% 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/Arrow_Order/prob_56__5184798_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:15:52.355

% Could-be-implicit typings (10)
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_Pr448479039le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    set_Pr367596371le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Sum____Type__Osum_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    set_Su139092479le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc16571293le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    set_op14741964le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    set_se1079004006le_alt : $tType).
thf(ty_n_t__Filter__Ofilter_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    filter777601580le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    set_Ar1665529862le_alt : $tType).
thf(ty_n_t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    arrow_1857593510le_alt : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (45)
thf(sy_c_BNF__Wellorder__Relation_Owo__rel_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    bNF_We2119369874le_alt : set_Pr367596371le_alt > $o).
thf(sy_c_Filter_Ocofinite_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    cofini1417700454le_alt : filter777601580le_alt).
thf(sy_c_Finite__Set_Ofinite_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    finite87608527le_alt : set_Ar1665529862le_alt > $o).
thf(sy_c_Finite__Set_Ofinite_001t__Option__Ooption_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    finite586828693le_alt : set_op14741964le_alt > $o).
thf(sy_c_Finite__Set_Ofinite_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    finite1252355508le_alt : set_Pr367596371le_alt > $o).
thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    finite855179311le_alt : set_se1079004006le_alt > $o).
thf(sy_c_Finite__Set_Ofinite_001t__Sum____Type__Osum_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    finite1403864904le_alt : set_Su139092479le_alt > $o).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    minus_1791297389le_alt : set_Ar1665529862le_alt > set_Ar1665529862le_alt > set_Ar1665529862le_alt).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    minus_467626412le_alt : set_Pr367596371le_alt > set_Pr367596371le_alt > set_Pr367596371le_alt).
thf(sy_c_Order__Relation_Olinear__order__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    order_318683099le_alt : set_Ar1665529862le_alt > set_Pr367596371le_alt > $o).
thf(sy_c_Order__Relation_Opartial__order__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    order_529098139le_alt : set_Ar1665529862le_alt > set_Pr367596371le_alt > $o).
thf(sy_c_Order__Relation_Ostrict__linear__order__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    order_257197092le_alt : set_Ar1665529862le_alt > set_Pr367596371le_alt > $o).
thf(sy_c_Order__Relation_Owell__order__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    order_1185271620le_alt : set_Ar1665529862le_alt > set_Pr367596371le_alt > $o).
thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_M_Eo_J, type,
    bot_bo1380086507_alt_o : arrow_1857593510le_alt > $o).
thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_M_Eo_J, type,
    bot_bo91657054_alt_o : produc16571293le_alt > $o).
thf(sy_c_Orderings_Obot__class_Obot_001t__Filter__Ofilter_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    bot_bo1687181976le_alt : filter777601580le_alt).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    bot_bo1127707250le_alt : set_Ar1665529862le_alt).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    bot_bo1596236775le_alt : set_Pr367596371le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_M_Eo_J, type,
    top_to516240647_alt_o : arrow_1857593510le_alt > $o).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_M_Eo_J, type,
    top_to1074038850_alt_o : produc16571293le_alt > $o).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    top_to958727510le_alt : set_Ar1665529862le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Option__Ooption_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    top_to1783219996le_alt : set_op14741964le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    top_to224369155le_alt : set_Pr367596371le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    top_to751966390le_alt : set_se1079004006le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Sum____Type__Osum_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    top_to213286735le_alt : set_Su139092479le_alt).
thf(sy_c_Relation_OId_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    id_Arr1939538434le_alt : set_Pr367596371le_alt).
thf(sy_c_Relation_Oantisym_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    antisy1745863240le_alt : set_Pr367596371le_alt > $o).
thf(sy_c_Relation_Oconverse_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    conver1781819635le_alt : set_Pr367596371le_alt > set_Pr367596371le_alt).
thf(sy_c_Relation_Oirrefl_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    irrefl1932292187le_alt : set_Pr367596371le_alt > $o).
thf(sy_c_Relation_Ototal__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    total_2034085930le_alt : set_Ar1665529862le_alt > set_Pr367596371le_alt > $o).
thf(sy_c_Relation_Ototal__on_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    total_608959769le_alt : set_Pr367596371le_alt > set_Pr448479039le_alt > $o).
thf(sy_c_Relation_Otrans_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    trans_1364318725le_alt : set_Pr367596371le_alt > $o).
thf(sy_c_Set_OCollect_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    collec1364151825le_alt : (arrow_1857593510le_alt > $o) > set_Ar1665529862le_alt).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    collec531981554le_alt : (produc16571293le_alt > $o) > set_Pr367596371le_alt).
thf(sy_c_Set_OPow_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    pow_Ar727917891le_alt : set_Ar1665529862le_alt > set_se1079004006le_alt).
thf(sy_c_Set_Oinsert_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    insert1093389942le_alt : arrow_1857593510le_alt > set_Ar1665529862le_alt > set_Ar1665529862le_alt).
thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    insert1454465485le_alt : produc16571293le_alt > set_Pr367596371le_alt > set_Pr367596371le_alt).
thf(sy_c_Transitive__Closure_Oacyclic_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    transi1222743157le_alt : set_Pr367596371le_alt > $o).
thf(sy_c_Wellfounded_Olex__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    lex_pr3395839le_alt : set_Pr367596371le_alt > set_Pr367596371le_alt > set_Pr448479039le_alt).
thf(sy_c_Wellfounded_Omeasure_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    measur1447705966le_alt : (arrow_1857593510le_alt > nat) > set_Pr367596371le_alt).
thf(sy_c_Wellfounded_Owf_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    wf_Arr1630868879le_alt : set_Pr367596371le_alt > $o).
thf(sy_c_Wellfounded_Owf_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    wf_Pro1951028468le_alt : set_Pr448479039le_alt > $o).
thf(sy_c_member_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    member519365071le_alt : arrow_1857593510le_alt > set_Ar1665529862le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    member2048039092le_alt : produc16571293le_alt > set_Pr367596371le_alt > $o).
thf(sy_v_r, type,
    r : set_Pr367596371le_alt).

% Relevant facts (109)
thf(fact_0_strict__linear__order__on__diff__Id, axiom,
    ((![A : set_Ar1665529862le_alt, R : set_Pr367596371le_alt]: ((order_318683099le_alt @ A @ R) => (order_257197092le_alt @ A @ (minus_467626412le_alt @ R @ id_Arr1939538434le_alt)))))). % strict_linear_order_on_diff_Id
thf(fact_1_DiffI, axiom,
    ((![C : arrow_1857593510le_alt, A : set_Ar1665529862le_alt, B : set_Ar1665529862le_alt]: ((member519365071le_alt @ C @ A) => ((~ ((member519365071le_alt @ C @ B))) => (member519365071le_alt @ C @ (minus_1791297389le_alt @ A @ B))))))). % DiffI
thf(fact_2_DiffI, axiom,
    ((![C : produc16571293le_alt, A : set_Pr367596371le_alt, B : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ A) => ((~ ((member2048039092le_alt @ C @ B))) => (member2048039092le_alt @ C @ (minus_467626412le_alt @ A @ B))))))). % DiffI
thf(fact_3_Diff__iff, axiom,
    ((![C : arrow_1857593510le_alt, A : set_Ar1665529862le_alt, B : set_Ar1665529862le_alt]: ((member519365071le_alt @ C @ (minus_1791297389le_alt @ A @ B)) = (((member519365071le_alt @ C @ A)) & ((~ ((member519365071le_alt @ C @ B))))))))). % Diff_iff
thf(fact_4_Diff__iff, axiom,
    ((![C : produc16571293le_alt, A : set_Pr367596371le_alt, B : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ (minus_467626412le_alt @ A @ B)) = (((member2048039092le_alt @ C @ A)) & ((~ ((member2048039092le_alt @ C @ B))))))))). % Diff_iff
thf(fact_5_Diff__idemp, axiom,
    ((![A : set_Pr367596371le_alt, B : set_Pr367596371le_alt]: ((minus_467626412le_alt @ (minus_467626412le_alt @ A @ B) @ B) = (minus_467626412le_alt @ A @ B))))). % Diff_idemp
thf(fact_6_UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % UNIV_I
thf(fact_7_UNIV__I, axiom,
    ((![X : arrow_1857593510le_alt]: (member519365071le_alt @ X @ top_to958727510le_alt)))). % UNIV_I
thf(fact_8_iso__tuple__UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % iso_tuple_UNIV_I
thf(fact_9_iso__tuple__UNIV__I, axiom,
    ((![X : arrow_1857593510le_alt]: (member519365071le_alt @ X @ top_to958727510le_alt)))). % iso_tuple_UNIV_I
thf(fact_10__092_060open_062_092_060exists_062r_O_Awell__order_Ar_092_060close_062, axiom,
    ((?[X_1 : set_Pr367596371le_alt]: (order_1185271620le_alt @ top_to958727510le_alt @ X_1)))). % \<open>\<exists>r. well_order r\<close>
thf(fact_11_DiffE, axiom,
    ((![C : arrow_1857593510le_alt, A : set_Ar1665529862le_alt, B : set_Ar1665529862le_alt]: ((member519365071le_alt @ C @ (minus_1791297389le_alt @ A @ B)) => (~ (((member519365071le_alt @ C @ A) => (member519365071le_alt @ C @ B)))))))). % DiffE
thf(fact_12_DiffE, axiom,
    ((![C : produc16571293le_alt, A : set_Pr367596371le_alt, B : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ (minus_467626412le_alt @ A @ B)) => (~ (((member2048039092le_alt @ C @ A) => (member2048039092le_alt @ C @ B)))))))). % DiffE
thf(fact_13_DiffD1, axiom,
    ((![C : arrow_1857593510le_alt, A : set_Ar1665529862le_alt, B : set_Ar1665529862le_alt]: ((member519365071le_alt @ C @ (minus_1791297389le_alt @ A @ B)) => (member519365071le_alt @ C @ A))))). % DiffD1
thf(fact_14_DiffD1, axiom,
    ((![C : produc16571293le_alt, A : set_Pr367596371le_alt, B : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ (minus_467626412le_alt @ A @ B)) => (member2048039092le_alt @ C @ A))))). % DiffD1
thf(fact_15_DiffD2, axiom,
    ((![C : arrow_1857593510le_alt, A : set_Ar1665529862le_alt, B : set_Ar1665529862le_alt]: ((member519365071le_alt @ C @ (minus_1791297389le_alt @ A @ B)) => (~ ((member519365071le_alt @ C @ B))))))). % DiffD2
thf(fact_16_DiffD2, axiom,
    ((![C : produc16571293le_alt, A : set_Pr367596371le_alt, B : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ (minus_467626412le_alt @ A @ B)) => (~ ((member2048039092le_alt @ C @ B))))))). % DiffD2
thf(fact_17_top__set__def, axiom,
    ((top_to958727510le_alt = (collec1364151825le_alt @ top_to516240647_alt_o)))). % top_set_def
thf(fact_18_well__order__on__def, axiom,
    ((order_1185271620le_alt = (^[A2 : set_Ar1665529862le_alt]: (^[R2 : set_Pr367596371le_alt]: (((order_318683099le_alt @ A2 @ R2)) & ((wf_Arr1630868879le_alt @ (minus_467626412le_alt @ R2 @ id_Arr1939538434le_alt))))))))). % well_order_on_def
thf(fact_19_UNIV__witness, axiom,
    ((?[X2 : produc16571293le_alt]: (member2048039092le_alt @ X2 @ top_to224369155le_alt)))). % UNIV_witness
thf(fact_20_UNIV__witness, axiom,
    ((?[X2 : arrow_1857593510le_alt]: (member519365071le_alt @ X2 @ top_to958727510le_alt)))). % UNIV_witness
thf(fact_21_UNIV__eq__I, axiom,
    ((![A : set_Pr367596371le_alt]: ((![X2 : produc16571293le_alt]: (member2048039092le_alt @ X2 @ A)) => (top_to224369155le_alt = A))))). % UNIV_eq_I
thf(fact_22_UNIV__eq__I, axiom,
    ((![A : set_Ar1665529862le_alt]: ((![X2 : arrow_1857593510le_alt]: (member519365071le_alt @ X2 @ A)) => (top_to958727510le_alt = A))))). % UNIV_eq_I
thf(fact_23_linear__order__on__acyclic, axiom,
    ((![A : set_Ar1665529862le_alt, R : set_Pr367596371le_alt]: ((order_318683099le_alt @ A @ R) => (transi1222743157le_alt @ (minus_467626412le_alt @ R @ id_Arr1939538434le_alt)))))). % linear_order_on_acyclic
thf(fact_24_well__order__on, axiom,
    ((![A : set_Ar1665529862le_alt]: (?[X_1 : set_Pr367596371le_alt]: (order_1185271620le_alt @ A @ X_1))))). % well_order_on
thf(fact_25_top__empty__eq, axiom,
    ((top_to1074038850_alt_o = (^[X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ top_to224369155le_alt))))). % top_empty_eq
thf(fact_26_top__empty__eq, axiom,
    ((top_to516240647_alt_o = (^[X3 : arrow_1857593510le_alt]: (member519365071le_alt @ X3 @ top_to958727510le_alt))))). % top_empty_eq
thf(fact_27_Diff__UNIV, axiom,
    ((![A : set_Ar1665529862le_alt]: ((minus_1791297389le_alt @ A @ top_to958727510le_alt) = bot_bo1127707250le_alt)))). % Diff_UNIV
thf(fact_28_Diff__UNIV, axiom,
    ((![A : set_Pr367596371le_alt]: ((minus_467626412le_alt @ A @ top_to224369155le_alt) = bot_bo1596236775le_alt)))). % Diff_UNIV
thf(fact_29_wo__rel_OWF, axiom,
    ((![R : set_Pr367596371le_alt]: ((bNF_We2119369874le_alt @ R) => (wf_Arr1630868879le_alt @ (minus_467626412le_alt @ R @ id_Arr1939538434le_alt)))))). % wo_rel.WF
thf(fact_30_linear__order__on__well__order__on, axiom,
    ((![R : set_Pr367596371le_alt, A : set_Ar1665529862le_alt]: ((finite1252355508le_alt @ R) => ((order_318683099le_alt @ A @ R) = (order_1185271620le_alt @ A @ R)))))). % linear_order_on_well_order_on
thf(fact_31_irrefl__diff__Id, axiom,
    ((![R : set_Pr367596371le_alt]: (irrefl1932292187le_alt @ (minus_467626412le_alt @ R @ id_Arr1939538434le_alt))))). % irrefl_diff_Id
thf(fact_32_total__on__diff__Id, axiom,
    ((![A : set_Ar1665529862le_alt, R : set_Pr367596371le_alt]: ((total_2034085930le_alt @ A @ (minus_467626412le_alt @ R @ id_Arr1939538434le_alt)) = (total_2034085930le_alt @ A @ R))))). % total_on_diff_Id
thf(fact_33_empty__iff, axiom,
    ((![C : produc16571293le_alt]: (~ ((member2048039092le_alt @ C @ bot_bo1596236775le_alt)))))). % empty_iff
thf(fact_34_empty__iff, axiom,
    ((![C : arrow_1857593510le_alt]: (~ ((member519365071le_alt @ C @ bot_bo1127707250le_alt)))))). % empty_iff
thf(fact_35_all__not__in__conv, axiom,
    ((![A : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: (~ ((member2048039092le_alt @ X3 @ A)))) = (A = bot_bo1596236775le_alt))))). % all_not_in_conv
thf(fact_36_all__not__in__conv, axiom,
    ((![A : set_Ar1665529862le_alt]: ((![X3 : arrow_1857593510le_alt]: (~ ((member519365071le_alt @ X3 @ A)))) = (A = bot_bo1127707250le_alt))))). % all_not_in_conv
thf(fact_37_Diff__empty, axiom,
    ((![A : set_Pr367596371le_alt]: ((minus_467626412le_alt @ A @ bot_bo1596236775le_alt) = A)))). % Diff_empty
thf(fact_38_empty__Diff, axiom,
    ((![A : set_Pr367596371le_alt]: ((minus_467626412le_alt @ bot_bo1596236775le_alt @ A) = bot_bo1596236775le_alt)))). % empty_Diff
thf(fact_39_Diff__cancel, axiom,
    ((![A : set_Pr367596371le_alt]: ((minus_467626412le_alt @ A @ A) = bot_bo1596236775le_alt)))). % Diff_cancel
thf(fact_40_emptyE, axiom,
    ((![A3 : produc16571293le_alt]: (~ ((member2048039092le_alt @ A3 @ bot_bo1596236775le_alt)))))). % emptyE
thf(fact_41_emptyE, axiom,
    ((![A3 : arrow_1857593510le_alt]: (~ ((member519365071le_alt @ A3 @ bot_bo1127707250le_alt)))))). % emptyE
thf(fact_42_equals0D, axiom,
    ((![A : set_Pr367596371le_alt, A3 : produc16571293le_alt]: ((A = bot_bo1596236775le_alt) => (~ ((member2048039092le_alt @ A3 @ A))))))). % equals0D
thf(fact_43_equals0D, axiom,
    ((![A : set_Ar1665529862le_alt, A3 : arrow_1857593510le_alt]: ((A = bot_bo1127707250le_alt) => (~ ((member519365071le_alt @ A3 @ A))))))). % equals0D
thf(fact_44_equals0I, axiom,
    ((![A : set_Pr367596371le_alt]: ((![Y : produc16571293le_alt]: (~ ((member2048039092le_alt @ Y @ A)))) => (A = bot_bo1596236775le_alt))))). % equals0I
thf(fact_45_equals0I, axiom,
    ((![A : set_Ar1665529862le_alt]: ((![Y : arrow_1857593510le_alt]: (~ ((member519365071le_alt @ Y @ A)))) => (A = bot_bo1127707250le_alt))))). % equals0I
thf(fact_46_ex__in__conv, axiom,
    ((![A : set_Pr367596371le_alt]: ((?[X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ A)) = (~ ((A = bot_bo1596236775le_alt))))))). % ex_in_conv
thf(fact_47_ex__in__conv, axiom,
    ((![A : set_Ar1665529862le_alt]: ((?[X3 : arrow_1857593510le_alt]: (member519365071le_alt @ X3 @ A)) = (~ ((A = bot_bo1127707250le_alt))))))). % ex_in_conv
thf(fact_48_well__order__on__empty, axiom,
    ((order_1185271620le_alt @ bot_bo1127707250le_alt @ bot_bo1596236775le_alt))). % well_order_on_empty
thf(fact_49_lnear__order__on__empty, axiom,
    ((order_318683099le_alt @ bot_bo1127707250le_alt @ bot_bo1596236775le_alt))). % lnear_order_on_empty
thf(fact_50_empty__not__UNIV, axiom,
    ((~ ((bot_bo1127707250le_alt = top_to958727510le_alt))))). % empty_not_UNIV
thf(fact_51_mem__Collect__eq, axiom,
    ((![A3 : produc16571293le_alt, P : produc16571293le_alt > $o]: ((member2048039092le_alt @ A3 @ (collec531981554le_alt @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_52_mem__Collect__eq, axiom,
    ((![A3 : arrow_1857593510le_alt, P : arrow_1857593510le_alt > $o]: ((member519365071le_alt @ A3 @ (collec1364151825le_alt @ P)) = (P @ A3))))). % mem_Collect_eq
thf(fact_53_Collect__mem__eq, axiom,
    ((![A : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ A))) = A)))). % Collect_mem_eq
thf(fact_54_Collect__mem__eq, axiom,
    ((![A : set_Ar1665529862le_alt]: ((collec1364151825le_alt @ (^[X3 : arrow_1857593510le_alt]: (member519365071le_alt @ X3 @ A))) = A)))). % Collect_mem_eq
thf(fact_55_finite__Diff, axiom,
    ((![A : set_Pr367596371le_alt, B : set_Pr367596371le_alt]: ((finite1252355508le_alt @ A) => (finite1252355508le_alt @ (minus_467626412le_alt @ A @ B)))))). % finite_Diff
thf(fact_56_finite__Diff2, axiom,
    ((![B : set_Pr367596371le_alt, A : set_Pr367596371le_alt]: ((finite1252355508le_alt @ B) => ((finite1252355508le_alt @ (minus_467626412le_alt @ A @ B)) = (finite1252355508le_alt @ A)))))). % finite_Diff2
thf(fact_57_finite__option__UNIV, axiom,
    (((finite586828693le_alt @ top_to1783219996le_alt) = (finite87608527le_alt @ top_to958727510le_alt)))). % finite_option_UNIV
thf(fact_58_finite__Plus__UNIV__iff, axiom,
    (((finite1403864904le_alt @ top_to213286735le_alt) = (((finite87608527le_alt @ top_to958727510le_alt)) & ((finite87608527le_alt @ top_to958727510le_alt)))))). % finite_Plus_UNIV_iff
thf(fact_59_wf__iff__acyclic__if__finite, axiom,
    ((![R : set_Pr367596371le_alt]: ((finite1252355508le_alt @ R) => ((wf_Arr1630868879le_alt @ R) = (transi1222743157le_alt @ R)))))). % wf_iff_acyclic_if_finite
thf(fact_60_finite__acyclic__wf, axiom,
    ((![R : set_Pr367596371le_alt]: ((finite1252355508le_alt @ R) => ((transi1222743157le_alt @ R) => (wf_Arr1630868879le_alt @ R)))))). % finite_acyclic_wf
thf(fact_61_finite__prod, axiom,
    (((finite1252355508le_alt @ top_to224369155le_alt) = (((finite87608527le_alt @ top_to958727510le_alt)) & ((finite87608527le_alt @ top_to958727510le_alt)))))). % finite_prod
thf(fact_62_finite__Prod__UNIV, axiom,
    (((finite87608527le_alt @ top_to958727510le_alt) => ((finite87608527le_alt @ top_to958727510le_alt) => (finite1252355508le_alt @ top_to224369155le_alt))))). % finite_Prod_UNIV
thf(fact_63_wf__empty, axiom,
    ((wf_Arr1630868879le_alt @ bot_bo1596236775le_alt))). % wf_empty
thf(fact_64_bot__empty__eq, axiom,
    ((bot_bo91657054_alt_o = (^[X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ bot_bo1596236775le_alt))))). % bot_empty_eq
thf(fact_65_bot__empty__eq, axiom,
    ((bot_bo1380086507_alt_o = (^[X3 : arrow_1857593510le_alt]: (member519365071le_alt @ X3 @ bot_bo1127707250le_alt))))). % bot_empty_eq
thf(fact_66_ex__new__if__finite, axiom,
    ((![A : set_Pr367596371le_alt]: ((~ ((finite1252355508le_alt @ top_to224369155le_alt))) => ((finite1252355508le_alt @ A) => (?[A4 : produc16571293le_alt]: (~ ((member2048039092le_alt @ A4 @ A))))))))). % ex_new_if_finite
thf(fact_67_ex__new__if__finite, axiom,
    ((![A : set_Ar1665529862le_alt]: ((~ ((finite87608527le_alt @ top_to958727510le_alt))) => ((finite87608527le_alt @ A) => (?[A4 : arrow_1857593510le_alt]: (~ ((member519365071le_alt @ A4 @ A))))))))). % ex_new_if_finite
thf(fact_68_Finite__Set_Ofinite__set, axiom,
    (((finite855179311le_alt @ top_to751966390le_alt) = (finite87608527le_alt @ top_to958727510le_alt)))). % Finite_Set.finite_set
thf(fact_69_Diff__infinite__finite, axiom,
    ((![T : set_Pr367596371le_alt, S : set_Pr367596371le_alt]: ((finite1252355508le_alt @ T) => ((~ ((finite1252355508le_alt @ S))) => (~ ((finite1252355508le_alt @ (minus_467626412le_alt @ S @ T))))))))). % Diff_infinite_finite
thf(fact_70_wf__acyclic, axiom,
    ((![R : set_Pr367596371le_alt]: ((wf_Arr1630868879le_alt @ R) => (transi1222743157le_alt @ R))))). % wf_acyclic
thf(fact_71_wf__imp__irrefl, axiom,
    ((![R : set_Pr367596371le_alt]: ((wf_Arr1630868879le_alt @ R) => (irrefl1932292187le_alt @ R))))). % wf_imp_irrefl
thf(fact_72_wf__measure, axiom,
    ((![F : arrow_1857593510le_alt > nat]: (wf_Arr1630868879le_alt @ (measur1447705966le_alt @ F))))). % wf_measure
thf(fact_73_total__lex__prod, axiom,
    ((![R : set_Pr367596371le_alt, S2 : set_Pr367596371le_alt]: ((total_2034085930le_alt @ top_to958727510le_alt @ R) => ((total_2034085930le_alt @ top_to958727510le_alt @ S2) => (total_608959769le_alt @ top_to224369155le_alt @ (lex_pr3395839le_alt @ R @ S2))))))). % total_lex_prod
thf(fact_74_partial__order__on__well__order__on, axiom,
    ((![R : set_Pr367596371le_alt, A : set_Ar1665529862le_alt]: ((finite1252355508le_alt @ R) => ((order_529098139le_alt @ A @ R) => (wf_Arr1630868879le_alt @ (minus_467626412le_alt @ R @ id_Arr1939538434le_alt))))))). % partial_order_on_well_order_on
thf(fact_75_partial__order__on__acyclic, axiom,
    ((![A : set_Ar1665529862le_alt, R : set_Pr367596371le_alt]: ((order_529098139le_alt @ A @ R) => (transi1222743157le_alt @ (minus_467626412le_alt @ R @ id_Arr1939538434le_alt)))))). % partial_order_on_acyclic
thf(fact_76_wf__lex__prod, axiom,
    ((![Ra : set_Pr367596371le_alt, Rb : set_Pr367596371le_alt]: ((wf_Arr1630868879le_alt @ Ra) => ((wf_Arr1630868879le_alt @ Rb) => (wf_Pro1951028468le_alt @ (lex_pr3395839le_alt @ Ra @ Rb))))))). % wf_lex_prod
thf(fact_77_linear__order__on__def, axiom,
    ((order_318683099le_alt = (^[A2 : set_Ar1665529862le_alt]: (^[R2 : set_Pr367596371le_alt]: (((order_529098139le_alt @ A2 @ R2)) & ((total_2034085930le_alt @ A2 @ R2)))))))). % linear_order_on_def
thf(fact_78_strict__linear__order__on__def, axiom,
    ((order_257197092le_alt = (^[A2 : set_Ar1665529862le_alt]: (^[R2 : set_Pr367596371le_alt]: (((trans_1364318725le_alt @ R2)) & ((((irrefl1932292187le_alt @ R2)) & ((total_2034085930le_alt @ A2 @ R2)))))))))). % strict_linear_order_on_def
thf(fact_79_trans__Id, axiom,
    ((trans_1364318725le_alt @ id_Arr1939538434le_alt))). % trans_Id
thf(fact_80_cofinite__bot, axiom,
    (((cofini1417700454le_alt = bot_bo1687181976le_alt) = (finite87608527le_alt @ top_to958727510le_alt)))). % cofinite_bot
thf(fact_81_trans__diff__Id, axiom,
    ((![R : set_Pr367596371le_alt]: ((trans_1364318725le_alt @ R) => ((antisy1745863240le_alt @ R) => (trans_1364318725le_alt @ (minus_467626412le_alt @ R @ id_Arr1939538434le_alt))))))). % trans_diff_Id
thf(fact_82_wf__converse, axiom,
    ((![R : set_Pr367596371le_alt]: ((irrefl1932292187le_alt @ R) => ((trans_1364318725le_alt @ R) => ((finite1252355508le_alt @ R) => (wf_Arr1630868879le_alt @ (conver1781819635le_alt @ R)))))))). % wf_converse
thf(fact_83_converse__Id, axiom,
    (((conver1781819635le_alt @ id_Arr1939538434le_alt) = id_Arr1939538434le_alt))). % converse_Id
thf(fact_84_linear__order__on__converse, axiom,
    ((![A : set_Ar1665529862le_alt, R : set_Pr367596371le_alt]: ((order_318683099le_alt @ A @ (conver1781819635le_alt @ R)) = (order_318683099le_alt @ A @ R))))). % linear_order_on_converse
thf(fact_85_antisym__Id, axiom,
    ((antisy1745863240le_alt @ id_Arr1939538434le_alt))). % antisym_Id
thf(fact_86_finite__acyclic__wf__converse, axiom,
    ((![R : set_Pr367596371le_alt]: ((finite1252355508le_alt @ R) => ((transi1222743157le_alt @ R) => (wf_Arr1630868879le_alt @ (conver1781819635le_alt @ R))))))). % finite_acyclic_wf_converse
thf(fact_87_Pow__UNIV, axiom,
    (((pow_Ar727917891le_alt @ top_to958727510le_alt) = top_to751966390le_alt))). % Pow_UNIV
thf(fact_88_insert__iff, axiom,
    ((![A3 : produc16571293le_alt, B2 : produc16571293le_alt, A : set_Pr367596371le_alt]: ((member2048039092le_alt @ A3 @ (insert1454465485le_alt @ B2 @ A)) = (((A3 = B2)) | ((member2048039092le_alt @ A3 @ A))))))). % insert_iff
thf(fact_89_insert__iff, axiom,
    ((![A3 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, A : set_Ar1665529862le_alt]: ((member519365071le_alt @ A3 @ (insert1093389942le_alt @ B2 @ A)) = (((A3 = B2)) | ((member519365071le_alt @ A3 @ A))))))). % insert_iff
thf(fact_90_insertCI, axiom,
    ((![A3 : produc16571293le_alt, B : set_Pr367596371le_alt, B2 : produc16571293le_alt]: (((~ ((member2048039092le_alt @ A3 @ B))) => (A3 = B2)) => (member2048039092le_alt @ A3 @ (insert1454465485le_alt @ B2 @ B)))))). % insertCI
thf(fact_91_insertCI, axiom,
    ((![A3 : arrow_1857593510le_alt, B : set_Ar1665529862le_alt, B2 : arrow_1857593510le_alt]: (((~ ((member519365071le_alt @ A3 @ B))) => (A3 = B2)) => (member519365071le_alt @ A3 @ (insert1093389942le_alt @ B2 @ B)))))). % insertCI
thf(fact_92_singletonI, axiom,
    ((![A3 : produc16571293le_alt]: (member2048039092le_alt @ A3 @ (insert1454465485le_alt @ A3 @ bot_bo1596236775le_alt))))). % singletonI
thf(fact_93_singletonI, axiom,
    ((![A3 : arrow_1857593510le_alt]: (member519365071le_alt @ A3 @ (insert1093389942le_alt @ A3 @ bot_bo1127707250le_alt))))). % singletonI
thf(fact_94_Diff__insert0, axiom,
    ((![X : arrow_1857593510le_alt, A : set_Ar1665529862le_alt, B : set_Ar1665529862le_alt]: ((~ ((member519365071le_alt @ X @ A))) => ((minus_1791297389le_alt @ A @ (insert1093389942le_alt @ X @ B)) = (minus_1791297389le_alt @ A @ B)))))). % Diff_insert0
thf(fact_95_Diff__insert0, axiom,
    ((![X : produc16571293le_alt, A : set_Pr367596371le_alt, B : set_Pr367596371le_alt]: ((~ ((member2048039092le_alt @ X @ A))) => ((minus_467626412le_alt @ A @ (insert1454465485le_alt @ X @ B)) = (minus_467626412le_alt @ A @ B)))))). % Diff_insert0
thf(fact_96_insert__Diff1, axiom,
    ((![X : arrow_1857593510le_alt, B : set_Ar1665529862le_alt, A : set_Ar1665529862le_alt]: ((member519365071le_alt @ X @ B) => ((minus_1791297389le_alt @ (insert1093389942le_alt @ X @ A) @ B) = (minus_1791297389le_alt @ A @ B)))))). % insert_Diff1
thf(fact_97_insert__Diff1, axiom,
    ((![X : produc16571293le_alt, B : set_Pr367596371le_alt, A : set_Pr367596371le_alt]: ((member2048039092le_alt @ X @ B) => ((minus_467626412le_alt @ (insert1454465485le_alt @ X @ A) @ B) = (minus_467626412le_alt @ A @ B)))))). % insert_Diff1
thf(fact_98_insert__Diff__single, axiom,
    ((![A3 : produc16571293le_alt, A : set_Pr367596371le_alt]: ((insert1454465485le_alt @ A3 @ (minus_467626412le_alt @ A @ (insert1454465485le_alt @ A3 @ bot_bo1596236775le_alt))) = (insert1454465485le_alt @ A3 @ A))))). % insert_Diff_single
thf(fact_99_finite__Diff__insert, axiom,
    ((![A : set_Pr367596371le_alt, A3 : produc16571293le_alt, B : set_Pr367596371le_alt]: ((finite1252355508le_alt @ (minus_467626412le_alt @ A @ (insert1454465485le_alt @ A3 @ B))) = (finite1252355508le_alt @ (minus_467626412le_alt @ A @ B)))))). % finite_Diff_insert
thf(fact_100_insert__UNIV, axiom,
    ((![X : arrow_1857593510le_alt]: ((insert1093389942le_alt @ X @ top_to958727510le_alt) = top_to958727510le_alt)))). % insert_UNIV
thf(fact_101_insert__Diff__if, axiom,
    ((![X : arrow_1857593510le_alt, B : set_Ar1665529862le_alt, A : set_Ar1665529862le_alt]: (((member519365071le_alt @ X @ B) => ((minus_1791297389le_alt @ (insert1093389942le_alt @ X @ A) @ B) = (minus_1791297389le_alt @ A @ B))) & ((~ ((member519365071le_alt @ X @ B))) => ((minus_1791297389le_alt @ (insert1093389942le_alt @ X @ A) @ B) = (insert1093389942le_alt @ X @ (minus_1791297389le_alt @ A @ B)))))))). % insert_Diff_if
thf(fact_102_insert__Diff__if, axiom,
    ((![X : produc16571293le_alt, B : set_Pr367596371le_alt, A : set_Pr367596371le_alt]: (((member2048039092le_alt @ X @ B) => ((minus_467626412le_alt @ (insert1454465485le_alt @ X @ A) @ B) = (minus_467626412le_alt @ A @ B))) & ((~ ((member2048039092le_alt @ X @ B))) => ((minus_467626412le_alt @ (insert1454465485le_alt @ X @ A) @ B) = (insert1454465485le_alt @ X @ (minus_467626412le_alt @ A @ B)))))))). % insert_Diff_if
thf(fact_103_mk__disjoint__insert, axiom,
    ((![A3 : produc16571293le_alt, A : set_Pr367596371le_alt]: ((member2048039092le_alt @ A3 @ A) => (?[B3 : set_Pr367596371le_alt]: ((A = (insert1454465485le_alt @ A3 @ B3)) & (~ ((member2048039092le_alt @ A3 @ B3))))))))). % mk_disjoint_insert
thf(fact_104_mk__disjoint__insert, axiom,
    ((![A3 : arrow_1857593510le_alt, A : set_Ar1665529862le_alt]: ((member519365071le_alt @ A3 @ A) => (?[B3 : set_Ar1665529862le_alt]: ((A = (insert1093389942le_alt @ A3 @ B3)) & (~ ((member519365071le_alt @ A3 @ B3))))))))). % mk_disjoint_insert
thf(fact_105_insert__eq__iff, axiom,
    ((![A3 : produc16571293le_alt, A : set_Pr367596371le_alt, B2 : produc16571293le_alt, B : set_Pr367596371le_alt]: ((~ ((member2048039092le_alt @ A3 @ A))) => ((~ ((member2048039092le_alt @ B2 @ B))) => (((insert1454465485le_alt @ A3 @ A) = (insert1454465485le_alt @ B2 @ B)) = (((((A3 = B2)) => ((A = B)))) & ((((~ ((A3 = B2)))) => ((?[C2 : set_Pr367596371le_alt]: (((A = (insert1454465485le_alt @ B2 @ C2))) & ((((~ ((member2048039092le_alt @ B2 @ C2)))) & ((((B = (insert1454465485le_alt @ A3 @ C2))) & ((~ ((member2048039092le_alt @ A3 @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_106_insert__eq__iff, axiom,
    ((![A3 : arrow_1857593510le_alt, A : set_Ar1665529862le_alt, B2 : arrow_1857593510le_alt, B : set_Ar1665529862le_alt]: ((~ ((member519365071le_alt @ A3 @ A))) => ((~ ((member519365071le_alt @ B2 @ B))) => (((insert1093389942le_alt @ A3 @ A) = (insert1093389942le_alt @ B2 @ B)) = (((((A3 = B2)) => ((A = B)))) & ((((~ ((A3 = B2)))) => ((?[C2 : set_Ar1665529862le_alt]: (((A = (insert1093389942le_alt @ B2 @ C2))) & ((((~ ((member519365071le_alt @ B2 @ C2)))) & ((((B = (insert1093389942le_alt @ A3 @ C2))) & ((~ ((member519365071le_alt @ A3 @ C2)))))))))))))))))))). % insert_eq_iff
thf(fact_107_insert__absorb, axiom,
    ((![A3 : produc16571293le_alt, A : set_Pr367596371le_alt]: ((member2048039092le_alt @ A3 @ A) => ((insert1454465485le_alt @ A3 @ A) = A))))). % insert_absorb
thf(fact_108_insert__absorb, axiom,
    ((![A3 : arrow_1857593510le_alt, A : set_Ar1665529862le_alt]: ((member519365071le_alt @ A3 @ A) => ((insert1093389942le_alt @ A3 @ A) = A))))). % insert_absorb

% Conjectures (3)
thf(conj_0, hypothesis,
    ((order_318683099le_alt @ top_to958727510le_alt @ r))).
thf(conj_1, hypothesis,
    ((wf_Arr1630868879le_alt @ (minus_467626412le_alt @ r @ id_Arr1939538434le_alt)))).
thf(conj_2, conjecture,
    ((?[L : set_Pr367596371le_alt]: (order_257197092le_alt @ top_to958727510le_alt @ L)))).
