% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/TypeSafe/prob_155__5335478_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:19:44.306

% Could-be-implicit typings (28)
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thf(ty_n_t__Value__Oval, type,
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% Explicit typings (83)
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thf(sy_c_Map_Odom_001t__List__Olist_It__String__Ochar_J_001t__Value__Oval, type,
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thf(sy_c_Objects_Ohext, type,
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thf(sy_c_Option_Ocombine__options_001t__Value__Oval, type,
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thf(sy_c_Option_Ooption_OSome_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Option_Ooption_OSome_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
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thf(sy_c_Option_Ooption_OSome_001t__Value__Oval, type,
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thf(sy_c_Option_Othese_001t__List__Olist_It__String__Ochar_J, type,
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thf(sy_c_Set_OCollect_001t__List__Olist_It__String__Ochar_J, type,
    collect_list_char : (list_char > $o) > set_list_char).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    collec2055896722on_val : (produc1172664615on_val > $o) > set_Pr1189492743on_val).
thf(sy_c_Set_Oinsert_001t__List__Olist_It__String__Ochar_J, type,
    insert_list_char : list_char > set_list_char > set_list_char).
thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__List__Olist_It__String__Ochar_J_J, type,
    insert523167969t_char : option_list_char > set_option_list_char > set_option_list_char).
thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    insert1333207736on_val : option2118145160on_val > set_op1111598910on_val > set_op1111598910on_val).
thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Set__Oset_It__List__Olist_It__String__Ochar_J_J_J, type,
    insert433234071t_char : option_set_list_char > set_op501702045t_char > set_op501702045t_char).
thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Value__Oval_J, type,
    insert_option_val : option_val > set_option_val > set_option_val).
thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    insert688092392on_val : produc266837688on_val > set_Pr2075231726on_val > set_Pr2075231726on_val).
thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    insert1971494647on_val : produc1172664615on_val > set_Pr1189492743on_val > set_Pr1189492743on_val).
thf(sy_c_Set_Oinsert_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    insert_set_list_char : set_list_char > set_set_list_char > set_set_list_char).
thf(sy_c_Set_Oinsert_001t__Value__Oval, type,
    insert_val : val > set_val > set_val).
thf(sy_c_SmallStep_Ored, type,
    red : list_P1234162913t_char > set_Pr1189492743on_val).
thf(sy_c_WellForm_Owf__prog_001t__Product____Type__Oprod_It__List__Olist_It__List__Olist_It__String__Ochar_J_J_Mt__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_J, type,
    wf_pro1229751607t_char : (list_P1234162913t_char > list_char > produc1259892823t_char > $o) > list_P1234162913t_char > $o).
thf(sy_c_member_001t__List__Olist_It__String__Ochar_J, type,
    member_list_char : list_char > set_list_char > $o).
thf(sy_c_member_001t__Option__Ooption_It__List__Olist_It__String__Ochar_J_J, type,
    member246349384t_char : option_list_char > set_option_list_char > $o).
thf(sy_c_member_001t__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member1048249375on_val : option2118145160on_val > set_op1111598910on_val > $o).
thf(sy_c_member_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_J, type,
    member1869742230on_val : option723652845on_val > set_op787718477on_val > $o).
thf(sy_c_member_001t__Option__Ooption_It__Set__Oset_It__List__Olist_It__String__Ochar_J_J_J, type,
    member1976670718t_char : option_set_list_char > set_op501702045t_char > $o).
thf(sy_c_member_001t__Option__Ooption_It__Value__Oval_J, type,
    member_option_val : option_val > set_option_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    member652041809on_val : produc515445032on_val > set_Pr723149704on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J, type,
    member1888679917on_val : produc1097884484on_val > set_Pr556513572on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J, type,
    member1296415951on_val : produc266837688on_val > set_Pr2075231726on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_Mt__Product____Type__Oprod_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Option__Ooption_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_M_062_It__Product____Type__Oprod_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Option__Ooption_It__Value__Oval_J_J_J_J_J, type,
    member354538064on_val : produc1172664615on_val > set_Pr1189492743on_val > $o).
thf(sy_c_member_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J, type,
    member_set_list_char : set_list_char > set_set_list_char > $o).
thf(sy_c_member_001t__Value__Oval, type,
    member_val : val > set_val > $o).
thf(sy_v_P, type,
    p : list_P1234162913t_char).
thf(sy_v_a______, type,
    a : nat > option2118145160on_val).
thf(sy_v_aa______, type,
    aa : nat > option2118145160on_val).
thf(sy_v_b______, type,
    b : list_char > option_val).
thf(sy_v_ba______, type,
    ba : list_char > option_val).
thf(sy_v_e_092_060_094sub_0622______, type,
    e_2 : exp_list_char).
thf(sy_v_e_Ha______, type,
    e_a : exp_list_char).
thf(sy_v_ea______, type,
    ea : exp_list_char).

% Relevant facts (212)
thf(fact_0_SeqRed_Oprems, axiom,
    ((d_list_char @ (seq_list_char @ ea @ e_2) @ (some_set_list_char @ (dom_list_char_val @ b))))). % SeqRed.prems
thf(fact_1_SeqRed_Ohyps_I2_J, axiom,
    (((d_list_char @ ea @ (some_set_list_char @ (dom_list_char_val @ b))) => (d_list_char @ e_a @ (some_set_list_char @ (dom_list_char_val @ ba)))))). % SeqRed.hyps(2)
thf(fact_2_SeqRed_Ohyps_I1_J, axiom,
    ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ ea @ (produc52622304on_val @ a @ b)) @ (produc2023458740on_val @ e_a @ (produc52622304on_val @ aa @ ba))) @ (red @ p)))). % SeqRed.hyps(1)
thf(fact_3_exp_Oinject_I11_J, axiom,
    ((![X111 : exp_list_char, X112 : exp_list_char, Y111 : exp_list_char, Y112 : exp_list_char]: (((seq_list_char @ X111 @ X112) = (seq_list_char @ Y111 @ Y112)) = (((X111 = Y111)) & ((X112 = Y112))))))). % exp.inject(11)
thf(fact_4_option_Oinject, axiom,
    ((![X2 : val, Y2 : val]: (((some_val @ X2) = (some_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_5_option_Oinject, axiom,
    ((![X2 : set_list_char, Y2 : set_list_char]: (((some_set_list_char @ X2) = (some_set_list_char @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_6_option_Oinject, axiom,
    ((![X2 : produc266837688on_val, Y2 : produc266837688on_val]: (((some_P1299442195on_val @ X2) = (some_P1299442195on_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_7_domD, axiom,
    ((![A : list_char, M : list_char > option_set_list_char]: ((member_list_char @ A @ (dom_li665594572t_char @ M)) => (?[B : set_list_char]: ((M @ A) = (some_set_list_char @ B))))))). % domD
thf(fact_8_domD, axiom,
    ((![A : list_char, M : list_char > option2118145160on_val]: ((member_list_char @ A @ (dom_li1284435309on_val @ M)) => (?[B : produc266837688on_val]: ((M @ A) = (some_P1299442195on_val @ B))))))). % domD
thf(fact_9_domD, axiom,
    ((![A : produc1172664615on_val, M : produc1172664615on_val > option_val]: ((member354538064on_val @ A @ (dom_Pr162898261al_val @ M)) => (?[B : val]: ((M @ A) = (some_val @ B))))))). % domD
thf(fact_10_domD, axiom,
    ((![A : list_char, M : list_char > option_val]: ((member_list_char @ A @ (dom_list_char_val @ M)) => (?[B : val]: ((M @ A) = (some_val @ B))))))). % domD
thf(fact_11_domD, axiom,
    ((![A : produc1172664615on_val, M : produc1172664615on_val > option_set_list_char]: ((member354538064on_val @ A @ (dom_Pr1335625324t_char @ M)) => (?[B : set_list_char]: ((M @ A) = (some_set_list_char @ B))))))). % domD
thf(fact_12_domD, axiom,
    ((![A : produc1172664615on_val, M : produc1172664615on_val > option2118145160on_val]: ((member354538064on_val @ A @ (dom_Pr269338893on_val @ M)) => (?[B : produc266837688on_val]: ((M @ A) = (some_P1299442195on_val @ B))))))). % domD
thf(fact_13_domI, axiom,
    ((![M : list_char > option_set_list_char, A : list_char, B2 : set_list_char]: (((M @ A) = (some_set_list_char @ B2)) => (member_list_char @ A @ (dom_li665594572t_char @ M)))))). % domI
thf(fact_14_domI, axiom,
    ((![M : list_char > option2118145160on_val, A : list_char, B2 : produc266837688on_val]: (((M @ A) = (some_P1299442195on_val @ B2)) => (member_list_char @ A @ (dom_li1284435309on_val @ M)))))). % domI
thf(fact_15_domI, axiom,
    ((![M : produc1172664615on_val > option_val, A : produc1172664615on_val, B2 : val]: (((M @ A) = (some_val @ B2)) => (member354538064on_val @ A @ (dom_Pr162898261al_val @ M)))))). % domI
thf(fact_16_domI, axiom,
    ((![M : list_char > option_val, A : list_char, B2 : val]: (((M @ A) = (some_val @ B2)) => (member_list_char @ A @ (dom_list_char_val @ M)))))). % domI
thf(fact_17_domI, axiom,
    ((![M : produc1172664615on_val > option_set_list_char, A : produc1172664615on_val, B2 : set_list_char]: (((M @ A) = (some_set_list_char @ B2)) => (member354538064on_val @ A @ (dom_Pr1335625324t_char @ M)))))). % domI
thf(fact_18_domI, axiom,
    ((![M : produc1172664615on_val > option2118145160on_val, A : produc1172664615on_val, B2 : produc266837688on_val]: (((M @ A) = (some_P1299442195on_val @ B2)) => (member354538064on_val @ A @ (dom_Pr269338893on_val @ M)))))). % domI
thf(fact_19_dom__const, axiom,
    ((![F : produc1172664615on_val > set_list_char]: ((dom_Pr1335625324t_char @ (^[X : produc1172664615on_val]: (some_set_list_char @ (F @ X)))) = top_to1683965271on_val)))). % dom_const
thf(fact_20_dom__const, axiom,
    ((![F : produc1172664615on_val > produc266837688on_val]: ((dom_Pr269338893on_val @ (^[X : produc1172664615on_val]: (some_P1299442195on_val @ (F @ X)))) = top_to1683965271on_val)))). % dom_const
thf(fact_21_dom__const, axiom,
    ((![F : list_char > set_list_char]: ((dom_li665594572t_char @ (^[X : list_char]: (some_set_list_char @ (F @ X)))) = top_to748628679t_char)))). % dom_const
thf(fact_22_dom__const, axiom,
    ((![F : list_char > produc266837688on_val]: ((dom_li1284435309on_val @ (^[X : list_char]: (some_P1299442195on_val @ (F @ X)))) = top_to748628679t_char)))). % dom_const
thf(fact_23_dom__const, axiom,
    ((![F : list_char > val]: ((dom_list_char_val @ (^[X : list_char]: (some_val @ (F @ X)))) = top_to748628679t_char)))). % dom_const
thf(fact_24_insert__dom, axiom,
    ((![F : produc1172664615on_val > option_set_list_char, X3 : produc1172664615on_val, Y : set_list_char]: (((F @ X3) = (some_set_list_char @ Y)) => ((insert1971494647on_val @ X3 @ (dom_Pr1335625324t_char @ F)) = (dom_Pr1335625324t_char @ F)))))). % insert_dom
thf(fact_25_insert__dom, axiom,
    ((![F : list_char > option_set_list_char, X3 : list_char, Y : set_list_char]: (((F @ X3) = (some_set_list_char @ Y)) => ((insert_list_char @ X3 @ (dom_li665594572t_char @ F)) = (dom_li665594572t_char @ F)))))). % insert_dom
thf(fact_26_insert__dom, axiom,
    ((![F : produc1172664615on_val > option2118145160on_val, X3 : produc1172664615on_val, Y : produc266837688on_val]: (((F @ X3) = (some_P1299442195on_val @ Y)) => ((insert1971494647on_val @ X3 @ (dom_Pr269338893on_val @ F)) = (dom_Pr269338893on_val @ F)))))). % insert_dom
thf(fact_27_insert__dom, axiom,
    ((![F : list_char > option2118145160on_val, X3 : list_char, Y : produc266837688on_val]: (((F @ X3) = (some_P1299442195on_val @ Y)) => ((insert_list_char @ X3 @ (dom_li1284435309on_val @ F)) = (dom_li1284435309on_val @ F)))))). % insert_dom
thf(fact_28_insert__dom, axiom,
    ((![F : list_char > option_val, X3 : list_char, Y : val]: (((F @ X3) = (some_val @ Y)) => ((insert_list_char @ X3 @ (dom_list_char_val @ F)) = (dom_list_char_val @ F)))))). % insert_dom
thf(fact_29_D__mono, axiom,
    ((![A2 : option_set_list_char, A3 : option_set_list_char, E : exp_list_char]: ((hyper_1448788648t_char @ A2 @ A3) => ((d_list_char @ E @ A2) => (d_list_char @ E @ A3)))))). % D_mono
thf(fact_30_D__mono_H, axiom,
    ((![E : exp_list_char, A2 : option_set_list_char, A3 : option_set_list_char]: ((d_list_char @ E @ A2) => ((hyper_1448788648t_char @ A2 @ A3) => (d_list_char @ E @ A3)))))). % D_mono'
thf(fact_31_combine__options__simps_I3_J, axiom,
    ((![F : set_list_char > set_list_char > set_list_char, A : set_list_char, B2 : set_list_char]: ((combin255359704t_char @ F @ (some_set_list_char @ A) @ (some_set_list_char @ B2)) = (some_set_list_char @ (F @ A @ B2)))))). % combine_options_simps(3)
thf(fact_32_combine__options__simps_I3_J, axiom,
    ((![F : produc266837688on_val > produc266837688on_val > produc266837688on_val, A : produc266837688on_val, B2 : produc266837688on_val]: ((combin1801280889on_val @ F @ (some_P1299442195on_val @ A) @ (some_P1299442195on_val @ B2)) = (some_P1299442195on_val @ (F @ A @ B2)))))). % combine_options_simps(3)
thf(fact_33_combine__options__simps_I3_J, axiom,
    ((![F : val > val > val, A : val, B2 : val]: ((combine_options_val @ F @ (some_val @ A) @ (some_val @ B2)) = (some_val @ (F @ A @ B2)))))). % combine_options_simps(3)
thf(fact_34_red__reds_OSeqRed, axiom,
    ((![E : exp_list_char, S : produc515445032on_val, E2 : exp_list_char, S2 : produc515445032on_val, P : list_P1234162913t_char, E_2 : exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S) @ (produc2023458740on_val @ E2 @ S2)) @ (red @ P)) => (member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ (seq_list_char @ E @ E_2) @ S) @ (produc2023458740on_val @ (seq_list_char @ E2 @ E_2) @ S2)) @ (red @ P)))))). % red_reds.SeqRed
thf(fact_35_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_36_prod__cases4, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (~ ((Y = (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D)))))))))))). % prod_cases4
thf(fact_37_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X3 : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B : exp_list_char, C : nat > option2118145160on_val, D : list_char > option_val]: (P @ (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B @ (produc52622304on_val @ C @ D))))) => (P @ X3))))). % prod_induct4
thf(fact_38_old_Oprod_Oinject, axiom,
    ((![A : produc1097884484on_val, B2 : produc1097884484on_val, A5 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B2) = (produc1069526295on_val @ A5 @ B3)) = (((A = A5)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_39_old_Oprod_Oinject, axiom,
    ((![A : exp_list_char, B2 : produc515445032on_val, A5 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A @ B2) = (produc2023458740on_val @ A5 @ B3)) = (((A = A5)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_40_old_Oprod_Oinject, axiom,
    ((![A : nat > option2118145160on_val, B2 : list_char > option_val, A5 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A @ B2) = (produc52622304on_val @ A5 @ B3)) = (((A = A5)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_41_old_Oprod_Oinject, axiom,
    ((![A : list_char, B2 : produc1257910179t_char > option_val, A5 : list_char, B3 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B2) = (produc904988266on_val @ A5 @ B3)) = (((A = A5)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_42_prod_Oinject, axiom,
    ((![X1 : produc1097884484on_val, X2 : produc1097884484on_val, Y1 : produc1097884484on_val, Y2 : produc1097884484on_val]: (((produc1069526295on_val @ X1 @ X2) = (produc1069526295on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_43_prod_Oinject, axiom,
    ((![X1 : exp_list_char, X2 : produc515445032on_val, Y1 : exp_list_char, Y2 : produc515445032on_val]: (((produc2023458740on_val @ X1 @ X2) = (produc2023458740on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_44_prod_Oinject, axiom,
    ((![X1 : nat > option2118145160on_val, X2 : list_char > option_val, Y1 : nat > option2118145160on_val, Y2 : list_char > option_val]: (((produc52622304on_val @ X1 @ X2) = (produc52622304on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_45_prod_Oinject, axiom,
    ((![X1 : list_char, X2 : produc1257910179t_char > option_val, Y1 : list_char, Y2 : produc1257910179t_char > option_val]: (((produc904988266on_val @ X1 @ X2) = (produc904988266on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_46_old_Oprod_Oinducts, axiom,
    ((![P : produc1172664615on_val > $o, Prod : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A4 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_47_old_Oprod_Oinducts, axiom,
    ((![P : produc1097884484on_val > $o, Prod : produc1097884484on_val]: ((![A4 : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A4 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_48_old_Oprod_Oinducts, axiom,
    ((![P : produc515445032on_val > $o, Prod : produc515445032on_val]: ((![A4 : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A4 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_49_old_Oprod_Oinducts, axiom,
    ((![P : produc266837688on_val > $o, Prod : produc266837688on_val]: ((![A4 : list_char, B : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A4 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_50_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A4 @ B)))))))))). % old.prod.exhaust
thf(fact_51_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A4 : exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A4 @ B)))))))))). % old.prod.exhaust
thf(fact_52_old_Oprod_Oexhaust, axiom,
    ((![Y : produc515445032on_val]: (~ ((![A4 : nat > option2118145160on_val, B : list_char > option_val]: (~ ((Y = (produc52622304on_val @ A4 @ B)))))))))). % old.prod.exhaust
thf(fact_53_old_Oprod_Oexhaust, axiom,
    ((![Y : produc266837688on_val]: (~ ((![A4 : list_char, B : produc1257910179t_char > option_val]: (~ ((Y = (produc904988266on_val @ A4 @ B)))))))))). % old.prod.exhaust
thf(fact_54_Pair__inject, axiom,
    ((![A : produc1097884484on_val, B2 : produc1097884484on_val, A5 : produc1097884484on_val, B3 : produc1097884484on_val]: (((produc1069526295on_val @ A @ B2) = (produc1069526295on_val @ A5 @ B3)) => (~ (((A = A5) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_55_Pair__inject, axiom,
    ((![A : exp_list_char, B2 : produc515445032on_val, A5 : exp_list_char, B3 : produc515445032on_val]: (((produc2023458740on_val @ A @ B2) = (produc2023458740on_val @ A5 @ B3)) => (~ (((A = A5) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_56_Pair__inject, axiom,
    ((![A : nat > option2118145160on_val, B2 : list_char > option_val, A5 : nat > option2118145160on_val, B3 : list_char > option_val]: (((produc52622304on_val @ A @ B2) = (produc52622304on_val @ A5 @ B3)) => (~ (((A = A5) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_57_Pair__inject, axiom,
    ((![A : list_char, B2 : produc1257910179t_char > option_val, A5 : list_char, B3 : produc1257910179t_char > option_val]: (((produc904988266on_val @ A @ B2) = (produc904988266on_val @ A5 @ B3)) => (~ (((A = A5) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_58_prod__cases, axiom,
    ((![P : produc1172664615on_val > $o, P2 : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B : produc1097884484on_val]: (P @ (produc1069526295on_val @ A4 @ B))) => (P @ P2))))). % prod_cases
thf(fact_59_prod__cases, axiom,
    ((![P : produc1097884484on_val > $o, P2 : produc1097884484on_val]: ((![A4 : exp_list_char, B : produc515445032on_val]: (P @ (produc2023458740on_val @ A4 @ B))) => (P @ P2))))). % prod_cases
thf(fact_60_prod__cases, axiom,
    ((![P : produc515445032on_val > $o, P2 : produc515445032on_val]: ((![A4 : nat > option2118145160on_val, B : list_char > option_val]: (P @ (produc52622304on_val @ A4 @ B))) => (P @ P2))))). % prod_cases
thf(fact_61_prod__cases, axiom,
    ((![P : produc266837688on_val > $o, P2 : produc266837688on_val]: ((![A4 : list_char, B : produc1257910179t_char > option_val]: (P @ (produc904988266on_val @ A4 @ B))) => (P @ P2))))). % prod_cases
thf(fact_62_surj__pair, axiom,
    ((![P2 : produc1172664615on_val]: (?[X4 : produc1097884484on_val, Y3 : produc1097884484on_val]: (P2 = (produc1069526295on_val @ X4 @ Y3)))))). % surj_pair
thf(fact_63_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X4 : exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X4 @ Y3)))))). % surj_pair
thf(fact_64_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X4 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P2 = (produc52622304on_val @ X4 @ Y3)))))). % surj_pair
thf(fact_65_surj__pair, axiom,
    ((![P2 : produc266837688on_val]: (?[X4 : list_char, Y3 : produc1257910179t_char > option_val]: (P2 = (produc904988266on_val @ X4 @ Y3)))))). % surj_pair
thf(fact_66_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X3 : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (P @ (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B @ C)))) => (P @ X3))))). % prod_induct3
thf(fact_67_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X3 : produc1097884484on_val]: ((![A4 : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2023458740on_val @ A4 @ (produc52622304on_val @ B @ C)))) => (P @ X3))))). % prod_induct3
thf(fact_68_prod__cases3, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (~ ((Y = (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B @ C))))))))))). % prod_cases3
thf(fact_69_prod__cases3, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A4 : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc2023458740on_val @ A4 @ (produc52622304on_val @ B @ C))))))))))). % prod_cases3
thf(fact_70_iso__tuple__UNIV__I, axiom,
    ((![X3 : produc1172664615on_val]: (member354538064on_val @ X3 @ top_to1683965271on_val)))). % iso_tuple_UNIV_I
thf(fact_71_iso__tuple__UNIV__I, axiom,
    ((![X3 : list_char]: (member_list_char @ X3 @ top_to748628679t_char)))). % iso_tuple_UNIV_I
thf(fact_72_UNIV__I, axiom,
    ((![X3 : produc1172664615on_val]: (member354538064on_val @ X3 @ top_to1683965271on_val)))). % UNIV_I
thf(fact_73_UNIV__I, axiom,
    ((![X3 : list_char]: (member_list_char @ X3 @ top_to748628679t_char)))). % UNIV_I
thf(fact_74_insert__absorb2, axiom,
    ((![X3 : list_char, A2 : set_list_char]: ((insert_list_char @ X3 @ (insert_list_char @ X3 @ A2)) = (insert_list_char @ X3 @ A2))))). % insert_absorb2
thf(fact_75_insert__iff, axiom,
    ((![A : produc1172664615on_val, B2 : produc1172664615on_val, A2 : set_Pr1189492743on_val]: ((member354538064on_val @ A @ (insert1971494647on_val @ B2 @ A2)) = (((A = B2)) | ((member354538064on_val @ A @ A2))))))). % insert_iff
thf(fact_76_insert__iff, axiom,
    ((![A : list_char, B2 : list_char, A2 : set_list_char]: ((member_list_char @ A @ (insert_list_char @ B2 @ A2)) = (((A = B2)) | ((member_list_char @ A @ A2))))))). % insert_iff
thf(fact_77_insertCI, axiom,
    ((![A : produc1172664615on_val, B4 : set_Pr1189492743on_val, B2 : produc1172664615on_val]: (((~ ((member354538064on_val @ A @ B4))) => (A = B2)) => (member354538064on_val @ A @ (insert1971494647on_val @ B2 @ B4)))))). % insertCI
thf(fact_78_insertCI, axiom,
    ((![A : list_char, B4 : set_list_char, B2 : list_char]: (((~ ((member_list_char @ A @ B4))) => (A = B2)) => (member_list_char @ A @ (insert_list_char @ B2 @ B4)))))). % insertCI
thf(fact_79_insert__UNIV, axiom,
    ((![X3 : list_char]: ((insert_list_char @ X3 @ top_to748628679t_char) = top_to748628679t_char)))). % insert_UNIV
thf(fact_80_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_81_mem__Collect__eq, axiom,
    ((![A : list_char, P : list_char > $o]: ((member_list_char @ A @ (collect_list_char @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_82_Collect__mem__eq, axiom,
    ((![A2 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X : produc1172664615on_val]: (member354538064on_val @ X @ A2))) = A2)))). % Collect_mem_eq
thf(fact_83_Collect__mem__eq, axiom,
    ((![A2 : set_list_char]: ((collect_list_char @ (^[X : list_char]: (member_list_char @ X @ A2))) = A2)))). % Collect_mem_eq
thf(fact_84_top__set__def, axiom,
    ((top_to748628679t_char = (collect_list_char @ top_top_list_char_o)))). % top_set_def
thf(fact_85_insertE, axiom,
    ((![A : produc1172664615on_val, B2 : produc1172664615on_val, A2 : set_Pr1189492743on_val]: ((member354538064on_val @ A @ (insert1971494647on_val @ B2 @ A2)) => ((~ ((A = B2))) => (member354538064on_val @ A @ A2)))))). % insertE
thf(fact_86_insertE, axiom,
    ((![A : list_char, B2 : list_char, A2 : set_list_char]: ((member_list_char @ A @ (insert_list_char @ B2 @ A2)) => ((~ ((A = B2))) => (member_list_char @ A @ A2)))))). % insertE
thf(fact_87_insertI1, axiom,
    ((![A : produc1172664615on_val, B4 : set_Pr1189492743on_val]: (member354538064on_val @ A @ (insert1971494647on_val @ A @ B4))))). % insertI1
thf(fact_88_insertI1, axiom,
    ((![A : list_char, B4 : set_list_char]: (member_list_char @ A @ (insert_list_char @ A @ B4))))). % insertI1
thf(fact_89_insertI2, axiom,
    ((![A : produc1172664615on_val, B4 : set_Pr1189492743on_val, B2 : produc1172664615on_val]: ((member354538064on_val @ A @ B4) => (member354538064on_val @ A @ (insert1971494647on_val @ B2 @ B4)))))). % insertI2
thf(fact_90_insertI2, axiom,
    ((![A : list_char, B4 : set_list_char, B2 : list_char]: ((member_list_char @ A @ B4) => (member_list_char @ A @ (insert_list_char @ B2 @ B4)))))). % insertI2
thf(fact_91_Set_Oset__insert, axiom,
    ((![X3 : produc1172664615on_val, A2 : set_Pr1189492743on_val]: ((member354538064on_val @ X3 @ A2) => (~ ((![B5 : set_Pr1189492743on_val]: ((A2 = (insert1971494647on_val @ X3 @ B5)) => (member354538064on_val @ X3 @ B5))))))))). % Set.set_insert
thf(fact_92_Set_Oset__insert, axiom,
    ((![X3 : list_char, A2 : set_list_char]: ((member_list_char @ X3 @ A2) => (~ ((![B5 : set_list_char]: ((A2 = (insert_list_char @ X3 @ B5)) => (member_list_char @ X3 @ B5))))))))). % Set.set_insert
thf(fact_93_insert__ident, axiom,
    ((![X3 : produc1172664615on_val, A2 : set_Pr1189492743on_val, B4 : set_Pr1189492743on_val]: ((~ ((member354538064on_val @ X3 @ A2))) => ((~ ((member354538064on_val @ X3 @ B4))) => (((insert1971494647on_val @ X3 @ A2) = (insert1971494647on_val @ X3 @ B4)) = (A2 = B4))))))). % insert_ident
thf(fact_94_insert__ident, axiom,
    ((![X3 : list_char, A2 : set_list_char, B4 : set_list_char]: ((~ ((member_list_char @ X3 @ A2))) => ((~ ((member_list_char @ X3 @ B4))) => (((insert_list_char @ X3 @ A2) = (insert_list_char @ X3 @ B4)) = (A2 = B4))))))). % insert_ident
thf(fact_95_insert__absorb, axiom,
    ((![A : produc1172664615on_val, A2 : set_Pr1189492743on_val]: ((member354538064on_val @ A @ A2) => ((insert1971494647on_val @ A @ A2) = A2))))). % insert_absorb
thf(fact_96_insert__absorb, axiom,
    ((![A : list_char, A2 : set_list_char]: ((member_list_char @ A @ A2) => ((insert_list_char @ A @ A2) = A2))))). % insert_absorb
thf(fact_97_insert__eq__iff, axiom,
    ((![A : produc1172664615on_val, A2 : set_Pr1189492743on_val, B2 : produc1172664615on_val, B4 : set_Pr1189492743on_val]: ((~ ((member354538064on_val @ A @ A2))) => ((~ ((member354538064on_val @ B2 @ B4))) => (((insert1971494647on_val @ A @ A2) = (insert1971494647on_val @ B2 @ B4)) = (((((A = B2)) => ((A2 = B4)))) & ((((~ ((A = B2)))) => ((?[C2 : set_Pr1189492743on_val]: (((A2 = (insert1971494647on_val @ B2 @ C2))) & ((((~ ((member354538064on_val @ B2 @ C2)))) & ((((B4 = (insert1971494647on_val @ A @ C2))) & ((~ ((member354538064on_val @ A @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_98_insert__eq__iff, axiom,
    ((![A : list_char, A2 : set_list_char, B2 : list_char, B4 : set_list_char]: ((~ ((member_list_char @ A @ A2))) => ((~ ((member_list_char @ B2 @ B4))) => (((insert_list_char @ A @ A2) = (insert_list_char @ B2 @ B4)) = (((((A = B2)) => ((A2 = B4)))) & ((((~ ((A = B2)))) => ((?[C2 : set_list_char]: (((A2 = (insert_list_char @ B2 @ C2))) & ((((~ ((member_list_char @ B2 @ C2)))) & ((((B4 = (insert_list_char @ A @ C2))) & ((~ ((member_list_char @ A @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_99_insert__commute, axiom,
    ((![X3 : list_char, Y : list_char, A2 : set_list_char]: ((insert_list_char @ X3 @ (insert_list_char @ Y @ A2)) = (insert_list_char @ Y @ (insert_list_char @ X3 @ A2)))))). % insert_commute
thf(fact_100_mk__disjoint__insert, axiom,
    ((![A : produc1172664615on_val, A2 : set_Pr1189492743on_val]: ((member354538064on_val @ A @ A2) => (?[B5 : set_Pr1189492743on_val]: ((A2 = (insert1971494647on_val @ A @ B5)) & (~ ((member354538064on_val @ A @ B5))))))))). % mk_disjoint_insert
thf(fact_101_mk__disjoint__insert, axiom,
    ((![A : list_char, A2 : set_list_char]: ((member_list_char @ A @ A2) => (?[B5 : set_list_char]: ((A2 = (insert_list_char @ A @ B5)) & (~ ((member_list_char @ A @ B5))))))))). % mk_disjoint_insert
thf(fact_102_UNIV__eq__I, axiom,
    ((![A2 : set_Pr1189492743on_val]: ((![X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ A2)) => (top_to1683965271on_val = A2))))). % UNIV_eq_I
thf(fact_103_UNIV__eq__I, axiom,
    ((![A2 : set_list_char]: ((![X4 : list_char]: (member_list_char @ X4 @ A2)) => (top_to748628679t_char = A2))))). % UNIV_eq_I
thf(fact_104_UNIV__witness, axiom,
    ((?[X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ top_to1683965271on_val)))). % UNIV_witness
thf(fact_105_UNIV__witness, axiom,
    ((?[X4 : list_char]: (member_list_char @ X4 @ top_to748628679t_char)))). % UNIV_witness
thf(fact_106_insert__compr, axiom,
    ((insert1971494647on_val = (^[A6 : produc1172664615on_val]: (^[B6 : set_Pr1189492743on_val]: (collec2055896722on_val @ (^[X : produc1172664615on_val]: (((X = A6)) | ((member354538064on_val @ X @ B6)))))))))). % insert_compr
thf(fact_107_insert__compr, axiom,
    ((insert_list_char = (^[A6 : list_char]: (^[B6 : set_list_char]: (collect_list_char @ (^[X : list_char]: (((X = A6)) | ((member_list_char @ X @ B6)))))))))). % insert_compr
thf(fact_108_insert__Collect, axiom,
    ((![A : list_char, P : list_char > $o]: ((insert_list_char @ A @ (collect_list_char @ P)) = (collect_list_char @ (^[U : list_char]: (((~ ((U = A)))) => ((P @ U))))))))). % insert_Collect
thf(fact_109_UNIV__def, axiom,
    ((top_to748628679t_char = (collect_list_char @ (^[X : list_char]: $true))))). % UNIV_def
thf(fact_110_red__lcl__incr, axiom,
    ((![E : exp_list_char, H_0 : nat > option2118145160on_val, L_0 : list_char > option_val, E2 : exp_list_char, H_1 : nat > option2118145160on_val, L_1 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H_0 @ L_0)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H_1 @ L_1))) @ (red @ P)) => (ord_le1836582007t_char @ (dom_list_char_val @ L_0) @ (dom_list_char_val @ L_1)))))). % red_lcl_incr
thf(fact_111_red__hext__incr, axiom,
    ((![E : exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, E2 : exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ (produc52622304on_val @ H @ L)) @ (produc2023458740on_val @ E2 @ (produc52622304on_val @ H2 @ L2))) @ (red @ P)) => (hext @ H @ H2))))). % red_hext_incr
thf(fact_112_these__insert__Some, axiom,
    ((![X3 : list_char, A2 : set_option_list_char]: ((these_list_char @ (insert523167969t_char @ (some_list_char @ X3) @ A2)) = (insert_list_char @ X3 @ (these_list_char @ A2)))))). % these_insert_Some
thf(fact_113_these__insert__Some, axiom,
    ((![X3 : set_list_char, A2 : set_op501702045t_char]: ((these_set_list_char @ (insert433234071t_char @ (some_set_list_char @ X3) @ A2)) = (insert_set_list_char @ X3 @ (these_set_list_char @ A2)))))). % these_insert_Some
thf(fact_114_these__insert__Some, axiom,
    ((![X3 : produc266837688on_val, A2 : set_op1111598910on_val]: ((these_538817979on_val @ (insert1333207736on_val @ (some_P1299442195on_val @ X3) @ A2)) = (insert688092392on_val @ X3 @ (these_538817979on_val @ A2)))))). % these_insert_Some
thf(fact_115_these__insert__Some, axiom,
    ((![X3 : val, A2 : set_option_val]: ((these_val @ (insert_option_val @ (some_val @ X3) @ A2)) = (insert_val @ X3 @ (these_val @ A2)))))). % these_insert_Some
thf(fact_116_top__empty__eq2, axiom,
    ((top_to1666156862_val_o = (^[X : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X @ Y4) @ top_to1683965271on_val)))))). % top_empty_eq2
thf(fact_117_top__empty__eq2, axiom,
    ((top_to2035973601_val_o = (^[X : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X @ Y4) @ top_to796958324on_val)))))). % top_empty_eq2
thf(fact_118_top__empty__eq2, axiom,
    ((top_to1645522895_val_o = (^[X : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X @ Y4) @ top_to374550744on_val)))))). % top_empty_eq2
thf(fact_119_top__empty__eq2, axiom,
    ((top_to1286271689_val_o = (^[X : list_char]: (^[Y4 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X @ Y4) @ top_to624090270on_val)))))). % top_empty_eq2
thf(fact_120_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S3 : set_Pr1189492743on_val]: (((^[X : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X @ Y4) @ R))) = (^[X : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X @ Y4) @ S3)))) = (R = S3))))). % pred_equals_eq2
thf(fact_121_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S3 : set_Pr556513572on_val]: (((^[X : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X @ Y4) @ R))) = (^[X : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X @ Y4) @ S3)))) = (R = S3))))). % pred_equals_eq2
thf(fact_122_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S3 : set_Pr723149704on_val]: (((^[X : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X @ Y4) @ R))) = (^[X : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X @ Y4) @ S3)))) = (R = S3))))). % pred_equals_eq2
thf(fact_123_pred__equals__eq2, axiom,
    ((![R : set_Pr2075231726on_val, S3 : set_Pr2075231726on_val]: (((^[X : list_char]: (^[Y4 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X @ Y4) @ R))) = (^[X : list_char]: (^[Y4 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X @ Y4) @ S3)))) = (R = S3))))). % pred_equals_eq2
thf(fact_124_order__refl, axiom,
    ((![X3 : set_list_char]: (ord_le1836582007t_char @ X3 @ X3)))). % order_refl
thf(fact_125_subsetI, axiom,
    ((![A2 : set_Pr1189492743on_val, B4 : set_Pr1189492743on_val]: ((![X4 : produc1172664615on_val]: ((member354538064on_val @ X4 @ A2) => (member354538064on_val @ X4 @ B4))) => (ord_le837504935on_val @ A2 @ B4))))). % subsetI
thf(fact_126_subsetI, axiom,
    ((![A2 : set_list_char, B4 : set_list_char]: ((![X4 : list_char]: ((member_list_char @ X4 @ A2) => (member_list_char @ X4 @ B4))) => (ord_le1836582007t_char @ A2 @ B4))))). % subsetI
thf(fact_127_subset__antisym, axiom,
    ((![A2 : set_list_char, B4 : set_list_char]: ((ord_le1836582007t_char @ A2 @ B4) => ((ord_le1836582007t_char @ B4 @ A2) => (A2 = B4)))))). % subset_antisym
thf(fact_128_insert__subset, axiom,
    ((![X3 : produc1172664615on_val, A2 : set_Pr1189492743on_val, B4 : set_Pr1189492743on_val]: ((ord_le837504935on_val @ (insert1971494647on_val @ X3 @ A2) @ B4) = (((member354538064on_val @ X3 @ B4)) & ((ord_le837504935on_val @ A2 @ B4))))))). % insert_subset
thf(fact_129_insert__subset, axiom,
    ((![X3 : list_char, A2 : set_list_char, B4 : set_list_char]: ((ord_le1836582007t_char @ (insert_list_char @ X3 @ A2) @ B4) = (((member_list_char @ X3 @ B4)) & ((ord_le1836582007t_char @ A2 @ B4))))))). % insert_subset
thf(fact_130_in__mono, axiom,
    ((![A2 : set_Pr1189492743on_val, B4 : set_Pr1189492743on_val, X3 : produc1172664615on_val]: ((ord_le837504935on_val @ A2 @ B4) => ((member354538064on_val @ X3 @ A2) => (member354538064on_val @ X3 @ B4)))))). % in_mono
thf(fact_131_in__mono, axiom,
    ((![A2 : set_list_char, B4 : set_list_char, X3 : list_char]: ((ord_le1836582007t_char @ A2 @ B4) => ((member_list_char @ X3 @ A2) => (member_list_char @ X3 @ B4)))))). % in_mono
thf(fact_132_subsetD, axiom,
    ((![A2 : set_Pr1189492743on_val, B4 : set_Pr1189492743on_val, C3 : produc1172664615on_val]: ((ord_le837504935on_val @ A2 @ B4) => ((member354538064on_val @ C3 @ A2) => (member354538064on_val @ C3 @ B4)))))). % subsetD
thf(fact_133_subsetD, axiom,
    ((![A2 : set_list_char, B4 : set_list_char, C3 : list_char]: ((ord_le1836582007t_char @ A2 @ B4) => ((member_list_char @ C3 @ A2) => (member_list_char @ C3 @ B4)))))). % subsetD
thf(fact_134_equalityE, axiom,
    ((![A2 : set_list_char, B4 : set_list_char]: ((A2 = B4) => (~ (((ord_le1836582007t_char @ A2 @ B4) => (~ ((ord_le1836582007t_char @ B4 @ A2)))))))))). % equalityE
thf(fact_135_subset__eq, axiom,
    ((ord_le837504935on_val = (^[A7 : set_Pr1189492743on_val]: (^[B6 : set_Pr1189492743on_val]: (![X : produc1172664615on_val]: (((member354538064on_val @ X @ A7)) => ((member354538064on_val @ X @ B6))))))))). % subset_eq
thf(fact_136_subset__eq, axiom,
    ((ord_le1836582007t_char = (^[A7 : set_list_char]: (^[B6 : set_list_char]: (![X : list_char]: (((member_list_char @ X @ A7)) => ((member_list_char @ X @ B6))))))))). % subset_eq
thf(fact_137_equalityD1, axiom,
    ((![A2 : set_list_char, B4 : set_list_char]: ((A2 = B4) => (ord_le1836582007t_char @ A2 @ B4))))). % equalityD1
thf(fact_138_equalityD2, axiom,
    ((![A2 : set_list_char, B4 : set_list_char]: ((A2 = B4) => (ord_le1836582007t_char @ B4 @ A2))))). % equalityD2
thf(fact_139_subset__iff, axiom,
    ((ord_le837504935on_val = (^[A7 : set_Pr1189492743on_val]: (^[B6 : set_Pr1189492743on_val]: (![T : produc1172664615on_val]: (((member354538064on_val @ T @ A7)) => ((member354538064on_val @ T @ B6))))))))). % subset_iff
thf(fact_140_subset__iff, axiom,
    ((ord_le1836582007t_char = (^[A7 : set_list_char]: (^[B6 : set_list_char]: (![T : list_char]: (((member_list_char @ T @ A7)) => ((member_list_char @ T @ B6))))))))). % subset_iff
thf(fact_141_subset__refl, axiom,
    ((![A2 : set_list_char]: (ord_le1836582007t_char @ A2 @ A2)))). % subset_refl
thf(fact_142_Collect__mono, axiom,
    ((![P : list_char > $o, Q : list_char > $o]: ((![X4 : list_char]: ((P @ X4) => (Q @ X4))) => (ord_le1836582007t_char @ (collect_list_char @ P) @ (collect_list_char @ Q)))))). % Collect_mono
thf(fact_143_subset__trans, axiom,
    ((![A2 : set_list_char, B4 : set_list_char, C4 : set_list_char]: ((ord_le1836582007t_char @ A2 @ B4) => ((ord_le1836582007t_char @ B4 @ C4) => (ord_le1836582007t_char @ A2 @ C4)))))). % subset_trans
thf(fact_144_set__eq__subset, axiom,
    (((^[Y5 : set_list_char]: (^[Z : set_list_char]: (Y5 = Z))) = (^[A7 : set_list_char]: (^[B6 : set_list_char]: (((ord_le1836582007t_char @ A7 @ B6)) & ((ord_le1836582007t_char @ B6 @ A7)))))))). % set_eq_subset
thf(fact_145_Collect__subset, axiom,
    ((![A2 : set_Pr1189492743on_val, P : produc1172664615on_val > $o]: (ord_le837504935on_val @ (collec2055896722on_val @ (^[X : produc1172664615on_val]: (((member354538064on_val @ X @ A2)) & ((P @ X))))) @ A2)))). % Collect_subset
thf(fact_146_Collect__subset, axiom,
    ((![A2 : set_list_char, P : list_char > $o]: (ord_le1836582007t_char @ (collect_list_char @ (^[X : list_char]: (((member_list_char @ X @ A2)) & ((P @ X))))) @ A2)))). % Collect_subset
thf(fact_147_Collect__mono__iff, axiom,
    ((![P : list_char > $o, Q : list_char > $o]: ((ord_le1836582007t_char @ (collect_list_char @ P) @ (collect_list_char @ Q)) = (![X : list_char]: (((P @ X)) => ((Q @ X)))))))). % Collect_mono_iff
thf(fact_148_order__subst1, axiom,
    ((![A : set_list_char, F : set_list_char > set_list_char, B2 : set_list_char, C3 : set_list_char]: ((ord_le1836582007t_char @ A @ (F @ B2)) => ((ord_le1836582007t_char @ B2 @ C3) => ((![X4 : set_list_char, Y3 : set_list_char]: ((ord_le1836582007t_char @ X4 @ Y3) => (ord_le1836582007t_char @ (F @ X4) @ (F @ Y3)))) => (ord_le1836582007t_char @ A @ (F @ C3)))))))). % order_subst1
thf(fact_149_order__subst2, axiom,
    ((![A : set_list_char, B2 : set_list_char, F : set_list_char > set_list_char, C3 : set_list_char]: ((ord_le1836582007t_char @ A @ B2) => ((ord_le1836582007t_char @ (F @ B2) @ C3) => ((![X4 : set_list_char, Y3 : set_list_char]: ((ord_le1836582007t_char @ X4 @ Y3) => (ord_le1836582007t_char @ (F @ X4) @ (F @ Y3)))) => (ord_le1836582007t_char @ (F @ A) @ C3))))))). % order_subst2
thf(fact_150_ord__eq__le__subst, axiom,
    ((![A : set_list_char, F : set_list_char > set_list_char, B2 : set_list_char, C3 : set_list_char]: ((A = (F @ B2)) => ((ord_le1836582007t_char @ B2 @ C3) => ((![X4 : set_list_char, Y3 : set_list_char]: ((ord_le1836582007t_char @ X4 @ Y3) => (ord_le1836582007t_char @ (F @ X4) @ (F @ Y3)))) => (ord_le1836582007t_char @ A @ (F @ C3)))))))). % ord_eq_le_subst
thf(fact_151_ord__le__eq__subst, axiom,
    ((![A : set_list_char, B2 : set_list_char, F : set_list_char > set_list_char, C3 : set_list_char]: ((ord_le1836582007t_char @ A @ B2) => (((F @ B2) = C3) => ((![X4 : set_list_char, Y3 : set_list_char]: ((ord_le1836582007t_char @ X4 @ Y3) => (ord_le1836582007t_char @ (F @ X4) @ (F @ Y3)))) => (ord_le1836582007t_char @ (F @ A) @ C3))))))). % ord_le_eq_subst
thf(fact_152_eq__iff, axiom,
    (((^[Y5 : set_list_char]: (^[Z : set_list_char]: (Y5 = Z))) = (^[X : set_list_char]: (^[Y4 : set_list_char]: (((ord_le1836582007t_char @ X @ Y4)) & ((ord_le1836582007t_char @ Y4 @ X)))))))). % eq_iff
thf(fact_153_antisym, axiom,
    ((![X3 : set_list_char, Y : set_list_char]: ((ord_le1836582007t_char @ X3 @ Y) => ((ord_le1836582007t_char @ Y @ X3) => (X3 = Y)))))). % antisym
thf(fact_154_eq__refl, axiom,
    ((![X3 : set_list_char, Y : set_list_char]: ((X3 = Y) => (ord_le1836582007t_char @ X3 @ Y))))). % eq_refl
thf(fact_155_order_Otrans, axiom,
    ((![A : set_list_char, B2 : set_list_char, C3 : set_list_char]: ((ord_le1836582007t_char @ A @ B2) => ((ord_le1836582007t_char @ B2 @ C3) => (ord_le1836582007t_char @ A @ C3)))))). % order.trans
thf(fact_156_antisym__conv, axiom,
    ((![Y : set_list_char, X3 : set_list_char]: ((ord_le1836582007t_char @ Y @ X3) => ((ord_le1836582007t_char @ X3 @ Y) = (X3 = Y)))))). % antisym_conv
thf(fact_157_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y5 : set_list_char]: (^[Z : set_list_char]: (Y5 = Z))) = (^[A6 : set_list_char]: (^[B7 : set_list_char]: (((ord_le1836582007t_char @ A6 @ B7)) & ((ord_le1836582007t_char @ B7 @ A6)))))))). % order_class.order.eq_iff
thf(fact_158_ord__eq__le__trans, axiom,
    ((![A : set_list_char, B2 : set_list_char, C3 : set_list_char]: ((A = B2) => ((ord_le1836582007t_char @ B2 @ C3) => (ord_le1836582007t_char @ A @ C3)))))). % ord_eq_le_trans
thf(fact_159_ord__le__eq__trans, axiom,
    ((![A : set_list_char, B2 : set_list_char, C3 : set_list_char]: ((ord_le1836582007t_char @ A @ B2) => ((B2 = C3) => (ord_le1836582007t_char @ A @ C3)))))). % ord_le_eq_trans
thf(fact_160_order__class_Oorder_Oantisym, axiom,
    ((![A : set_list_char, B2 : set_list_char]: ((ord_le1836582007t_char @ A @ B2) => ((ord_le1836582007t_char @ B2 @ A) => (A = B2)))))). % order_class.order.antisym
thf(fact_161_order__trans, axiom,
    ((![X3 : set_list_char, Y : set_list_char, Z2 : set_list_char]: ((ord_le1836582007t_char @ X3 @ Y) => ((ord_le1836582007t_char @ Y @ Z2) => (ord_le1836582007t_char @ X3 @ Z2)))))). % order_trans
thf(fact_162_dual__order_Orefl, axiom,
    ((![A : set_list_char]: (ord_le1836582007t_char @ A @ A)))). % dual_order.refl
thf(fact_163_dual__order_Otrans, axiom,
    ((![B2 : set_list_char, A : set_list_char, C3 : set_list_char]: ((ord_le1836582007t_char @ B2 @ A) => ((ord_le1836582007t_char @ C3 @ B2) => (ord_le1836582007t_char @ C3 @ A)))))). % dual_order.trans
thf(fact_164_dual__order_Oeq__iff, axiom,
    (((^[Y5 : set_list_char]: (^[Z : set_list_char]: (Y5 = Z))) = (^[A6 : set_list_char]: (^[B7 : set_list_char]: (((ord_le1836582007t_char @ B7 @ A6)) & ((ord_le1836582007t_char @ A6 @ B7)))))))). % dual_order.eq_iff
thf(fact_165_dual__order_Oantisym, axiom,
    ((![B2 : set_list_char, A : set_list_char]: ((ord_le1836582007t_char @ B2 @ A) => ((ord_le1836582007t_char @ A @ B2) => (A = B2)))))). % dual_order.antisym
thf(fact_166_top__greatest, axiom,
    ((![A : set_list_char]: (ord_le1836582007t_char @ A @ top_to748628679t_char)))). % top_greatest
thf(fact_167_top_Oextremum__unique, axiom,
    ((![A : set_list_char]: ((ord_le1836582007t_char @ top_to748628679t_char @ A) = (A = top_to748628679t_char))))). % top.extremum_unique
thf(fact_168_top_Oextremum__uniqueI, axiom,
    ((![A : set_list_char]: ((ord_le1836582007t_char @ top_to748628679t_char @ A) => (A = top_to748628679t_char))))). % top.extremum_uniqueI
thf(fact_169_insert__mono, axiom,
    ((![C4 : set_list_char, D2 : set_list_char, A : list_char]: ((ord_le1836582007t_char @ C4 @ D2) => (ord_le1836582007t_char @ (insert_list_char @ A @ C4) @ (insert_list_char @ A @ D2)))))). % insert_mono
thf(fact_170_subset__insert, axiom,
    ((![X3 : produc1172664615on_val, A2 : set_Pr1189492743on_val, B4 : set_Pr1189492743on_val]: ((~ ((member354538064on_val @ X3 @ A2))) => ((ord_le837504935on_val @ A2 @ (insert1971494647on_val @ X3 @ B4)) = (ord_le837504935on_val @ A2 @ B4)))))). % subset_insert
thf(fact_171_subset__insert, axiom,
    ((![X3 : list_char, A2 : set_list_char, B4 : set_list_char]: ((~ ((member_list_char @ X3 @ A2))) => ((ord_le1836582007t_char @ A2 @ (insert_list_char @ X3 @ B4)) = (ord_le1836582007t_char @ A2 @ B4)))))). % subset_insert
thf(fact_172_subset__insertI, axiom,
    ((![B4 : set_list_char, A : list_char]: (ord_le1836582007t_char @ B4 @ (insert_list_char @ A @ B4))))). % subset_insertI
thf(fact_173_subset__insertI2, axiom,
    ((![A2 : set_list_char, B4 : set_list_char, B2 : list_char]: ((ord_le1836582007t_char @ A2 @ B4) => (ord_le1836582007t_char @ A2 @ (insert_list_char @ B2 @ B4)))))). % subset_insertI2
thf(fact_174_subset__UNIV, axiom,
    ((![A2 : set_list_char]: (ord_le1836582007t_char @ A2 @ top_to748628679t_char)))). % subset_UNIV
thf(fact_175_in__these__eq, axiom,
    ((![X3 : produc1172664615on_val, A2 : set_op787718477on_val]: ((member354538064on_val @ X3 @ (these_1398366820on_val @ A2)) = (member1869742230on_val @ (some_P83435532on_val @ X3) @ A2))))). % in_these_eq
thf(fact_176_in__these__eq, axiom,
    ((![X3 : list_char, A2 : set_option_list_char]: ((member_list_char @ X3 @ (these_list_char @ A2)) = (member246349384t_char @ (some_list_char @ X3) @ A2))))). % in_these_eq
thf(fact_177_in__these__eq, axiom,
    ((![X3 : set_list_char, A2 : set_op501702045t_char]: ((member_set_list_char @ X3 @ (these_set_list_char @ A2)) = (member1976670718t_char @ (some_set_list_char @ X3) @ A2))))). % in_these_eq
thf(fact_178_in__these__eq, axiom,
    ((![X3 : produc266837688on_val, A2 : set_op1111598910on_val]: ((member1296415951on_val @ X3 @ (these_538817979on_val @ A2)) = (member1048249375on_val @ (some_P1299442195on_val @ X3) @ A2))))). % in_these_eq
thf(fact_179_in__these__eq, axiom,
    ((![X3 : val, A2 : set_option_val]: ((member_val @ X3 @ (these_val @ A2)) = (member_option_val @ (some_val @ X3) @ A2))))). % in_these_eq
thf(fact_180_top__empty__eq, axiom,
    ((top_to1455478342_val_o = (^[X : produc1172664615on_val]: (member354538064on_val @ X @ top_to1683965271on_val))))). % top_empty_eq
thf(fact_181_top__empty__eq, axiom,
    ((top_top_list_char_o = (^[X : list_char]: (member_list_char @ X @ top_to748628679t_char))))). % top_empty_eq
thf(fact_182_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_183_insert__subsetI, axiom,
    ((![X3 : produc1172664615on_val, A2 : set_Pr1189492743on_val, X5 : set_Pr1189492743on_val]: ((member354538064on_val @ X3 @ A2) => ((ord_le837504935on_val @ X5 @ A2) => (ord_le837504935on_val @ (insert1971494647on_val @ X3 @ X5) @ A2)))))). % insert_subsetI
thf(fact_184_insert__subsetI, axiom,
    ((![X3 : list_char, A2 : set_list_char, X5 : set_list_char]: ((member_list_char @ X3 @ A2) => ((ord_le1836582007t_char @ X5 @ A2) => (ord_le1836582007t_char @ (insert_list_char @ X3 @ X5) @ A2)))))). % insert_subsetI
thf(fact_185_subrelI, axiom,
    ((![R2 : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: ((![X4 : produc1097884484on_val, Y3 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ X4 @ Y3) @ R2) => (member354538064on_val @ (produc1069526295on_val @ X4 @ Y3) @ S))) => (ord_le837504935on_val @ R2 @ S))))). % subrelI
thf(fact_186_subrelI, axiom,
    ((![R2 : set_Pr556513572on_val, S : set_Pr556513572on_val]: ((![X4 : exp_list_char, Y3 : produc515445032on_val]: ((member1888679917on_val @ (produc2023458740on_val @ X4 @ Y3) @ R2) => (member1888679917on_val @ (produc2023458740on_val @ X4 @ Y3) @ S))) => (ord_le131203268on_val @ R2 @ S))))). % subrelI
thf(fact_187_subrelI, axiom,
    ((![R2 : set_Pr723149704on_val, S : set_Pr723149704on_val]: ((![X4 : nat > option2118145160on_val, Y3 : list_char > option_val]: ((member652041809on_val @ (produc52622304on_val @ X4 @ Y3) @ R2) => (member652041809on_val @ (produc52622304on_val @ X4 @ Y3) @ S))) => (ord_le930806568on_val @ R2 @ S))))). % subrelI
thf(fact_188_subrelI, axiom,
    ((![R2 : set_Pr2075231726on_val, S : set_Pr2075231726on_val]: ((![X4 : list_char, Y3 : produc1257910179t_char > option_val]: ((member1296415951on_val @ (produc904988266on_val @ X4 @ Y3) @ R2) => (member1296415951on_val @ (produc904988266on_val @ X4 @ Y3) @ S))) => (ord_le1071216206on_val @ R2 @ S))))). % subrelI
thf(fact_189_pred__subset__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S3 : set_Pr1189492743on_val]: ((ord_le1677030286_val_o @ (^[X : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X @ Y4) @ R))) @ (^[X : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X @ Y4) @ S3)))) = (ord_le837504935on_val @ R @ S3))))). % pred_subset_eq2
thf(fact_190_pred__subset__eq2, axiom,
    ((![R : set_Pr556513572on_val, S3 : set_Pr556513572on_val]: ((ord_le383107121_val_o @ (^[X : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X @ Y4) @ R))) @ (^[X : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X @ Y4) @ S3)))) = (ord_le131203268on_val @ R @ S3))))). % pred_subset_eq2
thf(fact_191_pred__subset__eq2, axiom,
    ((![R : set_Pr723149704on_val, S3 : set_Pr723149704on_val]: ((ord_le752245279_val_o @ (^[X : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X @ Y4) @ R))) @ (^[X : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X @ Y4) @ S3)))) = (ord_le930806568on_val @ R @ S3))))). % pred_subset_eq2
thf(fact_192_pred__subset__eq2, axiom,
    ((![R : set_Pr2075231726on_val, S3 : set_Pr2075231726on_val]: ((ord_le1192209529_val_o @ (^[X : list_char]: (^[Y4 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X @ Y4) @ R))) @ (^[X : list_char]: (^[Y4 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X @ Y4) @ S3)))) = (ord_le1071216206on_val @ R @ S3))))). % pred_subset_eq2
thf(fact_193_pred__subset__eq, axiom,
    ((![R : set_Pr1189492743on_val, S3 : set_Pr1189492743on_val]: ((ord_le14618614_val_o @ (^[X : produc1172664615on_val]: (member354538064on_val @ X @ R)) @ (^[X : produc1172664615on_val]: (member354538064on_val @ X @ S3))) = (ord_le837504935on_val @ R @ S3))))). % pred_subset_eq
thf(fact_194_pred__subset__eq, axiom,
    ((![R : set_list_char, S3 : set_list_char]: ((ord_le1945897678char_o @ (^[X : list_char]: (member_list_char @ X @ R)) @ (^[X : list_char]: (member_list_char @ X @ S3))) = (ord_le1836582007t_char @ R @ S3))))). % pred_subset_eq
thf(fact_195_less__eq__set__def, axiom,
    ((ord_le837504935on_val = (^[A7 : set_Pr1189492743on_val]: (^[B6 : set_Pr1189492743on_val]: (ord_le14618614_val_o @ (^[X : produc1172664615on_val]: (member354538064on_val @ X @ A7)) @ (^[X : produc1172664615on_val]: (member354538064on_val @ X @ B6)))))))). % less_eq_set_def
thf(fact_196_less__eq__set__def, axiom,
    ((ord_le1836582007t_char = (^[A7 : set_list_char]: (^[B6 : set_list_char]: (ord_le1945897678char_o @ (^[X : list_char]: (member_list_char @ X @ A7)) @ (^[X : list_char]: (member_list_char @ X @ B6)))))))). % less_eq_set_def
thf(fact_197_ssubst__Pair__rhs, axiom,
    ((![R2 : produc1097884484on_val, S : produc1097884484on_val, R : set_Pr1189492743on_val, S2 : produc1097884484on_val]: ((member354538064on_val @ (produc1069526295on_val @ R2 @ S) @ R) => ((S2 = S) => (member354538064on_val @ (produc1069526295on_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_198_ssubst__Pair__rhs, axiom,
    ((![R2 : exp_list_char, S : produc515445032on_val, R : set_Pr556513572on_val, S2 : produc515445032on_val]: ((member1888679917on_val @ (produc2023458740on_val @ R2 @ S) @ R) => ((S2 = S) => (member1888679917on_val @ (produc2023458740on_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_199_ssubst__Pair__rhs, axiom,
    ((![R2 : nat > option2118145160on_val, S : list_char > option_val, R : set_Pr723149704on_val, S2 : list_char > option_val]: ((member652041809on_val @ (produc52622304on_val @ R2 @ S) @ R) => ((S2 = S) => (member652041809on_val @ (produc52622304on_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_200_ssubst__Pair__rhs, axiom,
    ((![R2 : list_char, S : produc1257910179t_char > option_val, R : set_Pr2075231726on_val, S2 : produc1257910179t_char > option_val]: ((member1296415951on_val @ (produc904988266on_val @ R2 @ S) @ R) => ((S2 = S) => (member1296415951on_val @ (produc904988266on_val @ R2 @ S2) @ R)))))). % ssubst_Pair_rhs
thf(fact_201_hextI, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val]: ((![A4 : nat, C5 : list_char, Fs : produc1257910179t_char > option_val]: (((H @ A4) = (some_P1299442195on_val @ (produc904988266on_val @ C5 @ Fs))) => (?[Fs2 : produc1257910179t_char > option_val]: ((H2 @ A4) = (some_P1299442195on_val @ (produc904988266on_val @ C5 @ Fs2)))))) => (hext @ H @ H2))))). % hextI
thf(fact_202_hext__def, axiom,
    ((hext = (^[H3 : nat > option2118145160on_val]: (^[H4 : nat > option2118145160on_val]: (![A6 : nat]: (![C2 : list_char]: (![Fs3 : produc1257910179t_char > option_val]: ((((H3 @ A6) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs3)))) => ((?[Fs4 : produc1257910179t_char > option_val]: ((H4 @ A6) = (some_P1299442195on_val @ (produc904988266on_val @ C2 @ Fs4)))))))))))))). % hext_def
thf(fact_203_hext__objD, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, A : nat, C4 : list_char, Fs5 : produc1257910179t_char > option_val]: ((hext @ H @ H2) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs5))) => (?[Fs6 : produc1257910179t_char > option_val]: ((H2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C4 @ Fs6))))))))). % hext_objD
thf(fact_204_hext__trans, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, H5 : nat > option2118145160on_val]: ((hext @ H @ H2) => ((hext @ H2 @ H5) => (hext @ H @ H5)))))). % hext_trans
thf(fact_205_prop__restrict, axiom,
    ((![X3 : produc1172664615on_val, Z3 : set_Pr1189492743on_val, X5 : set_Pr1189492743on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ X3 @ Z3) => ((ord_le837504935on_val @ Z3 @ (collec2055896722on_val @ (^[X : produc1172664615on_val]: (((member354538064on_val @ X @ X5)) & ((P @ X)))))) => (P @ X3)))))). % prop_restrict
thf(fact_206_prop__restrict, axiom,
    ((![X3 : list_char, Z3 : set_list_char, X5 : set_list_char, P : list_char > $o]: ((member_list_char @ X3 @ Z3) => ((ord_le1836582007t_char @ Z3 @ (collect_list_char @ (^[X : list_char]: (((member_list_char @ X @ X5)) & ((P @ X)))))) => (P @ X3)))))). % prop_restrict
thf(fact_207_Collect__restrict, axiom,
    ((![X5 : set_Pr1189492743on_val, P : produc1172664615on_val > $o]: (ord_le837504935on_val @ (collec2055896722on_val @ (^[X : produc1172664615on_val]: (((member354538064on_val @ X @ X5)) & ((P @ X))))) @ X5)))). % Collect_restrict
thf(fact_208_Collect__restrict, axiom,
    ((![X5 : set_list_char, P : list_char > $o]: (ord_le1836582007t_char @ (collect_list_char @ (^[X : list_char]: (((member_list_char @ X @ X5)) & ((P @ X))))) @ X5)))). % Collect_restrict
thf(fact_209_conj__subset__def, axiom,
    ((![A2 : set_list_char, P : list_char > $o, Q : list_char > $o]: ((ord_le1836582007t_char @ A2 @ (collect_list_char @ (^[X : list_char]: (((P @ X)) & ((Q @ X)))))) = (((ord_le1836582007t_char @ A2 @ (collect_list_char @ P))) & ((ord_le1836582007t_char @ A2 @ (collect_list_char @ Q)))))))). % conj_subset_def
thf(fact_210_subset__CollectI, axiom,
    ((![B4 : set_Pr1189492743on_val, A2 : set_Pr1189492743on_val, Q : produc1172664615on_val > $o, P : produc1172664615on_val > $o]: ((ord_le837504935on_val @ B4 @ A2) => ((![X4 : produc1172664615on_val]: ((member354538064on_val @ X4 @ B4) => ((Q @ X4) => (P @ X4)))) => (ord_le837504935on_val @ (collec2055896722on_val @ (^[X : produc1172664615on_val]: (((member354538064on_val @ X @ B4)) & ((Q @ X))))) @ (collec2055896722on_val @ (^[X : produc1172664615on_val]: (((member354538064on_val @ X @ A2)) & ((P @ X))))))))))). % subset_CollectI
thf(fact_211_subset__CollectI, axiom,
    ((![B4 : set_list_char, A2 : set_list_char, Q : list_char > $o, P : list_char > $o]: ((ord_le1836582007t_char @ B4 @ A2) => ((![X4 : list_char]: ((member_list_char @ X4 @ B4) => ((Q @ X4) => (P @ X4)))) => (ord_le1836582007t_char @ (collect_list_char @ (^[X : list_char]: (((member_list_char @ X @ B4)) & ((Q @ X))))) @ (collect_list_char @ (^[X : list_char]: (((member_list_char @ X @ A2)) & ((P @ X))))))))))). % subset_CollectI

% Conjectures (1)
thf(conj_0, conjecture,
    ((d_list_char @ (seq_list_char @ e_a @ e_2) @ (some_set_list_char @ (dom_list_char_val @ ba))))).
