% 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_162__5335642_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:19:48.496

% Could-be-implicit typings (39)
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% Explicit typings (103)
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    member1888679917on_val : produc1097884484on_val > set_Pr556513572on_val > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_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,
    member184158439on_val : produc335961278on_val > set_Pr1511552798on_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__Product____Type__Oprod_It__Product____Type__Oprod_It__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_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__List__Olist_It__Expr__Oexp_It__List__Olist_It__String__Ochar_J_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,
    member1689761872on_val : produc655058983on_val > set_Pr208351751on_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_Ha______, type,
    e_a : exp_list_char).
thf(sy_v_ea______, type,
    ea : exp_list_char).
thf(sy_v_esa______, type,
    esa : list_exp_list_char).

% Relevant facts (249)
thf(fact_0_ListRed1_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)))))). % ListRed1.hyps(2)
thf(fact_1_ListRed1_Oprems, axiom,
    ((d_s_list_char @ (cons_exp_list_char @ ea @ esa) @ (some_set_list_char @ (dom_list_char_val @ b))))). % ListRed1.prems
thf(fact_2_ListRed1_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)))). % ListRed1.hyps(1)
thf(fact_3_option_Oinject, axiom,
    ((![X2 : val, Y2 : val]: (((some_val @ X2) = (some_val @ Y2)) = (X2 = Y2))))). % option.inject
thf(fact_4_option_Oinject, axiom,
    ((![X2 : exp_list_char, Y2 : exp_list_char]: (((some_exp_list_char @ X2) = (some_exp_list_char @ 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_list_Oinject, axiom,
    ((![X21 : produc266837688on_val, X22 : list_P561327688on_val, Y21 : produc266837688on_val, Y22 : list_P561327688on_val]: (((cons_P1611801218on_val @ X21 @ X22) = (cons_P1611801218on_val @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_8_list_Oinject, axiom,
    ((![X21 : set_list_char, X22 : list_set_list_char, Y21 : set_list_char, Y22 : list_set_list_char]: (((cons_set_list_char @ X21 @ X22) = (cons_set_list_char @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_9_list_Oinject, axiom,
    ((![X21 : exp_list_char, X22 : list_exp_list_char, Y21 : exp_list_char, Y22 : list_exp_list_char]: (((cons_exp_list_char @ X21 @ X22) = (cons_exp_list_char @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
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 : produc655058983on_val, M : produc655058983on_val > option_set_list_char]: ((member1689761872on_val @ A @ (dom_Pr1148610668t_char @ M)) => (?[B : set_list_char]: ((M @ A) = (some_set_list_char @ B))))))). % domD
thf(fact_13_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_14_domD, axiom,
    ((![A : produc655058983on_val, M : produc655058983on_val > option2118145160on_val]: ((member1689761872on_val @ A @ (dom_Pr2073570061on_val @ M)) => (?[B : produc266837688on_val]: ((M @ A) = (some_P1299442195on_val @ B))))))). % domD
thf(fact_15_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_16_domD, axiom,
    ((![A : list_char, M : list_char > option_exp_list_char]: ((member_list_char @ A @ (dom_li2068074582t_char @ M)) => (?[B : exp_list_char]: ((M @ A) = (some_exp_list_char @ B))))))). % domD
thf(fact_17_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_18_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_19_domD, axiom,
    ((![A : produc655058983on_val, M : produc655058983on_val > option_val]: ((member1689761872on_val @ A @ (dom_Pr1128399701al_val @ M)) => (?[B : val]: ((M @ A) = (some_val @ B))))))). % domD
thf(fact_20_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_21_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_22_domI, axiom,
    ((![M : produc655058983on_val > option_set_list_char, A : produc655058983on_val, B2 : set_list_char]: (((M @ A) = (some_set_list_char @ B2)) => (member1689761872on_val @ A @ (dom_Pr1148610668t_char @ M)))))). % domI
thf(fact_23_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_24_domI, axiom,
    ((![M : produc655058983on_val > option2118145160on_val, A : produc655058983on_val, B2 : produc266837688on_val]: (((M @ A) = (some_P1299442195on_val @ B2)) => (member1689761872on_val @ A @ (dom_Pr2073570061on_val @ M)))))). % domI
thf(fact_25_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_26_domI, axiom,
    ((![M : list_char > option_exp_list_char, A : list_char, B2 : exp_list_char]: (((M @ A) = (some_exp_list_char @ B2)) => (member_list_char @ A @ (dom_li2068074582t_char @ M)))))). % domI
thf(fact_27_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_28_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_29_domI, axiom,
    ((![M : produc655058983on_val > option_val, A : produc655058983on_val, B2 : val]: (((M @ A) = (some_val @ B2)) => (member1689761872on_val @ A @ (dom_Pr1128399701al_val @ M)))))). % domI
thf(fact_30_not__Cons__self2, axiom,
    ((![X : produc266837688on_val, Xs : list_P561327688on_val]: (~ (((cons_P1611801218on_val @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_31_not__Cons__self2, axiom,
    ((![X : set_list_char, Xs : list_set_list_char]: (~ (((cons_set_list_char @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_32_not__Cons__self2, axiom,
    ((![X : exp_list_char, Xs : list_exp_list_char]: (~ (((cons_exp_list_char @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_33_dom__const, axiom,
    ((![F : produc655058983on_val > set_list_char]: ((dom_Pr1148610668t_char @ (^[X3 : produc655058983on_val]: (some_set_list_char @ (F @ X3)))) = top_to140144471on_val)))). % dom_const
thf(fact_34_dom__const, axiom,
    ((![F : produc1172664615on_val > set_list_char]: ((dom_Pr1335625324t_char @ (^[X3 : produc1172664615on_val]: (some_set_list_char @ (F @ X3)))) = top_to1683965271on_val)))). % dom_const
thf(fact_35_dom__const, axiom,
    ((![F : produc655058983on_val > produc266837688on_val]: ((dom_Pr2073570061on_val @ (^[X3 : produc655058983on_val]: (some_P1299442195on_val @ (F @ X3)))) = top_to140144471on_val)))). % dom_const
thf(fact_36_dom__const, axiom,
    ((![F : produc1172664615on_val > produc266837688on_val]: ((dom_Pr269338893on_val @ (^[X3 : produc1172664615on_val]: (some_P1299442195on_val @ (F @ X3)))) = top_to1683965271on_val)))). % dom_const
thf(fact_37_dom__const, axiom,
    ((![F : list_char > set_list_char]: ((dom_li665594572t_char @ (^[X3 : list_char]: (some_set_list_char @ (F @ X3)))) = top_to748628679t_char)))). % dom_const
thf(fact_38_dom__const, axiom,
    ((![F : list_char > produc266837688on_val]: ((dom_li1284435309on_val @ (^[X3 : list_char]: (some_P1299442195on_val @ (F @ X3)))) = top_to748628679t_char)))). % dom_const
thf(fact_39_dom__const, axiom,
    ((![F : list_char > exp_list_char]: ((dom_li2068074582t_char @ (^[X3 : list_char]: (some_exp_list_char @ (F @ X3)))) = top_to748628679t_char)))). % dom_const
thf(fact_40_dom__const, axiom,
    ((![F : list_char > val]: ((dom_list_char_val @ (^[X3 : list_char]: (some_val @ (F @ X3)))) = top_to748628679t_char)))). % dom_const
thf(fact_41_find_Osimps_I2_J, axiom,
    ((![P : val > $o, X : val, Xs : list_val]: (((P @ X) => ((find_val @ P @ (cons_val @ X @ Xs)) = (some_val @ X))) & ((~ ((P @ X))) => ((find_val @ P @ (cons_val @ X @ Xs)) = (find_val @ P @ Xs))))))). % find.simps(2)
thf(fact_42_find_Osimps_I2_J, axiom,
    ((![P : exp_list_char > $o, X : exp_list_char, Xs : list_exp_list_char]: (((P @ X) => ((find_exp_list_char @ P @ (cons_exp_list_char @ X @ Xs)) = (some_exp_list_char @ X))) & ((~ ((P @ X))) => ((find_exp_list_char @ P @ (cons_exp_list_char @ X @ Xs)) = (find_exp_list_char @ P @ Xs))))))). % find.simps(2)
thf(fact_43_find_Osimps_I2_J, axiom,
    ((![P : set_list_char > $o, X : set_list_char, Xs : list_set_list_char]: (((P @ X) => ((find_set_list_char @ P @ (cons_set_list_char @ X @ Xs)) = (some_set_list_char @ X))) & ((~ ((P @ X))) => ((find_set_list_char @ P @ (cons_set_list_char @ X @ Xs)) = (find_set_list_char @ P @ Xs))))))). % find.simps(2)
thf(fact_44_find_Osimps_I2_J, axiom,
    ((![P : produc266837688on_val > $o, X : produc266837688on_val, Xs : list_P561327688on_val]: (((P @ X) => ((find_P779475868on_val @ P @ (cons_P1611801218on_val @ X @ Xs)) = (some_P1299442195on_val @ X))) & ((~ ((P @ X))) => ((find_P779475868on_val @ P @ (cons_P1611801218on_val @ X @ Xs)) = (find_P779475868on_val @ P @ Xs))))))). % find.simps(2)
thf(fact_45_Shift__def, axiom,
    ((bNF_Gr570830962t_char = (^[Kl : set_list_char]: (^[K : char]: (collect_list_char @ (^[Kl2 : list_char]: (member_list_char @ (cons_char @ K @ Kl2) @ Kl)))))))). % Shift_def
thf(fact_46_Shift__def, axiom,
    ((bNF_Gr1163592170t_char = (^[Kl : set_li2075023665t_char]: (^[K : exp_list_char]: (collec2120005820t_char @ (^[Kl2 : list_exp_list_char]: (member1706778746t_char @ (cons_exp_list_char @ K @ Kl2) @ Kl)))))))). % Shift_def
thf(fact_47_Shift__def, axiom,
    ((bNF_Gr238663385on_val = (^[Kl : set_li2591742on_val]: (^[K : produc266837688on_val]: (collec403479581on_val @ (^[Kl2 : list_P561327688on_val]: (member1068094687on_val @ (cons_P1611801218on_val @ K @ Kl2) @ Kl)))))))). % Shift_def
thf(fact_48_Shift__def, axiom,
    ((bNF_Gr1458295864t_char = (^[Kl : set_li793461341t_char]: (^[K : set_list_char]: (collec2023285244t_char @ (^[Kl2 : list_set_list_char]: (member1264478910t_char @ (cons_set_list_char @ K @ Kl2) @ Kl)))))))). % Shift_def
thf(fact_49_insert__dom, axiom,
    ((![F : produc655058983on_val > option_set_list_char, X : produc655058983on_val, Y : set_list_char]: (((F @ X) = (some_set_list_char @ Y)) => ((insert363480567on_val @ X @ (dom_Pr1148610668t_char @ F)) = (dom_Pr1148610668t_char @ F)))))). % insert_dom
thf(fact_50_insert__dom, axiom,
    ((![F : produc1172664615on_val > option_set_list_char, X : produc1172664615on_val, Y : set_list_char]: (((F @ X) = (some_set_list_char @ Y)) => ((insert1971494647on_val @ X @ (dom_Pr1335625324t_char @ F)) = (dom_Pr1335625324t_char @ F)))))). % insert_dom
thf(fact_51_insert__dom, axiom,
    ((![F : produc655058983on_val > option2118145160on_val, X : produc655058983on_val, Y : produc266837688on_val]: (((F @ X) = (some_P1299442195on_val @ Y)) => ((insert363480567on_val @ X @ (dom_Pr2073570061on_val @ F)) = (dom_Pr2073570061on_val @ F)))))). % insert_dom
thf(fact_52_insert__dom, axiom,
    ((![F : produc1172664615on_val > option2118145160on_val, X : produc1172664615on_val, Y : produc266837688on_val]: (((F @ X) = (some_P1299442195on_val @ Y)) => ((insert1971494647on_val @ X @ (dom_Pr269338893on_val @ F)) = (dom_Pr269338893on_val @ F)))))). % insert_dom
thf(fact_53_insert__dom, axiom,
    ((![F : list_char > option_val, X : list_char, Y : val]: (((F @ X) = (some_val @ Y)) => ((insert_list_char @ X @ (dom_list_char_val @ F)) = (dom_list_char_val @ F)))))). % insert_dom
thf(fact_54_Ds__mono, axiom,
    ((![A2 : option_set_list_char, A3 : option_set_list_char, Es : list_exp_list_char]: ((hyper_1448788648t_char @ A2 @ A3) => ((d_s_list_char @ Es @ A2) => (d_s_list_char @ Es @ A3)))))). % Ds_mono
thf(fact_55_Ds__mono_H, axiom,
    ((![Es : list_exp_list_char, A2 : option_set_list_char, A3 : option_set_list_char]: ((d_s_list_char @ Es @ A2) => ((hyper_1448788648t_char @ A2 @ A3) => (d_s_list_char @ Es @ A3)))))). % Ds_mono'
thf(fact_56_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_57_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_58_ShiftD, axiom,
    ((![Kl3 : list_char, Kl4 : set_list_char, K2 : char]: ((member_list_char @ Kl3 @ (bNF_Gr570830962t_char @ Kl4 @ K2)) => (member_list_char @ (cons_char @ K2 @ Kl3) @ Kl4))))). % ShiftD
thf(fact_59_ShiftD, axiom,
    ((![Kl3 : list_exp_list_char, Kl4 : set_li2075023665t_char, K2 : exp_list_char]: ((member1706778746t_char @ Kl3 @ (bNF_Gr1163592170t_char @ Kl4 @ K2)) => (member1706778746t_char @ (cons_exp_list_char @ K2 @ Kl3) @ Kl4))))). % ShiftD
thf(fact_60_ShiftD, axiom,
    ((![Kl3 : list_P561327688on_val, Kl4 : set_li2591742on_val, K2 : produc266837688on_val]: ((member1068094687on_val @ Kl3 @ (bNF_Gr238663385on_val @ Kl4 @ K2)) => (member1068094687on_val @ (cons_P1611801218on_val @ K2 @ Kl3) @ Kl4))))). % ShiftD
thf(fact_61_ShiftD, axiom,
    ((![Kl3 : list_set_list_char, Kl4 : set_li793461341t_char, K2 : set_list_char]: ((member1264478910t_char @ Kl3 @ (bNF_Gr1458295864t_char @ Kl4 @ K2)) => (member1264478910t_char @ (cons_set_list_char @ K2 @ Kl3) @ Kl4))))). % ShiftD
thf(fact_62_local_Owf, axiom,
    ((wf_pro1229751607t_char @ wf_J_mdecl @ p))). % local.wf
thf(fact_63_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_64_prod__induct4, axiom,
    ((![P : produc1172664615on_val > $o, X : 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 @ X))))). % prod_induct4
thf(fact_65_UNIV__I, axiom,
    ((![X : produc1172664615on_val]: (member354538064on_val @ X @ top_to1683965271on_val)))). % UNIV_I
thf(fact_66_UNIV__I, axiom,
    ((![X : produc655058983on_val]: (member1689761872on_val @ X @ top_to140144471on_val)))). % UNIV_I
thf(fact_67_UNIV__I, axiom,
    ((![X : list_char]: (member_list_char @ X @ top_to748628679t_char)))). % UNIV_I
thf(fact_68_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_69_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_70_old_Oprod_Oinject, axiom,
    ((![A : list_exp_list_char, B2 : produc515445032on_val, A5 : list_exp_list_char, B3 : produc515445032on_val]: (((produc1725134254on_val @ A @ B2) = (produc1725134254on_val @ A5 @ B3)) = (((A = A5)) & ((B2 = B3))))))). % old.prod.inject
thf(fact_71_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_72_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_73_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_74_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_75_prod_Oinject, axiom,
    ((![X1 : list_exp_list_char, X2 : produc515445032on_val, Y1 : list_exp_list_char, Y2 : produc515445032on_val]: (((produc1725134254on_val @ X1 @ X2) = (produc1725134254on_val @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_76_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_77_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_78_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_79_insert__iff, axiom,
    ((![A : produc655058983on_val, B2 : produc655058983on_val, A2 : set_Pr208351751on_val]: ((member1689761872on_val @ A @ (insert363480567on_val @ B2 @ A2)) = (((A = B2)) | ((member1689761872on_val @ A @ A2))))))). % insert_iff
thf(fact_80_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_81_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_82_insertCI, axiom,
    ((![A : produc655058983on_val, B4 : set_Pr208351751on_val, B2 : produc655058983on_val]: (((~ ((member1689761872on_val @ A @ B4))) => (A = B2)) => (member1689761872on_val @ A @ (insert363480567on_val @ B2 @ B4)))))). % insertCI
thf(fact_83_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_84_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_85_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_86_old_Oprod_Oinducts, axiom,
    ((![P : produc335961278on_val > $o, Prod : produc335961278on_val]: ((![A4 : list_exp_list_char, B : produc515445032on_val]: (P @ (produc1725134254on_val @ A4 @ B))) => (P @ Prod))))). % old.prod.inducts
thf(fact_87_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_88_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_89_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1172664615on_val]: (~ ((![A4 : produc1097884484on_val, B : produc1097884484on_val]: (~ ((Y = (produc1069526295on_val @ A4 @ B)))))))))). % old.prod.exhaust
thf(fact_90_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_91_old_Oprod_Oexhaust, axiom,
    ((![Y : produc335961278on_val]: (~ ((![A4 : list_exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc1725134254on_val @ A4 @ B)))))))))). % old.prod.exhaust
thf(fact_92_old_Oprod_Oexhaust, axiom,
    ((![Y : produc1097884484on_val]: (~ ((![A4 : exp_list_char, B : produc515445032on_val]: (~ ((Y = (produc2023458740on_val @ A4 @ B)))))))))). % old.prod.exhaust
thf(fact_93_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_94_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_95_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_96_Pair__inject, axiom,
    ((![A : list_exp_list_char, B2 : produc515445032on_val, A5 : list_exp_list_char, B3 : produc515445032on_val]: (((produc1725134254on_val @ A @ B2) = (produc1725134254on_val @ A5 @ B3)) => (~ (((A = A5) => (~ ((B2 = B3)))))))))). % Pair_inject
thf(fact_97_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_98_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_99_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_100_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_101_prod__cases, axiom,
    ((![P : produc335961278on_val > $o, P2 : produc335961278on_val]: ((![A4 : list_exp_list_char, B : produc515445032on_val]: (P @ (produc1725134254on_val @ A4 @ B))) => (P @ P2))))). % prod_cases
thf(fact_102_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_103_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_104_surj__pair, axiom,
    ((![P2 : produc1172664615on_val]: (?[X4 : produc1097884484on_val, Y3 : produc1097884484on_val]: (P2 = (produc1069526295on_val @ X4 @ Y3)))))). % surj_pair
thf(fact_105_surj__pair, axiom,
    ((![P2 : produc266837688on_val]: (?[X4 : list_char, Y3 : produc1257910179t_char > option_val]: (P2 = (produc904988266on_val @ X4 @ Y3)))))). % surj_pair
thf(fact_106_surj__pair, axiom,
    ((![P2 : produc335961278on_val]: (?[X4 : list_exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc1725134254on_val @ X4 @ Y3)))))). % surj_pair
thf(fact_107_surj__pair, axiom,
    ((![P2 : produc1097884484on_val]: (?[X4 : exp_list_char, Y3 : produc515445032on_val]: (P2 = (produc2023458740on_val @ X4 @ Y3)))))). % surj_pair
thf(fact_108_surj__pair, axiom,
    ((![P2 : produc515445032on_val]: (?[X4 : nat > option2118145160on_val, Y3 : list_char > option_val]: (P2 = (produc52622304on_val @ X4 @ Y3)))))). % surj_pair
thf(fact_109_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_110_mk__disjoint__insert, axiom,
    ((![A : produc655058983on_val, A2 : set_Pr208351751on_val]: ((member1689761872on_val @ A @ A2) => (?[B5 : set_Pr208351751on_val]: ((A2 = (insert363480567on_val @ A @ B5)) & (~ ((member1689761872on_val @ A @ B5))))))))). % mk_disjoint_insert
thf(fact_111_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_112_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_113_insert__eq__iff, axiom,
    ((![A : produc655058983on_val, A2 : set_Pr208351751on_val, B2 : produc655058983on_val, B4 : set_Pr208351751on_val]: ((~ ((member1689761872on_val @ A @ A2))) => ((~ ((member1689761872on_val @ B2 @ B4))) => (((insert363480567on_val @ A @ A2) = (insert363480567on_val @ B2 @ B4)) = (((((A = B2)) => ((A2 = B4)))) & ((((~ ((A = B2)))) => ((?[C2 : set_Pr208351751on_val]: (((A2 = (insert363480567on_val @ B2 @ C2))) & ((((~ ((member1689761872on_val @ B2 @ C2)))) & ((((B4 = (insert363480567on_val @ A @ C2))) & ((~ ((member1689761872on_val @ A @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_114_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_115_insert__absorb, axiom,
    ((![A : produc1172664615on_val, A2 : set_Pr1189492743on_val]: ((member354538064on_val @ A @ A2) => ((insert1971494647on_val @ A @ A2) = A2))))). % insert_absorb
thf(fact_116_insert__absorb, axiom,
    ((![A : produc655058983on_val, A2 : set_Pr208351751on_val]: ((member1689761872on_val @ A @ A2) => ((insert363480567on_val @ A @ A2) = A2))))). % insert_absorb
thf(fact_117_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_118_insert__ident, axiom,
    ((![X : produc1172664615on_val, A2 : set_Pr1189492743on_val, B4 : set_Pr1189492743on_val]: ((~ ((member354538064on_val @ X @ A2))) => ((~ ((member354538064on_val @ X @ B4))) => (((insert1971494647on_val @ X @ A2) = (insert1971494647on_val @ X @ B4)) = (A2 = B4))))))). % insert_ident
thf(fact_119_insert__ident, axiom,
    ((![X : produc655058983on_val, A2 : set_Pr208351751on_val, B4 : set_Pr208351751on_val]: ((~ ((member1689761872on_val @ X @ A2))) => ((~ ((member1689761872on_val @ X @ B4))) => (((insert363480567on_val @ X @ A2) = (insert363480567on_val @ X @ B4)) = (A2 = B4))))))). % insert_ident
thf(fact_120_insert__ident, axiom,
    ((![X : list_char, A2 : set_list_char, B4 : set_list_char]: ((~ ((member_list_char @ X @ A2))) => ((~ ((member_list_char @ X @ B4))) => (((insert_list_char @ X @ A2) = (insert_list_char @ X @ B4)) = (A2 = B4))))))). % insert_ident
thf(fact_121_Set_Oset__insert, axiom,
    ((![X : produc1172664615on_val, A2 : set_Pr1189492743on_val]: ((member354538064on_val @ X @ A2) => (~ ((![B5 : set_Pr1189492743on_val]: ((A2 = (insert1971494647on_val @ X @ B5)) => (member354538064on_val @ X @ B5))))))))). % Set.set_insert
thf(fact_122_Set_Oset__insert, axiom,
    ((![X : produc655058983on_val, A2 : set_Pr208351751on_val]: ((member1689761872on_val @ X @ A2) => (~ ((![B5 : set_Pr208351751on_val]: ((A2 = (insert363480567on_val @ X @ B5)) => (member1689761872on_val @ X @ B5))))))))). % Set.set_insert
thf(fact_123_Set_Oset__insert, axiom,
    ((![X : list_char, A2 : set_list_char]: ((member_list_char @ X @ A2) => (~ ((![B5 : set_list_char]: ((A2 = (insert_list_char @ X @ B5)) => (member_list_char @ X @ B5))))))))). % Set.set_insert
thf(fact_124_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_125_insertI2, axiom,
    ((![A : produc655058983on_val, B4 : set_Pr208351751on_val, B2 : produc655058983on_val]: ((member1689761872on_val @ A @ B4) => (member1689761872on_val @ A @ (insert363480567on_val @ B2 @ B4)))))). % insertI2
thf(fact_126_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_127_mem__Collect__eq, axiom,
    ((![A : produc1172664615on_val, P : produc1172664615on_val > $o]: ((member354538064on_val @ A @ (collec2055896722on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_128_mem__Collect__eq, axiom,
    ((![A : produc655058983on_val, P : produc655058983on_val > $o]: ((member1689761872on_val @ A @ (collec105960082on_val @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_129_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_130_Collect__mem__eq, axiom,
    ((![A2 : set_Pr1189492743on_val]: ((collec2055896722on_val @ (^[X3 : produc1172664615on_val]: (member354538064on_val @ X3 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_131_Collect__mem__eq, axiom,
    ((![A2 : set_Pr208351751on_val]: ((collec105960082on_val @ (^[X3 : produc655058983on_val]: (member1689761872on_val @ X3 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_132_Collect__mem__eq, axiom,
    ((![A2 : set_list_char]: ((collect_list_char @ (^[X3 : list_char]: (member_list_char @ X3 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_133_insertI1, axiom,
    ((![A : produc1172664615on_val, B4 : set_Pr1189492743on_val]: (member354538064on_val @ A @ (insert1971494647on_val @ A @ B4))))). % insertI1
thf(fact_134_insertI1, axiom,
    ((![A : produc655058983on_val, B4 : set_Pr208351751on_val]: (member1689761872on_val @ A @ (insert363480567on_val @ A @ B4))))). % insertI1
thf(fact_135_insertI1, axiom,
    ((![A : list_char, B4 : set_list_char]: (member_list_char @ A @ (insert_list_char @ A @ B4))))). % insertI1
thf(fact_136_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_137_insertE, axiom,
    ((![A : produc655058983on_val, B2 : produc655058983on_val, A2 : set_Pr208351751on_val]: ((member1689761872on_val @ A @ (insert363480567on_val @ B2 @ A2)) => ((~ ((A = B2))) => (member1689761872on_val @ A @ A2)))))). % insertE
thf(fact_138_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_139_UNIV__witness, axiom,
    ((?[X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ top_to1683965271on_val)))). % UNIV_witness
thf(fact_140_UNIV__witness, axiom,
    ((?[X4 : produc655058983on_val]: (member1689761872on_val @ X4 @ top_to140144471on_val)))). % UNIV_witness
thf(fact_141_UNIV__witness, axiom,
    ((?[X4 : list_char]: (member_list_char @ X4 @ top_to748628679t_char)))). % UNIV_witness
thf(fact_142_UNIV__eq__I, axiom,
    ((![A2 : set_Pr1189492743on_val]: ((![X4 : produc1172664615on_val]: (member354538064on_val @ X4 @ A2)) => (top_to1683965271on_val = A2))))). % UNIV_eq_I
thf(fact_143_UNIV__eq__I, axiom,
    ((![A2 : set_Pr208351751on_val]: ((![X4 : produc655058983on_val]: (member1689761872on_val @ X4 @ A2)) => (top_to140144471on_val = A2))))). % UNIV_eq_I
thf(fact_144_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_145_insert__compr, axiom,
    ((insert1971494647on_val = (^[A6 : produc1172664615on_val]: (^[B6 : set_Pr1189492743on_val]: (collec2055896722on_val @ (^[X3 : produc1172664615on_val]: (((X3 = A6)) | ((member354538064on_val @ X3 @ B6)))))))))). % insert_compr
thf(fact_146_insert__compr, axiom,
    ((insert363480567on_val = (^[A6 : produc655058983on_val]: (^[B6 : set_Pr208351751on_val]: (collec105960082on_val @ (^[X3 : produc655058983on_val]: (((X3 = A6)) | ((member1689761872on_val @ X3 @ B6)))))))))). % insert_compr
thf(fact_147_insert__compr, axiom,
    ((insert_list_char = (^[A6 : list_char]: (^[B6 : set_list_char]: (collect_list_char @ (^[X3 : list_char]: (((X3 = A6)) | ((member_list_char @ X3 @ B6)))))))))). % insert_compr
thf(fact_148_UNIV__def, axiom,
    ((top_to748628679t_char = (collect_list_char @ (^[X3 : list_char]: $true))))). % UNIV_def
thf(fact_149_prod__induct3, axiom,
    ((![P : produc1172664615on_val > $o, X : produc1172664615on_val]: ((![A4 : produc1097884484on_val, B : exp_list_char, C : produc515445032on_val]: (P @ (produc1069526295on_val @ A4 @ (produc2023458740on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_150_prod__induct3, axiom,
    ((![P : produc335961278on_val > $o, X : produc335961278on_val]: ((![A4 : list_exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc1725134254on_val @ A4 @ (produc52622304on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_151_prod__induct3, axiom,
    ((![P : produc1097884484on_val > $o, X : produc1097884484on_val]: ((![A4 : exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (P @ (produc2023458740on_val @ A4 @ (produc52622304on_val @ B @ C)))) => (P @ X))))). % prod_induct3
thf(fact_152_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_153_prod__cases3, axiom,
    ((![Y : produc335961278on_val]: (~ ((![A4 : list_exp_list_char, B : nat > option2118145160on_val, C : list_char > option_val]: (~ ((Y = (produc1725134254on_val @ A4 @ (produc52622304on_val @ B @ C))))))))))). % prod_cases3
thf(fact_154_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_155_insert__UNIV, axiom,
    ((![X : list_char]: ((insert_list_char @ X @ top_to748628679t_char) = top_to748628679t_char)))). % insert_UNIV
thf(fact_156_iso__tuple__UNIV__I, axiom,
    ((![X : produc1172664615on_val]: (member354538064on_val @ X @ top_to1683965271on_val)))). % iso_tuple_UNIV_I
thf(fact_157_iso__tuple__UNIV__I, axiom,
    ((![X : produc655058983on_val]: (member1689761872on_val @ X @ top_to140144471on_val)))). % iso_tuple_UNIV_I
thf(fact_158_iso__tuple__UNIV__I, axiom,
    ((![X : list_char]: (member_list_char @ X @ top_to748628679t_char)))). % iso_tuple_UNIV_I
thf(fact_159_Succ__Shift, axiom,
    ((![Kl4 : set_li2075023665t_char, K2 : exp_list_char, Kl3 : list_exp_list_char]: ((bNF_Gr71413094t_char @ (bNF_Gr1163592170t_char @ Kl4 @ K2) @ Kl3) = (bNF_Gr71413094t_char @ Kl4 @ (cons_exp_list_char @ K2 @ Kl3)))))). % Succ_Shift
thf(fact_160_Succ__Shift, axiom,
    ((![Kl4 : set_li2591742on_val, K2 : produc266837688on_val, Kl3 : list_P561327688on_val]: ((bNF_Gr1536412765on_val @ (bNF_Gr238663385on_val @ Kl4 @ K2) @ Kl3) = (bNF_Gr1536412765on_val @ Kl4 @ (cons_P1611801218on_val @ K2 @ Kl3)))))). % Succ_Shift
thf(fact_161_Succ__Shift, axiom,
    ((![Kl4 : set_li793461341t_char, K2 : set_list_char, Kl3 : list_set_list_char]: ((bNF_Gr540445116t_char @ (bNF_Gr1458295864t_char @ Kl4 @ K2) @ Kl3) = (bNF_Gr540445116t_char @ Kl4 @ (cons_set_list_char @ K2 @ Kl3)))))). % Succ_Shift
thf(fact_162_these__insert__Some, axiom,
    ((![X : set_list_char, A2 : set_op501702045t_char]: ((these_set_list_char @ (insert433234071t_char @ (some_set_list_char @ X) @ A2)) = (insert_set_list_char @ X @ (these_set_list_char @ A2)))))). % these_insert_Some
thf(fact_163_these__insert__Some, axiom,
    ((![X : produc266837688on_val, A2 : set_op1111598910on_val]: ((these_538817979on_val @ (insert1333207736on_val @ (some_P1299442195on_val @ X) @ A2)) = (insert688092392on_val @ X @ (these_538817979on_val @ A2)))))). % these_insert_Some
thf(fact_164_these__insert__Some, axiom,
    ((![X : val, A2 : set_option_val]: ((these_val @ (insert_option_val @ (some_val @ X) @ A2)) = (insert_val @ X @ (these_val @ A2)))))). % these_insert_Some
thf(fact_165_these__insert__Some, axiom,
    ((![X : exp_list_char, A2 : set_op1331236337t_char]: ((these_exp_list_char @ (insert1781375201t_char @ (some_exp_list_char @ X) @ A2)) = (insert_exp_list_char @ X @ (these_exp_list_char @ A2)))))). % these_insert_Some
thf(fact_166_pred__equals__eq2, axiom,
    ((![R : set_Pr208351751on_val, S : set_Pr208351751on_val]: (((^[X3 : produc335961278on_val]: (^[Y4 : produc335961278on_val]: (member1689761872on_val @ (produc245869591on_val @ X3 @ Y4) @ R))) = (^[X3 : produc335961278on_val]: (^[Y4 : produc335961278on_val]: (member1689761872on_val @ (produc245869591on_val @ X3 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_167_pred__equals__eq2, axiom,
    ((![R : set_Pr1189492743on_val, S : set_Pr1189492743on_val]: (((^[X3 : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X3 @ Y4) @ R))) = (^[X3 : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X3 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_168_pred__equals__eq2, axiom,
    ((![R : set_Pr2075231726on_val, S : set_Pr2075231726on_val]: (((^[X3 : list_char]: (^[Y4 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X3 @ Y4) @ R))) = (^[X3 : list_char]: (^[Y4 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X3 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_169_pred__equals__eq2, axiom,
    ((![R : set_Pr1511552798on_val, S : set_Pr1511552798on_val]: (((^[X3 : list_exp_list_char]: (^[Y4 : produc515445032on_val]: (member184158439on_val @ (produc1725134254on_val @ X3 @ Y4) @ R))) = (^[X3 : list_exp_list_char]: (^[Y4 : produc515445032on_val]: (member184158439on_val @ (produc1725134254on_val @ X3 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_170_pred__equals__eq2, axiom,
    ((![R : set_Pr556513572on_val, S : set_Pr556513572on_val]: (((^[X3 : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X3 @ Y4) @ R))) = (^[X3 : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X3 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_171_pred__equals__eq2, axiom,
    ((![R : set_Pr723149704on_val, S : set_Pr723149704on_val]: (((^[X3 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X3 @ Y4) @ R))) = (^[X3 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X3 @ Y4) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_172_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_173_order__refl, axiom,
    ((![X : set_list_char]: (ord_le1836582007t_char @ X @ X)))). % order_refl
thf(fact_174_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_175_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_176_subsetI, axiom,
    ((![A2 : set_Pr208351751on_val, B4 : set_Pr208351751on_val]: ((![X4 : produc655058983on_val]: ((member1689761872on_val @ X4 @ A2) => (member1689761872on_val @ X4 @ B4))) => (ord_le1331145127on_val @ A2 @ B4))))). % subsetI
thf(fact_177_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_178_insert__subset, axiom,
    ((![X : produc1172664615on_val, A2 : set_Pr1189492743on_val, B4 : set_Pr1189492743on_val]: ((ord_le837504935on_val @ (insert1971494647on_val @ X @ A2) @ B4) = (((member354538064on_val @ X @ B4)) & ((ord_le837504935on_val @ A2 @ B4))))))). % insert_subset
thf(fact_179_insert__subset, axiom,
    ((![X : produc655058983on_val, A2 : set_Pr208351751on_val, B4 : set_Pr208351751on_val]: ((ord_le1331145127on_val @ (insert363480567on_val @ X @ A2) @ B4) = (((member1689761872on_val @ X @ B4)) & ((ord_le1331145127on_val @ A2 @ B4))))))). % insert_subset
thf(fact_180_insert__subset, axiom,
    ((![X : list_char, A2 : set_list_char, B4 : set_list_char]: ((ord_le1836582007t_char @ (insert_list_char @ X @ A2) @ B4) = (((member_list_char @ X @ B4)) & ((ord_le1836582007t_char @ A2 @ B4))))))). % insert_subset
thf(fact_181_Collect__mono__iff, axiom,
    ((![P : list_char > $o, Q : list_char > $o]: ((ord_le1836582007t_char @ (collect_list_char @ P) @ (collect_list_char @ Q)) = (![X3 : list_char]: (((P @ X3)) => ((Q @ X3)))))))). % Collect_mono_iff
thf(fact_182_Collect__subset, axiom,
    ((![A2 : set_Pr1189492743on_val, P : produc1172664615on_val > $o]: (ord_le837504935on_val @ (collec2055896722on_val @ (^[X3 : produc1172664615on_val]: (((member354538064on_val @ X3 @ A2)) & ((P @ X3))))) @ A2)))). % Collect_subset
thf(fact_183_Collect__subset, axiom,
    ((![A2 : set_Pr208351751on_val, P : produc655058983on_val > $o]: (ord_le1331145127on_val @ (collec105960082on_val @ (^[X3 : produc655058983on_val]: (((member1689761872on_val @ X3 @ A2)) & ((P @ X3))))) @ A2)))). % Collect_subset
thf(fact_184_Collect__subset, axiom,
    ((![A2 : set_list_char, P : list_char > $o]: (ord_le1836582007t_char @ (collect_list_char @ (^[X3 : list_char]: (((member_list_char @ X3 @ A2)) & ((P @ X3))))) @ A2)))). % Collect_subset
thf(fact_185_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_186_subset__trans, axiom,
    ((![A2 : set_list_char, B4 : set_list_char, C3 : set_list_char]: ((ord_le1836582007t_char @ A2 @ B4) => ((ord_le1836582007t_char @ B4 @ C3) => (ord_le1836582007t_char @ A2 @ C3)))))). % subset_trans
thf(fact_187_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_188_subset__refl, axiom,
    ((![A2 : set_list_char]: (ord_le1836582007t_char @ A2 @ A2)))). % subset_refl
thf(fact_189_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_190_subset__iff, axiom,
    ((ord_le1331145127on_val = (^[A7 : set_Pr208351751on_val]: (^[B6 : set_Pr208351751on_val]: (![T : produc655058983on_val]: (((member1689761872on_val @ T @ A7)) => ((member1689761872on_val @ T @ B6))))))))). % subset_iff
thf(fact_191_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_192_equalityD2, axiom,
    ((![A2 : set_list_char, B4 : set_list_char]: ((A2 = B4) => (ord_le1836582007t_char @ B4 @ A2))))). % equalityD2
thf(fact_193_equalityD1, axiom,
    ((![A2 : set_list_char, B4 : set_list_char]: ((A2 = B4) => (ord_le1836582007t_char @ A2 @ B4))))). % equalityD1
thf(fact_194_subset__eq, axiom,
    ((ord_le837504935on_val = (^[A7 : set_Pr1189492743on_val]: (^[B6 : set_Pr1189492743on_val]: (![X3 : produc1172664615on_val]: (((member354538064on_val @ X3 @ A7)) => ((member354538064on_val @ X3 @ B6))))))))). % subset_eq
thf(fact_195_subset__eq, axiom,
    ((ord_le1331145127on_val = (^[A7 : set_Pr208351751on_val]: (^[B6 : set_Pr208351751on_val]: (![X3 : produc655058983on_val]: (((member1689761872on_val @ X3 @ A7)) => ((member1689761872on_val @ X3 @ B6))))))))). % subset_eq
thf(fact_196_subset__eq, axiom,
    ((ord_le1836582007t_char = (^[A7 : set_list_char]: (^[B6 : set_list_char]: (![X3 : list_char]: (((member_list_char @ X3 @ A7)) => ((member_list_char @ X3 @ B6))))))))). % subset_eq
thf(fact_197_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_198_subsetD, axiom,
    ((![A2 : set_Pr1189492743on_val, B4 : set_Pr1189492743on_val, C4 : produc1172664615on_val]: ((ord_le837504935on_val @ A2 @ B4) => ((member354538064on_val @ C4 @ A2) => (member354538064on_val @ C4 @ B4)))))). % subsetD
thf(fact_199_subsetD, axiom,
    ((![A2 : set_Pr208351751on_val, B4 : set_Pr208351751on_val, C4 : produc655058983on_val]: ((ord_le1331145127on_val @ A2 @ B4) => ((member1689761872on_val @ C4 @ A2) => (member1689761872on_val @ C4 @ B4)))))). % subsetD
thf(fact_200_subsetD, axiom,
    ((![A2 : set_list_char, B4 : set_list_char, C4 : list_char]: ((ord_le1836582007t_char @ A2 @ B4) => ((member_list_char @ C4 @ A2) => (member_list_char @ C4 @ B4)))))). % subsetD
thf(fact_201_in__mono, axiom,
    ((![A2 : set_Pr1189492743on_val, B4 : set_Pr1189492743on_val, X : produc1172664615on_val]: ((ord_le837504935on_val @ A2 @ B4) => ((member354538064on_val @ X @ A2) => (member354538064on_val @ X @ B4)))))). % in_mono
thf(fact_202_in__mono, axiom,
    ((![A2 : set_Pr208351751on_val, B4 : set_Pr208351751on_val, X : produc655058983on_val]: ((ord_le1331145127on_val @ A2 @ B4) => ((member1689761872on_val @ X @ A2) => (member1689761872on_val @ X @ B4)))))). % in_mono
thf(fact_203_in__mono, axiom,
    ((![A2 : set_list_char, B4 : set_list_char, X : list_char]: ((ord_le1836582007t_char @ A2 @ B4) => ((member_list_char @ X @ A2) => (member_list_char @ X @ B4)))))). % in_mono
thf(fact_204_subset__Collect__iff, axiom,
    ((![B4 : set_Pr1189492743on_val, A2 : set_Pr1189492743on_val, P : produc1172664615on_val > $o]: ((ord_le837504935on_val @ B4 @ A2) => ((ord_le837504935on_val @ B4 @ (collec2055896722on_val @ (^[X3 : produc1172664615on_val]: (((member354538064on_val @ X3 @ A2)) & ((P @ X3)))))) = (![X3 : produc1172664615on_val]: (((member354538064on_val @ X3 @ B4)) => ((P @ X3))))))))). % subset_Collect_iff
thf(fact_205_subset__Collect__iff, axiom,
    ((![B4 : set_Pr208351751on_val, A2 : set_Pr208351751on_val, P : produc655058983on_val > $o]: ((ord_le1331145127on_val @ B4 @ A2) => ((ord_le1331145127on_val @ B4 @ (collec105960082on_val @ (^[X3 : produc655058983on_val]: (((member1689761872on_val @ X3 @ A2)) & ((P @ X3)))))) = (![X3 : produc655058983on_val]: (((member1689761872on_val @ X3 @ B4)) => ((P @ X3))))))))). % subset_Collect_iff
thf(fact_206_subset__Collect__iff, axiom,
    ((![B4 : set_list_char, A2 : set_list_char, P : list_char > $o]: ((ord_le1836582007t_char @ B4 @ A2) => ((ord_le1836582007t_char @ B4 @ (collect_list_char @ (^[X3 : list_char]: (((member_list_char @ X3 @ A2)) & ((P @ X3)))))) = (![X3 : list_char]: (((member_list_char @ X3 @ B4)) => ((P @ X3))))))))). % subset_Collect_iff
thf(fact_207_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 @ (^[X3 : produc1172664615on_val]: (((member354538064on_val @ X3 @ B4)) & ((Q @ X3))))) @ (collec2055896722on_val @ (^[X3 : produc1172664615on_val]: (((member354538064on_val @ X3 @ A2)) & ((P @ X3))))))))))). % subset_CollectI
thf(fact_208_subset__CollectI, axiom,
    ((![B4 : set_Pr208351751on_val, A2 : set_Pr208351751on_val, Q : produc655058983on_val > $o, P : produc655058983on_val > $o]: ((ord_le1331145127on_val @ B4 @ A2) => ((![X4 : produc655058983on_val]: ((member1689761872on_val @ X4 @ B4) => ((Q @ X4) => (P @ X4)))) => (ord_le1331145127on_val @ (collec105960082on_val @ (^[X3 : produc655058983on_val]: (((member1689761872on_val @ X3 @ B4)) & ((Q @ X3))))) @ (collec105960082on_val @ (^[X3 : produc655058983on_val]: (((member1689761872on_val @ X3 @ A2)) & ((P @ X3))))))))))). % subset_CollectI
thf(fact_209_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 @ (^[X3 : list_char]: (((member_list_char @ X3 @ B4)) & ((Q @ X3))))) @ (collect_list_char @ (^[X3 : list_char]: (((member_list_char @ X3 @ A2)) & ((P @ X3))))))))))). % subset_CollectI
thf(fact_210_top_Oextremum__uniqueI, axiom,
    ((![A : set_list_char]: ((ord_le1836582007t_char @ top_to748628679t_char @ A) => (A = top_to748628679t_char))))). % top.extremum_uniqueI
thf(fact_211_top_Oextremum__unique, axiom,
    ((![A : set_list_char]: ((ord_le1836582007t_char @ top_to748628679t_char @ A) = (A = top_to748628679t_char))))). % top.extremum_unique
thf(fact_212_top__greatest, axiom,
    ((![A : set_list_char]: (ord_le1836582007t_char @ A @ top_to748628679t_char)))). % top_greatest
thf(fact_213_order__subst1, axiom,
    ((![A : set_list_char, F : set_list_char > set_list_char, B2 : set_list_char, C4 : set_list_char]: ((ord_le1836582007t_char @ A @ (F @ B2)) => ((ord_le1836582007t_char @ B2 @ C4) => ((![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 @ C4)))))))). % order_subst1
thf(fact_214_order__subst2, axiom,
    ((![A : set_list_char, B2 : set_list_char, F : set_list_char > set_list_char, C4 : set_list_char]: ((ord_le1836582007t_char @ A @ B2) => ((ord_le1836582007t_char @ (F @ B2) @ C4) => ((![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) @ C4))))))). % order_subst2
thf(fact_215_ord__eq__le__subst, axiom,
    ((![A : set_list_char, F : set_list_char > set_list_char, B2 : set_list_char, C4 : set_list_char]: ((A = (F @ B2)) => ((ord_le1836582007t_char @ B2 @ C4) => ((![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 @ C4)))))))). % ord_eq_le_subst
thf(fact_216_ord__le__eq__subst, axiom,
    ((![A : set_list_char, B2 : set_list_char, F : set_list_char > set_list_char, C4 : set_list_char]: ((ord_le1836582007t_char @ A @ B2) => (((F @ B2) = C4) => ((![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) @ C4))))))). % ord_le_eq_subst
thf(fact_217_eq__iff, axiom,
    (((^[Y5 : set_list_char]: (^[Z : set_list_char]: (Y5 = Z))) = (^[X3 : set_list_char]: (^[Y4 : set_list_char]: (((ord_le1836582007t_char @ X3 @ Y4)) & ((ord_le1836582007t_char @ Y4 @ X3)))))))). % eq_iff
thf(fact_218_antisym, axiom,
    ((![X : set_list_char, Y : set_list_char]: ((ord_le1836582007t_char @ X @ Y) => ((ord_le1836582007t_char @ Y @ X) => (X = Y)))))). % antisym
thf(fact_219_eq__refl, axiom,
    ((![X : set_list_char, Y : set_list_char]: ((X = Y) => (ord_le1836582007t_char @ X @ Y))))). % eq_refl
thf(fact_220_order_Otrans, axiom,
    ((![A : set_list_char, B2 : set_list_char, C4 : set_list_char]: ((ord_le1836582007t_char @ A @ B2) => ((ord_le1836582007t_char @ B2 @ C4) => (ord_le1836582007t_char @ A @ C4)))))). % order.trans
thf(fact_221_antisym__conv, axiom,
    ((![Y : set_list_char, X : set_list_char]: ((ord_le1836582007t_char @ Y @ X) => ((ord_le1836582007t_char @ X @ Y) = (X = Y)))))). % antisym_conv
thf(fact_222_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_223_ord__eq__le__trans, axiom,
    ((![A : set_list_char, B2 : set_list_char, C4 : set_list_char]: ((A = B2) => ((ord_le1836582007t_char @ B2 @ C4) => (ord_le1836582007t_char @ A @ C4)))))). % ord_eq_le_trans
thf(fact_224_ord__le__eq__trans, axiom,
    ((![A : set_list_char, B2 : set_list_char, C4 : set_list_char]: ((ord_le1836582007t_char @ A @ B2) => ((B2 = C4) => (ord_le1836582007t_char @ A @ C4)))))). % ord_le_eq_trans
thf(fact_225_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_226_order__trans, axiom,
    ((![X : set_list_char, Y : set_list_char, Z2 : set_list_char]: ((ord_le1836582007t_char @ X @ Y) => ((ord_le1836582007t_char @ Y @ Z2) => (ord_le1836582007t_char @ X @ Z2)))))). % order_trans
thf(fact_227_dual__order_Orefl, axiom,
    ((![A : set_list_char]: (ord_le1836582007t_char @ A @ A)))). % dual_order.refl
thf(fact_228_dual__order_Otrans, axiom,
    ((![B2 : set_list_char, A : set_list_char, C4 : set_list_char]: ((ord_le1836582007t_char @ B2 @ A) => ((ord_le1836582007t_char @ C4 @ B2) => (ord_le1836582007t_char @ C4 @ A)))))). % dual_order.trans
thf(fact_229_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_230_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_231_top__empty__eq, axiom,
    ((top_to1455478342_val_o = (^[X3 : produc1172664615on_val]: (member354538064on_val @ X3 @ top_to1683965271on_val))))). % top_empty_eq
thf(fact_232_top__empty__eq, axiom,
    ((top_to1406902342_val_o = (^[X3 : produc655058983on_val]: (member1689761872on_val @ X3 @ top_to140144471on_val))))). % top_empty_eq
thf(fact_233_top__empty__eq, axiom,
    ((top_top_list_char_o = (^[X3 : list_char]: (member_list_char @ X3 @ top_to748628679t_char))))). % top_empty_eq
thf(fact_234_top__empty__eq2, axiom,
    ((top_to420008382_val_o = (^[X3 : produc335961278on_val]: (^[Y4 : produc335961278on_val]: (member1689761872on_val @ (produc245869591on_val @ X3 @ Y4) @ top_to140144471on_val)))))). % top_empty_eq2
thf(fact_235_top__empty__eq2, axiom,
    ((top_to1666156862_val_o = (^[X3 : produc1097884484on_val]: (^[Y4 : produc1097884484on_val]: (member354538064on_val @ (produc1069526295on_val @ X3 @ Y4) @ top_to1683965271on_val)))))). % top_empty_eq2
thf(fact_236_top__empty__eq2, axiom,
    ((top_to1286271689_val_o = (^[X3 : list_char]: (^[Y4 : produc1257910179t_char > option_val]: (member1296415951on_val @ (produc904988266on_val @ X3 @ Y4) @ top_to624090270on_val)))))). % top_empty_eq2
thf(fact_237_top__empty__eq2, axiom,
    ((top_to1309089767_val_o = (^[X3 : list_exp_list_char]: (^[Y4 : produc515445032on_val]: (member184158439on_val @ (produc1725134254on_val @ X3 @ Y4) @ top_to127038574on_val)))))). % top_empty_eq2
thf(fact_238_top__empty__eq2, axiom,
    ((top_to2035973601_val_o = (^[X3 : exp_list_char]: (^[Y4 : produc515445032on_val]: (member1888679917on_val @ (produc2023458740on_val @ X3 @ Y4) @ top_to796958324on_val)))))). % top_empty_eq2
thf(fact_239_top__empty__eq2, axiom,
    ((top_to1645522895_val_o = (^[X3 : nat > option2118145160on_val]: (^[Y4 : list_char > option_val]: (member652041809on_val @ (produc52622304on_val @ X3 @ Y4) @ top_to374550744on_val)))))). % top_empty_eq2
thf(fact_240_top__set__def, axiom,
    ((top_to748628679t_char = (collect_list_char @ top_top_list_char_o)))). % top_set_def
thf(fact_241_red__reds_OListRed1, axiom,
    ((![E : exp_list_char, S2 : produc515445032on_val, E2 : exp_list_char, S3 : produc515445032on_val, P : list_P1234162913t_char, Es : list_exp_list_char]: ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E @ S2) @ (produc2023458740on_val @ E2 @ S3)) @ (red @ P)) => (member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ (cons_exp_list_char @ E @ Es) @ S2) @ (produc1725134254on_val @ (cons_exp_list_char @ E2 @ Es) @ S3)) @ (reds @ P)))))). % red_reds.ListRed1
thf(fact_242_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_243_reds__hext__incr, axiom,
    ((![Es : list_exp_list_char, H : nat > option2118145160on_val, L : list_char > option_val, Es2 : list_exp_list_char, H2 : nat > option2118145160on_val, L2 : list_char > option_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es @ (produc52622304on_val @ H @ L)) @ (produc1725134254on_val @ Es2 @ (produc52622304on_val @ H2 @ L2))) @ (reds @ P)) => (hext @ H @ H2))))). % reds_hext_incr
thf(fact_244_hext__refl, axiom,
    ((![H : nat > option2118145160on_val]: (hext @ H @ H)))). % hext_refl
thf(fact_245_reds_Osimps, axiom,
    ((![A1 : list_exp_list_char, A22 : produc515445032on_val, A32 : list_exp_list_char, A42 : produc515445032on_val, P : list_P1234162913t_char]: ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ A1 @ A22) @ (produc1725134254on_val @ A32 @ A42)) @ (reds @ P)) = (((?[E3 : exp_list_char]: (?[S4 : produc515445032on_val]: (?[E4 : exp_list_char]: (?[S5 : produc515445032on_val]: (?[Es3 : list_exp_list_char]: (((A1 = (cons_exp_list_char @ E3 @ Es3))) & ((((A22 = S4)) & ((((A32 = (cons_exp_list_char @ E4 @ Es3))) & ((((A42 = S5)) & ((member354538064on_val @ (produc1069526295on_val @ (produc2023458740on_val @ E3 @ S4) @ (produc2023458740on_val @ E4 @ S5)) @ (red @ P)))))))))))))))) | ((?[Es3 : list_exp_list_char]: (?[S4 : produc515445032on_val]: (?[Es4 : list_exp_list_char]: (?[S5 : produc515445032on_val]: (?[V : val]: (((A1 = (cons_exp_list_char @ (val_list_char @ V) @ Es3))) & ((((A22 = S4)) & ((((A32 = (cons_exp_list_char @ (val_list_char @ V) @ Es4))) & ((((A42 = S5)) & ((member1689761872on_val @ (produc245869591on_val @ (produc1725134254on_val @ Es3 @ S4) @ (produc1725134254on_val @ Es4 @ S5)) @ (reds @ P))))))))))))))))))))). % reds.simps
thf(fact_246_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_247_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_248_hext__objD, axiom,
    ((![H : nat > option2118145160on_val, H2 : nat > option2118145160on_val, A : nat, C3 : list_char, Fs5 : produc1257910179t_char > option_val]: ((hext @ H @ H2) => (((H @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs5))) => (?[Fs6 : produc1257910179t_char > option_val]: ((H2 @ A) = (some_P1299442195on_val @ (produc904988266on_val @ C3 @ Fs6))))))))). % hext_objD

% Conjectures (1)
thf(conj_0, conjecture,
    ((d_s_list_char @ (cons_exp_list_char @ e_a @ esa) @ (some_set_list_char @ (dom_list_char_val @ ba))))).
