred_subset_eq
thf(fact_656_pred__subset__eq,axiom,
    ! [R2: set_li1159382662694783132od_c_a,S3: set_li1159382662694783132od_c_a] :
      ( ( ord_le2170622466739808161_c_a_o
        @ ^ [X2: list_P6327159017948738492od_c_a] : ( member7410604586820865893od_c_a @ X2 @ R2 )
        @ ^ [X2: list_P6327159017948738492od_c_a] : ( member7410604586820865893od_c_a @ X2 @ S3 ) )
      = ( ord_le2998388488506175548od_c_a @ R2 @ S3 ) ) ).

% pred_subset_eq
thf(fact_657__092_060open_062_IpM_M_AdM_J_A_092_060in_062_Am__traversal__paths__with__witness_AM_Aq_Arepetition__sets_Am_092_060close_062,axiom,
    member6493638300815972283_set_a @ ( produc6508649944902238466_set_a @ pM @ dM ) @ ( traver6421790936065540696_a_b_c @ m @ q2 @ repetition_sets @ m3 ) ).

% \<open>(pM, dM) \<in> m_traversal_paths_with_witness M q repetition_sets m\<close>
thf(fact_658_transition__subset__paths,axiom,
    ! [S3: fsm_a_b_c,M: fsm_a_b_c,P3: list_P6327159017948738492od_c_a] :
      ( ( ord_le3226338165915859510od_c_a @ ( transitions_a_b_c @ S3 ) @ ( transitions_a_b_c @ M ) )
     => ( ( member_a @ ( initial_a_b_c @ S3 ) @ ( states_a_b_c @ M ) )
       => ( ( ( inputs_a_b_c @ S3 )
            = ( inputs_a_b_c @ M ) )
         => ( ( ( outputs_a_b_c @ S3 )
              = ( outputs_a_b_c @ M ) )
           => ( ( path_a_b_c @ S3 @ ( initial_a_b_c @ S3 ) @ P3 )
             => ( path_a_b_c @ M @ ( initial_a_b_c @ S3 ) @ P3 ) ) ) ) ) ) ).

% transition_subset_paths
thf(fact_659_transition__subset__paths,axiom,
    ! [S3: fsm_e_b_c,M: fsm_e_b_c,P3: list_P1631280100260380348od_c_e] :
      ( ( ord_le7753831285082277174od_c_e @ ( transitions_e_b_c @ S3 ) @ ( transitions_e_b_c @ M ) )
     => ( ( member_e @ ( initial_e_b_c @ S3 ) @ ( states_e_b_c @ M ) )
       => ( ( ( inputs_e_b_c @ S3 )
            = ( inputs_e_b_c @ M ) )
         => ( ( ( outputs_e_b_c @ S3 )
              = ( outputs_e_b_c @ M ) )
           => ( ( path_e_b_c @ S3 @ ( initial_e_b_c @ S3 ) @ P3 )
             => ( path_e_b_c @ M @ ( initial_e_b_c @ S3 ) @ P3 ) ) ) ) ) ) ).

% transition_subset_paths
thf(fact_660_is__singleton__the__elem,axiom,
    ( is_sin490879544914702512od_c_a
    = ( ^ [A6: set_li1159382662694783132od_c_a] :
          ( A6
          = ( insert4789241225314331020od_c_a @ ( the_el1763048914609152049od_c_a @ A6 ) @ bot_bo6236370880139903240od_c_a ) ) ) ) ).

% is_singleton_the_elem
thf(fact_661_is__singleton__the__elem,axiom,
    ( is_singleton_b
    = ( ^ [A6: set_b] :
          ( A6
          = ( insert_b @ ( the_elem_b @ A6 ) @ bot_bot_set_b ) ) ) ) ).

% is_singleton_the_elem
thf(fact_662_is__singleton__the__elem,axiom,
    ( is_sin881476898019872092od_d_d
    = ( ^ [A6: set_Pr9130538228769002824od_d_d] :
          ( A6
          = ( insert4898623881593564728od_d_d @ ( the_el3065921582757905117od_d_d @ A6 ) @ bot_bo7612717905841165748od_d_d ) ) ) ) ).

% is_singleton_the_elem
thf(fact_663_is__singleton__the__elem,axiom,
    ( is_singleton_e
    = ( ^ [A6: set_e] :
          ( A6
          = ( insert_e @ ( the_elem_e @ A6 ) @ bot_bot_set_e ) ) ) ) ).

% is_singleton_the_elem
thf(fact_664_defined__inputs_H_Oelims,axiom,
    ! [X: produc1131530811689391470od_b_c > set_Pr9130538228769002824od_d_d,Xa: set_li6436108459499378894od_b_c,Xb: product_prod_d_d,Y: set_li6436108459499378894od_b_c] :
      ( ( ( define6034045810747146583_d_b_c @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( collec2280997390073109977od_b_c
          @ ^ [X2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X2 @ Xa )
              & ( ( X @ ( produc789315387819617246od_b_c @ Xb @ X2 ) )
               != bot_bo7612717905841165748od_d_d ) ) ) ) ) ).

% defined_inputs'.elims
thf(fact_665_defined__inputs_H_Oelims,axiom,
    ! [X: produc237856837205686018_d_d_e > set_Pr9130538228769002824od_d_d,Xa: set_e,Xb: product_prod_d_d,Y: set_e] :
      ( ( ( define1113123821233513539_d_b_c @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( collect_e
          @ ^ [X2: e] :
              ( ( member_e @ X2 @ Xa )
              & ( ( X @ ( produc2127501618627392498_d_d_e @ Xb @ X2 ) )
               != bot_bo7612717905841165748od_d_d ) ) ) ) ) ).

% defined_inputs'.elims
thf(fact_666_defined__inputs_H_Oelims,axiom,
    ! [X: produc237856824295999615_d_d_b > set_Pr9130538228769002824od_d_d,Xa: set_b,Xb: product_prod_d_d,Y: set_b] :
      ( ( ( define3475433036543686406_d_b_c @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( collect_b
          @ ^ [X2: b] :
              ( ( member_b @ X2 @ Xa )
              & ( ( X @ ( produc2127501618627392495_d_d_b @ Xb @ X2 ) )
               != bot_bo7612717905841165748od_d_d ) ) ) ) ) ).

% defined_inputs'.elims
thf(fact_667_defined__inputs_H_Oelims,axiom,
    ! [X: produc237856819992770814_d_d_a > set_Pr9130538228769002824od_d_d,Xa: set_a,Xb: product_prod_d_d,Y: set_a] :
      ( ( ( define1188412096028818759_d_b_c @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( collect_a
          @ ^ [X2: a] :
              ( ( member_a @ X2 @ Xa )
              & ( ( X @ ( produc2127501618627392494_d_d_a @ Xb @ X2 ) )
               != bot_bo7612717905841165748od_d_d ) ) ) ) ) ).

% defined_inputs'.elims
thf(fact_668_defined__inputs_H_Oelims,axiom,
    ! [X: produc6682638544672851260od_c_a > set_Pr9130538228769002824od_d_d,Xa: set_li1159382662694783132od_c_a,Xb: product_prod_d_d,Y: set_li1159382662694783132od_c_a] :
      ( ( ( define9203645899367123209_d_b_c @ X @ Xa @ Xb )
        = Y )
     => ( Y
        = ( collec6273869032445462695od_c_a
          @ ^ [X2: list_P6327159017948738492od_c_a] :
              ( ( member7410604586820865893od_c_a @ X2 @ Xa )
              & ( ( X @ ( produc77691509023767724od_c_a @ Xb @ X2 ) )
               != bot_bo7612717905841165748od_d_d ) ) ) ) ) ).

% defined_inputs'.elims
thf(fact_669_defined__inputs_H_Osimps,axiom,
    ( define6034045810747146583_d_b_c
    = ( ^ [HM: produc1131530811689391470od_b_c > set_Pr9130538228769002824od_d_d,IM: set_li6436108459499378894od_b_c,Q5: product_prod_d_d] :
          ( collec2280997390073109977od_b_c
          @ ^ [X2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X2 @ IM )
              & ( ( HM @ ( produc789315387819617246od_b_c @ Q5 @ X2 ) )
               != bot_bo7612717905841165748od_d_d ) ) ) ) ) ).

% defined_inputs'.simps
thf(fact_670_defined__inputs_H_Osimps,axiom,
    ( define1113123821233513539_d_b_c
    = ( ^ [HM: produc237856837205686018_d_d_e > set_Pr9130538228769002824od_d_d,IM: set_e,Q5: product_prod_d_d] :
          ( collect_e
          @ ^ [X2: e] :
              ( ( member_e @ X2 @ IM )
              & ( ( HM @ ( produc2127501618627392498_d_d_e @ Q5 @ X2 ) )
               != bot_bo7612717905841165748od_d_d ) ) ) ) ) ).

% defined_inputs'.simps
thf(fact_671_defined__inputs_H_Osimps,axiom,
    ( define3475433036543686406_d_b_c
    = ( ^ [HM: produc237856824295999615_d_d_b > set_Pr9130538228769002824od_d_d,IM: set_b,Q5: product_prod_d_d] :
          ( collect_b
          @ ^ [X2: b] :
              ( ( member_b @ X2 @ IM )
              & ( ( HM @ ( produc2127501618627392495_d_d_b @ Q5 @ X2 ) )
               != bot_bo7612717905841165748od_d_d ) ) ) ) ) ).

% defined_inputs'.simps
thf(fact_672_defined__inputs_H_Osimps,axiom,
    ( define1188412096028818759_d_b_c
    = ( ^ [HM: produc237856819992770814_d_d_a > set_Pr9130538228769002824od_d_d,IM: set_a,Q5: product_prod_d_d] :
          ( collect_a
          @ ^ [X2: a] :
              ( ( member_a @ X2 @ IM )
              & ( ( HM @ ( produc2127501618627392494_d_d_a @ Q5 @ X2 ) )
               != bot_bo7612717905841165748od_d_d ) ) ) ) ) ).

% defined_inputs'.simps
thf(fact_673_defined__inputs_H_Osimps,axiom,
    ( define9203645899367123209_d_b_c
    = ( ^ [HM: produc6682638544672851260od_c_a > set_Pr9130538228769002824od_d_d,IM: set_li1159382662694783132od_c_a,Q5: product_prod_d_d] :
          ( collec6273869032445462695od_c_a
          @ ^ [X2: list_P6327159017948738492od_c_a] :
              ( ( member7410604586820865893od_c_a @ X2 @ IM )
              & ( ( HM @ ( produc77691509023767724od_c_a @ Q5 @ X2 ) )
               != bot_bo7612717905841165748od_d_d ) ) ) ) ) ).

% defined_inputs'.simps
thf(fact_674__092_060open_062_092_060not_062_AL_AM_H_A_092_060subseteq_062_AL_AM_092_060close_062,axiom,
    ~ ( ord_le282488521294790766od_b_c @ ( lS_e_b_c @ m2 @ ( initial_e_b_c @ m2 ) ) @ ( lS_a_b_c @ m @ ( initial_a_b_c @ m ) ) ) ).

% \<open>\<not> L M' \<subseteq> L M\<close>
thf(fact_675_subset__singleton__iff__Uniq,axiom,
    ! [A2: set_b] :
      ( ( ? [A3: b] : ( ord_less_eq_set_b @ A2 @ ( insert_b @ A3 @ bot_bot_set_b ) ) )
      = ( uniq_b
        @ ^ [X2: b] : ( member_b @ X2 @ A2 ) ) ) ).

% subset_singleton_iff_Uniq
thf(fact_676_subset__singleton__iff__Uniq,axiom,
    ! [A2: set_Pr9130538228769002824od_d_d] :
      ( ( ? [A3: produc4859908366599477352od_d_d] : ( ord_le7464911323401878760od_d_d @ A2 @ ( insert4898623881593564728od_d_d @ A3 @ bot_bo7612717905841165748od_d_d ) ) )
      = ( uniq_P8127067242775337837od_d_d
        @ ^ [X2: produc4859908366599477352od_d_d] : ( member73601632213084689od_d_d @ X2 @ A2 ) ) ) ).

% subset_singleton_iff_Uniq
thf(fact_677_subset__singleton__iff__Uniq,axiom,
    ! [A2: set_e] :
      ( ( ? [A3: e] : ( ord_less_eq_set_e @ A2 @ ( insert_e @ A3 @ bot_bot_set_e ) ) )
      = ( uniq_e
        @ ^ [X2: e] : ( member_e @ X2 @ A2 ) ) ) ).

% subset_singleton_iff_Uniq
thf(fact_678_subset__singleton__iff__Uniq,axiom,
    ! [A2: set_li6436108459499378894od_b_c] :
      ( ( ? [A3: list_P903359562653991662od_b_c] : ( ord_le282488521294790766od_b_c @ A2 @ ( insert6227932334100060350od_b_c @ A3 @ bot_bo4166481423041325370od_b_c ) ) )
      = ( uniq_l3276245616726852083od_b_c
        @ ^ [X2: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ X2 @ A2 ) ) ) ).

% subset_singleton_iff_Uniq
thf(fact_679_subset__singleton__iff__Uniq,axiom,
    ! [A2: set_a] :
      ( ( ? [A3: a] : ( ord_less_eq_set_a @ A2 @ ( insert_a @ A3 @ bot_bot_set_a ) ) )
      = ( uniq_a
        @ ^ [X2: a] : ( member_a @ X2 @ A2 ) ) ) ).

% subset_singleton_iff_Uniq
thf(fact_680_subset__singleton__iff__Uniq,axiom,
    ! [A2: set_li1159382662694783132od_c_a] :
      ( ( ? [A3: list_P6327159017948738492od_c_a] : ( ord_le2998388488506175548od_c_a @ A2 @ ( insert4789241225314331020od_c_a @ A3 @ bot_bo6236370880139903240od_c_a ) ) )
      = ( uniq_l6319900816830666945od_c_a
        @ ^ [X2: list_P6327159017948738492od_c_a] : ( member7410604586820865893od_c_a @ X2 @ A2 ) ) ) ).

% subset_singleton_iff_Uniq
thf(fact_681_initial__preamble__simps_I4_J,axiom,
    ! [M: fsm_a_b_c] :
      ( ( outputs_a_b_c @ ( state_4132440018836379711_a_b_c @ M ) )
      = ( outputs_a_b_c @ M ) ) ).

% initial_preamble_simps(4)
thf(fact_682_the__elem__eq,axiom,
    ! [X: list_P6327159017948738492od_c_a] :
      ( ( the_el1763048914609152049od_c_a @ ( insert4789241225314331020od_c_a @ X @ bot_bo6236370880139903240od_c_a ) )
      = X ) ).

% the_elem_eq
thf(fact_683_the__elem__eq,axiom,
    ! [X: b] :
      ( ( the_elem_b @ ( insert_b @ X @ bot_bot_set_b ) )
      = X ) ).

% the_elem_eq
thf(fact_684_the__elem__eq,axiom,
    ! [X: produc4859908366599477352od_d_d] :
      ( ( the_el3065921582757905117od_d_d @ ( insert4898623881593564728od_d_d @ X @ bot_bo7612717905841165748od_d_d ) )
      = X ) ).

% the_elem_eq
thf(fact_685_the__elem__eq,axiom,
    ! [X: e] :
      ( ( the_elem_e @ ( insert_e @ X @ bot_bot_set_e ) )
      = X ) ).

% the_elem_eq
thf(fact_686_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_687_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_688_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_689_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_690_minimal__sequence__to__failure__extending__preamble__ex,axiom,
    ! [M: fsm_e_b_c,PS2: set_Pr3196004308281305772_e_b_c,M4: fsm_a_b_c] :
      ( ( member4860428038910100853_e_b_c @ ( produc7661930123357470396_e_b_c @ ( initial_e_b_c @ M ) @ ( state_8070570405879350851_e_b_c @ M ) ) @ PS2 )
     => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ M4 @ ( initial_a_b_c @ M4 ) ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
       => ~ ! [P6: list_P1631280100260380348od_c_e,Io: list_P903359562653991662od_b_c] :
              ~ ( state_4449257559556048854_b_c_a @ M @ M4 @ PS2 @ P6 @ Io ) ) ) ).

% minimal_sequence_to_failure_extending_preamble_ex
thf(fact_691_minimal__sequence__to__failure__extending__preamble__ex,axiom,
    ! [M: fsm_e_b_c,PS2: set_Pr3196004308281305772_e_b_c,M4: fsm_e_b_c] :
      ( ( member4860428038910100853_e_b_c @ ( produc7661930123357470396_e_b_c @ ( initial_e_b_c @ M ) @ ( state_8070570405879350851_e_b_c @ M ) ) @ PS2 )
     => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_e_b_c @ M4 @ ( initial_e_b_c @ M4 ) ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
       => ~ ! [P6: list_P1631280100260380348od_c_e,Io: list_P903359562653991662od_b_c] :
              ~ ( state_4449257559556048858_b_c_e @ M @ M4 @ PS2 @ P6 @ Io ) ) ) ).

% minimal_sequence_to_failure_extending_preamble_ex
thf(fact_692_minimal__sequence__to__failure__extending__preamble__ex,axiom,
    ! [M: fsm_a_b_c,PS2: set_Pr2640454425625433516_a_b_c,M4: fsm_a_b_c] :
      ( ( member997585926662434933_a_b_c @ ( produc2795441082327197628_a_b_c @ ( initial_a_b_c @ M ) @ ( state_4132440018836379711_a_b_c @ M ) ) @ PS2 )
     => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ M4 @ ( initial_a_b_c @ M4 ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
       => ~ ! [P6: list_P6327159017948738492od_c_a,Io: list_P903359562653991662od_b_c] :
              ~ ( state_7720781447231630554_b_c_a @ M @ M4 @ PS2 @ P6 @ Io ) ) ) ).

% minimal_sequence_to_failure_extending_preamble_ex
thf(fact_693_minimal__sequence__to__failure__extending__preamble__ex,axiom,
    ! [M: fsm_a_b_c,PS2: set_Pr2640454425625433516_a_b_c,M4: fsm_e_b_c] :
      ( ( member997585926662434933_a_b_c @ ( produc2795441082327197628_a_b_c @ ( initial_a_b_c @ M ) @ ( state_4132440018836379711_a_b_c @ M ) ) @ PS2 )
     => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_e_b_c @ M4 @ ( initial_e_b_c @ M4 ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
       => ~ ! [P6: list_P6327159017948738492od_c_a,Io: list_P903359562653991662od_b_c] :
              ~ ( state_7720781447231630558_b_c_e @ M @ M4 @ PS2 @ P6 @ Io ) ) ) ).

% minimal_sequence_to_failure_extending_preamble_ex
thf(fact_694_sequence__to__failure__extending__preamble__ex,axiom,
    ! [M: fsm_e_b_c,PS2: set_Pr3196004308281305772_e_b_c,M4: fsm_a_b_c] :
      ( ( member4860428038910100853_e_b_c @ ( produc7661930123357470396_e_b_c @ ( initial_e_b_c @ M ) @ ( state_8070570405879350851_e_b_c @ M ) ) @ PS2 )
     => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ M4 @ ( initial_a_b_c @ M4 ) ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
       => ~ ! [P6: list_P1631280100260380348od_c_e,Io: list_P903359562653991662od_b_c] :
              ~ ( state_1973296770126915959_b_c_a @ M @ M4 @ PS2 @ P6 @ Io ) ) ) ).

% sequence_to_failure_extending_preamble_ex
thf(fact_695_sequence__to__failure__extending__preamble__ex,axiom,
    ! [M: fsm_e_b_c,PS2: set_Pr3196004308281305772_e_b_c,M4: fsm_e_b_c] :
      ( ( member4860428038910100853_e_b_c @ ( produc7661930123357470396_e_b_c @ ( initial_e_b_c @ M ) @ ( state_8070570405879350851_e_b_c @ M ) ) @ PS2 )
     => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_e_b_c @ M4 @ ( initial_e_b_c @ M4 ) ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) )
       => ~ ! [P6: list_P1631280100260380348od_c_e,Io: list_P903359562653991662od_b_c] :
              ~ ( state_1973296770126915963_b_c_e @ M @ M4 @ PS2 @ P6 @ Io ) ) ) ).

% sequence_to_failure_extending_preamble_ex
thf(fact_696_sequence__to__failure__extending__preamble__ex,axiom,
    ! [M: fsm_a_b_c,PS2: set_Pr2640454425625433516_a_b_c,M4: fsm_a_b_c] :
      ( ( member997585926662434933_a_b_c @ ( produc2795441082327197628_a_b_c @ ( initial_a_b_c @ M ) @ ( state_4132440018836379711_a_b_c @ M ) ) @ PS2 )
     => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ M4 @ ( initial_a_b_c @ M4 ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
       => ~ ! [P6: list_P6327159017948738492od_c_a,Io: list_P903359562653991662od_b_c] :
              ~ ( state_5244820657802497659_b_c_a @ M @ M4 @ PS2 @ P6 @ Io ) ) ) ).

% sequence_to_failure_extending_preamble_ex
thf(fact_697_sequence__to__failure__extending__preamble__ex,axiom,
    ! [M: fsm_a_b_c,PS2: set_Pr2640454425625433516_a_b_c,M4: fsm_e_b_c] :
      ( ( member997585926662434933_a_b_c @ ( produc2795441082327197628_a_b_c @ ( initial_a_b_c @ M ) @ ( state_4132440018836379711_a_b_c @ M ) ) @ PS2 )
     => ( ~ ( ord_le282488521294790766od_b_c @ ( lS_e_b_c @ M4 @ ( initial_e_b_c @ M4 ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) )
       => ~ ! [P6: list_P6327159017948738492od_c_a,Io: list_P903359562653991662od_b_c] :
              ~ ( state_5244820657802497663_b_c_e @ M @ M4 @ PS2 @ P6 @ Io ) ) ) ).

% sequence_to_failure_extending_preamble_ex
thf(fact_698__092_060open_062dM_A_092_060in_062_Aset_Arepetition__sets_092_060close_062,axiom,
    member7983343339038529360_set_a @ dM @ ( set_Pr7878197726666307004_set_a @ repetition_sets ) ).

% \<open>dM \<in> set repetition_sets\<close>
thf(fact_699_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_700_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_701_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_702_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_703_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_704_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_705_is__submachine_Osimps,axiom,
    ( is_submachine_e_b_c
    = ( ^ [A6: fsm_e_b_c,B3: fsm_e_b_c] :
          ( ( ( initial_e_b_c @ A6 )
            = ( initial_e_b_c @ B3 ) )
          & ( ord_le7753831285082277174od_c_e @ ( transitions_e_b_c @ A6 ) @ ( transitions_e_b_c @ B3 ) )
          & ( ( inputs_e_b_c @ A6 )
            = ( inputs_e_b_c @ B3 ) )
          & ( ( outputs_e_b_c @ A6 )
            = ( outputs_e_b_c @ B3 ) )
          & ( ord_less_eq_set_e @ ( states_e_b_c @ A6 ) @ ( states_e_b_c @ B3 ) ) ) ) ) ).

% is_submachine.simps
thf(fact_706_is__submachine_Osimps,axiom,
    ( is_submachine_a_b_c
    = ( ^ [A6: fsm_a_b_c,B3: fsm_a_b_c] :
          ( ( ( initial_a_b_c @ A6 )
            = ( initial_a_b_c @ B3 ) )
          & ( ord_le3226338165915859510od_c_a @ ( transitions_a_b_c @ A6 ) @ ( transitions_a_b_c @ B3 ) )
          & ( ( inputs_a_b_c @ A6 )
            = ( inputs_a_b_c @ B3 ) )
          & ( ( outputs_a_b_c @ A6 )
            = ( outputs_a_b_c @ B3 ) )
          & ( ord_less_eq_set_a @ ( states_a_b_c @ A6 ) @ ( states_a_b_c @ B3 ) ) ) ) ) ).

% is_submachine.simps
thf(fact_707_observable__paths__for__io,axiom,
    ! [M: fsm_a_b_c,Io5: list_P903359562653991662od_b_c,Q3: a] :
      ( ( observable_a_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io5 @ ( lS_a_b_c @ M @ Q3 ) )
       => ~ ! [P6: list_P6327159017948738492od_c_a] :
              ( ( paths_for_io_a_b_c @ M @ Q3 @ Io5 )
             != ( insert4789241225314331020od_c_a @ P6 @ bot_bo6236370880139903240od_c_a ) ) ) ) ).

% observable_paths_for_io
thf(fact_708_observable__paths__for__io,axiom,
    ! [M: fsm_e_b_c,Io5: list_P903359562653991662od_b_c,Q3: e] :
      ( ( observable_e_b_c @ M )
     => ( ( member6330420149250801815od_b_c @ Io5 @ ( lS_e_b_c @ M @ Q3 ) )
       => ~ ! [P6: list_P1631280100260380348od_c_e] :
              ( ( paths_for_io_e_b_c @ M @ Q3 @ Io5 )
             != ( insert93362307625972876od_c_e @ P6 @ bot_bo5086634708187433992od_c_e ) ) ) ) ).

% observable_paths_for_io
thf(fact_709_target__nil,axiom,
    ! [Q3: a] :
      ( ( target_a_b_c @ Q3 @ nil_Pr1342775757158464060od_c_a )
      = Q3 ) ).

% target_nil
thf(fact_710_submachine__simps_I1_J,axiom,
    ! [A2: fsm_a_b_c,B: fsm_a_b_c] :
      ( ( is_submachine_a_b_c @ A2 @ B )
     => ( ( initial_a_b_c @ A2 )
        = ( initial_a_b_c @ B ) ) ) ).

% submachine_simps(1)
thf(fact_711_submachine__simps_I1_J,axiom,
    ! [A2: fsm_e_b_c,B: fsm_e_b_c] :
      ( ( is_submachine_e_b_c @ A2 @ B )
     => ( ( initial_e_b_c @ A2 )
        = ( initial_e_b_c @ B ) ) ) ).

% submachine_simps(1)
thf(fact_712_submachine__path,axiom,
    ! [A2: fsm_a_b_c,B: fsm_a_b_c,Q3: a,P3: list_P6327159017948738492od_c_a] :
      ( ( is_submachine_a_b_c @ A2 @ B )
     => ( ( path_a_b_c @ A2 @ Q3 @ P3 )
       => ( path_a_b_c @ B @ Q3 @ P3 ) ) ) ).

% submachine_path
thf(fact_713_submachine__simps_I3_J,axiom,
    ! [A2: fsm_e_b_c,B: fsm_e_b_c] :
      ( ( is_submachine_e_b_c @ A2 @ B )
     => ( ( inputs_e_b_c @ A2 )
        = ( inputs_e_b_c @ B ) ) ) ).

% submachine_simps(3)
thf(fact_714_submachine__simps_I3_J,axiom,
    ! [A2: fsm_a_b_c,B: fsm_a_b_c] :
      ( ( is_submachine_a_b_c @ A2 @ B )
     => ( ( inputs_a_b_c @ A2 )
        = ( inputs_a_b_c @ B ) ) ) ).

% submachine_simps(3)
thf(fact_715_submachine__observable,axiom,
    ! [S3: fsm_a_b_c,M: fsm_a_b_c] :
      ( ( is_submachine_a_b_c @ S3 @ M )
     => ( ( observable_a_b_c @ M )
       => ( observable_a_b_c @ S3 ) ) ) ).

% submachine_observable
thf(fact_716_submachine__observable,axiom,
    ! [S3: fsm_e_b_c,M: fsm_e_b_c] :
      ( ( is_submachine_e_b_c @ S3 @ M )
     => ( ( observable_e_b_c @ M )
       => ( observable_e_b_c @ S3 ) ) ) ).

% submachine_observable
thf(fact_717_nil,axiom,
    ! [Q3: a,M: fsm_a_b_c] :
      ( ( member_a @ Q3 @ ( states_a_b_c @ M ) )
     => ( path_a_b_c @ M @ Q3 @ nil_Pr1342775757158464060od_c_a ) ) ).

% nil
thf(fact_718_path__nil__elim,axiom,
    ! [M: fsm_a_b_c,Q3: a] :
      ( ( path_a_b_c @ M @ Q3 @ nil_Pr1342775757158464060od_c_a )
     => ( member_a @ Q3 @ ( states_a_b_c @ M ) ) ) ).

% path_nil_elim
thf(fact_719_submachine__simps_I2_J,axiom,
    ! [A2: fsm_a_b_c,B: fsm_a_b_c] :
      ( ( is_submachine_a_b_c @ A2 @ B )
     => ( ord_less_eq_set_a @ ( states_a_b_c @ A2 ) @ ( states_a_b_c @ B ) ) ) ).

% submachine_simps(2)
thf(fact_720_submachine__path__initial,axiom,
    ! [A2: fsm_a_b_c,B: fsm_a_b_c,P3: list_P6327159017948738492od_c_a] :
      ( ( is_submachine_a_b_c @ A2 @ B )
     => ( ( path_a_b_c @ A2 @ ( initial_a_b_c @ A2 ) @ P3 )
       => ( path_a_b_c @ B @ ( initial_a_b_c @ B ) @ P3 ) ) ) ).

% submachine_path_initial
thf(fact_721_submachine__path__initial,axiom,
    ! [A2: fsm_e_b_c,B: fsm_e_b_c,P3: list_P1631280100260380348od_c_e] :
      ( ( is_submachine_e_b_c @ A2 @ B )
     => ( ( path_e_b_c @ A2 @ ( initial_e_b_c @ A2 ) @ P3 )
       => ( path_e_b_c @ B @ ( initial_e_b_c @ B ) @ P3 ) ) ) ).

% submachine_path_initial
thf(fact_722_language__io_I1_J,axiom,
    ! [Io5: list_P903359562653991662od_b_c,M: fsm_e_b_c,Q3: e,X: b,Y: c] :
      ( ( member6330420149250801815od_b_c @ Io5 @ ( lS_e_b_c @ M @ Q3 ) )
     => ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X @ Y ) @ ( set_Product_prod_b_c2 @ Io5 ) )
       => ( member_b @ X @ ( inputs_e_b_c @ M ) ) ) ) ).

% language_io(1)
thf(fact_723_language__io_I1_J,axiom,
    ! [Io5: list_P903359562653991662od_b_c,M: fsm_a_b_c,Q3: a,X: b,Y: c] :
      ( ( member6330420149250801815od_b_c @ Io5 @ ( lS_a_b_c @ M @ Q3 ) )
     => ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X @ Y ) @ ( set_Product_prod_b_c2 @ Io5 ) )
       => ( member_b @ X @ ( inputs_a_b_c @ M ) ) ) ) ).

% language_io(1)
thf(fact_724_language__io_I2_J,axiom,
    ! [Io5: list_P903359562653991662od_b_c,M: fsm_e_b_c,Q3: e,X: b,Y: c] :
      ( ( member6330420149250801815od_b_c @ Io5 @ ( lS_e_b_c @ M @ Q3 ) )
     => ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X @ Y ) @ ( set_Product_prod_b_c2 @ Io5 ) )
       => ( member_c @ Y @ ( outputs_e_b_c @ M ) ) ) ) ).

% language_io(2)
thf(fact_725_language__io_I2_J,axiom,
    ! [Io5: list_P903359562653991662od_b_c,M: fsm_a_b_c,Q3: a,X: b,Y: c] :
      ( ( member6330420149250801815od_b_c @ Io5 @ ( lS_a_b_c @ M @ Q3 ) )
     => ( ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X @ Y ) @ ( set_Product_prod_b_c2 @ Io5 ) )
       => ( member_c @ Y @ ( outputs_a_b_c @ M ) ) ) ) ).

% language_io(2)
thf(fact_726_submachine__language,axiom,
    ! [S3: fsm_a_b_c,M: fsm_a_b_c] :
      ( ( is_submachine_a_b_c @ S3 @ M )
     => ( ord_le282488521294790766od_b_c @ ( lS_a_b_c @ S3 @ ( initial_a_b_c @ S3 ) ) @ ( lS_a_b_c @ M @ ( initial_a_b_c @ M ) ) ) ) ).

% submachine_language
thf(fact_727_submachine__language,axiom,
    ! [S3: fsm_e_b_c,M: fsm_e_b_c] :
      ( ( is_submachine_e_b_c @ S3 @ M )
     => ( ord_le282488521294790766od_b_c @ ( lS_e_b_c @ S3 @ ( initial_e_b_c @ S3 ) ) @ ( lS_e_b_c @ M @ ( initial_e_b_c @ M ) ) ) ) ).

% submachine_language
thf(fact_728_set__empty,axiom,
    ! [Xs: list_P903359562653991662od_b_c] :
      ( ( ( set_Product_prod_b_c2 @ Xs )
        = bot_bo2863795366942399540od_b_c )
      = ( Xs = nil_Product_prod_b_c ) ) ).

% set_empty
thf(fact_729_set__empty,axiom,
    ! [Xs: list_P6327159017948738492od_c_a] :
      ( ( ( set_Pr5664641634098845387od_c_a @ Xs )
        = bot_bo267491471446728962od_c_a )
      = ( Xs = nil_Pr1342775757158464060od_c_a ) ) ).

% set_empty
thf(fact_730_set__empty,axiom,
    ! [Xs: list_P3660316430366008877_set_a] :
      ( ( ( set_Pr7878197726666307004_set_a @ Xs )
        = bot_bo5799363139946352499_set_a )
      = ( Xs = nil_Pr4665773148637758253_set_a ) ) ).

% set_empty
thf(fact_731_set__empty,axiom,
    ! [Xs: list_l8907847357763382004od_b_c] :
      ( ( ( set_li4480668622519654659od_b_c @ Xs )
        = bot_bo4166481423041325370od_b_c )
      = ( Xs = nil_li8071162985807626740od_b_c ) ) ).

% set_empty
thf(fact_732_set__empty,axiom,
    ! [Xs: list_b] :
      ( ( ( set_b2 @ Xs )
        = bot_bot_set_b )
      = ( Xs = nil_b ) ) ).

% set_empty
thf(fact_733_set__empty,axiom,
    ! [Xs: list_P4069430723938770798od_d_d] :
      ( ( ( set_Pr5977834532684968573od_d_d @ Xs )
        = bot_bo7612717905841165748od_d_d )
      = ( Xs = nil_Pr7808195664186560366od_d_d ) ) ).

% set_empty
thf(fact_734_set__empty,axiom,
    ! [Xs: list_e] :
      ( ( ( set_e2 @ Xs )
        = bot_bot_set_e )
      = ( Xs = nil_e ) ) ).

% set_empty
thf(fact_735_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_736_set__empty2,axiom,
    ! [Xs: list_P6327159017948738492od_c_a] :
      ( ( bot_bo267491471446728962od_c_a
        = ( set_Pr5664641634098845387od_c_a @ Xs ) )
      = ( Xs = nil_Pr1342775757158464060od_c_a ) ) ).

% set_empty2
thf(fact_737_set__empty2,axiom,
    ! [Xs: list_P3660316430366008877_set_a] :
      ( ( bot_bo5799363139946352499_set_a
        = ( set_Pr7878197726666307004_set_a @ Xs ) )
      = ( Xs = nil_Pr4665773148637758253_set_a ) ) ).

% set_empty2
thf(fact_738_set__empty2,axiom,
    ! [Xs: list_l8907847357763382004od_b_c] :
      ( ( bot_bo4166481423041325370od_b_c
        = ( set_li4480668622519654659od_b_c @ Xs ) )
      = ( Xs = nil_li8071162985807626740od_b_c ) ) ).

% set_empty2
thf(fact_739_set__empty2,axiom,
    ! [Xs: list_b] :
      ( ( bot_bot_set_b
        = ( set_b2 @ Xs ) )
      = ( Xs = nil_b ) ) ).

% set_empty2
thf(fact_740_set__empty2,axiom,
    ! [Xs: list_P4069430723938770798od_d_d] :
      ( ( bot_bo7612717905841165748od_d_d
        = ( set_Pr5977834532684968573od_d_d @ Xs ) )
      = ( Xs = nil_Pr7808195664186560366od_d_d ) ) ).

% set_empty2
thf(fact_741_set__empty2,axiom,
    ! [Xs: list_e] :
      ( ( bot_bot_set_e
        = ( set_e2 @ Xs ) )
      = ( Xs = nil_e ) ) ).

% set_empty2
thf(fact_742_t7,axiom,
    ! [D: produc1703568184450464039_set_a] :
      ( ( member7983343339038529360_set_a @ D @ ( set_Pr7878197726666307004_set_a @ repetition_sets ) )
     => ( ord_less_eq_set_a @ ( produc9088895665703139587_set_a @ D ) @ ( states_a_b_c @ m ) ) ) ).

% t7
thf(fact_743_t5,axiom,
    ! [Q3: a] :
      ( ( member_a @ Q3 @ ( states_a_b_c @ m ) )
     => ? [X3: produc1703568184450464039_set_a] :
          ( ( member7983343339038529360_set_a @ X3 @ ( set_Pr7878197726666307004_set_a @ repetition_sets ) )
          & ( member_a @ Q3 @ ( produc9088895665703139587_set_a @ X3 ) ) ) ) ).

% t5
thf(fact_744_t8,axiom,
    ! [D: produc1703568184450464039_set_a] :
      ( ( member7983343339038529360_set_a @ D @ ( set_Pr7878197726666307004_set_a @ repetition_sets ) )
     => ( ord_less_eq_set_a @ ( produc1983107199584856133_set_a @ D ) @ ( produc9088895665703139587_set_a @ D ) ) ) ).

% t8
thf(fact_745_empty__set,axiom,
    ( bot_bo2863795366942399540od_b_c
    = ( set_Product_prod_b_c2 @ nil_Product_prod_b_c ) ) ).

% empty_set
thf(fact_746_empty__set,axiom,
    ( bot_bo267491471446728962od_c_a
    = ( set_Pr5664641634098845387od_c_a @ nil_Pr1342775757158464060od_c_a ) ) ).

% empty_set
thf(fact_747_empty__set,axiom,
    ( bot_bo5799363139946352499_set_a
    = ( set_Pr7878197726666307004_set_a @ nil_Pr4665773148637758253_set_a ) ) ).

% empty_set
thf(fact_748_empty__set,axiom,
    ( bot_bo4166481423041325370od_b_c
    = ( set_li4480668622519654659od_b_c @ nil_li8071162985807626740od_b_c ) ) ).

% empty_set
thf(fact_749_empty__set,axiom,
    ( bot_bot_set_b
    = ( set_b2 @ nil_b ) ) ).

% empty_set
thf(fact_750_empty__set,axiom,
    ( bot_bo7612717905841165748od_d_d
    = ( set_Pr5977834532684968573od_d_d @ nil_Pr7808195664186560366od_d_d ) ) ).

% empty_set
thf(fact_751_empty__set,axiom,
    ( bot_bot_set_e
    = ( set_e2 @ nil_e ) ) ).

% empty_set
thf(fact_752_create__fsm__from__self,axiom,
    ! [M5: fsm_a_b_c] :
      ( M5
      = ( create3933655864275538163_a_b_c @ ( initial_a_b_c @ M5 ) @ ( states_a_b_c @ M5 ) @ ( inputs_a_b_c @ M5 ) @ ( outputs_a_b_c @ M5 ) @ ( transitions_a_b_c @ M5 ) ) ) ).

% create_fsm_from_self
thf(fact_753_create__fsm__from__self,axiom,
    ! [M5: fsm_e_b_c] :
      ( M5
      = ( create7871786251318509303_e_b_c @ ( initial_e_b_c @ M5 ) @ ( states_e_b_c @ M5 ) @ ( inputs_e_b_c @ M5 ) @ ( outputs_e_b_c @ M5 ) @ ( transitions_e_b_c @ M5 ) ) ) ).

% create_fsm_from_self
thf(fact_754_prod_Ocollapse,axiom,
    ! [Prod: product_prod_d_d] :
      ( ( product_Pair_d_d @ ( product_fst_d_d @ Prod ) @ ( product_snd_d_d @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_755_prod_Ocollapse,axiom,
    ! [Prod: produc3220416805844688357od_c_a] :
      ( ( produc3580641852002036821od_c_a @ ( produc4637894536740104257od_c_a @ Prod ) @ ( produc5527568727691618435od_c_a @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_756_prod_Ocollapse,axiom,
    ! [Prod: product_prod_a_a] :
      ( ( product_Pair_a_a @ ( product_fst_a_a @ Prod ) @ ( product_snd_a_a @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_757_prod_Ocollapse,axiom,
    ! [Prod: product_prod_c_a] :
      ( ( product_Pair_c_a @ ( product_fst_c_a @ Prod ) @ ( product_snd_c_a @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_758_prod_Ocollapse,axiom,
    ! [Prod: produc8838969699183119820_a_b_c] :
      ( ( produc2795441082327197628_a_b_c @ ( produc2620512763296580520_a_b_c @ Prod ) @ ( produc4728557313310798826_a_b_c @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_759_prod_Ocollapse,axiom,
    ! [Prod: produc1703568184450464039_set_a] :
      ( ( produc9088192753505129239_set_a @ ( produc9088895665703139587_set_a @ Prod ) @ ( produc1983107199584856133_set_a @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_760_prod_Ocollapse,axiom,
    ! [Prod: produc2669932201312201782od_c_a] :
      ( ( produc5762801557034676134od_c_a @ ( produc4225943634317630866od_c_a @ Prod ) @ ( produc8088130389382527188od_c_a @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_761_prod_Ocollapse,axiom,
    ! [Prod: produc2133359284458116493od_c_a] :
      ( ( produc3440865914000881661od_c_a @ ( produc301949074746585577od_c_a @ Prod ) @ ( produc5221446324160585515od_c_a @ Prod ) )
      = Prod ) ).

% prod.collapse
thf(fact_762_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_763_fsm__transition__output,axiom,
    ! [T: produc3205353004677322104od_c_a,M: fsm_Pr1886043760914421514_a_a_b] :
      ( ( member6508725278956418977od_c_a @ T @ ( transi2941759273464634107_a_a_b @ M ) )
     => ( member_b @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) @ ( output2371653660386375239_a_a_b @ M ) ) ) ).

% fsm_transition_output
thf(fact_764_fsm__transition__output,axiom,
    ! [T: produc2669932201312201782od_c_a,M: fsm_a_b_c] :
      ( ( member5502040268208861279od_c_a @ T @ ( transitions_a_b_c @ M ) )
     => ( member_c @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) @ ( outputs_a_b_c @ M ) ) ) ).

% fsm_transition_output
thf(fact_765_eq__fst__iff,axiom,
    ! [A: d,P3: product_prod_d_d] :
      ( ( A
        = ( product_fst_d_d @ P3 ) )
      = ( ? [B7: d] :
            ( P3
            = ( product_Pair_d_d @ A @ B7 ) ) ) ) ).

% eq_fst_iff
thf(fact_766_eq__fst__iff,axiom,
    ! [A: a,P3: produc3220416805844688357od_c_a] :
      ( ( A
        = ( produc4637894536740104257od_c_a @ P3 ) )
      = ( ? [B7: list_P6327159017948738492od_c_a] :
            ( P3
            = ( produc3580641852002036821od_c_a @ A @ B7 ) ) ) ) ).

% eq_fst_iff
thf(fact_767_eq__fst__iff,axiom,
    ! [A: a,P3: product_prod_a_a] :
      ( ( A
        = ( product_fst_a_a @ P3 ) )
      = ( ? [B7: a] :
            ( P3
            = ( product_Pair_a_a @ A @ B7 ) ) ) ) ).

% eq_fst_iff
thf(fact_768_eq__fst__iff,axiom,
    ! [A: set_a,P3: produc1703568184450464039_set_a] :
      ( ( A
        = ( produc9088895665703139587_set_a @ P3 ) )
      = ( ? [B7: set_a] :
            ( P3
            = ( produc9088192753505129239_set_a @ A @ B7 ) ) ) ) ).

% eq_fst_iff
thf(fact_769_eq__fst__iff,axiom,
    ! [A: c,P3: product_prod_c_a] :
      ( ( A
        = ( product_fst_c_a @ P3 ) )
      = ( ? [B7: a] :
            ( P3
            = ( product_Pair_c_a @ A @ B7 ) ) ) ) ).

% eq_fst_iff
thf(fact_770_eq__fst__iff,axiom,
    ! [A: b,P3: produc2133359284458116493od_c_a] :
      ( ( A
        = ( produc301949074746585577od_c_a @ P3 ) )
      = ( ? [B7: product_prod_c_a] :
            ( P3
            = ( produc3440865914000881661od_c_a @ A @ B7 ) ) ) ) ).

% eq_fst_iff
thf(fact_771_eq__fst__iff,axiom,
    ! [A: b,P3: product_prod_b_c] :
      ( ( A
        = ( product_fst_b_c @ P3 ) )
      = ( ? [B7: c] :
            ( P3
            = ( product_Pair_b_c @ A @ B7 ) ) ) ) ).

% eq_fst_iff
thf(fact_772_eq__fst__iff,axiom,
    ! [A: a,P3: produc8838969699183119820_a_b_c] :
      ( ( A
        = ( produc2620512763296580520_a_b_c @ P3 ) )
      = ( ? [B7: fsm_a_b_c] :
            ( P3
            = ( produc2795441082327197628_a_b_c @ A @ B7 ) ) ) ) ).

% eq_fst_iff
thf(fact_773_fst__conv,axiom,
    ! [X1: d,X22: d] :
      ( ( product_fst_d_d @ ( product_Pair_d_d @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_774_fst__conv,axiom,
    ! [X1: a,X22: list_P6327159017948738492od_c_a] :
      ( ( produc4637894536740104257od_c_a @ ( produc3580641852002036821od_c_a @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_775_fst__conv,axiom,
    ! [X1: a,X22: a] :
      ( ( product_fst_a_a @ ( product_Pair_a_a @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_776_fst__conv,axiom,
    ! [X1: set_a,X22: set_a] :
      ( ( produc9088895665703139587_set_a @ ( produc9088192753505129239_set_a @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_777_fst__conv,axiom,
    ! [X1: c,X22: a] :
      ( ( product_fst_c_a @ ( product_Pair_c_a @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_778_fst__conv,axiom,
    ! [X1: b,X22: product_prod_c_a] :
      ( ( produc301949074746585577od_c_a @ ( produc3440865914000881661od_c_a @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_779_fst__conv,axiom,
    ! [X1: b,X22: c] :
      ( ( product_fst_b_c @ ( product_Pair_b_c @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_780_fst__conv,axiom,
    ! [X1: a,X22: fsm_a_b_c] :
      ( ( produc2620512763296580520_a_b_c @ ( produc2795441082327197628_a_b_c @ X1 @ X22 ) )
      = X1 ) ).

% fst_conv
thf(fact_781_fst__eqD,axiom,
    ! [X: d,Y: d,A: d] :
      ( ( ( product_fst_d_d @ ( product_Pair_d_d @ X @ Y ) )
        = A )
     => ( X = A ) ) ).

% fst_eqD
thf(fact_782_fst__eqD,axiom,
    ! [X: a,Y: list_P6327159017948738492od_c_a,A: a] :
      ( ( ( produc4637894536740104257od_c_a @ ( produc3580641852002036821od_c_a @ X @ Y ) )
        = A )
     => ( X = A ) ) ).

% fst_eqD
thf(fact_783_fst__eqD,axiom,
    ! [X: a,Y: a,A: a] :
      ( ( ( product_fst_a_a @ ( product_Pair_a_a @ X @ Y ) )
        = A )
     => ( X = A ) ) ).

% fst_eqD
thf(fact_784_fst__eqD,axiom,
    ! [X: set_a,Y: set_a,A: set_a] :
      ( ( ( produc9088895665703139587_set_a @ ( produc9088192753505129239_set_a @ X @ Y ) )
        = A )
     => ( X = A ) ) ).

% fst_eqD
thf(fact_785_fst__eqD,axiom,
    ! [X: c,Y: a,A: c] :
      ( ( ( product_fst_c_a @ ( product_Pair_c_a @ X @ Y ) )
        = A )
     => ( X = A ) ) ).

% fst_eqD
thf(fact_786_fst__eqD,axiom,
    ! [X: b,Y: product_prod_c_a,A: b] :
      ( ( ( produc301949074746585577od_c_a @ ( produc3440865914000881661od_c_a @ X @ Y ) )
        = A )
     => ( X = A ) ) ).

% fst_eqD
thf(fact_787_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_788_fst__eqD,axiom,
    ! [X: a,Y: fsm_a_b_c,A: a] :
      ( ( ( produc2620512763296580520_a_b_c @ ( produc2795441082327197628_a_b_c @ X @ Y ) )
        = A )
     => ( X = A ) ) ).

% fst_eqD
thf(fact_789_fstI,axiom,
    ! [X: product_prod_d_d,Y: d,Z2: d] :
      ( ( X
        = ( product_Pair_d_d @ Y @ Z2 ) )
     => ( ( product_fst_d_d @ X )
        = Y ) ) ).

% fstI
thf(fact_790_fstI,axiom,
    ! [X: produc3220416805844688357od_c_a,Y: a,Z2: list_P6327159017948738492od_c_a] :
      ( ( X
        = ( produc3580641852002036821od_c_a @ Y @ Z2 ) )
     => ( ( produc4637894536740104257od_c_a @ X )
        = Y ) ) ).

% fstI
thf(fact_791_fstI,axiom,
    ! [X: product_prod_a_a,Y: a,Z2: a] :
      ( ( X
        = ( product_Pair_a_a @ Y @ Z2 ) )
     => ( ( product_fst_a_a @ X )
        = Y ) ) ).

% fstI
thf(fact_792_fstI,axiom,
    ! [X: produc1703568184450464039_set_a,Y: set_a,Z2: set_a] :
      ( ( X
        = ( produc9088192753505129239_set_a @ Y @ Z2 ) )
     => ( ( produc9088895665703139587_set_a @ X )
        = Y ) ) ).

% fstI
thf(fact_793_fstI,axiom,
    ! [X: product_prod_c_a,Y: c,Z2: a] :
      ( ( X
        = ( product_Pair_c_a @ Y @ Z2 ) )
     => ( ( product_fst_c_a @ X )
        = Y ) ) ).

% fstI
thf(fact_794_fstI,axiom,
    ! [X: produc2133359284458116493od_c_a,Y: b,Z2: product_prod_c_a] :
      ( ( X
        = ( produc3440865914000881661od_c_a @ Y @ Z2 ) )
     => ( ( produc301949074746585577od_c_a @ X )
        = Y ) ) ).

% fstI
thf(fact_795_fstI,axiom,
    ! [X: product_prod_b_c,Y: b,Z2: c] :
      ( ( X
        = ( product_Pair_b_c @ Y @ Z2 ) )
     => ( ( product_fst_b_c @ X )
        = Y ) ) ).

% fstI
thf(fact_796_fstI,axiom,
    ! [X: produc8838969699183119820_a_b_c,Y: a,Z2: fsm_a_b_c] :
      ( ( X
        = ( produc2795441082327197628_a_b_c @ Y @ Z2 ) )
     => ( ( produc2620512763296580520_a_b_c @ X )
        = Y ) ) ).

% fstI
thf(fact_797_prod__eq__iff,axiom,
    ( ( ^ [Y3: product_prod_c_a,Z: product_prod_c_a] : ( Y3 = Z ) )
    = ( ^ [S4: product_prod_c_a,T2: product_prod_c_a] :
          ( ( ( product_fst_c_a @ S4 )
            = ( product_fst_c_a @ T2 ) )
          & ( ( product_snd_c_a @ S4 )
            = ( product_snd_c_a @ T2 ) ) ) ) ) ).

% prod_eq_iff
thf(fact_798_prod__eq__iff,axiom,
    ( ( ^ [Y3: produc8838969699183119820_a_b_c,Z: produc8838969699183119820_a_b_c] : ( Y3 = Z ) )
    = ( ^ [S4: produc8838969699183119820_a_b_c,T2: produc8838969699183119820_a_b_c] :
          ( ( ( produc2620512763296580520_a_b_c @ S4 )
            = ( produc2620512763296580520_a_b_c @ T2 ) )
          & ( ( produc4728557313310798826_a_b_c @ S4 )
            = ( produc4728557313310798826_a_b_c @ T2 ) ) ) ) ) ).

% prod_eq_iff
thf(fact_799_prod__eq__iff,axiom,
    ( ( ^ [Y3: produc1703568184450464039_set_a,Z: produc1703568184450464039_set_a] : ( Y3 = Z ) )
    = ( ^ [S4: produc1703568184450464039_set_a,T2: produc1703568184450464039_set_a] :
          ( ( ( produc9088895665703139587_set_a @ S4 )
            = ( produc9088895665703139587_set_a @ T2 ) )
          & ( ( produc1983107199584856133_set_a @ S4 )
            = ( produc1983107199584856133_set_a @ T2 ) ) ) ) ) ).

% prod_eq_iff
thf(fact_800_prod__eq__iff,axiom,
    ( ( ^ [Y3: produc2669932201312201782od_c_a,Z: produc2669932201312201782od_c_a] : ( Y3 = Z ) )
    = ( ^ [S4: produc2669932201312201782od_c_a,T2: produc2669932201312201782od_c_a] :
          ( ( ( produc4225943634317630866od_c_a @ S4 )
            = ( produc4225943634317630866od_c_a @ T2 ) )
          & ( ( produc8088130389382527188od_c_a @ S4 )
            = ( produc8088130389382527188od_c_a @ T2 ) ) ) ) ) ).

% prod_eq_iff
thf(fact_801_prod__eq__iff,axiom,
    ( ( ^ [Y3: produc2133359284458116493od_c_a,Z: produc2133359284458116493od_c_a] : ( Y3 = Z ) )
    = ( ^ [S4: produc2133359284458116493od_c_a,T2: produc2133359284458116493od_c_a] :
          ( ( ( produc301949074746585577od_c_a @ S4 )
            = ( produc301949074746585577od_c_a @ T2 ) )
          & ( ( produc5221446324160585515od_c_a @ S4 )
            = ( produc5221446324160585515od_c_a @ T2 ) ) ) ) ) ).

% prod_eq_iff
thf(fact_802_prod__eq__iff,axiom,
    ( ( ^ [Y3: product_prod_b_c,Z: product_prod_b_c] : ( Y3 = Z ) )
    = ( ^ [S4: product_prod_b_c,T2: product_prod_b_c] :
          ( ( ( product_fst_b_c @ S4 )
            = ( product_fst_b_c @ T2 ) )
          & ( ( product_snd_b_c @ S4 )
            = ( product_snd_b_c @ T2 ) ) ) ) ) ).

% prod_eq_iff
thf(fact_803_prod__eqI,axiom,
    ! [P3: product_prod_c_a,Q3: product_prod_c_a] :
      ( ( ( product_fst_c_a @ P3 )
        = ( product_fst_c_a @ Q3 ) )
     => ( ( ( product_snd_c_a @ P3 )
          = ( product_snd_c_a @ Q3 ) )
       => ( P3 = Q3 ) ) ) ).

% prod_eqI
thf(fact_804_prod__eqI,axiom,
    ! [P3: produc8838969699183119820_a_b_c,Q3: produc8838969699183119820_a_b_c] :
      ( ( ( produc2620512763296580520_a_b_c @ P3 )
        = ( produc2620512763296580520_a_b_c @ Q3 ) )
     => ( ( ( produc4728557313310798826_a_b_c @ P3 )
          = ( produc4728557313310798826_a_b_c @ Q3 ) )
       => ( P3 = Q3 ) ) ) ).

% prod_eqI
thf(fact_805_prod__eqI,axiom,
    ! [P3: produc1703568184450464039_set_a,Q3: produc1703568184450464039_set_a] :
      ( ( ( produc9088895665703139587_set_a @ P3 )
        = ( produc9088895665703139587_set_a @ Q3 ) )
     => ( ( ( produc1983107199584856133_set_a @ P3 )
          = ( produc1983107199584856133_set_a @ Q3 ) )
       => ( P3 = Q3 ) ) ) ).

% prod_eqI
thf(fact_806_prod__eqI,axiom,
    ! [P3: produc2669932201312201782od_c_a,Q3: produc2669932201312201782od_c_a] :
      ( ( ( produc4225943634317630866od_c_a @ P3 )
        = ( produc4225943634317630866od_c_a @ Q3 ) )
     => ( ( ( produc8088130389382527188od_c_a @ P3 )
          = ( produc8088130389382527188od_c_a @ Q3 ) )
       => ( P3 = Q3 ) ) ) ).

% prod_eqI
thf(fact_807_prod__eqI,axiom,
    ! [P3: produc2133359284458116493od_c_a,Q3: produc2133359284458116493od_c_a] :
      ( ( ( produc301949074746585577od_c_a @ P3 )
        = ( produc301949074746585577od_c_a @ Q3 ) )
     => ( ( ( produc5221446324160585515od_c_a @ P3 )
          = ( produc5221446324160585515od_c_a @ Q3 ) )
       => ( P3 = Q3 ) ) ) ).

% prod_eqI
thf(fact_808_prod__eqI,axiom,
    ! [P3: product_prod_b_c,Q3: product_prod_b_c] :
      ( ( ( product_fst_b_c @ P3 )
        = ( product_fst_b_c @ Q3 ) )
     => ( ( ( product_snd_b_c @ P3 )
          = ( product_snd_b_c @ Q3 ) )
       => ( P3 = Q3 ) ) ) ).

% prod_eqI
thf(fact_809_prod_Oexpand,axiom,
    ! [Prod: product_prod_c_a,Prod2: product_prod_c_a] :
      ( ( ( ( product_fst_c_a @ Prod )
          = ( product_fst_c_a @ Prod2 ) )
        & ( ( product_snd_c_a @ Prod )
          = ( product_snd_c_a @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_810_prod_Oexpand,axiom,
    ! [Prod: produc8838969699183119820_a_b_c,Prod2: produc8838969699183119820_a_b_c] :
      ( ( ( ( produc2620512763296580520_a_b_c @ Prod )
          = ( produc2620512763296580520_a_b_c @ Prod2 ) )
        & ( ( produc4728557313310798826_a_b_c @ Prod )
          = ( produc4728557313310798826_a_b_c @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_811_prod_Oexpand,axiom,
    ! [Prod: produc1703568184450464039_set_a,Prod2: produc1703568184450464039_set_a] :
      ( ( ( ( produc9088895665703139587_set_a @ Prod )
          = ( produc9088895665703139587_set_a @ Prod2 ) )
        & ( ( produc1983107199584856133_set_a @ Prod )
          = ( produc1983107199584856133_set_a @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_812_prod_Oexpand,axiom,
    ! [Prod: produc2669932201312201782od_c_a,Prod2: produc2669932201312201782od_c_a] :
      ( ( ( ( produc4225943634317630866od_c_a @ Prod )
          = ( produc4225943634317630866od_c_a @ Prod2 ) )
        & ( ( produc8088130389382527188od_c_a @ Prod )
          = ( produc8088130389382527188od_c_a @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_813_prod_Oexpand,axiom,
    ! [Prod: produc2133359284458116493od_c_a,Prod2: produc2133359284458116493od_c_a] :
      ( ( ( ( produc301949074746585577od_c_a @ Prod )
          = ( produc301949074746585577od_c_a @ Prod2 ) )
        & ( ( produc5221446324160585515od_c_a @ Prod )
          = ( produc5221446324160585515od_c_a @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_814_prod_Oexpand,axiom,
    ! [Prod: product_prod_b_c,Prod2: product_prod_b_c] :
      ( ( ( ( product_fst_b_c @ Prod )
          = ( product_fst_b_c @ Prod2 ) )
        & ( ( product_snd_b_c @ Prod )
          = ( product_snd_b_c @ Prod2 ) ) )
     => ( Prod = Prod2 ) ) ).

% prod.expand
thf(fact_815_observable__transition__unique,axiom,
    ! [M: fsm_e_b_c,T: produc4050040609193146166od_c_e] :
      ( ( observable_e_b_c @ M )
     => ( ( member6882148676089805663od_c_e @ T @ ( transitions_e_b_c @ M ) )
       => ? [X3: produc4050040609193146166od_c_e] :
            ( ( member6882148676089805663od_c_e @ X3 @ ( transitions_e_b_c @ M ) )
            & ( ( produc6751554238685325970od_c_e @ X3 )
              = ( produc6751554238685325970od_c_e @ T ) )
            & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ X3 ) )
              = ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T ) ) )
            & ( ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ X3 ) ) )
              = ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T ) ) ) )
            & ! [Y5: produc4050040609193146166od_c_e] :
                ( ( ( member6882148676089805663od_c_e @ Y5 @ ( transitions_e_b_c @ M ) )
                  & ( ( produc6751554238685325970od_c_e @ Y5 )
                    = ( produc6751554238685325970od_c_e @ T ) )
                  & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Y5 ) )
                    = ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T ) ) )
                  & ( ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ Y5 ) ) )
                    = ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T ) ) ) ) )
               => ( Y5 = X3 ) ) ) ) ) ).

% observable_transition_unique
thf(fact_816_observable__transition__unique,axiom,
    ! [M: fsm_Pr1886043760914421514_a_a_b,T: produc3205353004677322104od_c_a] :
      ( ( observ2964502264774598958_a_a_b @ M )
     => ( ( member6508725278956418977od_c_a @ T @ ( transi2941759273464634107_a_a_b @ M ) )
       => ? [X3: produc3205353004677322104od_c_a] :
            ( ( member6508725278956418977od_c_a @ X3 @ ( transi2941759273464634107_a_a_b @ M ) )
            & ( ( produc8171714036265584980od_c_a @ X3 )
              = ( produc8171714036265584980od_c_a @ T ) )
            & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X3 ) )
              = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) )
            & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X3 ) ) )
              = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) )
            & ! [Y5: produc3205353004677322104od_c_a] :
                ( ( ( member6508725278956418977od_c_a @ Y5 @ ( transi2941759273464634107_a_a_b @ M ) )
                  & ( ( produc8171714036265584980od_c_a @ Y5 )
                    = ( produc8171714036265584980od_c_a @ T ) )
                  & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Y5 ) )
                    = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Y5 ) ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) ) )
               => ( Y5 = X3 ) ) ) ) ) ).

% observable_transition_unique
thf(fact_817_observable__transition__unique,axiom,
    ! [M: fsm_a_b_c,T: produc2669932201312201782od_c_a] :
      ( ( observable_a_b_c @ M )
     => ( ( member5502040268208861279od_c_a @ T @ ( transitions_a_b_c @ M ) )
       => ? [X3: produc2669932201312201782od_c_a] :
            ( ( member5502040268208861279od_c_a @ X3 @ ( transitions_a_b_c @ M ) )
            & ( ( produc4225943634317630866od_c_a @ X3 )
              = ( produc4225943634317630866od_c_a @ T ) )
            & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) )
              = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) )
            & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) ) )
              = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) )
            & ! [Y5: produc2669932201312201782od_c_a] :
                ( ( ( member5502040268208861279od_c_a @ Y5 @ ( transitions_a_b_c @ M ) )
                  & ( ( produc4225943634317630866od_c_a @ Y5 )
                    = ( produc4225943634317630866od_c_a @ T ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Y5 ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) )
                  & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Y5 ) ) )
                    = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) ) )
               => ( Y5 = X3 ) ) ) ) ) ).

% observable_transition_unique
thf(fact_818_observable_Osimps,axiom,
    ( observable_e_b_c
    = ( ^ [M2: fsm_e_b_c] :
        ! [X2: produc4050040609193146166od_c_e] :
          ( ( member6882148676089805663od_c_e @ X2 @ ( transitions_e_b_c @ M2 ) )
         => ! [Y2: produc4050040609193146166od_c_e] :
              ( ( member6882148676089805663od_c_e @ Y2 @ ( transitions_e_b_c @ M2 ) )
             => ( ( ( ( produc6751554238685325970od_c_e @ X2 )
                    = ( produc6751554238685325970od_c_e @ Y2 ) )
                  & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ X2 ) )
                    = ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Y2 ) ) )
                  & ( ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ X2 ) ) )
                    = ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ Y2 ) ) ) ) )
               => ( ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ X2 ) ) )
                  = ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ Y2 ) ) ) ) ) ) ) ) ) ).

% observable.simps
thf(fact_819_observable_Osimps,axiom,
    ( observ2964502264774598958_a_a_b
    = ( ^ [M2: fsm_Pr1886043760914421514_a_a_b] :
        ! [X2: produc3205353004677322104od_c_a] :
          ( ( member6508725278956418977od_c_a @ X2 @ ( transi2941759273464634107_a_a_b @ M2 ) )
         => ! [Y2: produc3205353004677322104od_c_a] :
              ( ( member6508725278956418977od_c_a @ Y2 @ ( transi2941759273464634107_a_a_b @ M2 ) )
             => ( ( ( ( produc8171714036265584980od_c_a @ X2 )
                    = ( produc8171714036265584980od_c_a @ Y2 ) )
                  & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) )
                    = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) ) ) )
               => ( ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) ) )
                  = ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) ) ) ) ) ) ) ) ).

% observable.simps
thf(fact_820_observable_Osimps,axiom,
    ( observable_a_b_c
    = ( ^ [M2: fsm_a_b_c] :
        ! [X2: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X2 @ ( transitions_a_b_c @ M2 ) )
         => ! [Y2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Y2 @ ( transitions_a_b_c @ M2 ) )
             => ( ( ( ( produc4225943634317630866od_c_a @ X2 )
                    = ( produc4225943634317630866od_c_a @ Y2 ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Y2 ) ) )
                  & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) ) )
                    = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Y2 ) ) ) ) )
               => ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) ) )
                  = ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Y2 ) ) ) ) ) ) ) ) ) ).

% observable.simps
thf(fact_821_observable_Oelims_I1_J,axiom,
    ! [X: fsm_e_b_c,Y: $o] :
      ( ( ( observable_e_b_c @ X )
        = Y )
     => ( Y
        = ( ! [X2: produc4050040609193146166od_c_e] :
              ( ( member6882148676089805663od_c_e @ X2 @ ( transitions_e_b_c @ X ) )
             => ! [Y2: produc4050040609193146166od_c_e] :
                  ( ( member6882148676089805663od_c_e @ Y2 @ ( transitions_e_b_c @ X ) )
                 => ( ( ( ( produc6751554238685325970od_c_e @ X2 )
                        = ( produc6751554238685325970od_c_e @ Y2 ) )
                      & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ X2 ) )
                        = ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Y2 ) ) )
                      & ( ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ X2 ) ) )
                        = ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ Y2 ) ) ) ) )
                   => ( ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ X2 ) ) )
                      = ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ Y2 ) ) ) ) ) ) ) ) ) ) ).

% observable.elims(1)
thf(fact_822_observable_Oelims_I1_J,axiom,
    ! [X: fsm_Pr1886043760914421514_a_a_b,Y: $o] :
      ( ( ( observ2964502264774598958_a_a_b @ X )
        = Y )
     => ( Y
        = ( ! [X2: produc3205353004677322104od_c_a] :
              ( ( member6508725278956418977od_c_a @ X2 @ ( transi2941759273464634107_a_a_b @ X ) )
             => ! [Y2: produc3205353004677322104od_c_a] :
                  ( ( member6508725278956418977od_c_a @ Y2 @ ( transi2941759273464634107_a_a_b @ X ) )
                 => ( ( ( ( produc8171714036265584980od_c_a @ X2 )
                        = ( produc8171714036265584980od_c_a @ Y2 ) )
                      & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) )
                        = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) )
                      & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) ) )
                        = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) ) ) )
                   => ( ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) ) )
                      = ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) ) ) ) ) ) ) ) ) ).

% observable.elims(1)
thf(fact_823_observable_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Y: $o] :
      ( ( ( observable_a_b_c @ X )
        = Y )
     => ( Y
        = ( ! [X2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ X2 @ ( transitions_a_b_c @ X ) )
             => ! [Y2: produc2669932201312201782od_c_a] :
                  ( ( member5502040268208861279od_c_a @ Y2 @ ( transitions_a_b_c @ X ) )
                 => ( ( ( ( produc4225943634317630866od_c_a @ X2 )
                        = ( produc4225943634317630866od_c_a @ Y2 ) )
                      & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) )
                        = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Y2 ) ) )
                      & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) ) )
                        = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Y2 ) ) ) ) )
                   => ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) ) )
                      = ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Y2 ) ) ) ) ) ) ) ) ) ) ).

% observable.elims(1)
thf(fact_824_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 ) )
         => ! [Xa2: produc4050040609193146166od_c_e] :
              ( ( member6882148676089805663od_c_e @ Xa2 @ ( transitions_e_b_c @ X ) )
             => ( ( ( ( produc6751554238685325970od_c_e @ X4 )
                    = ( produc6751554238685325970od_c_e @ Xa2 ) )
                  & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ X4 ) )
                    = ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Xa2 ) ) )
                  & ( ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ X4 ) ) )
                    = ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ Xa2 ) ) ) ) )
               => ( ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ X4 ) ) )
                  = ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ Xa2 ) ) ) ) ) ) ) ) ).

% observable.elims(2)
thf(fact_825_observable_Oelims_I2_J,axiom,
    ! [X: fsm_Pr1886043760914421514_a_a_b] :
      ( ( observ2964502264774598958_a_a_b @ X )
     => ! [X4: produc3205353004677322104od_c_a] :
          ( ( member6508725278956418977od_c_a @ X4 @ ( transi2941759273464634107_a_a_b @ X ) )
         => ! [Xa2: produc3205353004677322104od_c_a] :
              ( ( member6508725278956418977od_c_a @ Xa2 @ ( transi2941759273464634107_a_a_b @ X ) )
             => ( ( ( ( produc8171714036265584980od_c_a @ X4 )
                    = ( produc8171714036265584980od_c_a @ Xa2 ) )
                  & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X4 ) )
                    = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Xa2 ) ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X4 ) ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Xa2 ) ) ) ) )
               => ( ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X4 ) ) )
                  = ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Xa2 ) ) ) ) ) ) ) ) ).

% observable.elims(2)
thf(fact_826_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 ) )
         => ! [Xa2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Xa2 @ ( transitions_a_b_c @ X ) )
             => ( ( ( ( produc4225943634317630866od_c_a @ X4 )
                    = ( produc4225943634317630866od_c_a @ Xa2 ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X4 ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xa2 ) ) )
                  & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X4 ) ) )
                    = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa2 ) ) ) ) )
               => ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X4 ) ) )
                  = ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa2 ) ) ) ) ) ) ) ) ).

% observable.elims(2)
thf(fact_827_observable_Oelims_I3_J,axiom,
    ! [X: fsm_e_b_c] :
      ( ~ ( observable_e_b_c @ X )
     => ~ ! [X3: produc4050040609193146166od_c_e] :
            ( ( member6882148676089805663od_c_e @ X3 @ ( transitions_e_b_c @ X ) )
           => ! [Xa3: produc4050040609193146166od_c_e] :
                ( ( member6882148676089805663od_c_e @ Xa3 @ ( transitions_e_b_c @ X ) )
               => ( ( ( ( produc6751554238685325970od_c_e @ X3 )
                      = ( produc6751554238685325970od_c_e @ Xa3 ) )
                    & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ X3 ) )
                      = ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Xa3 ) ) )
                    & ( ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ X3 ) ) )
                      = ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ Xa3 ) ) ) ) )
                 => ( ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ X3 ) ) )
                    = ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ Xa3 ) ) ) ) ) ) ) ) ).

% observable.elims(3)
thf(fact_828_observable_Oelims_I3_J,axiom,
    ! [X: fsm_Pr1886043760914421514_a_a_b] :
      ( ~ ( observ2964502264774598958_a_a_b @ X )
     => ~ ! [X3: produc3205353004677322104od_c_a] :
            ( ( member6508725278956418977od_c_a @ X3 @ ( transi2941759273464634107_a_a_b @ X ) )
           => ! [Xa3: produc3205353004677322104od_c_a] :
                ( ( member6508725278956418977od_c_a @ Xa3 @ ( transi2941759273464634107_a_a_b @ X ) )
               => ( ( ( ( produc8171714036265584980od_c_a @ X3 )
                      = ( produc8171714036265584980od_c_a @ Xa3 ) )
                    & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X3 ) )
                      = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Xa3 ) ) )
                    & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X3 ) ) )
                      = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Xa3 ) ) ) ) )
                 => ( ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X3 ) ) )
                    = ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Xa3 ) ) ) ) ) ) ) ) ).

% observable.elims(3)
thf(fact_829_observable_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ~ ( observable_a_b_c @ X )
     => ~ ! [X3: produc2669932201312201782od_c_a] :
            ( ( member5502040268208861279od_c_a @ X3 @ ( transitions_a_b_c @ X ) )
           => ! [Xa3: produc2669932201312201782od_c_a] :
                ( ( member5502040268208861279od_c_a @ Xa3 @ ( transitions_a_b_c @ X ) )
               => ( ( ( ( produc4225943634317630866od_c_a @ X3 )
                      = ( produc4225943634317630866od_c_a @ Xa3 ) )
                    & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) )
                      = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xa3 ) ) )
                    & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) ) )
                      = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa3 ) ) ) ) )
                 => ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) ) )
                    = ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa3 ) ) ) ) ) ) ) ) ).

% observable.elims(3)
thf(fact_830_deterministic_Oelims_I3_J,axiom,
    ! [X: fsm_Pr1886043760914421514_a_a_b] :
      ( ~ ( determ4061018006534944583_a_a_b @ X )
     => ~ ! [X3: produc3205353004677322104od_c_a] :
            ( ( member6508725278956418977od_c_a @ X3 @ ( transi2941759273464634107_a_a_b @ X ) )
           => ! [Xa3: produc3205353004677322104od_c_a] :
                ( ( member6508725278956418977od_c_a @ Xa3 @ ( transi2941759273464634107_a_a_b @ X ) )
               => ( ( ( ( produc8171714036265584980od_c_a @ X3 )
                      = ( produc8171714036265584980od_c_a @ Xa3 ) )
                    & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X3 ) )
                      = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Xa3 ) ) ) )
                 => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X3 ) ) )
                      = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Xa3 ) ) ) )
                    & ( ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X3 ) ) )
                      = ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Xa3 ) ) ) ) ) ) ) ) ) ).

% deterministic.elims(3)
thf(fact_831_deterministic_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ~ ( deterministic_a_b_c @ X )
     => ~ ! [X3: produc2669932201312201782od_c_a] :
            ( ( member5502040268208861279od_c_a @ X3 @ ( transitions_a_b_c @ X ) )
           => ! [Xa3: produc2669932201312201782od_c_a] :
                ( ( member5502040268208861279od_c_a @ Xa3 @ ( transitions_a_b_c @ X ) )
               => ( ( ( ( produc4225943634317630866od_c_a @ X3 )
                      = ( produc4225943634317630866od_c_a @ Xa3 ) )
                    & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) )
                      = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xa3 ) ) ) )
                 => ( ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) ) )
                      = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa3 ) ) ) )
                    & ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) ) )
                      = ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa3 ) ) ) ) ) ) ) ) ) ).

% deterministic.elims(3)
thf(fact_832_deterministic_Oelims_I2_J,axiom,
    ! [X: fsm_Pr1886043760914421514_a_a_b] :
      ( ( determ4061018006534944583_a_a_b @ X )
     => ! [X4: produc3205353004677322104od_c_a] :
          ( ( member6508725278956418977od_c_a @ X4 @ ( transi2941759273464634107_a_a_b @ X ) )
         => ! [Xa2: produc3205353004677322104od_c_a] :
              ( ( member6508725278956418977od_c_a @ Xa2 @ ( transi2941759273464634107_a_a_b @ X ) )
             => ( ( ( ( produc8171714036265584980od_c_a @ X4 )
                    = ( produc8171714036265584980od_c_a @ Xa2 ) )
                  & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X4 ) )
                    = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Xa2 ) ) ) )
               => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X4 ) ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Xa2 ) ) ) )
                  & ( ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X4 ) ) )
                    = ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Xa2 ) ) ) ) ) ) ) ) ) ).

% deterministic.elims(2)
thf(fact_833_deterministic_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ( deterministic_a_b_c @ X )
     => ! [X4: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X4 @ ( transitions_a_b_c @ X ) )
         => ! [Xa2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Xa2 @ ( transitions_a_b_c @ X ) )
             => ( ( ( ( produc4225943634317630866od_c_a @ X4 )
                    = ( produc4225943634317630866od_c_a @ Xa2 ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X4 ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xa2 ) ) ) )
               => ( ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X4 ) ) )
                    = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa2 ) ) ) )
                  & ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X4 ) ) )
                    = ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xa2 ) ) ) ) ) ) ) ) ) ).

% deterministic.elims(2)
thf(fact_834_deterministic_Oelims_I1_J,axiom,
    ! [X: fsm_Pr1886043760914421514_a_a_b,Y: $o] :
      ( ( ( determ4061018006534944583_a_a_b @ X )
        = Y )
     => ( Y
        = ( ! [X2: produc3205353004677322104od_c_a] :
              ( ( member6508725278956418977od_c_a @ X2 @ ( transi2941759273464634107_a_a_b @ X ) )
             => ! [Y2: produc3205353004677322104od_c_a] :
                  ( ( member6508725278956418977od_c_a @ Y2 @ ( transi2941759273464634107_a_a_b @ X ) )
                 => ( ( ( ( produc8171714036265584980od_c_a @ X2 )
                        = ( produc8171714036265584980od_c_a @ Y2 ) )
                      & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) )
                        = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) ) )
                   => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) ) )
                        = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) ) )
                      & ( ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) ) )
                        = ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) ) ) ) ) ) ) ) ) ) ).

% deterministic.elims(1)
thf(fact_835_deterministic_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Y: $o] :
      ( ( ( deterministic_a_b_c @ X )
        = Y )
     => ( Y
        = ( ! [X2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ X2 @ ( transitions_a_b_c @ X ) )
             => ! [Y2: produc2669932201312201782od_c_a] :
                  ( ( member5502040268208861279od_c_a @ Y2 @ ( transitions_a_b_c @ X ) )
                 => ( ( ( ( produc4225943634317630866od_c_a @ X2 )
                        = ( produc4225943634317630866od_c_a @ Y2 ) )
                      & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) )
                        = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Y2 ) ) ) )
                   => ( ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) ) )
                        = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Y2 ) ) ) )
                      & ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) ) )
                        = ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Y2 ) ) ) ) ) ) ) ) ) ) ) ).

% deterministic.elims(1)
thf(fact_836_deterministic_Osimps,axiom,
    ( determ4061018006534944583_a_a_b
    = ( ^ [M2: fsm_Pr1886043760914421514_a_a_b] :
        ! [X2: produc3205353004677322104od_c_a] :
          ( ( member6508725278956418977od_c_a @ X2 @ ( transi2941759273464634107_a_a_b @ M2 ) )
         => ! [Y2: produc3205353004677322104od_c_a] :
              ( ( member6508725278956418977od_c_a @ Y2 @ ( transi2941759273464634107_a_a_b @ M2 ) )
             => ( ( ( ( produc8171714036265584980od_c_a @ X2 )
                    = ( produc8171714036265584980od_c_a @ Y2 ) )
                  & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) )
                    = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) ) )
               => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) ) )
                  & ( ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) ) )
                    = ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Y2 ) ) ) ) ) ) ) ) ) ) ).

% deterministic.simps
thf(fact_837_deterministic_Osimps,axiom,
    ( deterministic_a_b_c
    = ( ^ [M2: fsm_a_b_c] :
        ! [X2: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X2 @ ( transitions_a_b_c @ M2 ) )
         => ! [Y2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Y2 @ ( transitions_a_b_c @ M2 ) )
             => ( ( ( ( produc4225943634317630866od_c_a @ X2 )
                    = ( produc4225943634317630866od_c_a @ Y2 ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Y2 ) ) ) )
               => ( ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) ) )
                    = ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Y2 ) ) ) )
                  & ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) ) )
                    = ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Y2 ) ) ) ) ) ) ) ) ) ) ).

% deterministic.simps
thf(fact_838_output__complete_Osimps,axiom,
    ( output1640370057126496855_a_a_b
    = ( ^ [M2: fsm_Pr1886043760914421514_a_a_b] :
        ! [X2: produc3205353004677322104od_c_a] :
          ( ( member6508725278956418977od_c_a @ X2 @ ( transi2941759273464634107_a_a_b @ M2 ) )
         => ! [Y2: b] :
              ( ( member_b @ Y2 @ ( output2371653660386375239_a_a_b @ M2 ) )
             => ? [Z3: produc3205353004677322104od_c_a] :
                  ( ( member6508725278956418977od_c_a @ Z3 @ ( transi2941759273464634107_a_a_b @ M2 ) )
                  & ( ( produc8171714036265584980od_c_a @ X2 )
                    = ( produc8171714036265584980od_c_a @ Z3 ) )
                  & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) )
                    = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Z3 ) ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Z3 ) ) )
                    = Y2 ) ) ) ) ) ) ).

% output_complete.simps
thf(fact_839_output__complete_Osimps,axiom,
    ( output3834324022317553264_a_b_c
    = ( ^ [M2: fsm_a_b_c] :
        ! [X2: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X2 @ ( transitions_a_b_c @ M2 ) )
         => ! [Y2: c] :
              ( ( member_c @ Y2 @ ( outputs_a_b_c @ M2 ) )
             => ? [Z3: produc2669932201312201782od_c_a] :
                  ( ( member5502040268208861279od_c_a @ Z3 @ ( transitions_a_b_c @ M2 ) )
                  & ( ( produc4225943634317630866od_c_a @ X2 )
                    = ( produc4225943634317630866od_c_a @ Z3 ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Z3 ) ) )
                  & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Z3 ) ) )
                    = Y2 ) ) ) ) ) ) ).

% output_complete.simps
thf(fact_840_output__complete_Oelims_I1_J,axiom,
    ! [X: fsm_Pr1886043760914421514_a_a_b,Y: $o] :
      ( ( ( output1640370057126496855_a_a_b @ X )
        = Y )
     => ( Y
        = ( ! [X2: produc3205353004677322104od_c_a] :
              ( ( member6508725278956418977od_c_a @ X2 @ ( transi2941759273464634107_a_a_b @ X ) )
             => ! [Y2: b] :
                  ( ( member_b @ Y2 @ ( output2371653660386375239_a_a_b @ X ) )
                 => ? [Z3: produc3205353004677322104od_c_a] :
                      ( ( member6508725278956418977od_c_a @ Z3 @ ( transi2941759273464634107_a_a_b @ X ) )
                      & ( ( produc8171714036265584980od_c_a @ X2 )
                        = ( produc8171714036265584980od_c_a @ Z3 ) )
                      & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X2 ) )
                        = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Z3 ) ) )
                      & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Z3 ) ) )
                        = Y2 ) ) ) ) ) ) ) ).

% output_complete.elims(1)
thf(fact_841_output__complete_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Y: $o] :
      ( ( ( output3834324022317553264_a_b_c @ X )
        = Y )
     => ( Y
        = ( ! [X2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ X2 @ ( transitions_a_b_c @ X ) )
             => ! [Y2: c] :
                  ( ( member_c @ Y2 @ ( outputs_a_b_c @ X ) )
                 => ? [Z3: produc2669932201312201782od_c_a] :
                      ( ( member5502040268208861279od_c_a @ Z3 @ ( transitions_a_b_c @ X ) )
                      & ( ( produc4225943634317630866od_c_a @ X2 )
                        = ( produc4225943634317630866od_c_a @ Z3 ) )
                      & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) )
                        = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Z3 ) ) )
                      & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Z3 ) ) )
                        = Y2 ) ) ) ) ) ) ) ).

% output_complete.elims(1)
thf(fact_842_output__complete_Oelims_I2_J,axiom,
    ! [X: fsm_Pr1886043760914421514_a_a_b] :
      ( ( output1640370057126496855_a_a_b @ X )
     => ! [X4: produc3205353004677322104od_c_a] :
          ( ( member6508725278956418977od_c_a @ X4 @ ( transi2941759273464634107_a_a_b @ X ) )
         => ! [Xa2: b] :
              ( ( member_b @ Xa2 @ ( output2371653660386375239_a_a_b @ X ) )
             => ? [Xb2: produc3205353004677322104od_c_a] :
                  ( ( member6508725278956418977od_c_a @ Xb2 @ ( transi2941759273464634107_a_a_b @ X ) )
                  & ( ( produc8171714036265584980od_c_a @ X4 )
                    = ( produc8171714036265584980od_c_a @ Xb2 ) )
                  & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X4 ) )
                    = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Xb2 ) ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Xb2 ) ) )
                    = Xa2 ) ) ) ) ) ).

% output_complete.elims(2)
thf(fact_843_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 ) )
         => ! [Xa2: c] :
              ( ( member_c @ Xa2 @ ( 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 ) ) )
                    = Xa2 ) ) ) ) ) ).

% output_complete.elims(2)
thf(fact_844_output__complete_Oelims_I3_J,axiom,
    ! [X: fsm_Pr1886043760914421514_a_a_b] :
      ( ~ ( output1640370057126496855_a_a_b @ X )
     => ~ ! [X3: produc3205353004677322104od_c_a] :
            ( ( member6508725278956418977od_c_a @ X3 @ ( transi2941759273464634107_a_a_b @ X ) )
           => ! [Xa3: b] :
                ( ( member_b @ Xa3 @ ( output2371653660386375239_a_a_b @ X ) )
               => ? [Xb3: produc3205353004677322104od_c_a] :
                    ( ( member6508725278956418977od_c_a @ Xb3 @ ( transi2941759273464634107_a_a_b @ X ) )
                    & ( ( produc8171714036265584980od_c_a @ X3 )
                      = ( produc8171714036265584980od_c_a @ Xb3 ) )
                    & ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ X3 ) )
                      = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ Xb3 ) ) )
                    & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ Xb3 ) ) )
                      = Xa3 ) ) ) ) ) ).

% output_complete.elims(3)
thf(fact_845_output__complete_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ~ ( output3834324022317553264_a_b_c @ X )
     => ~ ! [X3: produc2669932201312201782od_c_a] :
            ( ( member5502040268208861279od_c_a @ X3 @ ( transitions_a_b_c @ X ) )
           => ! [Xa3: c] :
                ( ( member_c @ Xa3 @ ( outputs_a_b_c @ X ) )
               => ? [Xb3: produc2669932201312201782od_c_a] :
                    ( ( member5502040268208861279od_c_a @ Xb3 @ ( transitions_a_b_c @ X ) )
                    & ( ( produc4225943634317630866od_c_a @ X3 )
                      = ( produc4225943634317630866od_c_a @ Xb3 ) )
                    & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) )
                      = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xb3 ) ) )
                    & ( ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ Xb3 ) ) )
                      = Xa3 ) ) ) ) ) ).

% output_complete.elims(3)
thf(fact_846_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_847_observable__transition__target__language__eq,axiom,
    ! [M: fsm_Pr1886043760914421514_a_a_b,T1: produc3205353004677322104od_c_a,T22: produc3205353004677322104od_c_a] :
      ( ( ( lS_Pro5114676609533226954_a_a_b @ M @ ( produc8171714036265584980od_c_a @ T1 ) )
        = ( lS_Pro5114676609533226954_a_a_b @ M @ ( produc8171714036265584980od_c_a @ T22 ) ) )
     => ( ( member6508725278956418977od_c_a @ T1 @ ( transi2941759273464634107_a_a_b @ M ) )
       => ( ( member6508725278956418977od_c_a @ T22 @ ( transi2941759273464634107_a_a_b @ M ) )
         => ( ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ T1 ) )
              = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ T22 ) ) )
           => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T1 ) ) )
                = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T22 ) ) ) )
             => ( ( observ2964502264774598958_a_a_b @ M )
               => ( ( lS_Pro5114676609533226954_a_a_b @ M @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T1 ) ) ) )
                  = ( lS_Pro5114676609533226954_a_a_b @ M @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T22 ) ) ) ) ) ) ) ) ) ) ) ).

% observable_transition_target_language_eq
thf(fact_848_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_849_surjective__pairing,axiom,
    ! [T: product_prod_d_d] :
      ( T
      = ( product_Pair_d_d @ ( product_fst_d_d @ T ) @ ( product_snd_d_d @ T ) ) ) ).

% surjective_pairing
thf(fact_850_surjective__pairing,axiom,
    ! [T: produc3220416805844688357od_c_a] :
      ( T
      = ( produc3580641852002036821od_c_a @ ( produc4637894536740104257od_c_a @ T ) @ ( produc5527568727691618435od_c_a @ T ) ) ) ).

% surjective_pairing
thf(fact_851_surjective__pairing,axiom,
    ! [T: product_prod_a_a] :
      ( T
      = ( product_Pair_a_a @ ( product_fst_a_a @ T ) @ ( product_snd_a_a @ T ) ) ) ).

% surjective_pairing
thf(fact_852_surjective__pairing,axiom,
    ! [T: product_prod_c_a] :
      ( T
      = ( product_Pair_c_a @ ( product_fst_c_a @ T ) @ ( product_snd_c_a @ T ) ) ) ).

% surjective_pairing
thf(fact_853_surjective__pairing,axiom,
    ! [T: produc8838969699183119820_a_b_c] :
      ( T
      = ( produc2795441082327197628_a_b_c @ ( produc2620512763296580520_a_b_c @ T ) @ ( produc4728557313310798826_a_b_c @ T ) ) ) ).

% surjective_pairing
thf(fact_854_surjective__pairing,axiom,
    ! [T: produc1703568184450464039_set_a] :
      ( T
      = ( produc9088192753505129239_set_a @ ( produc9088895665703139587_set_a @ T ) @ ( produc1983107199584856133_set_a @ T ) ) ) ).

% surjective_pairing
thf(fact_855_surjective__pairing,axiom,
    ! [T: produc2669932201312201782od_c_a] :
      ( T
      = ( produc5762801557034676134od_c_a @ ( produc4225943634317630866od_c_a @ T ) @ ( produc8088130389382527188od_c_a @ T ) ) ) ).

% surjective_pairing
thf(fact_856_surjective__pairing,axiom,
    ! [T: produc2133359284458116493od_c_a] :
      ( T
      = ( produc3440865914000881661od_c_a @ ( produc301949074746585577od_c_a @ T ) @ ( produc5221446324160585515od_c_a @ T ) ) ) ).

% surjective_pairing
thf(fact_857_surjective__pairing,axiom,
    ! [T: product_prod_b_c] :
      ( T
      = ( product_Pair_b_c @ ( product_fst_b_c @ T ) @ ( product_snd_b_c @ T ) ) ) ).

% surjective_pairing
thf(fact_858_prod_Oexhaust__sel,axiom,
    ! [Prod: product_prod_d_d] :
      ( Prod
      = ( product_Pair_d_d @ ( product_fst_d_d @ Prod ) @ ( product_snd_d_d @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_859_prod_Oexhaust__sel,axiom,
    ! [Prod: produc3220416805844688357od_c_a] :
      ( Prod
      = ( produc3580641852002036821od_c_a @ ( produc4637894536740104257od_c_a @ Prod ) @ ( produc5527568727691618435od_c_a @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_860_prod_Oexhaust__sel,axiom,
    ! [Prod: product_prod_a_a] :
      ( Prod
      = ( product_Pair_a_a @ ( product_fst_a_a @ Prod ) @ ( product_snd_a_a @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_861_prod_Oexhaust__sel,axiom,
    ! [Prod: product_prod_c_a] :
      ( Prod
      = ( product_Pair_c_a @ ( product_fst_c_a @ Prod ) @ ( product_snd_c_a @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_862_prod_Oexhaust__sel,axiom,
    ! [Prod: produc8838969699183119820_a_b_c] :
      ( Prod
      = ( produc2795441082327197628_a_b_c @ ( produc2620512763296580520_a_b_c @ Prod ) @ ( produc4728557313310798826_a_b_c @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_863_prod_Oexhaust__sel,axiom,
    ! [Prod: produc1703568184450464039_set_a] :
      ( Prod
      = ( produc9088192753505129239_set_a @ ( produc9088895665703139587_set_a @ Prod ) @ ( produc1983107199584856133_set_a @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_864_prod_Oexhaust__sel,axiom,
    ! [Prod: produc2669932201312201782od_c_a] :
      ( Prod
      = ( produc5762801557034676134od_c_a @ ( produc4225943634317630866od_c_a @ Prod ) @ ( produc8088130389382527188od_c_a @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_865_prod_Oexhaust__sel,axiom,
    ! [Prod: produc2133359284458116493od_c_a] :
      ( Prod
      = ( produc3440865914000881661od_c_a @ ( produc301949074746585577od_c_a @ Prod ) @ ( produc5221446324160585515od_c_a @ Prod ) ) ) ).

% prod.exhaust_sel
thf(fact_866_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_867_observable__transition__target__language__subset,axiom,
    ! [M: fsm_Pr1886043760914421514_a_a_b,T1: produc3205353004677322104od_c_a,T22: produc3205353004677322104od_c_a] :
      ( ( ord_le153002609085230766od_a_b @ ( lS_Pro5114676609533226954_a_a_b @ M @ ( produc8171714036265584980od_c_a @ T1 ) ) @ ( lS_Pro5114676609533226954_a_a_b @ M @ ( produc8171714036265584980od_c_a @ T22 ) ) )
     => ( ( member6508725278956418977od_c_a @ T1 @ ( transi2941759273464634107_a_a_b @ M ) )
       => ( ( member6508725278956418977od_c_a @ T22 @ ( transi2941759273464634107_a_a_b @ M ) )
         => ( ( ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ T1 ) )
              = ( produc4225943634317630866od_c_a @ ( produc4643634399596806294od_c_a @ T22 ) ) )
           => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T1 ) ) )
                = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T22 ) ) ) )
             => ( ( observ2964502264774598958_a_a_b @ M )
               => ( ord_le153002609085230766od_a_b @ ( lS_Pro5114676609533226954_a_a_b @ M @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T1 ) ) ) ) @ ( lS_Pro5114676609533226954_a_a_b @ M @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T22 ) ) ) ) ) ) ) ) ) ) ) ).

% observable_transition_target_language_subset
thf(fact_868_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_869_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_870_neq__if__length__neq,axiom,
    ! [Xs: list_P903359562653991662od_b_c,Ys: list_P903359562653991662od_b_c] :
      ( ( ( size_s3392097710323735898od_b_c @ Xs )
       != ( size_s3392097710323735898od_b_c @ Ys ) )
     => ( Xs != Ys ) ) ).

% neq_if_length_neq
thf(fact_871_Ex__list__of__length,axiom,
    ! [N: nat] :
    ? [Xs2: list_P903359562653991662od_b_c] :
      ( ( size_s3392097710323735898od_b_c @ Xs2 )
      = N ) ).

% Ex_list_of_length
thf(fact_872_path__transitions,axiom,
    ! [M: fsm_a_b_c,Q3: a,P3: list_P6327159017948738492od_c_a] :
      ( ( path_a_b_c @ M @ Q3 @ P3 )
     => ( ord_le3226338165915859510od_c_a @ ( set_Pr5664641634098845387od_c_a @ P3 ) @ ( transitions_a_b_c @ M ) ) ) ).

% path_transitions
thf(fact_873_transitions__subset__path,axiom,
    ! [P3: list_P6327159017948738492od_c_a,M: fsm_a_b_c,S3: fsm_a_b_c,Q3: a] :
      ( ( ord_le3226338165915859510od_c_a @ ( set_Pr5664641634098845387od_c_a @ P3 ) @ ( transitions_a_b_c @ M ) )
     => ( ( P3 != nil_Pr1342775757158464060od_c_a )
       => ( ( path_a_b_c @ S3 @ Q3 @ P3 )
         => ( path_a_b_c @ M @ Q3 @ P3 ) ) ) ) ).

% transitions_subset_path
thf(fact_874_subset__code_I1_J,axiom,
    ! [Xs: list_e,B: set_e] :
      ( ( ord_less_eq_set_e @ ( set_e2 @ Xs ) @ B )
      = ( ! [X2: e] :
            ( ( member_e @ X2 @ ( set_e2 @ Xs ) )
           => ( member_e @ X2 @ B ) ) ) ) ).

% subset_code(1)
thf(fact_875_subset__code_I1_J,axiom,
    ! [Xs: list_b,B: set_b] :
      ( ( ord_less_eq_set_b @ ( set_b2 @ Xs ) @ B )
      = ( ! [X2: b] :
            ( ( member_b @ X2 @ ( set_b2 @ Xs ) )
           => ( member_b @ X2 @ B ) ) ) ) ).

% subset_code(1)
thf(fact_876_subset__code_I1_J,axiom,
    ! [Xs: list_P3660316430366008877_set_a,B: set_Pr5845495582615845127_set_a] :
      ( ( ord_le8376522849517564071_set_a @ ( set_Pr7878197726666307004_set_a @ Xs ) @ B )
      = ( ! [X2: produc1703568184450464039_set_a] :
            ( ( member7983343339038529360_set_a @ X2 @ ( set_Pr7878197726666307004_set_a @ Xs ) )
           => ( member7983343339038529360_set_a @ X2 @ B ) ) ) ) ).

% subset_code(1)
thf(fact_877_subset__code_I1_J,axiom,
    ! [Xs: list_l8907847357763382004od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ ( set_li4480668622519654659od_b_c @ Xs ) @ B )
      = ( ! [X2: list_P903359562653991662od_b_c] :
            ( ( member6330420149250801815od_b_c @ X2 @ ( set_li4480668622519654659od_b_c @ Xs ) )
           => ( member6330420149250801815od_b_c @ X2 @ B ) ) ) ) ).

% subset_code(1)
thf(fact_878_subset__code_I1_J,axiom,
    ! [Xs: list_a,B: set_a] :
      ( ( ord_less_eq_set_a @ ( set_a2 @ Xs ) @ B )
      = ( ! [X2: a] :
            ( ( member_a @ X2 @ ( set_a2 @ Xs ) )
           => ( member_a @ X2 @ B ) ) ) ) ).

% subset_code(1)
thf(fact_879_subset__code_I1_J,axiom,
    ! [Xs: list_l2826717958560394946od_c_a,B: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ ( set_li8663184538779258833od_c_a @ Xs ) @ B )
      = ( ! [X2: list_P6327159017948738492od_c_a] :
            ( ( member7410604586820865893od_c_a @ X2 @ ( set_li8663184538779258833od_c_a @ Xs ) )
           => ( member7410604586820865893od_c_a @ X2 @ B ) ) ) ) ).

% subset_code(1)
thf(fact_880_m__traversal__path__exist,axiom,
    ! [M: fsm_e_b_c,Q3: e,D2: list_P155772862829444397_set_e,M5: nat] :
      ( ( comple1615236469910841452_e_b_c @ M )
     => ( ( member_e @ Q3 @ ( states_e_b_c @ M ) )
       => ( ( ( inputs_e_b_c @ M )
           != bot_bot_set_b )
         => ( ! [Q6: e] :
                ( ( member_e @ Q6 @ ( states_e_b_c @ M ) )
               => ? [X4: produc7939552493815042087_set_e] :
                    ( ( member4995955611548331600_set_e @ X4 @ ( set_Pr4890809999176109244_set_e @ D2 ) )
                    & ( member_e @ Q6 @ ( produc5817371795240473091_set_e @ X4 ) ) ) )
           => ( ! [D3: produc7939552493815042087_set_e] :
                  ( ( member4995955611548331600_set_e @ D3 @ ( set_Pr4890809999176109244_set_e @ D2 ) )
                 => ( ord_less_eq_set_e @ ( produc7934955365976965445_set_e @ D3 ) @ ( produc5817371795240473091_set_e @ D3 ) ) )
             => ? [P7: list_P1631280100260380348od_c_e,D4: produc7939552493815042087_set_e] : ( member2883834373507867579_set_e @ ( produc3416001857640500482_set_e @ P7 @ D4 ) @ ( traver1136549286253736028_e_b_c @ M @ Q3 @ D2 @ M5 ) ) ) ) ) ) ) ).

% m_traversal_path_exist
thf(fact_881_m__traversal__path__exist,axiom,
    ! [M: fsm_a_b_c,Q3: a,D2: list_P3660316430366008877_set_a,M5: nat] :
      ( ( comple6900478119722646120_a_b_c @ M )
     => ( ( member_a @ Q3 @ ( states_a_b_c @ M ) )
       => ( ( ( inputs_a_b_c @ M )
           != bot_bot_set_b )
         => ( ! [Q6: a] :
                ( ( member_a @ Q6 @ ( states_a_b_c @ M ) )
               => ? [X4: produc1703568184450464039_set_a] :
                    ( ( member7983343339038529360_set_a @ X4 @ ( set_Pr7878197726666307004_set_a @ D2 ) )
                    & ( member_a @ Q6 @ ( produc9088895665703139587_set_a @ X4 ) ) ) )
           => ( ! [D3: produc1703568184450464039_set_a] :
                  ( ( member7983343339038529360_set_a @ D3 @ ( set_Pr7878197726666307004_set_a @ D2 ) )
                 => ( ord_less_eq_set_a @ ( produc1983107199584856133_set_a @ D3 ) @ ( produc9088895665703139587_set_a @ D3 ) ) )
             => ? [P7: list_P6327159017948738492od_c_a,D4: produc1703568184450464039_set_a] : ( member6493638300815972283_set_a @ ( produc6508649944902238466_set_a @ P7 @ D4 ) @ ( traver6421790936065540696_a_b_c @ M @ Q3 @ D2 @ M5 ) ) ) ) ) ) ) ).

% m_traversal_path_exist
thf(fact_882_t9,axiom,
    ! [D: produc1703568184450464039_set_a,Q14: a,Q22: a] :
      ( ( member7983343339038529360_set_a @ D @ ( set_Pr7878197726666307004_set_a @ repetition_sets ) )
     => ( ( member_a @ Q14 @ ( produc9088895665703139587_set_a @ D ) )
       => ( ( member_a @ Q22 @ ( produc9088895665703139587_set_a @ D ) )
         => ( ( Q14 != Q22 )
           => ( ( separators @ ( product_Pair_a_a @ Q14 @ Q22 ) )
             != bot_bo7612717905841165748od_d_d ) ) ) ) ) ).

% t9
thf(fact_883_add__transition__simps_I4_J,axiom,
    ! [T: produc5343229610332254449od_e_e,M: fsm_e_e_e] :
      ( ( member_e @ ( produc3561935336479904205od_e_e @ T ) @ ( states_e_e_e @ M ) )
     => ( ( member_e @ ( produc2032089063873476136od_e_e @ ( produc7424122091544800527od_e_e @ T ) ) @ ( inputs_e_e_e @ M ) )
       => ( ( member_e @ ( product_fst_e_e @ ( produc6951586313287476074od_e_e @ ( produc7424122091544800527od_e_e @ T ) ) ) @ ( outputs_e_e_e @ M ) )
         => ( ( member_e @ ( product_snd_e_e @ ( produc6951586313287476074od_e_e @ ( produc7424122091544800527od_e_e @ T ) ) ) @ ( states_e_e_e @ M ) )
           => ( ( transitions_e_e_e @ ( add_transition_e_e_e @ M @ T ) )
              = ( insert1555131780188278465od_e_e @ T @ ( transitions_e_e_e @ M ) ) ) ) ) ) ) ).

% add_transition_simps(4)
thf(fact_884_add__transition__simps_I4_J,axiom,
    ! [T: produc6614590355691243316od_b_e,M: fsm_e_e_b] :
      ( ( member_e @ ( produc5468882338294864272od_b_e @ T ) @ ( states_e_e_b @ M ) )
     => ( ( member_e @ ( produc1171083772936728427od_b_e @ ( produc107697056504984786od_b_e @ T ) ) @ ( inputs_e_e_b @ M ) )
       => ( ( member_b @ ( product_fst_b_e @ ( produc6090581022350728365od_b_e @ ( produc107697056504984786od_b_e @ T ) ) ) @ ( outputs_e_e_b @ M ) )
         => ( ( member_e @ ( product_snd_b_e @ ( produc6090581022350728365od_b_e @ ( produc107697056504984786od_b_e @ T ) ) ) @ ( states_e_e_b @ M ) )
           => ( ( transitions_e_e_b @ ( add_transition_e_e_b @ M @ T ) )
              = ( insert2826492525547267332od_b_e @ T @ ( transitions_e_e_b @ M ) ) ) ) ) ) ) ).

% add_transition_simps(4)
thf(fact_885_add__transition__simps_I4_J,axiom,
    ! [T: produc3963919925192647669od_a_e,M: fsm_e_e_a] :
      ( ( member_e @ ( produc6104531338899850961od_a_e @ T ) @ ( states_e_e_a @ M ) )
     => ( ( member_e @ ( produc3958539354909404460od_a_e @ ( produc743346057109971475od_a_e @ T ) ) @ ( inputs_e_e_a @ M ) )
       => ( ( member_a @ ( product_fst_a_e @ ( produc8878036604323404398od_a_e @ ( produc743346057109971475od_a_e @ T ) ) ) @ ( outputs_e_e_a @ M ) )
         => ( ( member_e @ ( product_snd_a_e @ ( produc8878036604323404398od_a_e @ ( produc743346057109971475od_a_e @ T ) ) ) @ ( states_e_e_a @ M ) )
           => ( ( transitions_e_e_a @ ( add_transition_e_e_a @ M @ T ) )
              = ( insert175822095048671685od_a_e @ T @ ( transitions_e_e_a @ M ) ) ) ) ) ) ) ).

% add_transition_simps(4)
thf(fact_886_add__transition__simps_I4_J,axiom,
    ! [T: produc4050040609193146166od_c_e,M: fsm_e_b_c] :
      ( ( member_e @ ( produc6751554238685325970od_c_e @ T ) @ ( states_e_b_c @ M ) )
     => ( ( member_b @ ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T ) ) @ ( inputs_e_b_c @ M ) )
       => ( ( member_c @ ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T ) ) ) @ ( outputs_e_b_c @ M ) )
         => ( ( member_e @ ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T ) ) ) @ ( states_e_b_c @ M ) )
           => ( ( transitions_e_b_c @ ( add_transition_e_b_c @ M @ T ) )
              = ( insert261942779049170182od_c_e @ T @ ( transitions_e_b_c @ M ) ) ) ) ) ) ) ).

% add_transition_simps(4)
thf(fact_887_add__transition__simps_I4_J,axiom,
    ! [T: produc128009433335561652od_e_e,M: fsm_e_b_e] :
      ( ( member_e @ ( produc5480256237475352592od_e_e @ T ) @ ( states_e_b_e @ M ) )
     => ( ( member_b @ ( produc3950409964868924523od_e_e @ ( produc119070955685473106od_e_e @ T ) ) @ ( inputs_e_b_e @ M ) )
       => ( ( member_e @ ( product_fst_e_e @ ( produc8869907214282924461od_e_e @ ( produc119070955685473106od_e_e @ T ) ) ) @ ( outputs_e_b_e @ M ) )
         => ( ( member_e @ ( product_snd_e_e @ ( produc8869907214282924461od_e_e @ ( produc119070955685473106od_e_e @ T ) ) ) @ ( states_e_b_e @ M ) )
           => ( ( transitions_e_b_e @ ( add_transition_e_b_e @ M @ T ) )
              = ( insert5563283640046361476od_e_e @ T @ ( transitions_e_b_e @ M ) ) ) ) ) ) ) ).

% add_transition_simps(4)
thf(fact_888_add__transition__simps_I4_J,axiom,
    ! [T: produc1399370178694550519od_b_e,M: fsm_e_b_b] :
      ( ( member_e @ ( produc7387203239290312659od_b_e @ T ) @ ( states_e_b_b @ M ) )
     => ( ( member_b @ ( produc3089404673932176814od_b_e @ ( produc2026017957500433173od_b_e @ T ) ) @ ( inputs_e_b_b @ M ) )
       => ( ( member_b @ ( product_fst_b_e @ ( produc8008901923346176752od_b_e @ ( produc2026017957500433173od_b_e @ T ) ) ) @ ( outputs_e_b_b @ M ) )
         => ( ( member_e @ ( product_snd_b_e @ ( produc8008901923346176752od_b_e @ ( produc2026017957500433173od_b_e @ T ) ) ) @ ( states_e_b_b @ M ) )
           => ( ( transitions_e_b_b @ ( add_transition_e_b_b @ M @ T ) )
              = ( insert6834644385405350343od_b_e @ T @ ( transitions_e_b_b @ M ) ) ) ) ) ) ) ).

% add_transition_simps(4)
thf(fact_889_add__transition__simps_I4_J,axiom,
    ! [T: produc7972071785050730680od_a_e,M: fsm_e_b_a] :
      ( ( member_e @ ( produc8022852239895299348od_a_e @ T ) @ ( states_e_b_a @ M ) )
     => ( ( member_b @ ( produc5876860255904852847od_a_e @ ( produc2661666958105419862od_a_e @ T ) ) @ ( inputs_e_b_a @ M ) )
       => ( ( member_a @ ( product_fst_a_e @ ( produc1572985468464076977od_a_e @ ( produc2661666958105419862od_a_e @ T ) ) ) @ ( outputs_e_b_a @ M ) )
         => ( ( member_e @ ( product_snd_a_e @ ( produc1572985468464076977od_a_e @ ( produc2661666958105419862od_a_e @ T ) ) ) @ ( states_e_b_a @ M ) )
           => ( ( transitions_e_b_a @ ( add_transition_e_b_a @ M @ T ) )
              = ( insert4183973954906754696od_a_e @ T @ ( transitions_e_b_a @ M ) ) ) ) ) ) ) ).

% add_transition_simps(4)
thf(fact_890_add__transition__simps_I4_J,axiom,
    ! [T: produc1464060053288255989od_e_e,M: fsm_e_a_e] :
      ( ( member_e @ ( produc6119696537807168721od_e_e @ T ) @ ( states_e_a_e @ M ) )
     => ( ( member_a @ ( produc4589850265200740652od_e_e @ ( produc758511256017289235od_e_e @ T ) ) @ ( inputs_e_a_e @ M ) )
       => ( ( member_e @ ( product_fst_e_e @ ( produc285975477759964782od_e_e @ ( produc758511256017289235od_e_e @ T ) ) ) @ ( outputs_e_a_e @ M ) )
         => ( ( member_e @ ( product_snd_e_e @ ( produc285975477759964782od_e_e @ ( produc758511256017289235od_e_e @ T ) ) ) @ ( states_e_a_e @ M ) )
           => ( ( transitions_e_a_e @ ( add_transition_e_a_e @ M @ T ) )
              = ( insert6899334259999055813od_e_e @ T @ ( transitions_e_a_e @ M ) ) ) ) ) ) ) ).

% add_transition_simps(4)
thf(fact_891_add__transition__simps_I4_J,axiom,
    ! [T: produc2735420798647244856od_b_e,M: fsm_e_a_b] :
      ( ( member_e @ ( produc8026643539622128788od_b_e @ T ) @ ( states_e_a_b @ M ) )
     => ( ( member_a @ ( produc3728844974263992943od_b_e @ ( produc2665458257832249302od_b_e @ T ) ) @ ( inputs_e_a_b @ M ) )
       => ( ( member_b @ ( product_fst_b_e @ ( produc8648342223677992881od_b_e @ ( produc2665458257832249302od_b_e @ T ) ) ) @ ( outputs_e_a_b @ M ) )
         => ( ( member_e @ ( product_snd_b_e @ ( produc8648342223677992881od_b_e @ ( produc2665458257832249302od_b_e @ T ) ) ) @ ( states_e_a_b @ M ) )
           => ( ( transitions_e_a_b @ ( add_transition_e_a_b @ M @ T ) )
              = ( insert8170695005358044680od_b_e @ T @ ( transitions_e_a_b @ M ) ) ) ) ) ) ) ).

% add_transition_simps(4)
thf(fact_892_add__transition__simps_I4_J,axiom,
    ! [T: produc84750368148649209od_a_e,M: fsm_e_a_a] :
      ( ( member_e @ ( produc8662292540227115477od_a_e @ T ) @ ( states_e_a_a @ M ) )
     => ( ( member_a @ ( produc6516300556236668976od_a_e @ ( produc3301107258437235991od_a_e @ T ) ) @ ( inputs_e_a_a @ M ) )
       => ( ( member_a @ ( product_fst_a_e @ ( produc2212425768795893106od_a_e @ ( produc3301107258437235991od_a_e @ T ) ) ) @ ( outputs_e_a_a @ M ) )
         => ( ( member_e @ ( product_snd_a_e @ ( produc2212425768795893106od_a_e @ ( produc3301107258437235991od_a_e @ T ) ) ) @ ( states_e_a_a @ M ) )
           => ( ( transitions_e_a_a @ ( add_transition_e_a_a @ M @ T ) )
              = ( insert5520024574859449033od_a_e @ T @ ( transitions_e_a_a @ M ) ) ) ) ) ) ) ).

% add_transition_simps(4)
thf(fact_893_add__transition__simps_I1_J,axiom,
    ! [T: produc5343229610332254449od_e_e,M: fsm_e_e_e] :
      ( ( member_e @ ( produc3561935336479904205od_e_e @ T ) @ ( states_e_e_e @ M ) )
     => ( ( member_e @ ( produc2032089063873476136od_e_e @ ( produc7424122091544800527od_e_e @ T ) ) @ ( inputs_e_e_e @ M ) )
       => ( ( member_e @ ( product_fst_e_e @ ( produc6951586313287476074od_e_e @ ( produc7424122091544800527od_e_e @ T ) ) ) @ ( outputs_e_e_e @ M ) )
         => ( ( member_e @ ( product_snd_e_e @ ( produc6951586313287476074od_e_e @ ( produc7424122091544800527od_e_e @ T ) ) ) @ ( states_e_e_e @ M ) )
           => ( ( initial_e_e_e @ ( add_transition_e_e_e @ M @ T ) )
              = ( initial_e_e_e @ M ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_894_add__transition__simps_I1_J,axiom,
    ! [T: produc6614590355691243316od_b_e,M: fsm_e_e_b] :
      ( ( member_e @ ( produc5468882338294864272od_b_e @ T ) @ ( states_e_e_b @ M ) )
     => ( ( member_e @ ( produc1171083772936728427od_b_e @ ( produc107697056504984786od_b_e @ T ) ) @ ( inputs_e_e_b @ M ) )
       => ( ( member_b @ ( product_fst_b_e @ ( produc6090581022350728365od_b_e @ ( produc107697056504984786od_b_e @ T ) ) ) @ ( outputs_e_e_b @ M ) )
         => ( ( member_e @ ( product_snd_b_e @ ( produc6090581022350728365od_b_e @ ( produc107697056504984786od_b_e @ T ) ) ) @ ( states_e_e_b @ M ) )
           => ( ( initial_e_e_b @ ( add_transition_e_e_b @ M @ T ) )
              = ( initial_e_e_b @ M ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_895_add__transition__simps_I1_J,axiom,
    ! [T: produc3963919925192647669od_a_e,M: fsm_e_e_a] :
      ( ( member_e @ ( produc6104531338899850961od_a_e @ T ) @ ( states_e_e_a @ M ) )
     => ( ( member_e @ ( produc3958539354909404460od_a_e @ ( produc743346057109971475od_a_e @ T ) ) @ ( inputs_e_e_a @ M ) )
       => ( ( member_a @ ( product_fst_a_e @ ( produc8878036604323404398od_a_e @ ( produc743346057109971475od_a_e @ T ) ) ) @ ( outputs_e_e_a @ M ) )
         => ( ( member_e @ ( product_snd_a_e @ ( produc8878036604323404398od_a_e @ ( produc743346057109971475od_a_e @ T ) ) ) @ ( states_e_e_a @ M ) )
           => ( ( initial_e_e_a @ ( add_transition_e_e_a @ M @ T ) )
              = ( initial_e_e_a @ M ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_896_add__transition__simps_I1_J,axiom,
    ! [T: produc128009433335561652od_e_e,M: fsm_e_b_e] :
      ( ( member_e @ ( produc5480256237475352592od_e_e @ T ) @ ( states_e_b_e @ M ) )
     => ( ( member_b @ ( produc3950409964868924523od_e_e @ ( produc119070955685473106od_e_e @ T ) ) @ ( inputs_e_b_e @ M ) )
       => ( ( member_e @ ( product_fst_e_e @ ( produc8869907214282924461od_e_e @ ( produc119070955685473106od_e_e @ T ) ) ) @ ( outputs_e_b_e @ M ) )
         => ( ( member_e @ ( product_snd_e_e @ ( produc8869907214282924461od_e_e @ ( produc119070955685473106od_e_e @ T ) ) ) @ ( states_e_b_e @ M ) )
           => ( ( initial_e_b_e @ ( add_transition_e_b_e @ M @ T ) )
              = ( initial_e_b_e @ M ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_897_add__transition__simps_I1_J,axiom,
    ! [T: produc1399370178694550519od_b_e,M: fsm_e_b_b] :
      ( ( member_e @ ( produc7387203239290312659od_b_e @ T ) @ ( states_e_b_b @ M ) )
     => ( ( member_b @ ( produc3089404673932176814od_b_e @ ( produc2026017957500433173od_b_e @ T ) ) @ ( inputs_e_b_b @ M ) )
       => ( ( member_b @ ( product_fst_b_e @ ( produc8008901923346176752od_b_e @ ( produc2026017957500433173od_b_e @ T ) ) ) @ ( outputs_e_b_b @ M ) )
         => ( ( member_e @ ( product_snd_b_e @ ( produc8008901923346176752od_b_e @ ( produc2026017957500433173od_b_e @ T ) ) ) @ ( states_e_b_b @ M ) )
           => ( ( initial_e_b_b @ ( add_transition_e_b_b @ M @ T ) )
              = ( initial_e_b_b @ M ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_898_add__transition__simps_I1_J,axiom,
    ! [T: produc7972071785050730680od_a_e,M: fsm_e_b_a] :
      ( ( member_e @ ( produc8022852239895299348od_a_e @ T ) @ ( states_e_b_a @ M ) )
     => ( ( member_b @ ( produc5876860255904852847od_a_e @ ( produc2661666958105419862od_a_e @ T ) ) @ ( inputs_e_b_a @ M ) )
       => ( ( member_a @ ( product_fst_a_e @ ( produc1572985468464076977od_a_e @ ( produc2661666958105419862od_a_e @ T ) ) ) @ ( outputs_e_b_a @ M ) )
         => ( ( member_e @ ( product_snd_a_e @ ( produc1572985468464076977od_a_e @ ( produc2661666958105419862od_a_e @ T ) ) ) @ ( states_e_b_a @ M ) )
           => ( ( initial_e_b_a @ ( add_transition_e_b_a @ M @ T ) )
              = ( initial_e_b_a @ M ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_899_add__transition__simps_I1_J,axiom,
    ! [T: produc1464060053288255989od_e_e,M: fsm_e_a_e] :
      ( ( member_e @ ( produc6119696537807168721od_e_e @ T ) @ ( states_e_a_e @ M ) )
     => ( ( member_a @ ( produc4589850265200740652od_e_e @ ( produc758511256017289235od_e_e @ T ) ) @ ( inputs_e_a_e @ M ) )
       => ( ( member_e @ ( product_fst_e_e @ ( produc285975477759964782od_e_e @ ( produc758511256017289235od_e_e @ T ) ) ) @ ( outputs_e_a_e @ M ) )
         => ( ( member_e @ ( product_snd_e_e @ ( produc285975477759964782od_e_e @ ( produc758511256017289235od_e_e @ T ) ) ) @ ( states_e_a_e @ M ) )
           => ( ( initial_e_a_e @ ( add_transition_e_a_e @ M @ T ) )
              = ( initial_e_a_e @ M ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_900_add__transition__simps_I1_J,axiom,
    ! [T: produc2735420798647244856od_b_e,M: fsm_e_a_b] :
      ( ( member_e @ ( produc8026643539622128788od_b_e @ T ) @ ( states_e_a_b @ M ) )
     => ( ( member_a @ ( produc3728844974263992943od_b_e @ ( produc2665458257832249302od_b_e @ T ) ) @ ( inputs_e_a_b @ M ) )
       => ( ( member_b @ ( product_fst_b_e @ ( produc8648342223677992881od_b_e @ ( produc2665458257832249302od_b_e @ T ) ) ) @ ( outputs_e_a_b @ M ) )
         => ( ( member_e @ ( product_snd_b_e @ ( produc8648342223677992881od_b_e @ ( produc2665458257832249302od_b_e @ T ) ) ) @ ( states_e_a_b @ M ) )
           => ( ( initial_e_a_b @ ( add_transition_e_a_b @ M @ T ) )
              = ( initial_e_a_b @ M ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_901_add__transition__simps_I1_J,axiom,
    ! [T: produc84750368148649209od_a_e,M: fsm_e_a_a] :
      ( ( member_e @ ( produc8662292540227115477od_a_e @ T ) @ ( states_e_a_a @ M ) )
     => ( ( member_a @ ( produc6516300556236668976od_a_e @ ( produc3301107258437235991od_a_e @ T ) ) @ ( inputs_e_a_a @ M ) )
       => ( ( member_a @ ( product_fst_a_e @ ( produc2212425768795893106od_a_e @ ( produc3301107258437235991od_a_e @ T ) ) ) @ ( outputs_e_a_a @ M ) )
         => ( ( member_e @ ( product_snd_a_e @ ( produc2212425768795893106od_a_e @ ( produc3301107258437235991od_a_e @ T ) ) ) @ ( states_e_a_a @ M ) )
           => ( ( initial_e_a_a @ ( add_transition_e_a_a @ M @ T ) )
              = ( initial_e_a_a @ M ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_902_add__transition__simps_I1_J,axiom,
    ! [T: produc6613991313635240113od_e_b,M: fsm_b_e_e] :
      ( ( member_b @ ( produc6279413401631520781od_e_b @ T ) @ ( states_b_e_e @ M ) )
     => ( ( member_e @ ( produc2032089050963789733od_e_b @ ( produc918228119841641295od_e_b @ T ) ) @ ( inputs_b_e_e @ M ) )
       => ( ( member_e @ ( product_fst_e_b @ ( produc6951586300377789671od_e_b @ ( produc918228119841641295od_e_b @ T ) ) ) @ ( outputs_b_e_e @ M ) )
         => ( ( member_b @ ( product_snd_e_b @ ( produc6951586300377789671od_e_b @ ( produc918228119841641295od_e_b @ T ) ) ) @ ( states_b_e_e @ M ) )
           => ( ( initial_b_e_e @ ( add_transition_b_e_e @ M @ T ) )
              = ( initial_b_e_e @ M ) ) ) ) ) ) ).

% add_transition_simps(1)
thf(fact_903_add__transition__simps_I5_J,axiom,
    ! [T: produc5343229610332254449od_e_e,M: fsm_e_e_e] :
      ( ( member_e @ ( produc3561935336479904205od_e_e @ T ) @ ( states_e_e_e @ M ) )
     => ( ( member_e @ ( produc2032089063873476136od_e_e @ ( produc7424122091544800527od_e_e @ T ) ) @ ( inputs_e_e_e @ M ) )
       => ( ( member_e @ ( product_fst_e_e @ ( produc6951586313287476074od_e_e @ ( produc7424122091544800527od_e_e @ T ) ) ) @ ( outputs_e_e_e @ M ) )
         => ( ( member_e @ ( product_snd_e_e @ ( produc6951586313287476074od_e_e @ ( produc7424122091544800527od_e_e @ T ) ) ) @ ( states_e_e_e @ M ) )
           => ( ( states_e_e_e @ ( add_transition_e_e_e @ M @ T ) )
              = ( states_e_e_e @ M ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_904_add__transition__simps_I5_J,axiom,
    ! [T: produc6614590355691243316od_b_e,M: fsm_e_e_b] :
      ( ( member_e @ ( produc5468882338294864272od_b_e @ T ) @ ( states_e_e_b @ M ) )
     => ( ( member_e @ ( produc1171083772936728427od_b_e @ ( produc107697056504984786od_b_e @ T ) ) @ ( inputs_e_e_b @ M ) )
       => ( ( member_b @ ( product_fst_b_e @ ( produc6090581022350728365od_b_e @ ( produc107697056504984786od_b_e @ T ) ) ) @ ( outputs_e_e_b @ M ) )
         => ( ( member_e @ ( product_snd_b_e @ ( produc6090581022350728365od_b_e @ ( produc107697056504984786od_b_e @ T ) ) ) @ ( states_e_e_b @ M ) )
           => ( ( states_e_e_b @ ( add_transition_e_e_b @ M @ T ) )
              = ( states_e_e_b @ M ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_905_add__transition__simps_I5_J,axiom,
    ! [T: produc3963919925192647669od_a_e,M: fsm_e_e_a] :
      ( ( member_e @ ( produc6104531338899850961od_a_e @ T ) @ ( states_e_e_a @ M ) )
     => ( ( member_e @ ( produc3958539354909404460od_a_e @ ( produc743346057109971475od_a_e @ T ) ) @ ( inputs_e_e_a @ M ) )
       => ( ( member_a @ ( product_fst_a_e @ ( produc8878036604323404398od_a_e @ ( produc743346057109971475od_a_e @ T ) ) ) @ ( outputs_e_e_a @ M ) )
         => ( ( member_e @ ( product_snd_a_e @ ( produc8878036604323404398od_a_e @ ( produc743346057109971475od_a_e @ T ) ) ) @ ( states_e_e_a @ M ) )
           => ( ( states_e_e_a @ ( add_transition_e_e_a @ M @ T ) )
              = ( states_e_e_a @ M ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_906_add__transition__simps_I5_J,axiom,
    ! [T: produc4050040609193146166od_c_e,M: fsm_e_b_c] :
      ( ( member_e @ ( produc6751554238685325970od_c_e @ T ) @ ( states_e_b_c @ M ) )
     => ( ( member_b @ ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T ) ) @ ( inputs_e_b_c @ M ) )
       => ( ( member_c @ ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T ) ) ) @ ( outputs_e_b_c @ M ) )
         => ( ( member_e @ ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T ) ) ) @ ( states_e_b_c @ M ) )
           => ( ( states_e_b_c @ ( add_transition_e_b_c @ M @ T ) )
              = ( states_e_b_c @ M ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_907_add__transition__simps_I5_J,axiom,
    ! [T: produc128009433335561652od_e_e,M: fsm_e_b_e] :
      ( ( member_e @ ( produc5480256237475352592od_e_e @ T ) @ ( states_e_b_e @ M ) )
     => ( ( member_b @ ( produc3950409964868924523od_e_e @ ( produc119070955685473106od_e_e @ T ) ) @ ( inputs_e_b_e @ M ) )
       => ( ( member_e @ ( product_fst_e_e @ ( produc8869907214282924461od_e_e @ ( produc119070955685473106od_e_e @ T ) ) ) @ ( outputs_e_b_e @ M ) )
         => ( ( member_e @ ( product_snd_e_e @ ( produc8869907214282924461od_e_e @ ( produc119070955685473106od_e_e @ T ) ) ) @ ( states_e_b_e @ M ) )
           => ( ( states_e_b_e @ ( add_transition_e_b_e @ M @ T ) )
              = ( states_e_b_e @ M ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_908_add__transition__simps_I5_J,axiom,
    ! [T: produc1399370178694550519od_b_e,M: fsm_e_b_b] :
      ( ( member_e @ ( produc7387203239290312659od_b_e @ T ) @ ( states_e_b_b @ M ) )
     => ( ( member_b @ ( produc3089404673932176814od_b_e @ ( produc2026017957500433173od_b_e @ T ) ) @ ( inputs_e_b_b @ M ) )
       => ( ( member_b @ ( product_fst_b_e @ ( produc8008901923346176752od_b_e @ ( produc2026017957500433173od_b_e @ T ) ) ) @ ( outputs_e_b_b @ M ) )
         => ( ( member_e @ ( product_snd_b_e @ ( produc8008901923346176752od_b_e @ ( produc2026017957500433173od_b_e @ T ) ) ) @ ( states_e_b_b @ M ) )
           => ( ( states_e_b_b @ ( add_transition_e_b_b @ M @ T ) )
              = ( states_e_b_b @ M ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_909_add__transition__simps_I5_J,axiom,
    ! [T: produc7972071785050730680od_a_e,M: fsm_e_b_a] :
      ( ( member_e @ ( produc8022852239895299348od_a_e @ T ) @ ( states_e_b_a @ M ) )
     => ( ( member_b @ ( produc5876860255904852847od_a_e @ ( produc2661666958105419862od_a_e @ T ) ) @ ( inputs_e_b_a @ M ) )
       => ( ( member_a @ ( product_fst_a_e @ ( produc1572985468464076977od_a_e @ ( produc2661666958105419862od_a_e @ T ) ) ) @ ( outputs_e_b_a @ M ) )
         => ( ( member_e @ ( product_snd_a_e @ ( produc1572985468464076977od_a_e @ ( produc2661666958105419862od_a_e @ T ) ) ) @ ( states_e_b_a @ M ) )
           => ( ( states_e_b_a @ ( add_transition_e_b_a @ M @ T ) )
              = ( states_e_b_a @ M ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_910_add__transition__simps_I5_J,axiom,
    ! [T: produc1464060053288255989od_e_e,M: fsm_e_a_e] :
      ( ( member_e @ ( produc6119696537807168721od_e_e @ T ) @ ( states_e_a_e @ M ) )
     => ( ( member_a @ ( produc4589850265200740652od_e_e @ ( produc758511256017289235od_e_e @ T ) ) @ ( inputs_e_a_e @ M ) )
       => ( ( member_e @ ( product_fst_e_e @ ( produc285975477759964782od_e_e @ ( produc758511256017289235od_e_e @ T ) ) ) @ ( outputs_e_a_e @ M ) )
         => ( ( member_e @ ( product_snd_e_e @ ( produc285975477759964782od_e_e @ ( produc758511256017289235od_e_e @ T ) ) ) @ ( states_e_a_e @ M ) )
           => ( ( states_e_a_e @ ( add_transition_e_a_e @ M @ T ) )
              = ( states_e_a_e @ M ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_911_add__transition__simps_I5_J,axiom,
    ! [T: produc2735420798647244856od_b_e,M: fsm_e_a_b] :
      ( ( member_e @ ( produc8026643539622128788od_b_e @ T ) @ ( states_e_a_b @ M ) )
     => ( ( member_a @ ( produc3728844974263992943od_b_e @ ( produc2665458257832249302od_b_e @ T ) ) @ ( inputs_e_a_b @ M ) )
       => ( ( member_b @ ( product_fst_b_e @ ( produc8648342223677992881od_b_e @ ( produc2665458257832249302od_b_e @ T ) ) ) @ ( outputs_e_a_b @ M ) )
         => ( ( member_e @ ( product_snd_b_e @ ( produc8648342223677992881od_b_e @ ( produc2665458257832249302od_b_e @ T ) ) ) @ ( states_e_a_b @ M ) )
           => ( ( states_e_a_b @ ( add_transition_e_a_b @ M @ T ) )
              = ( states_e_a_b @ M ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_912_add__transition__simps_I5_J,axiom,
    ! [T: produc84750368148649209od_a_e,M: fsm_e_a_a] :
      ( ( member_e @ ( produc8662292540227115477od_a_e @ T ) @ ( states_e_a_a @ M ) )
     => ( ( member_a @ ( produc6516300556236668976od_a_e @ ( produc3301107258437235991od_a_e @ T ) ) @ ( inputs_e_a_a @ M ) )
       => ( ( member_a @ ( product_fst_a_e @ ( produc2212425768795893106od_a_e @ ( produc3301107258437235991od_a_e @ T ) ) ) @ ( outputs_e_a_a @ M ) )
         => ( ( member_e @ ( product_snd_a_e @ ( produc2212425768795893106od_a_e @ ( produc3301107258437235991od_a_e @ T ) ) ) @ ( states_e_a_a @ M ) )
           => ( ( states_e_a_a @ ( add_transition_e_a_a @ M @ T ) )
              = ( states_e_a_a @ M ) ) ) ) ) ) ).

% add_transition_simps(5)
thf(fact_913_add__transition__simps_I3_J,axiom,
    ! [T: produc5343229610332254449od_e_e,M: fsm_e_e_e] :
      ( ( member_e @ ( produc3561935336479904205od_e_e @ T ) @ ( states_e_e_e @ M ) )
     => ( ( member_e @ ( produc2032089063873476136od_e_e @ ( produc7424122091544800527od_e_e @ T ) ) @ ( inputs_e_e_e @ M ) )
       => ( ( member_e @ ( product_fst_e_e @ ( produc6951586313287476074od_e_e @ ( produc7424122091544800527od_e_e @ T ) ) ) @ ( outputs_e_e_e @ M ) )
         => ( ( member_e @ ( product_snd_e_e @ ( produc6951586313287476074od_e_e @ ( produc7424122091544800527od_e_e @ T ) ) ) @ ( states_e_e_e @ M ) )
           => ( ( outputs_e_e_e @ ( add_transition_e_e_e @ M @ T ) )
              = ( outputs_e_e_e @ M ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_914_add__transition__simps_I3_J,axiom,
    ! [T: produc6614590355691243316od_b_e,M: fsm_e_e_b] :
      ( ( member_e @ ( produc5468882338294864272od_b_e @ T ) @ ( states_e_e_b @ M ) )
     => ( ( member_e @ ( produc1171083772936728427od_b_e @ ( produc107697056504984786od_b_e @ T ) ) @ ( inputs_e_e_b @ M ) )
       => ( ( member_b @ ( product_fst_b_e @ ( produc6090581022350728365od_b_e @ ( produc107697056504984786od_b_e @ T ) ) ) @ ( outputs_e_e_b @ M ) )
         => ( ( member_e @ ( product_snd_b_e @ ( produc6090581022350728365od_b_e @ ( produc107697056504984786od_b_e @ T ) ) ) @ ( states_e_e_b @ M ) )
           => ( ( outputs_e_e_b @ ( add_transition_e_e_b @ M @ T ) )
              = ( outputs_e_e_b @ M ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_915_add__transition__simps_I3_J,axiom,
    ! [T: produc3963919925192647669od_a_e,M: fsm_e_e_a] :
      ( ( member_e @ ( produc6104531338899850961od_a_e @ T ) @ ( states_e_e_a @ M ) )
     => ( ( member_e @ ( produc3958539354909404460od_a_e @ ( produc743346057109971475od_a_e @ T ) ) @ ( inputs_e_e_a @ M ) )
       => ( ( member_a @ ( product_fst_a_e @ ( produc8878036604323404398od_a_e @ ( produc743346057109971475od_a_e @ T ) ) ) @ ( outputs_e_e_a @ M ) )
         => ( ( member_e @ ( product_snd_a_e @ ( produc8878036604323404398od_a_e @ ( produc743346057109971475od_a_e @ T ) ) ) @ ( states_e_e_a @ M ) )
           => ( ( outputs_e_e_a @ ( add_transition_e_e_a @ M @ T ) )
              = ( outputs_e_e_a @ M ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_916_add__transition__simps_I3_J,axiom,
    ! [T: produc4050040609193146166od_c_e,M: fsm_e_b_c] :
      ( ( member_e @ ( produc6751554238685325970od_c_e @ T ) @ ( states_e_b_c @ M ) )
     => ( ( member_b @ ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T ) ) @ ( inputs_e_b_c @ M ) )
       => ( ( member_c @ ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T ) ) ) @ ( outputs_e_b_c @ M ) )
         => ( ( member_e @ ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T ) ) ) @ ( states_e_b_c @ M ) )
           => ( ( outputs_e_b_c @ ( add_transition_e_b_c @ M @ T ) )
              = ( outputs_e_b_c @ M ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_917_add__transition__simps_I3_J,axiom,
    ! [T: produc128009433335561652od_e_e,M: fsm_e_b_e] :
      ( ( member_e @ ( produc5480256237475352592od_e_e @ T ) @ ( states_e_b_e @ M ) )
     => ( ( member_b @ ( produc3950409964868924523od_e_e @ ( produc119070955685473106od_e_e @ T ) ) @ ( inputs_e_b_e @ M ) )
       => ( ( member_e @ ( product_fst_e_e @ ( produc8869907214282924461od_e_e @ ( produc119070955685473106od_e_e @ T ) ) ) @ ( outputs_e_b_e @ M ) )
         => ( ( member_e @ ( product_snd_e_e @ ( produc8869907214282924461od_e_e @ ( produc119070955685473106od_e_e @ T ) ) ) @ ( states_e_b_e @ M ) )
           => ( ( outputs_e_b_e @ ( add_transition_e_b_e @ M @ T ) )
              = ( outputs_e_b_e @ M ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_918_add__transition__simps_I3_J,axiom,
    ! [T: produc1399370178694550519od_b_e,M: fsm_e_b_b] :
      ( ( member_e @ ( produc7387203239290312659od_b_e @ T ) @ ( states_e_b_b @ M ) )
     => ( ( member_b @ ( produc3089404673932176814od_b_e @ ( produc2026017957500433173od_b_e @ T ) ) @ ( inputs_e_b_b @ M ) )
       => ( ( member_b @ ( product_fst_b_e @ ( produc8008901923346176752od_b_e @ ( produc2026017957500433173od_b_e @ T ) ) ) @ ( outputs_e_b_b @ M ) )
         => ( ( member_e @ ( product_snd_b_e @ ( produc8008901923346176752od_b_e @ ( produc2026017957500433173od_b_e @ T ) ) ) @ ( states_e_b_b @ M ) )
           => ( ( outputs_e_b_b @ ( add_transition_e_b_b @ M @ T ) )
              = ( outputs_e_b_b @ M ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_919_add__transition__simps_I3_J,axiom,
    ! [T: produc7972071785050730680od_a_e,M: fsm_e_b_a] :
      ( ( member_e @ ( produc8022852239895299348od_a_e @ T ) @ ( states_e_b_a @ M ) )
     => ( ( member_b @ ( produc5876860255904852847od_a_e @ ( produc2661666958105419862od_a_e @ T ) ) @ ( inputs_e_b_a @ M ) )
       => ( ( member_a @ ( product_fst_a_e @ ( produc1572985468464076977od_a_e @ ( produc2661666958105419862od_a_e @ T ) ) ) @ ( outputs_e_b_a @ M ) )
         => ( ( member_e @ ( product_snd_a_e @ ( produc1572985468464076977od_a_e @ ( produc2661666958105419862od_a_e @ T ) ) ) @ ( states_e_b_a @ M ) )
           => ( ( outputs_e_b_a @ ( add_transition_e_b_a @ M @ T ) )
              = ( outputs_e_b_a @ M ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_920_add__transition__simps_I3_J,axiom,
    ! [T: produc1464060053288255989od_e_e,M: fsm_e_a_e] :
      ( ( member_e @ ( produc6119696537807168721od_e_e @ T ) @ ( states_e_a_e @ M ) )
     => ( ( member_a @ ( produc4589850265200740652od_e_e @ ( produc758511256017289235od_e_e @ T ) ) @ ( inputs_e_a_e @ M ) )
       => ( ( member_e @ ( product_fst_e_e @ ( produc285975477759964782od_e_e @ ( produc758511256017289235od_e_e @ T ) ) ) @ ( outputs_e_a_e @ M ) )
         => ( ( member_e @ ( product_snd_e_e @ ( produc285975477759964782od_e_e @ ( produc758511256017289235od_e_e @ T ) ) ) @ ( states_e_a_e @ M ) )
           => ( ( outputs_e_a_e @ ( add_transition_e_a_e @ M @ T ) )
              = ( outputs_e_a_e @ M ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_921_add__transition__simps_I3_J,axiom,
    ! [T: produc2735420798647244856od_b_e,M: fsm_e_a_b] :
      ( ( member_e @ ( produc8026643539622128788od_b_e @ T ) @ ( states_e_a_b @ M ) )
     => ( ( member_a @ ( produc3728844974263992943od_b_e @ ( produc2665458257832249302od_b_e @ T ) ) @ ( inputs_e_a_b @ M ) )
       => ( ( member_b @ ( product_fst_b_e @ ( produc8648342223677992881od_b_e @ ( produc2665458257832249302od_b_e @ T ) ) ) @ ( outputs_e_a_b @ M ) )
         => ( ( member_e @ ( product_snd_b_e @ ( produc8648342223677992881od_b_e @ ( produc2665458257832249302od_b_e @ T ) ) ) @ ( states_e_a_b @ M ) )
           => ( ( outputs_e_a_b @ ( add_transition_e_a_b @ M @ T ) )
              = ( outputs_e_a_b @ M ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_922_add__transition__simps_I3_J,axiom,
    ! [T: produc84750368148649209od_a_e,M: fsm_e_a_a] :
      ( ( member_e @ ( produc8662292540227115477od_a_e @ T ) @ ( states_e_a_a @ M ) )
     => ( ( member_a @ ( produc6516300556236668976od_a_e @ ( produc3301107258437235991od_a_e @ T ) ) @ ( inputs_e_a_a @ M ) )
       => ( ( member_a @ ( product_fst_a_e @ ( produc2212425768795893106od_a_e @ ( produc3301107258437235991od_a_e @ T ) ) ) @ ( outputs_e_a_a @ M ) )
         => ( ( member_e @ ( product_snd_a_e @ ( produc2212425768795893106od_a_e @ ( produc3301107258437235991od_a_e @ T ) ) ) @ ( states_e_a_a @ M ) )
           => ( ( outputs_e_a_a @ ( add_transition_e_a_a @ M @ T ) )
              = ( outputs_e_a_a @ M ) ) ) ) ) ) ).

% add_transition_simps(3)
thf(fact_923_add__transition__simps_I2_J,axiom,
    ! [T: produc5343229610332254449od_e_e,M: fsm_e_e_e] :
      ( ( member_e @ ( produc3561935336479904205od_e_e @ T ) @ ( states_e_e_e @ M ) )
     => ( ( member_e @ ( produc2032089063873476136od_e_e @ ( produc7424122091544800527od_e_e @ T ) ) @ ( inputs_e_e_e @ M ) )
       => ( ( member_e @ ( product_fst_e_e @ ( produc6951586313287476074od_e_e @ ( produc7424122091544800527od_e_e @ T ) ) ) @ ( outputs_e_e_e @ M ) )
         => ( ( member_e @ ( product_snd_e_e @ ( produc6951586313287476074od_e_e @ ( produc7424122091544800527od_e_e @ T ) ) ) @ ( states_e_e_e @ M ) )
           => ( ( inputs_e_e_e @ ( add_transition_e_e_e @ M @ T ) )
              = ( inputs_e_e_e @ M ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_924_add__transition__simps_I2_J,axiom,
    ! [T: produc6614590355691243316od_b_e,M: fsm_e_e_b] :
      ( ( member_e @ ( produc5468882338294864272od_b_e @ T ) @ ( states_e_e_b @ M ) )
     => ( ( member_e @ ( produc1171083772936728427od_b_e @ ( produc107697056504984786od_b_e @ T ) ) @ ( inputs_e_e_b @ M ) )
       => ( ( member_b @ ( product_fst_b_e @ ( produc6090581022350728365od_b_e @ ( produc107697056504984786od_b_e @ T ) ) ) @ ( outputs_e_e_b @ M ) )
         => ( ( member_e @ ( product_snd_b_e @ ( produc6090581022350728365od_b_e @ ( produc107697056504984786od_b_e @ T ) ) ) @ ( states_e_e_b @ M ) )
           => ( ( inputs_e_e_b @ ( add_transition_e_e_b @ M @ T ) )
              = ( inputs_e_e_b @ M ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_925_add__transition__simps_I2_J,axiom,
    ! [T: produc3963919925192647669od_a_e,M: fsm_e_e_a] :
      ( ( member_e @ ( produc6104531338899850961od_a_e @ T ) @ ( states_e_e_a @ M ) )
     => ( ( member_e @ ( produc3958539354909404460od_a_e @ ( produc743346057109971475od_a_e @ T ) ) @ ( inputs_e_e_a @ M ) )
       => ( ( member_a @ ( product_fst_a_e @ ( produc8878036604323404398od_a_e @ ( produc743346057109971475od_a_e @ T ) ) ) @ ( outputs_e_e_a @ M ) )
         => ( ( member_e @ ( product_snd_a_e @ ( produc8878036604323404398od_a_e @ ( produc743346057109971475od_a_e @ T ) ) ) @ ( states_e_e_a @ M ) )
           => ( ( inputs_e_e_a @ ( add_transition_e_e_a @ M @ T ) )
              = ( inputs_e_e_a @ M ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_926_add__transition__simps_I2_J,axiom,
    ! [T: produc4050040609193146166od_c_e,M: fsm_e_b_c] :
      ( ( member_e @ ( produc6751554238685325970od_c_e @ T ) @ ( states_e_b_c @ M ) )
     => ( ( member_b @ ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T ) ) @ ( inputs_e_b_c @ M ) )
       => ( ( member_c @ ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T ) ) ) @ ( outputs_e_b_c @ M ) )
         => ( ( member_e @ ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T ) ) ) @ ( states_e_b_c @ M ) )
           => ( ( inputs_e_b_c @ ( add_transition_e_b_c @ M @ T ) )
              = ( inputs_e_b_c @ M ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_927_add__transition__simps_I2_J,axiom,
    ! [T: produc128009433335561652od_e_e,M: fsm_e_b_e] :
      ( ( member_e @ ( produc5480256237475352592od_e_e @ T ) @ ( states_e_b_e @ M ) )
     => ( ( member_b @ ( produc3950409964868924523od_e_e @ ( produc119070955685473106od_e_e @ T ) ) @ ( inputs_e_b_e @ M ) )
       => ( ( member_e @ ( product_fst_e_e @ ( produc8869907214282924461od_e_e @ ( produc119070955685473106od_e_e @ T ) ) ) @ ( outputs_e_b_e @ M ) )
         => ( ( member_e @ ( product_snd_e_e @ ( produc8869907214282924461od_e_e @ ( produc119070955685473106od_e_e @ T ) ) ) @ ( states_e_b_e @ M ) )
           => ( ( inputs_e_b_e @ ( add_transition_e_b_e @ M @ T ) )
              = ( inputs_e_b_e @ M ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_928_add__transition__simps_I2_J,axiom,
    ! [T: produc1399370178694550519od_b_e,M: fsm_e_b_b] :
      ( ( member_e @ ( produc7387203239290312659od_b_e @ T ) @ ( states_e_b_b @ M ) )
     => ( ( member_b @ ( produc3089404673932176814od_b_e @ ( produc2026017957500433173od_b_e @ T ) ) @ ( inputs_e_b_b @ M ) )
       => ( ( member_b @ ( product_fst_b_e @ ( produc8008901923346176752od_b_e @ ( produc2026017957500433173od_b_e @ T ) ) ) @ ( outputs_e_b_b @ M ) )
         => ( ( member_e @ ( product_snd_b_e @ ( produc8008901923346176752od_b_e @ ( produc2026017957500433173od_b_e @ T ) ) ) @ ( states_e_b_b @ M ) )
           => ( ( inputs_e_b_b @ ( add_transition_e_b_b @ M @ T ) )
              = ( inputs_e_b_b @ M ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_929_add__transition__simps_I2_J,axiom,
    ! [T: produc7972071785050730680od_a_e,M: fsm_e_b_a] :
      ( ( member_e @ ( produc8022852239895299348od_a_e @ T ) @ ( states_e_b_a @ M ) )
     => ( ( member_b @ ( produc5876860255904852847od_a_e @ ( produc2661666958105419862od_a_e @ T ) ) @ ( inputs_e_b_a @ M ) )
       => ( ( member_a @ ( product_fst_a_e @ ( produc1572985468464076977od_a_e @ ( produc2661666958105419862od_a_e @ T ) ) ) @ ( outputs_e_b_a @ M ) )
         => ( ( member_e @ ( product_snd_a_e @ ( produc1572985468464076977od_a_e @ ( produc2661666958105419862od_a_e @ T ) ) ) @ ( states_e_b_a @ M ) )
           => ( ( inputs_e_b_a @ ( add_transition_e_b_a @ M @ T ) )
              = ( inputs_e_b_a @ M ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_930_add__transition__simps_I2_J,axiom,
    ! [T: produc1464060053288255989od_e_e,M: fsm_e_a_e] :
      ( ( member_e @ ( produc6119696537807168721od_e_e @ T ) @ ( states_e_a_e @ M ) )
     => ( ( member_a @ ( produc4589850265200740652od_e_e @ ( produc758511256017289235od_e_e @ T ) ) @ ( inputs_e_a_e @ M ) )
       => ( ( member_e @ ( product_fst_e_e @ ( produc285975477759964782od_e_e @ ( produc758511256017289235od_e_e @ T ) ) ) @ ( outputs_e_a_e @ M ) )
         => ( ( member_e @ ( product_snd_e_e @ ( produc285975477759964782od_e_e @ ( produc758511256017289235od_e_e @ T ) ) ) @ ( states_e_a_e @ M ) )
           => ( ( inputs_e_a_e @ ( add_transition_e_a_e @ M @ T ) )
              = ( inputs_e_a_e @ M ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_931_add__transition__simps_I2_J,axiom,
    ! [T: produc2735420798647244856od_b_e,M: fsm_e_a_b] :
      ( ( member_e @ ( produc8026643539622128788od_b_e @ T ) @ ( states_e_a_b @ M ) )
     => ( ( member_a @ ( produc3728844974263992943od_b_e @ ( produc2665458257832249302od_b_e @ T ) ) @ ( inputs_e_a_b @ M ) )
       => ( ( member_b @ ( product_fst_b_e @ ( produc8648342223677992881od_b_e @ ( produc2665458257832249302od_b_e @ T ) ) ) @ ( outputs_e_a_b @ M ) )
         => ( ( member_e @ ( product_snd_b_e @ ( produc8648342223677992881od_b_e @ ( produc2665458257832249302od_b_e @ T ) ) ) @ ( states_e_a_b @ M ) )
           => ( ( inputs_e_a_b @ ( add_transition_e_a_b @ M @ T ) )
              = ( inputs_e_a_b @ M ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_932_add__transition__simps_I2_J,axiom,
    ! [T: produc84750368148649209od_a_e,M: fsm_e_a_a] :
      ( ( member_e @ ( produc8662292540227115477od_a_e @ T ) @ ( states_e_a_a @ M ) )
     => ( ( member_a @ ( produc6516300556236668976od_a_e @ ( produc3301107258437235991od_a_e @ T ) ) @ ( inputs_e_a_a @ M ) )
       => ( ( member_a @ ( product_fst_a_e @ ( produc2212425768795893106od_a_e @ ( produc3301107258437235991od_a_e @ T ) ) ) @ ( outputs_e_a_a @ M ) )
         => ( ( member_e @ ( product_snd_a_e @ ( produc2212425768795893106od_a_e @ ( produc3301107258437235991od_a_e @ T ) ) ) @ ( states_e_a_a @ M ) )
           => ( ( inputs_e_a_a @ ( add_transition_e_a_a @ M @ T ) )
              = ( inputs_e_a_a @ M ) ) ) ) ) ) ).

% add_transition_simps(2)
thf(fact_933_fsm__transition__source,axiom,
    ! [T: produc2669932201312201782od_c_a,M: fsm_a_b_c] :
      ( ( member5502040268208861279od_c_a @ T @ ( transitions_a_b_c @ M ) )
     => ( member_a @ ( produc4225943634317630866od_c_a @ T ) @ ( states_a_b_c @ M ) ) ) ).

% fsm_transition_source
thf(fact_934_fsm__transition__input,axiom,
    ! [T: produc4050040609193146166od_c_e,M: fsm_e_b_c] :
      ( ( member6882148676089805663od_c_e @ T @ ( transitions_e_b_c @ M ) )
     => ( member_b @ ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T ) ) @ ( inputs_e_b_c @ M ) ) ) ).

% fsm_transition_input
thf(fact_935_fsm__transition__input,axiom,
    ! [T: produc2669932201312201782od_c_a,M: fsm_a_b_c] :
      ( ( member5502040268208861279od_c_a @ T @ ( transitions_a_b_c @ M ) )
     => ( member_b @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) @ ( inputs_a_b_c @ M ) ) ) ).

% fsm_transition_input
thf(fact_936_single__input_Osimps,axiom,
    ( single_input_a_b_c
    = ( ^ [M2: fsm_a_b_c] :
        ! [X2: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X2 @ ( transitions_a_b_c @ M2 ) )
         => ! [Y2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Y2 @ ( transitions_a_b_c @ M2 ) )
             => ( ( ( produc4225943634317630866od_c_a @ X2 )
                  = ( produc4225943634317630866od_c_a @ Y2 ) )
               => ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) )
                  = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Y2 ) ) ) ) ) ) ) ) ).

% single_input.simps
thf(fact_937_single__input_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Y: $o] :
      ( ( ( single_input_a_b_c @ X )
        = Y )
     => ( Y
        = ( ! [X2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ X2 @ ( transitions_a_b_c @ X ) )
             => ! [Y2: produc2669932201312201782od_c_a] :
                  ( ( member5502040268208861279od_c_a @ Y2 @ ( transitions_a_b_c @ X ) )
                 => ( ( ( produc4225943634317630866od_c_a @ X2 )
                      = ( produc4225943634317630866od_c_a @ Y2 ) )
                   => ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) )
                      = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Y2 ) ) ) ) ) ) ) ) ) ).

% single_input.elims(1)
thf(fact_938_single__input_Oelims_I2_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ( single_input_a_b_c @ X )
     => ! [X4: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X4 @ ( transitions_a_b_c @ X ) )
         => ! [Xa2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Xa2 @ ( transitions_a_b_c @ X ) )
             => ( ( ( produc4225943634317630866od_c_a @ X4 )
                  = ( produc4225943634317630866od_c_a @ Xa2 ) )
               => ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X4 ) )
                  = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xa2 ) ) ) ) ) ) ) ).

% single_input.elims(2)
thf(fact_939_single__input_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ~ ( single_input_a_b_c @ X )
     => ~ ! [X3: produc2669932201312201782od_c_a] :
            ( ( member5502040268208861279od_c_a @ X3 @ ( transitions_a_b_c @ X ) )
           => ! [Xa3: produc2669932201312201782od_c_a] :
                ( ( member5502040268208861279od_c_a @ Xa3 @ ( transitions_a_b_c @ X ) )
               => ( ( ( produc4225943634317630866od_c_a @ X3 )
                    = ( produc4225943634317630866od_c_a @ Xa3 ) )
                 => ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xa3 ) ) ) ) ) ) ) ).

% single_input.elims(3)
thf(fact_940_completely__specified_Oelims_I3_J,axiom,
    ! [X: fsm_a_b_c] :
      ( ~ ( comple6900478119722646120_a_b_c @ X )
     => ~ ! [X3: a] :
            ( ( member_a @ X3 @ ( states_a_b_c @ X ) )
           => ! [Xa3: b] :
                ( ( member_b @ Xa3 @ ( inputs_a_b_c @ X ) )
               => ? [Xb3: produc2669932201312201782od_c_a] :
                    ( ( member5502040268208861279od_c_a @ Xb3 @ ( transitions_a_b_c @ X ) )
                    & ( ( produc4225943634317630866od_c_a @ Xb3 )
                      = X3 )
                    & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Xb3 ) )
                      = Xa3 ) ) ) ) ) ).

% completely_specified.elims(3)
thf(fact_941_completely__specified_Oelims_I3_J,axiom,
    ! [X: fsm_e_b_c] :
      ( ~ ( comple1615236469910841452_e_b_c @ X )
     => ~ ! [X3: e] :
            ( ( member_e @ X3 @ ( states_e_b_c @ X ) )
           => ! [Xa3: b] :
                ( ( member_b @ Xa3 @ ( inputs_e_b_c @ X ) )
               => ? [Xb3: produc4050040609193146166od_c_e] :
                    ( ( member6882148676089805663od_c_e @ Xb3 @ ( transitions_e_b_c @ X ) )
                    & ( ( produc6751554238685325970od_c_e @ Xb3 )
                      = X3 )
                    & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Xb3 ) )
                      = Xa3 ) ) ) ) ) ).

% completely_specified.elims(3)
thf(fact_942_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 ) )
         => ! [Xa2: b] :
              ( ( member_b @ Xa2 @ ( 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 ) )
                    = Xa2 ) ) ) ) ) ).

% completely_specified.elims(2)
thf(fact_943_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 ) )
         => ! [Xa2: b] :
              ( ( member_b @ Xa2 @ ( 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 ) )
                    = Xa2 ) ) ) ) ) ).

% completely_specified.elims(2)
thf(fact_944_completely__specified_Oelims_I1_J,axiom,
    ! [X: fsm_a_b_c,Y: $o] :
      ( ( ( comple6900478119722646120_a_b_c @ X )
        = Y )
     => ( Y
        = ( ! [X2: a] :
              ( ( member_a @ X2 @ ( states_a_b_c @ X ) )
             => ! [Y2: b] :
                  ( ( member_b @ Y2 @ ( inputs_a_b_c @ X ) )
                 => ? [Z3: produc2669932201312201782od_c_a] :
                      ( ( member5502040268208861279od_c_a @ Z3 @ ( transitions_a_b_c @ X ) )
                      & ( ( produc4225943634317630866od_c_a @ Z3 )
                        = X2 )
                      & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Z3 ) )
                        = Y2 ) ) ) ) ) ) ) ).

% completely_specified.elims(1)
thf(fact_945_completely__specified_Oelims_I1_J,axiom,
    ! [X: fsm_e_b_c,Y: $o] :
      ( ( ( comple1615236469910841452_e_b_c @ X )
        = Y )
     => ( Y
        = ( ! [X2: e] :
              ( ( member_e @ X2 @ ( states_e_b_c @ X ) )
             => ! [Y2: b] :
                  ( ( member_b @ Y2 @ ( inputs_e_b_c @ X ) )
                 => ? [Z3: produc4050040609193146166od_c_e] :
                      ( ( member6882148676089805663od_c_e @ Z3 @ ( transitions_e_b_c @ X ) )
                      & ( ( produc6751554238685325970od_c_e @ Z3 )
                        = X2 )
                      & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Z3 ) )
                        = Y2 ) ) ) ) ) ) ) ).

% completely_specified.elims(1)
thf(fact_946_completely__specified_Osimps,axiom,
    ( comple6900478119722646120_a_b_c
    = ( ^ [M2: fsm_a_b_c] :
        ! [X2: a] :
          ( ( member_a @ X2 @ ( states_a_b_c @ M2 ) )
         => ! [Y2: b] :
              ( ( member_b @ Y2 @ ( inputs_a_b_c @ M2 ) )
             => ? [Z3: produc2669932201312201782od_c_a] :
                  ( ( member5502040268208861279od_c_a @ Z3 @ ( transitions_a_b_c @ M2 ) )
                  & ( ( produc4225943634317630866od_c_a @ Z3 )
                    = X2 )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Z3 ) )
                    = Y2 ) ) ) ) ) ) ).

% completely_specified.simps
thf(fact_947_completely__specified_Osimps,axiom,
    ( comple1615236469910841452_e_b_c
    = ( ^ [M2: fsm_e_b_c] :
        ! [X2: e] :
          ( ( member_e @ X2 @ ( states_e_b_c @ M2 ) )
         => ! [Y2: b] :
              ( ( member_b @ Y2 @ ( inputs_e_b_c @ M2 ) )
             => ? [Z3: produc4050040609193146166od_c_e] :
                  ( ( member6882148676089805663od_c_e @ Z3 @ ( transitions_e_b_c @ M2 ) )
                  & ( ( produc6751554238685325970od_c_e @ Z3 )
                    = X2 )
                  & ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ Z3 ) )
                    = Y2 ) ) ) ) ) ) ).

% completely_specified.simps
thf(fact_948_completely__specified__path__extension,axiom,
    ! [M: fsm_a_b_c,Q3: a,P3: list_P6327159017948738492od_c_a,X: b] :
      ( ( comple6900478119722646120_a_b_c @ M )
     => ( ( member_a @ Q3 @ ( states_a_b_c @ M ) )
       => ( ( path_a_b_c @ M @ Q3 @ P3 )
         => ( ( member_b @ X @ ( inputs_a_b_c @ M ) )
           => ~ ! [T3: produc2669932201312201782od_c_a] :
                  ( ( member5502040268208861279od_c_a @ T3 @ ( transitions_a_b_c @ M ) )
                 => ( ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T3 ) )
                      = X )
                   => ( ( produc4225943634317630866od_c_a @ T3 )
                     != ( target_a_b_c @ Q3 @ P3 ) ) ) ) ) ) ) ) ).

% completely_specified_path_extension
thf(fact_949_completely__specified__path__extension,axiom,
    ! [M: fsm_e_b_c,Q3: e,P3: list_P1631280100260380348od_c_e,X: b] :
      ( ( comple1615236469910841452_e_b_c @ M )
     => ( ( member_e @ Q3 @ ( states_e_b_c @ M ) )
       => ( ( path_e_b_c @ M @ Q3 @ P3 )
         => ( ( member_b @ X @ ( inputs_e_b_c @ M ) )
           => ~ ! [T3: produc4050040609193146166od_c_e] :
                  ( ( member6882148676089805663od_c_e @ T3 @ ( transitions_e_b_c @ M ) )
                 => ( ( ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) )
                      = X )
                   => ( ( produc6751554238685325970od_c_e @ T3 )
                     != ( target_e_b_c @ Q3 @ P3 ) ) ) ) ) ) ) ) ).

% completely_specified_path_extension
thf(fact_950_cyclic__path__transition__states__property_I2_J,axiom,
    ! [P3: list_P6327159017948738492od_c_a,P2: a > $o,M: fsm_a_b_c,Q3: a] :
      ( ? [X4: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X4 @ ( set_Pr5664641634098845387od_c_a @ P3 ) )
          & ( P2 @ ( produc4225943634317630866od_c_a @ X4 ) ) )
     => ( ! [X3: produc2669932201312201782od_c_a] :
            ( ( member5502040268208861279od_c_a @ X3 @ ( set_Pr5664641634098845387od_c_a @ P3 ) )
           => ( ( P2 @ ( produc4225943634317630866od_c_a @ X3 ) )
             => ( P2 @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) ) ) ) ) )
       => ( ( path_a_b_c @ M @ Q3 @ P3 )
         => ( ( ( target_a_b_c @ Q3 @ P3 )
              = Q3 )
           => ! [X4: produc2669932201312201782od_c_a] :
                ( ( member5502040268208861279od_c_a @ X4 @ ( set_Pr5664641634098845387od_c_a @ P3 ) )
               => ( P2 @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X4 ) ) ) ) ) ) ) ) ) ).

% cyclic_path_transition_states_property(2)
thf(fact_951_cyclic__path__transition__states__property_I2_J,axiom,
    ! [P3: list_P1562850763667305982od_c_a,P2: product_prod_c_a > $o,M: fsm_Pr1886043760914421514_a_a_b,Q3: product_prod_c_a] :
      ( ? [X4: produc3205353004677322104od_c_a] :
          ( ( member6508725278956418977od_c_a @ X4 @ ( set_Pr6987804667698513421od_c_a @ P3 ) )
          & ( P2 @ ( produc8171714036265584980od_c_a @ X4 ) ) )
     => ( ! [X3: produc3205353004677322104od_c_a] :
            ( ( member6508725278956418977od_c_a @ X3 @ ( set_Pr6987804667698513421od_c_a @ P3 ) )
           => ( ( P2 @ ( produc8171714036265584980od_c_a @ X3 ) )
             => ( P2 @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X3 ) ) ) ) ) )
       => ( ( path_P1107610407223809260_a_a_b @ M @ Q3 @ P3 )
         => ( ( ( target6303326113586172192_a_a_b @ Q3 @ P3 )
              = Q3 )
           => ! [X4: produc3205353004677322104od_c_a] :
                ( ( member6508725278956418977od_c_a @ X4 @ ( set_Pr6987804667698513421od_c_a @ P3 ) )
               => ( P2 @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X4 ) ) ) ) ) ) ) ) ) ).

% cyclic_path_transition_states_property(2)
thf(fact_952_cyclic__path__transition__states__property_I1_J,axiom,
    ! [P3: list_P6327159017948738492od_c_a,P2: a > $o,M: fsm_a_b_c,Q3: a] :
      ( ? [X4: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X4 @ ( set_Pr5664641634098845387od_c_a @ P3 ) )
          & ( P2 @ ( produc4225943634317630866od_c_a @ X4 ) ) )
     => ( ! [X3: produc2669932201312201782od_c_a] :
            ( ( member5502040268208861279od_c_a @ X3 @ ( set_Pr5664641634098845387od_c_a @ P3 ) )
           => ( ( P2 @ ( produc4225943634317630866od_c_a @ X3 ) )
             => ( P2 @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) ) ) ) ) )
       => ( ( path_a_b_c @ M @ Q3 @ P3 )
         => ( ( ( target_a_b_c @ Q3 @ P3 )
              = Q3 )
           => ! [X4: produc2669932201312201782od_c_a] :
                ( ( member5502040268208861279od_c_a @ X4 @ ( set_Pr5664641634098845387od_c_a @ P3 ) )
               => ( P2 @ ( produc4225943634317630866od_c_a @ X4 ) ) ) ) ) ) ) ).

% cyclic_path_transition_states_property(1)
thf(fact_953_cyclic__path__transition__states__property_I1_J,axiom,
    ! [P3: list_P1562850763667305982od_c_a,P2: product_prod_c_a > $o,M: fsm_Pr1886043760914421514_a_a_b,Q3: product_prod_c_a] :
      ( ? [X4: produc3205353004677322104od_c_a] :
          ( ( member6508725278956418977od_c_a @ X4 @ ( set_Pr6987804667698513421od_c_a @ P3 ) )
          & ( P2 @ ( produc8171714036265584980od_c_a @ X4 ) ) )
     => ( ! [X3: produc3205353004677322104od_c_a] :
            ( ( member6508725278956418977od_c_a @ X3 @ ( set_Pr6987804667698513421od_c_a @ P3 ) )
           => ( ( P2 @ ( produc8171714036265584980od_c_a @ X3 ) )
             => ( P2 @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X3 ) ) ) ) ) )
       => ( ( path_P1107610407223809260_a_a_b @ M @ Q3 @ P3 )
         => ( ( ( target6303326113586172192_a_a_b @ Q3 @ P3 )
              = Q3 )
           => ! [X4: produc3205353004677322104od_c_a] :
                ( ( member6508725278956418977od_c_a @ X4 @ ( set_Pr6987804667698513421od_c_a @ P3 ) )
               => ( P2 @ ( produc8171714036265584980od_c_a @ X4 ) ) ) ) ) ) ) ).

% cyclic_path_transition_states_property(1)
thf(fact_954_cycle__incoming__transition__ex,axiom,
    ! [M: fsm_a_b_c,Q3: a,P3: list_P6327159017948738492od_c_a,T: produc2669932201312201782od_c_a] :
      ( ( path_a_b_c @ M @ Q3 @ P3 )
     => ( ( P3 != nil_Pr1342775757158464060od_c_a )
       => ( ( ( target_a_b_c @ Q3 @ P3 )
            = Q3 )
         => ( ( member5502040268208861279od_c_a @ T @ ( set_Pr5664641634098845387od_c_a @ P3 ) )
           => ? [X3: produc2669932201312201782od_c_a] :
                ( ( member5502040268208861279od_c_a @ X3 @ ( set_Pr5664641634098845387od_c_a @ P3 ) )
                & ( ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ X3 ) ) )
                  = ( produc4225943634317630866od_c_a @ T ) ) ) ) ) ) ) ).

% cycle_incoming_transition_ex
thf(fact_955_cycle__incoming__transition__ex,axiom,
    ! [M: fsm_Pr1886043760914421514_a_a_b,Q3: product_prod_c_a,P3: list_P1562850763667305982od_c_a,T: produc3205353004677322104od_c_a] :
      ( ( path_P1107610407223809260_a_a_b @ M @ Q3 @ P3 )
     => ( ( P3 != nil_Pr7913020553331505022od_c_a )
       => ( ( ( target6303326113586172192_a_a_b @ Q3 @ P3 )
            = Q3 )
         => ( ( member6508725278956418977od_c_a @ T @ ( set_Pr6987804667698513421od_c_a @ P3 ) )
           => ? [X3: produc3205353004677322104od_c_a] :
                ( ( member6508725278956418977od_c_a @ X3 @ ( set_Pr6987804667698513421od_c_a @ P3 ) )
                & ( ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ X3 ) ) )
                  = ( produc8171714036265584980od_c_a @ T ) ) ) ) ) ) ) ).

% cycle_incoming_transition_ex
thf(fact_956_retains__outputs__for__states__and__inputs__def,axiom,
    ( retain2430384024318543025_a_b_c
    = ( ^ [M2: fsm_a_b_c,S5: fsm_a_b_c] :
        ! [X2: produc2669932201312201782od_c_a] :
          ( ( member5502040268208861279od_c_a @ X2 @ ( transitions_a_b_c @ S5 ) )
         => ! [Y2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ Y2 @ ( transitions_a_b_c @ M2 ) )
             => ( ( ( ( produc4225943634317630866od_c_a @ X2 )
                    = ( produc4225943634317630866od_c_a @ Y2 ) )
                  & ( ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ X2 ) )
                    = ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ Y2 ) ) ) )
               => ( member5502040268208861279od_c_a @ Y2 @ ( transitions_a_b_c @ S5 ) ) ) ) ) ) ) ).

% retains_outputs_for_states_and_inputs_def
thf(fact_957_add__transitions__simps_I1_J,axiom,
    ! [Ts: set_Pr1000306023933041105od_e_e,M: fsm_e_e_e] :
      ( ! [T3: produc5343229610332254449od_e_e] :
          ( ( member8175337677228913946od_e_e @ T3 @ Ts )
         => ( ( member_e @ ( produc3561935336479904205od_e_e @ T3 ) @ ( states_e_e_e @ M ) )
            & ( member_e @ ( produc2032089063873476136od_e_e @ ( produc7424122091544800527od_e_e @ T3 ) ) @ ( inputs_e_e_e @ M ) )
            & ( member_e @ ( product_fst_e_e @ ( produc6951586313287476074od_e_e @ ( produc7424122091544800527od_e_e @ T3 ) ) ) @ ( outputs_e_e_e @ M ) )
            & ( member_e @ ( product_snd_e_e @ ( produc6951586313287476074od_e_e @ ( produc7424122091544800527od_e_e @ T3 ) ) ) @ ( states_e_e_e @ M ) ) ) )
     => ( ( initial_e_e_e @ ( add_tr5767337170662267792_e_e_e @ M @ Ts ) )
        = ( initial_e_e_e @ M ) ) ) ).

% add_transitions_simps(1)
thf(fact_958_add__transitions__simps_I1_J,axiom,
    ! [Ts: set_Pr2358468001143520916od_b_e,M: fsm_e_e_b] :
      ( ! [T3: produc6614590355691243316od_b_e] :
          ( ( member223326385733127005od_b_e @ T3 @ Ts )
         => ( ( member_e @ ( produc5468882338294864272od_b_e @ T3 ) @ ( states_e_e_b @ M ) )
            & ( member_e @ ( produc1171083772936728427od_b_e @ ( produc107697056504984786od_b_e @ T3 ) ) @ ( inputs_e_e_b @ M ) )
            & ( member_b @ ( product_fst_b_e @ ( produc6090581022350728365od_b_e @ ( produc107697056504984786od_b_e @ T3 ) ) ) @ ( outputs_e_e_b @ M ) )
            & ( member_e @ ( product_snd_b_e @ ( produc6090581022350728365od_b_e @ ( produc107697056504984786od_b_e @ T3 ) ) ) @ ( states_e_e_b @ M ) ) ) )
     => ( ( initial_e_e_b @ ( add_tr5767337170662267789_e_e_b @ M @ Ts ) )
        = ( initial_e_e_b @ M ) ) ) ).

% add_transitions_simps(1)
thf(fact_959_add__transitions__simps_I1_J,axiom,
    ! [Ts: set_Pr2811188660213680853od_a_e,M: fsm_e_e_a] :
      ( ! [T3: produc3963919925192647669od_a_e] :
          ( ( member6796027992089307166od_a_e @ T3 @ Ts )
         => ( ( member_e @ ( produc6104531338899850961od_a_e @ T3 ) @ ( states_e_e_a @ M ) )
            & ( member_e @ ( produc3958539354909404460od_a_e @ ( produc743346057109971475od_a_e @ T3 ) ) @ ( inputs_e_e_a @ M ) )
            & ( member_a @ ( product_fst_a_e @ ( produc8878036604323404398od_a_e @ ( produc743346057109971475od_a_e @ T3 ) ) ) @ ( outputs_e_e_a @ M ) )
            & ( member_e @ ( product_snd_a_e @ ( produc8878036604323404398od_a_e @ ( produc743346057109971475od_a_e @ T3 ) ) ) @ ( states_e_e_a @ M ) ) ) )
     => ( ( initial_e_e_a @ ( add_tr5767337170662267788_e_e_a @ M @ Ts ) )
        = ( initial_e_e_a @ M ) ) ) ).

% add_transitions_simps(1)
thf(fact_960_add__transitions__simps_I1_J,axiom,
    ! [Ts: set_Pr2756303814962165012od_e_e,M: fsm_e_b_e] :
      ( ! [T3: produc128009433335561652od_e_e] :
          ( ( member2960117500232221149od_e_e @ T3 @ Ts )
         => ( ( member_e @ ( produc5480256237475352592od_e_e @ T3 ) @ ( states_e_b_e @ M ) )
            & ( member_b @ ( produc3950409964868924523od_e_e @ ( produc119070955685473106od_e_e @ T3 ) ) @ ( inputs_e_b_e @ M ) )
            & ( member_e @ ( product_fst_e_e @ ( produc8869907214282924461od_e_e @ ( produc119070955685473106od_e_e @ T3 ) ) ) @ ( outputs_e_b_e @ M ) )
            & ( member_e @ ( product_snd_e_e @ ( produc8869907214282924461od_e_e @ ( produc119070955685473106od_e_e @ T3 ) ) ) @ ( states_e_b_e @ M ) ) ) )
     => ( ( initial_e_b_e @ ( add_tr4906331879725520083_e_b_e @ M @ Ts ) )
        = ( initial_e_b_e @ M ) ) ) ).

% add_transitions_simps(1)
thf(fact_961_add__transitions__simps_I1_J,axiom,
    ! [Ts: set_Pr4114465792172644823od_b_e,M: fsm_e_b_b] :
      ( ! [T3: produc1399370178694550519od_b_e] :
          ( ( member4231478245591210016od_b_e @ T3 @ Ts )
         => ( ( member_e @ ( produc7387203239290312659od_b_e @ T3 ) @ ( states_e_b_b @ M ) )
            & ( member_b @ ( produc3089404673932176814od_b_e @ ( produc2026017957500433173od_b_e @ T3 ) ) @ ( inputs_e_b_b @ M ) )
            & ( member_b @ ( product_fst_b_e @ ( produc8008901923346176752od_b_e @ ( produc2026017957500433173od_b_e @ T3 ) ) ) @ ( outputs_e_b_b @ M ) )
            & ( member_e @ ( product_snd_b_e @ ( produc8008901923346176752od_b_e @ ( produc2026017957500433173od_b_e @ T3 ) ) ) @ ( states_e_b_b @ M ) ) ) )
     => ( ( initial_e_b_b @ ( add_tr4906331879725520080_e_b_b @ M @ Ts ) )
        = ( initial_e_b_b @ M ) ) ) ).

% add_transitions_simps(1)
thf(fact_962_add__transitions__simps_I1_J,axiom,
    ! [Ts: set_Pr4567186451242804760od_a_e,M: fsm_e_b_a] :
      ( ! [T3: produc7972071785050730680od_a_e] :
          ( ( member1580807815092614369od_a_e @ T3 @ Ts )
         => ( ( member_e @ ( produc8022852239895299348od_a_e @ T3 ) @ ( states_e_b_a @ M ) )
            & ( member_b @ ( produc5876860255904852847od_a_e @ ( produc2661666958105419862od_a_e @ T3 ) ) @ ( inputs_e_b_a @ M ) )
            & ( member_a @ ( product_fst_a_e @ ( produc1572985468464076977od_a_e @ ( produc2661666958105419862od_a_e @ T3 ) ) ) @ ( outputs_e_b_a @ M ) )
            & ( member_e @ ( product_snd_a_e @ ( produc1572985468464076977od_a_e @ ( produc2661666958105419862od_a_e @ T3 ) ) ) @ ( states_e_b_a @ M ) ) ) )
     => ( ( initial_e_b_a @ ( add_tr4906331879725520079_e_b_a @ M @ Ts ) )
        = ( initial_e_b_a @ M ) ) ) ).

% add_transitions_simps(1)
thf(fact_963_add__transitions__simps_I1_J,axiom,
    ! [Ts: set_Pr3341636411971872981od_e_e,M: fsm_e_a_e] :
      ( ! [T3: produc1464060053288255989od_e_e] :
          ( ( member4296168120184915486od_e_e @ T3 @ Ts )
         => ( ( member_e @ ( produc6119696537807168721od_e_e @ T3 ) @ ( states_e_a_e @ M ) )
            & ( member_a @ ( produc4589850265200740652od_e_e @ ( produc758511256017289235od_e_e @ T3 ) ) @ ( inputs_e_a_e @ M ) )
            & ( member_e @ ( product_fst_e_e @ ( produc285975477759964782od_e_e @ ( produc758511256017289235od_e_e @ T3 ) ) ) @ ( outputs_e_a_e @ M ) )
            & ( member_e @ ( product_snd_e_e @ ( produc285975477759964782od_e_e @ ( produc758511256017289235od_e_e @ T3 ) ) ) @ ( states_e_a_e @ M ) ) ) )
     => ( ( initial_e_a_e @ ( add_tr7693787461698196116_e_a_e @ M @ Ts ) )
        = ( initial_e_a_e @ M ) ) ) ).

% add_transitions_simps(1)
thf(fact_964_add__transitions__simps_I1_J,axiom,
    ! [Ts: set_Pr4699798389182352792od_b_e,M: fsm_e_a_b] :
      ( ! [T3: produc2735420798647244856od_b_e] :
          ( ( member5567528865543904353od_b_e @ T3 @ Ts )
         => ( ( member_e @ ( produc8026643539622128788od_b_e @ T3 ) @ ( states_e_a_b @ M ) )
            & ( member_a @ ( produc3728844974263992943od_b_e @ ( produc2665458257832249302od_b_e @ T3 ) ) @ ( inputs_e_a_b @ M ) )
            & ( member_b @ ( product_fst_b_e @ ( produc8648342223677992881od_b_e @ ( produc2665458257832249302od_b_e @ T3 ) ) ) @ ( outputs_e_a_b @ M ) )
            & ( member_e @ ( product_snd_b_e @ ( produc8648342223677992881od_b_e @ ( produc2665458257832249302od_b_e @ T3 ) ) ) @ ( states_e_a_b @ M ) ) ) )
     => ( ( initial_e_a_b @ ( add_tr7693787461698196113_e_a_b @ M @ Ts ) )
        = ( initial_e_a_b @ M ) ) ) ).

% add_transitions_simps(1)
thf(fact_965_add__transitions__simps_I1_J,axiom,
    ! [Ts: set_Pr5152519048252512729od_a_e,M: fsm_e_a_a] :
      ( ! [T3: produc84750368148649209od_a_e] :
          ( ( member2916858435045308706od_a_e @ T3 @ Ts )
         => ( ( member_e @ ( produc8662292540227115477od_a_e @ T3 ) @ ( states_e_a_a @ M ) )
            & ( member_a @ ( produc6516300556236668976od_a_e @ ( produc3301107258437235991od_a_e @ T3 ) ) @ ( inputs_e_a_a @ M ) )
            & ( member_a @ ( product_fst_a_e @ ( produc2212425768795893106od_a_e @ ( produc3301107258437235991od_a_e @ T3 ) ) ) @ ( outputs_e_a_a @ M ) )
            & ( member_e @ ( product_snd_a_e @ ( produc2212425768795893106od_a_e @ ( produc3301107258437235991od_a_e @ T3 ) ) ) @ ( states_e_a_a @ M ) ) ) )
     => ( ( initial_e_a_a @ ( add_tr7693787461698196112_e_a_a @ M @ Ts ) )
        = ( initial_e_a_a @ M ) ) ) ).

% add_transitions_simps(1)
thf(fact_966_add__transitions__simps_I1_J,axiom,
    ! [Ts: set_Pr9133901230626697617od_e_b,M: fsm_b_e_e] :
      ( ! [T3: produc6613991313635240113od_e_b] :
          ( ( member222727343677123802od_e_b @ T3 @ Ts )
         => ( ( member_b @ ( produc6279413401631520781od_e_b @ T3 ) @ ( states_b_e_e @ M ) )
            & ( member_e @ ( produc2032089050963789733od_e_b @ ( produc918228119841641295od_e_b @ T3 ) ) @ ( inputs_b_e_e @ M ) )
            & ( member_e @ ( product_fst_e_b @ ( produc6951586300377789671od_e_b @ ( produc918228119841641295od_e_b @ T3 ) ) ) @ ( outputs_b_e_e @ M ) )
            & ( member_b @ ( product_snd_e_b @ ( produc6951586300377789671od_e_b @ ( produc918228119841641295od_e_b @ T3 ) ) ) @ ( states_b_e_e @ M ) ) ) )
     => ( ( initial_b_e_e @ ( add_tr7425425398807427341_b_e_e @ M @ Ts ) )
        = ( initial_b_e_e @ M ) ) ) ).

% add_transitions_simps(1)
thf(fact_967_add__transitions__simps_I4_J,axiom,
    ! [Ts: set_Pr1000306023933041105od_e_e,M: fsm_e_e_e] :
      ( ! [T3: produc5343229610332254449od_e_e] :
          ( ( member8175337677228913946od_e_e @ T3 @ Ts )
         => ( ( member_e @ ( produc3561935336479904205od_e_e @ T3 ) @ ( states_e_e_e @ M ) )
            & ( member_e @ ( produc2032089063873476136od_e_e @ ( produc7424122091544800527od_e_e @ T3 ) ) @ ( inputs_e_e_e @ M ) )
            & ( member_e @ ( product_fst_e_e @ ( produc6951586313287476074od_e_e @ ( produc7424122091544800527od_e_e @ T3 ) ) ) @ ( outputs_e_e_e @ M ) )
            & ( member_e @ ( product_snd_e_e @ ( produc6951586313287476074od_e_e @ ( produc7424122091544800527od_e_e @ T3 ) ) ) @ ( states_e_e_e @ M ) ) ) )
     => ( ( outputs_e_e_e @ ( add_tr5767337170662267792_e_e_e @ M @ Ts ) )
        = ( outputs_e_e_e @ M ) ) ) ).

% add_transitions_simps(4)
thf(fact_968_add__transitions__simps_I4_J,axiom,
    ! [Ts: set_Pr2358468001143520916od_b_e,M: fsm_e_e_b] :
      ( ! [T3: produc6614590355691243316od_b_e] :
          ( ( member223326385733127005od_b_e @ T3 @ Ts )
         => ( ( member_e @ ( produc5468882338294864272od_b_e @ T3 ) @ ( states_e_e_b @ M ) )
            & ( member_e @ ( produc1171083772936728427od_b_e @ ( produc107697056504984786od_b_e @ T3 ) ) @ ( inputs_e_e_b @ M ) )
            & ( member_b @ ( product_fst_b_e @ ( produc6090581022350728365od_b_e @ ( produc107697056504984786od_b_e @ T3 ) ) ) @ ( outputs_e_e_b @ M ) )
            & ( member_e @ ( product_snd_b_e @ ( produc6090581022350728365od_b_e @ ( produc107697056504984786od_b_e @ T3 ) ) ) @ ( states_e_e_b @ M ) ) ) )
     => ( ( outputs_e_e_b @ ( add_tr5767337170662267789_e_e_b @ M @ Ts ) )
        = ( outputs_e_e_b @ M ) ) ) ).

% add_transitions_simps(4)
thf(fact_969_add__transitions__simps_I4_J,axiom,
    ! [Ts: set_Pr2811188660213680853od_a_e,M: fsm_e_e_a] :
      ( ! [T3: produc3963919925192647669od_a_e] :
          ( ( member6796027992089307166od_a_e @ T3 @ Ts )
         => ( ( member_e @ ( produc6104531338899850961od_a_e @ T3 ) @ ( states_e_e_a @ M ) )
            & ( member_e @ ( produc3958539354909404460od_a_e @ ( produc743346057109971475od_a_e @ T3 ) ) @ ( inputs_e_e_a @ M ) )
            & ( member_a @ ( product_fst_a_e @ ( produc8878036604323404398od_a_e @ ( produc743346057109971475od_a_e @ T3 ) ) ) @ ( outputs_e_e_a @ M ) )
            & ( member_e @ ( product_snd_a_e @ ( produc8878036604323404398od_a_e @ ( produc743346057109971475od_a_e @ T3 ) ) ) @ ( states_e_e_a @ M ) ) ) )
     => ( ( outputs_e_e_a @ ( add_tr5767337170662267788_e_e_a @ M @ Ts ) )
        = ( outputs_e_e_a @ M ) ) ) ).

% add_transitions_simps(4)
thf(fact_970_add__transitions__simps_I4_J,axiom,
    ! [Ts: set_Pr3661745133102484886od_c_e,M: fsm_e_b_c] :
      ( ! [T3: produc4050040609193146166od_c_e] :
          ( ( member6882148676089805663od_c_e @ T3 @ Ts )
         => ( ( member_e @ ( produc6751554238685325970od_c_e @ T3 ) @ ( states_e_b_c @ M ) )
            & ( member_b @ ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) @ ( inputs_e_b_c @ M ) )
            & ( member_c @ ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) ) @ ( outputs_e_b_c @ M ) )
            & ( member_e @ ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) ) @ ( states_e_b_c @ M ) ) ) )
     => ( ( outputs_e_b_c @ ( add_tr4906331879725520081_e_b_c @ M @ Ts ) )
        = ( outputs_e_b_c @ M ) ) ) ).

% add_transitions_simps(4)
thf(fact_971_add__transitions__simps_I4_J,axiom,
    ! [Ts: set_Pr2756303814962165012od_e_e,M: fsm_e_b_e] :
      ( ! [T3: produc128009433335561652od_e_e] :
          ( ( member2960117500232221149od_e_e @ T3 @ Ts )
         => ( ( member_e @ ( produc5480256237475352592od_e_e @ T3 ) @ ( states_e_b_e @ M ) )
            & ( member_b @ ( produc3950409964868924523od_e_e @ ( produc119070955685473106od_e_e @ T3 ) ) @ ( inputs_e_b_e @ M ) )
            & ( member_e @ ( product_fst_e_e @ ( produc8869907214282924461od_e_e @ ( produc119070955685473106od_e_e @ T3 ) ) ) @ ( outputs_e_b_e @ M ) )
            & ( member_e @ ( product_snd_e_e @ ( produc8869907214282924461od_e_e @ ( produc119070955685473106od_e_e @ T3 ) ) ) @ ( states_e_b_e @ M ) ) ) )
     => ( ( outputs_e_b_e @ ( add_tr4906331879725520083_e_b_e @ M @ Ts ) )
        = ( outputs_e_b_e @ M ) ) ) ).

% add_transitions_simps(4)
thf(fact_972_add__transitions__simps_I4_J,axiom,
    ! [Ts: set_Pr4114465792172644823od_b_e,M: fsm_e_b_b] :
      ( ! [T3: produc1399370178694550519od_b_e] :
          ( ( member4231478245591210016od_b_e @ T3 @ Ts )
         => ( ( member_e @ ( produc7387203239290312659od_b_e @ T3 ) @ ( states_e_b_b @ M ) )
            & ( member_b @ ( produc3089404673932176814od_b_e @ ( produc2026017957500433173od_b_e @ T3 ) ) @ ( inputs_e_b_b @ M ) )
            & ( member_b @ ( product_fst_b_e @ ( produc8008901923346176752od_b_e @ ( produc2026017957500433173od_b_e @ T3 ) ) ) @ ( outputs_e_b_b @ M ) )
            & ( member_e @ ( product_snd_b_e @ ( produc8008901923346176752od_b_e @ ( produc2026017957500433173od_b_e @ T3 ) ) ) @ ( states_e_b_b @ M ) ) ) )
     => ( ( outputs_e_b_b @ ( add_tr4906331879725520080_e_b_b @ M @ Ts ) )
        = ( outputs_e_b_b @ M ) ) ) ).

% add_transitions_simps(4)
thf(fact_973_add__transitions__simps_I4_J,axiom,
    ! [Ts: set_Pr4567186451242804760od_a_e,M: fsm_e_b_a] :
      ( ! [T3: produc7972071785050730680od_a_e] :
          ( ( member1580807815092614369od_a_e @ T3 @ Ts )
         => ( ( member_e @ ( produc8022852239895299348od_a_e @ T3 ) @ ( states_e_b_a @ M ) )
            & ( member_b @ ( produc5876860255904852847od_a_e @ ( produc2661666958105419862od_a_e @ T3 ) ) @ ( inputs_e_b_a @ M ) )
            & ( member_a @ ( product_fst_a_e @ ( produc1572985468464076977od_a_e @ ( produc2661666958105419862od_a_e @ T3 ) ) ) @ ( outputs_e_b_a @ M ) )
            & ( member_e @ ( product_snd_a_e @ ( produc1572985468464076977od_a_e @ ( produc2661666958105419862od_a_e @ T3 ) ) ) @ ( states_e_b_a @ M ) ) ) )
     => ( ( outputs_e_b_a @ ( add_tr4906331879725520079_e_b_a @ M @ Ts ) )
        = ( outputs_e_b_a @ M ) ) ) ).

% add_transitions_simps(4)
thf(fact_974_add__transitions__simps_I4_J,axiom,
    ! [Ts: set_Pr3341636411971872981od_e_e,M: fsm_e_a_e] :
      ( ! [T3: produc1464060053288255989od_e_e] :
          ( ( member4296168120184915486od_e_e @ T3 @ Ts )
         => ( ( member_e @ ( produc6119696537807168721od_e_e @ T3 ) @ ( states_e_a_e @ M ) )
            & ( member_a @ ( produc4589850265200740652od_e_e @ ( produc758511256017289235od_e_e @ T3 ) ) @ ( inputs_e_a_e @ M ) )
            & ( member_e @ ( product_fst_e_e @ ( produc285975477759964782od_e_e @ ( produc758511256017289235od_e_e @ T3 ) ) ) @ ( outputs_e_a_e @ M ) )
            & ( member_e @ ( product_snd_e_e @ ( produc285975477759964782od_e_e @ ( produc758511256017289235od_e_e @ T3 ) ) ) @ ( states_e_a_e @ M ) ) ) )
     => ( ( outputs_e_a_e @ ( add_tr7693787461698196116_e_a_e @ M @ Ts ) )
        = ( outputs_e_a_e @ M ) ) ) ).

% add_transitions_simps(4)
thf(fact_975_add__transitions__simps_I4_J,axiom,
    ! [Ts: set_Pr4699798389182352792od_b_e,M: fsm_e_a_b] :
      ( ! [T3: produc2735420798647244856od_b_e] :
          ( ( member5567528865543904353od_b_e @ T3 @ Ts )
         => ( ( member_e @ ( produc8026643539622128788od_b_e @ T3 ) @ ( states_e_a_b @ M ) )
            & ( member_a @ ( produc3728844974263992943od_b_e @ ( produc2665458257832249302od_b_e @ T3 ) ) @ ( inputs_e_a_b @ M ) )
            & ( member_b @ ( product_fst_b_e @ ( produc8648342223677992881od_b_e @ ( produc2665458257832249302od_b_e @ T3 ) ) ) @ ( outputs_e_a_b @ M ) )
            & ( member_e @ ( product_snd_b_e @ ( produc8648342223677992881od_b_e @ ( produc2665458257832249302od_b_e @ T3 ) ) ) @ ( states_e_a_b @ M ) ) ) )
     => ( ( outputs_e_a_b @ ( add_tr7693787461698196113_e_a_b @ M @ Ts ) )
        = ( outputs_e_a_b @ M ) ) ) ).

% add_transitions_simps(4)
thf(fact_976_add__transitions__simps_I4_J,axiom,
    ! [Ts: set_Pr5152519048252512729od_a_e,M: fsm_e_a_a] :
      ( ! [T3: produc84750368148649209od_a_e] :
          ( ( member2916858435045308706od_a_e @ T3 @ Ts )
         => ( ( member_e @ ( produc8662292540227115477od_a_e @ T3 ) @ ( states_e_a_a @ M ) )
            & ( member_a @ ( produc6516300556236668976od_a_e @ ( produc3301107258437235991od_a_e @ T3 ) ) @ ( inputs_e_a_a @ M ) )
            & ( member_a @ ( product_fst_a_e @ ( produc2212425768795893106od_a_e @ ( produc3301107258437235991od_a_e @ T3 ) ) ) @ ( outputs_e_a_a @ M ) )
            & ( member_e @ ( product_snd_a_e @ ( produc2212425768795893106od_a_e @ ( produc3301107258437235991od_a_e @ T3 ) ) ) @ ( states_e_a_a @ M ) ) ) )
     => ( ( outputs_e_a_a @ ( add_tr7693787461698196112_e_a_a @ M @ Ts ) )
        = ( outputs_e_a_a @ M ) ) ) ).

% add_transitions_simps(4)
thf(fact_977_add__transitions__simps_I3_J,axiom,
    ! [Ts: set_Pr1000306023933041105od_e_e,M: fsm_e_e_e] :
      ( ! [T3: produc5343229610332254449od_e_e] :
          ( ( member8175337677228913946od_e_e @ T3 @ Ts )
         => ( ( member_e @ ( produc3561935336479904205od_e_e @ T3 ) @ ( states_e_e_e @ M ) )
            & ( member_e @ ( produc2032089063873476136od_e_e @ ( produc7424122091544800527od_e_e @ T3 ) ) @ ( inputs_e_e_e @ M ) )
            & ( member_e @ ( product_fst_e_e @ ( produc6951586313287476074od_e_e @ ( produc7424122091544800527od_e_e @ T3 ) ) ) @ ( outputs_e_e_e @ M ) )
            & ( member_e @ ( product_snd_e_e @ ( produc6951586313287476074od_e_e @ ( produc7424122091544800527od_e_e @ T3 ) ) ) @ ( states_e_e_e @ M ) ) ) )
     => ( ( inputs_e_e_e @ ( add_tr5767337170662267792_e_e_e @ M @ Ts ) )
        = ( inputs_e_e_e @ M ) ) ) ).

% add_transitions_simps(3)
thf(fact_978_add__transitions__simps_I3_J,axiom,
    ! [Ts: set_Pr2358468001143520916od_b_e,M: fsm_e_e_b] :
      ( ! [T3: produc6614590355691243316od_b_e] :
          ( ( member223326385733127005od_b_e @ T3 @ Ts )
         => ( ( member_e @ ( produc5468882338294864272od_b_e @ T3 ) @ ( states_e_e_b @ M ) )
            & ( member_e @ ( produc1171083772936728427od_b_e @ ( produc107697056504984786od_b_e @ T3 ) ) @ ( inputs_e_e_b @ M ) )
            & ( member_b @ ( product_fst_b_e @ ( produc6090581022350728365od_b_e @ ( produc107697056504984786od_b_e @ T3 ) ) ) @ ( outputs_e_e_b @ M ) )
            & ( member_e @ ( product_snd_b_e @ ( produc6090581022350728365od_b_e @ ( produc107697056504984786od_b_e @ T3 ) ) ) @ ( states_e_e_b @ M ) ) ) )
     => ( ( inputs_e_e_b @ ( add_tr5767337170662267789_e_e_b @ M @ Ts ) )
        = ( inputs_e_e_b @ M ) ) ) ).

% add_transitions_simps(3)
thf(fact_979_add__transitions__simps_I3_J,axiom,
    ! [Ts: set_Pr2811188660213680853od_a_e,M: fsm_e_e_a] :
      ( ! [T3: produc3963919925192647669od_a_e] :
          ( ( member6796027992089307166od_a_e @ T3 @ Ts )
         => ( ( member_e @ ( produc6104531338899850961od_a_e @ T3 ) @ ( states_e_e_a @ M ) )
            & ( member_e @ ( produc3958539354909404460od_a_e @ ( produc743346057109971475od_a_e @ T3 ) ) @ ( inputs_e_e_a @ M ) )
            & ( member_a @ ( product_fst_a_e @ ( produc8878036604323404398od_a_e @ ( produc743346057109971475od_a_e @ T3 ) ) ) @ ( outputs_e_e_a @ M ) )
            & ( member_e @ ( product_snd_a_e @ ( produc8878036604323404398od_a_e @ ( produc743346057109971475od_a_e @ T3 ) ) ) @ ( states_e_e_a @ M ) ) ) )
     => ( ( inputs_e_e_a @ ( add_tr5767337170662267788_e_e_a @ M @ Ts ) )
        = ( inputs_e_e_a @ M ) ) ) ).

% add_transitions_simps(3)
thf(fact_980_add__transitions__simps_I3_J,axiom,
    ! [Ts: set_Pr3661745133102484886od_c_e,M: fsm_e_b_c] :
      ( ! [T3: produc4050040609193146166od_c_e] :
          ( ( member6882148676089805663od_c_e @ T3 @ Ts )
         => ( ( member_e @ ( produc6751554238685325970od_c_e @ T3 ) @ ( states_e_b_c @ M ) )
            & ( member_b @ ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) @ ( inputs_e_b_c @ M ) )
            & ( member_c @ ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) ) @ ( outputs_e_b_c @ M ) )
            & ( member_e @ ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) ) @ ( states_e_b_c @ M ) ) ) )
     => ( ( inputs_e_b_c @ ( add_tr4906331879725520081_e_b_c @ M @ Ts ) )
        = ( inputs_e_b_c @ M ) ) ) ).

% add_transitions_simps(3)
thf(fact_981_add__transitions__simps_I3_J,axiom,
    ! [Ts: set_Pr2756303814962165012od_e_e,M: fsm_e_b_e] :
      ( ! [T3: produc128009433335561652od_e_e] :
          ( ( member2960117500232221149od_e_e @ T3 @ Ts )
         => ( ( member_e @ ( produc5480256237475352592od_e_e @ T3 ) @ ( states_e_b_e @ M ) )
            & ( member_b @ ( produc3950409964868924523od_e_e @ ( produc119070955685473106od_e_e @ T3 ) ) @ ( inputs_e_b_e @ M ) )
            & ( member_e @ ( product_fst_e_e @ ( produc8869907214282924461od_e_e @ ( produc119070955685473106od_e_e @ T3 ) ) ) @ ( outputs_e_b_e @ M ) )
            & ( member_e @ ( product_snd_e_e @ ( produc8869907214282924461od_e_e @ ( produc119070955685473106od_e_e @ T3 ) ) ) @ ( states_e_b_e @ M ) ) ) )
     => ( ( inputs_e_b_e @ ( add_tr4906331879725520083_e_b_e @ M @ Ts ) )
        = ( inputs_e_b_e @ M ) ) ) ).

% add_transitions_simps(3)
thf(fact_982_add__transitions__simps_I3_J,axiom,
    ! [Ts: set_Pr4114465792172644823od_b_e,M: fsm_e_b_b] :
      ( ! [T3: produc1399370178694550519od_b_e] :
          ( ( member4231478245591210016od_b_e @ T3 @ Ts )
         => ( ( member_e @ ( produc7387203239290312659od_b_e @ T3 ) @ ( states_e_b_b @ M ) )
            & ( member_b @ ( produc3089404673932176814od_b_e @ ( produc2026017957500433173od_b_e @ T3 ) ) @ ( inputs_e_b_b @ M ) )
            & ( member_b @ ( product_fst_b_e @ ( produc8008901923346176752od_b_e @ ( produc2026017957500433173od_b_e @ T3 ) ) ) @ ( outputs_e_b_b @ M ) )
            & ( member_e @ ( product_snd_b_e @ ( produc8008901923346176752od_b_e @ ( produc2026017957500433173od_b_e @ T3 ) ) ) @ ( states_e_b_b @ M ) ) ) )
     => ( ( inputs_e_b_b @ ( add_tr4906331879725520080_e_b_b @ M @ Ts ) )
        = ( inputs_e_b_b @ M ) ) ) ).

% add_transitions_simps(3)
thf(fact_983_add__transitions__simps_I3_J,axiom,
    ! [Ts: set_Pr4567186451242804760od_a_e,M: fsm_e_b_a] :
      ( ! [T3: produc7972071785050730680od_a_e] :
          ( ( member1580807815092614369od_a_e @ T3 @ Ts )
         => ( ( member_e @ ( produc8022852239895299348od_a_e @ T3 ) @ ( states_e_b_a @ M ) )
            & ( member_b @ ( produc5876860255904852847od_a_e @ ( produc2661666958105419862od_a_e @ T3 ) ) @ ( inputs_e_b_a @ M ) )
            & ( member_a @ ( product_fst_a_e @ ( produc1572985468464076977od_a_e @ ( produc2661666958105419862od_a_e @ T3 ) ) ) @ ( outputs_e_b_a @ M ) )
            & ( member_e @ ( product_snd_a_e @ ( produc1572985468464076977od_a_e @ ( produc2661666958105419862od_a_e @ T3 ) ) ) @ ( states_e_b_a @ M ) ) ) )
     => ( ( inputs_e_b_a @ ( add_tr4906331879725520079_e_b_a @ M @ Ts ) )
        = ( inputs_e_b_a @ M ) ) ) ).

% add_transitions_simps(3)
thf(fact_984_add__transitions__simps_I3_J,axiom,
    ! [Ts: set_Pr3341636411971872981od_e_e,M: fsm_e_a_e] :
      ( ! [T3: produc1464060053288255989od_e_e] :
          ( ( member4296168120184915486od_e_e @ T3 @ Ts )
         => ( ( member_e @ ( produc6119696537807168721od_e_e @ T3 ) @ ( states_e_a_e @ M ) )
            & ( member_a @ ( produc4589850265200740652od_e_e @ ( produc758511256017289235od_e_e @ T3 ) ) @ ( inputs_e_a_e @ M ) )
            & ( member_e @ ( product_fst_e_e @ ( produc285975477759964782od_e_e @ ( produc758511256017289235od_e_e @ T3 ) ) ) @ ( outputs_e_a_e @ M ) )
            & ( member_e @ ( product_snd_e_e @ ( produc285975477759964782od_e_e @ ( produc758511256017289235od_e_e @ T3 ) ) ) @ ( states_e_a_e @ M ) ) ) )
     => ( ( inputs_e_a_e @ ( add_tr7693787461698196116_e_a_e @ M @ Ts ) )
        = ( inputs_e_a_e @ M ) ) ) ).

% add_transitions_simps(3)
thf(fact_985_add__transitions__simps_I3_J,axiom,
    ! [Ts: set_Pr4699798389182352792od_b_e,M: fsm_e_a_b] :
      ( ! [T3: produc2735420798647244856od_b_e] :
          ( ( member5567528865543904353od_b_e @ T3 @ Ts )
         => ( ( member_e @ ( produc8026643539622128788od_b_e @ T3 ) @ ( states_e_a_b @ M ) )
            & ( member_a @ ( produc3728844974263992943od_b_e @ ( produc2665458257832249302od_b_e @ T3 ) ) @ ( inputs_e_a_b @ M ) )
            & ( member_b @ ( product_fst_b_e @ ( produc8648342223677992881od_b_e @ ( produc2665458257832249302od_b_e @ T3 ) ) ) @ ( outputs_e_a_b @ M ) )
            & ( member_e @ ( product_snd_b_e @ ( produc8648342223677992881od_b_e @ ( produc2665458257832249302od_b_e @ T3 ) ) ) @ ( states_e_a_b @ M ) ) ) )
     => ( ( inputs_e_a_b @ ( add_tr7693787461698196113_e_a_b @ M @ Ts ) )
        = ( inputs_e_a_b @ M ) ) ) ).

% add_transitions_simps(3)
thf(fact_986_add__transitions__simps_I3_J,axiom,
    ! [Ts: set_Pr5152519048252512729od_a_e,M: fsm_e_a_a] :
      ( ! [T3: produc84750368148649209od_a_e] :
          ( ( member2916858435045308706od_a_e @ T3 @ Ts )
         => ( ( member_e @ ( produc8662292540227115477od_a_e @ T3 ) @ ( states_e_a_a @ M ) )
            & ( member_a @ ( produc6516300556236668976od_a_e @ ( produc3301107258437235991od_a_e @ T3 ) ) @ ( inputs_e_a_a @ M ) )
            & ( member_a @ ( product_fst_a_e @ ( produc2212425768795893106od_a_e @ ( produc3301107258437235991od_a_e @ T3 ) ) ) @ ( outputs_e_a_a @ M ) )
            & ( member_e @ ( product_snd_a_e @ ( produc2212425768795893106od_a_e @ ( produc3301107258437235991od_a_e @ T3 ) ) ) @ ( states_e_a_a @ M ) ) ) )
     => ( ( inputs_e_a_a @ ( add_tr7693787461698196112_e_a_a @ M @ Ts ) )
        = ( inputs_e_a_a @ M ) ) ) ).

% add_transitions_simps(3)
thf(fact_987_add__transitions__simps_I2_J,axiom,
    ! [Ts: set_Pr1000306023933041105od_e_e,M: fsm_e_e_e] :
      ( ! [T3: produc5343229610332254449od_e_e] :
          ( ( member8175337677228913946od_e_e @ T3 @ Ts )
         => ( ( member_e @ ( produc3561935336479904205od_e_e @ T3 ) @ ( states_e_e_e @ M ) )
            & ( member_e @ ( produc2032089063873476136od_e_e @ ( produc7424122091544800527od_e_e @ T3 ) ) @ ( inputs_e_e_e @ M ) )
            & ( member_e @ ( product_fst_e_e @ ( produc6951586313287476074od_e_e @ ( produc7424122091544800527od_e_e @ T3 ) ) ) @ ( outputs_e_e_e @ M ) )
            & ( member_e @ ( product_snd_e_e @ ( produc6951586313287476074od_e_e @ ( produc7424122091544800527od_e_e @ T3 ) ) ) @ ( states_e_e_e @ M ) ) ) )
     => ( ( states_e_e_e @ ( add_tr5767337170662267792_e_e_e @ M @ Ts ) )
        = ( states_e_e_e @ M ) ) ) ).

% add_transitions_simps(2)
thf(fact_988_add__transitions__simps_I2_J,axiom,
    ! [Ts: set_Pr2358468001143520916od_b_e,M: fsm_e_e_b] :
      ( ! [T3: produc6614590355691243316od_b_e] :
          ( ( member223326385733127005od_b_e @ T3 @ Ts )
         => ( ( member_e @ ( produc5468882338294864272od_b_e @ T3 ) @ ( states_e_e_b @ M ) )
            & ( member_e @ ( produc1171083772936728427od_b_e @ ( produc107697056504984786od_b_e @ T3 ) ) @ ( inputs_e_e_b @ M ) )
            & ( member_b @ ( product_fst_b_e @ ( produc6090581022350728365od_b_e @ ( produc107697056504984786od_b_e @ T3 ) ) ) @ ( outputs_e_e_b @ M ) )
            & ( member_e @ ( product_snd_b_e @ ( produc6090581022350728365od_b_e @ ( produc107697056504984786od_b_e @ T3 ) ) ) @ ( states_e_e_b @ M ) ) ) )
     => ( ( states_e_e_b @ ( add_tr5767337170662267789_e_e_b @ M @ Ts ) )
        = ( states_e_e_b @ M ) ) ) ).

% add_transitions_simps(2)
thf(fact_989_add__transitions__simps_I2_J,axiom,
    ! [Ts: set_Pr2811188660213680853od_a_e,M: fsm_e_e_a] :
      ( ! [T3: produc3963919925192647669od_a_e] :
          ( ( member6796027992089307166od_a_e @ T3 @ Ts )
         => ( ( member_e @ ( produc6104531338899850961od_a_e @ T3 ) @ ( states_e_e_a @ M ) )
            & ( member_e @ ( produc3958539354909404460od_a_e @ ( produc743346057109971475od_a_e @ T3 ) ) @ ( inputs_e_e_a @ M ) )
            & ( member_a @ ( product_fst_a_e @ ( produc8878036604323404398od_a_e @ ( produc743346057109971475od_a_e @ T3 ) ) ) @ ( outputs_e_e_a @ M ) )
            & ( member_e @ ( product_snd_a_e @ ( produc8878036604323404398od_a_e @ ( produc743346057109971475od_a_e @ T3 ) ) ) @ ( states_e_e_a @ M ) ) ) )
     => ( ( states_e_e_a @ ( add_tr5767337170662267788_e_e_a @ M @ Ts ) )
        = ( states_e_e_a @ M ) ) ) ).

% add_transitions_simps(2)
thf(fact_990_add__transitions__simps_I2_J,axiom,
    ! [Ts: set_Pr3661745133102484886od_c_e,M: fsm_e_b_c] :
      ( ! [T3: produc4050040609193146166od_c_e] :
          ( ( member6882148676089805663od_c_e @ T3 @ Ts )
         => ( ( member_e @ ( produc6751554238685325970od_c_e @ T3 ) @ ( states_e_b_c @ M ) )
            & ( member_b @ ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) @ ( inputs_e_b_c @ M ) )
            & ( member_c @ ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) ) @ ( outputs_e_b_c @ M ) )
            & ( member_e @ ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) ) @ ( states_e_b_c @ M ) ) ) )
     => ( ( states_e_b_c @ ( add_tr4906331879725520081_e_b_c @ M @ Ts ) )
        = ( states_e_b_c @ M ) ) ) ).

% add_transitions_simps(2)
thf(fact_991_add__transitions__simps_I2_J,axiom,
    ! [Ts: set_Pr2756303814962165012od_e_e,M: fsm_e_b_e] :
      ( ! [T3: produc128009433335561652od_e_e] :
          ( ( member2960117500232221149od_e_e @ T3 @ Ts )
         => ( ( member_e @ ( produc5480256237475352592od_e_e @ T3 ) @ ( states_e_b_e @ M ) )
            & ( member_b @ ( produc3950409964868924523od_e_e @ ( produc119070955685473106od_e_e @ T3 ) ) @ ( inputs_e_b_e @ M ) )
            & ( member_e @ ( product_fst_e_e @ ( produc8869907214282924461od_e_e @ ( produc119070955685473106od_e_e @ T3 ) ) ) @ ( outputs_e_b_e @ M ) )
            & ( member_e @ ( product_snd_e_e @ ( produc8869907214282924461od_e_e @ ( produc119070955685473106od_e_e @ T3 ) ) ) @ ( states_e_b_e @ M ) ) ) )
     => ( ( states_e_b_e @ ( add_tr4906331879725520083_e_b_e @ M @ Ts ) )
        = ( states_e_b_e @ M ) ) ) ).

% add_transitions_simps(2)
thf(fact_992_add__transitions__simps_I2_J,axiom,
    ! [Ts: set_Pr4114465792172644823od_b_e,M: fsm_e_b_b] :
      ( ! [T3: produc1399370178694550519od_b_e] :
          ( ( member4231478245591210016od_b_e @ T3 @ Ts )
         => ( ( member_e @ ( produc7387203239290312659od_b_e @ T3 ) @ ( states_e_b_b @ M ) )
            & ( member_b @ ( produc3089404673932176814od_b_e @ ( produc2026017957500433173od_b_e @ T3 ) ) @ ( inputs_e_b_b @ M ) )
            & ( member_b @ ( product_fst_b_e @ ( produc8008901923346176752od_b_e @ ( produc2026017957500433173od_b_e @ T3 ) ) ) @ ( outputs_e_b_b @ M ) )
            & ( member_e @ ( product_snd_b_e @ ( produc8008901923346176752od_b_e @ ( produc2026017957500433173od_b_e @ T3 ) ) ) @ ( states_e_b_b @ M ) ) ) )
     => ( ( states_e_b_b @ ( add_tr4906331879725520080_e_b_b @ M @ Ts ) )
        = ( states_e_b_b @ M ) ) ) ).

% add_transitions_simps(2)
thf(fact_993_add__transitions__simps_I2_J,axiom,
    ! [Ts: set_Pr4567186451242804760od_a_e,M: fsm_e_b_a] :
      ( ! [T3: produc7972071785050730680od_a_e] :
          ( ( member1580807815092614369od_a_e @ T3 @ Ts )
         => ( ( member_e @ ( produc8022852239895299348od_a_e @ T3 ) @ ( states_e_b_a @ M ) )
            & ( member_b @ ( produc5876860255904852847od_a_e @ ( produc2661666958105419862od_a_e @ T3 ) ) @ ( inputs_e_b_a @ M ) )
            & ( member_a @ ( product_fst_a_e @ ( produc1572985468464076977od_a_e @ ( produc2661666958105419862od_a_e @ T3 ) ) ) @ ( outputs_e_b_a @ M ) )
            & ( member_e @ ( product_snd_a_e @ ( produc1572985468464076977od_a_e @ ( produc2661666958105419862od_a_e @ T3 ) ) ) @ ( states_e_b_a @ M ) ) ) )
     => ( ( states_e_b_a @ ( add_tr4906331879725520079_e_b_a @ M @ Ts ) )
        = ( states_e_b_a @ M ) ) ) ).

% add_transitions_simps(2)
thf(fact_994_add__transitions__simps_I2_J,axiom,
    ! [Ts: set_Pr3341636411971872981od_e_e,M: fsm_e_a_e] :
      ( ! [T3: produc1464060053288255989od_e_e] :
          ( ( member4296168120184915486od_e_e @ T3 @ Ts )
         => ( ( member_e @ ( produc6119696537807168721od_e_e @ T3 ) @ ( states_e_a_e @ M ) )
            & ( member_a @ ( produc4589850265200740652od_e_e @ ( produc758511256017289235od_e_e @ T3 ) ) @ ( inputs_e_a_e @ M ) )
            & ( member_e @ ( product_fst_e_e @ ( produc285975477759964782od_e_e @ ( produc758511256017289235od_e_e @ T3 ) ) ) @ ( outputs_e_a_e @ M ) )
            & ( member_e @ ( product_snd_e_e @ ( produc285975477759964782od_e_e @ ( produc758511256017289235od_e_e @ T3 ) ) ) @ ( states_e_a_e @ M ) ) ) )
     => ( ( states_e_a_e @ ( add_tr7693787461698196116_e_a_e @ M @ Ts ) )
        = ( states_e_a_e @ M ) ) ) ).

% add_transitions_simps(2)
thf(fact_995_add__transitions__simps_I2_J,axiom,
    ! [Ts: set_Pr4699798389182352792od_b_e,M: fsm_e_a_b] :
      ( ! [T3: produc2735420798647244856od_b_e] :
          ( ( member5567528865543904353od_b_e @ T3 @ Ts )
         => ( ( member_e @ ( produc8026643539622128788od_b_e @ T3 ) @ ( states_e_a_b @ M ) )
            & ( member_a @ ( produc3728844974263992943od_b_e @ ( produc2665458257832249302od_b_e @ T3 ) ) @ ( inputs_e_a_b @ M ) )
            & ( member_b @ ( product_fst_b_e @ ( produc8648342223677992881od_b_e @ ( produc2665458257832249302od_b_e @ T3 ) ) ) @ ( outputs_e_a_b @ M ) )
            & ( member_e @ ( product_snd_b_e @ ( produc8648342223677992881od_b_e @ ( produc2665458257832249302od_b_e @ T3 ) ) ) @ ( states_e_a_b @ M ) ) ) )
     => ( ( states_e_a_b @ ( add_tr7693787461698196113_e_a_b @ M @ Ts ) )
        = ( states_e_a_b @ M ) ) ) ).

% add_transitions_simps(2)
thf(fact_996_add__transitions__simps_I2_J,axiom,
    ! [Ts: set_Pr5152519048252512729od_a_e,M: fsm_e_a_a] :
      ( ! [T3: produc84750368148649209od_a_e] :
          ( ( member2916858435045308706od_a_e @ T3 @ Ts )
         => ( ( member_e @ ( produc8662292540227115477od_a_e @ T3 ) @ ( states_e_a_a @ M ) )
            & ( member_a @ ( produc6516300556236668976od_a_e @ ( produc3301107258437235991od_a_e @ T3 ) ) @ ( inputs_e_a_a @ M ) )
            & ( member_a @ ( product_fst_a_e @ ( produc2212425768795893106od_a_e @ ( produc3301107258437235991od_a_e @ T3 ) ) ) @ ( outputs_e_a_a @ M ) )
            & ( member_e @ ( product_snd_a_e @ ( produc2212425768795893106od_a_e @ ( produc3301107258437235991od_a_e @ T3 ) ) ) @ ( states_e_a_a @ M ) ) ) )
     => ( ( states_e_a_a @ ( add_tr7693787461698196112_e_a_a @ M @ Ts ) )
        = ( states_e_a_a @ M ) ) ) ).

% add_transitions_simps(2)
thf(fact_997__092_060open_062fst_A_Ilast_Aio_J_A_092_060in_062_AFSM_Oinputs_AM_H_092_060close_062,axiom,
    member_b @ ( product_fst_b_c @ ( last_P6003269694912247047od_b_c @ io ) ) @ ( inputs_e_b_c @ m2 ) ).

% \<open>fst (last io) \<in> FSM.inputs M'\<close>
thf(fact_998__092_060open_062fst_A_Ilast_Aio_J_A_092_060in_062_AFSM_Oinputs_AM_092_060close_062,axiom,
    member_b @ ( product_fst_b_c @ ( last_P6003269694912247047od_b_c @ io ) ) @ ( inputs_a_b_c @ m ) ).

% \<open>fst (last io) \<in> FSM.inputs M\<close>
thf(fact_999_last__in__set,axiom,
    ! [As: list_l2826717958560394946od_c_a] :
      ( ( As != nil_li2790768921375229634od_c_a )
     => ( member7410604586820865893od_c_a @ ( last_l4004486932838600923od_c_a @ As ) @ ( set_li8663184538779258833od_c_a @ As ) ) ) ).

% last_in_set
thf(fact_1000_last__in__set,axiom,
    ! [As: list_e] :
      ( ( As != nil_e )
     => ( member_e @ ( last_e @ As ) @ ( set_e2 @ As ) ) ) ).

% last_in_set
thf(fact_1001_last__in__set,axiom,
    ! [As: list_b] :
      ( ( As != nil_b )
     => ( member_b @ ( last_b @ As ) @ ( set_b2 @ As ) ) ) ).

% last_in_set
thf(fact_1002_last__in__set,axiom,
    ! [As: list_a] :
      ( ( As != nil_a )
     => ( member_a @ ( last_a @ As ) @ ( set_a2 @ As ) ) ) ).

% last_in_set
thf(fact_1003_last__in__set,axiom,
    ! [As: list_P903359562653991662od_b_c] :
      ( ( As != nil_Product_prod_b_c )
     => ( member7862447941013992593od_b_c @ ( last_P6003269694912247047od_b_c @ As ) @ ( set_Product_prod_b_c2 @ As ) ) ) ).

% last_in_set
thf(fact_1004_last__in__set,axiom,
    ! [As: list_P6327159017948738492od_c_a] :
      ( ( As != nil_Pr1342775757158464060od_c_a )
     => ( member5502040268208861279od_c_a @ ( last_P7542784938880197845od_c_a @ As ) @ ( set_Pr5664641634098845387od_c_a @ As ) ) ) ).

% last_in_set
thf(fact_1005_last__in__set,axiom,
    ! [As: list_P3660316430366008877_set_a] :
      ( ( As != nil_Pr4665773148637758253_set_a )
     => ( member7983343339038529360_set_a @ ( last_P1813955410594260934_set_a @ As ) @ ( set_Pr7878197726666307004_set_a @ As ) ) ) ).

% last_in_set
thf(fact_1006_last__in__set,axiom,
    ! [As: list_l8907847357763382004od_b_c] :
      ( ( As != nil_li8071162985807626740od_b_c )
     => ( member6330420149250801815od_b_c @ ( last_l931685513881243149od_b_c @ As ) @ ( set_li4480668622519654659od_b_c @ As ) ) ) ).

% last_in_set
thf(fact_1007_add__transition__with__components__simps_I5_J,axiom,
    ! [M: fsm_a_b_c,T: produc2669932201312201782od_c_a] :
      ( ( states_a_b_c @ ( add_tr8224572408740125824_a_b_c @ M @ T ) )
      = ( insert_a @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) @ ( insert_a @ ( produc4225943634317630866od_c_a @ T ) @ ( states_a_b_c @ M ) ) ) ) ).

% add_transition_with_components_simps(5)
thf(fact_1008_add__transition__with__components__simps_I5_J,axiom,
    ! [M: fsm_Pr1886043760914421514_a_a_b,T: produc3205353004677322104od_c_a] :
      ( ( states367398909958982703_a_a_b @ ( add_tr5093536917197733991_a_a_b @ M @ T ) )
      = ( insert8183397254950580085od_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) @ ( insert8183397254950580085od_c_a @ ( produc8171714036265584980od_c_a @ T ) @ ( states367398909958982703_a_a_b @ M ) ) ) ) ).

% add_transition_with_components_simps(5)
thf(fact_1009_t3,axiom,
    ! [A2: fsm_d_b_c,D1: d,D22: d,Q14: a,Q22: a] :
      ( ( member73601632213084689od_d_d @ ( produc3676634857637483352od_d_d @ A2 @ ( product_Pair_d_d @ D1 @ D22 ) ) @ ( separators @ ( product_Pair_a_a @ Q14 @ Q22 ) ) )
     => ( ( member73601632213084689od_d_d @ ( produc3676634857637483352od_d_d @ A2 @ ( product_Pair_d_d @ D22 @ D1 ) ) @ ( separators @ ( product_Pair_a_a @ Q22 @ Q14 ) ) )
        & ( state_8910485216943051357_b_c_d @ m @ Q14 @ Q22 @ A2 @ D1 @ D22 ) ) ) ).

% t3
thf(fact_1010_add__transition__with__components__simps_I3_J,axiom,
    ! [M: fsm_Pr1886043760914421514_a_a_b,T: produc3205353004677322104od_c_a] :
      ( ( output2371653660386375239_a_a_b @ ( add_tr5093536917197733991_a_a_b @ M @ T ) )
      = ( insert_b @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T ) ) ) @ ( output2371653660386375239_a_a_b @ M ) ) ) ).

% add_transition_with_components_simps(3)
thf(fact_1011_add__transition__with__components__simps_I3_J,axiom,
    ! [M: fsm_a_b_c,T: produc2669932201312201782od_c_a] :
      ( ( outputs_a_b_c @ ( add_tr8224572408740125824_a_b_c @ M @ T ) )
      = ( insert_c @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) ) @ ( outputs_a_b_c @ M ) ) ) ).

% add_transition_with_components_simps(3)
thf(fact_1012_filter__states__simps_I5_J,axiom,
    ! [P2: e > $o,M: fsm_e_b_c] :
      ( ( P2 @ ( initial_e_b_c @ M ) )
     => ( ( transitions_e_b_c @ ( filter_states_e_b_c @ M @ P2 ) )
        = ( collec561809896775794081od_c_e
          @ ^ [T2: produc4050040609193146166od_c_e] :
              ( ( member6882148676089805663od_c_e @ T2 @ ( transitions_e_b_c @ M ) )
              & ( P2 @ ( produc6751554238685325970od_c_e @ T2 ) )
              & ( P2 @ ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T2 ) ) ) ) ) ) ) ) ).

% filter_states_simps(5)
thf(fact_1013_filter__states__simps_I5_J,axiom,
    ! [P2: a > $o,M: fsm_a_b_c] :
      ( ( P2 @ ( initial_a_b_c @ M ) )
     => ( ( transitions_a_b_c @ ( filter_states_a_b_c @ M @ P2 ) )
        = ( collec8405073525749625505od_c_a
          @ ^ [T2: produc2669932201312201782od_c_a] :
              ( ( member5502040268208861279od_c_a @ T2 @ ( transitions_a_b_c @ M ) )
              & ( P2 @ ( produc4225943634317630866od_c_a @ T2 ) )
              & ( P2 @ ( product_snd_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) ) ) ) ) ) ).

% filter_states_simps(5)
thf(fact_1014_filter__states__simps_I5_J,axiom,
    ! [P2: product_prod_c_a > $o,M: fsm_Pr1886043760914421514_a_a_b] :
      ( ( P2 @ ( initia681974817753967189_a_a_b @ M ) )
     => ( ( transi2941759273464634107_a_a_b @ ( filter1780482953621413783_a_a_b @ M @ P2 ) )
        = ( collec7519840507084740067od_c_a
          @ ^ [T2: produc3205353004677322104od_c_a] :
              ( ( member6508725278956418977od_c_a @ T2 @ ( transi2941759273464634107_a_a_b @ M ) )
              & ( P2 @ ( produc8171714036265584980od_c_a @ T2 ) )
              & ( P2 @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ ( produc4643634399596806294od_c_a @ T2 ) ) ) ) ) ) ) ) ).

% filter_states_simps(5)
thf(fact_1015_add__transitions__simps_I5_J,axiom,
    ! [Ts: set_Pr1000306023933041105od_e_e,M: fsm_e_e_e] :
      ( ! [T3: produc5343229610332254449od_e_e] :
          ( ( member8175337677228913946od_e_e @ T3 @ Ts )
         => ( ( member_e @ ( produc3561935336479904205od_e_e @ T3 ) @ ( states_e_e_e @ M ) )
            & ( member_e @ ( produc2032089063873476136od_e_e @ ( produc7424122091544800527od_e_e @ T3 ) ) @ ( inputs_e_e_e @ M ) )
            & ( member_e @ ( product_fst_e_e @ ( produc6951586313287476074od_e_e @ ( produc7424122091544800527od_e_e @ T3 ) ) ) @ ( outputs_e_e_e @ M ) )
            & ( member_e @ ( product_snd_e_e @ ( produc6951586313287476074od_e_e @ ( produc7424122091544800527od_e_e @ T3 ) ) ) @ ( states_e_e_e @ M ) ) ) )
     => ( ( transitions_e_e_e @ ( add_tr5767337170662267792_e_e_e @ M @ Ts ) )
        = ( sup_su593565138194795429od_e_e @ ( transitions_e_e_e @ M ) @ Ts ) ) ) ).

% add_transitions_simps(5)
thf(fact_1016_add__transitions__simps_I5_J,axiom,
    ! [Ts: set_Pr2358468001143520916od_b_e,M: fsm_e_e_b] :
      ( ! [T3: produc6614590355691243316od_b_e] :
          ( ( member223326385733127005od_b_e @ T3 @ Ts )
         => ( ( member_e @ ( produc5468882338294864272od_b_e @ T3 ) @ ( states_e_e_b @ M ) )
            & ( member_e @ ( produc1171083772936728427od_b_e @ ( produc107697056504984786od_b_e @ T3 ) ) @ ( inputs_e_e_b @ M ) )
            & ( member_b @ ( product_fst_b_e @ ( produc6090581022350728365od_b_e @ ( produc107697056504984786od_b_e @ T3 ) ) ) @ ( outputs_e_e_b @ M ) )
            & ( member_e @ ( product_snd_b_e @ ( produc6090581022350728365od_b_e @ ( produc107697056504984786od_b_e @ T3 ) ) ) @ ( states_e_e_b @ M ) ) ) )
     => ( ( transitions_e_e_b @ ( add_tr5767337170662267789_e_e_b @ M @ Ts ) )
        = ( sup_su1951727115405275240od_b_e @ ( transitions_e_e_b @ M ) @ Ts ) ) ) ).

% add_transitions_simps(5)
thf(fact_1017_add__transitions__simps_I5_J,axiom,
    ! [Ts: set_Pr2811188660213680853od_a_e,M: fsm_e_e_a] :
      ( ! [T3: produc3963919925192647669od_a_e] :
          ( ( member6796027992089307166od_a_e @ T3 @ Ts )
         => ( ( member_e @ ( produc6104531338899850961od_a_e @ T3 ) @ ( states_e_e_a @ M ) )
            & ( member_e @ ( produc3958539354909404460od_a_e @ ( produc743346057109971475od_a_e @ T3 ) ) @ ( inputs_e_e_a @ M ) )
            & ( member_a @ ( product_fst_a_e @ ( produc8878036604323404398od_a_e @ ( produc743346057109971475od_a_e @ T3 ) ) ) @ ( outputs_e_e_a @ M ) )
            & ( member_e @ ( product_snd_a_e @ ( produc8878036604323404398od_a_e @ ( produc743346057109971475od_a_e @ T3 ) ) ) @ ( states_e_e_a @ M ) ) ) )
     => ( ( transitions_e_e_a @ ( add_tr5767337170662267788_e_e_a @ M @ Ts ) )
        = ( sup_su2404447774475435177od_a_e @ ( transitions_e_e_a @ M ) @ Ts ) ) ) ).

% add_transitions_simps(5)
thf(fact_1018_add__transitions__simps_I5_J,axiom,
    ! [Ts: set_Pr3661745133102484886od_c_e,M: fsm_e_b_c] :
      ( ! [T3: produc4050040609193146166od_c_e] :
          ( ( member6882148676089805663od_c_e @ T3 @ Ts )
         => ( ( member_e @ ( produc6751554238685325970od_c_e @ T3 ) @ ( states_e_b_c @ M ) )
            & ( member_b @ ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) @ ( inputs_e_b_c @ M ) )
            & ( member_c @ ( product_fst_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) ) @ ( outputs_e_b_c @ M ) )
            & ( member_e @ ( product_snd_c_e @ ( produc5221446341373500719od_c_e @ ( produc1390368956895446484od_c_e @ T3 ) ) ) @ ( states_e_b_c @ M ) ) ) )
     => ( ( transitions_e_b_c @ ( add_tr4906331879725520081_e_b_c @ M @ Ts ) )
        = ( sup_su3255004247364239210od_c_e @ ( transitions_e_b_c @ M ) @ Ts ) ) ) ).

% add_transitions_simps(5)
thf(fact_1019_add__transitions__simps_I5_J,axiom,
    ! [Ts: set_Pr2756303814962165012od_e_e,M: fsm_e_b_e] :
      ( ! [T3: produc128009433335561652od_e_e] :
          ( ( member2960117500232221149od_e_e @ T3 @ Ts )
         => ( ( member_e @ ( produc5480256237475352592od_e_e @ T3 ) @ ( states_e_b_e @ M ) )
            & ( member_b @ ( produc3950409964868924523od_e_e @ ( produc119070955685473106od_e_e @ T3 ) ) @ ( inputs_e_b_e @ M ) )
            & ( member_e @ ( product_fst_e_e @ ( produc8869907214282924461od_e_e @ ( produc119070955685473106od_e_e @ T3 ) ) ) @ ( outputs_e_b_e @ M ) )
            & ( member_e @ ( product_snd_e_e @ ( produc8869907214282924461od_e_e @ ( produc119070955685473106od_e_e @ T3 ) ) ) @ ( states_e_b_e @ M ) ) ) )
     => ( ( transitions_e_b_e @ ( add_tr4906331879725520083_e_b_e @ M @ Ts ) )
        = ( sup_su2349562929223919336od_e_e @ ( transitions_e_b_e @ M ) @ Ts ) ) ) ).

% add_transitions_simps(5)
thf(fact_1020_add__transitions__simps_I5_J,axiom,
    ! [Ts: set_Pr4114465792172644823od_b_e,M: fsm_e_b_b] :
      ( ! [T3: produc1399370178694550519od_b_e] :
          ( ( member4231478245591210016od_b_e @ T3 @ Ts )
         => ( ( member_e @ ( produc7387203239290312659od_b_e @ T3 ) @ ( states_e_b_b @ M ) )
            & ( member_b @ ( produc3089404673932176814od_b_e @ ( produc2026017957500433173od_b_e @ T3 ) ) @ ( inputs_e_b_b @ M ) )
            & ( member_b @ ( product_fst_b_e @ ( produc8008901923346176752od_b_e @ ( produc2026017957500433173od_b_e @ T3 ) ) ) @ ( outputs_e_b_b @ M ) )
            & ( member_e @ ( product_snd_b_e @ ( produc8008901923346176752od_b_e @ ( produc2026017957500433173od_b_e @ T3 ) ) ) @ ( states_e_b_b @ M ) ) ) )
     => ( ( transitions_e_b_b @ ( add_tr4906331879725520080_e_b_b @ M @ Ts ) )
        = ( sup_su3707724906434399147od_b_e @ ( transitions_e_b_b @ M ) @ Ts ) ) ) ).

% add_transitions_simps(5)
thf(fact_1021_add__transitions__simps_I5_J,axiom,
    ! [Ts: set_Pr4567186451242804760od_a_e,M: fsm_e_b_a] :
      ( ! [T3: produc7972071785050730680od_a_e] :
          ( ( member1580807815092614369od_a_e @ T3 @ Ts )
         => ( ( member_e @ ( produc8022852239895299348od_a_e @ T3 ) @ ( states_e_b_a @ M ) )
            & ( member_b @ ( produc5876860255904852847od_a_e @ ( produc2661666958105419862od_a_e @ T3 ) ) @ ( inputs_e_b_a @ M ) )
            & ( member_a @ ( product_fst_a_e @ ( produc1572985468464076977od_a_e @ ( produc2661666958105419862od_a_e @ T3 ) ) ) @ ( outputs_e_b_a @ M ) )
            & ( member_e @ ( product_snd_a_e @ ( produc1572985468464076977od_a_e @ ( produc2661666958105419862od_a_e @ T3 ) ) ) @ ( states_e_b_a @ M ) ) ) )
     => ( ( transitions_e_b_a @ ( add_tr4906331879725520079_e_b_a @ M @ Ts ) )
        = ( sup_su4160445565504559084od_a_e @ ( transitions_e_b_a @ M ) @ Ts ) ) ) ).

% add_transitions_simps(5)
thf(fact_1022_add__transitions__simps_I5_J,axiom,
    ! [Ts: set_Pr3341636411971872981od_e_e,M: fsm_e_a_e] :
      ( ! [T3: produc1464060053288255989od_e_e] :
          ( ( member4296168120184915486od_e_e @ T3 @ Ts )
         => ( ( member_e @ ( produc6119696537807168721od_e_e @ T3 ) @ ( states_e_a_e @ M ) )
            & ( member_a @ ( produc4589850265200740652od_e_e @ ( produc758511256017289235od_e_e @ T3 ) ) @ ( inputs_e_a_e @ M ) )
            & ( member_e @ ( product_fst_e_e @ ( produc285975477759964782od_e_e @ ( produc758511256017289235od_e_e @ T3 ) ) ) @ ( outputs_e_a_e @ M ) )
            & ( member_e @ ( product_snd_e_e @ ( produc285975477759964782od_e_e @ ( produc758511256017289235od_e_e @ T3 ) ) ) @ ( states_e_a_e @ M ) ) ) )
     => ( ( transitions_e_a_e @ ( add_tr7693787461698196116_e_a_e @ M @ Ts ) )
        = ( sup_su2934895526233627305od_e_e @ ( transitions_e_a_e @ M ) @ Ts ) ) ) ).

% add_transitions_simps(5)
thf(fact_1023_add__transitions__simps_I5_J,axiom,
    ! [Ts: set_Pr4699798389182352792od_b_e,M: fsm_e_a_b] :
      ( ! [T3: produc2735420798647244856od_b_e] :
          ( ( member5567528865543904353od_b_e @ T3 @ Ts )
         => ( ( member_e @ ( produc8026643539622128788od_b_e @ T3 ) @ ( states_e_a_b @ M ) )
            & ( member_a @ ( produc3728844974263992943od_b_e @ ( produc2665458257832249302od_b_e @ T3 ) ) @ ( inputs_e_a_b @ M ) )
            & ( member_b @ ( product_fst_b_e @ ( produc8648342223677992881od_b_e @ ( produc2665458257832249302od_b_e @ T3 ) ) ) @ ( outputs_e_a_b @ M ) )
            & ( member_e @ ( product_snd_b_e @ ( produc8648342223677992881od_b_e @ ( produc2665458257832249302od_b_e @ T3 ) ) ) @ ( states_e_a_b @ M ) ) ) )
     => ( ( transitions_e_a_b @ ( add_tr7693787461698196113_e_a_b @ M @ Ts ) )
        = ( sup_su4293057503444107116od_b_e @ ( transitions_e_a_b @ M ) @ Ts ) ) ) ).

% add_transitions_simps(5)
thf(fact_1024_add__transitions__simps_I5_J,axiom,
    ! [Ts: set_Pr5152519048252512729od_a_e,M: fsm_e_a_a] :
      ( ! [T3: produc84750368148649209od_a_e] :
          ( ( member2916858435045308706od_a_e @ T3 @ Ts )
         => ( ( member_e @ ( produc8662292540227115477od_a_e @ T3 ) @ ( states_e_a_a @ M ) )
            & ( member_a @ ( produc6516300556236668976od_a_e @ ( produc3301107258437235991od_a_e @ T3 ) ) @ ( inputs_e_a_a @ M ) )
            & ( member_a @ ( product_fst_a_e @ ( produc2212425768795893106od_a_e @ ( produc3301107258437235991od_a_e @ T3 ) ) ) @ ( outputs_e_a_a @ M ) )
            & ( member_e @ ( product_snd_a_e @ ( produc2212425768795893106od_a_e @ ( produc3301107258437235991od_a_e @ T3 ) ) ) @ ( states_e_a_a @ M ) ) ) )
     => ( ( transitions_e_a_a @ ( add_tr7693787461698196112_e_a_a @ M @ Ts ) )
        = ( sup_su4745778162514267053od_a_e @ ( transitions_e_a_a @ M ) @ Ts ) ) ) ).

% add_transitions_simps(5)
thf(fact_1025_add__transition__with__components__simps_I2_J,axiom,
    ! [M: fsm_e_b_c,T: produc4050040609193146166od_c_e] :
      ( ( inputs_e_b_c @ ( add_tr2939330758928321156_e_b_c @ M @ T ) )
      = ( insert_b @ ( produc301949091959500781od_c_e @ ( produc1390368956895446484od_c_e @ T ) ) @ ( inputs_e_b_c @ M ) ) ) ).

% add_transition_with_components_simps(2)
thf(fact_1026_add__transition__with__components__simps_I2_J,axiom,
    ! [M: fsm_a_b_c,T: produc2669932201312201782od_c_a] :
      ( ( inputs_a_b_c @ ( add_tr8224572408740125824_a_b_c @ M @ T ) )
      = ( insert_b @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T ) ) @ ( inputs_a_b_c @ M ) ) ) ).

% add_transition_with_components_simps(2)
thf(fact_1027_Un__iff,axiom,
    ! [C2: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ C2 @ ( sup_su3823046536922626210od_b_c @ A2 @ B ) )
      = ( ( member6330420149250801815od_b_c @ C2 @ A2 )
        | ( member6330420149250801815od_b_c @ C2 @ B ) ) ) ).

% Un_iff
thf(fact_1028_Un__iff,axiom,
    ! [C2: list_P6327159017948738492od_c_a,A2: set_li1159382662694783132od_c_a,B: set_li1159382662694783132od_c_a] :
      ( ( member7410604586820865893od_c_a @ C2 @ ( sup_su500200128730103920od_c_a @ A2 @ B ) )
      = ( ( member7410604586820865893od_c_a @ C2 @ A2 )
        | ( member7410604586820865893od_c_a @ C2 @ B ) ) ) ).

% Un_iff
thf(fact_1029_Un__iff,axiom,
    ! [C2: e,A2: set_e,B: set_e] :
      ( ( member_e @ C2 @ ( sup_sup_set_e @ A2 @ B ) )
      = ( ( member_e @ C2 @ A2 )
        | ( member_e @ C2 @ B ) ) ) ).

% Un_iff
thf(fact_1030_Un__iff,axiom,
    ! [C2: b,A2: set_b,B: set_b] :
      ( ( member_b @ C2 @ ( sup_sup_set_b @ A2 @ B ) )
      = ( ( member_b @ C2 @ A2 )
        | ( member_b @ C2 @ B ) ) ) ).

% Un_iff
thf(fact_1031_Un__iff,axiom,
    ! [C2: a,A2: set_a,B: set_a] :
      ( ( member_a @ C2 @ ( sup_sup_set_a @ A2 @ B ) )
      = ( ( member_a @ C2 @ A2 )
        | ( member_a @ C2 @ B ) ) ) ).

% Un_iff
thf(fact_1032_UnCI,axiom,
    ! [C2: list_P903359562653991662od_b_c,B: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( ~ ( member6330420149250801815od_b_c @ C2 @ B )
       => ( member6330420149250801815od_b_c @ C2 @ A2 ) )
     => ( member6330420149250801815od_b_c @ C2 @ ( sup_su3823046536922626210od_b_c @ A2 @ B ) ) ) ).

% UnCI
thf(fact_1033_UnCI,axiom,
    ! [C2: list_P6327159017948738492od_c_a,B: set_li1159382662694783132od_c_a,A2: set_li1159382662694783132od_c_a] :
      ( ( ~ ( member7410604586820865893od_c_a @ C2 @ B )
       => ( member7410604586820865893od_c_a @ C2 @ A2 ) )
     => ( member7410604586820865893od_c_a @ C2 @ ( sup_su500200128730103920od_c_a @ A2 @ B ) ) ) ).

% UnCI
thf(fact_1034_UnCI,axiom,
    ! [C2: e,B: set_e,A2: set_e] :
      ( ( ~ ( member_e @ C2 @ B )
       => ( member_e @ C2 @ A2 ) )
     => ( member_e @ C2 @ ( sup_sup_set_e @ A2 @ B ) ) ) ).

% UnCI
thf(fact_1035_UnCI,axiom,
    ! [C2: b,B: set_b,A2: set_b] :
      ( ( ~ ( member_b @ C2 @ B )
       => ( member_b @ C2 @ A2 ) )
     => ( member_b @ C2 @ ( sup_sup_set_b @ A2 @ B ) ) ) ).

% UnCI
thf(fact_1036_UnCI,axiom,
    ! [C2: a,B: set_a,A2: set_a] :
      ( ( ~ ( member_a @ C2 @ B )
       => ( member_a @ C2 @ A2 ) )
     => ( member_a @ C2 @ ( sup_sup_set_a @ A2 @ B ) ) ) ).

% UnCI
thf(fact_1037_Un__empty,axiom,
    ! [A2: set_b,B: set_b] :
      ( ( ( sup_sup_set_b @ A2 @ B )
        = bot_bot_set_b )
      = ( ( A2 = bot_bot_set_b )
        & ( B = bot_bot_set_b ) ) ) ).

% Un_empty
thf(fact_1038_Un__empty,axiom,
    ! [A2: set_Pr9130538228769002824od_d_d,B: set_Pr9130538228769002824od_d_d] :
      ( ( ( sup_su3647555221267236124od_d_d @ A2 @ B )
        = bot_bo7612717905841165748od_d_d )
      = ( ( A2 = bot_bo7612717905841165748od_d_d )
        & ( B = bot_bo7612717905841165748od_d_d ) ) ) ).

% Un_empty
thf(fact_1039_Un__empty,axiom,
    ! [A2: set_e,B: set_e] :
      ( ( ( sup_sup_set_e @ A2 @ B )
        = bot_bot_set_e )
      = ( ( A2 = bot_bot_set_e )
        & ( B = bot_bot_set_e ) ) ) ).

% Un_empty
thf(fact_1040_Un__subset__iff,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c,C3: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ ( sup_su3823046536922626210od_b_c @ A2 @ B ) @ C3 )
      = ( ( ord_le282488521294790766od_b_c @ A2 @ C3 )
        & ( ord_le282488521294790766od_b_c @ B @ C3 ) ) ) ).

% Un_subset_iff
thf(fact_1041_Un__subset__iff,axiom,
    ! [A2: set_a,B: set_a,C3: set_a] :
      ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ A2 @ B ) @ C3 )
      = ( ( ord_less_eq_set_a @ A2 @ C3 )
        & ( ord_less_eq_set_a @ B @ C3 ) ) ) ).

% Un_subset_iff
thf(fact_1042_Un__subset__iff,axiom,
    ! [A2: set_li1159382662694783132od_c_a,B: set_li1159382662694783132od_c_a,C3: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ ( sup_su500200128730103920od_c_a @ A2 @ B ) @ C3 )
      = ( ( ord_le2998388488506175548od_c_a @ A2 @ C3 )
        & ( ord_le2998388488506175548od_c_a @ B @ C3 ) ) ) ).

% Un_subset_iff
thf(fact_1043_Un__insert__right,axiom,
    ! [A2: set_li1159382662694783132od_c_a,A: list_P6327159017948738492od_c_a,B: set_li1159382662694783132od_c_a] :
      ( ( sup_su500200128730103920od_c_a @ A2 @ ( insert4789241225314331020od_c_a @ A @ B ) )
      = ( insert4789241225314331020od_c_a @ A @ ( sup_su500200128730103920od_c_a @ A2 @ B ) ) ) ).

% Un_insert_right
thf(fact_1044_Un__insert__right,axiom,
    ! [A2: set_e,A: e,B: set_e] :
      ( ( sup_sup_set_e @ A2 @ ( insert_e @ A @ B ) )
      = ( insert_e @ A @ ( sup_sup_set_e @ A2 @ B ) ) ) ).

% Un_insert_right
thf(fact_1045_Un__insert__left,axiom,
    ! [A: list_P6327159017948738492od_c_a,B: set_li1159382662694783132od_c_a,C3: set_li1159382662694783132od_c_a] :
      ( ( sup_su500200128730103920od_c_a @ ( insert4789241225314331020od_c_a @ A @ B ) @ C3 )
      = ( insert4789241225314331020od_c_a @ A @ ( sup_su500200128730103920od_c_a @ B @ C3 ) ) ) ).

% Un_insert_left
thf(fact_1046_Un__insert__left,axiom,
    ! [A: e,B: set_e,C3: set_e] :
      ( ( sup_sup_set_e @ ( insert_e @ A @ B ) @ C3 )
      = ( insert_e @ A @ ( sup_sup_set_e @ B @ C3 ) ) ) ).

% Un_insert_left
thf(fact_1047_filter__states__simps_I1_J,axiom,
    ! [P2: a > $o,M: fsm_a_b_c] :
      ( ( P2 @ ( initial_a_b_c @ M ) )
     => ( ( initial_a_b_c @ ( filter_states_a_b_c @ M @ P2 ) )
        = ( initial_a_b_c @ M ) ) ) ).

% filter_states_simps(1)
thf(fact_1048_filter__states__simps_I1_J,axiom,
    ! [P2: e > $o,M: fsm_e_b_c] :
      ( ( P2 @ ( initial_e_b_c @ M ) )
     => ( ( initial_e_b_c @ ( filter_states_e_b_c @ M @ P2 ) )
        = ( initial_e_b_c @ M ) ) ) ).

% filter_states_simps(1)
thf(fact_1049_add__transition__with__components__simps_I1_J,axiom,
    ! [M: fsm_a_b_c,T: produc2669932201312201782od_c_a] :
      ( ( initial_a_b_c @ ( add_tr8224572408740125824_a_b_c @ M @ T ) )
      = ( initial_a_b_c @ M ) ) ).

% add_transition_with_components_simps(1)
thf(fact_1050_add__transition__with__components__simps_I1_J,axiom,
    ! [M: fsm_e_b_c,T: produc4050040609193146166od_c_e] :
      ( ( initial_e_b_c @ ( add_tr2939330758928321156_e_b_c @ M @ T ) )
      = ( initial_e_b_c @ M ) ) ).

% add_transition_with_components_simps(1)
thf(fact_1051_filter__states__simps_I3_J,axiom,
    ! [P2: a > $o,M: fsm_a_b_c] :
      ( ( P2 @ ( initial_a_b_c @ M ) )
     => ( ( inputs_a_b_c @ ( filter_states_a_b_c @ M @ P2 ) )
        = ( inputs_a_b_c @ M ) ) ) ).

% filter_states_simps(3)
thf(fact_1052_filter__states__simps_I3_J,axiom,
    ! [P2: e > $o,M: fsm_e_b_c] :
      ( ( P2 @ ( initial_e_b_c @ M ) )
     => ( ( inputs_e_b_c @ ( filter_states_e_b_c @ M @ P2 ) )
        = ( inputs_e_b_c @ M ) ) ) ).

% filter_states_simps(3)
thf(fact_1053_filter__states__simps_I4_J,axiom,
    ! [P2: a > $o,M: fsm_a_b_c] :
      ( ( P2 @ ( initial_a_b_c @ M ) )
     => ( ( outputs_a_b_c @ ( filter_states_a_b_c @ M @ P2 ) )
        = ( outputs_a_b_c @ M ) ) ) ).

% filter_states_simps(4)
thf(fact_1054_filter__states__simps_I4_J,axiom,
    ! [P2: e > $o,M: fsm_e_b_c] :
      ( ( P2 @ ( initial_e_b_c @ M ) )
     => ( ( outputs_e_b_c @ ( filter_states_e_b_c @ M @ P2 ) )
        = ( outputs_e_b_c @ M ) ) ) ).

% filter_states_simps(4)
thf(fact_1055_is__separator__sym,axiom,
    ! [M: fsm_a_b_c,Q14: a,Q22: a,A2: fsm_d_b_c,T1: d,T22: d] :
      ( ( state_8910485216943051357_b_c_d @ M @ Q14 @ Q22 @ A2 @ T1 @ T22 )
     => ( state_8910485216943051357_b_c_d @ M @ Q22 @ Q14 @ A2 @ T22 @ T1 ) ) ).

% is_separator_sym
thf(fact_1056_is__separator__simps_I14_J,axiom,
    ! [M: fsm_a_b_c,Q14: a,Q22: a,A2: fsm_d_b_c,T1: d,T22: d] :
      ( ( state_8910485216943051357_b_c_d @ M @ Q14 @ Q22 @ A2 @ T1 @ T22 )
     => ( Q14 != Q22 ) ) ).

% is_separator_simps(14)
thf(fact_1057_is__separator__simps_I15_J,axiom,
    ! [M: fsm_a_b_c,Q14: a,Q22: a,A2: fsm_d_b_c,T1: d,T22: d] :
      ( ( state_8910485216943051357_b_c_d @ M @ Q14 @ Q22 @ A2 @ T1 @ T22 )
     => ( T1 != T22 ) ) ).

% is_separator_simps(15)
thf(fact_1058_Collect__disj__eq,axiom,
    ! [P2: list_P6327159017948738492od_c_a > $o,Q4: list_P6327159017948738492od_c_a > $o] :
      ( ( collec6273869032445462695od_c_a
        @ ^ [X2: list_P6327159017948738492od_c_a] :
            ( ( P2 @ X2 )
            | ( Q4 @ X2 ) ) )
      = ( sup_su500200128730103920od_c_a @ ( collec6273869032445462695od_c_a @ P2 ) @ ( collec6273869032445462695od_c_a @ Q4 ) ) ) ).

% Collect_disj_eq
thf(fact_1059_Un__def,axiom,
    ( sup_su3823046536922626210od_b_c
    = ( ^ [A6: set_li6436108459499378894od_b_c,B3: set_li6436108459499378894od_b_c] :
          ( collec2280997390073109977od_b_c
          @ ^ [X2: list_P903359562653991662od_b_c] :
              ( ( member6330420149250801815od_b_c @ X2 @ A6 )
              | ( member6330420149250801815od_b_c @ X2 @ B3 ) ) ) ) ) ).

% Un_def
thf(fact_1060_Un__def,axiom,
    ( sup_sup_set_e
    = ( ^ [A6: set_e,B3: set_e] :
          ( collect_e
          @ ^ [X2: e] :
              ( ( member_e @ X2 @ A6 )
              | ( member_e @ X2 @ B3 ) ) ) ) ) ).

% Un_def
thf(fact_1061_Un__def,axiom,
    ( sup_sup_set_b
    = ( ^ [A6: set_b,B3: set_b] :
          ( collect_b
          @ ^ [X2: b] :
              ( ( member_b @ X2 @ A6 )
              | ( member_b @ X2 @ B3 ) ) ) ) ) ).

% Un_def
thf(fact_1062_Un__def,axiom,
    ( sup_sup_set_a
    = ( ^ [A6: set_a,B3: set_a] :
          ( collect_a
          @ ^ [X2: a] :
              ( ( member_a @ X2 @ A6 )
              | ( member_a @ X2 @ B3 ) ) ) ) ) ).

% Un_def
thf(fact_1063_Un__def,axiom,
    ( sup_su500200128730103920od_c_a
    = ( ^ [A6: set_li1159382662694783132od_c_a,B3: set_li1159382662694783132od_c_a] :
          ( collec6273869032445462695od_c_a
          @ ^ [X2: list_P6327159017948738492od_c_a] :
              ( ( member7410604586820865893od_c_a @ X2 @ A6 )
              | ( member7410604586820865893od_c_a @ X2 @ B3 ) ) ) ) ) ).

% Un_def
thf(fact_1064_UnI2,axiom,
    ! [C2: list_P903359562653991662od_b_c,B: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ C2 @ B )
     => ( member6330420149250801815od_b_c @ C2 @ ( sup_su3823046536922626210od_b_c @ A2 @ B ) ) ) ).

% UnI2
thf(fact_1065_UnI2,axiom,
    ! [C2: list_P6327159017948738492od_c_a,B: set_li1159382662694783132od_c_a,A2: set_li1159382662694783132od_c_a] :
      ( ( member7410604586820865893od_c_a @ C2 @ B )
     => ( member7410604586820865893od_c_a @ C2 @ ( sup_su500200128730103920od_c_a @ A2 @ B ) ) ) ).

% UnI2
thf(fact_1066_UnI2,axiom,
    ! [C2: e,B: set_e,A2: set_e] :
      ( ( member_e @ C2 @ B )
     => ( member_e @ C2 @ ( sup_sup_set_e @ A2 @ B ) ) ) ).

% UnI2
thf(fact_1067_UnI2,axiom,
    ! [C2: b,B: set_b,A2: set_b] :
      ( ( member_b @ C2 @ B )
     => ( member_b @ C2 @ ( sup_sup_set_b @ A2 @ B ) ) ) ).

% UnI2
thf(fact_1068_UnI2,axiom,
    ! [C2: a,B: set_a,A2: set_a] :
      ( ( member_a @ C2 @ B )
     => ( member_a @ C2 @ ( sup_sup_set_a @ A2 @ B ) ) ) ).

% UnI2
thf(fact_1069_UnI1,axiom,
    ! [C2: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ C2 @ A2 )
     => ( member6330420149250801815od_b_c @ C2 @ ( sup_su3823046536922626210od_b_c @ A2 @ B ) ) ) ).

% UnI1
thf(fact_1070_UnI1,axiom,
    ! [C2: list_P6327159017948738492od_c_a,A2: set_li1159382662694783132od_c_a,B: set_li1159382662694783132od_c_a] :
      ( ( member7410604586820865893od_c_a @ C2 @ A2 )
     => ( member7410604586820865893od_c_a @ C2 @ ( sup_su500200128730103920od_c_a @ A2 @ B ) ) ) ).

% UnI1
thf(fact_1071_UnI1,axiom,
    ! [C2: e,A2: set_e,B: set_e] :
      ( ( member_e @ C2 @ A2 )
     => ( member_e @ C2 @ ( sup_sup_set_e @ A2 @ B ) ) ) ).

% UnI1
thf(fact_1072_UnI1,axiom,
    ! [C2: b,A2: set_b,B: set_b] :
      ( ( member_b @ C2 @ A2 )
     => ( member_b @ C2 @ ( sup_sup_set_b @ A2 @ B ) ) ) ).

% UnI1
thf(fact_1073_UnI1,axiom,
    ! [C2: a,A2: set_a,B: set_a] :
      ( ( member_a @ C2 @ A2 )
     => ( member_a @ C2 @ ( sup_sup_set_a @ A2 @ B ) ) ) ).

% UnI1
thf(fact_1074_UnE,axiom,
    ! [C2: list_P903359562653991662od_b_c,A2: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( member6330420149250801815od_b_c @ C2 @ ( sup_su3823046536922626210od_b_c @ A2 @ B ) )
     => ( ~ ( member6330420149250801815od_b_c @ C2 @ A2 )
       => ( member6330420149250801815od_b_c @ C2 @ B ) ) ) ).

% UnE
thf(fact_1075_UnE,axiom,
    ! [C2: list_P6327159017948738492od_c_a,A2: set_li1159382662694783132od_c_a,B: set_li1159382662694783132od_c_a] :
      ( ( member7410604586820865893od_c_a @ C2 @ ( sup_su500200128730103920od_c_a @ A2 @ B ) )
     => ( ~ ( member7410604586820865893od_c_a @ C2 @ A2 )
       => ( member7410604586820865893od_c_a @ C2 @ B ) ) ) ).

% UnE
thf(fact_1076_UnE,axiom,
    ! [C2: e,A2: set_e,B: set_e] :
      ( ( member_e @ C2 @ ( sup_sup_set_e @ A2 @ B ) )
     => ( ~ ( member_e @ C2 @ A2 )
       => ( member_e @ C2 @ B ) ) ) ).

% UnE
thf(fact_1077_UnE,axiom,
    ! [C2: b,A2: set_b,B: set_b] :
      ( ( member_b @ C2 @ ( sup_sup_set_b @ A2 @ B ) )
     => ( ~ ( member_b @ C2 @ A2 )
       => ( member_b @ C2 @ B ) ) ) ).

% UnE
thf(fact_1078_UnE,axiom,
    ! [C2: a,A2: set_a,B: set_a] :
      ( ( member_a @ C2 @ ( sup_sup_set_a @ A2 @ B ) )
     => ( ~ ( member_a @ C2 @ A2 )
       => ( member_a @ C2 @ B ) ) ) ).

% UnE
thf(fact_1079_Un__empty__right,axiom,
    ! [A2: set_b] :
      ( ( sup_sup_set_b @ A2 @ bot_bot_set_b )
      = A2 ) ).

% Un_empty_right
thf(fact_1080_Un__empty__right,axiom,
    ! [A2: set_Pr9130538228769002824od_d_d] :
      ( ( sup_su3647555221267236124od_d_d @ A2 @ bot_bo7612717905841165748od_d_d )
      = A2 ) ).

% Un_empty_right
thf(fact_1081_Un__empty__right,axiom,
    ! [A2: set_e] :
      ( ( sup_sup_set_e @ A2 @ bot_bot_set_e )
      = A2 ) ).

% Un_empty_right
thf(fact_1082_Un__empty__left,axiom,
    ! [B: set_b] :
      ( ( sup_sup_set_b @ bot_bot_set_b @ B )
      = B ) ).

% Un_empty_left
thf(fact_1083_Un__empty__left,axiom,
    ! [B: set_Pr9130538228769002824od_d_d] :
      ( ( sup_su3647555221267236124od_d_d @ bot_bo7612717905841165748od_d_d @ B )
      = B ) ).

% Un_empty_left
thf(fact_1084_Un__empty__left,axiom,
    ! [B: set_e] :
      ( ( sup_sup_set_e @ bot_bot_set_e @ B )
      = B ) ).

% Un_empty_left
thf(fact_1085_subset__Un__eq,axiom,
    ( ord_le282488521294790766od_b_c
    = ( ^ [A6: set_li6436108459499378894od_b_c,B3: set_li6436108459499378894od_b_c] :
          ( ( sup_su3823046536922626210od_b_c @ A6 @ B3 )
          = B3 ) ) ) ).

% subset_Un_eq
thf(fact_1086_subset__Un__eq,axiom,
    ( ord_less_eq_set_a
    = ( ^ [A6: set_a,B3: set_a] :
          ( ( sup_sup_set_a @ A6 @ B3 )
          = B3 ) ) ) ).

% subset_Un_eq
thf(fact_1087_subset__Un__eq,axiom,
    ( ord_le2998388488506175548od_c_a
    = ( ^ [A6: set_li1159382662694783132od_c_a,B3: set_li1159382662694783132od_c_a] :
          ( ( sup_su500200128730103920od_c_a @ A6 @ B3 )
          = B3 ) ) ) ).

% subset_Un_eq
thf(fact_1088_subset__UnE,axiom,
    ! [C3: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ C3 @ ( sup_su3823046536922626210od_b_c @ A2 @ B ) )
     => ~ ! [A7: set_li6436108459499378894od_b_c] :
            ( ( ord_le282488521294790766od_b_c @ A7 @ A2 )
           => ! [B8: set_li6436108459499378894od_b_c] :
                ( ( ord_le282488521294790766od_b_c @ B8 @ B )
               => ( C3
                 != ( sup_su3823046536922626210od_b_c @ A7 @ B8 ) ) ) ) ) ).

% subset_UnE
thf(fact_1089_subset__UnE,axiom,
    ! [C3: set_a,A2: set_a,B: set_a] :
      ( ( ord_less_eq_set_a @ C3 @ ( sup_sup_set_a @ A2 @ B ) )
     => ~ ! [A7: set_a] :
            ( ( ord_less_eq_set_a @ A7 @ A2 )
           => ! [B8: set_a] :
                ( ( ord_less_eq_set_a @ B8 @ B )
               => ( C3
                 != ( sup_sup_set_a @ A7 @ B8 ) ) ) ) ) ).

% subset_UnE
thf(fact_1090_subset__UnE,axiom,
    ! [C3: set_li1159382662694783132od_c_a,A2: set_li1159382662694783132od_c_a,B: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ C3 @ ( sup_su500200128730103920od_c_a @ A2 @ B ) )
     => ~ ! [A7: set_li1159382662694783132od_c_a] :
            ( ( ord_le2998388488506175548od_c_a @ A7 @ A2 )
           => ! [B8: set_li1159382662694783132od_c_a] :
                ( ( ord_le2998388488506175548od_c_a @ B8 @ B )
               => ( C3
                 != ( sup_su500200128730103920od_c_a @ A7 @ B8 ) ) ) ) ) ).

% subset_UnE
thf(fact_1091_Un__absorb2,axiom,
    ! [B: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ B @ A2 )
     => ( ( sup_su3823046536922626210od_b_c @ A2 @ B )
        = A2 ) ) ).

% Un_absorb2
thf(fact_1092_Un__absorb2,axiom,
    ! [B: set_a,A2: set_a] :
      ( ( ord_less_eq_set_a @ B @ A2 )
     => ( ( sup_sup_set_a @ A2 @ B )
        = A2 ) ) ).

% Un_absorb2
thf(fact_1093_Un__absorb2,axiom,
    ! [B: set_li1159382662694783132od_c_a,A2: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ B @ A2 )
     => ( ( sup_su500200128730103920od_c_a @ A2 @ B )
        = A2 ) ) ).

% Un_absorb2
thf(fact_1094_Un__absorb1,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A2 @ B )
     => ( ( sup_su3823046536922626210od_b_c @ A2 @ B )
        = B ) ) ).

% Un_absorb1
thf(fact_1095_Un__absorb1,axiom,
    ! [A2: set_a,B: set_a] :
      ( ( ord_less_eq_set_a @ A2 @ B )
     => ( ( sup_sup_set_a @ A2 @ B )
        = B ) ) ).

% Un_absorb1
thf(fact_1096_Un__absorb1,axiom,
    ! [A2: set_li1159382662694783132od_c_a,B: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ A2 @ B )
     => ( ( sup_su500200128730103920od_c_a @ A2 @ B )
        = B ) ) ).

% Un_absorb1
thf(fact_1097_Un__upper2,axiom,
    ! [B: set_li6436108459499378894od_b_c,A2: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ B @ ( sup_su3823046536922626210od_b_c @ A2 @ B ) ) ).

% Un_upper2
thf(fact_1098_Un__upper2,axiom,
    ! [B: set_a,A2: set_a] : ( ord_less_eq_set_a @ B @ ( sup_sup_set_a @ A2 @ B ) ) ).

% Un_upper2
thf(fact_1099_Un__upper2,axiom,
    ! [B: set_li1159382662694783132od_c_a,A2: set_li1159382662694783132od_c_a] : ( ord_le2998388488506175548od_c_a @ B @ ( sup_su500200128730103920od_c_a @ A2 @ B ) ) ).

% Un_upper2
thf(fact_1100_Un__upper1,axiom,
    ! [A2: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ A2 @ ( sup_su3823046536922626210od_b_c @ A2 @ B ) ) ).

% Un_upper1
thf(fact_1101_Un__upper1,axiom,
    ! [A2: set_a,B: set_a] : ( ord_less_eq_set_a @ A2 @ ( sup_sup_set_a @ A2 @ B ) ) ).

% Un_upper1
thf(fact_1102_Un__upper1,axiom,
    ! [A2: set_li1159382662694783132od_c_a,B: set_li1159382662694783132od_c_a] : ( ord_le2998388488506175548od_c_a @ A2 @ ( sup_su500200128730103920od_c_a @ A2 @ B ) ) ).

% Un_upper1
thf(fact_1103_Un__least,axiom,
    ! [A2: set_li6436108459499378894od_b_c,C3: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A2 @ C3 )
     => ( ( ord_le282488521294790766od_b_c @ B @ C3 )
       => ( ord_le282488521294790766od_b_c @ ( sup_su3823046536922626210od_b_c @ A2 @ B ) @ C3 ) ) ) ).

% Un_least
thf(fact_1104_Un__least,axiom,
    ! [A2: set_a,C3: set_a,B: set_a] :
      ( ( ord_less_eq_set_a @ A2 @ C3 )
     => ( ( ord_less_eq_set_a @ B @ C3 )
       => ( ord_less_eq_set_a @ ( sup_sup_set_a @ A2 @ B ) @ C3 ) ) ) ).

% Un_least
thf(fact_1105_Un__least,axiom,
    ! [A2: set_li1159382662694783132od_c_a,C3: set_li1159382662694783132od_c_a,B: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ A2 @ C3 )
     => ( ( ord_le2998388488506175548od_c_a @ B @ C3 )
       => ( ord_le2998388488506175548od_c_a @ ( sup_su500200128730103920od_c_a @ A2 @ B ) @ C3 ) ) ) ).

% Un_least
thf(fact_1106_Un__mono,axiom,
    ! [A2: set_li6436108459499378894od_b_c,C3: set_li6436108459499378894od_b_c,B: set_li6436108459499378894od_b_c,D2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A2 @ C3 )
     => ( ( ord_le282488521294790766od_b_c @ B @ D2 )
       => ( ord_le282488521294790766od_b_c @ ( sup_su3823046536922626210od_b_c @ A2 @ B ) @ ( sup_su3823046536922626210od_b_c @ C3 @ D2 ) ) ) ) ).

% Un_mono
thf(fact_1107_Un__mono,axiom,
    ! [A2: set_a,C3: set_a,B: set_a,D2: set_a] :
      ( ( ord_less_eq_set_a @ A2 @ C3 )
     => ( ( ord_less_eq_set_a @ B @ D2 )
       => ( ord_less_eq_set_a @ ( sup_sup_set_a @ A2 @ B ) @ ( sup_sup_set_a @ C3 @ D2 ) ) ) ) ).

% Un_mono
thf(fact_1108_Un__mono,axiom,
    ! [A2: set_li1159382662694783132od_c_a,C3: set_li1159382662694783132od_c_a,B: set_li1159382662694783132od_c_a,D2: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ A2 @ C3 )
     => ( ( ord_le2998388488506175548od_c_a @ B @ D2 )
       => ( ord_le2998388488506175548od_c_a @ ( sup_su500200128730103920od_c_a @ A2 @ B ) @ ( sup_su500200128730103920od_c_a @ C3 @ D2 ) ) ) ) ).

% Un_mono
thf(fact_1109_separator__initial_I2_J,axiom,
    ! [M: fsm_a_b_c,Q14: a,Q22: a,A2: fsm_d_b_c,T1: d,T22: d] :
      ( ( state_8910485216943051357_b_c_d @ M @ Q14 @ Q22 @ A2 @ T1 @ T22 )
     => ( ( initial_d_b_c @ A2 )
       != T22 ) ) ).

% separator_initial(2)
thf(fact_1110_separator__initial_I1_J,axiom,
    ! [M: fsm_a_b_c,Q14: a,Q22: a,A2: fsm_d_b_c,T1: d,T22: d] :
      ( ( state_8910485216943051357_b_c_d @ M @ Q14 @ Q22 @ A2 @ T1 @ T22 )
     => ( ( initial_d_b_c @ A2 )
       != T1 ) ) ).

% separator_initial(1)
thf(fact_1111_is__separator__separated__state__is__state_I2_J,axiom,
    ! [M: fsm_a_b_c,Q14: a,Q22: a,A2: fsm_d_b_c,T1: d,T22: d] :
      ( ( state_8910485216943051357_b_c_d @ M @ Q14 @ Q22 @ A2 @ T1 @ T22 )
     => ( member_a @ Q22 @ ( states_a_b_c @ M ) ) ) ).

% is_separator_separated_state_is_state(2)
thf(fact_1112_is__separator__separated__state__is__state_I1_J,axiom,
    ! [M: fsm_a_b_c,Q14: a,Q22: a,A2: fsm_d_b_c,T1: d,T22: d] :
      ( ( state_8910485216943051357_b_c_d @ M @ Q14 @ Q22 @ A2 @ T1 @ T22 )
     => ( member_a @ Q14 @ ( states_a_b_c @ M ) ) ) ).

% is_separator_separated_state_is_state(1)
thf(fact_1113_is__separator__simps_I3_J,axiom,
    ! [M: fsm_a_b_c,Q14: a,Q22: a,A2: fsm_d_b_c,T1: d,T22: d] :
      ( ( state_8910485216943051357_b_c_d @ M @ Q14 @ Q22 @ A2 @ T1 @ T22 )
     => ( observable_d_b_c @ A2 ) ) ).

% is_separator_simps(3)
thf(fact_1114_is__separator__simps_I1_J,axiom,
    ! [M: fsm_a_b_c,Q14: a,Q22: a,A2: fsm_d_b_c,T1: d,T22: d] :
      ( ( state_8910485216943051357_b_c_d @ M @ Q14 @ Q22 @ A2 @ T1 @ T22 )
     => ( single_input_d_b_c @ A2 ) ) ).

% is_separator_simps(1)
thf(fact_1115_insert__def,axiom,
    ( insert_e
    = ( ^ [A3: e] :
          ( sup_sup_set_e
          @ ( collect_e
            @ ^ [X2: e] : ( X2 = A3 ) ) ) ) ) ).

% insert_def
thf(fact_1116_insert__def,axiom,
    ( insert4789241225314331020od_c_a
    = ( ^ [A3: list_P6327159017948738492od_c_a] :
          ( sup_su500200128730103920od_c_a
          @ ( collec6273869032445462695od_c_a
            @ ^ [X2: list_P6327159017948738492od_c_a] : ( X2 = A3 ) ) ) ) ) ).

% insert_def
thf(fact_1117_insert__is__Un,axiom,
    ( insert4789241225314331020od_c_a
    = ( ^ [A3: list_P6327159017948738492od_c_a] : ( sup_su500200128730103920od_c_a @ ( insert4789241225314331020od_c_a @ A3 @ bot_bo6236370880139903240od_c_a ) ) ) ) ).

% insert_is_Un
thf(fact_1118_insert__is__Un,axiom,
    ( insert_b
    = ( ^ [A3: b] : ( sup_sup_set_b @ ( insert_b @ A3 @ bot_bot_set_b ) ) ) ) ).

% insert_is_Un
thf(fact_1119_insert__is__Un,axiom,
    ( insert4898623881593564728od_d_d
    = ( ^ [A3: produc4859908366599477352od_d_d] : ( sup_su3647555221267236124od_d_d @ ( insert4898623881593564728od_d_d @ A3 @ bot_bo7612717905841165748od_d_d ) ) ) ) ).

% insert_is_Un
thf(fact_1120_insert__is__Un,axiom,
    ( insert_e
    = ( ^ [A3: e] : ( sup_sup_set_e @ ( insert_e @ A3 @ bot_bot_set_e ) ) ) ) ).

% insert_is_Un
thf(fact_1121_Un__singleton__iff,axiom,
    ! [A2: set_li1159382662694783132od_c_a,B: set_li1159382662694783132od_c_a,X: list_P6327159017948738492od_c_a] :
      ( ( ( sup_su500200128730103920od_c_a @ A2 @ B )
        = ( insert4789241225314331020od_c_a @ X @ bot_bo6236370880139903240od_c_a ) )
      = ( ( ( A2 = bot_bo6236370880139903240od_c_a )
          & ( B
            = ( insert4789241225314331020od_c_a @ X @ bot_bo6236370880139903240od_c_a ) ) )
        | ( ( A2
            = ( insert4789241225314331020od_c_a @ X @ bot_bo6236370880139903240od_c_a ) )
          & ( B = bot_bo6236370880139903240od_c_a ) )
        | ( ( A2
            = ( insert4789241225314331020od_c_a @ X @ bot_bo6236370880139903240od_c_a ) )
          & ( B
            = ( insert4789241225314331020od_c_a @ X @ bot_bo6236370880139903240od_c_a ) ) ) ) ) ).

% Un_singleton_iff
thf(fact_1122_Un__singleton__iff,axiom,
    ! [A2: set_b,B: set_b,X: b] :
      ( ( ( sup_sup_set_b @ A2 @ B )
        = ( insert_b @ X @ bot_bot_set_b ) )
      = ( ( ( A2 = bot_bot_set_b )
          & ( B
            = ( insert_b @ X @ bot_bot_set_b ) ) )
        | ( ( A2
            = ( insert_b @ X @ bot_bot_set_b ) )
          & ( B = bot_bot_set_b ) )
        | ( ( A2
            = ( insert_b @ X @ bot_bot_set_b ) )
          & ( B
            = ( insert_b @ X @ bot_bot_set_b ) ) ) ) ) ).

% Un_singleton_iff
thf(fact_1123_Un__singleton__iff,axiom,
    ! [A2: set_Pr9130538228769002824od_d_d,B: set_Pr9130538228769002824od_d_d,X: produc4859908366599477352od_d_d] :
      ( ( ( sup_su3647555221267236124od_d_d @ A2 @ B )
        = ( insert4898623881593564728od_d_d @ X @ bot_bo7612717905841165748od_d_d ) )
      = ( ( ( A2 = bot_bo7612717905841165748od_d_d )
          & ( B
            = ( insert4898623881593564728od_d_d @ X @ bot_bo7612717905841165748od_d_d ) ) )
        | ( ( A2
            = ( insert4898623881593564728od_d_d @ X @ bot_bo7612717905841165748od_d_d ) )
          & ( B = bot_bo7612717905841165748od_d_d ) )
        | ( ( A2
            = ( insert4898623881593564728od_d_d @ X @ bot_bo7612717905841165748od_d_d ) )
          & ( B
            = ( insert4898623881593564728od_d_d @ X @ bot_bo7612717905841165748od_d_d ) ) ) ) ) ).

% Un_singleton_iff
thf(fact_1124_Un__singleton__iff,axiom,
    ! [A2: set_e,B: set_e,X: e] :
      ( ( ( sup_sup_set_e @ A2 @ B )
        = ( insert_e @ X @ bot_bot_set_e ) )
      = ( ( ( A2 = bot_bot_set_e )
          & ( B
            = ( insert_e @ X @ bot_bot_set_e ) ) )
        | ( ( A2
            = ( insert_e @ X @ bot_bot_set_e ) )
          & ( B = bot_bot_set_e ) )
        | ( ( A2
            = ( insert_e @ X @ bot_bot_set_e ) )
          & ( B
            = ( insert_e @ X @ bot_bot_set_e ) ) ) ) ) ).

% Un_singleton_iff
thf(fact_1125_singleton__Un__iff,axiom,
    ! [X: list_P6327159017948738492od_c_a,A2: set_li1159382662694783132od_c_a,B: set_li1159382662694783132od_c_a] :
      ( ( ( insert4789241225314331020od_c_a @ X @ bot_bo6236370880139903240od_c_a )
        = ( sup_su500200128730103920od_c_a @ A2 @ B ) )
      = ( ( ( A2 = bot_bo6236370880139903240od_c_a )
          & ( B
            = ( insert4789241225314331020od_c_a @ X @ bot_bo6236370880139903240od_c_a ) ) )
        | ( ( A2
            = ( insert4789241225314331020od_c_a @ X @ bot_bo6236370880139903240od_c_a ) )
          & ( B = bot_bo6236370880139903240od_c_a ) )
        | ( ( A2
            = ( insert4789241225314331020od_c_a @ X @ bot_bo6236370880139903240od_c_a ) )
          & ( B
            = ( insert4789241225314331020od_c_a @ X @ bot_bo6236370880139903240od_c_a ) ) ) ) ) ).

% singleton_Un_iff
thf(fact_1126_singleton__Un__iff,axiom,
    ! [X: b,A2: set_b,B: set_b] :
      ( ( ( insert_b @ X @ bot_bot_set_b )
        = ( sup_sup_set_b @ A2 @ B ) )
      = ( ( ( A2 = bot_bot_set_b )
          & ( B
            = ( insert_b @ X @ bot_bot_set_b ) ) )
        | ( ( A2
            = ( insert_b @ X @ bot_bot_set_b ) )
          & ( B = bot_bot_set_b ) )
        | ( ( A2
            = ( insert_b @ X @ bot_bot_set_b ) )
          & ( B
            = ( insert_b @ X @ bot_bot_set_b ) ) ) ) ) ).

% singleton_Un_iff
thf(fact_1127_singleton__Un__iff,axiom,
    ! [X: produc4859908366599477352od_d_d,A2: set_Pr9130538228769002824od_d_d,B: set_Pr9130538228769002824od_d_d] :
      ( ( ( insert4898623881593564728od_d_d @ X @ bot_bo7612717905841165748od_d_d )
        = ( sup_su3647555221267236124od_d_d @ A2 @ B ) )
      = ( ( ( A2 = bot_bo7612717905841165748od_d_d )
          & ( B
            = ( insert4898623881593564728od_d_d @ X @ bot_bo7612717905841165748od_d_d ) ) )
        | ( ( A2
            = ( insert4898623881593564728od_d_d @ X @ bot_bo7612717905841165748od_d_d ) )
          & ( B = bot_bo7612717905841165748od_d_d ) )
        | ( ( A2
            = ( insert4898623881593564728od_d_d @ X @ bot_bo7612717905841165748od_d_d ) )
          & ( B
            = ( insert4898623881593564728od_d_d @ X @ bot_bo7612717905841165748od_d_d ) ) ) ) ) ).

% singleton_Un_iff
thf(fact_1128_singleton__Un__iff,axiom,
    ! [X: e,A2: set_e,B: set_e] :
      ( ( ( insert_e @ X @ bot_bot_set_e )
        = ( sup_sup_set_e @ A2 @ B ) )
      = ( ( ( A2 = bot_bot_set_e )
          & ( B
            = ( insert_e @ X @ bot_bot_set_e ) ) )
        | ( ( A2
            = ( insert_e @ X @ bot_bot_set_e ) )
          & ( B = bot_bot_set_e ) )
        | ( ( A2
            = ( insert_e @ X @ bot_bot_set_e ) )
          & ( B
            = ( insert_e @ X @ bot_bot_set_e ) ) ) ) ) ).

% singleton_Un_iff
thf(fact_1129_is__separator__simps_I16_J,axiom,
    ! [M: fsm_e_b_c,Q14: e,Q22: e,A2: fsm_e_b_c,T1: e,T22: e] :
      ( ( state_5638961329267469658_b_c_e @ M @ Q14 @ Q22 @ A2 @ T1 @ T22 )
     => ( ord_less_eq_set_b @ ( inputs_e_b_c @ A2 ) @ ( inputs_e_b_c @ M ) ) ) ).

% is_separator_simps(16)
thf(fact_1130_is__separator__simps_I16_J,axiom,
    ! [M: fsm_a_b_c,Q14: a,Q22: a,A2: fsm_e_b_c,T1: e,T22: e] :
      ( ( state_8910485216943051358_b_c_e @ M @ Q14 @ Q22 @ A2 @ T1 @ T22 )
     => ( ord_less_eq_set_b @ ( inputs_e_b_c @ A2 ) @ ( inputs_a_b_c @ M ) ) ) ).

% is_separator_simps(16)
thf(fact_1131_is__separator__simps_I16_J,axiom,
    ! [M: fsm_e_b_c,Q14: e,Q22: e,A2: fsm_a_b_c,T1: a,T22: a] :
      ( ( state_5638961329267469654_b_c_a @ M @ Q14 @ Q22 @ A2 @ T1 @ T22 )
     => ( ord_less_eq_set_b @ ( inputs_a_b_c @ A2 ) @ ( inputs_e_b_c @ M ) ) ) ).

% is_separator_simps(16)
thf(fact_1132_is__separator__simps_I16_J,axiom,
    ! [M: fsm_a_b_c,Q14: a,Q22: a,A2: fsm_a_b_c,T1: a,T22: a] :
      ( ( state_8910485216943051354_b_c_a @ M @ Q14 @ Q22 @ A2 @ T1 @ T22 )
     => ( ord_less_eq_set_b @ ( inputs_a_b_c @ A2 ) @ ( inputs_a_b_c @ M ) ) ) ).

% is_separator_simps(16)
thf(fact_1133_is__separator__simps_I16_J,axiom,
    ! [M: fsm_a_b_c,Q14: a,Q22: a,A2: fsm_d_b_c,T1: d,T22: d] :
      ( ( state_8910485216943051357_b_c_d @ M @ Q14 @ Q22 @ A2 @ T1 @ T22 )
     => ( ord_less_eq_set_b @ ( inputs_d_b_c @ A2 ) @ ( inputs_a_b_c @ M ) ) ) ).

% is_separator_simps(16)
thf(fact_1134_filter__states__submachine,axiom,
    ! [P2: a > $o,M: fsm_a_b_c] :
      ( ( P2 @ ( initial_a_b_c @ M ) )
     => ( is_submachine_a_b_c @ ( filter_states_a_b_c @ M @ P2 ) @ M ) ) ).

% filter_states_submachine
thf(fact_1135_filter__states__submachine,axiom,
    ! [P2: e > $o,M: fsm_e_b_c] :
      ( ( P2 @ ( initial_e_b_c @ M ) )
     => ( is_submachine_e_b_c @ ( filter_states_e_b_c @ M @ P2 ) @ M ) ) ).

% filter_states_submachine
thf(fact_1136_sup__bot_Oright__neutral,axiom,
    ! [A: set_b] :
      ( ( sup_sup_set_b @ A @ bot_bot_set_b )
      = A ) ).

% sup_bot.right_neutral
thf(fact_1137_sup__bot_Oright__neutral,axiom,
    ! [A: set_Pr9130538228769002824od_d_d] :
      ( ( sup_su3647555221267236124od_d_d @ A @ bot_bo7612717905841165748od_d_d )
      = A ) ).

% sup_bot.right_neutral
thf(fact_1138_sup__bot_Oright__neutral,axiom,
    ! [A: set_e] :
      ( ( sup_sup_set_e @ A @ bot_bot_set_e )
      = A ) ).

% sup_bot.right_neutral
thf(fact_1139_sup__bot_Oneutr__eq__iff,axiom,
    ! [A: set_b,B2: set_b] :
      ( ( bot_bot_set_b
        = ( sup_sup_set_b @ A @ B2 ) )
      = ( ( A = bot_bot_set_b )
        & ( B2 = bot_bot_set_b ) ) ) ).

% sup_bot.neutr_eq_iff
thf(fact_1140_sup__bot_Oneutr__eq__iff,axiom,
    ! [A: set_Pr9130538228769002824od_d_d,B2: set_Pr9130538228769002824od_d_d] :
      ( ( bot_bo7612717905841165748od_d_d
        = ( sup_su3647555221267236124od_d_d @ A @ B2 ) )
      = ( ( A = bot_bo7612717905841165748od_d_d )
        & ( B2 = bot_bo7612717905841165748od_d_d ) ) ) ).

% sup_bot.neutr_eq_iff
thf(fact_1141_sup__bot_Oneutr__eq__iff,axiom,
    ! [A: set_e,B2: set_e] :
      ( ( bot_bot_set_e
        = ( sup_sup_set_e @ A @ B2 ) )
      = ( ( A = bot_bot_set_e )
        & ( B2 = bot_bot_set_e ) ) ) ).

% sup_bot.neutr_eq_iff
thf(fact_1142_sup__bot_Oleft__neutral,axiom,
    ! [A: set_b] :
      ( ( sup_sup_set_b @ bot_bot_set_b @ A )
      = A ) ).

% sup_bot.left_neutral
thf(fact_1143_sup__bot_Oleft__neutral,axiom,
    ! [A: set_Pr9130538228769002824od_d_d] :
      ( ( sup_su3647555221267236124od_d_d @ bot_bo7612717905841165748od_d_d @ A )
      = A ) ).

% sup_bot.left_neutral
thf(fact_1144_sup__bot_Oleft__neutral,axiom,
    ! [A: set_e] :
      ( ( sup_sup_set_e @ bot_bot_set_e @ A )
      = A ) ).

% sup_bot.left_neutral
thf(fact_1145_sup__bot_Oeq__neutr__iff,axiom,
    ! [A: set_b,B2: set_b] :
      ( ( ( sup_sup_set_b @ A @ B2 )
        = bot_bot_set_b )
      = ( ( A = bot_bot_set_b )
        & ( B2 = bot_bot_set_b ) ) ) ).

% sup_bot.eq_neutr_iff
thf(fact_1146_sup__bot_Oeq__neutr__iff,axiom,
    ! [A: set_Pr9130538228769002824od_d_d,B2: set_Pr9130538228769002824od_d_d] :
      ( ( ( sup_su3647555221267236124od_d_d @ A @ B2 )
        = bot_bo7612717905841165748od_d_d )
      = ( ( A = bot_bo7612717905841165748od_d_d )
        & ( B2 = bot_bo7612717905841165748od_d_d ) ) ) ).

% sup_bot.eq_neutr_iff
thf(fact_1147_sup__bot_Oeq__neutr__iff,axiom,
    ! [A: set_e,B2: set_e] :
      ( ( ( sup_sup_set_e @ A @ B2 )
        = bot_bot_set_e )
      = ( ( A = bot_bot_set_e )
        & ( B2 = bot_bot_set_e ) ) ) ).

% sup_bot.eq_neutr_iff
thf(fact_1148_sup__eq__bot__iff,axiom,
    ! [X: set_b,Y: set_b] :
      ( ( ( sup_sup_set_b @ X @ Y )
        = bot_bot_set_b )
      = ( ( X = bot_bot_set_b )
        & ( Y = bot_bot_set_b ) ) ) ).

% sup_eq_bot_iff
thf(fact_1149_sup__eq__bot__iff,axiom,
    ! [X: set_Pr9130538228769002824od_d_d,Y: set_Pr9130538228769002824od_d_d] :
      ( ( ( sup_su3647555221267236124od_d_d @ X @ Y )
        = bot_bo7612717905841165748od_d_d )
      = ( ( X = bot_bo7612717905841165748od_d_d )
        & ( Y = bot_bo7612717905841165748od_d_d ) ) ) ).

% sup_eq_bot_iff
thf(fact_1150_sup__eq__bot__iff,axiom,
    ! [X: set_e,Y: set_e] :
      ( ( ( sup_sup_set_e @ X @ Y )
        = bot_bot_set_e )
      = ( ( X = bot_bot_set_e )
        & ( Y = bot_bot_set_e ) ) ) ).

% sup_eq_bot_iff
thf(fact_1151_bot__eq__sup__iff,axiom,
    ! [X: set_b,Y: set_b] :
      ( ( bot_bot_set_b
        = ( sup_sup_set_b @ X @ Y ) )
      = ( ( X = bot_bot_set_b )
        & ( Y = bot_bot_set_b ) ) ) ).

% bot_eq_sup_iff
thf(fact_1152_bot__eq__sup__iff,axiom,
    ! [X: set_Pr9130538228769002824od_d_d,Y: set_Pr9130538228769002824od_d_d] :
      ( ( bot_bo7612717905841165748od_d_d
        = ( sup_su3647555221267236124od_d_d @ X @ Y ) )
      = ( ( X = bot_bo7612717905841165748od_d_d )
        & ( Y = bot_bo7612717905841165748od_d_d ) ) ) ).

% bot_eq_sup_iff
thf(fact_1153_bot__eq__sup__iff,axiom,
    ! [X: set_e,Y: set_e] :
      ( ( bot_bot_set_e
        = ( sup_sup_set_e @ X @ Y ) )
      = ( ( X = bot_bot_set_e )
        & ( Y = bot_bot_set_e ) ) ) ).

% bot_eq_sup_iff
thf(fact_1154_le__sup__iff,axiom,
    ! [X: nat,Y: nat,Z2: nat] :
      ( ( ord_less_eq_nat @ ( sup_sup_nat @ X @ Y ) @ Z2 )
      = ( ( ord_less_eq_nat @ X @ Z2 )
        & ( ord_less_eq_nat @ Y @ Z2 ) ) ) ).

% le_sup_iff
thf(fact_1155_le__sup__iff,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c,Z2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ ( sup_su3823046536922626210od_b_c @ X @ Y ) @ Z2 )
      = ( ( ord_le282488521294790766od_b_c @ X @ Z2 )
        & ( ord_le282488521294790766od_b_c @ Y @ Z2 ) ) ) ).

% le_sup_iff
thf(fact_1156_le__sup__iff,axiom,
    ! [X: set_a,Y: set_a,Z2: set_a] :
      ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ X @ Y ) @ Z2 )
      = ( ( ord_less_eq_set_a @ X @ Z2 )
        & ( ord_less_eq_set_a @ Y @ Z2 ) ) ) ).

% le_sup_iff
thf(fact_1157_le__sup__iff,axiom,
    ! [X: set_li1159382662694783132od_c_a,Y: set_li1159382662694783132od_c_a,Z2: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ ( sup_su500200128730103920od_c_a @ X @ Y ) @ Z2 )
      = ( ( ord_le2998388488506175548od_c_a @ X @ Z2 )
        & ( ord_le2998388488506175548od_c_a @ Y @ Z2 ) ) ) ).

% le_sup_iff
thf(fact_1158_sup_Obounded__iff,axiom,
    ! [B2: nat,C2: nat,A: nat] :
      ( ( ord_less_eq_nat @ ( sup_sup_nat @ B2 @ C2 ) @ A )
      = ( ( ord_less_eq_nat @ B2 @ A )
        & ( ord_less_eq_nat @ C2 @ A ) ) ) ).

% sup.bounded_iff
thf(fact_1159_sup_Obounded__iff,axiom,
    ! [B2: set_li6436108459499378894od_b_c,C2: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ ( sup_su3823046536922626210od_b_c @ B2 @ C2 ) @ A )
      = ( ( ord_le282488521294790766od_b_c @ B2 @ A )
        & ( ord_le282488521294790766od_b_c @ C2 @ A ) ) ) ).

% sup.bounded_iff
thf(fact_1160_sup_Obounded__iff,axiom,
    ! [B2: set_a,C2: set_a,A: set_a] :
      ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ B2 @ C2 ) @ A )
      = ( ( ord_less_eq_set_a @ B2 @ A )
        & ( ord_less_eq_set_a @ C2 @ A ) ) ) ).

% sup.bounded_iff
thf(fact_1161_sup_Obounded__iff,axiom,
    ! [B2: set_li1159382662694783132od_c_a,C2: set_li1159382662694783132od_c_a,A: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ ( sup_su500200128730103920od_c_a @ B2 @ C2 ) @ A )
      = ( ( ord_le2998388488506175548od_c_a @ B2 @ A )
        & ( ord_le2998388488506175548od_c_a @ C2 @ A ) ) ) ).

% sup.bounded_iff
thf(fact_1162_sup__bot__left,axiom,
    ! [X: set_b] :
      ( ( sup_sup_set_b @ bot_bot_set_b @ X )
      = X ) ).

% sup_bot_left
thf(fact_1163_sup__bot__left,axiom,
    ! [X: set_Pr9130538228769002824od_d_d] :
      ( ( sup_su3647555221267236124od_d_d @ bot_bo7612717905841165748od_d_d @ X )
      = X ) ).

% sup_bot_left
thf(fact_1164_sup__bot__left,axiom,
    ! [X: set_e] :
      ( ( sup_sup_set_e @ bot_bot_set_e @ X )
      = X ) ).

% sup_bot_left
thf(fact_1165_sup__bot__right,axiom,
    ! [X: set_b] :
      ( ( sup_sup_set_b @ X @ bot_bot_set_b )
      = X ) ).

% sup_bot_right
thf(fact_1166_sup__bot__right,axiom,
    ! [X: set_Pr9130538228769002824od_d_d] :
      ( ( sup_su3647555221267236124od_d_d @ X @ bot_bo7612717905841165748od_d_d )
      = X ) ).

% sup_bot_right
thf(fact_1167_sup__bot__right,axiom,
    ! [X: set_e] :
      ( ( sup_sup_set_e @ X @ bot_bot_set_e )
      = X ) ).

% sup_bot_right
thf(fact_1168_sup__Un__eq,axiom,
    ! [R2: set_li6436108459499378894od_b_c,S3: set_li6436108459499378894od_b_c] :
      ( ( sup_su1384278580622331579_b_c_o
        @ ^ [X2: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ X2 @ R2 )
        @ ^ [X2: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ X2 @ S3 ) )
      = ( ^ [X2: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ X2 @ ( sup_su3823046536922626210od_b_c @ R2 @ S3 ) ) ) ) ).

% sup_Un_eq
thf(fact_1169_sup__Un__eq,axiom,
    ! [R2: set_li1159382662694783132od_c_a,S3: set_li1159382662694783132od_c_a] :
      ( ( sup_su8395262273515319405_c_a_o
        @ ^ [X2: list_P6327159017948738492od_c_a] : ( member7410604586820865893od_c_a @ X2 @ R2 )
        @ ^ [X2: list_P6327159017948738492od_c_a] : ( member7410604586820865893od_c_a @ X2 @ S3 ) )
      = ( ^ [X2: list_P6327159017948738492od_c_a] : ( member7410604586820865893od_c_a @ X2 @ ( sup_su500200128730103920od_c_a @ R2 @ S3 ) ) ) ) ).

% sup_Un_eq
thf(fact_1170_sup__Un__eq,axiom,
    ! [R2: set_e,S3: set_e] :
      ( ( sup_sup_e_o
        @ ^ [X2: e] : ( member_e @ X2 @ R2 )
        @ ^ [X2: e] : ( member_e @ X2 @ S3 ) )
      = ( ^ [X2: e] : ( member_e @ X2 @ ( sup_sup_set_e @ R2 @ S3 ) ) ) ) ).

% sup_Un_eq
thf(fact_1171_sup__Un__eq,axiom,
    ! [R2: set_b,S3: set_b] :
      ( ( sup_sup_b_o
        @ ^ [X2: b] : ( member_b @ X2 @ R2 )
        @ ^ [X2: b] : ( member_b @ X2 @ S3 ) )
      = ( ^ [X2: b] : ( member_b @ X2 @ ( sup_sup_set_b @ R2 @ S3 ) ) ) ) ).

% sup_Un_eq
thf(fact_1172_sup__Un__eq,axiom,
    ! [R2: set_a,S3: set_a] :
      ( ( sup_sup_a_o
        @ ^ [X2: a] : ( member_a @ X2 @ R2 )
        @ ^ [X2: a] : ( member_a @ X2 @ S3 ) )
      = ( ^ [X2: a] : ( member_a @ X2 @ ( sup_sup_set_a @ R2 @ S3 ) ) ) ) ).

% sup_Un_eq
thf(fact_1173_sup__set__def,axiom,
    ( sup_su3823046536922626210od_b_c
    = ( ^ [A6: set_li6436108459499378894od_b_c,B3: set_li6436108459499378894od_b_c] :
          ( collec2280997390073109977od_b_c
          @ ( sup_su1384278580622331579_b_c_o
            @ ^ [X2: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ X2 @ A6 )
            @ ^ [X2: list_P903359562653991662od_b_c] : ( member6330420149250801815od_b_c @ X2 @ B3 ) ) ) ) ) ).

% sup_set_def
thf(fact_1174_sup__set__def,axiom,
    ( sup_sup_set_e
    = ( ^ [A6: set_e,B3: set_e] :
          ( collect_e
          @ ( sup_sup_e_o
            @ ^ [X2: e] : ( member_e @ X2 @ A6 )
            @ ^ [X2: e] : ( member_e @ X2 @ B3 ) ) ) ) ) ).

% sup_set_def
thf(fact_1175_sup__set__def,axiom,
    ( sup_sup_set_b
    = ( ^ [A6: set_b,B3: set_b] :
          ( collect_b
          @ ( sup_sup_b_o
            @ ^ [X2: b] : ( member_b @ X2 @ A6 )
            @ ^ [X2: b] : ( member_b @ X2 @ B3 ) ) ) ) ) ).

% sup_set_def
thf(fact_1176_sup__set__def,axiom,
    ( sup_sup_set_a
    = ( ^ [A6: set_a,B3: set_a] :
          ( collect_a
          @ ( sup_sup_a_o
            @ ^ [X2: a] : ( member_a @ X2 @ A6 )
            @ ^ [X2: a] : ( member_a @ X2 @ B3 ) ) ) ) ) ).

% sup_set_def
thf(fact_1177_sup__set__def,axiom,
    ( sup_su500200128730103920od_c_a
    = ( ^ [A6: set_li1159382662694783132od_c_a,B3: set_li1159382662694783132od_c_a] :
          ( collec6273869032445462695od_c_a
          @ ( sup_su8395262273515319405_c_a_o
            @ ^ [X2: list_P6327159017948738492od_c_a] : ( member7410604586820865893od_c_a @ X2 @ A6 )
            @ ^ [X2: list_P6327159017948738492od_c_a] : ( member7410604586820865893od_c_a @ X2 @ B3 ) ) ) ) ) ).

% sup_set_def
thf(fact_1178_sup__Un__eq2,axiom,
    ! [R2: set_Product_prod_d_d,S3: set_Product_prod_d_d] :
      ( ( sup_sup_d_d_o
        @ ^ [X2: d,Y2: d] : ( member2287536781371869328od_d_d @ ( product_Pair_d_d @ X2 @ Y2 ) @ R2 )
        @ ^ [X2: d,Y2: d] : ( member2287536781371869328od_d_d @ ( product_Pair_d_d @ X2 @ Y2 ) @ S3 ) )
      = ( ^ [X2: d,Y2: d] : ( member2287536781371869328od_d_d @ ( product_Pair_d_d @ X2 @ Y2 ) @ ( sup_su1354413899923735579od_d_d @ R2 @ S3 ) ) ) ) ).

% sup_Un_eq2
thf(fact_1179_sup__Un__eq2,axiom,
    ! [R2: set_Product_prod_b_c,S3: set_Product_prod_b_c] :
      ( ( sup_sup_b_c_o
        @ ^ [X2: b,Y2: c] : ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ R2 )
        @ ^ [X2: b,Y2: c] : ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ S3 ) )
      = ( ^ [X2: b,Y2: c] : ( member7862447941013992593od_b_c @ ( product_Pair_b_c @ X2 @ Y2 ) @ ( sup_su2554677861087362972od_b_c @ R2 @ S3 ) ) ) ) ).

% sup_Un_eq2
thf(fact_1180_sup__Un__eq2,axiom,
    ! [R2: set_Pr5230154892316275013od_c_a,S3: set_Pr5230154892316275013od_c_a] :
      ( ( sup_su555677013020292228_c_a_o
        @ ^ [X2: a,Y2: list_P6327159017948738492od_c_a] : ( member3484049051949443214od_c_a @ ( produc3580641852002036821od_c_a @ X2 @ Y2 ) @ R2 )
        @ ^ [X2: a,Y2: list_P6327159017948738492od_c_a] : ( member3484049051949443214od_c_a @ ( produc3580641852002036821od_c_a @ X2 @ Y2 ) @ S3 ) )
      = ( ^ [X2: a,Y2: list_P6327159017948738492od_c_a] : ( member3484049051949443214od_c_a @ ( produc3580641852002036821od_c_a @ X2 @ Y2 ) @ ( sup_su5122447508292908313od_c_a @ R2 @ S3 ) ) ) ) ).

% sup_Un_eq2
thf(fact_1181_sup__Un__eq2,axiom,
    ! [R2: set_Pr2640454425625433516_a_b_c,S3: set_Pr2640454425625433516_a_b_c] :
      ( ( sup_su2825556494838030557_b_c_o
        @ ^ [X2: a,Y2: fsm_a_b_c] : ( member997585926662434933_a_b_c @ ( produc2795441082327197628_a_b_c @ X2 @ Y2 ) @ R2 )
        @ ^ [X2: a,Y2: fsm_a_b_c] : ( member997585926662434933_a_b_c @ ( produc2795441082327197628_a_b_c @ X2 @ Y2 ) @ S3 ) )
      = ( ^ [X2: a,Y2: fsm_a_b_c] : ( member997585926662434933_a_b_c @ ( produc2795441082327197628_a_b_c @ X2 @ Y2 ) @ ( sup_su7650654951151286656_a_b_c @ R2 @ S3 ) ) ) ) ).

% sup_Un_eq2
thf(fact_1182_sup__Un__eq2,axiom,
    ! [R2: set_Product_prod_a_a,S3: set_Product_prod_a_a] :
      ( ( sup_sup_a_a_o
        @ ^ [X2: a,Y2: a] : ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X2 @ Y2 ) @ R2 )
        @ ^ [X2: a,Y2: a] : ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X2 @ Y2 ) @ S3 ) )
      = ( ^ [X2: a,Y2: a] : ( member1426531477525435216od_a_a @ ( product_Pair_a_a @ X2 @ Y2 ) @ ( sup_su3048258781599657691od_a_a @ R2 @ S3 ) ) ) ) ).

% sup_Un_eq2
thf(fact_1183_separator__language_I4_J,axiom,
    ! [M: fsm_e_b_c,Q14: e,Q22: e,A2: fsm_a_b_c,T1: a,T22: a,Io5: list_P903359562653991662od_b_c] :
      ( ( state_5638961329267469654_b_c_a @ M @ Q14 @ Q22 @ A2 @ T1 @ T22 )
     => ( ( member6330420149250801815od_b_c @ Io5 @ ( lS_a_b_c @ A2 @ ( initial_a_b_c @ A2 ) ) )
       => ( member6330420149250801815od_b_c @ Io5 @ ( sup_su3823046536922626210od_b_c @ ( lS_e_b_c @ M @ Q14 ) @ ( lS_e_b_c @ M @ Q22 ) ) ) ) ) ).

% separator_language(4)
thf(fact_1184_separator__language_I4_J,axiom,
    ! [M: fsm_a_b_c,Q14: a,Q22: a,A2: fsm_a_b_c,T1: a,T22: a,Io5: list_P903359562653991662od_b_c] :
      ( ( state_8910485216943051354_b_c_a @ M @ Q14 @ Q22 @ A2 @ T1 @ T22 )
     => ( ( member6330420149250801815od_b_c @ Io5 @ ( lS_a_b_c @ A2 @ ( initial_a_b_c @ A2 ) ) )
       => ( member6330420149250801815od_b_c @ Io5 @ ( sup_su3823046536922626210od_b_c @ ( lS_a_b_c @ M @ Q14 ) @ ( lS_a_b_c @ M @ Q22 ) ) ) ) ) ).

% separator_language(4)
thf(fact_1185_separator__language_I4_J,axiom,
    ! [M: fsm_e_b_c,Q14: e,Q22: e,A2: fsm_e_b_c,T1: e,T22: e,Io5: list_P903359562653991662od_b_c] :
      ( ( state_5638961329267469658_b_c_e @ M @ Q14 @ Q22 @ A2 @ T1 @ T22 )
     => ( ( member6330420149250801815od_b_c @ Io5 @ ( lS_e_b_c @ A2 @ ( initial_e_b_c @ A2 ) ) )
       => ( member6330420149250801815od_b_c @ Io5 @ ( sup_su3823046536922626210od_b_c @ ( lS_e_b_c @ M @ Q14 ) @ ( lS_e_b_c @ M @ Q22 ) ) ) ) ) ).

% separator_language(4)
thf(fact_1186_separator__language_I4_J,axiom,
    ! [M: fsm_a_b_c,Q14: a,Q22: a,A2: fsm_e_b_c,T1: e,T22: e,Io5: list_P903359562653991662od_b_c] :
      ( ( state_8910485216943051358_b_c_e @ M @ Q14 @ Q22 @ A2 @ T1 @ T22 )
     => ( ( member6330420149250801815od_b_c @ Io5 @ ( lS_e_b_c @ A2 @ ( initial_e_b_c @ A2 ) ) )
       => ( member6330420149250801815od_b_c @ Io5 @ ( sup_su3823046536922626210od_b_c @ ( lS_a_b_c @ M @ Q14 ) @ ( lS_a_b_c @ M @ Q22 ) ) ) ) ) ).

% separator_language(4)
thf(fact_1187_separator__language_I4_J,axiom,
    ! [M: fsm_a_b_c,Q14: a,Q22: a,A2: fsm_d_b_c,T1: d,T22: d,Io5: list_P903359562653991662od_b_c] :
      ( ( state_8910485216943051357_b_c_d @ M @ Q14 @ Q22 @ A2 @ T1 @ T22 )
     => ( ( member6330420149250801815od_b_c @ Io5 @ ( lS_d_b_c @ A2 @ ( initial_d_b_c @ A2 ) ) )
       => ( member6330420149250801815od_b_c @ Io5 @ ( sup_su3823046536922626210od_b_c @ ( lS_a_b_c @ M @ Q14 ) @ ( lS_a_b_c @ M @ Q22 ) ) ) ) ) ).

% separator_language(4)
thf(fact_1188_sup_OcoboundedI2,axiom,
    ! [C2: nat,B2: nat,A: nat] :
      ( ( ord_less_eq_nat @ C2 @ B2 )
     => ( ord_less_eq_nat @ C2 @ ( sup_sup_nat @ A @ B2 ) ) ) ).

% sup.coboundedI2
thf(fact_1189_sup_OcoboundedI2,axiom,
    ! [C2: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ C2 @ B2 )
     => ( ord_le282488521294790766od_b_c @ C2 @ ( sup_su3823046536922626210od_b_c @ A @ B2 ) ) ) ).

% sup.coboundedI2
thf(fact_1190_sup_OcoboundedI2,axiom,
    ! [C2: set_a,B2: set_a,A: set_a] :
      ( ( ord_less_eq_set_a @ C2 @ B2 )
     => ( ord_less_eq_set_a @ C2 @ ( sup_sup_set_a @ A @ B2 ) ) ) ).

% sup.coboundedI2
thf(fact_1191_sup_OcoboundedI2,axiom,
    ! [C2: set_li1159382662694783132od_c_a,B2: set_li1159382662694783132od_c_a,A: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ C2 @ B2 )
     => ( ord_le2998388488506175548od_c_a @ C2 @ ( sup_su500200128730103920od_c_a @ A @ B2 ) ) ) ).

% sup.coboundedI2
thf(fact_1192_sup_OcoboundedI1,axiom,
    ! [C2: nat,A: nat,B2: nat] :
      ( ( ord_less_eq_nat @ C2 @ A )
     => ( ord_less_eq_nat @ C2 @ ( sup_sup_nat @ A @ B2 ) ) ) ).

% sup.coboundedI1
thf(fact_1193_sup_OcoboundedI1,axiom,
    ! [C2: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ C2 @ A )
     => ( ord_le282488521294790766od_b_c @ C2 @ ( sup_su3823046536922626210od_b_c @ A @ B2 ) ) ) ).

% sup.coboundedI1
thf(fact_1194_sup_OcoboundedI1,axiom,
    ! [C2: set_a,A: set_a,B2: set_a] :
      ( ( ord_less_eq_set_a @ C2 @ A )
     => ( ord_less_eq_set_a @ C2 @ ( sup_sup_set_a @ A @ B2 ) ) ) ).

% sup.coboundedI1
thf(fact_1195_sup_OcoboundedI1,axiom,
    ! [C2: set_li1159382662694783132od_c_a,A: set_li1159382662694783132od_c_a,B2: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ C2 @ A )
     => ( ord_le2998388488506175548od_c_a @ C2 @ ( sup_su500200128730103920od_c_a @ A @ B2 ) ) ) ).

% sup.coboundedI1
thf(fact_1196_sup_Oabsorb__iff2,axiom,
    ( ord_less_eq_nat
    = ( ^ [A3: nat,B7: nat] :
          ( ( sup_sup_nat @ A3 @ B7 )
          = B7 ) ) ) ).

% sup.absorb_iff2
thf(fact_1197_sup_Oabsorb__iff2,axiom,
    ( ord_le282488521294790766od_b_c
    = ( ^ [A3: set_li6436108459499378894od_b_c,B7: set_li6436108459499378894od_b_c] :
          ( ( sup_su3823046536922626210od_b_c @ A3 @ B7 )
          = B7 ) ) ) ).

% sup.absorb_iff2
thf(fact_1198_sup_Oabsorb__iff2,axiom,
    ( ord_less_eq_set_a
    = ( ^ [A3: set_a,B7: set_a] :
          ( ( sup_sup_set_a @ A3 @ B7 )
          = B7 ) ) ) ).

% sup.absorb_iff2
thf(fact_1199_sup_Oabsorb__iff2,axiom,
    ( ord_le2998388488506175548od_c_a
    = ( ^ [A3: set_li1159382662694783132od_c_a,B7: set_li1159382662694783132od_c_a] :
          ( ( sup_su500200128730103920od_c_a @ A3 @ B7 )
          = B7 ) ) ) ).

% sup.absorb_iff2
thf(fact_1200_sup_Oabsorb__iff1,axiom,
    ( ord_less_eq_nat
    = ( ^ [B7: nat,A3: nat] :
          ( ( sup_sup_nat @ A3 @ B7 )
          = A3 ) ) ) ).

% sup.absorb_iff1
thf(fact_1201_sup_Oabsorb__iff1,axiom,
    ( ord_le282488521294790766od_b_c
    = ( ^ [B7: set_li6436108459499378894od_b_c,A3: set_li6436108459499378894od_b_c] :
          ( ( sup_su3823046536922626210od_b_c @ A3 @ B7 )
          = A3 ) ) ) ).

% sup.absorb_iff1
thf(fact_1202_sup_Oabsorb__iff1,axiom,
    ( ord_less_eq_set_a
    = ( ^ [B7: set_a,A3: set_a] :
          ( ( sup_sup_set_a @ A3 @ B7 )
          = A3 ) ) ) ).

% sup.absorb_iff1
thf(fact_1203_sup_Oabsorb__iff1,axiom,
    ( ord_le2998388488506175548od_c_a
    = ( ^ [B7: set_li1159382662694783132od_c_a,A3: set_li1159382662694783132od_c_a] :
          ( ( sup_su500200128730103920od_c_a @ A3 @ B7 )
          = A3 ) ) ) ).

% sup.absorb_iff1
thf(fact_1204_sup_Ocobounded2,axiom,
    ! [B2: nat,A: nat] : ( ord_less_eq_nat @ B2 @ ( sup_sup_nat @ A @ B2 ) ) ).

% sup.cobounded2
thf(fact_1205_sup_Ocobounded2,axiom,
    ! [B2: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ B2 @ ( sup_su3823046536922626210od_b_c @ A @ B2 ) ) ).

% sup.cobounded2
thf(fact_1206_sup_Ocobounded2,axiom,
    ! [B2: set_a,A: set_a] : ( ord_less_eq_set_a @ B2 @ ( sup_sup_set_a @ A @ B2 ) ) ).

% sup.cobounded2
thf(fact_1207_sup_Ocobounded2,axiom,
    ! [B2: set_li1159382662694783132od_c_a,A: set_li1159382662694783132od_c_a] : ( ord_le2998388488506175548od_c_a @ B2 @ ( sup_su500200128730103920od_c_a @ A @ B2 ) ) ).

% sup.cobounded2
thf(fact_1208_sup_Ocobounded1,axiom,
    ! [A: nat,B2: nat] : ( ord_less_eq_nat @ A @ ( sup_sup_nat @ A @ B2 ) ) ).

% sup.cobounded1
thf(fact_1209_sup_Ocobounded1,axiom,
    ! [A: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ A @ ( sup_su3823046536922626210od_b_c @ A @ B2 ) ) ).

% sup.cobounded1
thf(fact_1210_sup_Ocobounded1,axiom,
    ! [A: set_a,B2: set_a] : ( ord_less_eq_set_a @ A @ ( sup_sup_set_a @ A @ B2 ) ) ).

% sup.cobounded1
thf(fact_1211_sup_Ocobounded1,axiom,
    ! [A: set_li1159382662694783132od_c_a,B2: set_li1159382662694783132od_c_a] : ( ord_le2998388488506175548od_c_a @ A @ ( sup_su500200128730103920od_c_a @ A @ B2 ) ) ).

% sup.cobounded1
thf(fact_1212_sup_Oorder__iff,axiom,
    ( ord_less_eq_nat
    = ( ^ [B7: nat,A3: nat] :
          ( A3
          = ( sup_sup_nat @ A3 @ B7 ) ) ) ) ).

% sup.order_iff
thf(fact_1213_sup_Oorder__iff,axiom,
    ( ord_le282488521294790766od_b_c
    = ( ^ [B7: set_li6436108459499378894od_b_c,A3: set_li6436108459499378894od_b_c] :
          ( A3
          = ( sup_su3823046536922626210od_b_c @ A3 @ B7 ) ) ) ) ).

% sup.order_iff
thf(fact_1214_sup_Oorder__iff,axiom,
    ( ord_less_eq_set_a
    = ( ^ [B7: set_a,A3: set_a] :
          ( A3
          = ( sup_sup_set_a @ A3 @ B7 ) ) ) ) ).

% sup.order_iff
thf(fact_1215_sup_Oorder__iff,axiom,
    ( ord_le2998388488506175548od_c_a
    = ( ^ [B7: set_li1159382662694783132od_c_a,A3: set_li1159382662694783132od_c_a] :
          ( A3
          = ( sup_su500200128730103920od_c_a @ A3 @ B7 ) ) ) ) ).

% sup.order_iff
thf(fact_1216_sup_OboundedI,axiom,
    ! [B2: nat,A: nat,C2: nat] :
      ( ( ord_less_eq_nat @ B2 @ A )
     => ( ( ord_less_eq_nat @ C2 @ A )
       => ( ord_less_eq_nat @ ( sup_sup_nat @ B2 @ C2 ) @ A ) ) ) ).

% sup.boundedI
thf(fact_1217_sup_OboundedI,axiom,
    ! [B2: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c,C2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ B2 @ A )
     => ( ( ord_le282488521294790766od_b_c @ C2 @ A )
       => ( ord_le282488521294790766od_b_c @ ( sup_su3823046536922626210od_b_c @ B2 @ C2 ) @ A ) ) ) ).

% sup.boundedI
thf(fact_1218_sup_OboundedI,axiom,
    ! [B2: set_a,A: set_a,C2: set_a] :
      ( ( ord_less_eq_set_a @ B2 @ A )
     => ( ( ord_less_eq_set_a @ C2 @ A )
       => ( ord_less_eq_set_a @ ( sup_sup_set_a @ B2 @ C2 ) @ A ) ) ) ).

% sup.boundedI
thf(fact_1219_sup_OboundedI,axiom,
    ! [B2: set_li1159382662694783132od_c_a,A: set_li1159382662694783132od_c_a,C2: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ B2 @ A )
     => ( ( ord_le2998388488506175548od_c_a @ C2 @ A )
       => ( ord_le2998388488506175548od_c_a @ ( sup_su500200128730103920od_c_a @ B2 @ C2 ) @ A ) ) ) ).

% sup.boundedI
thf(fact_1220_sup_OboundedE,axiom,
    ! [B2: nat,C2: nat,A: nat] :
      ( ( ord_less_eq_nat @ ( sup_sup_nat @ B2 @ C2 ) @ A )
     => ~ ( ( ord_less_eq_nat @ B2 @ A )
         => ~ ( ord_less_eq_nat @ C2 @ A ) ) ) ).

% sup.boundedE
thf(fact_1221_sup_OboundedE,axiom,
    ! [B2: set_li6436108459499378894od_b_c,C2: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ ( sup_su3823046536922626210od_b_c @ B2 @ C2 ) @ A )
     => ~ ( ( ord_le282488521294790766od_b_c @ B2 @ A )
         => ~ ( ord_le282488521294790766od_b_c @ C2 @ A ) ) ) ).

% sup.boundedE
thf(fact_1222_sup_OboundedE,axiom,
    ! [B2: set_a,C2: set_a,A: set_a] :
      ( ( ord_less_eq_set_a @ ( sup_sup_set_a @ B2 @ C2 ) @ A )
     => ~ ( ( ord_less_eq_set_a @ B2 @ A )
         => ~ ( ord_less_eq_set_a @ C2 @ A ) ) ) ).

% sup.boundedE
thf(fact_1223_sup_OboundedE,axiom,
    ! [B2: set_li1159382662694783132od_c_a,C2: set_li1159382662694783132od_c_a,A: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ ( sup_su500200128730103920od_c_a @ B2 @ C2 ) @ A )
     => ~ ( ( ord_le2998388488506175548od_c_a @ B2 @ A )
         => ~ ( ord_le2998388488506175548od_c_a @ C2 @ A ) ) ) ).

% sup.boundedE
thf(fact_1224_sup__absorb2,axiom,
    ! [X: nat,Y: nat] :
      ( ( ord_less_eq_nat @ X @ Y )
     => ( ( sup_sup_nat @ X @ Y )
        = Y ) ) ).

% sup_absorb2
thf(fact_1225_sup__absorb2,axiom,
    ! [X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ X @ Y )
     => ( ( sup_su3823046536922626210od_b_c @ X @ Y )
        = Y ) ) ).

% sup_absorb2
thf(fact_1226_sup__absorb2,axiom,
    ! [X: set_a,Y: set_a] :
      ( ( ord_less_eq_set_a @ X @ Y )
     => ( ( sup_sup_set_a @ X @ Y )
        = Y ) ) ).

% sup_absorb2
thf(fact_1227_sup__absorb2,axiom,
    ! [X: set_li1159382662694783132od_c_a,Y: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ X @ Y )
     => ( ( sup_su500200128730103920od_c_a @ X @ Y )
        = Y ) ) ).

% sup_absorb2
thf(fact_1228_sup__absorb1,axiom,
    ! [Y: nat,X: nat] :
      ( ( ord_less_eq_nat @ Y @ X )
     => ( ( sup_sup_nat @ X @ Y )
        = X ) ) ).

% sup_absorb1
thf(fact_1229_sup__absorb1,axiom,
    ! [Y: set_li6436108459499378894od_b_c,X: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ Y @ X )
     => ( ( sup_su3823046536922626210od_b_c @ X @ Y )
        = X ) ) ).

% sup_absorb1
thf(fact_1230_sup__absorb1,axiom,
    ! [Y: set_a,X: set_a] :
      ( ( ord_less_eq_set_a @ Y @ X )
     => ( ( sup_sup_set_a @ X @ Y )
        = X ) ) ).

% sup_absorb1
thf(fact_1231_sup__absorb1,axiom,
    ! [Y: set_li1159382662694783132od_c_a,X: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ Y @ X )
     => ( ( sup_su500200128730103920od_c_a @ X @ Y )
        = X ) ) ).

% sup_absorb1
thf(fact_1232_sup_Oabsorb2,axiom,
    ! [A: nat,B2: nat] :
      ( ( ord_less_eq_nat @ A @ B2 )
     => ( ( sup_sup_nat @ A @ B2 )
        = B2 ) ) ).

% sup.absorb2
thf(fact_1233_sup_Oabsorb2,axiom,
    ! [A: set_li6436108459499378894od_b_c,B2: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ A @ B2 )
     => ( ( sup_su3823046536922626210od_b_c @ A @ B2 )
        = B2 ) ) ).

% sup.absorb2
thf(fact_1234_sup_Oabsorb2,axiom,
    ! [A: set_a,B2: set_a] :
      ( ( ord_less_eq_set_a @ A @ B2 )
     => ( ( sup_sup_set_a @ A @ B2 )
        = B2 ) ) ).

% sup.absorb2
thf(fact_1235_sup_Oabsorb2,axiom,
    ! [A: set_li1159382662694783132od_c_a,B2: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ A @ B2 )
     => ( ( sup_su500200128730103920od_c_a @ A @ B2 )
        = B2 ) ) ).

% sup.absorb2
thf(fact_1236_sup_Oabsorb1,axiom,
    ! [B2: nat,A: nat] :
      ( ( ord_less_eq_nat @ B2 @ A )
     => ( ( sup_sup_nat @ A @ B2 )
        = A ) ) ).

% sup.absorb1
thf(fact_1237_sup_Oabsorb1,axiom,
    ! [B2: set_li6436108459499378894od_b_c,A: set_li6436108459499378894od_b_c] :
      ( ( ord_le282488521294790766od_b_c @ B2 @ A )
     => ( ( sup_su3823046536922626210od_b_c @ A @ B2 )
        = A ) ) ).

% sup.absorb1
thf(fact_1238_sup_Oabsorb1,axiom,
    ! [B2: set_a,A: set_a] :
      ( ( ord_less_eq_set_a @ B2 @ A )
     => ( ( sup_sup_set_a @ A @ B2 )
        = A ) ) ).

% sup.absorb1
thf(fact_1239_sup_Oabsorb1,axiom,
    ! [B2: set_li1159382662694783132od_c_a,A: set_li1159382662694783132od_c_a] :
      ( ( ord_le2998388488506175548od_c_a @ B2 @ A )
     => ( ( sup_su500200128730103920od_c_a @ A @ B2 )
        = A ) ) ).

% sup.absorb1
thf(fact_1240_sup__unique,axiom,
    ! [F: set_li6436108459499378894od_b_c > set_li6436108459499378894od_b_c > set_li6436108459499378894od_b_c,X: set_li6436108459499378894od_b_c,Y: set_li6436108459499378894od_b_c] :
      ( ! [X3: set_li6436108459499378894od_b_c,Y4: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ X3 @ ( F @ X3 @ Y4 ) )
     => ( ! [X3: set_li6436108459499378894od_b_c,Y4: set_li6436108459499378894od_b_c] : ( ord_le282488521294790766od_b_c @ Y4 @ ( F @ X3 @ Y4 ) )
       => ( ! [X3: set_li6436108459499378894od_b_c,Y4: set_li6436108459499378894od_b_c,Z5: set_li6436108459499378894od_b_c] :
              ( ( ord_le282488521294790766od_b_c @ Y4 @ X3 )
             => ( ( ord_le282488521294790766od_b_c @ Z5 @ X3 )
               => ( ord_le282488521294790766od_b_c @ ( F @ Y4 @ Z5 ) @ X3 ) ) )
         => ( ( sup_su3823046536922626210od_b_c @ X @ Y )
            = ( F @ X @ Y ) ) ) ) ) ).

% sup_unique
thf(fact_1241_sup__unique,axiom,
    ! [F: set_a > set_a > set_a,X: set_a,Y: set_a] :
      ( ! [X3: set_a,Y4: set_a] : ( ord_less_eq_set_a @ X3 @ ( F @ X3 @ Y4 ) )
     => ( ! [X3: set_a,Y4: set_a] : ( ord_less_eq_set_a @ Y4 @ ( F @ X3 @ Y4 ) )
       => ( ! [X3: set_a,Y4: set_a,Z5: set_a] :
              ( ( ord_less_eq_set_a @ Y4 @ X3 )
             => ( ( ord_less_eq_set_a @ Z5 @ X3 )
               => ( ord_less_eq_set_a @ ( F @ Y4 @ Z5 ) @ X3 ) ) )
         => ( ( sup_sup_set_a @ X @ Y )
            = ( F @ X @ Y ) ) ) ) ) ).

% sup_unique
thf(fact_1242_sup__unique,axiom,
    ! [F: set_li1159382662694783132od_c_a > set_li1159382662694783132od_c_a > set_li1159382662694783132od_c_a,X: set_li1159382662694783132od_c_a,Y: set_li1159382662694783132od_c_a] :
      ( ! [X3: set_li1159382662694783132od_c_a,Y4: set_li1159382662694783132od_c_a] : ( ord_le2998388488506175548od_c_a @ X3 @ ( F @ X3 @ Y4 ) )
     => ( ! [X3: set_li1159382662694783132od_c_a,Y4: set_li1159382662694783132od_c_a] : ( ord_le2998388488506175548od_c_a @ Y4 @ ( F @ X3 @ Y4 ) )
       => ( ! [X3: set_li1159382662694783132od_c_a,Y4: set_li1159382662694783132od_c_a,Z5: set_li1159382662694783132od_c_a] :
              ( ( ord_le2998388488506175548od_c_a @ Y4 @ X3 )
             => ( ( ord_le2998388488506175548od_c_a @ Z5 @ X3 )
               => ( ord_le2998388488506175548od_c_a @ ( F @ Y4 @ Z5 ) @ X3 ) ) )
         => ( ( sup_su500200128730103920od_c_a @ X @ Y )
            = ( F @ X @ Y ) ) ) ) ) ).

% sup_unique
thf(fact_1243_RP__targets,axiom,
    ! [PR: list_P6327159017948738492od_c_a,Q7: a] :
      ( ( member7410604586820865893od_c_a @ PR @ ( test_RP_a_b_c_e @ m @ ( target_a_b_c @ ( initial_a_b_c @ m ) @ pP ) @ Q7 @ pP @ pM @ prs @ m2 ) )
     => ? [Q6: e] :
          ( ( io_targets_e_b_c @ m2
            @ ( map_Pr776894537227705078od_b_c
              @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
              @ PR )
            @ ( initial_e_b_c @ m2 ) )
          = ( insert_e @ Q6 @ bot_bot_set_e ) ) ) ).

% RP_targets
thf(fact_1244__092_060open_062io_A_061_Ap__io_ApM_A_064_AioEx_092_060close_062,axiom,
    ( io
    = ( append2547753245680614915od_b_c
      @ ( map_Pr776894537227705078od_b_c
        @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
        @ pM )
      @ ioEx ) ) ).

% \<open>io = p_io pM @ ioEx\<close>
thf(fact_1245__092_060open_062p__io_ApP_A_064_Aio_A_092_060notin_062_AL_AM_092_060close_062,axiom,
    ~ ( member6330420149250801815od_b_c
      @ ( append2547753245680614915od_b_c
        @ ( map_Pr776894537227705078od_b_c
          @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
          @ pP )
        @ io )
      @ ( lS_a_b_c @ m @ ( initial_a_b_c @ m ) ) ) ).

% \<open>p_io pP @ io \<notin> L M\<close>
thf(fact_1246__092_060open_062p__io_ApP_A_064_Aio_A_092_060in_062_AL_AM_H_092_060close_062,axiom,
    ( member6330420149250801815od_b_c
    @ ( append2547753245680614915od_b_c
      @ ( map_Pr776894537227705078od_b_c
        @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
        @ pP )
      @ io )
    @ ( lS_e_b_c @ m2 @ ( initial_e_b_c @ m2 ) ) ) ).

% \<open>p_io pP @ io \<in> L M'\<close>
thf(fact_1247_no__shared__targets__for__distinct__states,axiom,
    ! [Q7: a,Q8: a,PR1: list_P6327159017948738492od_c_a,PR2: list_P6327159017948738492od_c_a] :
      ( ( Q7 != Q8 )
     => ( ( member_a @ Q7 @ ( produc9088895665703139587_set_a @ dM ) )
       => ( ( member_a @ Q8 @ ( produc9088895665703139587_set_a @ dM ) )
         => ( ( member7410604586820865893od_c_a @ PR1 @ ( test_RP_a_b_c_e @ m @ q2 @ Q7 @ pP @ pM @ prs @ m2 ) )
           => ( ( member7410604586820865893od_c_a @ PR2 @ ( test_RP_a_b_c_e @ m @ q2 @ Q8 @ pP @ pM @ prs @ m2 ) )
             => ( ( inf_inf_set_e
                  @ ( io_targets_e_b_c @ m2
                    @ ( map_Pr776894537227705078od_b_c
                      @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
                      @ PR1 )
                    @ ( initial_e_b_c @ m2 ) )
                  @ ( io_targets_e_b_c @ m2
                    @ ( map_Pr776894537227705078od_b_c
                      @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
                      @ PR2 )
                    @ ( initial_e_b_c @ m2 ) ) )
                = bot_bot_set_e ) ) ) ) ) ) ).

% no_shared_targets_for_distinct_states
thf(fact_1248_no__shared__targets__for__identical__states,axiom,
    ! [PR1: list_P6327159017948738492od_c_a,Q7: a,PR2: list_P6327159017948738492od_c_a] :
      ( ( member7410604586820865893od_c_a @ PR1 @ ( test_RP_a_b_c_e @ m @ ( target_a_b_c @ ( initial_a_b_c @ m ) @ pP ) @ Q7 @ pP @ pM @ prs @ m2 ) )
     => ( ( member7410604586820865893od_c_a @ PR2 @ ( test_RP_a_b_c_e @ m @ ( target_a_b_c @ ( initial_a_b_c @ m ) @ pP ) @ Q7 @ pP @ pM @ prs @ m2 ) )
       => ( ( PR1 != PR2 )
         => ( ( inf_inf_set_e
              @ ( io_targets_e_b_c @ m2
                @ ( map_Pr776894537227705078od_b_c
                  @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
                  @ PR1 )
                @ ( initial_e_b_c @ m2 ) )
              @ ( io_targets_e_b_c @ m2
                @ ( map_Pr776894537227705078od_b_c
                  @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
                  @ PR2 )
                @ ( initial_e_b_c @ m2 ) ) )
            = bot_bot_set_e ) ) ) ) ).

% no_shared_targets_for_identical_states
thf(fact_1249__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062pM_AdM_AioEx_O_A_092_060lbrakk_062_IpM_M_AdM_J_A_092_060in_062_Am__traversal__paths__with__witness_AM_Aq_Arepetition__sets_Am_059_Aio_A_061_Ap__io_ApM_A_064_AioEx_059_AioEx_A_092_060noteq_062_A_091_093_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
    ~ ! [PM: list_P6327159017948738492od_c_a] :
        ( ? [DM: produc1703568184450464039_set_a] : ( member6493638300815972283_set_a @ ( produc6508649944902238466_set_a @ PM @ DM ) @ ( traver6421790936065540696_a_b_c @ m @ q2 @ repetition_sets @ m3 ) )
       => ! [IoEx: list_P903359562653991662od_b_c] :
            ( ( io
              = ( append2547753245680614915od_b_c
                @ ( map_Pr776894537227705078od_b_c
                  @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
                  @ PM )
                @ IoEx ) )
           => ( IoEx = nil_Product_prod_b_c ) ) ) ).

% \<open>\<And>thesis. (\<And>pM dM ioEx. \<lbrakk>(pM, dM) \<in> m_traversal_paths_with_witness M q repetition_sets m; io = p_io pM @ ioEx; ioEx \<noteq> []\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_1250__092_060open_062p__io_ApP_A_064_Ap__io_ApM_A_092_060in_062_AL_AM_H_092_060close_062,axiom,
    ( member6330420149250801815od_b_c
    @ ( append2547753245680614915od_b_c
      @ ( map_Pr776894537227705078od_b_c
        @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
        @ pP )
      @ ( map_Pr776894537227705078od_b_c
        @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
        @ pM ) )
    @ ( lS_e_b_c @ m2 @ ( initial_e_b_c @ m2 ) ) ) ).

% \<open>p_io pP @ p_io pM \<in> L M'\<close>
thf(fact_1251_pass1,axiom,
    ! [Q3: a,P2: fsm_a_b_c,Io5: list_P903359562653991662od_b_c,X: b,Y: c,Y6: c] :
      ( ( member997585926662434933_a_b_c @ ( produc2795441082327197628_a_b_c @ Q3 @ P2 ) @ prs )
     => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) ) @ ( lS_a_b_c @ P2 @ ( initial_a_b_c @ P2 ) ) )
       => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y6 ) @ nil_Product_prod_b_c ) ) @ ( lS_e_b_c @ m2 @ ( initial_e_b_c @ m2 ) ) )
         => ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ Io5 @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y6 ) @ nil_Product_prod_b_c ) ) @ ( lS_a_b_c @ P2 @ ( initial_a_b_c @ P2 ) ) ) ) ) ) ).

% pass1
thf(fact_1252__092_060open_062p__io_ApP_A_064_Abutlast_Aio_A_092_060in_062_AL_AM_092_060close_062,axiom,
    ( member6330420149250801815od_b_c
    @ ( append2547753245680614915od_b_c
      @ ( map_Pr776894537227705078od_b_c
        @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
        @ pP )
      @ ( butlas5354910156707045818od_b_c @ io ) )
    @ ( lS_a_b_c @ m @ ( initial_a_b_c @ m ) ) ) ).

% \<open>p_io pP @ butlast io \<in> L M\<close>
thf(fact_1253__092_060open_062butlast_Aio_A_061_Ap__io_ApM_A_064_AioX_092_060close_062,axiom,
    ( ( butlas5354910156707045818od_b_c @ io )
    = ( append2547753245680614915od_b_c
      @ ( map_Pr776894537227705078od_b_c
        @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
        @ pM )
      @ ioX ) ) ).

% \<open>butlast io = p_io pM @ ioX\<close>
thf(fact_1254__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062q_AP_O_A_092_060lbrakk_062q_A_092_060in_062_AFSM_Ostates_AM_059_A_Iq_M_AP_J_A_092_060in_062_Aprs_059_Apath_AP_A_IFSM_Oinitial_AP_J_ApP_059_Atarget_A_IFSM_Oinitial_AP_J_ApP_A_061_Aq_059_Ap__io_ApP_A_064_Abutlast_Aio_A_092_060in_062_AL_AM_059_Ap__io_ApP_A_064_Aio_A_092_060notin_062_AL_AM_059_Ap__io_ApP_A_064_Aio_A_092_060in_062_AL_AM_H_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
    ~ ! [Q6: a] :
        ( ( member_a @ Q6 @ ( states_a_b_c @ m ) )
       => ! [P8: fsm_a_b_c] :
            ( ( member997585926662434933_a_b_c @ ( produc2795441082327197628_a_b_c @ Q6 @ P8 ) @ prs )
           => ( ( path_a_b_c @ P8 @ ( initial_a_b_c @ P8 ) @ pP )
             => ( ( ( target_a_b_c @ ( initial_a_b_c @ P8 ) @ pP )
                  = Q6 )
               => ( ( member6330420149250801815od_b_c
                    @ ( append2547753245680614915od_b_c
                      @ ( map_Pr776894537227705078od_b_c
                        @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
                        @ pP )
                      @ ( butlas5354910156707045818od_b_c @ io ) )
                    @ ( lS_a_b_c @ m @ ( initial_a_b_c @ m ) ) )
                 => ( ~ ( member6330420149250801815od_b_c
                        @ ( append2547753245680614915od_b_c
                          @ ( map_Pr776894537227705078od_b_c
                            @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
                            @ pP )
                          @ io )
                        @ ( lS_a_b_c @ m @ ( initial_a_b_c @ m ) ) )
                   => ~ ( member6330420149250801815od_b_c
                        @ ( append2547753245680614915od_b_c
                          @ ( map_Pr776894537227705078od_b_c
                            @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
                            @ pP )
                          @ io )
                        @ ( lS_e_b_c @ m2 @ ( initial_e_b_c @ m2 ) ) ) ) ) ) ) ) ) ).

% \<open>\<And>thesis. (\<And>q P. \<lbrakk>q \<in> FSM.states M; (q, P) \<in> prs; path P (FSM.initial P) pP; target (FSM.initial P) pP = q; p_io pP @ butlast io \<in> L M; p_io pP @ io \<notin> L M; p_io pP @ io \<in> L M'\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_1255__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ioX_O_Abutlast_Aio_A_061_Ap__io_ApM_A_064_AioX_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
    ~ ! [IoX: list_P903359562653991662od_b_c] :
        ( ( butlas5354910156707045818od_b_c @ io )
       != ( append2547753245680614915od_b_c
          @ ( map_Pr776894537227705078od_b_c
            @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
            @ pM )
          @ IoX ) ) ).

% \<open>\<And>thesis. (\<And>ioX. butlast io = p_io pM @ ioX \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_1256__092_060open_062io_A_061_Abutlast_Aio_A_064_A_091_Ifst_A_Ilast_Aio_J_M_Asnd_A_Ilast_Aio_J_J_093_092_060close_062,axiom,
    ( io
    = ( append2547753245680614915od_b_c @ ( butlas5354910156707045818od_b_c @ io ) @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ ( product_fst_b_c @ ( last_P6003269694912247047od_b_c @ io ) ) @ ( product_snd_b_c @ ( last_P6003269694912247047od_b_c @ io ) ) ) @ nil_Product_prod_b_c ) ) ) ).

% \<open>io = butlast io @ [(fst (last io), snd (last io))]\<close>
thf(fact_1257_t8_H,axiom,
    ! [D: produc1703568184450464039_set_a] :
      ( ( member7983343339038529360_set_a @ D @ ( set_Pr7878197726666307004_set_a @ repetition_sets ) )
     => ( ( produc1983107199584856133_set_a @ D )
        = ( inf_inf_set_a @ ( produc9088895665703139587_set_a @ D ) @ ( image_3273489647386116407_b_c_a @ produc2620512763296580520_a_b_c @ prs ) ) ) ) ).

% t8'
thf(fact_1258_snd__dM__prop,axiom,
    ! [Q7: a] :
      ( ( member_a @ Q7 @ ( produc1983107199584856133_set_a @ dM ) )
     => ( ( comple2307003627140970447_set_e
          @ ( image_6475989668741808299_set_e
            @ ^ [PR3: list_P6327159017948738492od_c_a] :
                ( io_targets_e_b_c @ m2
                @ ( map_Pr776894537227705078od_b_c
                  @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
                  @ PR3 )
                @ ( initial_e_b_c @ m2 ) )
            @ ( test_RP_a_b_c_e @ m @ q2 @ Q7 @ pP @ pM @ prs @ m2 ) ) )
       != ( comple2307003627140970447_set_e
          @ ( image_6475989668741808299_set_e
            @ ^ [PR3: list_P6327159017948738492od_c_a] :
                ( io_targets_e_b_c @ m2
                @ ( map_Pr776894537227705078od_b_c
                  @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
                  @ PR3 )
                @ ( initial_e_b_c @ m2 ) )
            @ ( test_R_a_b_c @ m @ q2 @ Q7 @ pP @ pM ) ) ) ) ) ).

% snd_dM_prop
thf(fact_1259__092_060open_062q_A_092_060in_062_Afst_A_096_Aprs_092_060close_062,axiom,
    member_a @ q2 @ ( image_3273489647386116407_b_c_a @ produc2620512763296580520_a_b_c @ prs ) ).

% \<open>q \<in> fst ` prs\<close>
thf(fact_1260__092_060open_062_I_092_060Union_062pR_092_060in_062RP_AM_Aq_Aq_H_ApP_ApM_Aprs_AM_H_O_Aio__targets_AM_H_A_Ip__io_ApR_J_A_IFSM_Oinitial_AM_H_J_J_A_092_060noteq_062_A_I_092_060Union_062pR_092_060in_062R_AM_Aq_Aq_H_ApP_ApM_O_Aio__targets_AM_H_A_Ip__io_ApR_J_A_IFSM_Oinitial_AM_H_J_J_092_060close_062,axiom,
    ( ( comple2307003627140970447_set_e
      @ ( image_6475989668741808299_set_e
        @ ^ [PR3: list_P6327159017948738492od_c_a] :
            ( io_targets_e_b_c @ m2
            @ ( map_Pr776894537227705078od_b_c
              @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
              @ PR3 )
            @ ( initial_e_b_c @ m2 ) )
        @ ( test_RP_a_b_c_e @ m @ q2 @ q @ pP @ pM @ prs @ m2 ) ) )
   != ( comple2307003627140970447_set_e
      @ ( image_6475989668741808299_set_e
        @ ^ [PR3: list_P6327159017948738492od_c_a] :
            ( io_targets_e_b_c @ m2
            @ ( map_Pr776894537227705078od_b_c
              @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
              @ PR3 )
            @ ( initial_e_b_c @ m2 ) )
        @ ( test_R_a_b_c @ m @ q2 @ q @ pP @ pM ) ) ) ) ).

% \<open>(\<Union>pR\<in>RP M q q' pP pM prs M'. io_targets M' (p_io pR) (FSM.initial M')) \<noteq> (\<Union>pR\<in>R M q q' pP pM. io_targets M' (p_io pR) (FSM.initial M'))\<close>
thf(fact_1261_pass3,axiom,
    ! [Q3: a,P2: fsm_a_b_c,PP2: list_P6327159017948738492od_c_a,PT: list_P6327159017948738492od_c_a,Q7: a,A2: fsm_d_b_c,D1: d,D22: d,QT: e] :
      ( ( member997585926662434933_a_b_c @ ( produc2795441082327197628_a_b_c @ Q3 @ P2 ) @ prs )
     => ( ( path_a_b_c @ P2 @ ( initial_a_b_c @ P2 ) @ PP2 )
       => ( ( ( target_a_b_c @ ( initial_a_b_c @ P2 ) @ PP2 )
            = Q3 )
         => ( ( member7410604586820865893od_c_a @ PT @ ( tps @ Q3 ) )
           => ( ( member6330420149250801815od_b_c
                @ ( append2547753245680614915od_b_c
                  @ ( map_Pr776894537227705078od_b_c
                    @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
                    @ PP2 )
                  @ ( map_Pr776894537227705078od_b_c
                    @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
                    @ PT ) )
                @ ( lS_e_b_c @ m2 @ ( initial_e_b_c @ m2 ) ) )
             => ( ( member_a @ Q7 @ ( rd_targets @ ( produc3580641852002036821od_c_a @ Q3 @ PT ) ) )
               => ( ( member73601632213084689od_d_d @ ( produc3676634857637483352od_d_d @ A2 @ ( product_Pair_d_d @ D1 @ D22 ) ) @ ( separators @ ( product_Pair_a_a @ ( target_a_b_c @ Q3 @ PT ) @ Q7 ) ) )
                 => ( ( member_e @ QT
                      @ ( io_targets_e_b_c @ m2
                        @ ( append2547753245680614915od_b_c
                          @ ( map_Pr776894537227705078od_b_c
                            @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
                            @ PP2 )
                          @ ( map_Pr776894537227705078od_b_c
                            @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
                            @ PT ) )
                        @ ( initial_e_b_c @ m2 ) ) )
                   => ( adapti9059566338866072926_b_c_d @ m2 @ A2 @ QT @ D22 ) ) ) ) ) ) ) ) ) ).

% pass3
thf(fact_1262_t12,axiom,
    ! [Q3: a,P3: list_P6327159017948738492od_c_a,D: produc1703568184450464039_set_a,Q14: a,Q22: a] :
      ( ( member_a @ Q3 @ ( image_3273489647386116407_b_c_a @ produc2620512763296580520_a_b_c @ prs ) )
     => ( ( member6493638300815972283_set_a @ ( produc6508649944902238466_set_a @ P3 @ D ) @ ( traver6421790936065540696_a_b_c @ m @ Q3 @ repetition_sets @ m3 ) )
       => ( ( Q14 != Q22 )
         => ( ( member_a @ Q14 @ ( produc1983107199584856133_set_a @ D ) )
           => ( ( member_a @ Q22 @ ( produc1983107199584856133_set_a @ D ) )
             => ( ( member7410604586820865893od_c_a @ nil_Pr1342775757158464060od_c_a @ ( tps @ Q14 ) )
                & ( member7410604586820865893od_c_a @ nil_Pr1342775757158464060od_c_a @ ( tps @ Q22 ) )
                & ( member_a @ Q14 @ ( rd_targets @ ( produc3580641852002036821od_c_a @ Q22 @ nil_Pr1342775757158464060od_c_a ) ) )
                & ( member_a @ Q22 @ ( rd_targets @ ( produc3580641852002036821od_c_a @ Q14 @ nil_Pr1342775757158464060od_c_a ) ) ) ) ) ) ) ) ) ).

% t12
thf(fact_1263_t11,axiom,
    ! [Q3: a,P3: list_P6327159017948738492od_c_a,D: produc1703568184450464039_set_a,P1: list_P6327159017948738492od_c_a,P22: list_P6327159017948738492od_c_a,Q7: a] :
      ( ( member_a @ Q3 @ ( image_3273489647386116407_b_c_a @ produc2620512763296580520_a_b_c @ prs ) )
     => ( ( member6493638300815972283_set_a @ ( produc6508649944902238466_set_a @ P3 @ D ) @ ( traver6421790936065540696_a_b_c @ m @ Q3 @ repetition_sets @ m3 ) )
       => ( ( P3
            = ( append3884164603879732689od_c_a @ P1 @ P22 ) )
         => ( ( member_a @ Q7 @ ( image_3273489647386116407_b_c_a @ produc2620512763296580520_a_b_c @ prs ) )
           => ( ( member_a @ ( target_a_b_c @ Q3 @ P1 ) @ ( produc9088895665703139587_set_a @ D ) )
             => ( ( member_a @ Q7 @ ( produc9088895665703139587_set_a @ D ) )
               => ( ( ( target_a_b_c @ Q3 @ P1 )
                   != Q7 )
                 => ( ( member7410604586820865893od_c_a @ P1 @ ( tps @ Q3 ) )
                    & ( member7410604586820865893od_c_a @ nil_Pr1342775757158464060od_c_a @ ( tps @ Q7 ) )
                    & ( member_a @ ( target_a_b_c @ Q3 @ P1 ) @ ( rd_targets @ ( produc3580641852002036821od_c_a @ Q7 @ nil_Pr1342775757158464060od_c_a ) ) )
                    & ( member_a @ Q7 @ ( rd_targets @ ( produc3580641852002036821od_c_a @ Q3 @ P1 ) ) ) ) ) ) ) ) ) ) ) ).

% t11
thf(fact_1264_t10,axiom,
    ! [Q3: a,P3: list_P6327159017948738492od_c_a,D: produc1703568184450464039_set_a,P1: list_P6327159017948738492od_c_a,P22: list_P6327159017948738492od_c_a,P32: list_P6327159017948738492od_c_a] :
      ( ( member_a @ Q3 @ ( image_3273489647386116407_b_c_a @ produc2620512763296580520_a_b_c @ prs ) )
     => ( ( member6493638300815972283_set_a @ ( produc6508649944902238466_set_a @ P3 @ D ) @ ( traver6421790936065540696_a_b_c @ m @ Q3 @ repetition_sets @ m3 ) )
       => ( ( P3
            = ( append3884164603879732689od_c_a @ P1 @ ( append3884164603879732689od_c_a @ P22 @ P32 ) ) )
         => ( ( P22 != nil_Pr1342775757158464060od_c_a )
           => ( ( member_a @ ( target_a_b_c @ Q3 @ P1 ) @ ( produc9088895665703139587_set_a @ D ) )
             => ( ( member_a @ ( target_a_b_c @ Q3 @ ( append3884164603879732689od_c_a @ P1 @ P22 ) ) @ ( produc9088895665703139587_set_a @ D ) )
               => ( ( ( target_a_b_c @ Q3 @ P1 )
                   != ( target_a_b_c @ Q3 @ ( append3884164603879732689od_c_a @ P1 @ P22 ) ) )
                 => ( ( member7410604586820865893od_c_a @ P1 @ ( tps @ Q3 ) )
                    & ( member7410604586820865893od_c_a @ ( append3884164603879732689od_c_a @ P1 @ P22 ) @ ( tps @ Q3 ) )
                    & ( member_a @ ( target_a_b_c @ Q3 @ P1 ) @ ( rd_targets @ ( produc3580641852002036821od_c_a @ Q3 @ ( append3884164603879732689od_c_a @ P1 @ P22 ) ) ) )
                    & ( member_a @ ( target_a_b_c @ Q3 @ ( append3884164603879732689od_c_a @ P1 @ P22 ) ) @ ( rd_targets @ ( produc3580641852002036821od_c_a @ Q3 @ P1 ) ) ) ) ) ) ) ) ) ) ) ).

% t10
thf(fact_1265_assms_I2_J,axiom,
    test_i4204698558891958671_b_c_d @ ( test_t5871526445387177708_b_c_d @ prs @ tps @ rd_targets @ separators ) @ m @ m3 ).

% assms(2)
thf(fact_1266_pass2,axiom,
    ! [Q3: a,P2: fsm_a_b_c,PP2: list_P6327159017948738492od_c_a,PT: list_P6327159017948738492od_c_a,IoT: list_P903359562653991662od_b_c,X: b,Y: c,Y6: c] :
      ( ( member997585926662434933_a_b_c @ ( produc2795441082327197628_a_b_c @ Q3 @ P2 ) @ prs )
     => ( ( path_a_b_c @ P2 @ ( initial_a_b_c @ P2 ) @ PP2 )
       => ( ( ( target_a_b_c @ ( initial_a_b_c @ P2 ) @ PP2 )
            = Q3 )
         => ( ( member7410604586820865893od_c_a @ PT @ ( tps @ Q3 ) )
           => ( ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ IoT @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y ) @ nil_Product_prod_b_c ) )
                @ ( set_li4480668622519654659od_b_c
                  @ ( prefix1131979855692807669od_b_c
                    @ ( map_Pr776894537227705078od_b_c
                      @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
                      @ PT ) ) ) )
             => ( ( member6330420149250801815od_b_c
                  @ ( append2547753245680614915od_b_c
                    @ ( map_Pr776894537227705078od_b_c
                      @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
                      @ PP2 )
                    @ ( append2547753245680614915od_b_c @ IoT @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y6 ) @ nil_Product_prod_b_c ) ) )
                  @ ( lS_e_b_c @ m2 @ ( initial_e_b_c @ m2 ) ) )
               => ? [PT2: list_P6327159017948738492od_c_a] :
                    ( ( member7410604586820865893od_c_a @ PT2 @ ( tps @ Q3 ) )
                    & ( member6330420149250801815od_b_c @ ( append2547753245680614915od_b_c @ IoT @ ( cons_P4529483553340347422od_b_c @ ( product_Pair_b_c @ X @ Y6 ) @ nil_Product_prod_b_c ) )
                      @ ( set_li4480668622519654659od_b_c
                        @ ( prefix1131979855692807669od_b_c
                          @ ( map_Pr776894537227705078od_b_c
                            @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
                            @ PT2 ) ) ) ) ) ) ) ) ) ) ) ).

% pass2
thf(fact_1267_assms_I1_J,axiom,
    test_p3809436039288090642_c_d_e @ m @ ( test_t5871526445387177708_b_c_d @ prs @ tps @ rd_targets @ separators ) @ m2 ).

% assms(1)
thf(fact_1268_repetition__sets__def,axiom,
    test_i4756896328399799264_b_c_d @ ( test_t5871526445387177708_b_c_d @ prs @ tps @ rd_targets @ separators ) @ m @ m3 @ repetition_sets ).

% repetition_sets_def
thf(fact_1269__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062repetition__sets_O_Aimplies__completeness__for__repetition__sets_A_ITest__Suite_Aprs_Atps_Ard__targets_Aseparators_J_AM_Am_Arepetition__sets_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
    ~ ! [Repetition_sets: list_P3660316430366008877_set_a] :
        ~ ( test_i4756896328399799264_b_c_d @ ( test_t5871526445387177708_b_c_d @ prs @ tps @ rd_targets @ separators ) @ m @ m3 @ Repetition_sets ) ).

% \<open>\<And>thesis. (\<And>repetition_sets. implies_completeness_for_repetition_sets (Test_Suite prs tps rd_targets separators) M m repetition_sets \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_1270_RP__card,axiom,
    ! [Q7: a] :
      ( ( finite_card_e
        @ ( comple2307003627140970447_set_e
          @ ( image_6475989668741808299_set_e
            @ ^ [PR3: list_P6327159017948738492od_c_a] :
                ( io_targets_e_b_c @ m2
                @ ( map_Pr776894537227705078od_b_c
                  @ ^ [T2: produc2669932201312201782od_c_a] : ( product_Pair_b_c @ ( produc301949074746585577od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) @ ( product_fst_c_a @ ( produc5221446324160585515od_c_a @ ( produc8088130389382527188od_c_a @ T2 ) ) ) )
                  @ PR3 )
                @ ( initial_e_b_c @ m2 ) )
            @ ( test_RP_a_b_c_e @ m @ ( target_a_b_c @ ( initial_a_b_c @ m ) @ pP ) @ Q7 @ pP @ pM @ prs @ m2 ) ) ) )
      = ( finite5661710215740019684od_c_a @ ( test_RP_a_b_c_e @ m @ ( target_a_b_c @ ( initial_a_b_c @ m ) @ pP ) @ Q7 @ pP @ pM @ prs @ m2 ) ) ) ).

% RP_card
thf(fact_1271_t6,axiom,
    ! [Q3: a] :
      ( ( member_a @ Q3 @ ( image_3273489647386116407_b_c_a @ produc2620512763296580520_a_b_c @ prs ) )
     => ( ( ord_le2998388488506175548od_c_a @ ( tps @ Q3 )
          @ ( collec6273869032445462695od_c_a
            @ ^ [P12: list_P6327159017948738492od_c_a] :
              ? [P23: list_P6327159017948738492od_c_a,D5: produc1703568184450464039_set_a] : ( member6493638300815972283_set_a @ ( produc6508649944902238466_set_a @ ( append3884164603879732689od_c_a @ P12 @ P23 ) @ D5 ) @ ( traver6421790936065540696_a_b_c @ m @ Q3 @ repetition_sets @ m3 ) ) ) )
        & ( ord_le2998388488506175548od_c_a @ ( image_865596521259543215od_c_a @ produc3242630202250842350_set_a @ ( traver6421790936065540696_a_b_c @ m @ Q3 @ repetition_sets @ m3 ) ) @ ( tps @ Q3 ) ) ) ) ).

% t6

% Helper facts (6)
thf(help_fChoice_1_1_fChoice_001tf__a_T,axiom,
    ! [P2: a > $o] :
      ( ( P2 @ ( fChoice_a @ P2 ) )
      = ( ? [X5: a] : ( P2 @ X5 ) ) ) ).

thf(help_fChoice_1_1_fChoice_001tf__b_T,axiom,
    ! [P2: b > $o] :
      ( ( P2 @ ( fChoice_b @ P2 ) )
      = ( ? [X5: b] : ( P2 @ X5 ) ) ) ).

thf(help_fChoice_1_1_fChoice_001tf__e_T,axiom,
    ! [P2: e > $o] :
      ( ( P2 @ ( fChoice_e @ P2 ) )
      = ( ? [X5: e] : ( P2 @ X5 ) ) ) ).

thf(help_fChoice_1_1_fChoice_001t__List__Olist_It__Product____Type__Oprod_Itf__b_Mtf__c_J_J_T,axiom,
    ! [P2: list_P903359562653991662od_b_c > $o] :
      ( ( P2 @ ( fChoic3287323656706165826od_b_c @ P2 ) )
      = ( ? [X5: list_P903359562653991662od_b_c] : ( P2 @ X5 ) ) ) ).

thf(help_fChoice_1_1_fChoice_001t__Product____Type__Oprod_It__FSM__Ofsm_Itf__d_Mtf__b_Mtf__c_J_Mt__Product____Type__Oprod_Itf__d_Mtf__d_J_J_T,axiom,
    ! [P2: produc4859908366599477352od_d_d > $o] :
      ( ( P2 @ ( fChoic8563934328396083644od_d_d @ P2 ) )
      = ( ? [X5: produc4859908366599477352od_d_d] : ( P2 @ X5 ) ) ) ).

thf(help_fChoice_1_1_fChoice_001t__List__Olist_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_Itf__b_Mt__Product____Type__Oprod_Itf__c_Mtf__a_J_J_J_J_T,axiom,
    ! [P2: list_P6327159017948738492od_c_a > $o] :
      ( ( P2 @ ( fChoic6541264315744621840od_c_a @ P2 ) )
      = ( ? [X5: list_P6327159017948738492od_c_a] : ( P2 @ X5 ) ) ) ).

% Conjectures (2)
thf(conj_0,hypothesis,
    ! [X4: list_P6327159017948738492od_c_a] :
      ( ( ( test_RP_a_b_c_e @ m @ q2 @ q @ pP @ pM @ prs @ m2 )
        = ( insert4789241225314331020od_c_a @ X4 @ ( test_R_a_b_c @ m @ q2 @ q @ pP @ pM ) ) )
     => thesisa ) ).

thf(conj_1,conjecture,
    thesisa ).

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