% 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_46__5184584_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:15:47.949

% Could-be-implicit typings (9)
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    set_Pr851393385le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    produc541234227le_alt : $tType).
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__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, type,
    produc1556433673le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_se2071012361le_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__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__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).

% Explicit typings (37)
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OLin, type,
    arrow_1848678355le_Lin : set_se2071012361le_alt).
thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    inf_in607321317le_alt : set_Pr367596371le_alt > set_Pr367596371le_alt > set_Pr367596371le_alt).
thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    inf_in322684315le_alt : set_se2071012361le_alt > set_se2071012361le_alt > set_se2071012361le_alt).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    sup_su1902543487le_alt : set_Pr367596371le_alt > set_Pr367596371le_alt > set_Pr367596371le_alt).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    sup_su255583029le_alt : set_se2071012361le_alt > set_se2071012361le_alt > set_se2071012361le_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_Opartial__order__on_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    order_555284456le_alt : set_Pr367596371le_alt > set_Pr448479039le_alt > $o).
thf(sy_c_Order__Relation_Opartial__order__on_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    order_215384990le_alt : set_se2071012361le_alt > set_Pr851393385le_alt > $o).
thf(sy_c_Order__Relation_Opreorder__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    order_1371535037le_alt : set_Ar1665529862le_alt > set_Pr367596371le_alt > $o).
thf(sy_c_Order__Relation_Orelation__of_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    order_1467990772le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt > $o) > set_Ar1665529862le_alt > set_Pr367596371le_alt).
thf(sy_c_Order__Relation_Orelation__of_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    order_543646927le_alt : (produc16571293le_alt > produc16571293le_alt > $o) > set_Pr367596371le_alt > set_Pr448479039le_alt).
thf(sy_c_Order__Relation_Orelation__of_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    order_931517573le_alt : (set_Pr367596371le_alt > set_Pr367596371le_alt > $o) > set_se2071012361le_alt > set_Pr851393385le_alt).
thf(sy_c_Product__Type_OPair_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1494124311le_alt : arrow_1857593510le_alt > arrow_1857593510le_alt > produc16571293le_alt).
thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc41061307le_alt : produc16571293le_alt > produc16571293le_alt > produc1556433673le_alt).
thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc1931840741le_alt : set_Pr367596371le_alt > set_Pr367596371le_alt > produc541234227le_alt).
thf(sy_c_Product__Type_Ocurry_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001_Eo, type,
    produc392997491_alt_o : (produc16571293le_alt > $o) > arrow_1857593510le_alt > arrow_1857593510le_alt > $o).
thf(sy_c_Product__Type_Oprod_Oswap_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1794822519le_alt : produc16571293le_alt > produc16571293le_alt).
thf(sy_c_Relation_OId__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    id_on_426682691le_alt : set_Ar1665529862le_alt > set_Pr367596371le_alt).
thf(sy_c_Relation_OId__on_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    id_on_714194496le_alt : set_Pr367596371le_alt > set_Pr448479039le_alt).
thf(sy_c_Relation_OId__on_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    id_on_1531570678le_alt : set_se2071012361le_alt > set_Pr851393385le_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_Oinv__image_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    inv_im155136540le_alt : set_Pr367596371le_alt > (arrow_1857593510le_alt > arrow_1857593510le_alt) > set_Pr367596371le_alt).
thf(sy_c_Relation_Osym_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    sym_Ar995335558le_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_Ototal__on_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    total_51659983le_alt : set_se2071012361le_alt > set_Pr851393385le_alt > $o).
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_OCollect_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    collec1399441576le_alt : (set_Pr367596371le_alt > $o) > set_se2071012361le_alt).
thf(sy_c_Transitive__Closure_Oacyclic_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    transi1222743157le_alt : set_Pr367596371le_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_c_member_001t__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, type,
    member2146260128le_alt : produc1556433673le_alt > set_Pr448479039le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    member1392960970le_alt : produc541234227le_alt > set_Pr851393385le_alt > $o).
thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member1334244458le_alt : set_Pr367596371le_alt > set_se2071012361le_alt > $o).
thf(sy_v_L, type,
    l : set_Pr367596371le_alt).

% Relevant facts (93)
thf(fact_0_converse__inject, axiom,
    ((![R : set_Pr367596371le_alt, S : set_Pr367596371le_alt]: (((conver1781819635le_alt @ R) = (conver1781819635le_alt @ S)) = (R = S))))). % converse_inject
thf(fact_1_converse__converse, axiom,
    ((![R : set_Pr367596371le_alt]: ((conver1781819635le_alt @ (conver1781819635le_alt @ R)) = R)))). % converse_converse
thf(fact_2_notin__Lin__iff, axiom,
    ((![L : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((~ ((X = Y))) => ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L))) = (member2048039092le_alt @ (produc1494124311le_alt @ Y @ X) @ L))))))). % notin_Lin_iff
thf(fact_3_preorder__on__converse, axiom,
    ((![A : set_Ar1665529862le_alt, R : set_Pr367596371le_alt]: ((order_1371535037le_alt @ A @ (conver1781819635le_alt @ R)) = (order_1371535037le_alt @ A @ R))))). % preorder_on_converse
thf(fact_4_converse__inv__image, axiom,
    ((![R2 : set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((conver1781819635le_alt @ (inv_im155136540le_alt @ R2 @ F)) = (inv_im155136540le_alt @ (conver1781819635le_alt @ R2) @ F))))). % converse_inv_image
thf(fact_5_acyclic__converse, axiom,
    ((![R : set_Pr367596371le_alt]: ((transi1222743157le_alt @ (conver1781819635le_alt @ R)) = (transi1222743157le_alt @ R))))). % acyclic_converse
thf(fact_6_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_7_partial__order__on__converse, axiom,
    ((![A : set_Ar1665529862le_alt, R : set_Pr367596371le_alt]: ((order_529098139le_alt @ A @ (conver1781819635le_alt @ R)) = (order_529098139le_alt @ A @ R))))). % partial_order_on_converse
thf(fact_8_converse__Id__on, axiom,
    ((![A : set_Ar1665529862le_alt]: ((conver1781819635le_alt @ (id_on_426682691le_alt @ A)) = (id_on_426682691le_alt @ A))))). % converse_Id_on
thf(fact_9_antisym__converse, axiom,
    ((![R : set_Pr367596371le_alt]: ((antisy1745863240le_alt @ (conver1781819635le_alt @ R)) = (antisy1745863240le_alt @ R))))). % antisym_converse
thf(fact_10_total__on__converse, axiom,
    ((![A : set_Ar1665529862le_alt, R : set_Pr367596371le_alt]: ((total_2034085930le_alt @ A @ (conver1781819635le_alt @ R)) = (total_2034085930le_alt @ A @ R))))). % total_on_converse
thf(fact_11_sym__converse, axiom,
    ((![R : set_Pr367596371le_alt]: ((sym_Ar995335558le_alt @ (conver1781819635le_alt @ R)) = (sym_Ar995335558le_alt @ R))))). % sym_converse
thf(fact_12_converse__iff, axiom,
    ((![A2 : arrow_1857593510le_alt, B : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B) @ (conver1781819635le_alt @ R)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ A2) @ R))))). % converse_iff
thf(fact_13_Id__onI, axiom,
    ((![A2 : set_Pr367596371le_alt, A : set_se2071012361le_alt]: ((member1334244458le_alt @ A2 @ A) => (member1392960970le_alt @ (produc1931840741le_alt @ A2 @ A2) @ (id_on_1531570678le_alt @ A)))))). % Id_onI
thf(fact_14_Id__onI, axiom,
    ((![A2 : produc16571293le_alt, A : set_Pr367596371le_alt]: ((member2048039092le_alt @ A2 @ A) => (member2146260128le_alt @ (produc41061307le_alt @ A2 @ A2) @ (id_on_714194496le_alt @ A)))))). % Id_onI
thf(fact_15_Id__onI, axiom,
    ((![A2 : arrow_1857593510le_alt, A : set_Ar1665529862le_alt]: ((member519365071le_alt @ A2 @ A) => (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ A2) @ (id_on_426682691le_alt @ A)))))). % Id_onI
thf(fact_16_in__inv__image, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, R : set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (inv_im155136540le_alt @ R @ F)) = (member2048039092le_alt @ (produc1494124311le_alt @ (F @ X) @ (F @ Y)) @ R))))). % in_inv_image
thf(fact_17_partial__order__onD_I3_J, axiom,
    ((![A : set_Ar1665529862le_alt, R : set_Pr367596371le_alt]: ((order_529098139le_alt @ A @ R) => (antisy1745863240le_alt @ R))))). % partial_order_onD(3)
thf(fact_18_symD, axiom,
    ((![R : set_Pr367596371le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt]: ((sym_Ar995335558le_alt @ R) => ((member2048039092le_alt @ (produc1494124311le_alt @ B @ A2) @ R) => (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B) @ R)))))). % symD
thf(fact_19_symE, axiom,
    ((![R : set_Pr367596371le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt]: ((sym_Ar995335558le_alt @ R) => ((member2048039092le_alt @ (produc1494124311le_alt @ B @ A2) @ R) => (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B) @ R)))))). % symE
thf(fact_20_symI, axiom,
    ((![R : set_Pr367596371le_alt]: ((![A3 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B2) @ R) => (member2048039092le_alt @ (produc1494124311le_alt @ B2 @ A3) @ R))) => (sym_Ar995335558le_alt @ R))))). % symI
thf(fact_21_Id__onE, axiom,
    ((![C : produc541234227le_alt, A : set_se2071012361le_alt]: ((member1392960970le_alt @ C @ (id_on_1531570678le_alt @ A)) => (~ ((![X2 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X2 @ A) => (~ ((C = (produc1931840741le_alt @ X2 @ X2)))))))))))). % Id_onE
thf(fact_22_Id__onE, axiom,
    ((![C : produc1556433673le_alt, A : set_Pr367596371le_alt]: ((member2146260128le_alt @ C @ (id_on_714194496le_alt @ A)) => (~ ((![X2 : produc16571293le_alt]: ((member2048039092le_alt @ X2 @ A) => (~ ((C = (produc41061307le_alt @ X2 @ X2)))))))))))). % Id_onE
thf(fact_23_Id__onE, axiom,
    ((![C : produc16571293le_alt, A : set_Ar1665529862le_alt]: ((member2048039092le_alt @ C @ (id_on_426682691le_alt @ A)) => (~ ((![X2 : arrow_1857593510le_alt]: ((member519365071le_alt @ X2 @ A) => (~ ((C = (produc1494124311le_alt @ X2 @ X2)))))))))))). % Id_onE
thf(fact_24_sym__def, axiom,
    ((sym_Ar995335558le_alt = (^[R3 : set_Pr367596371le_alt]: (![X3 : arrow_1857593510le_alt]: (![Y2 : arrow_1857593510le_alt]: (((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y2) @ R3)) => ((member2048039092le_alt @ (produc1494124311le_alt @ Y2 @ X3) @ R3))))))))). % sym_def
thf(fact_25_antisymD, axiom,
    ((![R : set_Pr367596371le_alt, A2 : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((antisy1745863240le_alt @ R) => ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B) @ R) => ((member2048039092le_alt @ (produc1494124311le_alt @ B @ A2) @ R) => (A2 = B))))))). % antisymD
thf(fact_26_antisymI, axiom,
    ((![R : set_Pr367596371le_alt]: ((![X2 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y3) @ R) => ((member2048039092le_alt @ (produc1494124311le_alt @ Y3 @ X2) @ R) => (X2 = Y3)))) => (antisy1745863240le_alt @ R))))). % antisymI
thf(fact_27_Id__on__eqI, axiom,
    ((![A2 : set_Pr367596371le_alt, B : set_Pr367596371le_alt, A : set_se2071012361le_alt]: ((A2 = B) => ((member1334244458le_alt @ A2 @ A) => (member1392960970le_alt @ (produc1931840741le_alt @ A2 @ B) @ (id_on_1531570678le_alt @ A))))))). % Id_on_eqI
thf(fact_28_Id__on__eqI, axiom,
    ((![A2 : produc16571293le_alt, B : produc16571293le_alt, A : set_Pr367596371le_alt]: ((A2 = B) => ((member2048039092le_alt @ A2 @ A) => (member2146260128le_alt @ (produc41061307le_alt @ A2 @ B) @ (id_on_714194496le_alt @ A))))))). % Id_on_eqI
thf(fact_29_Id__on__eqI, axiom,
    ((![A2 : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A : set_Ar1665529862le_alt]: ((A2 = B) => ((member519365071le_alt @ A2 @ A) => (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B) @ (id_on_426682691le_alt @ A))))))). % Id_on_eqI
thf(fact_30_Id__on__iff, axiom,
    ((![X : set_Pr367596371le_alt, Y : set_Pr367596371le_alt, A : set_se2071012361le_alt]: ((member1392960970le_alt @ (produc1931840741le_alt @ X @ Y) @ (id_on_1531570678le_alt @ A)) = (((X = Y)) & ((member1334244458le_alt @ X @ A))))))). % Id_on_iff
thf(fact_31_Id__on__iff, axiom,
    ((![X : produc16571293le_alt, Y : produc16571293le_alt, A : set_Pr367596371le_alt]: ((member2146260128le_alt @ (produc41061307le_alt @ X @ Y) @ (id_on_714194496le_alt @ A)) = (((X = Y)) & ((member2048039092le_alt @ X @ A))))))). % Id_on_iff
thf(fact_32_Id__on__iff, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, A : set_Ar1665529862le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (id_on_426682691le_alt @ A)) = (((X = Y)) & ((member519365071le_alt @ X @ A))))))). % Id_on_iff
thf(fact_33_sym__Id__on, axiom,
    ((![A : set_Ar1665529862le_alt]: (sym_Ar995335558le_alt @ (id_on_426682691le_alt @ A))))). % sym_Id_on
thf(fact_34_total__onI, axiom,
    ((![A : set_se2071012361le_alt, R : set_Pr851393385le_alt]: ((![X2 : set_Pr367596371le_alt, Y3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X2 @ A) => ((member1334244458le_alt @ Y3 @ A) => ((~ ((X2 = Y3))) => ((member1392960970le_alt @ (produc1931840741le_alt @ X2 @ Y3) @ R) | (member1392960970le_alt @ (produc1931840741le_alt @ Y3 @ X2) @ R)))))) => (total_51659983le_alt @ A @ R))))). % total_onI
thf(fact_35_total__onI, axiom,
    ((![A : set_Pr367596371le_alt, R : set_Pr448479039le_alt]: ((![X2 : produc16571293le_alt, Y3 : produc16571293le_alt]: ((member2048039092le_alt @ X2 @ A) => ((member2048039092le_alt @ Y3 @ A) => ((~ ((X2 = Y3))) => ((member2146260128le_alt @ (produc41061307le_alt @ X2 @ Y3) @ R) | (member2146260128le_alt @ (produc41061307le_alt @ Y3 @ X2) @ R)))))) => (total_608959769le_alt @ A @ R))))). % total_onI
thf(fact_36_total__onI, axiom,
    ((![A : set_Ar1665529862le_alt, R : set_Pr367596371le_alt]: ((![X2 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((member519365071le_alt @ X2 @ A) => ((member519365071le_alt @ Y3 @ A) => ((~ ((X2 = Y3))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y3) @ R) | (member2048039092le_alt @ (produc1494124311le_alt @ Y3 @ X2) @ R)))))) => (total_2034085930le_alt @ A @ R))))). % total_onI
thf(fact_37_antisym__def, axiom,
    ((antisy1745863240le_alt = (^[R3 : set_Pr367596371le_alt]: (![X3 : arrow_1857593510le_alt]: (![Y2 : arrow_1857593510le_alt]: (((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y2) @ R3)) => ((((member2048039092le_alt @ (produc1494124311le_alt @ Y2 @ X3) @ R3)) => ((X3 = Y2))))))))))). % antisym_def
thf(fact_38_total__on__def, axiom,
    ((total_2034085930le_alt = (^[A4 : set_Ar1665529862le_alt]: (^[R3 : set_Pr367596371le_alt]: (![X3 : arrow_1857593510le_alt]: (((member519365071le_alt @ X3 @ A4)) => ((![Y2 : arrow_1857593510le_alt]: (((member519365071le_alt @ Y2 @ A4)) => ((((~ ((X3 = Y2)))) => ((((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y2) @ R3)) | ((member2048039092le_alt @ (produc1494124311le_alt @ Y2 @ X3) @ R3)))))))))))))))). % total_on_def
thf(fact_39_antisym__Id__on, axiom,
    ((![A : set_Ar1665529862le_alt]: (antisy1745863240le_alt @ (id_on_426682691le_alt @ A))))). % antisym_Id_on
thf(fact_40_sym__inv__image, axiom,
    ((![R : set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((sym_Ar995335558le_alt @ R) => (sym_Ar995335558le_alt @ (inv_im155136540le_alt @ R @ F)))))). % sym_inv_image
thf(fact_41_linear__order__on__def, axiom,
    ((order_318683099le_alt = (^[A4 : set_Ar1665529862le_alt]: (^[R3 : set_Pr367596371le_alt]: (((order_529098139le_alt @ A4 @ R3)) & ((total_2034085930le_alt @ A4 @ R3)))))))). % linear_order_on_def
thf(fact_42_partial__order__on__def, axiom,
    ((order_529098139le_alt = (^[A4 : set_Ar1665529862le_alt]: (^[R3 : set_Pr367596371le_alt]: (((order_1371535037le_alt @ A4 @ R3)) & ((antisy1745863240le_alt @ R3)))))))). % partial_order_on_def
thf(fact_43_converse_Oinducts, axiom,
    ((![X1 : arrow_1857593510le_alt, X22 : arrow_1857593510le_alt, R : set_Pr367596371le_alt, P : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: ((member2048039092le_alt @ (produc1494124311le_alt @ X1 @ X22) @ (conver1781819635le_alt @ R)) => ((![A3 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B2) @ R) => (P @ B2 @ A3))) => (P @ X1 @ X22)))))). % converse.inducts
thf(fact_44_converse_Ointros, axiom,
    ((![A2 : arrow_1857593510le_alt, B : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B) @ R) => (member2048039092le_alt @ (produc1494124311le_alt @ B @ A2) @ (conver1781819635le_alt @ R)))))). % converse.intros
thf(fact_45_converse_Osimps, axiom,
    ((![A1 : arrow_1857593510le_alt, A22 : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A1 @ A22) @ (conver1781819635le_alt @ R)) = (?[A5 : arrow_1857593510le_alt]: (?[B3 : arrow_1857593510le_alt]: (((A1 = B3)) & ((((A22 = A5)) & ((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B3) @ R))))))))))). % converse.simps
thf(fact_46_converse_Ocases, axiom,
    ((![A1 : arrow_1857593510le_alt, A22 : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A1 @ A22) @ (conver1781819635le_alt @ R)) => (member2048039092le_alt @ (produc1494124311le_alt @ A22 @ A1) @ R))))). % converse.cases
thf(fact_47_converseE, axiom,
    ((![Yx : produc16571293le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ Yx @ (conver1781819635le_alt @ R)) => (~ ((![X2 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((Yx = (produc1494124311le_alt @ Y3 @ X2)) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y3) @ R))))))))))). % converseE
thf(fact_48_converseD, axiom,
    ((![A2 : arrow_1857593510le_alt, B : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B) @ (conver1781819635le_alt @ R)) => (member2048039092le_alt @ (produc1494124311le_alt @ B @ A2) @ R))))). % converseD
thf(fact_49_sym__conv__converse__eq, axiom,
    ((sym_Ar995335558le_alt = (^[R3 : set_Pr367596371le_alt]: ((conver1781819635le_alt @ R3) = R3))))). % sym_conv_converse_eq
thf(fact_50_prod_Oinject, axiom,
    ((![X1 : arrow_1857593510le_alt, X22 : arrow_1857593510le_alt, Y1 : arrow_1857593510le_alt, Y22 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ X1 @ X22) = (produc1494124311le_alt @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_51_old_Oprod_Oinject, axiom,
    ((![A2 : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A6 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A2 @ B) = (produc1494124311le_alt @ A6 @ B4)) = (((A2 = A6)) & ((B = B4))))))). % old.prod.inject
thf(fact_52_surj__pair, axiom,
    ((![P2 : produc16571293le_alt]: (?[X2 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: (P2 = (produc1494124311le_alt @ X2 @ Y3)))))). % surj_pair
thf(fact_53_prod__cases, axiom,
    ((![P : produc16571293le_alt > $o, P2 : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (P @ (produc1494124311le_alt @ A3 @ B2))) => (P @ P2))))). % prod_cases
thf(fact_54_Pair__inject, axiom,
    ((![A2 : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A6 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A2 @ B) = (produc1494124311le_alt @ A6 @ B4)) => (~ (((A2 = A6) => (~ ((B = B4)))))))))). % Pair_inject
thf(fact_55_mem__Collect__eq, axiom,
    ((![A2 : set_Pr367596371le_alt, P : set_Pr367596371le_alt > $o]: ((member1334244458le_alt @ A2 @ (collec1399441576le_alt @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_56_mem__Collect__eq, axiom,
    ((![A2 : produc16571293le_alt, P : produc16571293le_alt > $o]: ((member2048039092le_alt @ A2 @ (collec531981554le_alt @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_57_Collect__mem__eq, axiom,
    ((![A : set_se2071012361le_alt]: ((collec1399441576le_alt @ (^[X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ A))) = A)))). % Collect_mem_eq
thf(fact_58_Collect__mem__eq, axiom,
    ((![A : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ A))) = A)))). % Collect_mem_eq
thf(fact_59_old_Oprod_Oinducts, axiom,
    ((![P : produc16571293le_alt > $o, Prod : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (P @ (produc1494124311le_alt @ A3 @ B2))) => (P @ Prod))))). % old.prod.inducts
thf(fact_60_old_Oprod_Oexhaust, axiom,
    ((![Y : produc16571293le_alt]: (~ ((![A3 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (~ ((Y = (produc1494124311le_alt @ A3 @ B2)))))))))). % old.prod.exhaust
thf(fact_61_ssubst__Pair__rhs, axiom,
    ((![R : arrow_1857593510le_alt, S : arrow_1857593510le_alt, R2 : set_Pr367596371le_alt, S2 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ R @ S) @ R2) => ((S2 = S) => (member2048039092le_alt @ (produc1494124311le_alt @ R @ S2) @ R2)))))). % ssubst_Pair_rhs
thf(fact_62_curryI, axiom,
    ((![F : produc16571293le_alt > $o, A2 : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((F @ (produc1494124311le_alt @ A2 @ B)) => (produc392997491_alt_o @ F @ A2 @ B))))). % curryI
thf(fact_63_curryD, axiom,
    ((![F : produc16571293le_alt > $o, A2 : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc392997491_alt_o @ F @ A2 @ B) => (F @ (produc1494124311le_alt @ A2 @ B)))))). % curryD
thf(fact_64_curryE, axiom,
    ((![F : produc16571293le_alt > $o, A2 : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc392997491_alt_o @ F @ A2 @ B) => (F @ (produc1494124311le_alt @ A2 @ B)))))). % curryE
thf(fact_65_partial__order__on__relation__ofI, axiom,
    ((![A : set_se2071012361le_alt, P : set_Pr367596371le_alt > set_Pr367596371le_alt > $o]: ((![A3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ A3 @ A) => (P @ A3 @ A3))) => ((![A3 : set_Pr367596371le_alt, B2 : set_Pr367596371le_alt, C2 : set_Pr367596371le_alt]: ((member1334244458le_alt @ A3 @ A) => ((member1334244458le_alt @ B2 @ A) => ((member1334244458le_alt @ C2 @ A) => ((P @ A3 @ B2) => ((P @ B2 @ C2) => (P @ A3 @ C2))))))) => ((![A3 : set_Pr367596371le_alt, B2 : set_Pr367596371le_alt]: ((member1334244458le_alt @ A3 @ A) => ((member1334244458le_alt @ B2 @ A) => ((P @ A3 @ B2) => ((P @ B2 @ A3) => (A3 = B2)))))) => (order_215384990le_alt @ A @ (order_931517573le_alt @ P @ A)))))))). % partial_order_on_relation_ofI
thf(fact_66_partial__order__on__relation__ofI, axiom,
    ((![A : set_Pr367596371le_alt, P : produc16571293le_alt > produc16571293le_alt > $o]: ((![A3 : produc16571293le_alt]: ((member2048039092le_alt @ A3 @ A) => (P @ A3 @ A3))) => ((![A3 : produc16571293le_alt, B2 : produc16571293le_alt, C2 : produc16571293le_alt]: ((member2048039092le_alt @ A3 @ A) => ((member2048039092le_alt @ B2 @ A) => ((member2048039092le_alt @ C2 @ A) => ((P @ A3 @ B2) => ((P @ B2 @ C2) => (P @ A3 @ C2))))))) => ((![A3 : produc16571293le_alt, B2 : produc16571293le_alt]: ((member2048039092le_alt @ A3 @ A) => ((member2048039092le_alt @ B2 @ A) => ((P @ A3 @ B2) => ((P @ B2 @ A3) => (A3 = B2)))))) => (order_555284456le_alt @ A @ (order_543646927le_alt @ P @ A)))))))). % partial_order_on_relation_ofI
thf(fact_67_partial__order__on__relation__ofI, axiom,
    ((![A : set_Ar1665529862le_alt, P : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: ((![A3 : arrow_1857593510le_alt]: ((member519365071le_alt @ A3 @ A) => (P @ A3 @ A3))) => ((![A3 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, C2 : arrow_1857593510le_alt]: ((member519365071le_alt @ A3 @ A) => ((member519365071le_alt @ B2 @ A) => ((member519365071le_alt @ C2 @ A) => ((P @ A3 @ B2) => ((P @ B2 @ C2) => (P @ A3 @ C2))))))) => ((![A3 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: ((member519365071le_alt @ A3 @ A) => ((member519365071le_alt @ B2 @ A) => ((P @ A3 @ B2) => ((P @ B2 @ A3) => (A3 = B2)))))) => (order_529098139le_alt @ A @ (order_1467990772le_alt @ P @ A)))))))). % partial_order_on_relation_ofI
thf(fact_68_swap__simp, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((produc1794822519le_alt @ (produc1494124311le_alt @ X @ Y)) = (produc1494124311le_alt @ Y @ X))))). % swap_simp
thf(fact_69_sym__Int__converse, axiom,
    ((![R : set_Pr367596371le_alt]: (sym_Ar995335558le_alt @ (inf_in607321317le_alt @ R @ (conver1781819635le_alt @ R)))))). % sym_Int_converse
thf(fact_70_sym__Un__converse, axiom,
    ((![R : set_Pr367596371le_alt]: (sym_Ar995335558le_alt @ (sup_su1902543487le_alt @ R @ (conver1781819635le_alt @ R)))))). % sym_Un_converse
thf(fact_71_converse__Un, axiom,
    ((![R : set_Pr367596371le_alt, S : set_Pr367596371le_alt]: ((conver1781819635le_alt @ (sup_su1902543487le_alt @ R @ S)) = (sup_su1902543487le_alt @ (conver1781819635le_alt @ R) @ (conver1781819635le_alt @ S)))))). % converse_Un
thf(fact_72_converse__Int, axiom,
    ((![R : set_Pr367596371le_alt, S : set_Pr367596371le_alt]: ((conver1781819635le_alt @ (inf_in607321317le_alt @ R @ S)) = (inf_in607321317le_alt @ (conver1781819635le_alt @ R) @ (conver1781819635le_alt @ S)))))). % converse_Int
thf(fact_73_IntI, axiom,
    ((![C : set_Pr367596371le_alt, A : set_se2071012361le_alt, B5 : set_se2071012361le_alt]: ((member1334244458le_alt @ C @ A) => ((member1334244458le_alt @ C @ B5) => (member1334244458le_alt @ C @ (inf_in322684315le_alt @ A @ B5))))))). % IntI
thf(fact_74_IntI, axiom,
    ((![C : produc16571293le_alt, A : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ A) => ((member2048039092le_alt @ C @ B5) => (member2048039092le_alt @ C @ (inf_in607321317le_alt @ A @ B5))))))). % IntI
thf(fact_75_Int__iff, axiom,
    ((![C : set_Pr367596371le_alt, A : set_se2071012361le_alt, B5 : set_se2071012361le_alt]: ((member1334244458le_alt @ C @ (inf_in322684315le_alt @ A @ B5)) = (((member1334244458le_alt @ C @ A)) & ((member1334244458le_alt @ C @ B5))))))). % Int_iff
thf(fact_76_Int__iff, axiom,
    ((![C : produc16571293le_alt, A : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ (inf_in607321317le_alt @ A @ B5)) = (((member2048039092le_alt @ C @ A)) & ((member2048039092le_alt @ C @ B5))))))). % Int_iff
thf(fact_77_UnCI, axiom,
    ((![C : set_Pr367596371le_alt, B5 : set_se2071012361le_alt, A : set_se2071012361le_alt]: (((~ ((member1334244458le_alt @ C @ B5))) => (member1334244458le_alt @ C @ A)) => (member1334244458le_alt @ C @ (sup_su255583029le_alt @ A @ B5)))))). % UnCI
thf(fact_78_UnCI, axiom,
    ((![C : produc16571293le_alt, B5 : set_Pr367596371le_alt, A : set_Pr367596371le_alt]: (((~ ((member2048039092le_alt @ C @ B5))) => (member2048039092le_alt @ C @ A)) => (member2048039092le_alt @ C @ (sup_su1902543487le_alt @ A @ B5)))))). % UnCI
thf(fact_79_Un__iff, axiom,
    ((![C : set_Pr367596371le_alt, A : set_se2071012361le_alt, B5 : set_se2071012361le_alt]: ((member1334244458le_alt @ C @ (sup_su255583029le_alt @ A @ B5)) = (((member1334244458le_alt @ C @ A)) | ((member1334244458le_alt @ C @ B5))))))). % Un_iff
thf(fact_80_Un__iff, axiom,
    ((![C : produc16571293le_alt, A : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ (sup_su1902543487le_alt @ A @ B5)) = (((member2048039092le_alt @ C @ A)) | ((member2048039092le_alt @ C @ B5))))))). % Un_iff
thf(fact_81_IntE, axiom,
    ((![C : set_Pr367596371le_alt, A : set_se2071012361le_alt, B5 : set_se2071012361le_alt]: ((member1334244458le_alt @ C @ (inf_in322684315le_alt @ A @ B5)) => (~ (((member1334244458le_alt @ C @ A) => (~ ((member1334244458le_alt @ C @ B5)))))))))). % IntE
thf(fact_82_IntE, axiom,
    ((![C : produc16571293le_alt, A : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ (inf_in607321317le_alt @ A @ B5)) => (~ (((member2048039092le_alt @ C @ A) => (~ ((member2048039092le_alt @ C @ B5)))))))))). % IntE
thf(fact_83_IntD1, axiom,
    ((![C : set_Pr367596371le_alt, A : set_se2071012361le_alt, B5 : set_se2071012361le_alt]: ((member1334244458le_alt @ C @ (inf_in322684315le_alt @ A @ B5)) => (member1334244458le_alt @ C @ A))))). % IntD1
thf(fact_84_IntD1, axiom,
    ((![C : produc16571293le_alt, A : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ (inf_in607321317le_alt @ A @ B5)) => (member2048039092le_alt @ C @ A))))). % IntD1
thf(fact_85_IntD2, axiom,
    ((![C : set_Pr367596371le_alt, A : set_se2071012361le_alt, B5 : set_se2071012361le_alt]: ((member1334244458le_alt @ C @ (inf_in322684315le_alt @ A @ B5)) => (member1334244458le_alt @ C @ B5))))). % IntD2
thf(fact_86_IntD2, axiom,
    ((![C : produc16571293le_alt, A : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ (inf_in607321317le_alt @ A @ B5)) => (member2048039092le_alt @ C @ B5))))). % IntD2
thf(fact_87_UnE, axiom,
    ((![C : set_Pr367596371le_alt, A : set_se2071012361le_alt, B5 : set_se2071012361le_alt]: ((member1334244458le_alt @ C @ (sup_su255583029le_alt @ A @ B5)) => ((~ ((member1334244458le_alt @ C @ A))) => (member1334244458le_alt @ C @ B5)))))). % UnE
thf(fact_88_UnE, axiom,
    ((![C : produc16571293le_alt, A : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ (sup_su1902543487le_alt @ A @ B5)) => ((~ ((member2048039092le_alt @ C @ A))) => (member2048039092le_alt @ C @ B5)))))). % UnE
thf(fact_89_UnI1, axiom,
    ((![C : set_Pr367596371le_alt, A : set_se2071012361le_alt, B5 : set_se2071012361le_alt]: ((member1334244458le_alt @ C @ A) => (member1334244458le_alt @ C @ (sup_su255583029le_alt @ A @ B5)))))). % UnI1
thf(fact_90_UnI1, axiom,
    ((![C : produc16571293le_alt, A : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ A) => (member2048039092le_alt @ C @ (sup_su1902543487le_alt @ A @ B5)))))). % UnI1
thf(fact_91_UnI2, axiom,
    ((![C : set_Pr367596371le_alt, B5 : set_se2071012361le_alt, A : set_se2071012361le_alt]: ((member1334244458le_alt @ C @ B5) => (member1334244458le_alt @ C @ (sup_su255583029le_alt @ A @ B5)))))). % UnI2
thf(fact_92_UnI2, axiom,
    ((![C : produc16571293le_alt, B5 : set_Pr367596371le_alt, A : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ B5) => (member2048039092le_alt @ C @ (sup_su1902543487le_alt @ A @ B5)))))). % UnI2

% Conjectures (1)
thf(conj_0, conjecture,
    (((member1334244458le_alt @ (conver1781819635le_alt @ l) @ arrow_1848678355le_Lin) = (member1334244458le_alt @ l @ arrow_1848678355le_Lin)))).
