ConnectPP---0.7.2.THM-Prf.s

%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : SWW473+1 : TPTP v9.3.1. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 09:07:55 AM UTC 2026

% Result   : Theorem 11.15s 11.48s
% Output   : Proof 11.25s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
fof(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a,axiom,
    ! [B_1_1,B_2] :
      ( is_fun_a_bool(B_2)
     => is_fun_a_bool(cOMBB_bool_bool_a(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a) ).

fof(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname,axiom,
    ! [B_1_1,B_2] :
      ( is_fun_pname_bool(B_2)
     => is_fun_pname_bool(cOMBB_647938656_pname(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname) ).

fof(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool,axiom,
    ! [B_1_1,B_2] :
      ( is_fun949378684l_bool(B_2)
     => is_fun949378684l_bool(cOMBB_2140588453a_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool) ).

fof(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_,axiom,
    ! [B_1_1,B_2] :
      ( is_fun1661590463l_bool(B_2)
     => is_fun1661590463l_bool(cOMBB_307249310e_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_) ).

fof(gsy_c_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool,axiom,
    ! [B_1_1,B_2] :
      ( is_fun_a_bool(B_2)
     => is_fun_a_bool(cOMBS_a_bool_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool) ).

fof(gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool,axiom,
    ! [B_1_1,B_2] :
      ( is_fun_pname_bool(B_2)
     => is_fun_pname_bool(cOMBS_568398431l_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool) ).

fof(gsy_c_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc__HOL__Obo,axiom,
    ! [B_1_1,B_2] :
      ( is_fun949378684l_bool(B_2)
     => is_fun949378684l_bool(cOMBS_1035972772l_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc__HOL__Obo) ).

fof(gsy_c_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t,axiom,
    ! [B_1_1,B_2] :
      ( is_fun1661590463l_bool(B_2)
     => is_fun1661590463l_bool(cOMBS_350070575l_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t) ).

fof(gsy_c_Finite__Set_Ofinite_000t__a,axiom,
    is_fun949378684l_bool(finite_finite_a),
    file('theBenchmark.p',gsy_c_Finite__Set_Ofinite_000t__a) ).

fof(gsy_c_Finite__Set_Ofinite_000tc__Com__Opname,hypothesis,
    is_fun1661590463l_bool(finite_finite_pname),
    file('theBenchmark.p',gsy_c_Finite__Set_Ofinite_000tc__Com__Opname) ).

fof(gsy_c_HOL_Oundefined_000t__a,axiom,
    is_a(undefined_a(x_a)),
    file('theBenchmark.p',gsy_c_HOL_Oundefined_000t__a) ).

fof(gsy_c_HOL_Oundefined_000tc__Com__Opname,axiom,
    is_pname(undefined_pname(pname)),
    file('theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Com__Opname) ).

fof(gsy_c_HOL_Oundefined_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
    is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool))),
    file('theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_It__a_Mtc__HOL__Obool_J) ).

fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
    is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))),
    file('theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).

fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool,axiom,
    is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))),
    file('theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool) ).

fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,axiom,
    is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))),
    file('theBenchmark.p',gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) ).

fof(gsy_c_Set_OCollect_000t__a,axiom,
    ! [B_1_1] :
      ( is_fun_a_bool(B_1_1)
     => is_fun_a_bool(collect_a(B_1_1)) ),
    file('theBenchmark.p',gsy_c_Set_OCollect_000t__a) ).

fof(gsy_c_Set_OCollect_000tc__Com__Opname,axiom,
    ! [B_1_1] :
      ( is_fun_pname_bool(B_1_1)
     => is_fun_pname_bool(collect_pname(B_1_1)) ),
    file('theBenchmark.p',gsy_c_Set_OCollect_000tc__Com__Opname) ).

fof(gsy_c_Set_OCollect_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1] :
      ( is_fun949378684l_bool(B_1_1)
     => is_fun949378684l_bool(collect_fun_a_bool(B_1_1)) ),
    file('theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_It__a_Mtc__HOL__Obool_J) ).

fof(gsy_c_Set_OCollect_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1] :
      ( is_fun1661590463l_bool(B_1_1)
     => is_fun1661590463l_bool(collec1974731493e_bool(B_1_1)) ),
    file('theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).

fof(gsy_c_Set_Oimage_000t__a_000t__a,axiom,
    ! [B_1_1,B_2] :
      ( is_fun_a_bool(B_2)
     => is_fun_a_bool(image_a_a(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_Set_Oimage_000t__a_000t__a) ).

fof(gsy_c_Set_Oimage_000t__a_000tc__Com__Opname,axiom,
    ! [B_1_1,B_2] :
      ( is_fun_a_bool(B_2)
     => is_fun_pname_bool(image_a_pname(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_Set_Oimage_000t__a_000tc__Com__Opname) ).

fof(gsy_c_Set_Oimage_000tc__Com__Opname_000t__a,hypothesis,
    ! [B_1_1,B_2] :
      ( is_fun_pname_bool(B_2)
     => is_fun_a_bool(image_pname_a(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000t__a) ).

fof(gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,axiom,
    ! [B_1_1,B_2] :
      ( is_fun_pname_bool(B_2)
     => is_fun_pname_bool(image_pname_pname(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname) ).

fof(gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1,B_2] :
      ( is_fun_pname_bool(B_2)
     => is_fun949378684l_bool(image_112932426a_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J) ).

fof(gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_,axiom,
    ! [B_1_1,B_2] :
      ( is_fun_pname_bool(B_2)
     => is_fun1661590463l_bool(image_47868345e_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_) ).

fof(gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a,axiom,
    ! [B_1_1,B_2] : is_fun_a_bool(image_nat_a(B_1_1,B_2)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a) ).

fof(gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname,axiom,
    ! [B_1_1,B_2] : is_fun_pname_bool(image_nat_pname(B_1_1,B_2)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname) ).

fof(gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1,B_2] : is_fun949378684l_bool(image_nat_fun_a_bool(B_1_1,B_2)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J) ).

fof(gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1,B_2] : is_fun1661590463l_bool(image_1655916159e_bool(B_1_1,B_2)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).

fof(gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a,axiom,
    ! [B_1_1,B_2] :
      ( is_fun949378684l_bool(B_2)
     => is_fun_a_bool(image_fun_a_bool_a(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a) ).

fof(gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname,axiom,
    ! [B_1_1,B_2] :
      ( is_fun949378684l_bool(B_2)
     => is_fun_pname_bool(image_1854862208_pname(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname) ).

fof(gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000t__a,axiom,
    ! [B_1_1,B_2] :
      ( is_fun1661590463l_bool(B_2)
     => is_fun_a_bool(image_876012084bool_a(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000t__a) ).

fof(gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opnam,axiom,
    ! [B_1_1,B_2] :
      ( is_fun1661590463l_bool(B_2)
     => is_fun_pname_bool(image_1283814551_pname(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opnam) ).

fof(gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000t__a,axiom,
    ! [B_1_1,B_2] : is_fun_a_bool(image_fun_nat_bool_a(B_1_1,B_2)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000t__a) ).

fof(gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname,axiom,
    ! [B_1_1,B_2] : is_fun_pname_bool(image_1921560913_pname(B_1_1,B_2)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname) ).

fof(gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0,axiom,
    ! [B_1_1,B_2] : is_fun_a_bool(image_573985017bool_a(B_1_1,B_2)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0) ).

fof(gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0_001,axiom,
    ! [B_1_1,B_2] : is_fun_pname_bool(image_990671762_pname(B_1_1,B_2)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0_001) ).

fof(gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL,axiom,
    ! [B_1_1,B_2] : is_fun_a_bool(image_349102846bool_a(B_1_1,B_2)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL) ).

fof(gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL_002,axiom,
    ! [B_1_1,B_2] : is_fun_pname_bool(image_1705983821_pname(B_1_1,B_2)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL_002) ).

fof(gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__,axiom,
    ! [B_1_1,B_2] : is_fun_a_bool(image_526090948bool_a(B_1_1,B_2)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__) ).

fof(gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL___003,axiom,
    ! [B_1_1,B_2] : is_fun_pname_bool(image_1604018183_pname(B_1_1,B_2)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL___003) ).

fof(gsy_c_Set_Oinsert_000t__a,hypothesis,
    ! [B_1_1,B_2] :
      ( ( is_fun_a_bool(B_2)
        & is_a(B_1_1) )
     => is_fun_a_bool(insert_a(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_Set_Oinsert_000t__a) ).

fof(gsy_c_Set_Oinsert_000tc__Com__Opname,axiom,
    ! [B_1_1,B_2] :
      ( ( is_fun_pname_bool(B_2)
        & is_pname(B_1_1) )
     => is_fun_pname_bool(insert_pname(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_Set_Oinsert_000tc__Com__Opname) ).

fof(gsy_c_Set_Oinsert_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1,B_2] :
      ( ( is_fun949378684l_bool(B_2)
        & is_fun_a_bool(B_1_1) )
     => is_fun949378684l_bool(insert_fun_a_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_Set_Oinsert_000tc__fun_It__a_Mtc__HOL__Obool_J) ).

fof(gsy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1,B_2] :
      ( ( is_fun1661590463l_bool(B_2)
        & is_fun_pname_bool(B_1_1) )
     => is_fun1661590463l_bool(insert1325755072e_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).

fof(gsy_c_hAPP_000t__a_000tc__HOL__Obool,axiom,
    ! [B_1_1,B_2] :
      ( ( is_a(B_2)
        & is_fun_a_bool(B_1_1) )
     => is_bool(hAPP_a_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_hAPP_000t__a_000tc__HOL__Obool) ).

fof(gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1,B_2] :
      ( is_a(B_2)
     => is_fun_a_bool(hAPP_a_fun_a_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J) ).

fof(gsy_c_hAPP_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1,B_2] :
      ( is_a(B_2)
     => is_fun_pname_bool(hAPP_a93125764e_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_hAPP_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).

fof(gsy_c_hAPP_000t__a_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J,hypothesis,
    ! [B_1_1,B_2] :
      ( is_a(B_2)
     => is_fun949378684l_bool(hAPP_a85458249l_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_hAPP_000t__a_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J) ).

fof(gsy_c_hAPP_000tc__Com__Opname_000t__a,hypothesis,
    ! [B_1_1,B_2] :
      ( is_pname(B_2)
     => is_a(hAPP_pname_a(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000t__a) ).

fof(gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool,axiom,
    ! [B_1_1,B_2] :
      ( ( is_pname(B_2)
        & is_fun_pname_bool(B_1_1) )
     => is_bool(hAPP_pname_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool) ).

fof(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1,B_2] :
      ( is_pname(B_2)
     => is_fun_a_bool(hAPP_p1534023578a_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J) ).

fof(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1,B_2] :
      ( is_pname(B_2)
     => is_fun_pname_bool(hAPP_p61793385e_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).

fof(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo,hypothesis,
    ! [B_1_1,B_2] :
      ( is_pname(B_2)
     => is_fun1661590463l_bool(hAPP_p338031245l_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).

fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,axiom,
    ! [B_1_1,B_2] :
      ( is_bool(B_2)
     => is_bool(hAPP_bool_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool,hypothesis,
    ! [B_1_1,B_2] : is_bool(hAPP_nat_bool(B_1_1,B_2)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1,B_2] : is_fun_a_bool(hAPP_nat_fun_a_bool(B_1_1,B_2)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1,B_2] : is_fun_pname_bool(hAPP_n1025906991e_bool(B_1_1,B_2)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).

fof(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool,hypothesis,
    ! [B_1_1,B_2] :
      ( ( is_fun_a_bool(B_2)
        & is_fun949378684l_bool(B_1_1) )
     => is_bool(hAPP_fun_a_bool_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).

fof(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1,B_2] :
      ( is_fun_a_bool(B_2)
     => is_fun_a_bool(hAPP_f2050579477a_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL__Obool_J) ).

fof(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__a_Mtc__HOL,hypothesis,
    ! [B_1_1,B_2] :
      ( is_fun_a_bool(B_2)
     => is_fun949378684l_bool(hAPP_f1631501043l_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__a_Mtc__HOL) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool,hypothesis,
    ! [B_1_1,B_2] :
      ( ( is_fun_pname_bool(B_2)
        & is_fun1661590463l_bool(B_1_1) )
     => is_bool(hAPP_f1664156314l_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op,axiom,
    ! [B_1_1,B_2] :
      ( is_fun_pname_bool(B_2)
     => is_fun_pname_bool(hAPP_f759274231e_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc,axiom,
    ! [B_1_1,B_2] :
      ( is_fun_pname_bool(B_2)
     => is_fun1661590463l_bool(hAPP_f434788991l_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
    ! [B_1_1,B_2] : is_bool(hAPP_f54304608l_bool(B_1_1,B_2)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc__,axiom,
    ! [B_1_1,B_2] :
      ( is_fun949378684l_bool(B_2)
     => is_bool(hAPP_f621171935l_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc__) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc___004,axiom,
    ! [B_1_1,B_2] :
      ( is_fun949378684l_bool(B_2)
     => is_fun949378684l_bool(hAPP_f2117159681l_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc___004) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo,axiom,
    ! [B_1_1,B_2] :
      ( is_fun1661590463l_bool(B_2)
     => is_bool(hAPP_f1935102916l_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_005,axiom,
    ! [B_1_1,B_2] :
      ( is_fun1661590463l_bool(B_2)
     => is_fun1661590463l_bool(hAPP_f559147733l_bool(B_1_1,B_2)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_005) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_,axiom,
    ! [B_1_1,B_2] : is_bool(hAPP_f1637334154l_bool(B_1_1,B_2)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_,axiom,
    ! [B_1_1,B_2] : is_bool(hAPP_f292226953l_bool(B_1_1,B_2)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__,axiom,
    ! [B_1_1,B_2] : is_bool(hAPP_f389811538l_bool(B_1_1,B_2)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HO,axiom,
    ! [B_1_1,B_2] : is_bool(hAPP_f937997336l_bool(B_1_1,B_2)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HO) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HO,axiom,
    ! [B_1_1,B_2] : is_bool(hAPP_f1363661463l_bool(B_1_1,B_2)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HO) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Oboo,axiom,
    ! [B_1_1,B_2] : is_bool(hAPP_f595608956l_bool(B_1_1,B_2)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
    ! [B_1_1,B_2] : is_bool(hAPP_f1295398978l_bool(B_1_1,B_2)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).

fof(gsy_v_G,hypothesis,
    is_fun_a_bool(g),
    file('theBenchmark.p',gsy_v_G) ).

fof(gsy_v_P,axiom,
    ! [B_1_1] :
      ( is_fun_a_bool(B_1_1)
     => is_fun949378684l_bool(p(B_1_1)) ),
    file('theBenchmark.p',gsy_v_P) ).

fof(gsy_v_U,hypothesis,
    is_fun_pname_bool(u),
    file('theBenchmark.p',gsy_v_U) ).

fof(gsy_v_pn,hypothesis,
    is_pname(pn),
    file('theBenchmark.p',gsy_v_pn) ).

fof(fact_0_assms_I1_J,axiom,
    ! [Ts,G] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Ts),G))
     => hBOOL(hAPP_fun_a_bool_bool(p(G),Ts)) ),
    file('theBenchmark.p',fact_0_assms_I1_J) ).

fof(fact_1_finite__Collect__subsets,axiom,
    ! [A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),A)))) ),
    file('theBenchmark.p',fact_1_finite__Collect__subsets) ).

fof(fact_2_finite__Collect__subsets,axiom,
    ! [A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),A)))) ),
    file('theBenchmark.p',fact_2_finite__Collect__subsets) ).

fof(fact_3_finite__Collect__subsets,axiom,
    ! [A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
     => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),A)))) ),
    file('theBenchmark.p',fact_3_finite__Collect__subsets) ).

fof(fact_4_finite__Collect__subsets,axiom,
    ! [A] :
      ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,A))
     => hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),A)))) ),
    file('theBenchmark.p',fact_4_finite__Collect__subsets) ).

fof(fact_5_finite__Collect__subsets,axiom,
    ! [A] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A))
     => hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),A)))) ),
    file('theBenchmark.p',fact_5_finite__Collect__subsets) ).

fof(fact_6_finite__Collect__subsets,axiom,
    ! [A] :
      ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,A))
     => hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),A)))) ),
    file('theBenchmark.p',fact_6_finite__Collect__subsets) ).

fof(fact_7_finite__Collect__subsets,axiom,
    ! [A] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
     => hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),A)))) ),
    file('theBenchmark.p',fact_7_finite__Collect__subsets) ).

fof(fact_8_finite__Collect__subsets,axiom,
    ! [A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),A)))) ),
    file('theBenchmark.p',fact_8_finite__Collect__subsets) ).

fof(fact_9_finite__Collect__subsets,axiom,
    ! [A] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
     => hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),A)))) ),
    file('theBenchmark.p',fact_9_finite__Collect__subsets) ).

fof(fact_10_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
     => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(H,F_1))) ),
    file('theBenchmark.p',fact_10_finite__imageI) ).

fof(fact_11_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,F_1))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(H,F_1))) ),
    file('theBenchmark.p',fact_11_finite__imageI) ).

fof(fact_12_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,F_1))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(H,F_1))) ),
    file('theBenchmark.p',fact_12_finite__imageI) ).

fof(fact_13_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,F_1))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(H,F_1))) ),
    file('theBenchmark.p',fact_13_finite__imageI) ).

fof(fact_14_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(H,F_1))) ),
    file('theBenchmark.p',fact_14_finite__imageI) ).

fof(fact_15_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(H,F_1))) ),
    file('theBenchmark.p',fact_15_finite__imageI) ).

fof(fact_16_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(H,F_1))) ),
    file('theBenchmark.p',fact_16_finite__imageI) ).

fof(fact_17_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(H,F_1))) ),
    file('theBenchmark.p',fact_17_finite__imageI) ).

fof(fact_18_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,F_1))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(H,F_1))) ),
    file('theBenchmark.p',fact_18_finite__imageI) ).

fof(fact_19_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,F_1))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(H,F_1))) ),
    file('theBenchmark.p',fact_19_finite__imageI) ).

fof(fact_20_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,F_1))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(H,F_1))) ),
    file('theBenchmark.p',fact_20_finite__imageI) ).

fof(fact_21_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(H,F_1))) ),
    file('theBenchmark.p',fact_21_finite__imageI) ).

fof(fact_22_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(H,F_1))) ),
    file('theBenchmark.p',fact_22_finite__imageI) ).

fof(fact_23_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(H,F_1))) ),
    file('theBenchmark.p',fact_23_finite__imageI) ).

fof(fact_24_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(H,F_1))) ),
    file('theBenchmark.p',fact_24_finite__imageI) ).

fof(fact_25_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
     => hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(H,F_1))) ),
    file('theBenchmark.p',fact_25_finite__imageI) ).

fof(fact_26_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
     => hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(H,F_1))) ),
    file('theBenchmark.p',fact_26_finite__imageI) ).

fof(fact_27_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
     => hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(H,F_1))) ),
    file('theBenchmark.p',fact_27_finite__imageI) ).

fof(fact_28_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
     => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(H,F_1))) ),
    file('theBenchmark.p',fact_28_finite__imageI) ).

fof(fact_29_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(H,F_1))) ),
    file('theBenchmark.p',fact_29_finite__imageI) ).

fof(fact_30_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
     => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(H,F_1))) ),
    file('theBenchmark.p',fact_30_finite__imageI) ).

fof(fact_31_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
     => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(H,F_1))) ),
    file('theBenchmark.p',fact_31_finite__imageI) ).

fof(fact_32_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
     => hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(H,F_1))) ),
    file('theBenchmark.p',fact_32_finite__imageI) ).

fof(fact_33_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
     => hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(H,F_1))) ),
    file('theBenchmark.p',fact_33_finite__imageI) ).

fof(fact_34_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
     => hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(H,F_1))) ),
    file('theBenchmark.p',fact_34_finite__imageI) ).

fof(fact_35_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
     => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(H,F_1))) ),
    file('theBenchmark.p',fact_35_finite__imageI) ).

fof(fact_36_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(H,F_1))) ),
    file('theBenchmark.p',fact_36_finite__imageI) ).

fof(fact_37_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
     => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(H,F_1))) ),
    file('theBenchmark.p',fact_37_finite__imageI) ).

fof(fact_38_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(H,F_1))) ),
    file('theBenchmark.p',fact_38_finite__imageI) ).

fof(fact_39_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1))
     => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(H,F_1))) ),
    file('theBenchmark.p',fact_39_finite__imageI) ).

fof(fact_40_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1))
     => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(H,F_1))) ),
    file('theBenchmark.p',fact_40_finite__imageI) ).

fof(fact_41_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1))
     => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(H,F_1))) ),
    file('theBenchmark.p',fact_41_finite__imageI) ).

fof(fact_42_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1))
     => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(H,F_1))) ),
    file('theBenchmark.p',fact_42_finite__imageI) ).

fof(fact_43_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(H,F_1))) ),
    file('theBenchmark.p',fact_43_finite__imageI) ).

fof(fact_44_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(H,F_1))) ),
    file('theBenchmark.p',fact_44_finite__imageI) ).

fof(fact_45_finite_OinsertI,axiom,
    ! [A_1,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
     => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(A_1,A))) ),
    file('theBenchmark.p',fact_45_finite_OinsertI) ).

fof(fact_46_finite_OinsertI,axiom,
    ! [A_1,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(A_1,A))) ),
    file('theBenchmark.p',fact_46_finite_OinsertI) ).

fof(fact_47_finite_OinsertI,axiom,
    ! [A_1,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_1,A))) ),
    file('theBenchmark.p',fact_47_finite_OinsertI) ).

fof(fact_48_finite_OinsertI,axiom,
    ! [A_1,A] :
      ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,A))
     => hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(A_1,A))) ),
    file('theBenchmark.p',fact_48_finite_OinsertI) ).

fof(fact_49_finite_OinsertI,axiom,
    ! [A_1,A] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A))
     => hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(A_1,A))) ),
    file('theBenchmark.p',fact_49_finite_OinsertI) ).

fof(fact_50_finite_OinsertI,axiom,
    ! [A_1,A] :
      ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,A))
     => hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(A_1,A))) ),
    file('theBenchmark.p',fact_50_finite_OinsertI) ).

fof(fact_51_finite_OinsertI,axiom,
    ! [A_1,A] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
     => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(A_1,A))) ),
    file('theBenchmark.p',fact_51_finite_OinsertI) ).

fof(fact_52_finite_OinsertI,axiom,
    ! [A_1,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_1,A))) ),
    file('theBenchmark.p',fact_52_finite_OinsertI) ).

fof(fact_53_finite_OinsertI,axiom,
    ! [A_1,A] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
     => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(A_1,A))) ),
    file('theBenchmark.p',fact_53_finite_OinsertI) ).

fof(fact_54_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A))) ),
    file('theBenchmark.p',fact_54_card__image__le) ).

fof(fact_55_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(F,A))),hAPP_fun_a_bool_nat(finite_card_a,A))) ),
    file('theBenchmark.p',fact_55_card__image__le) ).

fof(fact_56_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(F,A))),hAPP_f696928925ol_nat(finite346522414t_bool,A))) ),
    file('theBenchmark.p',fact_56_card__image__le) ).

fof(fact_57_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(F,A))),hAPP_f55526627ol_nat(finite1340463720e_bool,A))) ),
    file('theBenchmark.p',fact_57_card__image__le) ).

fof(fact_58_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(F,A))),hAPP_f2009550088ol_nat(finite1306199131a_bool,A))) ),
    file('theBenchmark.p',fact_58_card__image__le) ).

fof(fact_59_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(F,A))),hAPP_fun_a_bool_nat(finite_card_a,A))) ),
    file('theBenchmark.p',fact_59_card__image__le) ).

fof(fact_60_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A))) ),
    file('theBenchmark.p',fact_60_card__image__le) ).

fof(fact_61_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A))) ),
    file('theBenchmark.p',fact_61_card__image__le) ).

fof(fact_62_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(F,A))),hAPP_f1690079119ol_nat(finite1352710292l_bool,A))) ),
    file('theBenchmark.p',fact_62_card__image__le) ).

fof(fact_63_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(F,A))),hAPP_f98387925ol_nat(finite269641166l_bool,A))) ),
    file('theBenchmark.p',fact_63_card__image__le) ).

fof(fact_64_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(F,A))),hAPP_f1253658590ol_nat(finite1659325229l_bool,A))) ),
    file('theBenchmark.p',fact_64_card__image__le) ).

fof(fact_65_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(F,A))),hAPP_f2009550088ol_nat(finite1306199131a_bool,A))) ),
    file('theBenchmark.p',fact_65_card__image__le) ).

fof(fact_66_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(F,A))),hAPP_f55526627ol_nat(finite1340463720e_bool,A))) ),
    file('theBenchmark.p',fact_66_card__image__le) ).

fof(fact_67_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(F,A))),hAPP_f696928925ol_nat(finite346522414t_bool,A))) ),
    file('theBenchmark.p',fact_67_card__image__le) ).

fof(fact_68_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(F,A))),hAPP_fun_a_bool_nat(finite_card_a,A))) ),
    file('theBenchmark.p',fact_68_card__image__le) ).

fof(fact_69_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A))) ),
    file('theBenchmark.p',fact_69_card__image__le) ).

fof(fact_70_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A))) ),
    file('theBenchmark.p',fact_70_card__image__le) ).

fof(fact_71_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A))) ),
    file('theBenchmark.p',fact_71_card__image__le) ).

fof(fact_72_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A))) ),
    file('theBenchmark.p',fact_72_card__image__le) ).

fof(fact_73_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A))) ),
    file('theBenchmark.p',fact_73_card__image__le) ).

fof(fact_74_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A))) ),
    file('theBenchmark.p',fact_74_card__image__le) ).

fof(fact_75_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A))) ),
    file('theBenchmark.p',fact_75_card__image__le) ).

fof(fact_76_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A))) ),
    file('theBenchmark.p',fact_76_card__image__le) ).

fof(fact_77_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(F,A))),hAPP_f696928925ol_nat(finite346522414t_bool,A))) ),
    file('theBenchmark.p',fact_77_card__image__le) ).

fof(fact_78_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(F,A))),hAPP_f55526627ol_nat(finite1340463720e_bool,A))) ),
    file('theBenchmark.p',fact_78_card__image__le) ).

fof(fact_79_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(F,A))),hAPP_f2009550088ol_nat(finite1306199131a_bool,A))) ),
    file('theBenchmark.p',fact_79_card__image__le) ).

fof(fact_80_card__mono,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A),B))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,A)),hAPP_f696928925ol_nat(finite346522414t_bool,B))) ) ),
    file('theBenchmark.p',fact_80_card__mono) ).

fof(fact_81_card__mono,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,A)),hAPP_f55526627ol_nat(finite1340463720e_bool,B))) ) ),
    file('theBenchmark.p',fact_81_card__mono) ).

fof(fact_82_card__mono,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A),B))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,A)),hAPP_f2009550088ol_nat(finite1306199131a_bool,B))) ) ),
    file('theBenchmark.p',fact_82_card__mono) ).

fof(fact_83_card__mono,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,A)),hAPP_f921600141ol_nat(finite_card_pname,B))) ) ),
    file('theBenchmark.p',fact_83_card__mono) ).

fof(fact_84_card__mono,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,A)),hAPP_fun_a_bool_nat(finite_card_a,B))) ) ),
    file('theBenchmark.p',fact_84_card__mono) ).

fof(fact_85_card__mono,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,A)),hAPP_f22106695ol_nat(finite_card_nat,B))) ) ),
    file('theBenchmark.p',fact_85_card__mono) ).

fof(fact_86_card__seteq,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A),B))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,B)),hAPP_f696928925ol_nat(finite346522414t_bool,A)))
         => A = B ) ) ),
    file('theBenchmark.p',fact_86_card__seteq) ).

fof(fact_87_card__seteq,axiom,
    ! [A,B] :
      ( ( is_fun1661590463l_bool(B)
        & is_fun1661590463l_bool(A) )
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
       => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B))
         => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,B)),hAPP_f55526627ol_nat(finite1340463720e_bool,A)))
           => A = B ) ) ) ),
    file('theBenchmark.p',fact_87_card__seteq) ).

fof(fact_88_card__seteq,axiom,
    ! [A,B] :
      ( ( is_fun949378684l_bool(B)
        & is_fun949378684l_bool(A) )
     => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))
       => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A),B))
         => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,B)),hAPP_f2009550088ol_nat(finite1306199131a_bool,A)))
           => A = B ) ) ) ),
    file('theBenchmark.p',fact_88_card__seteq) ).

fof(fact_89_card__seteq,axiom,
    ! [A,B] :
      ( ( is_fun_pname_bool(B)
        & is_fun_pname_bool(A) )
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
         => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,B)),hAPP_f921600141ol_nat(finite_card_pname,A)))
           => A = B ) ) ) ),
    file('theBenchmark.p',fact_89_card__seteq) ).

fof(fact_90_card__seteq,axiom,
    ! [A,B] :
      ( ( is_fun_a_bool(B)
        & is_fun_a_bool(A) )
     => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))
       => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
         => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,B)),hAPP_fun_a_bool_nat(finite_card_a,A)))
           => A = B ) ) ) ),
    file('theBenchmark.p',fact_90_card__seteq) ).

fof(fact_91_card__seteq,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,B)),hAPP_f22106695ol_nat(finite_card_nat,A)))
         => A = B ) ) ),
    file('theBenchmark.p',fact_91_card__seteq) ).

fof(fact_92_card__insert__le,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,A)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_2,A)))) ),
    file('theBenchmark.p',fact_92_card__insert__le) ).

fof(fact_93_card__insert__le,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,A)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_2,A)))) ),
    file('theBenchmark.p',fact_93_card__insert__le) ).

fof(fact_94_card__insert__le,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,A)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_2,A)))) ),
    file('theBenchmark.p',fact_94_card__insert__le) ).

fof(fact_95_card__insert__le,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,A)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_2,A)))) ),
    file('theBenchmark.p',fact_95_card__insert__le) ).

fof(fact_96_card__insert__le,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,A)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_2,A)))) ),
    file('theBenchmark.p',fact_96_card__insert__le) ).

fof(fact_97_card__insert__le,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,A)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_2,A)))) ),
    file('theBenchmark.p',fact_97_card__insert__le) ).

fof(fact_98_card__insert__if,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
     => ( ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_2),A))
         => hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,A)) )
        & ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_2),A))
         => hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_2,A)) = hAPP_f696928925ol_nat(finite346522414t_bool,A) ) ) ),
    file('theBenchmark.p',fact_98_card__insert__if) ).

fof(fact_99_card__insert__if,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
         => hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,A)) )
        & ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
         => hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_2,A)) = hAPP_f55526627ol_nat(finite1340463720e_bool,A) ) ) ),
    file('theBenchmark.p',fact_99_card__insert__if) ).

fof(fact_100_card__insert__if,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
     => ( ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_2),A))
         => hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,A)) )
        & ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_2),A))
         => hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_2,A)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,A) ) ) ),
    file('theBenchmark.p',fact_100_card__insert__if) ).

fof(fact_101_card__insert__if,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
         => hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_2,A)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,A)) )
        & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
         => hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_2,A)) = hAPP_f22106695ol_nat(finite_card_nat,A) ) ) ),
    file('theBenchmark.p',fact_101_card__insert__if) ).

fof(fact_102_card__insert__if,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
         => hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_2,A)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,A)) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
         => hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_2,A)) = hAPP_f921600141ol_nat(finite_card_pname,A) ) ) ),
    file('theBenchmark.p',fact_102_card__insert__if) ).

fof(fact_103_card__insert__if,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
     => ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
         => hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_2,A)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,A)) )
        & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
         => hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_2,A)) = hAPP_fun_a_bool_nat(finite_card_a,A) ) ) ),
    file('theBenchmark.p',fact_103_card__insert__if) ).

fof(fact_104_card__insert__disjoint,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
     => ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_2),A))
       => hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,A)) ) ),
    file('theBenchmark.p',fact_104_card__insert__disjoint) ).

fof(fact_105_card__insert__disjoint,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
       => hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,A)) ) ),
    file('theBenchmark.p',fact_105_card__insert__disjoint) ).

fof(fact_106_card__insert__disjoint,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
     => ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_2),A))
       => hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,A)) ) ),
    file('theBenchmark.p',fact_106_card__insert__disjoint) ).

fof(fact_107_card__insert__disjoint,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_2,A)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,A)) ) ),
    file('theBenchmark.p',fact_107_card__insert__disjoint) ).

fof(fact_108_card__insert__disjoint,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
       => hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_2,A)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,A)) ) ),
    file('theBenchmark.p',fact_108_card__insert__disjoint) ).

fof(fact_109_card__insert__disjoint,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
     => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
       => hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_2,A)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,A)) ) ),
    file('theBenchmark.p',fact_109_card__insert__disjoint) ).

fof(fact_110_finite__Collect__conjI,axiom,
    ! [Q_1,Pa] :
      ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Q_1)))
        | hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Pa))) )
     => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,Pa),Q_1)))) ),
    file('theBenchmark.p',fact_110_finite__Collect__conjI) ).

fof(fact_111_finite__Collect__conjI,axiom,
    ! [Q_1,Pa] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1)))
        | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Pa))) )
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,Pa),Q_1)))) ),
    file('theBenchmark.p',fact_111_finite__Collect__conjI) ).

fof(fact_112_finite__Collect__conjI,axiom,
    ! [Q_1,Pa] :
      ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Q_1)))
        | hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Pa))) )
     => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,Pa),Q_1)))) ),
    file('theBenchmark.p',fact_112_finite__Collect__conjI) ).

fof(fact_113_finite__Collect__conjI,axiom,
    ! [Q_1,Pa] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Q_1)))
        | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Pa))) )
     => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,Pa),Q_1)))) ),
    file('theBenchmark.p',fact_113_finite__Collect__conjI) ).

fof(fact_114_finite__Collect__conjI,axiom,
    ! [Q_1,Pa] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1)))
        | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Pa))) )
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,Pa),Q_1)))) ),
    file('theBenchmark.p',fact_114_finite__Collect__conjI) ).

fof(fact_115_finite__Collect__conjI,axiom,
    ! [Q_1,Pa] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_1)))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Pa))) )
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,Pa),Q_1)))) ),
    file('theBenchmark.p',fact_115_finite__Collect__conjI) ).

fof(fact_116_Suc__diff__le,axiom,
    ! [N_1,M_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_2))
     => hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M_2)),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(M_2),N_1)) ),
    file('theBenchmark.p',fact_116_Suc__diff__le) ).

fof(fact_117_finite__Collect__le__nat,axiom,
    ! [K] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),K)))),
    file('theBenchmark.p',fact_117_finite__Collect__le__nat) ).

fof(fact_118_card__Collect__le__nat,axiom,
    ! [Na] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),Na))) = hAPP_nat_nat(suc,Na),
    file('theBenchmark.p',fact_118_card__Collect__le__nat) ).

fof(fact_119_Suc__inject,axiom,
    ! [X,Y] :
      ( hAPP_nat_nat(suc,X) = hAPP_nat_nat(suc,Y)
     => X = Y ),
    file('theBenchmark.p',fact_119_Suc__inject) ).

fof(fact_120_nat_Oinject,axiom,
    ! [Nat_1,Nat] :
      ( hAPP_nat_nat(suc,Nat_1) = hAPP_nat_nat(suc,Nat)
    <=> Nat_1 = Nat ),
    file('theBenchmark.p',fact_120_nat_Oinject) ).

fof(fact_121_Suc__n__not__n,axiom,
    ! [N_1] : hAPP_nat_nat(suc,N_1) != N_1,
    file('theBenchmark.p',fact_121_Suc__n__not__n) ).

fof(fact_122_n__not__Suc__n,axiom,
    ! [N_1] : N_1 != hAPP_nat_nat(suc,N_1),
    file('theBenchmark.p',fact_122_n__not__Suc__n) ).

fof(fact_123_le__antisym,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_2))
       => M_2 = N_1 ) ),
    file('theBenchmark.p',fact_123_le__antisym) ).

fof(fact_124_le__trans,axiom,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),K_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),K_1)) ) ),
    file('theBenchmark.p',fact_124_le__trans) ).

fof(fact_125_eq__imp__le,axiom,
    ! [M_2,N_1] :
      ( M_2 = N_1
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ),
    file('theBenchmark.p',fact_125_eq__imp__le) ).

fof(fact_126_nat__le__linear,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ),
    file('theBenchmark.p',fact_126_nat__le__linear) ).

fof(fact_127_le__refl,axiom,
    ! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),N_1)),
    file('theBenchmark.p',fact_127_le__refl) ).

fof(fact_128_diff__commute,axiom,
    ! [I_1,J,K_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I_1),J)),K_1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I_1),K_1)),J),
    file('theBenchmark.p',fact_128_diff__commute) ).

fof(fact_129_finite__Collect__disjI,axiom,
    ! [Pa,Q_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,Pa),Q_1))))
    <=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1)))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Pa))) ) ),
    file('theBenchmark.p',fact_129_finite__Collect__disjI) ).

fof(fact_130_finite__Collect__disjI,axiom,
    ! [Pa,Q_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,Pa),Q_1))))
    <=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Q_1)))
        & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Pa))) ) ),
    file('theBenchmark.p',fact_130_finite__Collect__disjI) ).

fof(fact_131_finite__Collect__disjI,axiom,
    ! [Pa,Q_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,Pa),Q_1))))
    <=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1)))
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Pa))) ) ),
    file('theBenchmark.p',fact_131_finite__Collect__disjI) ).

fof(fact_132_finite__Collect__disjI,axiom,
    ! [Pa,Q_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,Pa),Q_1))))
    <=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Q_1)))
        & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Pa))) ) ),
    file('theBenchmark.p',fact_132_finite__Collect__disjI) ).

fof(fact_133_finite__Collect__disjI,axiom,
    ! [Pa,Q_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,Pa),Q_1))))
    <=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_1)))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Pa))) ) ),
    file('theBenchmark.p',fact_133_finite__Collect__disjI) ).

fof(fact_134_finite__Collect__disjI,axiom,
    ! [Pa,Q_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,Pa),Q_1))))
    <=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Q_1)))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Pa))) ) ),
    file('theBenchmark.p',fact_134_finite__Collect__disjI) ).

fof(fact_135_finite__insert,axiom,
    ! [A_1,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(A_1,A)))
    <=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    file('theBenchmark.p',fact_135_finite__insert) ).

fof(fact_136_finite__insert,axiom,
    ! [A_1,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_1,A)))
    <=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    file('theBenchmark.p',fact_136_finite__insert) ).

fof(fact_137_finite__insert,axiom,
    ! [A_1,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(A_1,A)))
    <=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    file('theBenchmark.p',fact_137_finite__insert) ).

fof(fact_138_finite__insert,axiom,
    ! [A_1,A] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(A_1,A)))
    <=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ),
    file('theBenchmark.p',fact_138_finite__insert) ).

fof(fact_139_finite__insert,axiom,
    ! [A_1,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_1,A)))
    <=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    file('theBenchmark.p',fact_139_finite__insert) ).

fof(fact_140_finite__insert,axiom,
    ! [A_1,A] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(A_1,A)))
    <=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) ),
    file('theBenchmark.p',fact_140_finite__insert) ).

fof(fact_141_finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A),B))
     => ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B))
       => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ) ),
    file('theBenchmark.p',fact_141_finite__subset) ).

fof(fact_142_finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ) ),
    file('theBenchmark.p',fact_142_finite__subset) ).

fof(fact_143_finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
     => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ) ),
    file('theBenchmark.p',fact_143_finite__subset) ).

fof(fact_144_finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A),B))
     => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))
       => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) ) ),
    file('theBenchmark.p',fact_144_finite__subset) ).

fof(fact_145_finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ) ),
    file('theBenchmark.p',fact_145_finite__subset) ).

fof(fact_146_finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ) ),
    file('theBenchmark.p',fact_146_finite__subset) ).

fof(fact_147_rev__finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A),B))
       => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ) ),
    file('theBenchmark.p',fact_147_rev__finite__subset) ).

fof(fact_148_rev__finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ) ),
    file('theBenchmark.p',fact_148_rev__finite__subset) ).

fof(fact_149_rev__finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ) ),
    file('theBenchmark.p',fact_149_rev__finite__subset) ).

fof(fact_150_rev__finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A),B))
       => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) ) ),
    file('theBenchmark.p',fact_150_rev__finite__subset) ).

fof(fact_151_rev__finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ) ),
    file('theBenchmark.p',fact_151_rev__finite__subset) ).

fof(fact_152_rev__finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ) ),
    file('theBenchmark.p',fact_152_rev__finite__subset) ).

fof(fact_153_Suc__leD,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ),
    file('theBenchmark.p',fact_153_Suc__leD) ).

fof(fact_154_le__SucE,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_1)))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
       => M_2 = hAPP_nat_nat(suc,N_1) ) ),
    file('theBenchmark.p',fact_154_le__SucE) ).

fof(fact_155_le__SucI,axiom,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_1))) ),
    file('theBenchmark.p',fact_155_le__SucI) ).

fof(fact_156_Suc__le__mono,axiom,
    ! [Na,M_3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M_3)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M_3)) ),
    file('theBenchmark.p',fact_156_Suc__le__mono) ).

fof(fact_157_le__Suc__eq,axiom,
    ! [M_3,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_3),hAPP_nat_nat(suc,Na)))
    <=> ( M_3 = hAPP_nat_nat(suc,Na)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_3),Na)) ) ),
    file('theBenchmark.p',fact_157_le__Suc__eq) ).

fof(fact_158_not__less__eq__eq,axiom,
    ! [M_3,Na] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_3),Na))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_3)) ),
    file('theBenchmark.p',fact_158_not__less__eq__eq) ).

fof(fact_159_Suc__n__not__le__n,axiom,
    ! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),N_1)),
    file('theBenchmark.p',fact_159_Suc__n__not__le__n) ).

fof(fact_160_Suc__diff__diff,axiom,
    ! [M_2,N_1,K_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M_2)),N_1)),hAPP_nat_nat(suc,K_1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M_2),N_1)),K_1),
    file('theBenchmark.p',fact_160_Suc__diff__diff) ).

fof(fact_161_diff__Suc__Suc,axiom,
    ! [M_2,N_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(minus_minus_nat(M_2),N_1),
    file('theBenchmark.p',fact_161_diff__Suc__Suc) ).

fof(fact_162_le__diff__iff,axiom,
    ! [Na,K,M_3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M_3))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),Na))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M_3),K)),hAPP_nat_nat(minus_minus_nat(Na),K)))
        <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_3),Na)) ) ) ),
    file('theBenchmark.p',fact_162_le__diff__iff) ).

fof(fact_163_Nat_Odiff__diff__eq,axiom,
    ! [N_1,K_1,M_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1))
       => hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M_2),K_1)),hAPP_nat_nat(minus_minus_nat(N_1),K_1)) = hAPP_nat_nat(minus_minus_nat(M_2),N_1) ) ),
    file('theBenchmark.p',fact_163_Nat_Odiff__diff__eq) ).

fof(fact_164_eq__diff__iff,axiom,
    ! [Na,K,M_3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M_3))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),Na))
       => ( hAPP_nat_nat(minus_minus_nat(M_3),K) = hAPP_nat_nat(minus_minus_nat(Na),K)
        <=> M_3 = Na ) ) ),
    file('theBenchmark.p',fact_164_eq__diff__iff) ).

fof(fact_165_diff__diff__cancel,axiom,
    ! [I_1,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),N_1))
     => hAPP_nat_nat(minus_minus_nat(N_1),hAPP_nat_nat(minus_minus_nat(N_1),I_1)) = I_1 ),
    file('theBenchmark.p',fact_165_diff__diff__cancel) ).

fof(fact_166_diff__le__mono,axiom,
    ! [L,M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M_2),L)),hAPP_nat_nat(minus_minus_nat(N_1),L))) ),
    file('theBenchmark.p',fact_166_diff__le__mono) ).

fof(fact_167_diff__le__mono2,axiom,
    ! [L,M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(L),N_1)),hAPP_nat_nat(minus_minus_nat(L),M_2))) ),
    file('theBenchmark.p',fact_167_diff__le__mono2) ).

fof(fact_168_diff__le__self,axiom,
    ! [M_2,N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M_2),N_1)),M_2)),
    file('theBenchmark.p',fact_168_diff__le__self) ).

fof(fact_169_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_pname_a(F,A)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) ) ),
    file('theBenchmark.p',fact_169_finite__surj) ).

fof(fact_170_finite__subset__image,axiom,
    ! [F,A,B] :
      ( is_fun_a_bool(B)
     => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))
       => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_pname_a(F,A)))
         => ? [C_2] :
              ( B = image_pname_a(F,C_2)
              & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_2))
              & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_2),A))
              & is_fun_pname_bool(C_2) ) ) ) ),
    file('theBenchmark.p',fact_170_finite__subset__image) ).

fof(fact_171_lift__Suc__mono__le,axiom,
    ! [Na,N_3,F] :
      ( ! [N_2] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,N_2)),hAPP_n1699378549t_bool(F,hAPP_nat_nat(suc,N_2))))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,Na)),hAPP_n1699378549t_bool(F,N_3))) ) ),
    file('theBenchmark.p',fact_171_lift__Suc__mono__le) ).

fof(fact_172_lift__Suc__mono__le,axiom,
    ! [Na,N_3,F] :
      ( ! [N_2] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(F,N_2)),hAPP_n1025906991e_bool(F,hAPP_nat_nat(suc,N_2))))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(F,Na)),hAPP_n1025906991e_bool(F,N_3))) ) ),
    file('theBenchmark.p',fact_172_lift__Suc__mono__le) ).

fof(fact_173_lift__Suc__mono__le,axiom,
    ! [Na,N_3,F] :
      ( ! [N_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,N_2)),hAPP_nat_nat(F,hAPP_nat_nat(suc,N_2))))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,Na)),hAPP_nat_nat(F,N_3))) ) ),
    file('theBenchmark.p',fact_173_lift__Suc__mono__le) ).

fof(fact_174_lift__Suc__mono__le,axiom,
    ! [Na,N_3,F] :
      ( ! [N_2] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(F,N_2)),hAPP_nat_fun_a_bool(F,hAPP_nat_nat(suc,N_2))))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(F,Na)),hAPP_nat_fun_a_bool(F,N_3))) ) ),
    file('theBenchmark.p',fact_174_lift__Suc__mono__le) ).

fof(fact_175_pigeonhole__infinite,axiom,
    ! [F,A] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(F,A)))
       => ? [X_1] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,F)),hAPP_pname_a(F,X_1))))))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
            & is_pname(X_1) ) ) ),
    file('theBenchmark.p',fact_175_pigeonhole__infinite) ).

fof(fact_176_image__eqI,axiom,
    ! [A,B_1,F,X_2] :
      ( B_1 = hAPP_pname_a(F,X_2)
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A))) ) ),
    file('theBenchmark.p',fact_176_image__eqI) ).

fof(fact_177_equalityI,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))
       => A = B ) ),
    file('theBenchmark.p',fact_177_equalityI) ).

fof(fact_178_equalityI,axiom,
    ! [A,B] :
      ( ( is_fun_pname_bool(B)
        & is_fun_pname_bool(A) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
         => A = B ) ) ),
    file('theBenchmark.p',fact_178_equalityI) ).

fof(fact_179_equalityI,axiom,
    ! [A,B] :
      ( ( is_fun_a_bool(B)
        & is_fun_a_bool(A) )
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
       => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A))
         => A = B ) ) ),
    file('theBenchmark.p',fact_179_equalityI) ).

fof(fact_180_subsetD,axiom,
    ! [C_1,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),B)) ) ),
    file('theBenchmark.p',fact_180_subsetD) ).

fof(fact_181_subsetD,axiom,
    ! [C_1,A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_1),A))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_1),B)) ) ),
    file('theBenchmark.p',fact_181_subsetD) ).

fof(fact_182_subsetD,axiom,
    ! [C_1,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),A))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),B)) ) ),
    file('theBenchmark.p',fact_182_subsetD) ).

fof(fact_183_insertCI,axiom,
    ! [B_1,A_1,B] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),B))
       => A_1 = B_1 )
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),insert_nat(B_1,B))) ),
    file('theBenchmark.p',fact_183_insertCI) ).

fof(fact_184_insertCI,axiom,
    ! [B_1,A_1,B] :
      ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),B))
       => A_1 = B_1 )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B_1,B))) ),
    file('theBenchmark.p',fact_184_insertCI) ).

fof(fact_185_insertCI,axiom,
    ! [B_1,A_1,B] :
      ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),B))
       => A_1 = B_1 )
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),insert_a(B_1,B))) ),
    file('theBenchmark.p',fact_185_insertCI) ).

fof(fact_186_insertE,axiom,
    ! [A_1,B_1,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),insert_nat(B_1,A)))
     => ( A_1 != B_1
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A)) ) ),
    file('theBenchmark.p',fact_186_insertE) ).

fof(fact_187_insertE,axiom,
    ! [A_1,B_1,A] :
      ( ( is_pname(B_1)
        & is_pname(A_1) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B_1,A)))
       => ( A_1 != B_1
         => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A)) ) ) ),
    file('theBenchmark.p',fact_187_insertE) ).

fof(fact_188_insertE,axiom,
    ! [A_1,B_1,A] :
      ( ( is_a(B_1)
        & is_a(A_1) )
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),insert_a(B_1,A)))
       => ( A_1 != B_1
         => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),A)) ) ) ),
    file('theBenchmark.p',fact_188_insertE) ).

fof(fact_189_insertI1,axiom,
    ! [A_1,B] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),insert_nat(A_1,B))),
    file('theBenchmark.p',fact_189_insertI1) ).

fof(fact_190_insertI1,axiom,
    ! [A_1,B] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(A_1,B))),
    file('theBenchmark.p',fact_190_insertI1) ).

fof(fact_191_insertI1,axiom,
    ! [A_1,B] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),insert_a(A_1,B))),
    file('theBenchmark.p',fact_191_insertI1) ).

fof(fact_192_insert__compr,axiom,
    ! [A_1,B] : insert_nat(A_1,B) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),B))),
    file('theBenchmark.p',fact_192_insert__compr) ).

fof(fact_193_insert__compr,axiom,
    ! [A_1,B] : insert_pname(A_1,B) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),B))),
    file('theBenchmark.p',fact_193_insert__compr) ).

fof(fact_194_insert__compr,axiom,
    ! [A_1,B] : insert_a(A_1,B) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),B))),
    file('theBenchmark.p',fact_194_insert__compr) ).

fof(fact_195_insert__compr,axiom,
    ! [A_1,B] : insert_fun_nat_bool(A_1,B) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),B))),
    file('theBenchmark.p',fact_195_insert__compr) ).

fof(fact_196_insert__compr,axiom,
    ! [A_1,B] : insert1325755072e_bool(A_1,B) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),B))),
    file('theBenchmark.p',fact_196_insert__compr) ).

fof(fact_197_insert__compr,axiom,
    ! [A_1,B] : insert_fun_a_bool(A_1,B) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),B))),
    file('theBenchmark.p',fact_197_insert__compr) ).

fof(fact_198_insert__Collect,axiom,
    ! [A_1,Pa] : insert_nat(A_1,collect_nat(Pa)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_1))),Pa)),
    file('theBenchmark.p',fact_198_insert__Collect) ).

fof(fact_199_insert__Collect,axiom,
    ! [A_1,Pa] : insert_pname(A_1,collect_pname(Pa)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_1))),Pa)),
    file('theBenchmark.p',fact_199_insert__Collect) ).

fof(fact_200_insert__Collect,axiom,
    ! [A_1,Pa] : insert_a(A_1,collect_a(Pa)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_1))),Pa)),
    file('theBenchmark.p',fact_200_insert__Collect) ).

fof(fact_201_insert__Collect,axiom,
    ! [A_1,Pa] : insert_fun_nat_bool(A_1,collect_fun_nat_bool(Pa)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_1))),Pa)),
    file('theBenchmark.p',fact_201_insert__Collect) ).

fof(fact_202_insert__Collect,axiom,
    ! [A_1,Pa] : insert1325755072e_bool(A_1,collec1974731493e_bool(Pa)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_1))),Pa)),
    file('theBenchmark.p',fact_202_insert__Collect) ).

fof(fact_203_insert__Collect,axiom,
    ! [A_1,Pa] : insert_fun_a_bool(A_1,collect_fun_a_bool(Pa)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_1))),Pa)),
    file('theBenchmark.p',fact_203_insert__Collect) ).

fof(fact_204_insert__absorb2,axiom,
    ! [X_2,A] : insert_nat(X_2,insert_nat(X_2,A)) = insert_nat(X_2,A),
    file('theBenchmark.p',fact_204_insert__absorb2) ).

fof(fact_205_insert__absorb2,axiom,
    ! [X_2,A] : insert_pname(X_2,insert_pname(X_2,A)) = insert_pname(X_2,A),
    file('theBenchmark.p',fact_205_insert__absorb2) ).

fof(fact_206_insert__absorb2,axiom,
    ! [X_2,A] : insert_a(X_2,insert_a(X_2,A)) = insert_a(X_2,A),
    file('theBenchmark.p',fact_206_insert__absorb2) ).

fof(fact_207_insert__commute,axiom,
    ! [X_2,Y_1,A] : insert_nat(X_2,insert_nat(Y_1,A)) = insert_nat(Y_1,insert_nat(X_2,A)),
    file('theBenchmark.p',fact_207_insert__commute) ).

fof(fact_208_insert__commute,axiom,
    ! [X_2,Y_1,A] : insert_pname(X_2,insert_pname(Y_1,A)) = insert_pname(Y_1,insert_pname(X_2,A)),
    file('theBenchmark.p',fact_208_insert__commute) ).

fof(fact_209_insert__commute,axiom,
    ! [X_2,Y_1,A] : insert_a(X_2,insert_a(Y_1,A)) = insert_a(Y_1,insert_a(X_2,A)),
    file('theBenchmark.p',fact_209_insert__commute) ).

fof(fact_210_insert__iff,axiom,
    ! [A_1,B_1,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),insert_nat(B_1,A)))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A))
        | A_1 = B_1 ) ),
    file('theBenchmark.p',fact_210_insert__iff) ).

fof(fact_211_insert__iff,axiom,
    ! [A_1,B_1,A] :
      ( ( is_pname(B_1)
        & is_pname(A_1) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B_1,A)))
      <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A))
          | A_1 = B_1 ) ) ),
    file('theBenchmark.p',fact_211_insert__iff) ).

fof(fact_212_insert__iff,axiom,
    ! [A_1,B_1,A] :
      ( ( is_a(B_1)
        & is_a(A_1) )
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),insert_a(B_1,A)))
      <=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),A))
          | A_1 = B_1 ) ) ),
    file('theBenchmark.p',fact_212_insert__iff) ).

fof(fact_213_insert__code,axiom,
    ! [Y_1,A,X_2] :
      ( hBOOL(hAPP_nat_bool(insert_nat(Y_1,A),X_2))
    <=> ( hBOOL(hAPP_nat_bool(A,X_2))
        | Y_1 = X_2 ) ),
    file('theBenchmark.p',fact_213_insert__code) ).

fof(fact_214_insert__code,axiom,
    ! [Y_1,A,X_2] :
      ( ( is_pname(X_2)
        & is_pname(Y_1) )
     => ( hBOOL(hAPP_pname_bool(insert_pname(Y_1,A),X_2))
      <=> ( hBOOL(hAPP_pname_bool(A,X_2))
          | Y_1 = X_2 ) ) ),
    file('theBenchmark.p',fact_214_insert__code) ).

fof(fact_215_insert__code,axiom,
    ! [Y_1,A,X_2] :
      ( ( is_a(X_2)
        & is_a(Y_1) )
     => ( hBOOL(hAPP_a_bool(insert_a(Y_1,A),X_2))
      <=> ( hBOOL(hAPP_a_bool(A,X_2))
          | Y_1 = X_2 ) ) ),
    file('theBenchmark.p',fact_215_insert__code) ).

fof(fact_216_insert__ident,axiom,
    ! [B,X_2,A] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B))
       => ( insert_nat(X_2,A) = insert_nat(X_2,B)
        <=> A = B ) ) ),
    file('theBenchmark.p',fact_216_insert__ident) ).

fof(fact_217_insert__ident,axiom,
    ! [B,X_2,A] :
      ( ( is_fun_pname_bool(A)
        & is_fun_pname_bool(B) )
     => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
       => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))
         => ( insert_pname(X_2,A) = insert_pname(X_2,B)
          <=> A = B ) ) ) ),
    file('theBenchmark.p',fact_217_insert__ident) ).

fof(fact_218_insert__ident,axiom,
    ! [B,X_2,A] :
      ( ( is_fun_a_bool(A)
        & is_fun_a_bool(B) )
     => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
       => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B))
         => ( insert_a(X_2,A) = insert_a(X_2,B)
          <=> A = B ) ) ) ),
    file('theBenchmark.p',fact_218_insert__ident) ).

fof(fact_219_insertI2,axiom,
    ! [B_1,A_1,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),B))
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),insert_nat(B_1,B))) ),
    file('theBenchmark.p',fact_219_insertI2) ).

fof(fact_220_insertI2,axiom,
    ! [B_1,A_1,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),B))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B_1,B))) ),
    file('theBenchmark.p',fact_220_insertI2) ).

fof(fact_221_insertI2,axiom,
    ! [B_1,A_1,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),B))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),insert_a(B_1,B))) ),
    file('theBenchmark.p',fact_221_insertI2) ).

fof(fact_222_insert__absorb,axiom,
    ! [A_1,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A))
     => insert_nat(A_1,A) = A ),
    file('theBenchmark.p',fact_222_insert__absorb) ).

fof(fact_223_insert__absorb,axiom,
    ! [A_1,A] :
      ( is_fun_pname_bool(A)
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A))
       => insert_pname(A_1,A) = A ) ),
    file('theBenchmark.p',fact_223_insert__absorb) ).

fof(fact_224_insert__absorb,axiom,
    ! [A_1,A] :
      ( is_fun_a_bool(A)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),A))
       => insert_a(A_1,A) = A ) ),
    file('theBenchmark.p',fact_224_insert__absorb) ).

fof(fact_225_subset__refl,axiom,
    ! [A] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),A)),
    file('theBenchmark.p',fact_225_subset__refl) ).

fof(fact_226_subset__refl,axiom,
    ! [A] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),A)),
    file('theBenchmark.p',fact_226_subset__refl) ).

fof(fact_227_subset__refl,axiom,
    ! [A] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),A)),
    file('theBenchmark.p',fact_227_subset__refl) ).

fof(fact_228_set__eq__subset,axiom,
    ! [A,B] :
      ( A = B
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ) ),
    file('theBenchmark.p',fact_228_set__eq__subset) ).

fof(fact_229_set__eq__subset,axiom,
    ! [A,B] :
      ( ( is_fun_pname_bool(B)
        & is_fun_pname_bool(A) )
     => ( A = B
      <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ) ) ),
    file('theBenchmark.p',fact_229_set__eq__subset) ).

fof(fact_230_set__eq__subset,axiom,
    ! [A,B] :
      ( ( is_fun_a_bool(B)
        & is_fun_a_bool(A) )
     => ( A = B
      <=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ) ) ),
    file('theBenchmark.p',fact_230_set__eq__subset) ).

fof(fact_231_equalityD1,axiom,
    ! [A,B] :
      ( A = B
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    file('theBenchmark.p',fact_231_equalityD1) ).

fof(fact_232_equalityD1,axiom,
    ! [A,B] :
      ( A = B
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ),
    file('theBenchmark.p',fact_232_equalityD1) ).

fof(fact_233_equalityD1,axiom,
    ! [A,B] :
      ( A = B
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ),
    file('theBenchmark.p',fact_233_equalityD1) ).

fof(fact_234_equalityD2,axiom,
    ! [A,B] :
      ( A = B
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) ),
    file('theBenchmark.p',fact_234_equalityD2) ).

fof(fact_235_equalityD2,axiom,
    ! [A,B] :
      ( A = B
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A)) ),
    file('theBenchmark.p',fact_235_equalityD2) ).

fof(fact_236_equalityD2,axiom,
    ! [A,B] :
      ( A = B
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A)) ),
    file('theBenchmark.p',fact_236_equalityD2) ).

fof(fact_237_in__mono,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) ) ),
    file('theBenchmark.p',fact_237_in__mono) ).

fof(fact_238_in__mono,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B)) ) ),
    file('theBenchmark.p',fact_238_in__mono) ).

fof(fact_239_in__mono,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) ) ),
    file('theBenchmark.p',fact_239_in__mono) ).

fof(fact_240_set__rev__mp,axiom,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) ) ),
    file('theBenchmark.p',fact_240_set__rev__mp) ).

fof(fact_241_set__rev__mp,axiom,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B)) ) ),
    file('theBenchmark.p',fact_241_set__rev__mp) ).

fof(fact_242_set__rev__mp,axiom,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) ) ),
    file('theBenchmark.p',fact_242_set__rev__mp) ).

fof(fact_243_set__mp,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) ) ),
    file('theBenchmark.p',fact_243_set__mp) ).

fof(fact_244_set__mp,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B)) ) ),
    file('theBenchmark.p',fact_244_set__mp) ).

fof(fact_245_set__mp,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) ) ),
    file('theBenchmark.p',fact_245_set__mp) ).

fof(fact_246_subset__trans,axiom,
    ! [C,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),C))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),C)) ) ),
    file('theBenchmark.p',fact_246_subset__trans) ).

fof(fact_247_subset__trans,axiom,
    ! [C,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C)) ) ),
    file('theBenchmark.p',fact_247_subset__trans) ).

fof(fact_248_subset__trans,axiom,
    ! [C,A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),C))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),C)) ) ),
    file('theBenchmark.p',fact_248_subset__trans) ).

fof(fact_249_equalityE,axiom,
    ! [A,B] :
      ( A = B
     => ~ ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
         => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) ) ),
    file('theBenchmark.p',fact_249_equalityE) ).

fof(fact_250_equalityE,axiom,
    ! [A,B] :
      ( A = B
     => ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
         => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A)) ) ),
    file('theBenchmark.p',fact_250_equalityE) ).

fof(fact_251_equalityE,axiom,
    ! [A,B] :
      ( A = B
     => ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
         => ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A)) ) ),
    file('theBenchmark.p',fact_251_equalityE) ).

fof(fact_252_mem__def,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
    <=> hBOOL(hAPP_nat_bool(A,X_2)) ),
    file('theBenchmark.p',fact_252_mem__def) ).

fof(fact_253_mem__def,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
    <=> hBOOL(hAPP_a_bool(A,X_2)) ),
    file('theBenchmark.p',fact_253_mem__def) ).

fof(fact_254_mem__def,axiom,
    ! [X_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
    <=> hBOOL(hAPP_pname_bool(A,X_2)) ),
    file('theBenchmark.p',fact_254_mem__def) ).

fof(fact_255_Collect__def,axiom,
    ! [Pa] :
      ( is_fun_pname_bool(Pa)
     => collect_pname(Pa) = Pa ),
    file('theBenchmark.p',fact_255_Collect__def) ).

fof(fact_256_Collect__def,axiom,
    ! [Pa] : collect_fun_nat_bool(Pa) = Pa,
    file('theBenchmark.p',fact_256_Collect__def) ).

fof(fact_257_Collect__def,axiom,
    ! [Pa] :
      ( is_fun1661590463l_bool(Pa)
     => collec1974731493e_bool(Pa) = Pa ),
    file('theBenchmark.p',fact_257_Collect__def) ).

fof(fact_258_Collect__def,axiom,
    ! [Pa] :
      ( is_fun949378684l_bool(Pa)
     => collect_fun_a_bool(Pa) = Pa ),
    file('theBenchmark.p',fact_258_Collect__def) ).

fof(fact_259_Collect__def,axiom,
    ! [Pa] : collect_nat(Pa) = Pa,
    file('theBenchmark.p',fact_259_Collect__def) ).

fof(fact_260_image__iff,axiom,
    ! [Z,F,A] :
      ( is_a(Z)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,Z),image_pname_a(F,A)))
      <=> ? [X_1] :
            ( Z = hAPP_pname_a(F,X_1)
            & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
            & is_pname(X_1) ) ) ),
    file('theBenchmark.p',fact_260_image__iff) ).

fof(fact_261_imageI,axiom,
    ! [F,X_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(F,X_2)),image_pname_a(F,A))) ),
    file('theBenchmark.p',fact_261_imageI) ).

fof(fact_262_rev__image__eqI,axiom,
    ! [B_1,F,X_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
     => ( B_1 = hAPP_pname_a(F,X_2)
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A))) ) ),
    file('theBenchmark.p',fact_262_rev__image__eqI) ).

fof(fact_263_insert__compr__raw,axiom,
    ! [X_1,Xa] : insert_nat(X_1,Xa) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X_1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),Xa))),
    file('theBenchmark.p',fact_263_insert__compr__raw) ).

fof(fact_264_insert__compr__raw,axiom,
    ! [X_1,Xa] : insert_pname(X_1,Xa) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X_1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),Xa))),
    file('theBenchmark.p',fact_264_insert__compr__raw) ).

fof(fact_265_insert__compr__raw,axiom,
    ! [X_1,Xa] : insert_a(X_1,Xa) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X_1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),Xa))),
    file('theBenchmark.p',fact_265_insert__compr__raw) ).

fof(fact_266_insert__compr__raw,axiom,
    ! [X_1,Xa] : insert_fun_nat_bool(X_1,Xa) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X_1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),Xa))),
    file('theBenchmark.p',fact_266_insert__compr__raw) ).

fof(fact_267_insert__compr__raw,axiom,
    ! [X_1,Xa] : insert1325755072e_bool(X_1,Xa) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X_1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),Xa))),
    file('theBenchmark.p',fact_267_insert__compr__raw) ).

fof(fact_268_insert__compr__raw,axiom,
    ! [X_1,Xa] : insert_fun_a_bool(X_1,Xa) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X_1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),Xa))),
    file('theBenchmark.p',fact_268_insert__compr__raw) ).

fof(fact_269_subset__insertI,axiom,
    ! [B,A_1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),insert_nat(A_1,B))),
    file('theBenchmark.p',fact_269_subset__insertI) ).

fof(fact_270_subset__insertI,axiom,
    ! [B,A_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),insert_pname(A_1,B))),
    file('theBenchmark.p',fact_270_subset__insertI) ).

fof(fact_271_subset__insertI,axiom,
    ! [B,A_1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),insert_a(A_1,B))),
    file('theBenchmark.p',fact_271_subset__insertI) ).

fof(fact_272_insert__subset,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X_2,A)),B))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) ) ),
    file('theBenchmark.p',fact_272_insert__subset) ).

fof(fact_273_insert__subset,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X_2,A)),B))
    <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) ) ),
    file('theBenchmark.p',fact_273_insert__subset) ).

fof(fact_274_insert__subset,axiom,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X_2,A)),B))
    <=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B)) ) ),
    file('theBenchmark.p',fact_274_insert__subset) ).

fof(fact_275_subset__insert,axiom,
    ! [B,X_2,A] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),insert_nat(X_2,B)))
      <=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ) ),
    file('theBenchmark.p',fact_275_subset__insert) ).

fof(fact_276_subset__insert,axiom,
    ! [B,X_2,A] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),insert_pname(X_2,B)))
      <=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ) ),
    file('theBenchmark.p',fact_276_subset__insert) ).

fof(fact_277_subset__insert,axiom,
    ! [B,X_2,A] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),insert_a(X_2,B)))
      <=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ) ),
    file('theBenchmark.p',fact_277_subset__insert) ).

fof(fact_278_subset__insertI2,axiom,
    ! [B_1,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),insert_nat(B_1,B))) ),
    file('theBenchmark.p',fact_278_subset__insertI2) ).

fof(fact_279_subset__insertI2,axiom,
    ! [B_1,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),insert_pname(B_1,B))) ),
    file('theBenchmark.p',fact_279_subset__insertI2) ).

fof(fact_280_subset__insertI2,axiom,
    ! [B_1,A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),insert_a(B_1,B))) ),
    file('theBenchmark.p',fact_280_subset__insertI2) ).

fof(fact_281_insert__mono,axiom,
    ! [A_1,C,D] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C),D))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(A_1,C)),insert_nat(A_1,D))) ),
    file('theBenchmark.p',fact_281_insert__mono) ).

fof(fact_282_insert__mono,axiom,
    ! [A_1,C,D] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),D))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(A_1,C)),insert_pname(A_1,D))) ),
    file('theBenchmark.p',fact_282_insert__mono) ).

fof(fact_283_insert__mono,axiom,
    ! [A_1,C,D] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C),D))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(A_1,C)),insert_a(A_1,D))) ),
    file('theBenchmark.p',fact_283_insert__mono) ).

fof(fact_284_image__insert,axiom,
    ! [F,A_1,B] : image_pname_a(F,insert_pname(A_1,B)) = insert_a(hAPP_pname_a(F,A_1),image_pname_a(F,B)),
    file('theBenchmark.p',fact_284_image__insert) ).

fof(fact_285_insert__image,axiom,
    ! [F,X_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
     => insert_a(hAPP_pname_a(F,X_2),image_pname_a(F,A)) = image_pname_a(F,A) ),
    file('theBenchmark.p',fact_285_insert__image) ).

fof(fact_286_subset__image__iff,axiom,
    ! [B,F,A] :
      ( is_fun_a_bool(B)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_pname_a(F,A)))
      <=> ? [AA] :
            ( B = image_pname_a(F,AA)
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,AA),A))
            & is_fun_pname_bool(AA) ) ) ),
    file('theBenchmark.p',fact_286_subset__image__iff) ).

fof(fact_287_image__mono,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(F,A)),image_pname_a(F,B))) ),
    file('theBenchmark.p',fact_287_image__mono) ).

fof(fact_288_imageE,axiom,
    ! [B_1,F,A] :
      ( is_a(B_1)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A)))
       => ~ ! [X_1] :
              ( is_pname(X_1)
             => ( B_1 = hAPP_pname_a(F,X_1)
               => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) ) ) ) ),
    file('theBenchmark.p',fact_288_imageE) ).

fof(fact_289_subsetI,axiom,
    ! [B,A] :
      ( ! [X_1] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) )
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    file('theBenchmark.p',fact_289_subsetI) ).

fof(fact_290_subsetI,axiom,
    ! [B,A] :
      ( ! [X_1] :
          ( is_a(X_1)
         => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
           => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B)) ) )
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ),
    file('theBenchmark.p',fact_290_subsetI) ).

fof(fact_291_subsetI,axiom,
    ! [B,A] :
      ( ! [X_1] :
          ( is_pname(X_1)
         => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
           => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) ) )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ),
    file('theBenchmark.p',fact_291_subsetI) ).

fof(fact_292_zero__induct__lemma,axiom,
    ! [I,Pa,K] :
      ( hBOOL(hAPP_nat_bool(Pa,K))
     => ( ! [N_2] :
            ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_2)))
           => hBOOL(hAPP_nat_bool(Pa,N_2)) )
       => hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(minus_minus_nat(K),I))) ) ),
    file('theBenchmark.p',fact_292_zero__induct__lemma) ).

fof(fact_293_Suc__le__D,axiom,
    ! [N_1,M_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),M_1))
     => ? [M] : M_1 = hAPP_nat_nat(suc,M) ),
    file('theBenchmark.p',fact_293_Suc__le__D) ).

fof(fact_294_image__subsetI,axiom,
    ! [F,B,A] :
      ( ! [X_1] :
          ( is_pname(X_1)
         => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
           => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(F,X_1)),B)) ) )
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(F,A)),B)) ),
    file('theBenchmark.p',fact_294_image__subsetI) ).

fof(fact_295_order__refl,axiom,
    ! [X_2] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),X_2)),
    file('theBenchmark.p',fact_295_order__refl) ).

fof(fact_296_order__refl,axiom,
    ! [X_2] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_2),X_2)),
    file('theBenchmark.p',fact_296_order__refl) ).

fof(fact_297_order__refl,axiom,
    ! [X_3] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_3),X_3)),
    file('theBenchmark.p',fact_297_order__refl) ).

fof(fact_298_order__refl,axiom,
    ! [X_2] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_2),X_2)),
    file('theBenchmark.p',fact_298_order__refl) ).

fof(fact_299_finite__nat__set__iff__bounded__le,axiom,
    ! [N] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N))
    <=> ? [M] :
        ! [X_1] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),M)) ) ),
    file('theBenchmark.p',fact_299_finite__nat__set__iff__bounded__le) ).

fof(help_fNot_1_1_U,axiom,
    ! [P] :
      ( ~ hBOOL(P)
      | ~ hBOOL(hAPP_bool_bool(fNot,P)) ),
    file('theBenchmark.p',help_fNot_1_1_U) ).

fof(help_fNot_2_1_U,axiom,
    ! [P] :
      ( hBOOL(hAPP_bool_bool(fNot,P))
      | hBOOL(P) ),
    file('theBenchmark.p',help_fNot_2_1_U) ).

fof(help_fconj_1_1_U,axiom,
    ! [Q,P] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
      | ~ hBOOL(Q)
      | ~ hBOOL(P) ),
    file('theBenchmark.p',help_fconj_1_1_U) ).

fof(help_fconj_2_1_U,axiom,
    ! [P,Q] :
      ( hBOOL(P)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) ),
    file('theBenchmark.p',help_fconj_2_1_U) ).

fof(help_fconj_3_1_U,axiom,
    ! [P,Q] :
      ( hBOOL(Q)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) ),
    file('theBenchmark.p',help_fconj_3_1_U) ).

fof(help_fdisj_1_1_U,axiom,
    ! [Q,P] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q))
      | ~ hBOOL(P) ),
    file('theBenchmark.p',help_fdisj_1_1_U) ).

fof(help_fdisj_2_1_U,axiom,
    ! [P,Q] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q))
      | ~ hBOOL(Q) ),
    file('theBenchmark.p',help_fdisj_2_1_U) ).

fof(help_fdisj_3_1_U,axiom,
    ! [P,Q] :
      ( hBOOL(Q)
      | hBOOL(P)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) ),
    file('theBenchmark.p',help_fdisj_3_1_U) ).

fof(help_fimplies_1_1_U,axiom,
    ! [Q,P] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q))
      | hBOOL(P) ),
    file('theBenchmark.p',help_fimplies_1_1_U) ).

fof(help_fimplies_2_1_U,axiom,
    ! [P,Q] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q))
      | ~ hBOOL(Q) ),
    file('theBenchmark.p',help_fimplies_2_1_U) ).

fof(help_fimplies_3_1_U,axiom,
    ! [P,Q] :
      ( hBOOL(Q)
      | ~ hBOOL(P)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)) ),
    file('theBenchmark.p',help_fimplies_3_1_U) ).

fof(help_fequal_1_1_fequal_000t__a_T,axiom,
    ! [X,Y] :
      ( ( is_a(Y)
        & is_a(X) )
     => ( X = Y
        | ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X),Y)) ) ),
    file('theBenchmark.p',help_fequal_1_1_fequal_000t__a_T) ).

fof(help_fequal_2_1_fequal_000t__a_T,axiom,
    ! [X,Y] :
      ( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X),Y))
      | X != Y ),
    file('theBenchmark.p',help_fequal_2_1_fequal_000t__a_T) ).

fof(help_fequal_1_1_fequal_000tc__Nat__Onat_T,axiom,
    ! [X,Y] :
      ( X = Y
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)) ),
    file('theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).

fof(help_fequal_2_1_fequal_000tc__Nat__Onat_T,axiom,
    ! [X,Y] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y))
      | X != Y ),
    file('theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).

fof(help_fequal_1_1_fequal_000tc__Com__Opname_T,axiom,
    ! [X,Y] :
      ( ( is_pname(Y)
        & is_pname(X) )
     => ( X = Y
        | ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X),Y)) ) ),
    file('theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Opname_T) ).

fof(help_fequal_2_1_fequal_000tc__Com__Opname_T,axiom,
    ! [X,Y] :
      ( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X),Y))
      | X != Y ),
    file('theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Opname_T) ).

fof(help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U,axiom,
    ! [P,Q,R] : hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(P),Q),R) = hAPP_a_bool(hAPP_a_fun_a_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U) ).

fof(help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T,axiom,
    ! [X,Y] :
      ( ( is_fun_a_bool(Y)
        & is_fun_a_bool(X) )
     => ( X = Y
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X),Y)) ) ),
    file('theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).

fof(help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T,axiom,
    ! [X,Y] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X),Y))
      | X != Y ),
    file('theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U,axiom,
    ! [P,Q,R] : hAPP_a_bool(cOMBB_bool_bool_a(P,Q),R) = hAPP_bool_bool(P,hAPP_a_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U) ).

fof(help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
    ! [P,Q,R] : hAPP_a_bool(cOMBS_a_bool_bool(P,Q),R) = hAPP_bool_bool(hAPP_a_fun_bool_bool(P,R),hAPP_a_bool(Q,R)),
    file('theBenchmark.p',help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U,axiom,
    ! [P,Q,R] : hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(P),Q),R) = hAPP_a_bool(hAPP_p1534023578a_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U) ).

fof(help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T,axiom,
    ! [X,Y] :
      ( X = Y
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X),Y)) ),
    file('theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).

fof(help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T,axiom,
    ! [X,Y] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X),Y))
      | X != Y ),
    file('theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).

fof(help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,axiom,
    ! [X,Y] :
      ( ( is_fun_pname_bool(Y)
        & is_fun_pname_bool(X) )
     => ( X = Y
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X),Y)) ) ),
    file('theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).

fof(help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,axiom,
    ! [X,Y] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X),Y))
      | X != Y ),
    file('theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).

fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U,axiom,
    ! [P,Q,R] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(P),Q),R) = hAPP_nat_bool(hAPP_n1699378549t_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
    ! [P,Q,R] : hAPP_nat_bool(cOMBB_bool_bool_nat(P,Q),R) = hAPP_bool_bool(P,hAPP_nat_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U) ).

fof(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
    ! [P,Q,R] : hAPP_nat_bool(cOMBS_nat_bool_bool(P,Q),R) = hAPP_bool_bool(hAPP_n1006566506l_bool(P,R),hAPP_nat_bool(Q,R)),
    file('theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U,axiom,
    ! [P,Q,R] : hAPP_pname_bool(cOMBB_647938656_pname(P,Q),R) = hAPP_bool_bool(P,hAPP_pname_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U) ).

fof(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
    ! [P,Q,R] : hAPP_pname_bool(cOMBS_568398431l_bool(P,Q),R) = hAPP_bool_bool(hAPP_p393069232l_bool(P,R),hAPP_pname_bool(Q,R)),
    file('theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U,axiom,
    ! [P,Q,R] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(P),Q),R) = hAPP_pname_bool(hAPP_p61793385e_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U) ).

fof(help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo,axiom,
    ! [P,Q,R] : hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(P),Q),R) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo) ).

fof(help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna,axiom,
    ! [P,Q,R] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(P,Q),R) = hAPP_a_fun_a_bool(P,hAPP_pname_a(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H,axiom,
    ! [P,Q,R] : hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(P,Q),R) = hAPP_bool_bool(P,hAPP_fun_a_bool_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
    ! [P,Q,R] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_a_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).

fof(help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_,axiom,
    ! [P,Q,R] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f198738859l_bool(P,R),hAPP_fun_a_bool_bool(Q,R)),
    file('theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_) ).

fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
    ! [P,Q,R] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(P),Q),R) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On,axiom,
    ! [P,Q,R] : hAPP_f54304608l_bool(cOMBB_238756964t_bool(P,Q),R) = hAPP_bool_bool(P,hAPP_f54304608l_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_006,axiom,
    ! [P,Q,R] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_nat_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_006) ).

fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo,axiom,
    ! [P,Q,R] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f1748468828l_bool(P,R),hAPP_f54304608l_bool(Q,R)),
    file('theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op,axiom,
    ! [P,Q,R] : hAPP_f1664156314l_bool(cOMBB_307249310e_bool(P,Q),R) = hAPP_bool_bool(P,hAPP_f1664156314l_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_007,axiom,
    ! [P,Q,R] : hAPP_p393069232l_bool(cOMBB_675860798_pname(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_pname_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_007) ).

fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O,axiom,
    ! [P,Q,R] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f1476298914l_bool(P,R),hAPP_f1664156314l_bool(Q,R)),
    file('theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O) ).

fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob,axiom,
    ! [P,Q,R] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(P),Q),R) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO,axiom,
    ! [P,Q,R] : hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(P),Q),R) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_008,axiom,
    ! [P,Q,R] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_fun_a_bool_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_008) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_,axiom,
    ! [P,Q,R] : hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(P),Q),R) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009,axiom,
    ! [P,Q,R] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f54304608l_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_010,axiom,
    ! [P,Q,R] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f1664156314l_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_010) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It,axiom,
    ! [P,Q,R] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(P),Q),R) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__,axiom,
    ! [P,Q,R] : hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(P),Q),R) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__011,axiom,
    ! [P,Q,R] : hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(P),Q),R) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__011) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_012,axiom,
    ! [P,Q,R] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(P),Q),R) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_012) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool,axiom,
    ! [P,Q,R] : hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(P),Q),R) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H,axiom,
    ! [P,Q,R] : hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(P),Q),R) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,axiom,
    ! [P,Q,R] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(P),Q),R) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H,axiom,
    ! [P,Q,R] : hAPP_f292226953l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(P),Q),R) = hAPP_f292226953l_bool(hAPP_f1050622307l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool,axiom,
    ! [P,Q,R] : hAPP_f937997336l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(P),Q),R) = hAPP_f937997336l_bool(hAPP_f760187903l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo,axiom,
    ! [P,Q,R] : hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(P),Q),R) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).

fof(conj_0,hypothesis,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
    file('theBenchmark.p',conj_0) ).

fof(conj_1,hypothesis,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
    file('theBenchmark.p',conj_1) ).

fof(conj_2,hypothesis,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))),
    file('theBenchmark.p',conj_2) ).

fof(conj_3,hypothesis,
    hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)),
    file('theBenchmark.p',conj_3) ).

fof(conj_4,hypothesis,
    hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
    file('theBenchmark.p',conj_4) ).

fof(conj_5,hypothesis,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)),
    file('theBenchmark.p',conj_5) ).

fof(conj_6,conjecture,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
    file('theBenchmark.p',conj_6) ).

fof(f_1_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun_a_bool(cOMBB_bool_bool_a(B_1_1,B_2))
      | ~ is_fun_a_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a]) ).

fof(f_1_2,plain,
    ! [U_1,U_0] :
      ( is_fun_a_bool(cOMBB_bool_bool_a(U_1,U_0))
      | ~ is_fun_a_bool(U_0) ),
    inference(variable_rename,[status(thm)],[f_1_1]) ).

cnf(f_1_3,plain,
    ( is_fun_a_bool(cOMBB_bool_bool_a(U_1,U_0))
    | ~ is_fun_a_bool(U_0) ),
    inference(clausify,[status(thm)],[f_1_2]) ).

fof(f_2_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun_pname_bool(cOMBB_647938656_pname(B_1_1,B_2))
      | ~ is_fun_pname_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname]) ).

fof(f_2_2,plain,
    ! [U_3,U_2] :
      ( is_fun_pname_bool(cOMBB_647938656_pname(U_3,U_2))
      | ~ is_fun_pname_bool(U_2) ),
    inference(variable_rename,[status(thm)],[f_2_1]) ).

cnf(f_2_3,plain,
    ( is_fun_pname_bool(cOMBB_647938656_pname(U_3,U_2))
    | ~ is_fun_pname_bool(U_2) ),
    inference(clausify,[status(thm)],[f_2_2]) ).

fof(f_3_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun949378684l_bool(cOMBB_2140588453a_bool(B_1_1,B_2))
      | ~ is_fun949378684l_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool]) ).

fof(f_3_2,plain,
    ! [U_5,U_4] :
      ( is_fun949378684l_bool(cOMBB_2140588453a_bool(U_5,U_4))
      | ~ is_fun949378684l_bool(U_4) ),
    inference(variable_rename,[status(thm)],[f_3_1]) ).

cnf(f_3_3,plain,
    ( is_fun949378684l_bool(cOMBB_2140588453a_bool(U_5,U_4))
    | ~ is_fun949378684l_bool(U_4) ),
    inference(clausify,[status(thm)],[f_3_2]) ).

fof(f_4_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun1661590463l_bool(cOMBB_307249310e_bool(B_1_1,B_2))
      | ~ is_fun1661590463l_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_]) ).

fof(f_4_2,plain,
    ! [U_7,U_6] :
      ( is_fun1661590463l_bool(cOMBB_307249310e_bool(U_7,U_6))
      | ~ is_fun1661590463l_bool(U_6) ),
    inference(variable_rename,[status(thm)],[f_4_1]) ).

cnf(f_4_3,plain,
    ( is_fun1661590463l_bool(cOMBB_307249310e_bool(U_7,U_6))
    | ~ is_fun1661590463l_bool(U_6) ),
    inference(clausify,[status(thm)],[f_4_2]) ).

fof(f_5_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun_a_bool(cOMBS_a_bool_bool(B_1_1,B_2))
      | ~ is_fun_a_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool]) ).

fof(f_5_2,plain,
    ! [U_9,U_8] :
      ( is_fun_a_bool(cOMBS_a_bool_bool(U_9,U_8))
      | ~ is_fun_a_bool(U_8) ),
    inference(variable_rename,[status(thm)],[f_5_1]) ).

cnf(f_5_3,plain,
    ( is_fun_a_bool(cOMBS_a_bool_bool(U_9,U_8))
    | ~ is_fun_a_bool(U_8) ),
    inference(clausify,[status(thm)],[f_5_2]) ).

fof(f_6_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun_pname_bool(cOMBS_568398431l_bool(B_1_1,B_2))
      | ~ is_fun_pname_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool]) ).

fof(f_6_2,plain,
    ! [U_11,U_10] :
      ( is_fun_pname_bool(cOMBS_568398431l_bool(U_11,U_10))
      | ~ is_fun_pname_bool(U_10) ),
    inference(variable_rename,[status(thm)],[f_6_1]) ).

cnf(f_6_3,plain,
    ( is_fun_pname_bool(cOMBS_568398431l_bool(U_11,U_10))
    | ~ is_fun_pname_bool(U_10) ),
    inference(clausify,[status(thm)],[f_6_2]) ).

fof(f_7_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun949378684l_bool(cOMBS_1035972772l_bool(B_1_1,B_2))
      | ~ is_fun949378684l_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc__HOL__Obo]) ).

fof(f_7_2,plain,
    ! [U_13,U_12] :
      ( is_fun949378684l_bool(cOMBS_1035972772l_bool(U_13,U_12))
      | ~ is_fun949378684l_bool(U_12) ),
    inference(variable_rename,[status(thm)],[f_7_1]) ).

cnf(f_7_3,plain,
    ( is_fun949378684l_bool(cOMBS_1035972772l_bool(U_13,U_12))
    | ~ is_fun949378684l_bool(U_12) ),
    inference(clausify,[status(thm)],[f_7_2]) ).

fof(f_8_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun1661590463l_bool(cOMBS_350070575l_bool(B_1_1,B_2))
      | ~ is_fun1661590463l_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t]) ).

fof(f_8_2,plain,
    ! [U_15,U_14] :
      ( is_fun1661590463l_bool(cOMBS_350070575l_bool(U_15,U_14))
      | ~ is_fun1661590463l_bool(U_14) ),
    inference(variable_rename,[status(thm)],[f_8_1]) ).

cnf(f_8_3,plain,
    ( is_fun1661590463l_bool(cOMBS_350070575l_bool(U_15,U_14))
    | ~ is_fun1661590463l_bool(U_14) ),
    inference(clausify,[status(thm)],[f_8_2]) ).

fof(f_9_1,plain,
    is_fun949378684l_bool(finite_finite_a),
    inference(fof_nnf,[status(thm)],[gsy_c_Finite__Set_Ofinite_000t__a]) ).

cnf(f_9_2,plain,
    is_fun949378684l_bool(finite_finite_a),
    inference(clausify,[status(thm)],[f_9_1]) ).

fof(f_10_1,plain,
    is_fun1661590463l_bool(finite_finite_pname),
    inference(fof_nnf,[status(thm)],[gsy_c_Finite__Set_Ofinite_000tc__Com__Opname]) ).

cnf(f_10_2,plain,
    is_fun1661590463l_bool(finite_finite_pname),
    inference(clausify,[status(thm)],[f_10_1]) ).

fof(f_11_1,plain,
    is_a(undefined_a(x_a)),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000t__a]) ).

cnf(f_11_2,plain,
    is_a(undefined_a(x_a)),
    inference(clausify,[status(thm)],[f_11_1]) ).

fof(f_12_1,plain,
    is_pname(undefined_pname(pname)),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__Com__Opname]) ).

cnf(f_12_2,plain,
    is_pname(undefined_pname(pname)),
    inference(clausify,[status(thm)],[f_12_1]) ).

fof(f_13_1,plain,
    is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool))),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).

cnf(f_13_2,plain,
    is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool))),
    inference(clausify,[status(thm)],[f_13_1]) ).

fof(f_14_1,plain,
    is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).

cnf(f_14_2,plain,
    is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))),
    inference(clausify,[status(thm)],[f_14_1]) ).

fof(f_15_1,plain,
    is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool]) ).

cnf(f_15_2,plain,
    is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))),
    inference(clausify,[status(thm)],[f_15_1]) ).

fof(f_16_1,plain,
    is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_]) ).

cnf(f_16_2,plain,
    is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))),
    inference(clausify,[status(thm)],[f_16_1]) ).

fof(f_17_1,plain,
    ! [B_1_1] :
      ( is_fun_a_bool(collect_a(B_1_1))
      | ~ is_fun_a_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_OCollect_000t__a]) ).

fof(f_17_2,plain,
    ! [U_16] :
      ( is_fun_a_bool(collect_a(U_16))
      | ~ is_fun_a_bool(U_16) ),
    inference(variable_rename,[status(thm)],[f_17_1]) ).

cnf(f_17_3,plain,
    ( is_fun_a_bool(collect_a(U_16))
    | ~ is_fun_a_bool(U_16) ),
    inference(clausify,[status(thm)],[f_17_2]) ).

fof(f_18_1,plain,
    ! [B_1_1] :
      ( is_fun_pname_bool(collect_pname(B_1_1))
      | ~ is_fun_pname_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_OCollect_000tc__Com__Opname]) ).

fof(f_18_2,plain,
    ! [U_17] :
      ( is_fun_pname_bool(collect_pname(U_17))
      | ~ is_fun_pname_bool(U_17) ),
    inference(variable_rename,[status(thm)],[f_18_1]) ).

cnf(f_18_3,plain,
    ( is_fun_pname_bool(collect_pname(U_17))
    | ~ is_fun_pname_bool(U_17) ),
    inference(clausify,[status(thm)],[f_18_2]) ).

fof(f_19_1,plain,
    ! [B_1_1] :
      ( is_fun949378684l_bool(collect_fun_a_bool(B_1_1))
      | ~ is_fun949378684l_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_OCollect_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).

fof(f_19_2,plain,
    ! [U_18] :
      ( is_fun949378684l_bool(collect_fun_a_bool(U_18))
      | ~ is_fun949378684l_bool(U_18) ),
    inference(variable_rename,[status(thm)],[f_19_1]) ).

cnf(f_19_3,plain,
    ( is_fun949378684l_bool(collect_fun_a_bool(U_18))
    | ~ is_fun949378684l_bool(U_18) ),
    inference(clausify,[status(thm)],[f_19_2]) ).

fof(f_20_1,plain,
    ! [B_1_1] :
      ( is_fun1661590463l_bool(collec1974731493e_bool(B_1_1))
      | ~ is_fun1661590463l_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_OCollect_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).

fof(f_20_2,plain,
    ! [U_19] :
      ( is_fun1661590463l_bool(collec1974731493e_bool(U_19))
      | ~ is_fun1661590463l_bool(U_19) ),
    inference(variable_rename,[status(thm)],[f_20_1]) ).

cnf(f_20_3,plain,
    ( is_fun1661590463l_bool(collec1974731493e_bool(U_19))
    | ~ is_fun1661590463l_bool(U_19) ),
    inference(clausify,[status(thm)],[f_20_2]) ).

fof(f_21_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun_a_bool(image_a_a(B_1_1,B_2))
      | ~ is_fun_a_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000t__a_000t__a]) ).

fof(f_21_2,plain,
    ! [U_21,U_20] :
      ( is_fun_a_bool(image_a_a(U_21,U_20))
      | ~ is_fun_a_bool(U_20) ),
    inference(variable_rename,[status(thm)],[f_21_1]) ).

cnf(f_21_3,plain,
    ( is_fun_a_bool(image_a_a(U_21,U_20))
    | ~ is_fun_a_bool(U_20) ),
    inference(clausify,[status(thm)],[f_21_2]) ).

fof(f_22_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun_pname_bool(image_a_pname(B_1_1,B_2))
      | ~ is_fun_a_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000t__a_000tc__Com__Opname]) ).

fof(f_22_2,plain,
    ! [U_23,U_22] :
      ( is_fun_pname_bool(image_a_pname(U_23,U_22))
      | ~ is_fun_a_bool(U_22) ),
    inference(variable_rename,[status(thm)],[f_22_1]) ).

cnf(f_22_3,plain,
    ( is_fun_pname_bool(image_a_pname(U_23,U_22))
    | ~ is_fun_a_bool(U_22) ),
    inference(clausify,[status(thm)],[f_22_2]) ).

fof(f_23_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun_a_bool(image_pname_a(B_1_1,B_2))
      | ~ is_fun_pname_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Com__Opname_000t__a]) ).

fof(f_23_2,plain,
    ! [U_25,U_24] :
      ( is_fun_a_bool(image_pname_a(U_25,U_24))
      | ~ is_fun_pname_bool(U_24) ),
    inference(variable_rename,[status(thm)],[f_23_1]) ).

cnf(f_23_3,plain,
    ( is_fun_a_bool(image_pname_a(U_25,U_24))
    | ~ is_fun_pname_bool(U_24) ),
    inference(clausify,[status(thm)],[f_23_2]) ).

fof(f_24_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun_pname_bool(image_pname_pname(B_1_1,B_2))
      | ~ is_fun_pname_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname]) ).

fof(f_24_2,plain,
    ! [U_27,U_26] :
      ( is_fun_pname_bool(image_pname_pname(U_27,U_26))
      | ~ is_fun_pname_bool(U_26) ),
    inference(variable_rename,[status(thm)],[f_24_1]) ).

cnf(f_24_3,plain,
    ( is_fun_pname_bool(image_pname_pname(U_27,U_26))
    | ~ is_fun_pname_bool(U_26) ),
    inference(clausify,[status(thm)],[f_24_2]) ).

fof(f_25_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun949378684l_bool(image_112932426a_bool(B_1_1,B_2))
      | ~ is_fun_pname_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).

fof(f_25_2,plain,
    ! [U_29,U_28] :
      ( is_fun949378684l_bool(image_112932426a_bool(U_29,U_28))
      | ~ is_fun_pname_bool(U_28) ),
    inference(variable_rename,[status(thm)],[f_25_1]) ).

cnf(f_25_3,plain,
    ( is_fun949378684l_bool(image_112932426a_bool(U_29,U_28))
    | ~ is_fun_pname_bool(U_28) ),
    inference(clausify,[status(thm)],[f_25_2]) ).

fof(f_26_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun1661590463l_bool(image_47868345e_bool(B_1_1,B_2))
      | ~ is_fun_pname_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_]) ).

fof(f_26_2,plain,
    ! [U_31,U_30] :
      ( is_fun1661590463l_bool(image_47868345e_bool(U_31,U_30))
      | ~ is_fun_pname_bool(U_30) ),
    inference(variable_rename,[status(thm)],[f_26_1]) ).

cnf(f_26_3,plain,
    ( is_fun1661590463l_bool(image_47868345e_bool(U_31,U_30))
    | ~ is_fun_pname_bool(U_30) ),
    inference(clausify,[status(thm)],[f_26_2]) ).

fof(f_27_1,plain,
    ! [B_1_1,B_2] : is_fun_a_bool(image_nat_a(B_1_1,B_2)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a]) ).

fof(f_27_2,plain,
    ! [U_33,U_32] : is_fun_a_bool(image_nat_a(U_33,U_32)),
    inference(variable_rename,[status(thm)],[f_27_1]) ).

cnf(f_27_3,plain,
    is_fun_a_bool(image_nat_a(U_33,U_32)),
    inference(clausify,[status(thm)],[f_27_2]) ).

fof(f_28_1,plain,
    ! [B_1_1,B_2] : is_fun_pname_bool(image_nat_pname(B_1_1,B_2)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname]) ).

fof(f_28_2,plain,
    ! [U_35,U_34] : is_fun_pname_bool(image_nat_pname(U_35,U_34)),
    inference(variable_rename,[status(thm)],[f_28_1]) ).

cnf(f_28_3,plain,
    is_fun_pname_bool(image_nat_pname(U_35,U_34)),
    inference(clausify,[status(thm)],[f_28_2]) ).

fof(f_29_1,plain,
    ! [B_1_1,B_2] : is_fun949378684l_bool(image_nat_fun_a_bool(B_1_1,B_2)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).

fof(f_29_2,plain,
    ! [U_37,U_36] : is_fun949378684l_bool(image_nat_fun_a_bool(U_37,U_36)),
    inference(variable_rename,[status(thm)],[f_29_1]) ).

cnf(f_29_3,plain,
    is_fun949378684l_bool(image_nat_fun_a_bool(U_37,U_36)),
    inference(clausify,[status(thm)],[f_29_2]) ).

fof(f_30_1,plain,
    ! [B_1_1,B_2] : is_fun1661590463l_bool(image_1655916159e_bool(B_1_1,B_2)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).

fof(f_30_2,plain,
    ! [U_39,U_38] : is_fun1661590463l_bool(image_1655916159e_bool(U_39,U_38)),
    inference(variable_rename,[status(thm)],[f_30_1]) ).

cnf(f_30_3,plain,
    is_fun1661590463l_bool(image_1655916159e_bool(U_39,U_38)),
    inference(clausify,[status(thm)],[f_30_2]) ).

fof(f_31_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun_a_bool(image_fun_a_bool_a(B_1_1,B_2))
      | ~ is_fun949378684l_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a]) ).

fof(f_31_2,plain,
    ! [U_41,U_40] :
      ( is_fun_a_bool(image_fun_a_bool_a(U_41,U_40))
      | ~ is_fun949378684l_bool(U_40) ),
    inference(variable_rename,[status(thm)],[f_31_1]) ).

cnf(f_31_3,plain,
    ( is_fun_a_bool(image_fun_a_bool_a(U_41,U_40))
    | ~ is_fun949378684l_bool(U_40) ),
    inference(clausify,[status(thm)],[f_31_2]) ).

fof(f_32_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun_pname_bool(image_1854862208_pname(B_1_1,B_2))
      | ~ is_fun949378684l_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname]) ).

fof(f_32_2,plain,
    ! [U_43,U_42] :
      ( is_fun_pname_bool(image_1854862208_pname(U_43,U_42))
      | ~ is_fun949378684l_bool(U_42) ),
    inference(variable_rename,[status(thm)],[f_32_1]) ).

cnf(f_32_3,plain,
    ( is_fun_pname_bool(image_1854862208_pname(U_43,U_42))
    | ~ is_fun949378684l_bool(U_42) ),
    inference(clausify,[status(thm)],[f_32_2]) ).

fof(f_33_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun_a_bool(image_876012084bool_a(B_1_1,B_2))
      | ~ is_fun1661590463l_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000t__a]) ).

fof(f_33_2,plain,
    ! [U_45,U_44] :
      ( is_fun_a_bool(image_876012084bool_a(U_45,U_44))
      | ~ is_fun1661590463l_bool(U_44) ),
    inference(variable_rename,[status(thm)],[f_33_1]) ).

cnf(f_33_3,plain,
    ( is_fun_a_bool(image_876012084bool_a(U_45,U_44))
    | ~ is_fun1661590463l_bool(U_44) ),
    inference(clausify,[status(thm)],[f_33_2]) ).

fof(f_34_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun_pname_bool(image_1283814551_pname(B_1_1,B_2))
      | ~ is_fun1661590463l_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opnam]) ).

fof(f_34_2,plain,
    ! [U_47,U_46] :
      ( is_fun_pname_bool(image_1283814551_pname(U_47,U_46))
      | ~ is_fun1661590463l_bool(U_46) ),
    inference(variable_rename,[status(thm)],[f_34_1]) ).

cnf(f_34_3,plain,
    ( is_fun_pname_bool(image_1283814551_pname(U_47,U_46))
    | ~ is_fun1661590463l_bool(U_46) ),
    inference(clausify,[status(thm)],[f_34_2]) ).

fof(f_35_1,plain,
    ! [B_1_1,B_2] : is_fun_a_bool(image_fun_nat_bool_a(B_1_1,B_2)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000t__a]) ).

fof(f_35_2,plain,
    ! [U_49,U_48] : is_fun_a_bool(image_fun_nat_bool_a(U_49,U_48)),
    inference(variable_rename,[status(thm)],[f_35_1]) ).

cnf(f_35_3,plain,
    is_fun_a_bool(image_fun_nat_bool_a(U_49,U_48)),
    inference(clausify,[status(thm)],[f_35_2]) ).

fof(f_36_1,plain,
    ! [B_1_1,B_2] : is_fun_pname_bool(image_1921560913_pname(B_1_1,B_2)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname]) ).

fof(f_36_2,plain,
    ! [U_51,U_50] : is_fun_pname_bool(image_1921560913_pname(U_51,U_50)),
    inference(variable_rename,[status(thm)],[f_36_1]) ).

cnf(f_36_3,plain,
    is_fun_pname_bool(image_1921560913_pname(U_51,U_50)),
    inference(clausify,[status(thm)],[f_36_2]) ).

fof(f_37_1,plain,
    ! [B_1_1,B_2] : is_fun_a_bool(image_573985017bool_a(B_1_1,B_2)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0]) ).

fof(f_37_2,plain,
    ! [U_53,U_52] : is_fun_a_bool(image_573985017bool_a(U_53,U_52)),
    inference(variable_rename,[status(thm)],[f_37_1]) ).

cnf(f_37_3,plain,
    is_fun_a_bool(image_573985017bool_a(U_53,U_52)),
    inference(clausify,[status(thm)],[f_37_2]) ).

fof(f_38_1,plain,
    ! [B_1_1,B_2] : is_fun_pname_bool(image_990671762_pname(B_1_1,B_2)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0_001]) ).

fof(f_38_2,plain,
    ! [U_55,U_54] : is_fun_pname_bool(image_990671762_pname(U_55,U_54)),
    inference(variable_rename,[status(thm)],[f_38_1]) ).

cnf(f_38_3,plain,
    is_fun_pname_bool(image_990671762_pname(U_55,U_54)),
    inference(clausify,[status(thm)],[f_38_2]) ).

fof(f_39_1,plain,
    ! [B_1_1,B_2] : is_fun_a_bool(image_349102846bool_a(B_1_1,B_2)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL]) ).

fof(f_39_2,plain,
    ! [U_57,U_56] : is_fun_a_bool(image_349102846bool_a(U_57,U_56)),
    inference(variable_rename,[status(thm)],[f_39_1]) ).

cnf(f_39_3,plain,
    is_fun_a_bool(image_349102846bool_a(U_57,U_56)),
    inference(clausify,[status(thm)],[f_39_2]) ).

fof(f_40_1,plain,
    ! [B_1_1,B_2] : is_fun_pname_bool(image_1705983821_pname(B_1_1,B_2)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL_002]) ).

fof(f_40_2,plain,
    ! [U_59,U_58] : is_fun_pname_bool(image_1705983821_pname(U_59,U_58)),
    inference(variable_rename,[status(thm)],[f_40_1]) ).

cnf(f_40_3,plain,
    is_fun_pname_bool(image_1705983821_pname(U_59,U_58)),
    inference(clausify,[status(thm)],[f_40_2]) ).

fof(f_41_1,plain,
    ! [B_1_1,B_2] : is_fun_a_bool(image_526090948bool_a(B_1_1,B_2)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__]) ).

fof(f_41_2,plain,
    ! [U_61,U_60] : is_fun_a_bool(image_526090948bool_a(U_61,U_60)),
    inference(variable_rename,[status(thm)],[f_41_1]) ).

cnf(f_41_3,plain,
    is_fun_a_bool(image_526090948bool_a(U_61,U_60)),
    inference(clausify,[status(thm)],[f_41_2]) ).

fof(f_42_1,plain,
    ! [B_1_1,B_2] : is_fun_pname_bool(image_1604018183_pname(B_1_1,B_2)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL___003]) ).

fof(f_42_2,plain,
    ! [U_63,U_62] : is_fun_pname_bool(image_1604018183_pname(U_63,U_62)),
    inference(variable_rename,[status(thm)],[f_42_1]) ).

cnf(f_42_3,plain,
    is_fun_pname_bool(image_1604018183_pname(U_63,U_62)),
    inference(clausify,[status(thm)],[f_42_2]) ).

fof(f_43_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun_a_bool(insert_a(B_1_1,B_2))
      | ~ is_fun_a_bool(B_2)
      | ~ is_a(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oinsert_000t__a]) ).

fof(f_43_2,plain,
    ! [U_65,U_64] :
      ( is_fun_a_bool(insert_a(U_65,U_64))
      | ~ is_fun_a_bool(U_64)
      | ~ is_a(U_65) ),
    inference(variable_rename,[status(thm)],[f_43_1]) ).

cnf(f_43_3,plain,
    ( is_fun_a_bool(insert_a(U_65,U_64))
    | ~ is_fun_a_bool(U_64)
    | ~ is_a(U_65) ),
    inference(clausify,[status(thm)],[f_43_2]) ).

fof(f_44_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun_pname_bool(insert_pname(B_1_1,B_2))
      | ~ is_fun_pname_bool(B_2)
      | ~ is_pname(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oinsert_000tc__Com__Opname]) ).

fof(f_44_2,plain,
    ! [U_67,U_66] :
      ( is_fun_pname_bool(insert_pname(U_67,U_66))
      | ~ is_fun_pname_bool(U_66)
      | ~ is_pname(U_67) ),
    inference(variable_rename,[status(thm)],[f_44_1]) ).

cnf(f_44_3,plain,
    ( is_fun_pname_bool(insert_pname(U_67,U_66))
    | ~ is_fun_pname_bool(U_66)
    | ~ is_pname(U_67) ),
    inference(clausify,[status(thm)],[f_44_2]) ).

fof(f_45_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun949378684l_bool(insert_fun_a_bool(B_1_1,B_2))
      | ~ is_fun949378684l_bool(B_2)
      | ~ is_fun_a_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oinsert_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).

fof(f_45_2,plain,
    ! [U_69,U_68] :
      ( is_fun949378684l_bool(insert_fun_a_bool(U_69,U_68))
      | ~ is_fun949378684l_bool(U_68)
      | ~ is_fun_a_bool(U_69) ),
    inference(variable_rename,[status(thm)],[f_45_1]) ).

cnf(f_45_3,plain,
    ( is_fun949378684l_bool(insert_fun_a_bool(U_69,U_68))
    | ~ is_fun949378684l_bool(U_68)
    | ~ is_fun_a_bool(U_69) ),
    inference(clausify,[status(thm)],[f_45_2]) ).

fof(f_46_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun1661590463l_bool(insert1325755072e_bool(B_1_1,B_2))
      | ~ is_fun1661590463l_bool(B_2)
      | ~ is_fun_pname_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).

fof(f_46_2,plain,
    ! [U_71,U_70] :
      ( is_fun1661590463l_bool(insert1325755072e_bool(U_71,U_70))
      | ~ is_fun1661590463l_bool(U_70)
      | ~ is_fun_pname_bool(U_71) ),
    inference(variable_rename,[status(thm)],[f_46_1]) ).

cnf(f_46_3,plain,
    ( is_fun1661590463l_bool(insert1325755072e_bool(U_71,U_70))
    | ~ is_fun1661590463l_bool(U_70)
    | ~ is_fun_pname_bool(U_71) ),
    inference(clausify,[status(thm)],[f_46_2]) ).

fof(f_47_1,plain,
    ! [B_1_1,B_2] :
      ( is_bool(hAPP_a_bool(B_1_1,B_2))
      | ~ is_a(B_2)
      | ~ is_fun_a_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000t__a_000tc__HOL__Obool]) ).

fof(f_47_2,plain,
    ! [U_73,U_72] :
      ( is_bool(hAPP_a_bool(U_73,U_72))
      | ~ is_a(U_72)
      | ~ is_fun_a_bool(U_73) ),
    inference(variable_rename,[status(thm)],[f_47_1]) ).

cnf(f_47_3,plain,
    ( is_bool(hAPP_a_bool(U_73,U_72))
    | ~ is_a(U_72)
    | ~ is_fun_a_bool(U_73) ),
    inference(clausify,[status(thm)],[f_47_2]) ).

fof(f_48_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun_a_bool(hAPP_a_fun_a_bool(B_1_1,B_2))
      | ~ is_a(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).

fof(f_48_2,plain,
    ! [U_75,U_74] :
      ( is_fun_a_bool(hAPP_a_fun_a_bool(U_75,U_74))
      | ~ is_a(U_74) ),
    inference(variable_rename,[status(thm)],[f_48_1]) ).

cnf(f_48_3,plain,
    ( is_fun_a_bool(hAPP_a_fun_a_bool(U_75,U_74))
    | ~ is_a(U_74) ),
    inference(clausify,[status(thm)],[f_48_2]) ).

fof(f_49_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun_pname_bool(hAPP_a93125764e_bool(B_1_1,B_2))
      | ~ is_a(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).

fof(f_49_2,plain,
    ! [U_77,U_76] :
      ( is_fun_pname_bool(hAPP_a93125764e_bool(U_77,U_76))
      | ~ is_a(U_76) ),
    inference(variable_rename,[status(thm)],[f_49_1]) ).

cnf(f_49_3,plain,
    ( is_fun_pname_bool(hAPP_a93125764e_bool(U_77,U_76))
    | ~ is_a(U_76) ),
    inference(clausify,[status(thm)],[f_49_2]) ).

fof(f_50_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun949378684l_bool(hAPP_a85458249l_bool(B_1_1,B_2))
      | ~ is_a(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000t__a_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J]) ).

fof(f_50_2,plain,
    ! [U_79,U_78] :
      ( is_fun949378684l_bool(hAPP_a85458249l_bool(U_79,U_78))
      | ~ is_a(U_78) ),
    inference(variable_rename,[status(thm)],[f_50_1]) ).

cnf(f_50_3,plain,
    ( is_fun949378684l_bool(hAPP_a85458249l_bool(U_79,U_78))
    | ~ is_a(U_78) ),
    inference(clausify,[status(thm)],[f_50_2]) ).

fof(f_51_1,plain,
    ! [B_1_1,B_2] :
      ( is_a(hAPP_pname_a(B_1_1,B_2))
      | ~ is_pname(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000t__a]) ).

fof(f_51_2,plain,
    ! [U_81,U_80] :
      ( is_a(hAPP_pname_a(U_81,U_80))
      | ~ is_pname(U_80) ),
    inference(variable_rename,[status(thm)],[f_51_1]) ).

cnf(f_51_3,plain,
    ( is_a(hAPP_pname_a(U_81,U_80))
    | ~ is_pname(U_80) ),
    inference(clausify,[status(thm)],[f_51_2]) ).

fof(f_52_1,plain,
    ! [B_1_1,B_2] :
      ( is_bool(hAPP_pname_bool(B_1_1,B_2))
      | ~ is_pname(B_2)
      | ~ is_fun_pname_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool]) ).

fof(f_52_2,plain,
    ! [U_83,U_82] :
      ( is_bool(hAPP_pname_bool(U_83,U_82))
      | ~ is_pname(U_82)
      | ~ is_fun_pname_bool(U_83) ),
    inference(variable_rename,[status(thm)],[f_52_1]) ).

cnf(f_52_3,plain,
    ( is_bool(hAPP_pname_bool(U_83,U_82))
    | ~ is_pname(U_82)
    | ~ is_fun_pname_bool(U_83) ),
    inference(clausify,[status(thm)],[f_52_2]) ).

fof(f_53_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun_a_bool(hAPP_p1534023578a_bool(B_1_1,B_2))
      | ~ is_pname(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).

fof(f_53_2,plain,
    ! [U_85,U_84] :
      ( is_fun_a_bool(hAPP_p1534023578a_bool(U_85,U_84))
      | ~ is_pname(U_84) ),
    inference(variable_rename,[status(thm)],[f_53_1]) ).

cnf(f_53_3,plain,
    ( is_fun_a_bool(hAPP_p1534023578a_bool(U_85,U_84))
    | ~ is_pname(U_84) ),
    inference(clausify,[status(thm)],[f_53_2]) ).

fof(f_54_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun_pname_bool(hAPP_p61793385e_bool(B_1_1,B_2))
      | ~ is_pname(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).

fof(f_54_2,plain,
    ! [U_87,U_86] :
      ( is_fun_pname_bool(hAPP_p61793385e_bool(U_87,U_86))
      | ~ is_pname(U_86) ),
    inference(variable_rename,[status(thm)],[f_54_1]) ).

cnf(f_54_3,plain,
    ( is_fun_pname_bool(hAPP_p61793385e_bool(U_87,U_86))
    | ~ is_pname(U_86) ),
    inference(clausify,[status(thm)],[f_54_2]) ).

fof(f_55_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun1661590463l_bool(hAPP_p338031245l_bool(B_1_1,B_2))
      | ~ is_pname(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo]) ).

fof(f_55_2,plain,
    ! [U_89,U_88] :
      ( is_fun1661590463l_bool(hAPP_p338031245l_bool(U_89,U_88))
      | ~ is_pname(U_88) ),
    inference(variable_rename,[status(thm)],[f_55_1]) ).

cnf(f_55_3,plain,
    ( is_fun1661590463l_bool(hAPP_p338031245l_bool(U_89,U_88))
    | ~ is_pname(U_88) ),
    inference(clausify,[status(thm)],[f_55_2]) ).

fof(f_56_1,plain,
    ! [B_1_1,B_2] :
      ( is_bool(hAPP_bool_bool(B_1_1,B_2))
      | ~ is_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool]) ).

fof(f_56_2,plain,
    ! [U_91,U_90] :
      ( is_bool(hAPP_bool_bool(U_91,U_90))
      | ~ is_bool(U_90) ),
    inference(variable_rename,[status(thm)],[f_56_1]) ).

cnf(f_56_3,plain,
    ( is_bool(hAPP_bool_bool(U_91,U_90))
    | ~ is_bool(U_90) ),
    inference(clausify,[status(thm)],[f_56_2]) ).

fof(f_57_1,plain,
    ! [B_1_1,B_2] : is_bool(hAPP_nat_bool(B_1_1,B_2)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool]) ).

fof(f_57_2,plain,
    ! [U_93,U_92] : is_bool(hAPP_nat_bool(U_93,U_92)),
    inference(variable_rename,[status(thm)],[f_57_1]) ).

cnf(f_57_3,plain,
    is_bool(hAPP_nat_bool(U_93,U_92)),
    inference(clausify,[status(thm)],[f_57_2]) ).

fof(f_58_1,plain,
    ! [B_1_1,B_2] : is_fun_a_bool(hAPP_nat_fun_a_bool(B_1_1,B_2)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).

fof(f_58_2,plain,
    ! [U_95,U_94] : is_fun_a_bool(hAPP_nat_fun_a_bool(U_95,U_94)),
    inference(variable_rename,[status(thm)],[f_58_1]) ).

cnf(f_58_3,plain,
    is_fun_a_bool(hAPP_nat_fun_a_bool(U_95,U_94)),
    inference(clausify,[status(thm)],[f_58_2]) ).

fof(f_59_1,plain,
    ! [B_1_1,B_2] : is_fun_pname_bool(hAPP_n1025906991e_bool(B_1_1,B_2)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).

fof(f_59_2,plain,
    ! [U_97,U_96] : is_fun_pname_bool(hAPP_n1025906991e_bool(U_97,U_96)),
    inference(variable_rename,[status(thm)],[f_59_1]) ).

cnf(f_59_3,plain,
    is_fun_pname_bool(hAPP_n1025906991e_bool(U_97,U_96)),
    inference(clausify,[status(thm)],[f_59_2]) ).

fof(f_60_1,plain,
    ! [B_1_1,B_2] :
      ( is_bool(hAPP_fun_a_bool_bool(B_1_1,B_2))
      | ~ is_fun_a_bool(B_2)
      | ~ is_fun949378684l_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool]) ).

fof(f_60_2,plain,
    ! [U_99,U_98] :
      ( is_bool(hAPP_fun_a_bool_bool(U_99,U_98))
      | ~ is_fun_a_bool(U_98)
      | ~ is_fun949378684l_bool(U_99) ),
    inference(variable_rename,[status(thm)],[f_60_1]) ).

cnf(f_60_3,plain,
    ( is_bool(hAPP_fun_a_bool_bool(U_99,U_98))
    | ~ is_fun_a_bool(U_98)
    | ~ is_fun949378684l_bool(U_99) ),
    inference(clausify,[status(thm)],[f_60_2]) ).

fof(f_61_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun_a_bool(hAPP_f2050579477a_bool(B_1_1,B_2))
      | ~ is_fun_a_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).

fof(f_61_2,plain,
    ! [U_101,U_100] :
      ( is_fun_a_bool(hAPP_f2050579477a_bool(U_101,U_100))
      | ~ is_fun_a_bool(U_100) ),
    inference(variable_rename,[status(thm)],[f_61_1]) ).

cnf(f_61_3,plain,
    ( is_fun_a_bool(hAPP_f2050579477a_bool(U_101,U_100))
    | ~ is_fun_a_bool(U_100) ),
    inference(clausify,[status(thm)],[f_61_2]) ).

fof(f_62_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun949378684l_bool(hAPP_f1631501043l_bool(B_1_1,B_2))
      | ~ is_fun_a_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__a_Mtc__HOL]) ).

fof(f_62_2,plain,
    ! [U_103,U_102] :
      ( is_fun949378684l_bool(hAPP_f1631501043l_bool(U_103,U_102))
      | ~ is_fun_a_bool(U_102) ),
    inference(variable_rename,[status(thm)],[f_62_1]) ).

cnf(f_62_3,plain,
    ( is_fun949378684l_bool(hAPP_f1631501043l_bool(U_103,U_102))
    | ~ is_fun_a_bool(U_102) ),
    inference(clausify,[status(thm)],[f_62_2]) ).

fof(f_63_1,plain,
    ! [B_1_1,B_2] :
      ( is_bool(hAPP_f1664156314l_bool(B_1_1,B_2))
      | ~ is_fun_pname_bool(B_2)
      | ~ is_fun1661590463l_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool]) ).

fof(f_63_2,plain,
    ! [U_105,U_104] :
      ( is_bool(hAPP_f1664156314l_bool(U_105,U_104))
      | ~ is_fun_pname_bool(U_104)
      | ~ is_fun1661590463l_bool(U_105) ),
    inference(variable_rename,[status(thm)],[f_63_1]) ).

cnf(f_63_3,plain,
    ( is_bool(hAPP_f1664156314l_bool(U_105,U_104))
    | ~ is_fun_pname_bool(U_104)
    | ~ is_fun1661590463l_bool(U_105) ),
    inference(clausify,[status(thm)],[f_63_2]) ).

fof(f_64_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun_pname_bool(hAPP_f759274231e_bool(B_1_1,B_2))
      | ~ is_fun_pname_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op]) ).

fof(f_64_2,plain,
    ! [U_107,U_106] :
      ( is_fun_pname_bool(hAPP_f759274231e_bool(U_107,U_106))
      | ~ is_fun_pname_bool(U_106) ),
    inference(variable_rename,[status(thm)],[f_64_1]) ).

cnf(f_64_3,plain,
    ( is_fun_pname_bool(hAPP_f759274231e_bool(U_107,U_106))
    | ~ is_fun_pname_bool(U_106) ),
    inference(clausify,[status(thm)],[f_64_2]) ).

fof(f_65_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun1661590463l_bool(hAPP_f434788991l_bool(B_1_1,B_2))
      | ~ is_fun_pname_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc]) ).

fof(f_65_2,plain,
    ! [U_109,U_108] :
      ( is_fun1661590463l_bool(hAPP_f434788991l_bool(U_109,U_108))
      | ~ is_fun_pname_bool(U_108) ),
    inference(variable_rename,[status(thm)],[f_65_1]) ).

cnf(f_65_3,plain,
    ( is_fun1661590463l_bool(hAPP_f434788991l_bool(U_109,U_108))
    | ~ is_fun_pname_bool(U_108) ),
    inference(clausify,[status(thm)],[f_65_2]) ).

fof(f_66_1,plain,
    ! [B_1_1,B_2] : is_bool(hAPP_f54304608l_bool(B_1_1,B_2)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool]) ).

fof(f_66_2,plain,
    ! [U_111,U_110] : is_bool(hAPP_f54304608l_bool(U_111,U_110)),
    inference(variable_rename,[status(thm)],[f_66_1]) ).

cnf(f_66_3,plain,
    is_bool(hAPP_f54304608l_bool(U_111,U_110)),
    inference(clausify,[status(thm)],[f_66_2]) ).

fof(f_67_1,plain,
    ! [B_1_1,B_2] :
      ( is_bool(hAPP_f621171935l_bool(B_1_1,B_2))
      | ~ is_fun949378684l_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc__]) ).

fof(f_67_2,plain,
    ! [U_113,U_112] :
      ( is_bool(hAPP_f621171935l_bool(U_113,U_112))
      | ~ is_fun949378684l_bool(U_112) ),
    inference(variable_rename,[status(thm)],[f_67_1]) ).

cnf(f_67_3,plain,
    ( is_bool(hAPP_f621171935l_bool(U_113,U_112))
    | ~ is_fun949378684l_bool(U_112) ),
    inference(clausify,[status(thm)],[f_67_2]) ).

fof(f_68_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun949378684l_bool(hAPP_f2117159681l_bool(B_1_1,B_2))
      | ~ is_fun949378684l_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc___004]) ).

fof(f_68_2,plain,
    ! [U_115,U_114] :
      ( is_fun949378684l_bool(hAPP_f2117159681l_bool(U_115,U_114))
      | ~ is_fun949378684l_bool(U_114) ),
    inference(variable_rename,[status(thm)],[f_68_1]) ).

cnf(f_68_3,plain,
    ( is_fun949378684l_bool(hAPP_f2117159681l_bool(U_115,U_114))
    | ~ is_fun949378684l_bool(U_114) ),
    inference(clausify,[status(thm)],[f_68_2]) ).

fof(f_69_1,plain,
    ! [B_1_1,B_2] :
      ( is_bool(hAPP_f1935102916l_bool(B_1_1,B_2))
      | ~ is_fun1661590463l_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo]) ).

fof(f_69_2,plain,
    ! [U_117,U_116] :
      ( is_bool(hAPP_f1935102916l_bool(U_117,U_116))
      | ~ is_fun1661590463l_bool(U_116) ),
    inference(variable_rename,[status(thm)],[f_69_1]) ).

cnf(f_69_3,plain,
    ( is_bool(hAPP_f1935102916l_bool(U_117,U_116))
    | ~ is_fun1661590463l_bool(U_116) ),
    inference(clausify,[status(thm)],[f_69_2]) ).

fof(f_70_1,plain,
    ! [B_1_1,B_2] :
      ( is_fun1661590463l_bool(hAPP_f559147733l_bool(B_1_1,B_2))
      | ~ is_fun1661590463l_bool(B_2) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_005]) ).

fof(f_70_2,plain,
    ! [U_119,U_118] :
      ( is_fun1661590463l_bool(hAPP_f559147733l_bool(U_119,U_118))
      | ~ is_fun1661590463l_bool(U_118) ),
    inference(variable_rename,[status(thm)],[f_70_1]) ).

cnf(f_70_3,plain,
    ( is_fun1661590463l_bool(hAPP_f559147733l_bool(U_119,U_118))
    | ~ is_fun1661590463l_bool(U_118) ),
    inference(clausify,[status(thm)],[f_70_2]) ).

fof(f_71_1,plain,
    ! [B_1_1,B_2] : is_bool(hAPP_f1637334154l_bool(B_1_1,B_2)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_]) ).

fof(f_71_2,plain,
    ! [U_121,U_120] : is_bool(hAPP_f1637334154l_bool(U_121,U_120)),
    inference(variable_rename,[status(thm)],[f_71_1]) ).

cnf(f_71_3,plain,
    is_bool(hAPP_f1637334154l_bool(U_121,U_120)),
    inference(clausify,[status(thm)],[f_71_2]) ).

fof(f_72_1,plain,
    ! [B_1_1,B_2] : is_bool(hAPP_f292226953l_bool(B_1_1,B_2)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_]) ).

fof(f_72_2,plain,
    ! [U_123,U_122] : is_bool(hAPP_f292226953l_bool(U_123,U_122)),
    inference(variable_rename,[status(thm)],[f_72_1]) ).

cnf(f_72_3,plain,
    is_bool(hAPP_f292226953l_bool(U_123,U_122)),
    inference(clausify,[status(thm)],[f_72_2]) ).

fof(f_73_1,plain,
    ! [B_1_1,B_2] : is_bool(hAPP_f389811538l_bool(B_1_1,B_2)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__]) ).

fof(f_73_2,plain,
    ! [U_125,U_124] : is_bool(hAPP_f389811538l_bool(U_125,U_124)),
    inference(variable_rename,[status(thm)],[f_73_1]) ).

cnf(f_73_3,plain,
    is_bool(hAPP_f389811538l_bool(U_125,U_124)),
    inference(clausify,[status(thm)],[f_73_2]) ).

fof(f_74_1,plain,
    ! [B_1_1,B_2] : is_bool(hAPP_f937997336l_bool(B_1_1,B_2)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HO]) ).

fof(f_74_2,plain,
    ! [U_127,U_126] : is_bool(hAPP_f937997336l_bool(U_127,U_126)),
    inference(variable_rename,[status(thm)],[f_74_1]) ).

cnf(f_74_3,plain,
    is_bool(hAPP_f937997336l_bool(U_127,U_126)),
    inference(clausify,[status(thm)],[f_74_2]) ).

fof(f_75_1,plain,
    ! [B_1_1,B_2] : is_bool(hAPP_f1363661463l_bool(B_1_1,B_2)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HO]) ).

fof(f_75_2,plain,
    ! [U_129,U_128] : is_bool(hAPP_f1363661463l_bool(U_129,U_128)),
    inference(variable_rename,[status(thm)],[f_75_1]) ).

cnf(f_75_3,plain,
    is_bool(hAPP_f1363661463l_bool(U_129,U_128)),
    inference(clausify,[status(thm)],[f_75_2]) ).

fof(f_76_1,plain,
    ! [B_1_1,B_2] : is_bool(hAPP_f595608956l_bool(B_1_1,B_2)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Oboo]) ).

fof(f_76_2,plain,
    ! [U_131,U_130] : is_bool(hAPP_f595608956l_bool(U_131,U_130)),
    inference(variable_rename,[status(thm)],[f_76_1]) ).

cnf(f_76_3,plain,
    is_bool(hAPP_f595608956l_bool(U_131,U_130)),
    inference(clausify,[status(thm)],[f_76_2]) ).

fof(f_77_1,plain,
    ! [B_1_1,B_2] : is_bool(hAPP_f1295398978l_bool(B_1_1,B_2)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_]) ).

fof(f_77_2,plain,
    ! [U_133,U_132] : is_bool(hAPP_f1295398978l_bool(U_133,U_132)),
    inference(variable_rename,[status(thm)],[f_77_1]) ).

cnf(f_77_3,plain,
    is_bool(hAPP_f1295398978l_bool(U_133,U_132)),
    inference(clausify,[status(thm)],[f_77_2]) ).

fof(f_78_1,plain,
    is_fun_a_bool(g),
    inference(fof_nnf,[status(thm)],[gsy_v_G]) ).

cnf(f_78_2,plain,
    is_fun_a_bool(g),
    inference(clausify,[status(thm)],[f_78_1]) ).

fof(f_79_1,plain,
    ! [B_1_1] :
      ( is_fun949378684l_bool(p(B_1_1))
      | ~ is_fun_a_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_v_P]) ).

fof(f_79_2,plain,
    ! [U_134] :
      ( is_fun949378684l_bool(p(U_134))
      | ~ is_fun_a_bool(U_134) ),
    inference(variable_rename,[status(thm)],[f_79_1]) ).

cnf(f_79_3,plain,
    ( is_fun949378684l_bool(p(U_134))
    | ~ is_fun_a_bool(U_134) ),
    inference(clausify,[status(thm)],[f_79_2]) ).

fof(f_80_1,plain,
    is_fun_pname_bool(u),
    inference(fof_nnf,[status(thm)],[gsy_v_U]) ).

cnf(f_80_2,plain,
    is_fun_pname_bool(u),
    inference(clausify,[status(thm)],[f_80_1]) ).

fof(f_81_1,plain,
    is_pname(pn),
    inference(fof_nnf,[status(thm)],[gsy_v_pn]) ).

cnf(f_81_2,plain,
    is_pname(pn),
    inference(clausify,[status(thm)],[f_81_1]) ).

fof(f_82_1,plain,
    ! [Ts,G] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(G),Ts))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Ts),G)) ),
    inference(fof_nnf,[status(thm)],[fact_0_assms_I1_J]) ).

fof(f_82_2,plain,
    ! [U_136,U_135] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(U_135),U_136))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_136),U_135)) ),
    inference(variable_rename,[status(thm)],[f_82_1]) ).

cnf(f_82_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(p(U_135),U_136))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_136),U_135)) ),
    inference(clausify,[status(thm)],[f_82_2]) ).

fof(f_83_1,plain,
    ! [A] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),A))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_1_finite__Collect__subsets]) ).

fof(f_83_2,plain,
    ! [U_137] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),U_137))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_137)) ),
    inference(variable_rename,[status(thm)],[f_83_1]) ).

cnf(f_83_3,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),U_137))))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_137)) ),
    inference(clausify,[status(thm)],[f_83_2]) ).

fof(f_84_1,plain,
    ! [A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),A))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_2_finite__Collect__subsets]) ).

fof(f_84_2,plain,
    ! [U_138] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),U_138))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_138)) ),
    inference(variable_rename,[status(thm)],[f_84_1]) ).

cnf(f_84_3,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),U_138))))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_138)) ),
    inference(clausify,[status(thm)],[f_84_2]) ).

fof(f_85_1,plain,
    ! [A] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),A))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_3_finite__Collect__subsets]) ).

fof(f_85_2,plain,
    ! [U_139] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),U_139))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_139)) ),
    inference(variable_rename,[status(thm)],[f_85_1]) ).

cnf(f_85_3,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),U_139))))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_139)) ),
    inference(clausify,[status(thm)],[f_85_2]) ).

fof(f_86_1,plain,
    ! [A] :
      ( hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),A))))
      | ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_4_finite__Collect__subsets]) ).

fof(f_86_2,plain,
    ! [U_140] :
      ( hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),U_140))))
      | ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,U_140)) ),
    inference(variable_rename,[status(thm)],[f_86_1]) ).

cnf(f_86_3,plain,
    ( hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),U_140))))
    | ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,U_140)) ),
    inference(clausify,[status(thm)],[f_86_2]) ).

fof(f_87_1,plain,
    ! [A] :
      ( hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),A))))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_5_finite__Collect__subsets]) ).

fof(f_87_2,plain,
    ! [U_141] :
      ( hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),U_141))))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_141)) ),
    inference(variable_rename,[status(thm)],[f_87_1]) ).

cnf(f_87_3,plain,
    ( hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),U_141))))
    | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_141)) ),
    inference(clausify,[status(thm)],[f_87_2]) ).

fof(f_88_1,plain,
    ! [A] :
      ( hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),A))))
      | ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_6_finite__Collect__subsets]) ).

fof(f_88_2,plain,
    ! [U_142] :
      ( hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),U_142))))
      | ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,U_142)) ),
    inference(variable_rename,[status(thm)],[f_88_1]) ).

cnf(f_88_3,plain,
    ( hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),U_142))))
    | ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,U_142)) ),
    inference(clausify,[status(thm)],[f_88_2]) ).

fof(f_89_1,plain,
    ! [A] :
      ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),A))))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_7_finite__Collect__subsets]) ).

fof(f_89_2,plain,
    ! [U_143] :
      ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),U_143))))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_143)) ),
    inference(variable_rename,[status(thm)],[f_89_1]) ).

cnf(f_89_3,plain,
    ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),U_143))))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_143)) ),
    inference(clausify,[status(thm)],[f_89_2]) ).

fof(f_90_1,plain,
    ! [A] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),A))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_8_finite__Collect__subsets]) ).

fof(f_90_2,plain,
    ! [U_144] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),U_144))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_144)) ),
    inference(variable_rename,[status(thm)],[f_90_1]) ).

cnf(f_90_3,plain,
    ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),U_144))))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_144)) ),
    inference(clausify,[status(thm)],[f_90_2]) ).

fof(f_91_1,plain,
    ! [A] :
      ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),A))))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_9_finite__Collect__subsets]) ).

fof(f_91_2,plain,
    ! [U_145] :
      ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),U_145))))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_145)) ),
    inference(variable_rename,[status(thm)],[f_91_1]) ).

cnf(f_91_3,plain,
    ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),U_145))))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_145)) ),
    inference(clausify,[status(thm)],[f_91_2]) ).

fof(f_92_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(H,F_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_10_finite__imageI]) ).

fof(f_92_2,plain,
    ! [U_147,U_146] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(U_147,U_146)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_146)) ),
    inference(variable_rename,[status(thm)],[f_92_1]) ).

cnf(f_92_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(U_147,U_146)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_146)) ),
    inference(clausify,[status(thm)],[f_92_2]) ).

fof(f_93_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(H,F_1)))
      | ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_11_finite__imageI]) ).

fof(f_93_2,plain,
    ! [U_149,U_148] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(U_149,U_148)))
      | ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,U_148)) ),
    inference(variable_rename,[status(thm)],[f_93_1]) ).

cnf(f_93_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(U_149,U_148)))
    | ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,U_148)) ),
    inference(clausify,[status(thm)],[f_93_2]) ).

fof(f_94_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(H,F_1)))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_12_finite__imageI]) ).

fof(f_94_2,plain,
    ! [U_151,U_150] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(U_151,U_150)))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_150)) ),
    inference(variable_rename,[status(thm)],[f_94_1]) ).

cnf(f_94_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(U_151,U_150)))
    | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_150)) ),
    inference(clausify,[status(thm)],[f_94_2]) ).

fof(f_95_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(H,F_1)))
      | ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_13_finite__imageI]) ).

fof(f_95_2,plain,
    ! [U_153,U_152] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(U_153,U_152)))
      | ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,U_152)) ),
    inference(variable_rename,[status(thm)],[f_95_1]) ).

cnf(f_95_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(U_153,U_152)))
    | ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,U_152)) ),
    inference(clausify,[status(thm)],[f_95_2]) ).

fof(f_96_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(H,F_1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_14_finite__imageI]) ).

fof(f_96_2,plain,
    ! [U_155,U_154] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(U_155,U_154)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_154)) ),
    inference(variable_rename,[status(thm)],[f_96_1]) ).

cnf(f_96_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(U_155,U_154)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_154)) ),
    inference(clausify,[status(thm)],[f_96_2]) ).

fof(f_97_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(H,F_1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_15_finite__imageI]) ).

fof(f_97_2,plain,
    ! [U_157,U_156] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(U_157,U_156)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_156)) ),
    inference(variable_rename,[status(thm)],[f_97_1]) ).

cnf(f_97_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(U_157,U_156)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_156)) ),
    inference(clausify,[status(thm)],[f_97_2]) ).

fof(f_98_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(H,F_1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_16_finite__imageI]) ).

fof(f_98_2,plain,
    ! [U_159,U_158] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(U_159,U_158)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_158)) ),
    inference(variable_rename,[status(thm)],[f_98_1]) ).

cnf(f_98_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(U_159,U_158)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_158)) ),
    inference(clausify,[status(thm)],[f_98_2]) ).

fof(f_99_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(H,F_1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_17_finite__imageI]) ).

fof(f_99_2,plain,
    ! [U_161,U_160] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(U_161,U_160)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_160)) ),
    inference(variable_rename,[status(thm)],[f_99_1]) ).

cnf(f_99_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(U_161,U_160)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_160)) ),
    inference(clausify,[status(thm)],[f_99_2]) ).

fof(f_100_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(H,F_1)))
      | ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_18_finite__imageI]) ).

fof(f_100_2,plain,
    ! [U_163,U_162] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(U_163,U_162)))
      | ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,U_162)) ),
    inference(variable_rename,[status(thm)],[f_100_1]) ).

cnf(f_100_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(U_163,U_162)))
    | ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,U_162)) ),
    inference(clausify,[status(thm)],[f_100_2]) ).

fof(f_101_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(H,F_1)))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_19_finite__imageI]) ).

fof(f_101_2,plain,
    ! [U_165,U_164] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(U_165,U_164)))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_164)) ),
    inference(variable_rename,[status(thm)],[f_101_1]) ).

cnf(f_101_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(U_165,U_164)))
    | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_164)) ),
    inference(clausify,[status(thm)],[f_101_2]) ).

fof(f_102_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(H,F_1)))
      | ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_20_finite__imageI]) ).

fof(f_102_2,plain,
    ! [U_167,U_166] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(U_167,U_166)))
      | ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,U_166)) ),
    inference(variable_rename,[status(thm)],[f_102_1]) ).

cnf(f_102_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(U_167,U_166)))
    | ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,U_166)) ),
    inference(clausify,[status(thm)],[f_102_2]) ).

fof(f_103_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(H,F_1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_21_finite__imageI]) ).

fof(f_103_2,plain,
    ! [U_169,U_168] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(U_169,U_168)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_168)) ),
    inference(variable_rename,[status(thm)],[f_103_1]) ).

cnf(f_103_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(U_169,U_168)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_168)) ),
    inference(clausify,[status(thm)],[f_103_2]) ).

fof(f_104_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(H,F_1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_22_finite__imageI]) ).

fof(f_104_2,plain,
    ! [U_171,U_170] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(U_171,U_170)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_170)) ),
    inference(variable_rename,[status(thm)],[f_104_1]) ).

cnf(f_104_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(U_171,U_170)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_170)) ),
    inference(clausify,[status(thm)],[f_104_2]) ).

fof(f_105_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(H,F_1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_23_finite__imageI]) ).

fof(f_105_2,plain,
    ! [U_173,U_172] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(U_173,U_172)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_172)) ),
    inference(variable_rename,[status(thm)],[f_105_1]) ).

cnf(f_105_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(U_173,U_172)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_172)) ),
    inference(clausify,[status(thm)],[f_105_2]) ).

fof(f_106_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(H,F_1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_24_finite__imageI]) ).

fof(f_106_2,plain,
    ! [U_175,U_174] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(U_175,U_174)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_174)) ),
    inference(variable_rename,[status(thm)],[f_106_1]) ).

cnf(f_106_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(U_175,U_174)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_174)) ),
    inference(clausify,[status(thm)],[f_106_2]) ).

fof(f_107_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(H,F_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_25_finite__imageI]) ).

fof(f_107_2,plain,
    ! [U_177,U_176] :
      ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(U_177,U_176)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_176)) ),
    inference(variable_rename,[status(thm)],[f_107_1]) ).

cnf(f_107_3,plain,
    ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(U_177,U_176)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_176)) ),
    inference(clausify,[status(thm)],[f_107_2]) ).

fof(f_108_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(H,F_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_26_finite__imageI]) ).

fof(f_108_2,plain,
    ! [U_179,U_178] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(U_179,U_178)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_178)) ),
    inference(variable_rename,[status(thm)],[f_108_1]) ).

cnf(f_108_3,plain,
    ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(U_179,U_178)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_178)) ),
    inference(clausify,[status(thm)],[f_108_2]) ).

fof(f_109_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(H,F_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_27_finite__imageI]) ).

fof(f_109_2,plain,
    ! [U_181,U_180] :
      ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(U_181,U_180)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_180)) ),
    inference(variable_rename,[status(thm)],[f_109_1]) ).

cnf(f_109_3,plain,
    ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(U_181,U_180)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_180)) ),
    inference(clausify,[status(thm)],[f_109_2]) ).

fof(f_110_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(H,F_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_28_finite__imageI]) ).

fof(f_110_2,plain,
    ! [U_183,U_182] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(U_183,U_182)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_182)) ),
    inference(variable_rename,[status(thm)],[f_110_1]) ).

cnf(f_110_3,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(U_183,U_182)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_182)) ),
    inference(clausify,[status(thm)],[f_110_2]) ).

fof(f_111_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(H,F_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_29_finite__imageI]) ).

fof(f_111_2,plain,
    ! [U_185,U_184] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(U_185,U_184)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_184)) ),
    inference(variable_rename,[status(thm)],[f_111_1]) ).

cnf(f_111_3,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(U_185,U_184)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_184)) ),
    inference(clausify,[status(thm)],[f_111_2]) ).

fof(f_112_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(H,F_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_30_finite__imageI]) ).

fof(f_112_2,plain,
    ! [U_187,U_186] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(U_187,U_186)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_186)) ),
    inference(variable_rename,[status(thm)],[f_112_1]) ).

cnf(f_112_3,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(U_187,U_186)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_186)) ),
    inference(clausify,[status(thm)],[f_112_2]) ).

fof(f_113_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(H,F_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_31_finite__imageI]) ).

fof(f_113_2,plain,
    ! [U_189,U_188] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(U_189,U_188)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_188)) ),
    inference(variable_rename,[status(thm)],[f_113_1]) ).

cnf(f_113_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(U_189,U_188)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_188)) ),
    inference(clausify,[status(thm)],[f_113_2]) ).

fof(f_114_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(H,F_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_32_finite__imageI]) ).

fof(f_114_2,plain,
    ! [U_191,U_190] :
      ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(U_191,U_190)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_190)) ),
    inference(variable_rename,[status(thm)],[f_114_1]) ).

cnf(f_114_3,plain,
    ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(U_191,U_190)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_190)) ),
    inference(clausify,[status(thm)],[f_114_2]) ).

fof(f_115_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(H,F_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_33_finite__imageI]) ).

fof(f_115_2,plain,
    ! [U_193,U_192] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(U_193,U_192)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_192)) ),
    inference(variable_rename,[status(thm)],[f_115_1]) ).

cnf(f_115_3,plain,
    ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(U_193,U_192)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_192)) ),
    inference(clausify,[status(thm)],[f_115_2]) ).

fof(f_116_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(H,F_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_34_finite__imageI]) ).

fof(f_116_2,plain,
    ! [U_195,U_194] :
      ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(U_195,U_194)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_194)) ),
    inference(variable_rename,[status(thm)],[f_116_1]) ).

cnf(f_116_3,plain,
    ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(U_195,U_194)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_194)) ),
    inference(clausify,[status(thm)],[f_116_2]) ).

fof(f_117_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(H,F_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_35_finite__imageI]) ).

fof(f_117_2,plain,
    ! [U_197,U_196] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(U_197,U_196)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_196)) ),
    inference(variable_rename,[status(thm)],[f_117_1]) ).

cnf(f_117_3,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(U_197,U_196)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_196)) ),
    inference(clausify,[status(thm)],[f_117_2]) ).

fof(f_118_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(H,F_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_36_finite__imageI]) ).

fof(f_118_2,plain,
    ! [U_199,U_198] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(U_199,U_198)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_198)) ),
    inference(variable_rename,[status(thm)],[f_118_1]) ).

cnf(f_118_3,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(U_199,U_198)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_198)) ),
    inference(clausify,[status(thm)],[f_118_2]) ).

fof(f_119_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(H,F_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_37_finite__imageI]) ).

fof(f_119_2,plain,
    ! [U_201,U_200] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(U_201,U_200)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_200)) ),
    inference(variable_rename,[status(thm)],[f_119_1]) ).

cnf(f_119_3,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(U_201,U_200)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_200)) ),
    inference(clausify,[status(thm)],[f_119_2]) ).

fof(f_120_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(H,F_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_38_finite__imageI]) ).

fof(f_120_2,plain,
    ! [U_203,U_202] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(U_203,U_202)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_202)) ),
    inference(variable_rename,[status(thm)],[f_120_1]) ).

cnf(f_120_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(U_203,U_202)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_202)) ),
    inference(clausify,[status(thm)],[f_120_2]) ).

fof(f_121_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(H,F_1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_39_finite__imageI]) ).

fof(f_121_2,plain,
    ! [U_205,U_204] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(U_205,U_204)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_204)) ),
    inference(variable_rename,[status(thm)],[f_121_1]) ).

cnf(f_121_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(U_205,U_204)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_204)) ),
    inference(clausify,[status(thm)],[f_121_2]) ).

fof(f_122_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(H,F_1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_40_finite__imageI]) ).

fof(f_122_2,plain,
    ! [U_207,U_206] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(U_207,U_206)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_206)) ),
    inference(variable_rename,[status(thm)],[f_122_1]) ).

cnf(f_122_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(U_207,U_206)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_206)) ),
    inference(clausify,[status(thm)],[f_122_2]) ).

fof(f_123_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(H,F_1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_41_finite__imageI]) ).

fof(f_123_2,plain,
    ! [U_209,U_208] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(U_209,U_208)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_208)) ),
    inference(variable_rename,[status(thm)],[f_123_1]) ).

cnf(f_123_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(U_209,U_208)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_208)) ),
    inference(clausify,[status(thm)],[f_123_2]) ).

fof(f_124_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(H,F_1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_42_finite__imageI]) ).

fof(f_124_2,plain,
    ! [U_211,U_210] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(U_211,U_210)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_210)) ),
    inference(variable_rename,[status(thm)],[f_124_1]) ).

cnf(f_124_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(U_211,U_210)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_210)) ),
    inference(clausify,[status(thm)],[f_124_2]) ).

fof(f_125_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(H,F_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_43_finite__imageI]) ).

fof(f_125_2,plain,
    ! [U_213,U_212] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(U_213,U_212)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_212)) ),
    inference(variable_rename,[status(thm)],[f_125_1]) ).

cnf(f_125_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(U_213,U_212)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_212)) ),
    inference(clausify,[status(thm)],[f_125_2]) ).

fof(f_126_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(H,F_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_44_finite__imageI]) ).

fof(f_126_2,plain,
    ! [U_215,U_214] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(U_215,U_214)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_214)) ),
    inference(variable_rename,[status(thm)],[f_126_1]) ).

cnf(f_126_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(U_215,U_214)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_214)) ),
    inference(clausify,[status(thm)],[f_126_2]) ).

fof(f_127_1,plain,
    ! [A_1,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(A_1,A)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_45_finite_OinsertI]) ).

fof(f_127_2,plain,
    ! [U_217,U_216] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(U_217,U_216)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_216)) ),
    inference(variable_rename,[status(thm)],[f_127_1]) ).

cnf(f_127_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(U_217,U_216)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_216)) ),
    inference(clausify,[status(thm)],[f_127_2]) ).

fof(f_128_1,plain,
    ! [A_1,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(A_1,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_46_finite_OinsertI]) ).

fof(f_128_2,plain,
    ! [U_219,U_218] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(U_219,U_218)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_218)) ),
    inference(variable_rename,[status(thm)],[f_128_1]) ).

cnf(f_128_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(U_219,U_218)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_218)) ),
    inference(clausify,[status(thm)],[f_128_2]) ).

fof(f_129_1,plain,
    ! [A_1,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_1,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_47_finite_OinsertI]) ).

fof(f_129_2,plain,
    ! [U_221,U_220] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_221,U_220)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_220)) ),
    inference(variable_rename,[status(thm)],[f_129_1]) ).

cnf(f_129_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_221,U_220)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_220)) ),
    inference(clausify,[status(thm)],[f_129_2]) ).

fof(f_130_1,plain,
    ! [A_1,A] :
      ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(A_1,A)))
      | ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_48_finite_OinsertI]) ).

fof(f_130_2,plain,
    ! [U_223,U_222] :
      ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(U_223,U_222)))
      | ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,U_222)) ),
    inference(variable_rename,[status(thm)],[f_130_1]) ).

cnf(f_130_3,plain,
    ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(U_223,U_222)))
    | ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,U_222)) ),
    inference(clausify,[status(thm)],[f_130_2]) ).

fof(f_131_1,plain,
    ! [A_1,A] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(A_1,A)))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_49_finite_OinsertI]) ).

fof(f_131_2,plain,
    ! [U_225,U_224] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(U_225,U_224)))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_224)) ),
    inference(variable_rename,[status(thm)],[f_131_1]) ).

cnf(f_131_3,plain,
    ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(U_225,U_224)))
    | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_224)) ),
    inference(clausify,[status(thm)],[f_131_2]) ).

fof(f_132_1,plain,
    ! [A_1,A] :
      ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(A_1,A)))
      | ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_50_finite_OinsertI]) ).

fof(f_132_2,plain,
    ! [U_227,U_226] :
      ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(U_227,U_226)))
      | ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,U_226)) ),
    inference(variable_rename,[status(thm)],[f_132_1]) ).

cnf(f_132_3,plain,
    ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(U_227,U_226)))
    | ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,U_226)) ),
    inference(clausify,[status(thm)],[f_132_2]) ).

fof(f_133_1,plain,
    ! [A_1,A] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(A_1,A)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_51_finite_OinsertI]) ).

fof(f_133_2,plain,
    ! [U_229,U_228] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(U_229,U_228)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_228)) ),
    inference(variable_rename,[status(thm)],[f_133_1]) ).

cnf(f_133_3,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(U_229,U_228)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_228)) ),
    inference(clausify,[status(thm)],[f_133_2]) ).

fof(f_134_1,plain,
    ! [A_1,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_1,A)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_52_finite_OinsertI]) ).

fof(f_134_2,plain,
    ! [U_231,U_230] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_231,U_230)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_230)) ),
    inference(variable_rename,[status(thm)],[f_134_1]) ).

cnf(f_134_3,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_231,U_230)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_230)) ),
    inference(clausify,[status(thm)],[f_134_2]) ).

fof(f_135_1,plain,
    ! [A_1,A] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(A_1,A)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_53_finite_OinsertI]) ).

fof(f_135_2,plain,
    ! [U_233,U_232] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(U_233,U_232)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_232)) ),
    inference(variable_rename,[status(thm)],[f_135_1]) ).

cnf(f_135_3,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(U_233,U_232)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_232)) ),
    inference(clausify,[status(thm)],[f_135_2]) ).

fof(f_136_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_54_card__image__le]) ).

fof(f_136_2,plain,
    ! [U_235,U_234] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(U_235,U_234))),hAPP_f921600141ol_nat(finite_card_pname,U_234)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_234)) ),
    inference(variable_rename,[status(thm)],[f_136_1]) ).

cnf(f_136_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(U_235,U_234))),hAPP_f921600141ol_nat(finite_card_pname,U_234)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_234)) ),
    inference(clausify,[status(thm)],[f_136_2]) ).

fof(f_137_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(F,A))),hAPP_fun_a_bool_nat(finite_card_a,A)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_55_card__image__le]) ).

fof(f_137_2,plain,
    ! [U_237,U_236] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(U_237,U_236))),hAPP_fun_a_bool_nat(finite_card_a,U_236)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_236)) ),
    inference(variable_rename,[status(thm)],[f_137_1]) ).

cnf(f_137_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(U_237,U_236))),hAPP_fun_a_bool_nat(finite_card_a,U_236)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_236)) ),
    inference(clausify,[status(thm)],[f_137_2]) ).

fof(f_138_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(F,A))),hAPP_f696928925ol_nat(finite346522414t_bool,A)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_56_card__image__le]) ).

fof(f_138_2,plain,
    ! [U_239,U_238] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(U_239,U_238))),hAPP_f696928925ol_nat(finite346522414t_bool,U_238)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_238)) ),
    inference(variable_rename,[status(thm)],[f_138_1]) ).

cnf(f_138_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(U_239,U_238))),hAPP_f696928925ol_nat(finite346522414t_bool,U_238)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_238)) ),
    inference(clausify,[status(thm)],[f_138_2]) ).

fof(f_139_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(F,A))),hAPP_f55526627ol_nat(finite1340463720e_bool,A)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_57_card__image__le]) ).

fof(f_139_2,plain,
    ! [U_241,U_240] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(U_241,U_240))),hAPP_f55526627ol_nat(finite1340463720e_bool,U_240)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_240)) ),
    inference(variable_rename,[status(thm)],[f_139_1]) ).

cnf(f_139_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(U_241,U_240))),hAPP_f55526627ol_nat(finite1340463720e_bool,U_240)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_240)) ),
    inference(clausify,[status(thm)],[f_139_2]) ).

fof(f_140_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(F,A))),hAPP_f2009550088ol_nat(finite1306199131a_bool,A)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_58_card__image__le]) ).

fof(f_140_2,plain,
    ! [U_243,U_242] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(U_243,U_242))),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_242)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_242)) ),
    inference(variable_rename,[status(thm)],[f_140_1]) ).

cnf(f_140_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(U_243,U_242))),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_242)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_242)) ),
    inference(clausify,[status(thm)],[f_140_2]) ).

fof(f_141_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(F,A))),hAPP_fun_a_bool_nat(finite_card_a,A)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_59_card__image__le]) ).

fof(f_141_2,plain,
    ! [U_245,U_244] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(U_245,U_244))),hAPP_fun_a_bool_nat(finite_card_a,U_244)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_244)) ),
    inference(variable_rename,[status(thm)],[f_141_1]) ).

cnf(f_141_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(U_245,U_244))),hAPP_fun_a_bool_nat(finite_card_a,U_244)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_244)) ),
    inference(clausify,[status(thm)],[f_141_2]) ).

fof(f_142_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_60_card__image__le]) ).

fof(f_142_2,plain,
    ! [U_247,U_246] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(U_247,U_246))),hAPP_f22106695ol_nat(finite_card_nat,U_246)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_246)) ),
    inference(variable_rename,[status(thm)],[f_142_1]) ).

cnf(f_142_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(U_247,U_246))),hAPP_f22106695ol_nat(finite_card_nat,U_246)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_246)) ),
    inference(clausify,[status(thm)],[f_142_2]) ).

fof(f_143_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_61_card__image__le]) ).

fof(f_143_2,plain,
    ! [U_249,U_248] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(U_249,U_248))),hAPP_f921600141ol_nat(finite_card_pname,U_248)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_248)) ),
    inference(variable_rename,[status(thm)],[f_143_1]) ).

cnf(f_143_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(U_249,U_248))),hAPP_f921600141ol_nat(finite_card_pname,U_248)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_248)) ),
    inference(clausify,[status(thm)],[f_143_2]) ).

fof(f_144_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(F,A))),hAPP_f1690079119ol_nat(finite1352710292l_bool,A)))
      | ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_62_card__image__le]) ).

fof(f_144_2,plain,
    ! [U_251,U_250] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(U_251,U_250))),hAPP_f1690079119ol_nat(finite1352710292l_bool,U_250)))
      | ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,U_250)) ),
    inference(variable_rename,[status(thm)],[f_144_1]) ).

cnf(f_144_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(U_251,U_250))),hAPP_f1690079119ol_nat(finite1352710292l_bool,U_250)))
    | ~ hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,U_250)) ),
    inference(clausify,[status(thm)],[f_144_2]) ).

fof(f_145_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(F,A))),hAPP_f98387925ol_nat(finite269641166l_bool,A)))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_63_card__image__le]) ).

fof(f_145_2,plain,
    ! [U_253,U_252] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(U_253,U_252))),hAPP_f98387925ol_nat(finite269641166l_bool,U_252)))
      | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_252)) ),
    inference(variable_rename,[status(thm)],[f_145_1]) ).

cnf(f_145_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(U_253,U_252))),hAPP_f98387925ol_nat(finite269641166l_bool,U_252)))
    | ~ hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,U_252)) ),
    inference(clausify,[status(thm)],[f_145_2]) ).

fof(f_146_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(F,A))),hAPP_f1253658590ol_nat(finite1659325229l_bool,A)))
      | ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_64_card__image__le]) ).

fof(f_146_2,plain,
    ! [U_255,U_254] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(U_255,U_254))),hAPP_f1253658590ol_nat(finite1659325229l_bool,U_254)))
      | ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,U_254)) ),
    inference(variable_rename,[status(thm)],[f_146_1]) ).

cnf(f_146_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(U_255,U_254))),hAPP_f1253658590ol_nat(finite1659325229l_bool,U_254)))
    | ~ hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,U_254)) ),
    inference(clausify,[status(thm)],[f_146_2]) ).

fof(f_147_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(F,A))),hAPP_f2009550088ol_nat(finite1306199131a_bool,A)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_65_card__image__le]) ).

fof(f_147_2,plain,
    ! [U_257,U_256] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(U_257,U_256))),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_256)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_256)) ),
    inference(variable_rename,[status(thm)],[f_147_1]) ).

cnf(f_147_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(U_257,U_256))),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_256)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_256)) ),
    inference(clausify,[status(thm)],[f_147_2]) ).

fof(f_148_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(F,A))),hAPP_f55526627ol_nat(finite1340463720e_bool,A)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_66_card__image__le]) ).

fof(f_148_2,plain,
    ! [U_259,U_258] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(U_259,U_258))),hAPP_f55526627ol_nat(finite1340463720e_bool,U_258)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_258)) ),
    inference(variable_rename,[status(thm)],[f_148_1]) ).

cnf(f_148_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(U_259,U_258))),hAPP_f55526627ol_nat(finite1340463720e_bool,U_258)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_258)) ),
    inference(clausify,[status(thm)],[f_148_2]) ).

fof(f_149_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(F,A))),hAPP_f696928925ol_nat(finite346522414t_bool,A)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_67_card__image__le]) ).

fof(f_149_2,plain,
    ! [U_261,U_260] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(U_261,U_260))),hAPP_f696928925ol_nat(finite346522414t_bool,U_260)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_260)) ),
    inference(variable_rename,[status(thm)],[f_149_1]) ).

cnf(f_149_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(U_261,U_260))),hAPP_f696928925ol_nat(finite346522414t_bool,U_260)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_260)) ),
    inference(clausify,[status(thm)],[f_149_2]) ).

fof(f_150_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(F,A))),hAPP_fun_a_bool_nat(finite_card_a,A)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_68_card__image__le]) ).

fof(f_150_2,plain,
    ! [U_263,U_262] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(U_263,U_262))),hAPP_fun_a_bool_nat(finite_card_a,U_262)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_262)) ),
    inference(variable_rename,[status(thm)],[f_150_1]) ).

cnf(f_150_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(U_263,U_262))),hAPP_fun_a_bool_nat(finite_card_a,U_262)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_262)) ),
    inference(clausify,[status(thm)],[f_150_2]) ).

fof(f_151_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_69_card__image__le]) ).

fof(f_151_2,plain,
    ! [U_265,U_264] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(U_265,U_264))),hAPP_f921600141ol_nat(finite_card_pname,U_264)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_264)) ),
    inference(variable_rename,[status(thm)],[f_151_1]) ).

cnf(f_151_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(U_265,U_264))),hAPP_f921600141ol_nat(finite_card_pname,U_264)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_264)) ),
    inference(clausify,[status(thm)],[f_151_2]) ).

fof(f_152_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_70_card__image__le]) ).

fof(f_152_2,plain,
    ! [U_267,U_266] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(U_267,U_266))),hAPP_f921600141ol_nat(finite_card_pname,U_266)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_266)) ),
    inference(variable_rename,[status(thm)],[f_152_1]) ).

cnf(f_152_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(U_267,U_266))),hAPP_f921600141ol_nat(finite_card_pname,U_266)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_266)) ),
    inference(clausify,[status(thm)],[f_152_2]) ).

fof(f_153_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_71_card__image__le]) ).

fof(f_153_2,plain,
    ! [U_269,U_268] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(U_269,U_268))),hAPP_f921600141ol_nat(finite_card_pname,U_268)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_268)) ),
    inference(variable_rename,[status(thm)],[f_153_1]) ).

cnf(f_153_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(U_269,U_268))),hAPP_f921600141ol_nat(finite_card_pname,U_268)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_268)) ),
    inference(clausify,[status(thm)],[f_153_2]) ).

fof(f_154_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_72_card__image__le]) ).

fof(f_154_2,plain,
    ! [U_271,U_270] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(U_271,U_270))),hAPP_f921600141ol_nat(finite_card_pname,U_270)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_270)) ),
    inference(variable_rename,[status(thm)],[f_154_1]) ).

cnf(f_154_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(U_271,U_270))),hAPP_f921600141ol_nat(finite_card_pname,U_270)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_270)) ),
    inference(clausify,[status(thm)],[f_154_2]) ).

fof(f_155_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_73_card__image__le]) ).

fof(f_155_2,plain,
    ! [U_273,U_272] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(U_273,U_272))),hAPP_f22106695ol_nat(finite_card_nat,U_272)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_272)) ),
    inference(variable_rename,[status(thm)],[f_155_1]) ).

cnf(f_155_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(U_273,U_272))),hAPP_f22106695ol_nat(finite_card_nat,U_272)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_272)) ),
    inference(clausify,[status(thm)],[f_155_2]) ).

fof(f_156_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_74_card__image__le]) ).

fof(f_156_2,plain,
    ! [U_275,U_274] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(U_275,U_274))),hAPP_f22106695ol_nat(finite_card_nat,U_274)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_274)) ),
    inference(variable_rename,[status(thm)],[f_156_1]) ).

cnf(f_156_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(U_275,U_274))),hAPP_f22106695ol_nat(finite_card_nat,U_274)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_274)) ),
    inference(clausify,[status(thm)],[f_156_2]) ).

fof(f_157_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_75_card__image__le]) ).

fof(f_157_2,plain,
    ! [U_277,U_276] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(U_277,U_276))),hAPP_f22106695ol_nat(finite_card_nat,U_276)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_276)) ),
    inference(variable_rename,[status(thm)],[f_157_1]) ).

cnf(f_157_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(U_277,U_276))),hAPP_f22106695ol_nat(finite_card_nat,U_276)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_276)) ),
    inference(clausify,[status(thm)],[f_157_2]) ).

fof(f_158_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_76_card__image__le]) ).

fof(f_158_2,plain,
    ! [U_279,U_278] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(U_279,U_278))),hAPP_f22106695ol_nat(finite_card_nat,U_278)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_278)) ),
    inference(variable_rename,[status(thm)],[f_158_1]) ).

cnf(f_158_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(U_279,U_278))),hAPP_f22106695ol_nat(finite_card_nat,U_278)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_278)) ),
    inference(clausify,[status(thm)],[f_158_2]) ).

fof(f_159_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(F,A))),hAPP_f696928925ol_nat(finite346522414t_bool,A)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_77_card__image__le]) ).

fof(f_159_2,plain,
    ! [U_281,U_280] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(U_281,U_280))),hAPP_f696928925ol_nat(finite346522414t_bool,U_280)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_280)) ),
    inference(variable_rename,[status(thm)],[f_159_1]) ).

cnf(f_159_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(U_281,U_280))),hAPP_f696928925ol_nat(finite346522414t_bool,U_280)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_280)) ),
    inference(clausify,[status(thm)],[f_159_2]) ).

fof(f_160_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(F,A))),hAPP_f55526627ol_nat(finite1340463720e_bool,A)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_78_card__image__le]) ).

fof(f_160_2,plain,
    ! [U_283,U_282] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(U_283,U_282))),hAPP_f55526627ol_nat(finite1340463720e_bool,U_282)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_282)) ),
    inference(variable_rename,[status(thm)],[f_160_1]) ).

cnf(f_160_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(U_283,U_282))),hAPP_f55526627ol_nat(finite1340463720e_bool,U_282)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_282)) ),
    inference(clausify,[status(thm)],[f_160_2]) ).

fof(f_161_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(F,A))),hAPP_f2009550088ol_nat(finite1306199131a_bool,A)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_79_card__image__le]) ).

fof(f_161_2,plain,
    ! [U_285,U_284] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(U_285,U_284))),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_284)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_284)) ),
    inference(variable_rename,[status(thm)],[f_161_1]) ).

cnf(f_161_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(U_285,U_284))),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_284)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_284)) ),
    inference(clausify,[status(thm)],[f_161_2]) ).

fof(f_162_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,A)),hAPP_f696928925ol_nat(finite346522414t_bool,B)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A),B))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B)) ),
    inference(fof_nnf,[status(thm)],[fact_80_card__mono]) ).

fof(f_162_2,plain,
    ! [U_287,U_286] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,U_287)),hAPP_f696928925ol_nat(finite346522414t_bool,U_286)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_287),U_286))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_286)) ),
    inference(variable_rename,[status(thm)],[f_162_1]) ).

cnf(f_162_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,U_287)),hAPP_f696928925ol_nat(finite346522414t_bool,U_286)))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_287),U_286))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_286)) ),
    inference(clausify,[status(thm)],[f_162_2]) ).

fof(f_163_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,A)),hAPP_f55526627ol_nat(finite1340463720e_bool,B)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) ),
    inference(fof_nnf,[status(thm)],[fact_81_card__mono]) ).

fof(f_163_2,plain,
    ! [U_289,U_288] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,U_289)),hAPP_f55526627ol_nat(finite1340463720e_bool,U_288)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_289),U_288))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_288)) ),
    inference(variable_rename,[status(thm)],[f_163_1]) ).

cnf(f_163_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,U_289)),hAPP_f55526627ol_nat(finite1340463720e_bool,U_288)))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_289),U_288))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_288)) ),
    inference(clausify,[status(thm)],[f_163_2]) ).

fof(f_164_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,A)),hAPP_f2009550088ol_nat(finite1306199131a_bool,B)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A),B))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B)) ),
    inference(fof_nnf,[status(thm)],[fact_82_card__mono]) ).

fof(f_164_2,plain,
    ! [U_291,U_290] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_291)),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_290)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_291),U_290))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_290)) ),
    inference(variable_rename,[status(thm)],[f_164_1]) ).

cnf(f_164_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_291)),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_290)))
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_291),U_290))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_290)) ),
    inference(clausify,[status(thm)],[f_164_2]) ).

fof(f_165_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,A)),hAPP_f921600141ol_nat(finite_card_pname,B)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ),
    inference(fof_nnf,[status(thm)],[fact_83_card__mono]) ).

fof(f_165_2,plain,
    ! [U_293,U_292] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,U_293)),hAPP_f921600141ol_nat(finite_card_pname,U_292)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_293),U_292))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_292)) ),
    inference(variable_rename,[status(thm)],[f_165_1]) ).

cnf(f_165_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,U_293)),hAPP_f921600141ol_nat(finite_card_pname,U_292)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_293),U_292))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_292)) ),
    inference(clausify,[status(thm)],[f_165_2]) ).

fof(f_166_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,A)),hAPP_fun_a_bool_nat(finite_card_a,B)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) ),
    inference(fof_nnf,[status(thm)],[fact_84_card__mono]) ).

fof(f_166_2,plain,
    ! [U_295,U_294] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,U_295)),hAPP_fun_a_bool_nat(finite_card_a,U_294)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_295),U_294))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_294)) ),
    inference(variable_rename,[status(thm)],[f_166_1]) ).

cnf(f_166_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,U_295)),hAPP_fun_a_bool_nat(finite_card_a,U_294)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_295),U_294))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_294)) ),
    inference(clausify,[status(thm)],[f_166_2]) ).

fof(f_167_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,A)),hAPP_f22106695ol_nat(finite_card_nat,B)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) ),
    inference(fof_nnf,[status(thm)],[fact_85_card__mono]) ).

fof(f_167_2,plain,
    ! [U_297,U_296] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,U_297)),hAPP_f22106695ol_nat(finite_card_nat,U_296)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_297),U_296))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_296)) ),
    inference(variable_rename,[status(thm)],[f_167_1]) ).

cnf(f_167_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,U_297)),hAPP_f22106695ol_nat(finite_card_nat,U_296)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_297),U_296))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_296)) ),
    inference(clausify,[status(thm)],[f_167_2]) ).

fof(f_168_1,plain,
    ! [A,B] :
      ( A = B
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,B)),hAPP_f696928925ol_nat(finite346522414t_bool,A)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A),B))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B)) ),
    inference(fof_nnf,[status(thm)],[fact_86_card__seteq]) ).

fof(f_168_2,plain,
    ! [U_299,U_298] :
      ( U_299 = U_298
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,U_298)),hAPP_f696928925ol_nat(finite346522414t_bool,U_299)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_299),U_298))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_298)) ),
    inference(variable_rename,[status(thm)],[f_168_1]) ).

cnf(f_168_3,plain,
    ( U_299 = U_298
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,U_298)),hAPP_f696928925ol_nat(finite346522414t_bool,U_299)))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_299),U_298))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_298)) ),
    inference(clausify,[status(thm)],[f_168_2]) ).

fof(f_169_1,plain,
    ! [A,B] :
      ( A = B
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,B)),hAPP_f55526627ol_nat(finite1340463720e_bool,A)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
      | ~ is_fun1661590463l_bool(B)
      | ~ is_fun1661590463l_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_87_card__seteq]) ).

fof(f_169_2,plain,
    ! [U_301,U_300] :
      ( U_301 = U_300
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,U_300)),hAPP_f55526627ol_nat(finite1340463720e_bool,U_301)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_301),U_300))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_300))
      | ~ is_fun1661590463l_bool(U_300)
      | ~ is_fun1661590463l_bool(U_301) ),
    inference(variable_rename,[status(thm)],[f_169_1]) ).

cnf(f_169_3,plain,
    ( U_301 = U_300
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,U_300)),hAPP_f55526627ol_nat(finite1340463720e_bool,U_301)))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_301),U_300))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_300))
    | ~ is_fun1661590463l_bool(U_300)
    | ~ is_fun1661590463l_bool(U_301) ),
    inference(clausify,[status(thm)],[f_169_2]) ).

fof(f_170_1,plain,
    ! [A,B] :
      ( A = B
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,B)),hAPP_f2009550088ol_nat(finite1306199131a_bool,A)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A),B))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))
      | ~ is_fun949378684l_bool(B)
      | ~ is_fun949378684l_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_88_card__seteq]) ).

fof(f_170_2,plain,
    ! [U_303,U_302] :
      ( U_303 = U_302
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_302)),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_303)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_303),U_302))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_302))
      | ~ is_fun949378684l_bool(U_302)
      | ~ is_fun949378684l_bool(U_303) ),
    inference(variable_rename,[status(thm)],[f_170_1]) ).

cnf(f_170_3,plain,
    ( U_303 = U_302
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_302)),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_303)))
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_303),U_302))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_302))
    | ~ is_fun949378684l_bool(U_302)
    | ~ is_fun949378684l_bool(U_303) ),
    inference(clausify,[status(thm)],[f_170_2]) ).

fof(f_171_1,plain,
    ! [A,B] :
      ( A = B
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,B)),hAPP_f921600141ol_nat(finite_card_pname,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ is_fun_pname_bool(B)
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_89_card__seteq]) ).

fof(f_171_2,plain,
    ! [U_305,U_304] :
      ( U_305 = U_304
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,U_304)),hAPP_f921600141ol_nat(finite_card_pname,U_305)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_305),U_304))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_304))
      | ~ is_fun_pname_bool(U_304)
      | ~ is_fun_pname_bool(U_305) ),
    inference(variable_rename,[status(thm)],[f_171_1]) ).

cnf(f_171_3,plain,
    ( U_305 = U_304
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,U_304)),hAPP_f921600141ol_nat(finite_card_pname,U_305)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_305),U_304))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_304))
    | ~ is_fun_pname_bool(U_304)
    | ~ is_fun_pname_bool(U_305) ),
    inference(clausify,[status(thm)],[f_171_2]) ).

fof(f_172_1,plain,
    ! [A,B] :
      ( A = B
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,B)),hAPP_fun_a_bool_nat(finite_card_a,A)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))
      | ~ is_fun_a_bool(B)
      | ~ is_fun_a_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_90_card__seteq]) ).

fof(f_172_2,plain,
    ! [U_307,U_306] :
      ( U_307 = U_306
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,U_306)),hAPP_fun_a_bool_nat(finite_card_a,U_307)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_307),U_306))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_306))
      | ~ is_fun_a_bool(U_306)
      | ~ is_fun_a_bool(U_307) ),
    inference(variable_rename,[status(thm)],[f_172_1]) ).

cnf(f_172_3,plain,
    ( U_307 = U_306
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,U_306)),hAPP_fun_a_bool_nat(finite_card_a,U_307)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_307),U_306))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_306))
    | ~ is_fun_a_bool(U_306)
    | ~ is_fun_a_bool(U_307) ),
    inference(clausify,[status(thm)],[f_172_2]) ).

fof(f_173_1,plain,
    ! [A,B] :
      ( A = B
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,B)),hAPP_f22106695ol_nat(finite_card_nat,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) ),
    inference(fof_nnf,[status(thm)],[fact_91_card__seteq]) ).

fof(f_173_2,plain,
    ! [U_309,U_308] :
      ( U_309 = U_308
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,U_308)),hAPP_f22106695ol_nat(finite_card_nat,U_309)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_309),U_308))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_308)) ),
    inference(variable_rename,[status(thm)],[f_173_1]) ).

cnf(f_173_3,plain,
    ( U_309 = U_308
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,U_308)),hAPP_f22106695ol_nat(finite_card_nat,U_309)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_309),U_308))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_308)) ),
    inference(clausify,[status(thm)],[f_173_2]) ).

fof(f_174_1,plain,
    ! [X_2,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,A)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_2,A))))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_92_card__insert__le]) ).

fof(f_174_2,plain,
    ! [U_311,U_310] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,U_310)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(U_311,U_310))))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_310)) ),
    inference(variable_rename,[status(thm)],[f_174_1]) ).

cnf(f_174_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,U_310)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(U_311,U_310))))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_310)) ),
    inference(clausify,[status(thm)],[f_174_2]) ).

fof(f_175_1,plain,
    ! [X_2,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,A)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_2,A))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_93_card__insert__le]) ).

fof(f_175_2,plain,
    ! [U_313,U_312] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,U_312)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(U_313,U_312))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_312)) ),
    inference(variable_rename,[status(thm)],[f_175_1]) ).

cnf(f_175_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,U_312)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(U_313,U_312))))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_312)) ),
    inference(clausify,[status(thm)],[f_175_2]) ).

fof(f_176_1,plain,
    ! [X_2,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,A)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_2,A))))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_94_card__insert__le]) ).

fof(f_176_2,plain,
    ! [U_315,U_314] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_314)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(U_315,U_314))))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_314)) ),
    inference(variable_rename,[status(thm)],[f_176_1]) ).

cnf(f_176_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_314)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(U_315,U_314))))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_314)) ),
    inference(clausify,[status(thm)],[f_176_2]) ).

fof(f_177_1,plain,
    ! [X_2,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,A)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_2,A))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_95_card__insert__le]) ).

fof(f_177_2,plain,
    ! [U_317,U_316] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,U_316)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(U_317,U_316))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_316)) ),
    inference(variable_rename,[status(thm)],[f_177_1]) ).

cnf(f_177_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,U_316)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(U_317,U_316))))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_316)) ),
    inference(clausify,[status(thm)],[f_177_2]) ).

fof(f_178_1,plain,
    ! [X_2,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,A)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_2,A))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_96_card__insert__le]) ).

fof(f_178_2,plain,
    ! [U_319,U_318] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,U_318)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(U_319,U_318))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_318)) ),
    inference(variable_rename,[status(thm)],[f_178_1]) ).

cnf(f_178_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,U_318)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(U_319,U_318))))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_318)) ),
    inference(clausify,[status(thm)],[f_178_2]) ).

fof(f_179_1,plain,
    ! [X_2,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,A)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_2,A))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_97_card__insert__le]) ).

fof(f_179_2,plain,
    ! [U_321,U_320] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,U_320)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(U_321,U_320))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_320)) ),
    inference(variable_rename,[status(thm)],[f_179_1]) ).

cnf(f_179_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,U_320)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(U_321,U_320))))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_320)) ),
    inference(clausify,[status(thm)],[f_179_2]) ).

fof(f_180_1,plain,
    ! [X_2,A] :
      ( ( ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,A))
          | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_2),A)) )
        & ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_2,A)) = hAPP_f696928925ol_nat(finite346522414t_bool,A)
          | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_2),A)) ) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_98_card__insert__if]) ).

fof(f_180_2,plain,
    ! [U_323,U_322] :
      ( ( ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(U_323,U_322)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,U_322))
          | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_323),U_322)) )
        & ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(U_323,U_322)) = hAPP_f696928925ol_nat(finite346522414t_bool,U_322)
          | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_323),U_322)) ) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_322)) ),
    inference(variable_rename,[status(thm)],[f_180_1]) ).

cnf(f_180_3,plain,
    ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(U_323,U_322)) = hAPP_f696928925ol_nat(finite346522414t_bool,U_322)
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_323),U_322))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_322)) ),
    inference(clausify,[status(thm)],[f_180_2]) ).

cnf(f_180_4,plain,
    ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(U_323,U_322)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,U_322))
    | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_323),U_322))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_322)) ),
    inference(clausify,[status(thm)],[f_180_2]) ).

fof(f_181_1,plain,
    ! [X_2,A] :
      ( ( ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,A))
          | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A)) )
        & ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_2,A)) = hAPP_f55526627ol_nat(finite1340463720e_bool,A)
          | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A)) ) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_99_card__insert__if]) ).

fof(f_181_2,plain,
    ! [U_325,U_324] :
      ( ( ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(U_325,U_324)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,U_324))
          | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_325),U_324)) )
        & ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(U_325,U_324)) = hAPP_f55526627ol_nat(finite1340463720e_bool,U_324)
          | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_325),U_324)) ) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_324)) ),
    inference(variable_rename,[status(thm)],[f_181_1]) ).

cnf(f_181_3,plain,
    ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(U_325,U_324)) = hAPP_f55526627ol_nat(finite1340463720e_bool,U_324)
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_325),U_324))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_324)) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

cnf(f_181_4,plain,
    ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(U_325,U_324)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,U_324))
    | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_325),U_324))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_324)) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

fof(f_182_1,plain,
    ! [X_2,A] :
      ( ( ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,A))
          | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_2),A)) )
        & ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_2,A)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,A)
          | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_2),A)) ) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_100_card__insert__if]) ).

fof(f_182_2,plain,
    ! [U_327,U_326] :
      ( ( ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(U_327,U_326)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_326))
          | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_327),U_326)) )
        & ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(U_327,U_326)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,U_326)
          | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_327),U_326)) ) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_326)) ),
    inference(variable_rename,[status(thm)],[f_182_1]) ).

cnf(f_182_3,plain,
    ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(U_327,U_326)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,U_326)
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_327),U_326))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_326)) ),
    inference(clausify,[status(thm)],[f_182_2]) ).

cnf(f_182_4,plain,
    ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(U_327,U_326)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_326))
    | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_327),U_326))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_326)) ),
    inference(clausify,[status(thm)],[f_182_2]) ).

fof(f_183_1,plain,
    ! [X_2,A] :
      ( ( ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_2,A)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,A))
          | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) )
        & ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_2,A)) = hAPP_f22106695ol_nat(finite_card_nat,A)
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_101_card__insert__if]) ).

fof(f_183_2,plain,
    ! [U_329,U_328] :
      ( ( ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(U_329,U_328)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,U_328))
          | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_329),U_328)) )
        & ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(U_329,U_328)) = hAPP_f22106695ol_nat(finite_card_nat,U_328)
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_329),U_328)) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_328)) ),
    inference(variable_rename,[status(thm)],[f_183_1]) ).

cnf(f_183_3,plain,
    ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(U_329,U_328)) = hAPP_f22106695ol_nat(finite_card_nat,U_328)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_329),U_328))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_328)) ),
    inference(clausify,[status(thm)],[f_183_2]) ).

cnf(f_183_4,plain,
    ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(U_329,U_328)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,U_328))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_329),U_328))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_328)) ),
    inference(clausify,[status(thm)],[f_183_2]) ).

fof(f_184_1,plain,
    ! [X_2,A] :
      ( ( ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_2,A)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,A))
          | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) )
        & ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_2,A)) = hAPP_f921600141ol_nat(finite_card_pname,A)
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) ) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_102_card__insert__if]) ).

fof(f_184_2,plain,
    ! [U_331,U_330] :
      ( ( ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(U_331,U_330)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,U_330))
          | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_331),U_330)) )
        & ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(U_331,U_330)) = hAPP_f921600141ol_nat(finite_card_pname,U_330)
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_331),U_330)) ) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_330)) ),
    inference(variable_rename,[status(thm)],[f_184_1]) ).

cnf(f_184_3,plain,
    ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(U_331,U_330)) = hAPP_f921600141ol_nat(finite_card_pname,U_330)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_331),U_330))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_330)) ),
    inference(clausify,[status(thm)],[f_184_2]) ).

cnf(f_184_4,plain,
    ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(U_331,U_330)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,U_330))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_331),U_330))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_330)) ),
    inference(clausify,[status(thm)],[f_184_2]) ).

fof(f_185_1,plain,
    ! [X_2,A] :
      ( ( ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_2,A)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,A))
          | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) )
        & ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_2,A)) = hAPP_fun_a_bool_nat(finite_card_a,A)
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) ) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_103_card__insert__if]) ).

fof(f_185_2,plain,
    ! [U_333,U_332] :
      ( ( ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(U_333,U_332)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,U_332))
          | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_333),U_332)) )
        & ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(U_333,U_332)) = hAPP_fun_a_bool_nat(finite_card_a,U_332)
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_333),U_332)) ) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_332)) ),
    inference(variable_rename,[status(thm)],[f_185_1]) ).

cnf(f_185_3,plain,
    ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(U_333,U_332)) = hAPP_fun_a_bool_nat(finite_card_a,U_332)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_333),U_332))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_332)) ),
    inference(clausify,[status(thm)],[f_185_2]) ).

cnf(f_185_4,plain,
    ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(U_333,U_332)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,U_332))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_333),U_332))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_332)) ),
    inference(clausify,[status(thm)],[f_185_2]) ).

fof(f_186_1,plain,
    ! [X_2,A] :
      ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,A))
      | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_2),A))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_104_card__insert__disjoint]) ).

fof(f_186_2,plain,
    ! [U_335,U_334] :
      ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(U_335,U_334)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,U_334))
      | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_335),U_334))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_334)) ),
    inference(variable_rename,[status(thm)],[f_186_1]) ).

cnf(f_186_3,plain,
    ( hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(U_335,U_334)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,U_334))
    | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_335),U_334))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_334)) ),
    inference(clausify,[status(thm)],[f_186_2]) ).

fof(f_187_1,plain,
    ! [X_2,A] :
      ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,A))
      | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_105_card__insert__disjoint]) ).

fof(f_187_2,plain,
    ! [U_337,U_336] :
      ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(U_337,U_336)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,U_336))
      | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_337),U_336))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_336)) ),
    inference(variable_rename,[status(thm)],[f_187_1]) ).

cnf(f_187_3,plain,
    ( hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(U_337,U_336)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,U_336))
    | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_337),U_336))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_336)) ),
    inference(clausify,[status(thm)],[f_187_2]) ).

fof(f_188_1,plain,
    ! [X_2,A] :
      ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,A))
      | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_2),A))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_106_card__insert__disjoint]) ).

fof(f_188_2,plain,
    ! [U_339,U_338] :
      ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(U_339,U_338)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_338))
      | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_339),U_338))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_338)) ),
    inference(variable_rename,[status(thm)],[f_188_1]) ).

cnf(f_188_3,plain,
    ( hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(U_339,U_338)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_338))
    | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_339),U_338))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_338)) ),
    inference(clausify,[status(thm)],[f_188_2]) ).

fof(f_189_1,plain,
    ! [X_2,A] :
      ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_2,A)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,A))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_107_card__insert__disjoint]) ).

fof(f_189_2,plain,
    ! [U_341,U_340] :
      ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(U_341,U_340)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,U_340))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_341),U_340))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_340)) ),
    inference(variable_rename,[status(thm)],[f_189_1]) ).

cnf(f_189_3,plain,
    ( hAPP_f22106695ol_nat(finite_card_nat,insert_nat(U_341,U_340)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,U_340))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_341),U_340))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_340)) ),
    inference(clausify,[status(thm)],[f_189_2]) ).

fof(f_190_1,plain,
    ! [X_2,A] :
      ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_2,A)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,A))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_108_card__insert__disjoint]) ).

fof(f_190_2,plain,
    ! [U_343,U_342] :
      ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(U_343,U_342)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,U_342))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_343),U_342))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_342)) ),
    inference(variable_rename,[status(thm)],[f_190_1]) ).

cnf(f_190_3,plain,
    ( hAPP_f921600141ol_nat(finite_card_pname,insert_pname(U_343,U_342)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,U_342))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_343),U_342))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_342)) ),
    inference(clausify,[status(thm)],[f_190_2]) ).

fof(f_191_1,plain,
    ! [X_2,A] :
      ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_2,A)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,A))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_109_card__insert__disjoint]) ).

fof(f_191_2,plain,
    ! [U_345,U_344] :
      ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(U_345,U_344)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,U_344))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_345),U_344))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_344)) ),
    inference(variable_rename,[status(thm)],[f_191_1]) ).

cnf(f_191_3,plain,
    ( hAPP_fun_a_bool_nat(finite_card_a,insert_a(U_345,U_344)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,U_344))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_345),U_344))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_344)) ),
    inference(clausify,[status(thm)],[f_191_2]) ).

fof(f_192_1,plain,
    ! [Q_1,Pa] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,Pa),Q_1))))
      | ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Q_1)))
        & ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Pa))) ) ),
    inference(fof_nnf,[status(thm)],[fact_110_finite__Collect__conjI]) ).

fof(f_192_2,plain,
    ! [U_347,U_346] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,U_346),U_347))))
      | ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_347)))
        & ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_346))) ) ),
    inference(variable_rename,[status(thm)],[f_192_1]) ).

cnf(f_192_3,plain,
    ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_346)))
    | hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,U_346),U_347)))) ),
    inference(clausify,[status(thm)],[f_192_2]) ).

cnf(f_192_4,plain,
    ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_347)))
    | hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,U_346),U_347)))) ),
    inference(clausify,[status(thm)],[f_192_2]) ).

fof(f_193_1,plain,
    ! [Q_1,Pa] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,Pa),Q_1))))
      | ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1)))
        & ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Pa))) ) ),
    inference(fof_nnf,[status(thm)],[fact_111_finite__Collect__conjI]) ).

fof(f_193_2,plain,
    ! [U_349,U_348] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,U_348),U_349))))
      | ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_349)))
        & ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_348))) ) ),
    inference(variable_rename,[status(thm)],[f_193_1]) ).

cnf(f_193_3,plain,
    ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_348)))
    | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,U_348),U_349)))) ),
    inference(clausify,[status(thm)],[f_193_2]) ).

cnf(f_193_4,plain,
    ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_349)))
    | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,U_348),U_349)))) ),
    inference(clausify,[status(thm)],[f_193_2]) ).

fof(f_194_1,plain,
    ! [Q_1,Pa] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,Pa),Q_1))))
      | ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Q_1)))
        & ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Pa))) ) ),
    inference(fof_nnf,[status(thm)],[fact_112_finite__Collect__conjI]) ).

fof(f_194_2,plain,
    ! [U_351,U_350] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,U_350),U_351))))
      | ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_351)))
        & ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_350))) ) ),
    inference(variable_rename,[status(thm)],[f_194_1]) ).

cnf(f_194_3,plain,
    ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_350)))
    | hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,U_350),U_351)))) ),
    inference(clausify,[status(thm)],[f_194_2]) ).

cnf(f_194_4,plain,
    ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_351)))
    | hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,U_350),U_351)))) ),
    inference(clausify,[status(thm)],[f_194_2]) ).

fof(f_195_1,plain,
    ! [Q_1,Pa] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,Pa),Q_1))))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Q_1)))
        & ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Pa))) ) ),
    inference(fof_nnf,[status(thm)],[fact_113_finite__Collect__conjI]) ).

fof(f_195_2,plain,
    ! [U_353,U_352] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,U_352),U_353))))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_353)))
        & ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_352))) ) ),
    inference(variable_rename,[status(thm)],[f_195_1]) ).

cnf(f_195_3,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_352)))
    | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,U_352),U_353)))) ),
    inference(clausify,[status(thm)],[f_195_2]) ).

cnf(f_195_4,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_353)))
    | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,U_352),U_353)))) ),
    inference(clausify,[status(thm)],[f_195_2]) ).

fof(f_196_1,plain,
    ! [Q_1,Pa] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,Pa),Q_1))))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1)))
        & ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Pa))) ) ),
    inference(fof_nnf,[status(thm)],[fact_114_finite__Collect__conjI]) ).

fof(f_196_2,plain,
    ! [U_355,U_354] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,U_354),U_355))))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_355)))
        & ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_354))) ) ),
    inference(variable_rename,[status(thm)],[f_196_1]) ).

cnf(f_196_3,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_354)))
    | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,U_354),U_355)))) ),
    inference(clausify,[status(thm)],[f_196_2]) ).

cnf(f_196_4,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_355)))
    | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,U_354),U_355)))) ),
    inference(clausify,[status(thm)],[f_196_2]) ).

fof(f_197_1,plain,
    ! [Q_1,Pa] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,Pa),Q_1))))
      | ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_1)))
        & ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Pa))) ) ),
    inference(fof_nnf,[status(thm)],[fact_115_finite__Collect__conjI]) ).

fof(f_197_2,plain,
    ! [U_357,U_356] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,U_356),U_357))))
      | ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_357)))
        & ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_356))) ) ),
    inference(variable_rename,[status(thm)],[f_197_1]) ).

cnf(f_197_3,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_356)))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,U_356),U_357)))) ),
    inference(clausify,[status(thm)],[f_197_2]) ).

cnf(f_197_4,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_357)))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,U_356),U_357)))) ),
    inference(clausify,[status(thm)],[f_197_2]) ).

fof(f_198_1,plain,
    ! [N_1,M_2] :
      ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M_2)),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(M_2),N_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_2)) ),
    inference(fof_nnf,[status(thm)],[fact_116_Suc__diff__le]) ).

fof(f_198_2,plain,
    ! [U_359,U_358] :
      ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,U_358)),U_359) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(U_358),U_359))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_359),U_358)) ),
    inference(variable_rename,[status(thm)],[f_198_1]) ).

cnf(f_198_3,plain,
    ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,U_358)),U_359) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(U_358),U_359))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_359),U_358)) ),
    inference(clausify,[status(thm)],[f_198_2]) ).

fof(f_199_1,plain,
    ! [K] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),K)))),
    inference(fof_nnf,[status(thm)],[fact_117_finite__Collect__le__nat]) ).

fof(f_199_2,plain,
    ! [U_360] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),U_360)))),
    inference(variable_rename,[status(thm)],[f_199_1]) ).

cnf(f_199_3,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),U_360)))),
    inference(clausify,[status(thm)],[f_199_2]) ).

fof(f_200_1,plain,
    ! [Na] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),Na))) = hAPP_nat_nat(suc,Na),
    inference(fof_nnf,[status(thm)],[fact_118_card__Collect__le__nat]) ).

fof(f_200_2,plain,
    ! [U_361] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),U_361))) = hAPP_nat_nat(suc,U_361),
    inference(variable_rename,[status(thm)],[f_200_1]) ).

cnf(f_200_3,plain,
    hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),U_361))) = hAPP_nat_nat(suc,U_361),
    inference(clausify,[status(thm)],[f_200_2]) ).

fof(f_201_1,plain,
    ! [X,Y] :
      ( X = Y
      | hAPP_nat_nat(suc,X) != hAPP_nat_nat(suc,Y) ),
    inference(fof_nnf,[status(thm)],[fact_119_Suc__inject]) ).

fof(f_201_2,plain,
    ! [U_363,U_362] :
      ( U_363 = U_362
      | hAPP_nat_nat(suc,U_363) != hAPP_nat_nat(suc,U_362) ),
    inference(variable_rename,[status(thm)],[f_201_1]) ).

cnf(f_201_3,plain,
    ( U_363 = U_362
    | hAPP_nat_nat(suc,U_363) != hAPP_nat_nat(suc,U_362) ),
    inference(clausify,[status(thm)],[f_201_2]) ).

fof(f_202_1,plain,
    ! [Nat_1,Nat] :
      ( ( hAPP_nat_nat(suc,Nat_1) = hAPP_nat_nat(suc,Nat)
        | Nat_1 != Nat )
      & ( Nat_1 = Nat
        | hAPP_nat_nat(suc,Nat_1) != hAPP_nat_nat(suc,Nat) ) ),
    inference(fof_nnf,[status(thm)],[fact_120_nat_Oinject]) ).

fof(f_202_2,plain,
    ! [U_365,U_364] :
      ( ( hAPP_nat_nat(suc,U_365) = hAPP_nat_nat(suc,U_364)
        | U_365 != U_364 )
      & ( U_365 = U_364
        | hAPP_nat_nat(suc,U_365) != hAPP_nat_nat(suc,U_364) ) ),
    inference(variable_rename,[status(thm)],[f_202_1]) ).

fof(f_202_3,plain,
    ( ! [U_369,U_367] :
        ( hAPP_nat_nat(suc,U_369) = hAPP_nat_nat(suc,U_367)
        | U_369 != U_367 )
    & ! [U_368,U_366] :
        ( U_368 = U_366
        | hAPP_nat_nat(suc,U_368) != hAPP_nat_nat(suc,U_366) ) ),
    inference(miniscope,[status(thm)],[f_202_2]) ).

cnf(f_202_4,plain,
    ( U_368 = U_366
    | hAPP_nat_nat(suc,U_368) != hAPP_nat_nat(suc,U_366) ),
    inference(clausify,[status(thm)],[f_202_3]) ).

cnf(f_202_5,plain,
    ( hAPP_nat_nat(suc,U_369) = hAPP_nat_nat(suc,U_367)
    | U_369 != U_367 ),
    inference(clausify,[status(thm)],[f_202_3]) ).

fof(f_203_1,plain,
    ! [N_1] : hAPP_nat_nat(suc,N_1) != N_1,
    inference(fof_nnf,[status(thm)],[fact_121_Suc__n__not__n]) ).

fof(f_203_2,plain,
    ! [U_370] : hAPP_nat_nat(suc,U_370) != U_370,
    inference(variable_rename,[status(thm)],[f_203_1]) ).

cnf(f_203_3,plain,
    hAPP_nat_nat(suc,U_370) != U_370,
    inference(clausify,[status(thm)],[f_203_2]) ).

fof(f_204_1,plain,
    ! [N_1] : N_1 != hAPP_nat_nat(suc,N_1),
    inference(fof_nnf,[status(thm)],[fact_122_n__not__Suc__n]) ).

fof(f_204_2,plain,
    ! [U_371] : U_371 != hAPP_nat_nat(suc,U_371),
    inference(variable_rename,[status(thm)],[f_204_1]) ).

cnf(f_204_3,plain,
    U_371 != hAPP_nat_nat(suc,U_371),
    inference(clausify,[status(thm)],[f_204_2]) ).

fof(f_205_1,plain,
    ! [M_2,N_1] :
      ( M_2 = N_1
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_123_le__antisym]) ).

fof(f_205_2,plain,
    ! [U_373,U_372] :
      ( U_373 = U_372
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_372),U_373))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_373),U_372)) ),
    inference(variable_rename,[status(thm)],[f_205_1]) ).

cnf(f_205_3,plain,
    ( U_373 = U_372
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_372),U_373))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_373),U_372)) ),
    inference(clausify,[status(thm)],[f_205_2]) ).

fof(f_206_1,plain,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),K_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),K_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_124_le__trans]) ).

fof(f_206_2,plain,
    ! [U_376,U_375,U_374] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_375),U_376))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_374),U_376))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_375),U_374)) ),
    inference(variable_rename,[status(thm)],[f_206_1]) ).

cnf(f_206_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_375),U_376))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_374),U_376))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_375),U_374)) ),
    inference(clausify,[status(thm)],[f_206_2]) ).

fof(f_207_1,plain,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
      | M_2 != N_1 ),
    inference(fof_nnf,[status(thm)],[fact_125_eq__imp__le]) ).

fof(f_207_2,plain,
    ! [U_378,U_377] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_378),U_377))
      | U_378 != U_377 ),
    inference(variable_rename,[status(thm)],[f_207_1]) ).

cnf(f_207_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_378),U_377))
    | U_378 != U_377 ),
    inference(clausify,[status(thm)],[f_207_2]) ).

fof(f_208_1,plain,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_2))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_126_nat__le__linear]) ).

fof(f_208_2,plain,
    ! [U_380,U_379] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_379),U_380))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_380),U_379)) ),
    inference(variable_rename,[status(thm)],[f_208_1]) ).

cnf(f_208_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_379),U_380))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_380),U_379)) ),
    inference(clausify,[status(thm)],[f_208_2]) ).

fof(f_209_1,plain,
    ! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),N_1)),
    inference(fof_nnf,[status(thm)],[fact_127_le__refl]) ).

fof(f_209_2,plain,
    ! [U_381] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_381),U_381)),
    inference(variable_rename,[status(thm)],[f_209_1]) ).

cnf(f_209_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_381),U_381)),
    inference(clausify,[status(thm)],[f_209_2]) ).

fof(f_210_1,plain,
    ! [I_1,J,K_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I_1),J)),K_1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I_1),K_1)),J),
    inference(fof_nnf,[status(thm)],[fact_128_diff__commute]) ).

fof(f_210_2,plain,
    ! [U_384,U_383,U_382] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_384),U_383)),U_382) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_384),U_382)),U_383),
    inference(variable_rename,[status(thm)],[f_210_1]) ).

cnf(f_210_3,plain,
    hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_384),U_383)),U_382) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_384),U_382)),U_383),
    inference(clausify,[status(thm)],[f_210_2]) ).

fof(f_211_1,plain,
    ! [Pa,Q_1] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,Pa),Q_1))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Pa))) )
      & ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1)))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Pa))) )
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,Pa),Q_1)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_129_finite__Collect__disjI]) ).

fof(f_211_2,plain,
    ! [U_386,U_385] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_386),U_385))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_385)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_386))) )
      & ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_385)))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_386))) )
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_386),U_385)))) ) ),
    inference(variable_rename,[status(thm)],[f_211_1]) ).

fof(f_211_3,plain,
    ( ! [U_390,U_388] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_390),U_388))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_388)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_390))) )
    & ! [U_389,U_387] :
        ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_387)))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_389))) )
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_389),U_387)))) ) ),
    inference(miniscope,[status(thm)],[f_211_2]) ).

cnf(f_211_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_389)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_389),U_387)))) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_387)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_389),U_387)))) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

cnf(f_211_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_390),U_388))))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_388)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_390))) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

fof(f_212_1,plain,
    ! [Pa,Q_1] :
      ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,Pa),Q_1))))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Q_1)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Pa))) )
      & ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Q_1)))
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Pa))) )
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,Pa),Q_1)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_130_finite__Collect__disjI]) ).

fof(f_212_2,plain,
    ! [U_392,U_391] :
      ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,U_392),U_391))))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_391)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_392))) )
      & ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_391)))
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_392))) )
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,U_392),U_391)))) ) ),
    inference(variable_rename,[status(thm)],[f_212_1]) ).

fof(f_212_3,plain,
    ( ! [U_396,U_394] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,U_396),U_394))))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_394)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_396))) )
    & ! [U_395,U_393] :
        ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_393)))
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_395))) )
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,U_395),U_393)))) ) ),
    inference(miniscope,[status(thm)],[f_212_2]) ).

cnf(f_212_4,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_395)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,U_395),U_393)))) ),
    inference(clausify,[status(thm)],[f_212_3]) ).

cnf(f_212_5,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_393)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,U_395),U_393)))) ),
    inference(clausify,[status(thm)],[f_212_3]) ).

cnf(f_212_6,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,U_396),U_394))))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_394)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_396))) ),
    inference(clausify,[status(thm)],[f_212_3]) ).

fof(f_213_1,plain,
    ! [Pa,Q_1] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,Pa),Q_1))))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Pa))) )
      & ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1)))
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Pa))) )
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,Pa),Q_1)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_131_finite__Collect__disjI]) ).

fof(f_213_2,plain,
    ! [U_398,U_397] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_398),U_397))))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_397)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_398))) )
      & ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_397)))
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_398))) )
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_398),U_397)))) ) ),
    inference(variable_rename,[status(thm)],[f_213_1]) ).

fof(f_213_3,plain,
    ( ! [U_402,U_400] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_402),U_400))))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_400)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_402))) )
    & ! [U_401,U_399] :
        ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_399)))
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_401))) )
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_401),U_399)))) ) ),
    inference(miniscope,[status(thm)],[f_213_2]) ).

cnf(f_213_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_401)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_401),U_399)))) ),
    inference(clausify,[status(thm)],[f_213_3]) ).

cnf(f_213_5,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_399)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_401),U_399)))) ),
    inference(clausify,[status(thm)],[f_213_3]) ).

cnf(f_213_6,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_402),U_400))))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_400)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_402))) ),
    inference(clausify,[status(thm)],[f_213_3]) ).

fof(f_214_1,plain,
    ! [Pa,Q_1] :
      ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,Pa),Q_1))))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Q_1)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Pa))) )
      & ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Q_1)))
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Pa))) )
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,Pa),Q_1)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_132_finite__Collect__disjI]) ).

fof(f_214_2,plain,
    ! [U_404,U_403] :
      ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,U_404),U_403))))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_403)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_404))) )
      & ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_403)))
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_404))) )
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,U_404),U_403)))) ) ),
    inference(variable_rename,[status(thm)],[f_214_1]) ).

fof(f_214_3,plain,
    ( ! [U_408,U_406] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,U_408),U_406))))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_406)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_408))) )
    & ! [U_407,U_405] :
        ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_405)))
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_407))) )
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,U_407),U_405)))) ) ),
    inference(miniscope,[status(thm)],[f_214_2]) ).

cnf(f_214_4,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_407)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,U_407),U_405)))) ),
    inference(clausify,[status(thm)],[f_214_3]) ).

cnf(f_214_5,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_405)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,U_407),U_405)))) ),
    inference(clausify,[status(thm)],[f_214_3]) ).

cnf(f_214_6,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,U_408),U_406))))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_406)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_408))) ),
    inference(clausify,[status(thm)],[f_214_3]) ).

fof(f_215_1,plain,
    ! [Pa,Q_1] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,Pa),Q_1))))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_1)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Pa))) )
      & ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_1)))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Pa))) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,Pa),Q_1)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_133_finite__Collect__disjI]) ).

fof(f_215_2,plain,
    ! [U_410,U_409] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,U_410),U_409))))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_409)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_410))) )
      & ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_409)))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_410))) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,U_410),U_409)))) ) ),
    inference(variable_rename,[status(thm)],[f_215_1]) ).

fof(f_215_3,plain,
    ( ! [U_414,U_412] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,U_414),U_412))))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_412)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_414))) )
    & ! [U_413,U_411] :
        ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_411)))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_413))) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,U_413),U_411)))) ) ),
    inference(miniscope,[status(thm)],[f_215_2]) ).

cnf(f_215_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_413)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,U_413),U_411)))) ),
    inference(clausify,[status(thm)],[f_215_3]) ).

cnf(f_215_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_411)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,U_413),U_411)))) ),
    inference(clausify,[status(thm)],[f_215_3]) ).

cnf(f_215_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,U_414),U_412))))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_412)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_414))) ),
    inference(clausify,[status(thm)],[f_215_3]) ).

fof(f_216_1,plain,
    ! [Pa,Q_1] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,Pa),Q_1))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Q_1)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Pa))) )
      & ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Q_1)))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Pa))) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,Pa),Q_1)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_134_finite__Collect__disjI]) ).

fof(f_216_2,plain,
    ! [U_416,U_415] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,U_416),U_415))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_415)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_416))) )
      & ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_415)))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_416))) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,U_416),U_415)))) ) ),
    inference(variable_rename,[status(thm)],[f_216_1]) ).

fof(f_216_3,plain,
    ( ! [U_420,U_418] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,U_420),U_418))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_418)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_420))) )
    & ! [U_419,U_417] :
        ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_417)))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_419))) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,U_419),U_417)))) ) ),
    inference(miniscope,[status(thm)],[f_216_2]) ).

cnf(f_216_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_419)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,U_419),U_417)))) ),
    inference(clausify,[status(thm)],[f_216_3]) ).

cnf(f_216_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_417)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,U_419),U_417)))) ),
    inference(clausify,[status(thm)],[f_216_3]) ).

cnf(f_216_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,U_420),U_418))))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_418)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_420))) ),
    inference(clausify,[status(thm)],[f_216_3]) ).

fof(f_217_1,plain,
    ! [A_1,A] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(A_1,A)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) )
      & ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(A_1,A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_135_finite__insert]) ).

fof(f_217_2,plain,
    ! [U_422,U_421] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(U_422,U_421)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_421)) )
      & ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_421))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(U_422,U_421))) ) ),
    inference(variable_rename,[status(thm)],[f_217_1]) ).

fof(f_217_3,plain,
    ( ! [U_426,U_424] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(U_426,U_424)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_424)) )
    & ! [U_425,U_423] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_423))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(U_425,U_423))) ) ),
    inference(miniscope,[status(thm)],[f_217_2]) ).

cnf(f_217_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_423))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(U_425,U_423))) ),
    inference(clausify,[status(thm)],[f_217_3]) ).

cnf(f_217_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(U_426,U_424)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_424)) ),
    inference(clausify,[status(thm)],[f_217_3]) ).

fof(f_218_1,plain,
    ! [A_1,A] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_1,A)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) )
      & ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_1,A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_136_finite__insert]) ).

fof(f_218_2,plain,
    ! [U_428,U_427] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_428,U_427)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_427)) )
      & ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_427))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_428,U_427))) ) ),
    inference(variable_rename,[status(thm)],[f_218_1]) ).

fof(f_218_3,plain,
    ( ! [U_432,U_430] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_432,U_430)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_430)) )
    & ! [U_431,U_429] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_429))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_431,U_429))) ) ),
    inference(miniscope,[status(thm)],[f_218_2]) ).

cnf(f_218_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_429))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_431,U_429))) ),
    inference(clausify,[status(thm)],[f_218_3]) ).

cnf(f_218_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(U_432,U_430)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_430)) ),
    inference(clausify,[status(thm)],[f_218_3]) ).

fof(f_219_1,plain,
    ! [A_1,A] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(A_1,A)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) )
      & ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(A_1,A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_137_finite__insert]) ).

fof(f_219_2,plain,
    ! [U_434,U_433] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(U_434,U_433)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_433)) )
      & ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_433))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(U_434,U_433))) ) ),
    inference(variable_rename,[status(thm)],[f_219_1]) ).

fof(f_219_3,plain,
    ( ! [U_438,U_436] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(U_438,U_436)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_436)) )
    & ! [U_437,U_435] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_435))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(U_437,U_435))) ) ),
    inference(miniscope,[status(thm)],[f_219_2]) ).

cnf(f_219_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_435))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(U_437,U_435))) ),
    inference(clausify,[status(thm)],[f_219_3]) ).

cnf(f_219_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(U_438,U_436)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_436)) ),
    inference(clausify,[status(thm)],[f_219_3]) ).

fof(f_220_1,plain,
    ! [A_1,A] :
      ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(A_1,A)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) )
      & ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(A_1,A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_138_finite__insert]) ).

fof(f_220_2,plain,
    ! [U_440,U_439] :
      ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(U_440,U_439)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_439)) )
      & ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_439))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(U_440,U_439))) ) ),
    inference(variable_rename,[status(thm)],[f_220_1]) ).

fof(f_220_3,plain,
    ( ! [U_444,U_442] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(U_444,U_442)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_442)) )
    & ! [U_443,U_441] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_441))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(U_443,U_441))) ) ),
    inference(miniscope,[status(thm)],[f_220_2]) ).

cnf(f_220_4,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_441))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(U_443,U_441))) ),
    inference(clausify,[status(thm)],[f_220_3]) ).

cnf(f_220_5,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(U_444,U_442)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_442)) ),
    inference(clausify,[status(thm)],[f_220_3]) ).

fof(f_221_1,plain,
    ! [A_1,A] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_1,A)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) )
      & ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_1,A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_139_finite__insert]) ).

fof(f_221_2,plain,
    ! [U_446,U_445] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_446,U_445)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_445)) )
      & ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_445))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_446,U_445))) ) ),
    inference(variable_rename,[status(thm)],[f_221_1]) ).

fof(f_221_3,plain,
    ( ! [U_450,U_448] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_450,U_448)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_448)) )
    & ! [U_449,U_447] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_447))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_449,U_447))) ) ),
    inference(miniscope,[status(thm)],[f_221_2]) ).

cnf(f_221_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_447))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_449,U_447))) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_5,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(U_450,U_448)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_448)) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

fof(f_222_1,plain,
    ! [A_1,A] :
      ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(A_1,A)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) )
      & ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(A_1,A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_140_finite__insert]) ).

fof(f_222_2,plain,
    ! [U_452,U_451] :
      ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(U_452,U_451)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_451)) )
      & ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_451))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(U_452,U_451))) ) ),
    inference(variable_rename,[status(thm)],[f_222_1]) ).

fof(f_222_3,plain,
    ( ! [U_456,U_454] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(U_456,U_454)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_454)) )
    & ! [U_455,U_453] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_453))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(U_455,U_453))) ) ),
    inference(miniscope,[status(thm)],[f_222_2]) ).

cnf(f_222_4,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_453))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(U_455,U_453))) ),
    inference(clausify,[status(thm)],[f_222_3]) ).

cnf(f_222_5,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(U_456,U_454)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_454)) ),
    inference(clausify,[status(thm)],[f_222_3]) ).

fof(f_223_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_141_finite__subset]) ).

fof(f_223_2,plain,
    ! [U_458,U_457] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_458))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_457))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_458),U_457)) ),
    inference(variable_rename,[status(thm)],[f_223_1]) ).

cnf(f_223_3,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_458))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_457))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_458),U_457)) ),
    inference(clausify,[status(thm)],[f_223_2]) ).

fof(f_224_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_142_finite__subset]) ).

fof(f_224_2,plain,
    ! [U_460,U_459] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_460))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_459))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_460),U_459)) ),
    inference(variable_rename,[status(thm)],[f_224_1]) ).

cnf(f_224_3,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_460))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_459))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_460),U_459)) ),
    inference(clausify,[status(thm)],[f_224_2]) ).

fof(f_225_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_143_finite__subset]) ).

fof(f_225_2,plain,
    ! [U_462,U_461] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_462))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_461))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_462),U_461)) ),
    inference(variable_rename,[status(thm)],[f_225_1]) ).

cnf(f_225_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_462))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_461))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_462),U_461)) ),
    inference(clausify,[status(thm)],[f_225_2]) ).

fof(f_226_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_144_finite__subset]) ).

fof(f_226_2,plain,
    ! [U_464,U_463] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_464))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_463))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_464),U_463)) ),
    inference(variable_rename,[status(thm)],[f_226_1]) ).

cnf(f_226_3,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_464))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_463))
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_464),U_463)) ),
    inference(clausify,[status(thm)],[f_226_2]) ).

fof(f_227_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_145_finite__subset]) ).

fof(f_227_2,plain,
    ! [U_466,U_465] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_466))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_465))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_466),U_465)) ),
    inference(variable_rename,[status(thm)],[f_227_1]) ).

cnf(f_227_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_466))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_465))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_466),U_465)) ),
    inference(clausify,[status(thm)],[f_227_2]) ).

fof(f_228_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_146_finite__subset]) ).

fof(f_228_2,plain,
    ! [U_468,U_467] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_468))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_467))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_468),U_467)) ),
    inference(variable_rename,[status(thm)],[f_228_1]) ).

cnf(f_228_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_468))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_467))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_468),U_467)) ),
    inference(clausify,[status(thm)],[f_228_2]) ).

fof(f_229_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A),B))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B)) ),
    inference(fof_nnf,[status(thm)],[fact_147_rev__finite__subset]) ).

fof(f_229_2,plain,
    ! [U_470,U_469] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_470))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_470),U_469))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_469)) ),
    inference(variable_rename,[status(thm)],[f_229_1]) ).

cnf(f_229_3,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_470))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_470),U_469))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_469)) ),
    inference(clausify,[status(thm)],[f_229_2]) ).

fof(f_230_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) ),
    inference(fof_nnf,[status(thm)],[fact_148_rev__finite__subset]) ).

fof(f_230_2,plain,
    ! [U_472,U_471] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_472))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_472),U_471))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_471)) ),
    inference(variable_rename,[status(thm)],[f_230_1]) ).

cnf(f_230_3,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_472))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_472),U_471))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_471)) ),
    inference(clausify,[status(thm)],[f_230_2]) ).

fof(f_231_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) ),
    inference(fof_nnf,[status(thm)],[fact_149_rev__finite__subset]) ).

fof(f_231_2,plain,
    ! [U_474,U_473] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_474))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_474),U_473))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_473)) ),
    inference(variable_rename,[status(thm)],[f_231_1]) ).

cnf(f_231_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_474))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_474),U_473))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_473)) ),
    inference(clausify,[status(thm)],[f_231_2]) ).

fof(f_232_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A),B))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B)) ),
    inference(fof_nnf,[status(thm)],[fact_150_rev__finite__subset]) ).

fof(f_232_2,plain,
    ! [U_476,U_475] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_476))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_476),U_475))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_475)) ),
    inference(variable_rename,[status(thm)],[f_232_1]) ).

cnf(f_232_3,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_476))
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_476),U_475))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_475)) ),
    inference(clausify,[status(thm)],[f_232_2]) ).

fof(f_233_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) ),
    inference(fof_nnf,[status(thm)],[fact_151_rev__finite__subset]) ).

fof(f_233_2,plain,
    ! [U_478,U_477] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_478))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_478),U_477))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_477)) ),
    inference(variable_rename,[status(thm)],[f_233_1]) ).

cnf(f_233_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_478))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_478),U_477))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_477)) ),
    inference(clausify,[status(thm)],[f_233_2]) ).

fof(f_234_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ),
    inference(fof_nnf,[status(thm)],[fact_152_rev__finite__subset]) ).

fof(f_234_2,plain,
    ! [U_480,U_479] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_480))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_480),U_479))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_479)) ),
    inference(variable_rename,[status(thm)],[f_234_1]) ).

cnf(f_234_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_480))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_480),U_479))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_479)) ),
    inference(clausify,[status(thm)],[f_234_2]) ).

fof(f_235_1,plain,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_153_Suc__leD]) ).

fof(f_235_2,plain,
    ! [U_482,U_481] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_482),U_481))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_482)),U_481)) ),
    inference(variable_rename,[status(thm)],[f_235_1]) ).

cnf(f_235_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_482),U_481))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_482)),U_481)) ),
    inference(clausify,[status(thm)],[f_235_2]) ).

fof(f_236_1,plain,
    ! [M_2,N_1] :
      ( M_2 = hAPP_nat_nat(suc,N_1)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_1))) ),
    inference(fof_nnf,[status(thm)],[fact_154_le__SucE]) ).

fof(f_236_2,plain,
    ! [U_484,U_483] :
      ( U_484 = hAPP_nat_nat(suc,U_483)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_484),U_483))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_484),hAPP_nat_nat(suc,U_483))) ),
    inference(variable_rename,[status(thm)],[f_236_1]) ).

cnf(f_236_3,plain,
    ( U_484 = hAPP_nat_nat(suc,U_483)
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_484),U_483))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_484),hAPP_nat_nat(suc,U_483))) ),
    inference(clausify,[status(thm)],[f_236_2]) ).

fof(f_237_1,plain,
    ! [M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_155_le__SucI]) ).

fof(f_237_2,plain,
    ! [U_486,U_485] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_486),hAPP_nat_nat(suc,U_485)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_486),U_485)) ),
    inference(variable_rename,[status(thm)],[f_237_1]) ).

cnf(f_237_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_486),hAPP_nat_nat(suc,U_485)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_486),U_485)) ),
    inference(clausify,[status(thm)],[f_237_2]) ).

fof(f_238_1,plain,
    ! [Na,M_3] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M_3)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M_3)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M_3))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M_3))) ) ),
    inference(fof_nnf,[status(thm)],[fact_156_Suc__le__mono]) ).

fof(f_238_2,plain,
    ! [U_488,U_487] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_488)),hAPP_nat_nat(suc,U_487)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_488),U_487)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_488),U_487))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_488)),hAPP_nat_nat(suc,U_487))) ) ),
    inference(variable_rename,[status(thm)],[f_238_1]) ).

fof(f_238_3,plain,
    ( ! [U_492,U_490] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_492)),hAPP_nat_nat(suc,U_490)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_492),U_490)) )
    & ! [U_491,U_489] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_491),U_489))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_491)),hAPP_nat_nat(suc,U_489))) ) ),
    inference(miniscope,[status(thm)],[f_238_2]) ).

cnf(f_238_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_491),U_489))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_491)),hAPP_nat_nat(suc,U_489))) ),
    inference(clausify,[status(thm)],[f_238_3]) ).

cnf(f_238_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_492)),hAPP_nat_nat(suc,U_490)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_492),U_490)) ),
    inference(clausify,[status(thm)],[f_238_3]) ).

fof(f_239_1,plain,
    ! [M_3,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_3),hAPP_nat_nat(suc,Na)))
        | ( M_3 != hAPP_nat_nat(suc,Na)
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_3),Na)) ) )
      & ( M_3 = hAPP_nat_nat(suc,Na)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_3),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_3),hAPP_nat_nat(suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_157_le__Suc__eq]) ).

fof(f_239_2,plain,
    ! [U_494,U_493] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_494),hAPP_nat_nat(suc,U_493)))
        | ( U_494 != hAPP_nat_nat(suc,U_493)
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_494),U_493)) ) )
      & ( U_494 = hAPP_nat_nat(suc,U_493)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_494),U_493))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_494),hAPP_nat_nat(suc,U_493))) ) ),
    inference(variable_rename,[status(thm)],[f_239_1]) ).

fof(f_239_3,plain,
    ( ! [U_498,U_496] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_498),hAPP_nat_nat(suc,U_496)))
        | ( U_498 != hAPP_nat_nat(suc,U_496)
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_498),U_496)) ) )
    & ! [U_497,U_495] :
        ( U_497 = hAPP_nat_nat(suc,U_495)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_497),U_495))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_497),hAPP_nat_nat(suc,U_495))) ) ),
    inference(miniscope,[status(thm)],[f_239_2]) ).

cnf(f_239_4,plain,
    ( U_497 = hAPP_nat_nat(suc,U_495)
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_497),U_495))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_497),hAPP_nat_nat(suc,U_495))) ),
    inference(clausify,[status(thm)],[f_239_3]) ).

cnf(f_239_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_498),U_496))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_498),hAPP_nat_nat(suc,U_496))) ),
    inference(clausify,[status(thm)],[f_239_3]) ).

cnf(f_239_6,plain,
    ( U_498 != hAPP_nat_nat(suc,U_496)
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_498),hAPP_nat_nat(suc,U_496))) ),
    inference(clausify,[status(thm)],[f_239_3]) ).

fof(f_240_1,plain,
    ! [M_3,Na] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_3),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_3)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_3))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_3),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_158_not__less__eq__eq]) ).

fof(f_240_2,plain,
    ! [U_500,U_499] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_500),U_499))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_499)),U_500)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_499)),U_500))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_500),U_499)) ) ),
    inference(variable_rename,[status(thm)],[f_240_1]) ).

fof(f_240_3,plain,
    ( ! [U_504,U_502] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_504),U_502))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_502)),U_504)) )
    & ! [U_503,U_501] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_501)),U_503))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_503),U_501)) ) ),
    inference(miniscope,[status(thm)],[f_240_2]) ).

cnf(f_240_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_501)),U_503))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_503),U_501)) ),
    inference(clausify,[status(thm)],[f_240_3]) ).

cnf(f_240_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_504),U_502))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_502)),U_504)) ),
    inference(clausify,[status(thm)],[f_240_3]) ).

fof(f_241_1,plain,
    ! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),N_1)),
    inference(fof_nnf,[status(thm)],[fact_159_Suc__n__not__le__n]) ).

fof(f_241_2,plain,
    ! [U_505] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_505)),U_505)),
    inference(variable_rename,[status(thm)],[f_241_1]) ).

cnf(f_241_3,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_505)),U_505)),
    inference(clausify,[status(thm)],[f_241_2]) ).

fof(f_242_1,plain,
    ! [M_2,N_1,K_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M_2)),N_1)),hAPP_nat_nat(suc,K_1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M_2),N_1)),K_1),
    inference(fof_nnf,[status(thm)],[fact_160_Suc__diff__diff]) ).

fof(f_242_2,plain,
    ! [U_508,U_507,U_506] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,U_508)),U_507)),hAPP_nat_nat(suc,U_506)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_508),U_507)),U_506),
    inference(variable_rename,[status(thm)],[f_242_1]) ).

cnf(f_242_3,plain,
    hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,U_508)),U_507)),hAPP_nat_nat(suc,U_506)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_508),U_507)),U_506),
    inference(clausify,[status(thm)],[f_242_2]) ).

fof(f_243_1,plain,
    ! [M_2,N_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(minus_minus_nat(M_2),N_1),
    inference(fof_nnf,[status(thm)],[fact_161_diff__Suc__Suc]) ).

fof(f_243_2,plain,
    ! [U_510,U_509] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,U_510)),hAPP_nat_nat(suc,U_509)) = hAPP_nat_nat(minus_minus_nat(U_510),U_509),
    inference(variable_rename,[status(thm)],[f_243_1]) ).

cnf(f_243_3,plain,
    hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,U_510)),hAPP_nat_nat(suc,U_509)) = hAPP_nat_nat(minus_minus_nat(U_510),U_509),
    inference(clausify,[status(thm)],[f_243_2]) ).

fof(f_244_1,plain,
    ! [Na,K,M_3] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M_3),K)),hAPP_nat_nat(minus_minus_nat(Na),K)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_3),Na)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_3),Na))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M_3),K)),hAPP_nat_nat(minus_minus_nat(Na),K))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),Na))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M_3)) ),
    inference(fof_nnf,[status(thm)],[fact_162_le__diff__iff]) ).

fof(f_244_2,plain,
    ! [U_513,U_512,U_511] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_511),U_512)),hAPP_nat_nat(minus_minus_nat(U_513),U_512)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_511),U_513)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_511),U_513))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_511),U_512)),hAPP_nat_nat(minus_minus_nat(U_513),U_512))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_512),U_513))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_512),U_511)) ),
    inference(variable_rename,[status(thm)],[f_244_1]) ).

cnf(f_244_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_511),U_513))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_511),U_512)),hAPP_nat_nat(minus_minus_nat(U_513),U_512)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_512),U_513))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_512),U_511)) ),
    inference(clausify,[status(thm)],[f_244_2]) ).

cnf(f_244_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_511),U_512)),hAPP_nat_nat(minus_minus_nat(U_513),U_512)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_511),U_513))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_512),U_513))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_512),U_511)) ),
    inference(clausify,[status(thm)],[f_244_2]) ).

fof(f_245_1,plain,
    ! [N_1,K_1,M_2] :
      ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M_2),K_1)),hAPP_nat_nat(minus_minus_nat(N_1),K_1)) = hAPP_nat_nat(minus_minus_nat(M_2),N_1)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M_2)) ),
    inference(fof_nnf,[status(thm)],[fact_163_Nat_Odiff__diff__eq]) ).

fof(f_245_2,plain,
    ! [U_516,U_515,U_514] :
      ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_514),U_515)),hAPP_nat_nat(minus_minus_nat(U_516),U_515)) = hAPP_nat_nat(minus_minus_nat(U_514),U_516)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_515),U_516))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_515),U_514)) ),
    inference(variable_rename,[status(thm)],[f_245_1]) ).

cnf(f_245_3,plain,
    ( hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(U_514),U_515)),hAPP_nat_nat(minus_minus_nat(U_516),U_515)) = hAPP_nat_nat(minus_minus_nat(U_514),U_516)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_515),U_516))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_515),U_514)) ),
    inference(clausify,[status(thm)],[f_245_2]) ).

fof(f_246_1,plain,
    ! [Na,K,M_3] :
      ( ( ( hAPP_nat_nat(minus_minus_nat(M_3),K) = hAPP_nat_nat(minus_minus_nat(Na),K)
          | M_3 != Na )
        & ( M_3 = Na
          | hAPP_nat_nat(minus_minus_nat(M_3),K) != hAPP_nat_nat(minus_minus_nat(Na),K) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),Na))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M_3)) ),
    inference(fof_nnf,[status(thm)],[fact_164_eq__diff__iff]) ).

fof(f_246_2,plain,
    ! [U_519,U_518,U_517] :
      ( ( ( hAPP_nat_nat(minus_minus_nat(U_517),U_518) = hAPP_nat_nat(minus_minus_nat(U_519),U_518)
          | U_517 != U_519 )
        & ( U_517 = U_519
          | hAPP_nat_nat(minus_minus_nat(U_517),U_518) != hAPP_nat_nat(minus_minus_nat(U_519),U_518) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_518),U_519))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_518),U_517)) ),
    inference(variable_rename,[status(thm)],[f_246_1]) ).

cnf(f_246_3,plain,
    ( U_517 = U_519
    | hAPP_nat_nat(minus_minus_nat(U_517),U_518) != hAPP_nat_nat(minus_minus_nat(U_519),U_518)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_518),U_519))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_518),U_517)) ),
    inference(clausify,[status(thm)],[f_246_2]) ).

cnf(f_246_4,plain,
    ( hAPP_nat_nat(minus_minus_nat(U_517),U_518) = hAPP_nat_nat(minus_minus_nat(U_519),U_518)
    | U_517 != U_519
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_518),U_519))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_518),U_517)) ),
    inference(clausify,[status(thm)],[f_246_2]) ).

fof(f_247_1,plain,
    ! [I_1,N_1] :
      ( hAPP_nat_nat(minus_minus_nat(N_1),hAPP_nat_nat(minus_minus_nat(N_1),I_1)) = I_1
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_165_diff__diff__cancel]) ).

fof(f_247_2,plain,
    ! [U_521,U_520] :
      ( hAPP_nat_nat(minus_minus_nat(U_520),hAPP_nat_nat(minus_minus_nat(U_520),U_521)) = U_521
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_521),U_520)) ),
    inference(variable_rename,[status(thm)],[f_247_1]) ).

cnf(f_247_3,plain,
    ( hAPP_nat_nat(minus_minus_nat(U_520),hAPP_nat_nat(minus_minus_nat(U_520),U_521)) = U_521
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_521),U_520)) ),
    inference(clausify,[status(thm)],[f_247_2]) ).

fof(f_248_1,plain,
    ! [L,M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M_2),L)),hAPP_nat_nat(minus_minus_nat(N_1),L)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_166_diff__le__mono]) ).

fof(f_248_2,plain,
    ! [U_524,U_523,U_522] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_523),U_524)),hAPP_nat_nat(minus_minus_nat(U_522),U_524)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_523),U_522)) ),
    inference(variable_rename,[status(thm)],[f_248_1]) ).

cnf(f_248_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_523),U_524)),hAPP_nat_nat(minus_minus_nat(U_522),U_524)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_523),U_522)) ),
    inference(clausify,[status(thm)],[f_248_2]) ).

fof(f_249_1,plain,
    ! [L,M_2,N_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(L),N_1)),hAPP_nat_nat(minus_minus_nat(L),M_2)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ),
    inference(fof_nnf,[status(thm)],[fact_167_diff__le__mono2]) ).

fof(f_249_2,plain,
    ! [U_527,U_526,U_525] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_527),U_525)),hAPP_nat_nat(minus_minus_nat(U_527),U_526)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_526),U_525)) ),
    inference(variable_rename,[status(thm)],[f_249_1]) ).

cnf(f_249_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_527),U_525)),hAPP_nat_nat(minus_minus_nat(U_527),U_526)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_526),U_525)) ),
    inference(clausify,[status(thm)],[f_249_2]) ).

fof(f_250_1,plain,
    ! [M_2,N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M_2),N_1)),M_2)),
    inference(fof_nnf,[status(thm)],[fact_168_diff__le__self]) ).

fof(f_250_2,plain,
    ! [U_529,U_528] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_529),U_528)),U_529)),
    inference(variable_rename,[status(thm)],[f_250_1]) ).

cnf(f_250_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(U_529),U_528)),U_529)),
    inference(clausify,[status(thm)],[f_250_2]) ).

fof(f_251_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_pname_a(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_169_finite__surj]) ).

fof(f_251_2,plain,
    ! [U_532,U_531,U_530] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_532))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_532),image_pname_a(U_531,U_530)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_530)) ),
    inference(variable_rename,[status(thm)],[f_251_1]) ).

cnf(f_251_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_532))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_532),image_pname_a(U_531,U_530)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_530)) ),
    inference(clausify,[status(thm)],[f_251_2]) ).

fof(f_252_1,plain,
    ! [F,A,B] :
      ( ? [C_2] :
          ( B = image_pname_a(F,C_2)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_2))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_2),A))
          & is_fun_pname_bool(C_2) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_pname_a(F,A)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))
      | ~ is_fun_a_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_170_finite__subset__image]) ).

fof(f_252_2,plain,
    ! [U_536,U_535,U_534] :
      ( ? [U_533] :
          ( U_534 = image_pname_a(U_536,U_533)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_533))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_533),U_535))
          & is_fun_pname_bool(U_533) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_534),image_pname_a(U_536,U_535)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_534))
      | ~ is_fun_a_bool(U_534) ),
    inference(variable_rename,[status(thm)],[f_252_1]) ).

fof(f_252_3,plain,
    ! [U_536,U_535,U_534] :
      ( ( U_534 = image_pname_a(U_536,sK1(U_536,U_535,U_534))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK1(U_536,U_535,U_534)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK1(U_536,U_535,U_534)),U_535))
        & is_fun_pname_bool(sK1(U_536,U_535,U_534)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_534),image_pname_a(U_536,U_535)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_534))
      | ~ is_fun_a_bool(U_534) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_533,sK1(U_536,U_535,U_534))],[f_252_2]) ).

cnf(f_252_4,plain,
    ( is_fun_pname_bool(sK1(U_536,U_535,U_534))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_534),image_pname_a(U_536,U_535)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_534))
    | ~ is_fun_a_bool(U_534) ),
    inference(clausify,[status(thm)],[f_252_3]) ).

cnf(f_252_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK1(U_536,U_535,U_534)),U_535))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_534),image_pname_a(U_536,U_535)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_534))
    | ~ is_fun_a_bool(U_534) ),
    inference(clausify,[status(thm)],[f_252_3]) ).

cnf(f_252_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK1(U_536,U_535,U_534)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_534),image_pname_a(U_536,U_535)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_534))
    | ~ is_fun_a_bool(U_534) ),
    inference(clausify,[status(thm)],[f_252_3]) ).

cnf(f_252_7,plain,
    ( U_534 = image_pname_a(U_536,sK1(U_536,U_535,U_534))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_534),image_pname_a(U_536,U_535)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_534))
    | ~ is_fun_a_bool(U_534) ),
    inference(clausify,[status(thm)],[f_252_3]) ).

fof(f_253_1,plain,
    ! [Na,N_3,F] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,Na)),hAPP_n1699378549t_bool(F,N_3)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
      | ? [N_2] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,N_2)),hAPP_n1699378549t_bool(F,hAPP_nat_nat(suc,N_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_171_lift__Suc__mono__le]) ).

fof(f_253_2,plain,
    ! [U_540,U_539,U_538] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_538,U_540)),hAPP_n1699378549t_bool(U_538,U_539)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_540),U_539))
      | ? [U_537] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_538,U_537)),hAPP_n1699378549t_bool(U_538,hAPP_nat_nat(suc,U_537)))) ),
    inference(variable_rename,[status(thm)],[f_253_1]) ).

fof(f_253_3,plain,
    ! [U_540,U_539,U_538] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_538,U_540)),hAPP_n1699378549t_bool(U_538,U_539)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_540),U_539))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_538,sK2(U_540,U_539,U_538))),hAPP_n1699378549t_bool(U_538,hAPP_nat_nat(suc,sK2(U_540,U_539,U_538))))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_537,sK2(U_540,U_539,U_538))],[f_253_2]) ).

cnf(f_253_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_538,U_540)),hAPP_n1699378549t_bool(U_538,U_539)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_540),U_539))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_538,sK2(U_540,U_539,U_538))),hAPP_n1699378549t_bool(U_538,hAPP_nat_nat(suc,sK2(U_540,U_539,U_538))))) ),
    inference(clausify,[status(thm)],[f_253_3]) ).

fof(f_254_1,plain,
    ! [Na,N_3,F] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(F,Na)),hAPP_n1025906991e_bool(F,N_3)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
      | ? [N_2] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(F,N_2)),hAPP_n1025906991e_bool(F,hAPP_nat_nat(suc,N_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_172_lift__Suc__mono__le]) ).

fof(f_254_2,plain,
    ! [U_544,U_543,U_542] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(U_542,U_544)),hAPP_n1025906991e_bool(U_542,U_543)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_544),U_543))
      | ? [U_541] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(U_542,U_541)),hAPP_n1025906991e_bool(U_542,hAPP_nat_nat(suc,U_541)))) ),
    inference(variable_rename,[status(thm)],[f_254_1]) ).

fof(f_254_3,plain,
    ! [U_544,U_543,U_542] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(U_542,U_544)),hAPP_n1025906991e_bool(U_542,U_543)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_544),U_543))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(U_542,sK3(U_544,U_543,U_542))),hAPP_n1025906991e_bool(U_542,hAPP_nat_nat(suc,sK3(U_544,U_543,U_542))))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_541,sK3(U_544,U_543,U_542))],[f_254_2]) ).

cnf(f_254_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(U_542,U_544)),hAPP_n1025906991e_bool(U_542,U_543)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_544),U_543))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(U_542,sK3(U_544,U_543,U_542))),hAPP_n1025906991e_bool(U_542,hAPP_nat_nat(suc,sK3(U_544,U_543,U_542))))) ),
    inference(clausify,[status(thm)],[f_254_3]) ).

fof(f_255_1,plain,
    ! [Na,N_3,F] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,Na)),hAPP_nat_nat(F,N_3)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
      | ? [N_2] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,N_2)),hAPP_nat_nat(F,hAPP_nat_nat(suc,N_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_173_lift__Suc__mono__le]) ).

fof(f_255_2,plain,
    ! [U_548,U_547,U_546] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_546,U_548)),hAPP_nat_nat(U_546,U_547)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_548),U_547))
      | ? [U_545] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_546,U_545)),hAPP_nat_nat(U_546,hAPP_nat_nat(suc,U_545)))) ),
    inference(variable_rename,[status(thm)],[f_255_1]) ).

fof(f_255_3,plain,
    ! [U_548,U_547,U_546] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_546,U_548)),hAPP_nat_nat(U_546,U_547)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_548),U_547))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_546,sK4(U_548,U_547,U_546))),hAPP_nat_nat(U_546,hAPP_nat_nat(suc,sK4(U_548,U_547,U_546))))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_545,sK4(U_548,U_547,U_546))],[f_255_2]) ).

cnf(f_255_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_546,U_548)),hAPP_nat_nat(U_546,U_547)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_548),U_547))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_546,sK4(U_548,U_547,U_546))),hAPP_nat_nat(U_546,hAPP_nat_nat(suc,sK4(U_548,U_547,U_546))))) ),
    inference(clausify,[status(thm)],[f_255_3]) ).

fof(f_256_1,plain,
    ! [Na,N_3,F] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(F,Na)),hAPP_nat_fun_a_bool(F,N_3)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
      | ? [N_2] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(F,N_2)),hAPP_nat_fun_a_bool(F,hAPP_nat_nat(suc,N_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_174_lift__Suc__mono__le]) ).

fof(f_256_2,plain,
    ! [U_552,U_551,U_550] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(U_550,U_552)),hAPP_nat_fun_a_bool(U_550,U_551)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_552),U_551))
      | ? [U_549] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(U_550,U_549)),hAPP_nat_fun_a_bool(U_550,hAPP_nat_nat(suc,U_549)))) ),
    inference(variable_rename,[status(thm)],[f_256_1]) ).

fof(f_256_3,plain,
    ! [U_552,U_551,U_550] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(U_550,U_552)),hAPP_nat_fun_a_bool(U_550,U_551)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_552),U_551))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(U_550,sK5(U_552,U_551,U_550))),hAPP_nat_fun_a_bool(U_550,hAPP_nat_nat(suc,sK5(U_552,U_551,U_550))))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_549,sK5(U_552,U_551,U_550))],[f_256_2]) ).

cnf(f_256_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(U_550,U_552)),hAPP_nat_fun_a_bool(U_550,U_551)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_552),U_551))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(U_550,sK5(U_552,U_551,U_550))),hAPP_nat_fun_a_bool(U_550,hAPP_nat_nat(suc,sK5(U_552,U_551,U_550))))) ),
    inference(clausify,[status(thm)],[f_256_3]) ).

fof(f_257_1,plain,
    ! [F,A] :
      ( ? [X_1] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,F)),hAPP_pname_a(F,X_1))))))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
          & is_pname(X_1) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(F,A)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_175_pigeonhole__infinite]) ).

fof(f_257_2,plain,
    ! [U_555,U_554] :
      ( ? [U_553] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_554)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,U_555)),hAPP_pname_a(U_555,U_553))))))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_553),U_554))
          & is_pname(U_553) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(U_555,U_554)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_554)) ),
    inference(variable_rename,[status(thm)],[f_257_1]) ).

fof(f_257_3,plain,
    ! [U_555,U_554] :
      ( ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_554)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,U_555)),hAPP_pname_a(U_555,sK6(U_555,U_554)))))))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK6(U_555,U_554)),U_554))
        & is_pname(sK6(U_555,U_554)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(U_555,U_554)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_554)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_553,sK6(U_555,U_554))],[f_257_2]) ).

cnf(f_257_4,plain,
    ( is_pname(sK6(U_555,U_554))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(U_555,U_554)))
    | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_554)) ),
    inference(clausify,[status(thm)],[f_257_3]) ).

cnf(f_257_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK6(U_555,U_554)),U_554))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(U_555,U_554)))
    | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_554)) ),
    inference(clausify,[status(thm)],[f_257_3]) ).

cnf(f_257_6,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_554)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,U_555)),hAPP_pname_a(U_555,sK6(U_555,U_554)))))))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(U_555,U_554)))
    | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_554)) ),
    inference(clausify,[status(thm)],[f_257_3]) ).

fof(f_258_1,plain,
    ! [A,B_1,F,X_2] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
      | B_1 != hAPP_pname_a(F,X_2) ),
    inference(fof_nnf,[status(thm)],[fact_176_image__eqI]) ).

fof(f_258_2,plain,
    ! [U_559,U_558,U_557,U_556] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_558),image_pname_a(U_557,U_559)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_556),U_559))
      | U_558 != hAPP_pname_a(U_557,U_556) ),
    inference(variable_rename,[status(thm)],[f_258_1]) ).

cnf(f_258_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_558),image_pname_a(U_557,U_559)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_556),U_559))
    | U_558 != hAPP_pname_a(U_557,U_556) ),
    inference(clausify,[status(thm)],[f_258_2]) ).

fof(f_259_1,plain,
    ! [A,B] :
      ( A = B
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_177_equalityI]) ).

fof(f_259_2,plain,
    ! [U_561,U_560] :
      ( U_561 = U_560
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_560),U_561))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_561),U_560)) ),
    inference(variable_rename,[status(thm)],[f_259_1]) ).

cnf(f_259_3,plain,
    ( U_561 = U_560
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_560),U_561))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_561),U_560)) ),
    inference(clausify,[status(thm)],[f_259_2]) ).

fof(f_260_1,plain,
    ! [A,B] :
      ( A = B
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
      | ~ is_fun_pname_bool(B)
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_178_equalityI]) ).

fof(f_260_2,plain,
    ! [U_563,U_562] :
      ( U_563 = U_562
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_562),U_563))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_563),U_562))
      | ~ is_fun_pname_bool(U_562)
      | ~ is_fun_pname_bool(U_563) ),
    inference(variable_rename,[status(thm)],[f_260_1]) ).

cnf(f_260_3,plain,
    ( U_563 = U_562
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_562),U_563))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_563),U_562))
    | ~ is_fun_pname_bool(U_562)
    | ~ is_fun_pname_bool(U_563) ),
    inference(clausify,[status(thm)],[f_260_2]) ).

fof(f_261_1,plain,
    ! [A,B] :
      ( A = B
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
      | ~ is_fun_a_bool(B)
      | ~ is_fun_a_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_179_equalityI]) ).

fof(f_261_2,plain,
    ! [U_565,U_564] :
      ( U_565 = U_564
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_564),U_565))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_565),U_564))
      | ~ is_fun_a_bool(U_564)
      | ~ is_fun_a_bool(U_565) ),
    inference(variable_rename,[status(thm)],[f_261_1]) ).

cnf(f_261_3,plain,
    ( U_565 = U_564
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_564),U_565))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_565),U_564))
    | ~ is_fun_a_bool(U_564)
    | ~ is_fun_a_bool(U_565) ),
    inference(clausify,[status(thm)],[f_261_2]) ).

fof(f_262_1,plain,
    ! [C_1,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),A))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_180_subsetD]) ).

fof(f_262_2,plain,
    ! [U_568,U_567,U_566] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_568),U_566))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_568),U_567))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_567),U_566)) ),
    inference(variable_rename,[status(thm)],[f_262_1]) ).

cnf(f_262_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_568),U_566))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_568),U_567))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_567),U_566)) ),
    inference(clausify,[status(thm)],[f_262_2]) ).

fof(f_263_1,plain,
    ! [C_1,A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_1),B))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_1),A))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_181_subsetD]) ).

fof(f_263_2,plain,
    ! [U_571,U_570,U_569] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_571),U_569))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_571),U_570))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_570),U_569)) ),
    inference(variable_rename,[status(thm)],[f_263_1]) ).

cnf(f_263_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_571),U_569))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_571),U_570))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_570),U_569)) ),
    inference(clausify,[status(thm)],[f_263_2]) ).

fof(f_264_1,plain,
    ! [C_1,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_182_subsetD]) ).

fof(f_264_2,plain,
    ! [U_574,U_573,U_572] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_574),U_572))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_574),U_573))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_573),U_572)) ),
    inference(variable_rename,[status(thm)],[f_264_1]) ).

cnf(f_264_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_574),U_572))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_574),U_573))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_573),U_572)) ),
    inference(clausify,[status(thm)],[f_264_2]) ).

fof(f_265_1,plain,
    ! [B_1,A_1,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),insert_nat(B_1,B)))
      | ( A_1 != B_1
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_183_insertCI]) ).

fof(f_265_2,plain,
    ! [U_577,U_576,U_575] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_576),insert_nat(U_577,U_575)))
      | ( U_576 != U_577
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_576),U_575)) ) ),
    inference(variable_rename,[status(thm)],[f_265_1]) ).

cnf(f_265_3,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_576),U_575))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_576),insert_nat(U_577,U_575))) ),
    inference(clausify,[status(thm)],[f_265_2]) ).

cnf(f_265_4,plain,
    ( U_576 != U_577
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_576),insert_nat(U_577,U_575))) ),
    inference(clausify,[status(thm)],[f_265_2]) ).

fof(f_266_1,plain,
    ! [B_1,A_1,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B_1,B)))
      | ( A_1 != B_1
        & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_184_insertCI]) ).

fof(f_266_2,plain,
    ! [U_580,U_579,U_578] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_579),insert_pname(U_580,U_578)))
      | ( U_579 != U_580
        & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_579),U_578)) ) ),
    inference(variable_rename,[status(thm)],[f_266_1]) ).

cnf(f_266_3,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_579),U_578))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_579),insert_pname(U_580,U_578))) ),
    inference(clausify,[status(thm)],[f_266_2]) ).

cnf(f_266_4,plain,
    ( U_579 != U_580
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_579),insert_pname(U_580,U_578))) ),
    inference(clausify,[status(thm)],[f_266_2]) ).

fof(f_267_1,plain,
    ! [B_1,A_1,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),insert_a(B_1,B)))
      | ( A_1 != B_1
        & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_185_insertCI]) ).

fof(f_267_2,plain,
    ! [U_583,U_582,U_581] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_582),insert_a(U_583,U_581)))
      | ( U_582 != U_583
        & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_582),U_581)) ) ),
    inference(variable_rename,[status(thm)],[f_267_1]) ).

cnf(f_267_3,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_582),U_581))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_582),insert_a(U_583,U_581))) ),
    inference(clausify,[status(thm)],[f_267_2]) ).

cnf(f_267_4,plain,
    ( U_582 != U_583
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_582),insert_a(U_583,U_581))) ),
    inference(clausify,[status(thm)],[f_267_2]) ).

fof(f_268_1,plain,
    ! [A_1,B_1,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A))
      | A_1 = B_1
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),insert_nat(B_1,A))) ),
    inference(fof_nnf,[status(thm)],[fact_186_insertE]) ).

fof(f_268_2,plain,
    ! [U_586,U_585,U_584] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_586),U_584))
      | U_586 = U_585
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_586),insert_nat(U_585,U_584))) ),
    inference(variable_rename,[status(thm)],[f_268_1]) ).

cnf(f_268_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_586),U_584))
    | U_586 = U_585
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_586),insert_nat(U_585,U_584))) ),
    inference(clausify,[status(thm)],[f_268_2]) ).

fof(f_269_1,plain,
    ! [A_1,B_1,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A))
      | A_1 = B_1
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B_1,A)))
      | ~ is_pname(B_1)
      | ~ is_pname(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_187_insertE]) ).

fof(f_269_2,plain,
    ! [U_589,U_588,U_587] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_589),U_587))
      | U_589 = U_588
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_589),insert_pname(U_588,U_587)))
      | ~ is_pname(U_588)
      | ~ is_pname(U_589) ),
    inference(variable_rename,[status(thm)],[f_269_1]) ).

fof(f_269_3,plain,
    ! [U_589,U_588] :
      ( ! [U_587] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_589),U_587))
          | U_589 = U_588
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_589),insert_pname(U_588,U_587))) )
      | ~ is_pname(U_588)
      | ~ is_pname(U_589) ),
    inference(miniscope,[status(thm)],[f_269_2]) ).

cnf(f_269_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_589),U_587))
    | U_589 = U_588
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_589),insert_pname(U_588,U_587)))
    | ~ is_pname(U_588)
    | ~ is_pname(U_589) ),
    inference(clausify,[status(thm)],[f_269_3]) ).

fof(f_270_1,plain,
    ! [A_1,B_1,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),A))
      | A_1 = B_1
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),insert_a(B_1,A)))
      | ~ is_a(B_1)
      | ~ is_a(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_188_insertE]) ).

fof(f_270_2,plain,
    ! [U_592,U_591,U_590] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_592),U_590))
      | U_592 = U_591
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_592),insert_a(U_591,U_590)))
      | ~ is_a(U_591)
      | ~ is_a(U_592) ),
    inference(variable_rename,[status(thm)],[f_270_1]) ).

fof(f_270_3,plain,
    ! [U_592,U_591] :
      ( ! [U_590] :
          ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_592),U_590))
          | U_592 = U_591
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_592),insert_a(U_591,U_590))) )
      | ~ is_a(U_591)
      | ~ is_a(U_592) ),
    inference(miniscope,[status(thm)],[f_270_2]) ).

cnf(f_270_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_592),U_590))
    | U_592 = U_591
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_592),insert_a(U_591,U_590)))
    | ~ is_a(U_591)
    | ~ is_a(U_592) ),
    inference(clausify,[status(thm)],[f_270_3]) ).

fof(f_271_1,plain,
    ! [A_1,B] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),insert_nat(A_1,B))),
    inference(fof_nnf,[status(thm)],[fact_189_insertI1]) ).

fof(f_271_2,plain,
    ! [U_594,U_593] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_594),insert_nat(U_594,U_593))),
    inference(variable_rename,[status(thm)],[f_271_1]) ).

cnf(f_271_3,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_594),insert_nat(U_594,U_593))),
    inference(clausify,[status(thm)],[f_271_2]) ).

fof(f_272_1,plain,
    ! [A_1,B] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(A_1,B))),
    inference(fof_nnf,[status(thm)],[fact_190_insertI1]) ).

fof(f_272_2,plain,
    ! [U_596,U_595] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_596),insert_pname(U_596,U_595))),
    inference(variable_rename,[status(thm)],[f_272_1]) ).

cnf(f_272_3,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_596),insert_pname(U_596,U_595))),
    inference(clausify,[status(thm)],[f_272_2]) ).

fof(f_273_1,plain,
    ! [A_1,B] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),insert_a(A_1,B))),
    inference(fof_nnf,[status(thm)],[fact_191_insertI1]) ).

fof(f_273_2,plain,
    ! [U_598,U_597] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_598),insert_a(U_598,U_597))),
    inference(variable_rename,[status(thm)],[f_273_1]) ).

cnf(f_273_3,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_598),insert_a(U_598,U_597))),
    inference(clausify,[status(thm)],[f_273_2]) ).

fof(f_274_1,plain,
    ! [A_1,B] : insert_nat(A_1,B) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),B))),
    inference(fof_nnf,[status(thm)],[fact_192_insert__compr]) ).

fof(f_274_2,plain,
    ! [U_600,U_599] : insert_nat(U_600,U_599) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_600)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_599))),
    inference(variable_rename,[status(thm)],[f_274_1]) ).

cnf(f_274_3,plain,
    insert_nat(U_600,U_599) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_600)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_599))),
    inference(clausify,[status(thm)],[f_274_2]) ).

fof(f_275_1,plain,
    ! [A_1,B] : insert_pname(A_1,B) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),B))),
    inference(fof_nnf,[status(thm)],[fact_193_insert__compr]) ).

fof(f_275_2,plain,
    ! [U_602,U_601] : insert_pname(U_602,U_601) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_602)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_601))),
    inference(variable_rename,[status(thm)],[f_275_1]) ).

cnf(f_275_3,plain,
    insert_pname(U_602,U_601) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_602)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_601))),
    inference(clausify,[status(thm)],[f_275_2]) ).

fof(f_276_1,plain,
    ! [A_1,B] : insert_a(A_1,B) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),B))),
    inference(fof_nnf,[status(thm)],[fact_194_insert__compr]) ).

fof(f_276_2,plain,
    ! [U_604,U_603] : insert_a(U_604,U_603) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_604)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_603))),
    inference(variable_rename,[status(thm)],[f_276_1]) ).

cnf(f_276_3,plain,
    insert_a(U_604,U_603) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_604)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_603))),
    inference(clausify,[status(thm)],[f_276_2]) ).

fof(f_277_1,plain,
    ! [A_1,B] : insert_fun_nat_bool(A_1,B) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),B))),
    inference(fof_nnf,[status(thm)],[fact_195_insert__compr]) ).

fof(f_277_2,plain,
    ! [U_606,U_605] : insert_fun_nat_bool(U_606,U_605) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_606)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),U_605))),
    inference(variable_rename,[status(thm)],[f_277_1]) ).

cnf(f_277_3,plain,
    insert_fun_nat_bool(U_606,U_605) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_606)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),U_605))),
    inference(clausify,[status(thm)],[f_277_2]) ).

fof(f_278_1,plain,
    ! [A_1,B] : insert1325755072e_bool(A_1,B) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),B))),
    inference(fof_nnf,[status(thm)],[fact_196_insert__compr]) ).

fof(f_278_2,plain,
    ! [U_608,U_607] : insert1325755072e_bool(U_608,U_607) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_608)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_607))),
    inference(variable_rename,[status(thm)],[f_278_1]) ).

cnf(f_278_3,plain,
    insert1325755072e_bool(U_608,U_607) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_608)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_607))),
    inference(clausify,[status(thm)],[f_278_2]) ).

fof(f_279_1,plain,
    ! [A_1,B] : insert_fun_a_bool(A_1,B) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),B))),
    inference(fof_nnf,[status(thm)],[fact_197_insert__compr]) ).

fof(f_279_2,plain,
    ! [U_610,U_609] : insert_fun_a_bool(U_610,U_609) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_610)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),U_609))),
    inference(variable_rename,[status(thm)],[f_279_1]) ).

cnf(f_279_3,plain,
    insert_fun_a_bool(U_610,U_609) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_610)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),U_609))),
    inference(clausify,[status(thm)],[f_279_2]) ).

fof(f_280_1,plain,
    ! [A_1,Pa] : insert_nat(A_1,collect_nat(Pa)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_1))),Pa)),
    inference(fof_nnf,[status(thm)],[fact_198_insert__Collect]) ).

fof(f_280_2,plain,
    ! [U_612,U_611] : insert_nat(U_612,collect_nat(U_611)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_612))),U_611)),
    inference(variable_rename,[status(thm)],[f_280_1]) ).

cnf(f_280_3,plain,
    insert_nat(U_612,collect_nat(U_611)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_612))),U_611)),
    inference(clausify,[status(thm)],[f_280_2]) ).

fof(f_281_1,plain,
    ! [A_1,Pa] : insert_pname(A_1,collect_pname(Pa)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_1))),Pa)),
    inference(fof_nnf,[status(thm)],[fact_199_insert__Collect]) ).

fof(f_281_2,plain,
    ! [U_614,U_613] : insert_pname(U_614,collect_pname(U_613)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_614))),U_613)),
    inference(variable_rename,[status(thm)],[f_281_1]) ).

cnf(f_281_3,plain,
    insert_pname(U_614,collect_pname(U_613)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_614))),U_613)),
    inference(clausify,[status(thm)],[f_281_2]) ).

fof(f_282_1,plain,
    ! [A_1,Pa] : insert_a(A_1,collect_a(Pa)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_1))),Pa)),
    inference(fof_nnf,[status(thm)],[fact_200_insert__Collect]) ).

fof(f_282_2,plain,
    ! [U_616,U_615] : insert_a(U_616,collect_a(U_615)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_616))),U_615)),
    inference(variable_rename,[status(thm)],[f_282_1]) ).

cnf(f_282_3,plain,
    insert_a(U_616,collect_a(U_615)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_616))),U_615)),
    inference(clausify,[status(thm)],[f_282_2]) ).

fof(f_283_1,plain,
    ! [A_1,Pa] : insert_fun_nat_bool(A_1,collect_fun_nat_bool(Pa)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_1))),Pa)),
    inference(fof_nnf,[status(thm)],[fact_201_insert__Collect]) ).

fof(f_283_2,plain,
    ! [U_618,U_617] : insert_fun_nat_bool(U_618,collect_fun_nat_bool(U_617)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_618))),U_617)),
    inference(variable_rename,[status(thm)],[f_283_1]) ).

cnf(f_283_3,plain,
    insert_fun_nat_bool(U_618,collect_fun_nat_bool(U_617)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_618))),U_617)),
    inference(clausify,[status(thm)],[f_283_2]) ).

fof(f_284_1,plain,
    ! [A_1,Pa] : insert1325755072e_bool(A_1,collec1974731493e_bool(Pa)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_1))),Pa)),
    inference(fof_nnf,[status(thm)],[fact_202_insert__Collect]) ).

fof(f_284_2,plain,
    ! [U_620,U_619] : insert1325755072e_bool(U_620,collec1974731493e_bool(U_619)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_620))),U_619)),
    inference(variable_rename,[status(thm)],[f_284_1]) ).

cnf(f_284_3,plain,
    insert1325755072e_bool(U_620,collec1974731493e_bool(U_619)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_620))),U_619)),
    inference(clausify,[status(thm)],[f_284_2]) ).

fof(f_285_1,plain,
    ! [A_1,Pa] : insert_fun_a_bool(A_1,collect_fun_a_bool(Pa)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_1))),Pa)),
    inference(fof_nnf,[status(thm)],[fact_203_insert__Collect]) ).

fof(f_285_2,plain,
    ! [U_622,U_621] : insert_fun_a_bool(U_622,collect_fun_a_bool(U_621)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_622))),U_621)),
    inference(variable_rename,[status(thm)],[f_285_1]) ).

cnf(f_285_3,plain,
    insert_fun_a_bool(U_622,collect_fun_a_bool(U_621)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_622))),U_621)),
    inference(clausify,[status(thm)],[f_285_2]) ).

fof(f_286_1,plain,
    ! [X_2,A] : insert_nat(X_2,insert_nat(X_2,A)) = insert_nat(X_2,A),
    inference(fof_nnf,[status(thm)],[fact_204_insert__absorb2]) ).

fof(f_286_2,plain,
    ! [U_624,U_623] : insert_nat(U_624,insert_nat(U_624,U_623)) = insert_nat(U_624,U_623),
    inference(variable_rename,[status(thm)],[f_286_1]) ).

cnf(f_286_3,plain,
    insert_nat(U_624,insert_nat(U_624,U_623)) = insert_nat(U_624,U_623),
    inference(clausify,[status(thm)],[f_286_2]) ).

fof(f_287_1,plain,
    ! [X_2,A] : insert_pname(X_2,insert_pname(X_2,A)) = insert_pname(X_2,A),
    inference(fof_nnf,[status(thm)],[fact_205_insert__absorb2]) ).

fof(f_287_2,plain,
    ! [U_626,U_625] : insert_pname(U_626,insert_pname(U_626,U_625)) = insert_pname(U_626,U_625),
    inference(variable_rename,[status(thm)],[f_287_1]) ).

cnf(f_287_3,plain,
    insert_pname(U_626,insert_pname(U_626,U_625)) = insert_pname(U_626,U_625),
    inference(clausify,[status(thm)],[f_287_2]) ).

fof(f_288_1,plain,
    ! [X_2,A] : insert_a(X_2,insert_a(X_2,A)) = insert_a(X_2,A),
    inference(fof_nnf,[status(thm)],[fact_206_insert__absorb2]) ).

fof(f_288_2,plain,
    ! [U_628,U_627] : insert_a(U_628,insert_a(U_628,U_627)) = insert_a(U_628,U_627),
    inference(variable_rename,[status(thm)],[f_288_1]) ).

cnf(f_288_3,plain,
    insert_a(U_628,insert_a(U_628,U_627)) = insert_a(U_628,U_627),
    inference(clausify,[status(thm)],[f_288_2]) ).

fof(f_289_1,plain,
    ! [X_2,Y_1,A] : insert_nat(X_2,insert_nat(Y_1,A)) = insert_nat(Y_1,insert_nat(X_2,A)),
    inference(fof_nnf,[status(thm)],[fact_207_insert__commute]) ).

fof(f_289_2,plain,
    ! [U_631,U_630,U_629] : insert_nat(U_631,insert_nat(U_630,U_629)) = insert_nat(U_630,insert_nat(U_631,U_629)),
    inference(variable_rename,[status(thm)],[f_289_1]) ).

cnf(f_289_3,plain,
    insert_nat(U_631,insert_nat(U_630,U_629)) = insert_nat(U_630,insert_nat(U_631,U_629)),
    inference(clausify,[status(thm)],[f_289_2]) ).

fof(f_290_1,plain,
    ! [X_2,Y_1,A] : insert_pname(X_2,insert_pname(Y_1,A)) = insert_pname(Y_1,insert_pname(X_2,A)),
    inference(fof_nnf,[status(thm)],[fact_208_insert__commute]) ).

fof(f_290_2,plain,
    ! [U_634,U_633,U_632] : insert_pname(U_634,insert_pname(U_633,U_632)) = insert_pname(U_633,insert_pname(U_634,U_632)),
    inference(variable_rename,[status(thm)],[f_290_1]) ).

cnf(f_290_3,plain,
    insert_pname(U_634,insert_pname(U_633,U_632)) = insert_pname(U_633,insert_pname(U_634,U_632)),
    inference(clausify,[status(thm)],[f_290_2]) ).

fof(f_291_1,plain,
    ! [X_2,Y_1,A] : insert_a(X_2,insert_a(Y_1,A)) = insert_a(Y_1,insert_a(X_2,A)),
    inference(fof_nnf,[status(thm)],[fact_209_insert__commute]) ).

fof(f_291_2,plain,
    ! [U_637,U_636,U_635] : insert_a(U_637,insert_a(U_636,U_635)) = insert_a(U_636,insert_a(U_637,U_635)),
    inference(variable_rename,[status(thm)],[f_291_1]) ).

cnf(f_291_3,plain,
    insert_a(U_637,insert_a(U_636,U_635)) = insert_a(U_636,insert_a(U_637,U_635)),
    inference(clausify,[status(thm)],[f_291_2]) ).

fof(f_292_1,plain,
    ! [A_1,B_1,A] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),insert_nat(B_1,A)))
        | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A))
          & A_1 != B_1 ) )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A))
        | A_1 = B_1
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),insert_nat(B_1,A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_210_insert__iff]) ).

fof(f_292_2,plain,
    ! [U_640,U_639,U_638] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_640),insert_nat(U_639,U_638)))
        | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_640),U_638))
          & U_640 != U_639 ) )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_640),U_638))
        | U_640 = U_639
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_640),insert_nat(U_639,U_638))) ) ),
    inference(variable_rename,[status(thm)],[f_292_1]) ).

fof(f_292_3,plain,
    ( ! [U_646,U_644,U_642] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_646),insert_nat(U_644,U_642)))
        | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_646),U_642))
          & U_646 != U_644 ) )
    & ! [U_645,U_643,U_641] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_645),U_641))
        | U_645 = U_643
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_645),insert_nat(U_643,U_641))) ) ),
    inference(miniscope,[status(thm)],[f_292_2]) ).

cnf(f_292_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_645),U_641))
    | U_645 = U_643
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_645),insert_nat(U_643,U_641))) ),
    inference(clausify,[status(thm)],[f_292_3]) ).

cnf(f_292_5,plain,
    ( U_646 != U_644
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_646),insert_nat(U_644,U_642))) ),
    inference(clausify,[status(thm)],[f_292_3]) ).

cnf(f_292_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_646),U_642))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_646),insert_nat(U_644,U_642))) ),
    inference(clausify,[status(thm)],[f_292_3]) ).

fof(f_293_1,plain,
    ! [A_1,B_1,A] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B_1,A)))
          | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A))
            & A_1 != B_1 ) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A))
          | A_1 = B_1
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B_1,A))) ) )
      | ~ is_pname(B_1)
      | ~ is_pname(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_211_insert__iff]) ).

fof(f_293_2,plain,
    ! [U_649,U_648,U_647] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_649),insert_pname(U_648,U_647)))
          | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_649),U_647))
            & U_649 != U_648 ) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_649),U_647))
          | U_649 = U_648
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_649),insert_pname(U_648,U_647))) ) )
      | ~ is_pname(U_648)
      | ~ is_pname(U_649) ),
    inference(variable_rename,[status(thm)],[f_293_1]) ).

fof(f_293_3,plain,
    ! [U_649,U_648] :
      ( ( ! [U_651] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_649),insert_pname(U_648,U_651)))
            | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_649),U_651))
              & U_649 != U_648 ) )
        & ! [U_650] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_649),U_650))
            | U_649 = U_648
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_649),insert_pname(U_648,U_650))) ) )
      | ~ is_pname(U_648)
      | ~ is_pname(U_649) ),
    inference(miniscope,[status(thm)],[f_293_2]) ).

cnf(f_293_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_649),U_650))
    | U_649 = U_648
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_649),insert_pname(U_648,U_650)))
    | ~ is_pname(U_648)
    | ~ is_pname(U_649) ),
    inference(clausify,[status(thm)],[f_293_3]) ).

cnf(f_293_5,plain,
    ( U_649 != U_648
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_649),insert_pname(U_648,U_651)))
    | ~ is_pname(U_648)
    | ~ is_pname(U_649) ),
    inference(clausify,[status(thm)],[f_293_3]) ).

cnf(f_293_6,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_649),U_651))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_649),insert_pname(U_648,U_651)))
    | ~ is_pname(U_648)
    | ~ is_pname(U_649) ),
    inference(clausify,[status(thm)],[f_293_3]) ).

fof(f_294_1,plain,
    ! [A_1,B_1,A] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),insert_a(B_1,A)))
          | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),A))
            & A_1 != B_1 ) )
        & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),A))
          | A_1 = B_1
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),insert_a(B_1,A))) ) )
      | ~ is_a(B_1)
      | ~ is_a(A_1) ),
    inference(fof_nnf,[status(thm)],[fact_212_insert__iff]) ).

fof(f_294_2,plain,
    ! [U_654,U_653,U_652] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_654),insert_a(U_653,U_652)))
          | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_654),U_652))
            & U_654 != U_653 ) )
        & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_654),U_652))
          | U_654 = U_653
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_654),insert_a(U_653,U_652))) ) )
      | ~ is_a(U_653)
      | ~ is_a(U_654) ),
    inference(variable_rename,[status(thm)],[f_294_1]) ).

fof(f_294_3,plain,
    ! [U_654,U_653] :
      ( ( ! [U_656] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_654),insert_a(U_653,U_656)))
            | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_654),U_656))
              & U_654 != U_653 ) )
        & ! [U_655] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_654),U_655))
            | U_654 = U_653
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_654),insert_a(U_653,U_655))) ) )
      | ~ is_a(U_653)
      | ~ is_a(U_654) ),
    inference(miniscope,[status(thm)],[f_294_2]) ).

cnf(f_294_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_654),U_655))
    | U_654 = U_653
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_654),insert_a(U_653,U_655)))
    | ~ is_a(U_653)
    | ~ is_a(U_654) ),
    inference(clausify,[status(thm)],[f_294_3]) ).

cnf(f_294_5,plain,
    ( U_654 != U_653
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_654),insert_a(U_653,U_656)))
    | ~ is_a(U_653)
    | ~ is_a(U_654) ),
    inference(clausify,[status(thm)],[f_294_3]) ).

cnf(f_294_6,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_654),U_656))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_654),insert_a(U_653,U_656)))
    | ~ is_a(U_653)
    | ~ is_a(U_654) ),
    inference(clausify,[status(thm)],[f_294_3]) ).

fof(f_295_1,plain,
    ! [Y_1,A,X_2] :
      ( ( hBOOL(hAPP_nat_bool(insert_nat(Y_1,A),X_2))
        | ( ~ hBOOL(hAPP_nat_bool(A,X_2))
          & Y_1 != X_2 ) )
      & ( hBOOL(hAPP_nat_bool(A,X_2))
        | Y_1 = X_2
        | ~ hBOOL(hAPP_nat_bool(insert_nat(Y_1,A),X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_213_insert__code]) ).

fof(f_295_2,plain,
    ! [U_659,U_658,U_657] :
      ( ( hBOOL(hAPP_nat_bool(insert_nat(U_659,U_658),U_657))
        | ( ~ hBOOL(hAPP_nat_bool(U_658,U_657))
          & U_659 != U_657 ) )
      & ( hBOOL(hAPP_nat_bool(U_658,U_657))
        | U_659 = U_657
        | ~ hBOOL(hAPP_nat_bool(insert_nat(U_659,U_658),U_657)) ) ),
    inference(variable_rename,[status(thm)],[f_295_1]) ).

fof(f_295_3,plain,
    ( ! [U_665,U_663,U_661] :
        ( hBOOL(hAPP_nat_bool(insert_nat(U_665,U_663),U_661))
        | ( ~ hBOOL(hAPP_nat_bool(U_663,U_661))
          & U_665 != U_661 ) )
    & ! [U_664,U_662,U_660] :
        ( hBOOL(hAPP_nat_bool(U_662,U_660))
        | U_664 = U_660
        | ~ hBOOL(hAPP_nat_bool(insert_nat(U_664,U_662),U_660)) ) ),
    inference(miniscope,[status(thm)],[f_295_2]) ).

cnf(f_295_4,plain,
    ( hBOOL(hAPP_nat_bool(U_662,U_660))
    | U_664 = U_660
    | ~ hBOOL(hAPP_nat_bool(insert_nat(U_664,U_662),U_660)) ),
    inference(clausify,[status(thm)],[f_295_3]) ).

cnf(f_295_5,plain,
    ( U_665 != U_661
    | hBOOL(hAPP_nat_bool(insert_nat(U_665,U_663),U_661)) ),
    inference(clausify,[status(thm)],[f_295_3]) ).

cnf(f_295_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_663,U_661))
    | hBOOL(hAPP_nat_bool(insert_nat(U_665,U_663),U_661)) ),
    inference(clausify,[status(thm)],[f_295_3]) ).

fof(f_296_1,plain,
    ! [Y_1,A,X_2] :
      ( ( ( hBOOL(hAPP_pname_bool(insert_pname(Y_1,A),X_2))
          | ( ~ hBOOL(hAPP_pname_bool(A,X_2))
            & Y_1 != X_2 ) )
        & ( hBOOL(hAPP_pname_bool(A,X_2))
          | Y_1 = X_2
          | ~ hBOOL(hAPP_pname_bool(insert_pname(Y_1,A),X_2)) ) )
      | ~ is_pname(X_2)
      | ~ is_pname(Y_1) ),
    inference(fof_nnf,[status(thm)],[fact_214_insert__code]) ).

fof(f_296_2,plain,
    ! [U_668,U_667,U_666] :
      ( ( ( hBOOL(hAPP_pname_bool(insert_pname(U_668,U_667),U_666))
          | ( ~ hBOOL(hAPP_pname_bool(U_667,U_666))
            & U_668 != U_666 ) )
        & ( hBOOL(hAPP_pname_bool(U_667,U_666))
          | U_668 = U_666
          | ~ hBOOL(hAPP_pname_bool(insert_pname(U_668,U_667),U_666)) ) )
      | ~ is_pname(U_666)
      | ~ is_pname(U_668) ),
    inference(variable_rename,[status(thm)],[f_296_1]) ).

cnf(f_296_3,plain,
    ( hBOOL(hAPP_pname_bool(U_667,U_666))
    | U_668 = U_666
    | ~ hBOOL(hAPP_pname_bool(insert_pname(U_668,U_667),U_666))
    | ~ is_pname(U_666)
    | ~ is_pname(U_668) ),
    inference(clausify,[status(thm)],[f_296_2]) ).

cnf(f_296_4,plain,
    ( U_668 != U_666
    | hBOOL(hAPP_pname_bool(insert_pname(U_668,U_667),U_666))
    | ~ is_pname(U_666)
    | ~ is_pname(U_668) ),
    inference(clausify,[status(thm)],[f_296_2]) ).

cnf(f_296_5,plain,
    ( ~ hBOOL(hAPP_pname_bool(U_667,U_666))
    | hBOOL(hAPP_pname_bool(insert_pname(U_668,U_667),U_666))
    | ~ is_pname(U_666)
    | ~ is_pname(U_668) ),
    inference(clausify,[status(thm)],[f_296_2]) ).

fof(f_297_1,plain,
    ! [Y_1,A,X_2] :
      ( ( ( hBOOL(hAPP_a_bool(insert_a(Y_1,A),X_2))
          | ( ~ hBOOL(hAPP_a_bool(A,X_2))
            & Y_1 != X_2 ) )
        & ( hBOOL(hAPP_a_bool(A,X_2))
          | Y_1 = X_2
          | ~ hBOOL(hAPP_a_bool(insert_a(Y_1,A),X_2)) ) )
      | ~ is_a(X_2)
      | ~ is_a(Y_1) ),
    inference(fof_nnf,[status(thm)],[fact_215_insert__code]) ).

fof(f_297_2,plain,
    ! [U_671,U_670,U_669] :
      ( ( ( hBOOL(hAPP_a_bool(insert_a(U_671,U_670),U_669))
          | ( ~ hBOOL(hAPP_a_bool(U_670,U_669))
            & U_671 != U_669 ) )
        & ( hBOOL(hAPP_a_bool(U_670,U_669))
          | U_671 = U_669
          | ~ hBOOL(hAPP_a_bool(insert_a(U_671,U_670),U_669)) ) )
      | ~ is_a(U_669)
      | ~ is_a(U_671) ),
    inference(variable_rename,[status(thm)],[f_297_1]) ).

cnf(f_297_3,plain,
    ( hBOOL(hAPP_a_bool(U_670,U_669))
    | U_671 = U_669
    | ~ hBOOL(hAPP_a_bool(insert_a(U_671,U_670),U_669))
    | ~ is_a(U_669)
    | ~ is_a(U_671) ),
    inference(clausify,[status(thm)],[f_297_2]) ).

cnf(f_297_4,plain,
    ( U_671 != U_669
    | hBOOL(hAPP_a_bool(insert_a(U_671,U_670),U_669))
    | ~ is_a(U_669)
    | ~ is_a(U_671) ),
    inference(clausify,[status(thm)],[f_297_2]) ).

cnf(f_297_5,plain,
    ( ~ hBOOL(hAPP_a_bool(U_670,U_669))
    | hBOOL(hAPP_a_bool(insert_a(U_671,U_670),U_669))
    | ~ is_a(U_669)
    | ~ is_a(U_671) ),
    inference(clausify,[status(thm)],[f_297_2]) ).

fof(f_298_1,plain,
    ! [B,X_2,A] :
      ( ( ( insert_nat(X_2,A) = insert_nat(X_2,B)
          | A != B )
        & ( A = B
          | insert_nat(X_2,A) != insert_nat(X_2,B) ) )
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_216_insert__ident]) ).

fof(f_298_2,plain,
    ! [U_674,U_673,U_672] :
      ( ( ( insert_nat(U_673,U_672) = insert_nat(U_673,U_674)
          | U_672 != U_674 )
        & ( U_672 = U_674
          | insert_nat(U_673,U_672) != insert_nat(U_673,U_674) ) )
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_673),U_674))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_673),U_672)) ),
    inference(variable_rename,[status(thm)],[f_298_1]) ).

cnf(f_298_3,plain,
    ( U_672 = U_674
    | insert_nat(U_673,U_672) != insert_nat(U_673,U_674)
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_673),U_674))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_673),U_672)) ),
    inference(clausify,[status(thm)],[f_298_2]) ).

cnf(f_298_4,plain,
    ( insert_nat(U_673,U_672) = insert_nat(U_673,U_674)
    | U_672 != U_674
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_673),U_674))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_673),U_672)) ),
    inference(clausify,[status(thm)],[f_298_2]) ).

fof(f_299_1,plain,
    ! [B,X_2,A] :
      ( ( ( insert_pname(X_2,A) = insert_pname(X_2,B)
          | A != B )
        & ( A = B
          | insert_pname(X_2,A) != insert_pname(X_2,B) ) )
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
      | ~ is_fun_pname_bool(A)
      | ~ is_fun_pname_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_217_insert__ident]) ).

fof(f_299_2,plain,
    ! [U_677,U_676,U_675] :
      ( ( ( insert_pname(U_676,U_675) = insert_pname(U_676,U_677)
          | U_675 != U_677 )
        & ( U_675 = U_677
          | insert_pname(U_676,U_675) != insert_pname(U_676,U_677) ) )
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_676),U_677))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_676),U_675))
      | ~ is_fun_pname_bool(U_675)
      | ~ is_fun_pname_bool(U_677) ),
    inference(variable_rename,[status(thm)],[f_299_1]) ).

cnf(f_299_3,plain,
    ( U_675 = U_677
    | insert_pname(U_676,U_675) != insert_pname(U_676,U_677)
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_676),U_677))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_676),U_675))
    | ~ is_fun_pname_bool(U_675)
    | ~ is_fun_pname_bool(U_677) ),
    inference(clausify,[status(thm)],[f_299_2]) ).

cnf(f_299_4,plain,
    ( insert_pname(U_676,U_675) = insert_pname(U_676,U_677)
    | U_675 != U_677
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_676),U_677))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_676),U_675))
    | ~ is_fun_pname_bool(U_675)
    | ~ is_fun_pname_bool(U_677) ),
    inference(clausify,[status(thm)],[f_299_2]) ).

fof(f_300_1,plain,
    ! [B,X_2,A] :
      ( ( ( insert_a(X_2,A) = insert_a(X_2,B)
          | A != B )
        & ( A = B
          | insert_a(X_2,A) != insert_a(X_2,B) ) )
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
      | ~ is_fun_a_bool(A)
      | ~ is_fun_a_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_218_insert__ident]) ).

fof(f_300_2,plain,
    ! [U_680,U_679,U_678] :
      ( ( ( insert_a(U_679,U_678) = insert_a(U_679,U_680)
          | U_678 != U_680 )
        & ( U_678 = U_680
          | insert_a(U_679,U_678) != insert_a(U_679,U_680) ) )
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_679),U_680))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_679),U_678))
      | ~ is_fun_a_bool(U_678)
      | ~ is_fun_a_bool(U_680) ),
    inference(variable_rename,[status(thm)],[f_300_1]) ).

cnf(f_300_3,plain,
    ( U_678 = U_680
    | insert_a(U_679,U_678) != insert_a(U_679,U_680)
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_679),U_680))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_679),U_678))
    | ~ is_fun_a_bool(U_678)
    | ~ is_fun_a_bool(U_680) ),
    inference(clausify,[status(thm)],[f_300_2]) ).

cnf(f_300_4,plain,
    ( insert_a(U_679,U_678) = insert_a(U_679,U_680)
    | U_678 != U_680
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_679),U_680))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_679),U_678))
    | ~ is_fun_a_bool(U_678)
    | ~ is_fun_a_bool(U_680) ),
    inference(clausify,[status(thm)],[f_300_2]) ).

fof(f_301_1,plain,
    ! [B_1,A_1,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),insert_nat(B_1,B)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_219_insertI2]) ).

fof(f_301_2,plain,
    ! [U_683,U_682,U_681] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_682),insert_nat(U_683,U_681)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_682),U_681)) ),
    inference(variable_rename,[status(thm)],[f_301_1]) ).

cnf(f_301_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_682),insert_nat(U_683,U_681)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_682),U_681)) ),
    inference(clausify,[status(thm)],[f_301_2]) ).

fof(f_302_1,plain,
    ! [B_1,A_1,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B_1,B)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_220_insertI2]) ).

fof(f_302_2,plain,
    ! [U_686,U_685,U_684] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_685),insert_pname(U_686,U_684)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_685),U_684)) ),
    inference(variable_rename,[status(thm)],[f_302_1]) ).

cnf(f_302_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_685),insert_pname(U_686,U_684)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_685),U_684)) ),
    inference(clausify,[status(thm)],[f_302_2]) ).

fof(f_303_1,plain,
    ! [B_1,A_1,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),insert_a(B_1,B)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_221_insertI2]) ).

fof(f_303_2,plain,
    ! [U_689,U_688,U_687] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_688),insert_a(U_689,U_687)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_688),U_687)) ),
    inference(variable_rename,[status(thm)],[f_303_1]) ).

cnf(f_303_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_688),insert_a(U_689,U_687)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_688),U_687)) ),
    inference(clausify,[status(thm)],[f_303_2]) ).

fof(f_304_1,plain,
    ! [A_1,A] :
      ( insert_nat(A_1,A) = A
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A)) ),
    inference(fof_nnf,[status(thm)],[fact_222_insert__absorb]) ).

fof(f_304_2,plain,
    ! [U_691,U_690] :
      ( insert_nat(U_691,U_690) = U_690
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_691),U_690)) ),
    inference(variable_rename,[status(thm)],[f_304_1]) ).

cnf(f_304_3,plain,
    ( insert_nat(U_691,U_690) = U_690
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_691),U_690)) ),
    inference(clausify,[status(thm)],[f_304_2]) ).

fof(f_305_1,plain,
    ! [A_1,A] :
      ( insert_pname(A_1,A) = A
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A))
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_223_insert__absorb]) ).

fof(f_305_2,plain,
    ! [U_693,U_692] :
      ( insert_pname(U_693,U_692) = U_692
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_693),U_692))
      | ~ is_fun_pname_bool(U_692) ),
    inference(variable_rename,[status(thm)],[f_305_1]) ).

cnf(f_305_3,plain,
    ( insert_pname(U_693,U_692) = U_692
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_693),U_692))
    | ~ is_fun_pname_bool(U_692) ),
    inference(clausify,[status(thm)],[f_305_2]) ).

fof(f_306_1,plain,
    ! [A_1,A] :
      ( insert_a(A_1,A) = A
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),A))
      | ~ is_fun_a_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_224_insert__absorb]) ).

fof(f_306_2,plain,
    ! [U_695,U_694] :
      ( insert_a(U_695,U_694) = U_694
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_695),U_694))
      | ~ is_fun_a_bool(U_694) ),
    inference(variable_rename,[status(thm)],[f_306_1]) ).

cnf(f_306_3,plain,
    ( insert_a(U_695,U_694) = U_694
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_695),U_694))
    | ~ is_fun_a_bool(U_694) ),
    inference(clausify,[status(thm)],[f_306_2]) ).

fof(f_307_1,plain,
    ! [A] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),A)),
    inference(fof_nnf,[status(thm)],[fact_225_subset__refl]) ).

fof(f_307_2,plain,
    ! [U_696] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_696),U_696)),
    inference(variable_rename,[status(thm)],[f_307_1]) ).

cnf(f_307_3,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_696),U_696)),
    inference(clausify,[status(thm)],[f_307_2]) ).

fof(f_308_1,plain,
    ! [A] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),A)),
    inference(fof_nnf,[status(thm)],[fact_226_subset__refl]) ).

fof(f_308_2,plain,
    ! [U_697] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_697),U_697)),
    inference(variable_rename,[status(thm)],[f_308_1]) ).

cnf(f_308_3,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_697),U_697)),
    inference(clausify,[status(thm)],[f_308_2]) ).

fof(f_309_1,plain,
    ! [A] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),A)),
    inference(fof_nnf,[status(thm)],[fact_227_subset__refl]) ).

fof(f_309_2,plain,
    ! [U_698] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_698),U_698)),
    inference(variable_rename,[status(thm)],[f_309_1]) ).

cnf(f_309_3,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_698),U_698)),
    inference(clausify,[status(thm)],[f_309_2]) ).

fof(f_310_1,plain,
    ! [A,B] :
      ( ( A = B
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) )
      & ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) )
        | A != B ) ),
    inference(fof_nnf,[status(thm)],[fact_228_set__eq__subset]) ).

fof(f_310_2,plain,
    ! [U_700,U_699] :
      ( ( U_700 = U_699
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_699),U_700))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_700),U_699)) )
      & ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_699),U_700))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_700),U_699)) )
        | U_700 != U_699 ) ),
    inference(variable_rename,[status(thm)],[f_310_1]) ).

fof(f_310_3,plain,
    ( ! [U_704,U_702] :
        ( U_704 = U_702
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_702),U_704))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_704),U_702)) )
    & ! [U_703,U_701] :
        ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_701),U_703))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_703),U_701)) )
        | U_703 != U_701 ) ),
    inference(miniscope,[status(thm)],[f_310_2]) ).

cnf(f_310_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_703),U_701))
    | U_703 != U_701 ),
    inference(clausify,[status(thm)],[f_310_3]) ).

cnf(f_310_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_701),U_703))
    | U_703 != U_701 ),
    inference(clausify,[status(thm)],[f_310_3]) ).

cnf(f_310_6,plain,
    ( U_704 = U_702
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_702),U_704))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_704),U_702)) ),
    inference(clausify,[status(thm)],[f_310_3]) ).

fof(f_311_1,plain,
    ! [A,B] :
      ( ( ( A = B
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) )
        & ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) )
          | A != B ) )
      | ~ is_fun_pname_bool(B)
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_229_set__eq__subset]) ).

fof(f_311_2,plain,
    ! [U_706,U_705] :
      ( ( ( U_706 = U_705
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_705),U_706))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_706),U_705)) )
        & ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_705),U_706))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_706),U_705)) )
          | U_706 != U_705 ) )
      | ~ is_fun_pname_bool(U_705)
      | ~ is_fun_pname_bool(U_706) ),
    inference(variable_rename,[status(thm)],[f_311_1]) ).

cnf(f_311_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_706),U_705))
    | U_706 != U_705
    | ~ is_fun_pname_bool(U_705)
    | ~ is_fun_pname_bool(U_706) ),
    inference(clausify,[status(thm)],[f_311_2]) ).

cnf(f_311_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_705),U_706))
    | U_706 != U_705
    | ~ is_fun_pname_bool(U_705)
    | ~ is_fun_pname_bool(U_706) ),
    inference(clausify,[status(thm)],[f_311_2]) ).

cnf(f_311_5,plain,
    ( U_706 = U_705
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_705),U_706))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_706),U_705))
    | ~ is_fun_pname_bool(U_705)
    | ~ is_fun_pname_bool(U_706) ),
    inference(clausify,[status(thm)],[f_311_2]) ).

fof(f_312_1,plain,
    ! [A,B] :
      ( ( ( A = B
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) )
        & ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) )
          | A != B ) )
      | ~ is_fun_a_bool(B)
      | ~ is_fun_a_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_230_set__eq__subset]) ).

fof(f_312_2,plain,
    ! [U_708,U_707] :
      ( ( ( U_708 = U_707
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_707),U_708))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_708),U_707)) )
        & ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_707),U_708))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_708),U_707)) )
          | U_708 != U_707 ) )
      | ~ is_fun_a_bool(U_707)
      | ~ is_fun_a_bool(U_708) ),
    inference(variable_rename,[status(thm)],[f_312_1]) ).

cnf(f_312_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_708),U_707))
    | U_708 != U_707
    | ~ is_fun_a_bool(U_707)
    | ~ is_fun_a_bool(U_708) ),
    inference(clausify,[status(thm)],[f_312_2]) ).

cnf(f_312_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_707),U_708))
    | U_708 != U_707
    | ~ is_fun_a_bool(U_707)
    | ~ is_fun_a_bool(U_708) ),
    inference(clausify,[status(thm)],[f_312_2]) ).

cnf(f_312_5,plain,
    ( U_708 = U_707
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_707),U_708))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_708),U_707))
    | ~ is_fun_a_bool(U_707)
    | ~ is_fun_a_bool(U_708) ),
    inference(clausify,[status(thm)],[f_312_2]) ).

fof(f_313_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_231_equalityD1]) ).

fof(f_313_2,plain,
    ! [U_710,U_709] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_710),U_709))
      | U_710 != U_709 ),
    inference(variable_rename,[status(thm)],[f_313_1]) ).

cnf(f_313_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_710),U_709))
    | U_710 != U_709 ),
    inference(clausify,[status(thm)],[f_313_2]) ).

fof(f_314_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_232_equalityD1]) ).

fof(f_314_2,plain,
    ! [U_712,U_711] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_712),U_711))
      | U_712 != U_711 ),
    inference(variable_rename,[status(thm)],[f_314_1]) ).

cnf(f_314_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_712),U_711))
    | U_712 != U_711 ),
    inference(clausify,[status(thm)],[f_314_2]) ).

fof(f_315_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_233_equalityD1]) ).

fof(f_315_2,plain,
    ! [U_714,U_713] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_714),U_713))
      | U_714 != U_713 ),
    inference(variable_rename,[status(thm)],[f_315_1]) ).

cnf(f_315_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_714),U_713))
    | U_714 != U_713 ),
    inference(clausify,[status(thm)],[f_315_2]) ).

fof(f_316_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_234_equalityD2]) ).

fof(f_316_2,plain,
    ! [U_716,U_715] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_715),U_716))
      | U_716 != U_715 ),
    inference(variable_rename,[status(thm)],[f_316_1]) ).

cnf(f_316_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_715),U_716))
    | U_716 != U_715 ),
    inference(clausify,[status(thm)],[f_316_2]) ).

fof(f_317_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_235_equalityD2]) ).

fof(f_317_2,plain,
    ! [U_718,U_717] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_717),U_718))
      | U_718 != U_717 ),
    inference(variable_rename,[status(thm)],[f_317_1]) ).

cnf(f_317_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_717),U_718))
    | U_718 != U_717 ),
    inference(clausify,[status(thm)],[f_317_2]) ).

fof(f_318_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A))
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_236_equalityD2]) ).

fof(f_318_2,plain,
    ! [U_720,U_719] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_719),U_720))
      | U_720 != U_719 ),
    inference(variable_rename,[status(thm)],[f_318_1]) ).

cnf(f_318_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_719),U_720))
    | U_720 != U_719 ),
    inference(clausify,[status(thm)],[f_318_2]) ).

fof(f_319_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_237_in__mono]) ).

fof(f_319_2,plain,
    ! [U_723,U_722,U_721] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_723),U_721))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_723),U_722))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_722),U_721)) ),
    inference(variable_rename,[status(thm)],[f_319_1]) ).

cnf(f_319_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_723),U_721))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_723),U_722))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_722),U_721)) ),
    inference(clausify,[status(thm)],[f_319_2]) ).

fof(f_320_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_238_in__mono]) ).

fof(f_320_2,plain,
    ! [U_726,U_725,U_724] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_726),U_724))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_726),U_725))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_725),U_724)) ),
    inference(variable_rename,[status(thm)],[f_320_1]) ).

cnf(f_320_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_726),U_724))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_726),U_725))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_725),U_724)) ),
    inference(clausify,[status(thm)],[f_320_2]) ).

fof(f_321_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_239_in__mono]) ).

fof(f_321_2,plain,
    ! [U_729,U_728,U_727] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_729),U_727))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_729),U_728))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_728),U_727)) ),
    inference(variable_rename,[status(thm)],[f_321_1]) ).

cnf(f_321_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_729),U_727))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_729),U_728))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_728),U_727)) ),
    inference(clausify,[status(thm)],[f_321_2]) ).

fof(f_322_1,plain,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_240_set__rev__mp]) ).

fof(f_322_2,plain,
    ! [U_732,U_731,U_730] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_731),U_732))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_730),U_732))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_731),U_730)) ),
    inference(variable_rename,[status(thm)],[f_322_1]) ).

cnf(f_322_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_731),U_732))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_730),U_732))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_731),U_730)) ),
    inference(clausify,[status(thm)],[f_322_2]) ).

fof(f_323_1,plain,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_241_set__rev__mp]) ).

fof(f_323_2,plain,
    ! [U_735,U_734,U_733] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_734),U_735))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_733),U_735))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_734),U_733)) ),
    inference(variable_rename,[status(thm)],[f_323_1]) ).

cnf(f_323_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_734),U_735))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_733),U_735))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_734),U_733)) ),
    inference(clausify,[status(thm)],[f_323_2]) ).

fof(f_324_1,plain,
    ! [B,X_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_242_set__rev__mp]) ).

fof(f_324_2,plain,
    ! [U_738,U_737,U_736] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_737),U_738))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_736),U_738))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_737),U_736)) ),
    inference(variable_rename,[status(thm)],[f_324_1]) ).

cnf(f_324_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_737),U_738))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_736),U_738))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_737),U_736)) ),
    inference(clausify,[status(thm)],[f_324_2]) ).

fof(f_325_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_243_set__mp]) ).

fof(f_325_2,plain,
    ! [U_741,U_740,U_739] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_741),U_739))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_741),U_740))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_740),U_739)) ),
    inference(variable_rename,[status(thm)],[f_325_1]) ).

cnf(f_325_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_741),U_739))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_741),U_740))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_740),U_739)) ),
    inference(clausify,[status(thm)],[f_325_2]) ).

fof(f_326_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_244_set__mp]) ).

fof(f_326_2,plain,
    ! [U_744,U_743,U_742] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_744),U_742))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_744),U_743))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_743),U_742)) ),
    inference(variable_rename,[status(thm)],[f_326_1]) ).

cnf(f_326_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_744),U_742))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_744),U_743))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_743),U_742)) ),
    inference(clausify,[status(thm)],[f_326_2]) ).

fof(f_327_1,plain,
    ! [X_2,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_245_set__mp]) ).

fof(f_327_2,plain,
    ! [U_747,U_746,U_745] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_747),U_745))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_747),U_746))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_746),U_745)) ),
    inference(variable_rename,[status(thm)],[f_327_1]) ).

cnf(f_327_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_747),U_745))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_747),U_746))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_746),U_745)) ),
    inference(clausify,[status(thm)],[f_327_2]) ).

fof(f_328_1,plain,
    ! [C,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),C))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),C))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_246_subset__trans]) ).

fof(f_328_2,plain,
    ! [U_750,U_749,U_748] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_749),U_750))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_748),U_750))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_749),U_748)) ),
    inference(variable_rename,[status(thm)],[f_328_1]) ).

cnf(f_328_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_749),U_750))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_748),U_750))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_749),U_748)) ),
    inference(clausify,[status(thm)],[f_328_2]) ).

fof(f_329_1,plain,
    ! [C,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_247_subset__trans]) ).

fof(f_329_2,plain,
    ! [U_753,U_752,U_751] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_752),U_753))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_751),U_753))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_752),U_751)) ),
    inference(variable_rename,[status(thm)],[f_329_1]) ).

cnf(f_329_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_752),U_753))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_751),U_753))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_752),U_751)) ),
    inference(clausify,[status(thm)],[f_329_2]) ).

fof(f_330_1,plain,
    ! [C,A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),C))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),C))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_248_subset__trans]) ).

fof(f_330_2,plain,
    ! [U_756,U_755,U_754] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_755),U_756))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_754),U_756))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_755),U_754)) ),
    inference(variable_rename,[status(thm)],[f_330_1]) ).

cnf(f_330_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_755),U_756))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_754),U_756))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_755),U_754)) ),
    inference(clausify,[status(thm)],[f_330_2]) ).

fof(f_331_1,plain,
    ! [A,B] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) )
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_249_equalityE]) ).

fof(f_331_2,plain,
    ! [U_758,U_757] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_757),U_758))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_758),U_757)) )
      | U_758 != U_757 ),
    inference(variable_rename,[status(thm)],[f_331_1]) ).

cnf(f_331_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_758),U_757))
    | U_758 != U_757 ),
    inference(clausify,[status(thm)],[f_331_2]) ).

cnf(f_331_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_757),U_758))
    | U_758 != U_757 ),
    inference(clausify,[status(thm)],[f_331_2]) ).

fof(f_332_1,plain,
    ! [A,B] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) )
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_250_equalityE]) ).

fof(f_332_2,plain,
    ! [U_760,U_759] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_759),U_760))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_760),U_759)) )
      | U_760 != U_759 ),
    inference(variable_rename,[status(thm)],[f_332_1]) ).

cnf(f_332_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_760),U_759))
    | U_760 != U_759 ),
    inference(clausify,[status(thm)],[f_332_2]) ).

cnf(f_332_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_759),U_760))
    | U_760 != U_759 ),
    inference(clausify,[status(thm)],[f_332_2]) ).

fof(f_333_1,plain,
    ! [A,B] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) )
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_251_equalityE]) ).

fof(f_333_2,plain,
    ! [U_762,U_761] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_761),U_762))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_762),U_761)) )
      | U_762 != U_761 ),
    inference(variable_rename,[status(thm)],[f_333_1]) ).

cnf(f_333_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_762),U_761))
    | U_762 != U_761 ),
    inference(clausify,[status(thm)],[f_333_2]) ).

cnf(f_333_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_761),U_762))
    | U_762 != U_761 ),
    inference(clausify,[status(thm)],[f_333_2]) ).

fof(f_334_1,plain,
    ! [X_2,A] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
        | ~ hBOOL(hAPP_nat_bool(A,X_2)) )
      & ( hBOOL(hAPP_nat_bool(A,X_2))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_252_mem__def]) ).

fof(f_334_2,plain,
    ! [U_764,U_763] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_764),U_763))
        | ~ hBOOL(hAPP_nat_bool(U_763,U_764)) )
      & ( hBOOL(hAPP_nat_bool(U_763,U_764))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_764),U_763)) ) ),
    inference(variable_rename,[status(thm)],[f_334_1]) ).

fof(f_334_3,plain,
    ( ! [U_768,U_766] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_768),U_766))
        | ~ hBOOL(hAPP_nat_bool(U_766,U_768)) )
    & ! [U_767,U_765] :
        ( hBOOL(hAPP_nat_bool(U_765,U_767))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_767),U_765)) ) ),
    inference(miniscope,[status(thm)],[f_334_2]) ).

cnf(f_334_4,plain,
    ( hBOOL(hAPP_nat_bool(U_765,U_767))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_767),U_765)) ),
    inference(clausify,[status(thm)],[f_334_3]) ).

cnf(f_334_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_768),U_766))
    | ~ hBOOL(hAPP_nat_bool(U_766,U_768)) ),
    inference(clausify,[status(thm)],[f_334_3]) ).

fof(f_335_1,plain,
    ! [X_2,A] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
        | ~ hBOOL(hAPP_a_bool(A,X_2)) )
      & ( hBOOL(hAPP_a_bool(A,X_2))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_253_mem__def]) ).

fof(f_335_2,plain,
    ! [U_770,U_769] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_770),U_769))
        | ~ hBOOL(hAPP_a_bool(U_769,U_770)) )
      & ( hBOOL(hAPP_a_bool(U_769,U_770))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_770),U_769)) ) ),
    inference(variable_rename,[status(thm)],[f_335_1]) ).

fof(f_335_3,plain,
    ( ! [U_774,U_772] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_774),U_772))
        | ~ hBOOL(hAPP_a_bool(U_772,U_774)) )
    & ! [U_773,U_771] :
        ( hBOOL(hAPP_a_bool(U_771,U_773))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_773),U_771)) ) ),
    inference(miniscope,[status(thm)],[f_335_2]) ).

cnf(f_335_4,plain,
    ( hBOOL(hAPP_a_bool(U_771,U_773))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_773),U_771)) ),
    inference(clausify,[status(thm)],[f_335_3]) ).

cnf(f_335_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_774),U_772))
    | ~ hBOOL(hAPP_a_bool(U_772,U_774)) ),
    inference(clausify,[status(thm)],[f_335_3]) ).

fof(f_336_1,plain,
    ! [X_2,A] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
        | ~ hBOOL(hAPP_pname_bool(A,X_2)) )
      & ( hBOOL(hAPP_pname_bool(A,X_2))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_254_mem__def]) ).

fof(f_336_2,plain,
    ! [U_776,U_775] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_776),U_775))
        | ~ hBOOL(hAPP_pname_bool(U_775,U_776)) )
      & ( hBOOL(hAPP_pname_bool(U_775,U_776))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_776),U_775)) ) ),
    inference(variable_rename,[status(thm)],[f_336_1]) ).

fof(f_336_3,plain,
    ( ! [U_780,U_778] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_780),U_778))
        | ~ hBOOL(hAPP_pname_bool(U_778,U_780)) )
    & ! [U_779,U_777] :
        ( hBOOL(hAPP_pname_bool(U_777,U_779))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_779),U_777)) ) ),
    inference(miniscope,[status(thm)],[f_336_2]) ).

cnf(f_336_4,plain,
    ( hBOOL(hAPP_pname_bool(U_777,U_779))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_779),U_777)) ),
    inference(clausify,[status(thm)],[f_336_3]) ).

cnf(f_336_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_780),U_778))
    | ~ hBOOL(hAPP_pname_bool(U_778,U_780)) ),
    inference(clausify,[status(thm)],[f_336_3]) ).

fof(f_337_1,plain,
    ! [Pa] :
      ( collect_pname(Pa) = Pa
      | ~ is_fun_pname_bool(Pa) ),
    inference(fof_nnf,[status(thm)],[fact_255_Collect__def]) ).

fof(f_337_2,plain,
    ! [U_781] :
      ( collect_pname(U_781) = U_781
      | ~ is_fun_pname_bool(U_781) ),
    inference(variable_rename,[status(thm)],[f_337_1]) ).

cnf(f_337_3,plain,
    ( collect_pname(U_781) = U_781
    | ~ is_fun_pname_bool(U_781) ),
    inference(clausify,[status(thm)],[f_337_2]) ).

fof(f_338_1,plain,
    ! [Pa] : collect_fun_nat_bool(Pa) = Pa,
    inference(fof_nnf,[status(thm)],[fact_256_Collect__def]) ).

fof(f_338_2,plain,
    ! [U_782] : collect_fun_nat_bool(U_782) = U_782,
    inference(variable_rename,[status(thm)],[f_338_1]) ).

cnf(f_338_3,plain,
    collect_fun_nat_bool(U_782) = U_782,
    inference(clausify,[status(thm)],[f_338_2]) ).

fof(f_339_1,plain,
    ! [Pa] :
      ( collec1974731493e_bool(Pa) = Pa
      | ~ is_fun1661590463l_bool(Pa) ),
    inference(fof_nnf,[status(thm)],[fact_257_Collect__def]) ).

fof(f_339_2,plain,
    ! [U_783] :
      ( collec1974731493e_bool(U_783) = U_783
      | ~ is_fun1661590463l_bool(U_783) ),
    inference(variable_rename,[status(thm)],[f_339_1]) ).

cnf(f_339_3,plain,
    ( collec1974731493e_bool(U_783) = U_783
    | ~ is_fun1661590463l_bool(U_783) ),
    inference(clausify,[status(thm)],[f_339_2]) ).

fof(f_340_1,plain,
    ! [Pa] :
      ( collect_fun_a_bool(Pa) = Pa
      | ~ is_fun949378684l_bool(Pa) ),
    inference(fof_nnf,[status(thm)],[fact_258_Collect__def]) ).

fof(f_340_2,plain,
    ! [U_784] :
      ( collect_fun_a_bool(U_784) = U_784
      | ~ is_fun949378684l_bool(U_784) ),
    inference(variable_rename,[status(thm)],[f_340_1]) ).

cnf(f_340_3,plain,
    ( collect_fun_a_bool(U_784) = U_784
    | ~ is_fun949378684l_bool(U_784) ),
    inference(clausify,[status(thm)],[f_340_2]) ).

fof(f_341_1,plain,
    ! [Pa] : collect_nat(Pa) = Pa,
    inference(fof_nnf,[status(thm)],[fact_259_Collect__def]) ).

fof(f_341_2,plain,
    ! [U_785] : collect_nat(U_785) = U_785,
    inference(variable_rename,[status(thm)],[f_341_1]) ).

cnf(f_341_3,plain,
    collect_nat(U_785) = U_785,
    inference(clausify,[status(thm)],[f_341_2]) ).

fof(f_342_1,plain,
    ! [Z,F,A] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,Z),image_pname_a(F,A)))
          | ! [X_1] :
              ( Z != hAPP_pname_a(F,X_1)
              | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
              | ~ is_pname(X_1) ) )
        & ( ? [X_1] :
              ( Z = hAPP_pname_a(F,X_1)
              & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
              & is_pname(X_1) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,Z),image_pname_a(F,A))) ) )
      | ~ is_a(Z) ),
    inference(fof_nnf,[status(thm)],[fact_260_image__iff]) ).

fof(f_342_2,plain,
    ! [U_790,U_789,U_788] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_790),image_pname_a(U_789,U_788)))
          | ! [U_787] :
              ( U_790 != hAPP_pname_a(U_789,U_787)
              | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_787),U_788))
              | ~ is_pname(U_787) ) )
        & ( ? [U_786] :
              ( U_790 = hAPP_pname_a(U_789,U_786)
              & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_786),U_788))
              & is_pname(U_786) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_790),image_pname_a(U_789,U_788))) ) )
      | ~ is_a(U_790) ),
    inference(variable_rename,[status(thm)],[f_342_1]) ).

fof(f_342_3,plain,
    ! [U_790] :
      ( ( ! [U_794,U_792] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_790),image_pname_a(U_794,U_792)))
            | ! [U_787] :
                ( U_790 != hAPP_pname_a(U_794,U_787)
                | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_787),U_792))
                | ~ is_pname(U_787) ) )
        & ! [U_793,U_791] :
            ( ? [U_786] :
                ( U_790 = hAPP_pname_a(U_793,U_786)
                & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_786),U_791))
                & is_pname(U_786) )
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_790),image_pname_a(U_793,U_791))) ) )
      | ~ is_a(U_790) ),
    inference(miniscope,[status(thm)],[f_342_2]) ).

fof(f_342_4,plain,
    ! [U_790] :
      ( ( ! [U_794,U_792] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_790),image_pname_a(U_794,U_792)))
            | ! [U_787] :
                ( U_790 != hAPP_pname_a(U_794,U_787)
                | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_787),U_792))
                | ~ is_pname(U_787) ) )
        & ! [U_793,U_791] :
            ( ( U_790 = hAPP_pname_a(U_793,sK7(U_790,U_793,U_791))
              & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK7(U_790,U_793,U_791)),U_791))
              & is_pname(sK7(U_790,U_793,U_791)) )
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_790),image_pname_a(U_793,U_791))) ) )
      | ~ is_a(U_790) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_786,sK7(U_790,U_793,U_791))],[f_342_3]) ).

cnf(f_342_5,plain,
    ( is_pname(sK7(U_790,U_793,U_791))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_790),image_pname_a(U_793,U_791)))
    | ~ is_a(U_790) ),
    inference(clausify,[status(thm)],[f_342_4]) ).

cnf(f_342_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK7(U_790,U_793,U_791)),U_791))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_790),image_pname_a(U_793,U_791)))
    | ~ is_a(U_790) ),
    inference(clausify,[status(thm)],[f_342_4]) ).

cnf(f_342_7,plain,
    ( U_790 = hAPP_pname_a(U_793,sK7(U_790,U_793,U_791))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_790),image_pname_a(U_793,U_791)))
    | ~ is_a(U_790) ),
    inference(clausify,[status(thm)],[f_342_4]) ).

cnf(f_342_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_790),image_pname_a(U_794,U_792)))
    | U_790 != hAPP_pname_a(U_794,U_787)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_787),U_792))
    | ~ is_pname(U_787)
    | ~ is_a(U_790) ),
    inference(clausify,[status(thm)],[f_342_4]) ).

fof(f_343_1,plain,
    ! [F,X_2,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(F,X_2)),image_pname_a(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_261_imageI]) ).

fof(f_343_2,plain,
    ! [U_797,U_796,U_795] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(U_797,U_796)),image_pname_a(U_797,U_795)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_796),U_795)) ),
    inference(variable_rename,[status(thm)],[f_343_1]) ).

cnf(f_343_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(U_797,U_796)),image_pname_a(U_797,U_795)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_796),U_795)) ),
    inference(clausify,[status(thm)],[f_343_2]) ).

fof(f_344_1,plain,
    ! [B_1,F,X_2,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A)))
      | B_1 != hAPP_pname_a(F,X_2)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_262_rev__image__eqI]) ).

fof(f_344_2,plain,
    ! [U_801,U_800,U_799,U_798] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_801),image_pname_a(U_800,U_798)))
      | U_801 != hAPP_pname_a(U_800,U_799)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_799),U_798)) ),
    inference(variable_rename,[status(thm)],[f_344_1]) ).

cnf(f_344_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_801),image_pname_a(U_800,U_798)))
    | U_801 != hAPP_pname_a(U_800,U_799)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_799),U_798)) ),
    inference(clausify,[status(thm)],[f_344_2]) ).

fof(f_345_1,plain,
    ! [X_1,Xa] : insert_nat(X_1,Xa) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X_1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),Xa))),
    inference(fof_nnf,[status(thm)],[fact_263_insert__compr__raw]) ).

fof(f_345_2,plain,
    ! [U_803,U_802] : insert_nat(U_803,U_802) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_803)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_802))),
    inference(variable_rename,[status(thm)],[f_345_1]) ).

cnf(f_345_3,plain,
    insert_nat(U_803,U_802) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_803)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_802))),
    inference(clausify,[status(thm)],[f_345_2]) ).

fof(f_346_1,plain,
    ! [X_1,Xa] : insert_pname(X_1,Xa) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X_1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),Xa))),
    inference(fof_nnf,[status(thm)],[fact_264_insert__compr__raw]) ).

fof(f_346_2,plain,
    ! [U_805,U_804] : insert_pname(U_805,U_804) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_805)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_804))),
    inference(variable_rename,[status(thm)],[f_346_1]) ).

cnf(f_346_3,plain,
    insert_pname(U_805,U_804) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_805)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_804))),
    inference(clausify,[status(thm)],[f_346_2]) ).

fof(f_347_1,plain,
    ! [X_1,Xa] : insert_a(X_1,Xa) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X_1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),Xa))),
    inference(fof_nnf,[status(thm)],[fact_265_insert__compr__raw]) ).

fof(f_347_2,plain,
    ! [U_807,U_806] : insert_a(U_807,U_806) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_807)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_806))),
    inference(variable_rename,[status(thm)],[f_347_1]) ).

cnf(f_347_3,plain,
    insert_a(U_807,U_806) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_807)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_806))),
    inference(clausify,[status(thm)],[f_347_2]) ).

fof(f_348_1,plain,
    ! [X_1,Xa] : insert_fun_nat_bool(X_1,Xa) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X_1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),Xa))),
    inference(fof_nnf,[status(thm)],[fact_266_insert__compr__raw]) ).

fof(f_348_2,plain,
    ! [U_809,U_808] : insert_fun_nat_bool(U_809,U_808) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_809)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),U_808))),
    inference(variable_rename,[status(thm)],[f_348_1]) ).

cnf(f_348_3,plain,
    insert_fun_nat_bool(U_809,U_808) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),U_809)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),U_808))),
    inference(clausify,[status(thm)],[f_348_2]) ).

fof(f_349_1,plain,
    ! [X_1,Xa] : insert1325755072e_bool(X_1,Xa) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X_1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),Xa))),
    inference(fof_nnf,[status(thm)],[fact_267_insert__compr__raw]) ).

fof(f_349_2,plain,
    ! [U_811,U_810] : insert1325755072e_bool(U_811,U_810) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_811)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_810))),
    inference(variable_rename,[status(thm)],[f_349_1]) ).

cnf(f_349_3,plain,
    insert1325755072e_bool(U_811,U_810) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),U_811)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),U_810))),
    inference(clausify,[status(thm)],[f_349_2]) ).

fof(f_350_1,plain,
    ! [X_1,Xa] : insert_fun_a_bool(X_1,Xa) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X_1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),Xa))),
    inference(fof_nnf,[status(thm)],[fact_268_insert__compr__raw]) ).

fof(f_350_2,plain,
    ! [U_813,U_812] : insert_fun_a_bool(U_813,U_812) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_813)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),U_812))),
    inference(variable_rename,[status(thm)],[f_350_1]) ).

cnf(f_350_3,plain,
    insert_fun_a_bool(U_813,U_812) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),U_813)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),U_812))),
    inference(clausify,[status(thm)],[f_350_2]) ).

fof(f_351_1,plain,
    ! [B,A_1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),insert_nat(A_1,B))),
    inference(fof_nnf,[status(thm)],[fact_269_subset__insertI]) ).

fof(f_351_2,plain,
    ! [U_815,U_814] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_815),insert_nat(U_814,U_815))),
    inference(variable_rename,[status(thm)],[f_351_1]) ).

cnf(f_351_3,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_815),insert_nat(U_814,U_815))),
    inference(clausify,[status(thm)],[f_351_2]) ).

fof(f_352_1,plain,
    ! [B,A_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),insert_pname(A_1,B))),
    inference(fof_nnf,[status(thm)],[fact_270_subset__insertI]) ).

fof(f_352_2,plain,
    ! [U_817,U_816] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_817),insert_pname(U_816,U_817))),
    inference(variable_rename,[status(thm)],[f_352_1]) ).

cnf(f_352_3,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_817),insert_pname(U_816,U_817))),
    inference(clausify,[status(thm)],[f_352_2]) ).

fof(f_353_1,plain,
    ! [B,A_1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),insert_a(A_1,B))),
    inference(fof_nnf,[status(thm)],[fact_271_subset__insertI]) ).

fof(f_353_2,plain,
    ! [U_819,U_818] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_819),insert_a(U_818,U_819))),
    inference(variable_rename,[status(thm)],[f_353_1]) ).

cnf(f_353_3,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_819),insert_a(U_818,U_819))),
    inference(clausify,[status(thm)],[f_353_2]) ).

fof(f_354_1,plain,
    ! [X_2,A,B] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X_2,A)),B))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) )
      & ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X_2,A)),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_272_insert__subset]) ).

fof(f_354_2,plain,
    ! [U_822,U_821,U_820] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(U_822,U_821)),U_820))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_821),U_820))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_822),U_820)) )
      & ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_821),U_820))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_822),U_820)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(U_822,U_821)),U_820)) ) ),
    inference(variable_rename,[status(thm)],[f_354_1]) ).

fof(f_354_3,plain,
    ( ! [U_828,U_826,U_824] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(U_828,U_826)),U_824))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_826),U_824))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_828),U_824)) )
    & ! [U_827,U_825,U_823] :
        ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_825),U_823))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_827),U_823)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(U_827,U_825)),U_823)) ) ),
    inference(miniscope,[status(thm)],[f_354_2]) ).

cnf(f_354_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_827),U_823))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(U_827,U_825)),U_823)) ),
    inference(clausify,[status(thm)],[f_354_3]) ).

cnf(f_354_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_825),U_823))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(U_827,U_825)),U_823)) ),
    inference(clausify,[status(thm)],[f_354_3]) ).

cnf(f_354_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(U_828,U_826)),U_824))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_826),U_824))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_828),U_824)) ),
    inference(clausify,[status(thm)],[f_354_3]) ).

fof(f_355_1,plain,
    ! [X_2,A,B] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X_2,A)),B))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) )
      & ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X_2,A)),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_273_insert__subset]) ).

fof(f_355_2,plain,
    ! [U_831,U_830,U_829] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_831,U_830)),U_829))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_830),U_829))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_831),U_829)) )
      & ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_830),U_829))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_831),U_829)) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_831,U_830)),U_829)) ) ),
    inference(variable_rename,[status(thm)],[f_355_1]) ).

fof(f_355_3,plain,
    ( ! [U_837,U_835,U_833] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_837,U_835)),U_833))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_835),U_833))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_837),U_833)) )
    & ! [U_836,U_834,U_832] :
        ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_834),U_832))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_836),U_832)) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_836,U_834)),U_832)) ) ),
    inference(miniscope,[status(thm)],[f_355_2]) ).

cnf(f_355_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_836),U_832))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_836,U_834)),U_832)) ),
    inference(clausify,[status(thm)],[f_355_3]) ).

cnf(f_355_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_834),U_832))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_836,U_834)),U_832)) ),
    inference(clausify,[status(thm)],[f_355_3]) ).

cnf(f_355_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_837,U_835)),U_833))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_835),U_833))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_837),U_833)) ),
    inference(clausify,[status(thm)],[f_355_3]) ).

fof(f_356_1,plain,
    ! [X_2,A,B] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X_2,A)),B))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B)) )
      & ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B)) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X_2,A)),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_274_insert__subset]) ).

fof(f_356_2,plain,
    ! [U_840,U_839,U_838] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(U_840,U_839)),U_838))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_839),U_838))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_840),U_838)) )
      & ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_839),U_838))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_840),U_838)) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(U_840,U_839)),U_838)) ) ),
    inference(variable_rename,[status(thm)],[f_356_1]) ).

fof(f_356_3,plain,
    ( ! [U_846,U_844,U_842] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(U_846,U_844)),U_842))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_844),U_842))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_846),U_842)) )
    & ! [U_845,U_843,U_841] :
        ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_843),U_841))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_845),U_841)) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(U_845,U_843)),U_841)) ) ),
    inference(miniscope,[status(thm)],[f_356_2]) ).

cnf(f_356_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_845),U_841))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(U_845,U_843)),U_841)) ),
    inference(clausify,[status(thm)],[f_356_3]) ).

cnf(f_356_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_843),U_841))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(U_845,U_843)),U_841)) ),
    inference(clausify,[status(thm)],[f_356_3]) ).

cnf(f_356_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(U_846,U_844)),U_842))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_844),U_842))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_846),U_842)) ),
    inference(clausify,[status(thm)],[f_356_3]) ).

fof(f_357_1,plain,
    ! [B,X_2,A] :
      ( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),insert_nat(X_2,B)))
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) )
        & ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),insert_nat(X_2,B))) ) )
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_275_subset__insert]) ).

fof(f_357_2,plain,
    ! [U_849,U_848,U_847] :
      ( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_847),insert_nat(U_848,U_849)))
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_847),U_849)) )
        & ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_847),U_849))
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_847),insert_nat(U_848,U_849))) ) )
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_848),U_847)) ),
    inference(variable_rename,[status(thm)],[f_357_1]) ).

cnf(f_357_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_847),U_849))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_847),insert_nat(U_848,U_849)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_848),U_847)) ),
    inference(clausify,[status(thm)],[f_357_2]) ).

cnf(f_357_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_847),insert_nat(U_848,U_849)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_847),U_849))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_848),U_847)) ),
    inference(clausify,[status(thm)],[f_357_2]) ).

fof(f_358_1,plain,
    ! [B,X_2,A] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),insert_pname(X_2,B)))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),insert_pname(X_2,B))) ) )
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_276_subset__insert]) ).

fof(f_358_2,plain,
    ! [U_852,U_851,U_850] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_850),insert_pname(U_851,U_852)))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_850),U_852)) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_850),U_852))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_850),insert_pname(U_851,U_852))) ) )
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_851),U_850)) ),
    inference(variable_rename,[status(thm)],[f_358_1]) ).

cnf(f_358_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_850),U_852))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_850),insert_pname(U_851,U_852)))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_851),U_850)) ),
    inference(clausify,[status(thm)],[f_358_2]) ).

cnf(f_358_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_850),insert_pname(U_851,U_852)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_850),U_852))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_851),U_850)) ),
    inference(clausify,[status(thm)],[f_358_2]) ).

fof(f_359_1,plain,
    ! [B,X_2,A] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),insert_a(X_2,B)))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) )
        & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),insert_a(X_2,B))) ) )
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_277_subset__insert]) ).

fof(f_359_2,plain,
    ! [U_855,U_854,U_853] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_853),insert_a(U_854,U_855)))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_853),U_855)) )
        & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_853),U_855))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_853),insert_a(U_854,U_855))) ) )
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_854),U_853)) ),
    inference(variable_rename,[status(thm)],[f_359_1]) ).

cnf(f_359_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_853),U_855))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_853),insert_a(U_854,U_855)))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_854),U_853)) ),
    inference(clausify,[status(thm)],[f_359_2]) ).

cnf(f_359_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_853),insert_a(U_854,U_855)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_853),U_855))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_854),U_853)) ),
    inference(clausify,[status(thm)],[f_359_2]) ).

fof(f_360_1,plain,
    ! [B_1,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),insert_nat(B_1,B)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_278_subset__insertI2]) ).

fof(f_360_2,plain,
    ! [U_858,U_857,U_856] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_857),insert_nat(U_858,U_856)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_857),U_856)) ),
    inference(variable_rename,[status(thm)],[f_360_1]) ).

cnf(f_360_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_857),insert_nat(U_858,U_856)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_857),U_856)) ),
    inference(clausify,[status(thm)],[f_360_2]) ).

fof(f_361_1,plain,
    ! [B_1,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),insert_pname(B_1,B)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_279_subset__insertI2]) ).

fof(f_361_2,plain,
    ! [U_861,U_860,U_859] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_860),insert_pname(U_861,U_859)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_860),U_859)) ),
    inference(variable_rename,[status(thm)],[f_361_1]) ).

cnf(f_361_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_860),insert_pname(U_861,U_859)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_860),U_859)) ),
    inference(clausify,[status(thm)],[f_361_2]) ).

fof(f_362_1,plain,
    ! [B_1,A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),insert_a(B_1,B)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_280_subset__insertI2]) ).

fof(f_362_2,plain,
    ! [U_864,U_863,U_862] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_863),insert_a(U_864,U_862)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_863),U_862)) ),
    inference(variable_rename,[status(thm)],[f_362_1]) ).

cnf(f_362_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_863),insert_a(U_864,U_862)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_863),U_862)) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

fof(f_363_1,plain,
    ! [A_1,C,D] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(A_1,C)),insert_nat(A_1,D)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C),D)) ),
    inference(fof_nnf,[status(thm)],[fact_281_insert__mono]) ).

fof(f_363_2,plain,
    ! [U_867,U_866,U_865] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(U_867,U_866)),insert_nat(U_867,U_865)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_866),U_865)) ),
    inference(variable_rename,[status(thm)],[f_363_1]) ).

cnf(f_363_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(U_867,U_866)),insert_nat(U_867,U_865)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_866),U_865)) ),
    inference(clausify,[status(thm)],[f_363_2]) ).

fof(f_364_1,plain,
    ! [A_1,C,D] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(A_1,C)),insert_pname(A_1,D)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),D)) ),
    inference(fof_nnf,[status(thm)],[fact_282_insert__mono]) ).

fof(f_364_2,plain,
    ! [U_870,U_869,U_868] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_870,U_869)),insert_pname(U_870,U_868)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_869),U_868)) ),
    inference(variable_rename,[status(thm)],[f_364_1]) ).

cnf(f_364_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(U_870,U_869)),insert_pname(U_870,U_868)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_869),U_868)) ),
    inference(clausify,[status(thm)],[f_364_2]) ).

fof(f_365_1,plain,
    ! [A_1,C,D] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(A_1,C)),insert_a(A_1,D)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C),D)) ),
    inference(fof_nnf,[status(thm)],[fact_283_insert__mono]) ).

fof(f_365_2,plain,
    ! [U_873,U_872,U_871] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(U_873,U_872)),insert_a(U_873,U_871)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_872),U_871)) ),
    inference(variable_rename,[status(thm)],[f_365_1]) ).

cnf(f_365_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(U_873,U_872)),insert_a(U_873,U_871)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_872),U_871)) ),
    inference(clausify,[status(thm)],[f_365_2]) ).

fof(f_366_1,plain,
    ! [F,A_1,B] : image_pname_a(F,insert_pname(A_1,B)) = insert_a(hAPP_pname_a(F,A_1),image_pname_a(F,B)),
    inference(fof_nnf,[status(thm)],[fact_284_image__insert]) ).

fof(f_366_2,plain,
    ! [U_876,U_875,U_874] : image_pname_a(U_876,insert_pname(U_875,U_874)) = insert_a(hAPP_pname_a(U_876,U_875),image_pname_a(U_876,U_874)),
    inference(variable_rename,[status(thm)],[f_366_1]) ).

cnf(f_366_3,plain,
    image_pname_a(U_876,insert_pname(U_875,U_874)) = insert_a(hAPP_pname_a(U_876,U_875),image_pname_a(U_876,U_874)),
    inference(clausify,[status(thm)],[f_366_2]) ).

fof(f_367_1,plain,
    ! [F,X_2,A] :
      ( insert_a(hAPP_pname_a(F,X_2),image_pname_a(F,A)) = image_pname_a(F,A)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_285_insert__image]) ).

fof(f_367_2,plain,
    ! [U_879,U_878,U_877] :
      ( insert_a(hAPP_pname_a(U_879,U_878),image_pname_a(U_879,U_877)) = image_pname_a(U_879,U_877)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_878),U_877)) ),
    inference(variable_rename,[status(thm)],[f_367_1]) ).

cnf(f_367_3,plain,
    ( insert_a(hAPP_pname_a(U_879,U_878),image_pname_a(U_879,U_877)) = image_pname_a(U_879,U_877)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_878),U_877)) ),
    inference(clausify,[status(thm)],[f_367_2]) ).

fof(f_368_1,plain,
    ! [B,F,A] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_pname_a(F,A)))
          | ! [AA] :
              ( B != image_pname_a(F,AA)
              | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,AA),A))
              | ~ is_fun_pname_bool(AA) ) )
        & ( ? [AA] :
              ( B = image_pname_a(F,AA)
              & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,AA),A))
              & is_fun_pname_bool(AA) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_pname_a(F,A))) ) )
      | ~ is_fun_a_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_286_subset__image__iff]) ).

fof(f_368_2,plain,
    ! [U_884,U_883,U_882] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_884),image_pname_a(U_883,U_882)))
          | ! [U_881] :
              ( U_884 != image_pname_a(U_883,U_881)
              | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_881),U_882))
              | ~ is_fun_pname_bool(U_881) ) )
        & ( ? [U_880] :
              ( U_884 = image_pname_a(U_883,U_880)
              & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_880),U_882))
              & is_fun_pname_bool(U_880) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_884),image_pname_a(U_883,U_882))) ) )
      | ~ is_fun_a_bool(U_884) ),
    inference(variable_rename,[status(thm)],[f_368_1]) ).

fof(f_368_3,plain,
    ! [U_884] :
      ( ( ! [U_888,U_886] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_884),image_pname_a(U_888,U_886)))
            | ! [U_881] :
                ( U_884 != image_pname_a(U_888,U_881)
                | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_881),U_886))
                | ~ is_fun_pname_bool(U_881) ) )
        & ! [U_887,U_885] :
            ( ? [U_880] :
                ( U_884 = image_pname_a(U_887,U_880)
                & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_880),U_885))
                & is_fun_pname_bool(U_880) )
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_884),image_pname_a(U_887,U_885))) ) )
      | ~ is_fun_a_bool(U_884) ),
    inference(miniscope,[status(thm)],[f_368_2]) ).

fof(f_368_4,plain,
    ! [U_884] :
      ( ( ! [U_888,U_886] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_884),image_pname_a(U_888,U_886)))
            | ! [U_881] :
                ( U_884 != image_pname_a(U_888,U_881)
                | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_881),U_886))
                | ~ is_fun_pname_bool(U_881) ) )
        & ! [U_887,U_885] :
            ( ( U_884 = image_pname_a(U_887,sK8(U_884,U_887,U_885))
              & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK8(U_884,U_887,U_885)),U_885))
              & is_fun_pname_bool(sK8(U_884,U_887,U_885)) )
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_884),image_pname_a(U_887,U_885))) ) )
      | ~ is_fun_a_bool(U_884) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_880,sK8(U_884,U_887,U_885))],[f_368_3]) ).

cnf(f_368_5,plain,
    ( is_fun_pname_bool(sK8(U_884,U_887,U_885))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_884),image_pname_a(U_887,U_885)))
    | ~ is_fun_a_bool(U_884) ),
    inference(clausify,[status(thm)],[f_368_4]) ).

cnf(f_368_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK8(U_884,U_887,U_885)),U_885))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_884),image_pname_a(U_887,U_885)))
    | ~ is_fun_a_bool(U_884) ),
    inference(clausify,[status(thm)],[f_368_4]) ).

cnf(f_368_7,plain,
    ( U_884 = image_pname_a(U_887,sK8(U_884,U_887,U_885))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_884),image_pname_a(U_887,U_885)))
    | ~ is_fun_a_bool(U_884) ),
    inference(clausify,[status(thm)],[f_368_4]) ).

cnf(f_368_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_884),image_pname_a(U_888,U_886)))
    | U_884 != image_pname_a(U_888,U_881)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_881),U_886))
    | ~ is_fun_pname_bool(U_881)
    | ~ is_fun_a_bool(U_884) ),
    inference(clausify,[status(thm)],[f_368_4]) ).

fof(f_369_1,plain,
    ! [F,A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(F,A)),image_pname_a(F,B)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_287_image__mono]) ).

fof(f_369_2,plain,
    ! [U_891,U_890,U_889] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(U_891,U_890)),image_pname_a(U_891,U_889)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_890),U_889)) ),
    inference(variable_rename,[status(thm)],[f_369_1]) ).

cnf(f_369_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(U_891,U_890)),image_pname_a(U_891,U_889)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_890),U_889)) ),
    inference(clausify,[status(thm)],[f_369_2]) ).

fof(f_370_1,plain,
    ! [B_1,F,A] :
      ( ? [X_1] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
          & B_1 = hAPP_pname_a(F,X_1)
          & is_pname(X_1) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A)))
      | ~ is_a(B_1) ),
    inference(fof_nnf,[status(thm)],[fact_288_imageE]) ).

fof(f_370_2,plain,
    ! [U_895,U_894,U_893] :
      ( ? [U_892] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_892),U_893))
          & U_895 = hAPP_pname_a(U_894,U_892)
          & is_pname(U_892) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_895),image_pname_a(U_894,U_893)))
      | ~ is_a(U_895) ),
    inference(variable_rename,[status(thm)],[f_370_1]) ).

fof(f_370_3,plain,
    ! [U_895] :
      ( ! [U_894,U_893] :
          ( ? [U_892] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_892),U_893))
              & U_895 = hAPP_pname_a(U_894,U_892)
              & is_pname(U_892) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_895),image_pname_a(U_894,U_893))) )
      | ~ is_a(U_895) ),
    inference(miniscope,[status(thm)],[f_370_2]) ).

fof(f_370_4,plain,
    ! [U_895] :
      ( ! [U_894,U_893] :
          ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK9(U_895,U_894,U_893)),U_893))
            & U_895 = hAPP_pname_a(U_894,sK9(U_895,U_894,U_893))
            & is_pname(sK9(U_895,U_894,U_893)) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_895),image_pname_a(U_894,U_893))) )
      | ~ is_a(U_895) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_892,sK9(U_895,U_894,U_893))],[f_370_3]) ).

cnf(f_370_5,plain,
    ( is_pname(sK9(U_895,U_894,U_893))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_895),image_pname_a(U_894,U_893)))
    | ~ is_a(U_895) ),
    inference(clausify,[status(thm)],[f_370_4]) ).

cnf(f_370_6,plain,
    ( U_895 = hAPP_pname_a(U_894,sK9(U_895,U_894,U_893))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_895),image_pname_a(U_894,U_893)))
    | ~ is_a(U_895) ),
    inference(clausify,[status(thm)],[f_370_4]) ).

cnf(f_370_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK9(U_895,U_894,U_893)),U_893))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_895),image_pname_a(U_894,U_893)))
    | ~ is_a(U_895) ),
    inference(clausify,[status(thm)],[f_370_4]) ).

fof(f_371_1,plain,
    ! [B,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_289_subsetI]) ).

fof(f_371_2,plain,
    ! [U_898,U_897] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_897),U_898))
      | ? [U_896] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_896),U_898))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_896),U_897)) ) ),
    inference(variable_rename,[status(thm)],[f_371_1]) ).

fof(f_371_3,plain,
    ! [U_898,U_897] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_897),U_898))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK10(U_898,U_897)),U_898))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK10(U_898,U_897)),U_897)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_896,sK10(U_898,U_897))],[f_371_2]) ).

cnf(f_371_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK10(U_898,U_897)),U_897))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_897),U_898)) ),
    inference(clausify,[status(thm)],[f_371_3]) ).

cnf(f_371_5,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK10(U_898,U_897)),U_898))
    | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_897),U_898)) ),
    inference(clausify,[status(thm)],[f_371_3]) ).

fof(f_372_1,plain,
    ! [B,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
          & is_a(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_290_subsetI]) ).

fof(f_372_2,plain,
    ! [U_901,U_900] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_900),U_901))
      | ? [U_899] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_899),U_901))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_899),U_900))
          & is_a(U_899) ) ),
    inference(variable_rename,[status(thm)],[f_372_1]) ).

fof(f_372_3,plain,
    ! [U_901,U_900] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_900),U_901))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK11(U_901,U_900)),U_901))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK11(U_901,U_900)),U_900))
        & is_a(sK11(U_901,U_900)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_899,sK11(U_901,U_900))],[f_372_2]) ).

cnf(f_372_4,plain,
    ( is_a(sK11(U_901,U_900))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_900),U_901)) ),
    inference(clausify,[status(thm)],[f_372_3]) ).

cnf(f_372_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK11(U_901,U_900)),U_900))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_900),U_901)) ),
    inference(clausify,[status(thm)],[f_372_3]) ).

cnf(f_372_6,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK11(U_901,U_900)),U_901))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_900),U_901)) ),
    inference(clausify,[status(thm)],[f_372_3]) ).

fof(f_373_1,plain,
    ! [B,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
          & is_pname(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_291_subsetI]) ).

fof(f_373_2,plain,
    ! [U_904,U_903] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_903),U_904))
      | ? [U_902] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_902),U_904))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_902),U_903))
          & is_pname(U_902) ) ),
    inference(variable_rename,[status(thm)],[f_373_1]) ).

fof(f_373_3,plain,
    ! [U_904,U_903] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_903),U_904))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK12(U_904,U_903)),U_904))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK12(U_904,U_903)),U_903))
        & is_pname(sK12(U_904,U_903)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_902,sK12(U_904,U_903))],[f_373_2]) ).

cnf(f_373_4,plain,
    ( is_pname(sK12(U_904,U_903))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_903),U_904)) ),
    inference(clausify,[status(thm)],[f_373_3]) ).

cnf(f_373_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK12(U_904,U_903)),U_903))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_903),U_904)) ),
    inference(clausify,[status(thm)],[f_373_3]) ).

cnf(f_373_6,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK12(U_904,U_903)),U_904))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_903),U_904)) ),
    inference(clausify,[status(thm)],[f_373_3]) ).

fof(f_374_1,plain,
    ! [I,Pa,K] :
      ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(minus_minus_nat(K),I)))
      | ? [N_2] :
          ( ~ hBOOL(hAPP_nat_bool(Pa,N_2))
          & hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_2))) )
      | ~ hBOOL(hAPP_nat_bool(Pa,K)) ),
    inference(fof_nnf,[status(thm)],[fact_292_zero__induct__lemma]) ).

fof(f_374_2,plain,
    ! [U_908,U_907,U_906] :
      ( hBOOL(hAPP_nat_bool(U_907,hAPP_nat_nat(minus_minus_nat(U_906),U_908)))
      | ? [U_905] :
          ( ~ hBOOL(hAPP_nat_bool(U_907,U_905))
          & hBOOL(hAPP_nat_bool(U_907,hAPP_nat_nat(suc,U_905))) )
      | ~ hBOOL(hAPP_nat_bool(U_907,U_906)) ),
    inference(variable_rename,[status(thm)],[f_374_1]) ).

fof(f_374_3,plain,
    ! [U_908,U_907,U_906] :
      ( hBOOL(hAPP_nat_bool(U_907,hAPP_nat_nat(minus_minus_nat(U_906),U_908)))
      | ( ~ hBOOL(hAPP_nat_bool(U_907,sK13(U_908,U_907,U_906)))
        & hBOOL(hAPP_nat_bool(U_907,hAPP_nat_nat(suc,sK13(U_908,U_907,U_906)))) )
      | ~ hBOOL(hAPP_nat_bool(U_907,U_906)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_905,sK13(U_908,U_907,U_906))],[f_374_2]) ).

cnf(f_374_4,plain,
    ( hBOOL(hAPP_nat_bool(U_907,hAPP_nat_nat(suc,sK13(U_908,U_907,U_906))))
    | hBOOL(hAPP_nat_bool(U_907,hAPP_nat_nat(minus_minus_nat(U_906),U_908)))
    | ~ hBOOL(hAPP_nat_bool(U_907,U_906)) ),
    inference(clausify,[status(thm)],[f_374_3]) ).

cnf(f_374_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_907,sK13(U_908,U_907,U_906)))
    | hBOOL(hAPP_nat_bool(U_907,hAPP_nat_nat(minus_minus_nat(U_906),U_908)))
    | ~ hBOOL(hAPP_nat_bool(U_907,U_906)) ),
    inference(clausify,[status(thm)],[f_374_3]) ).

fof(f_375_1,plain,
    ! [N_1,M_1] :
      ( ? [M] : M_1 = hAPP_nat_nat(suc,M)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_293_Suc__le__D]) ).

fof(f_375_2,plain,
    ! [U_911,U_910] :
      ( ? [U_909] : U_910 = hAPP_nat_nat(suc,U_909)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_911)),U_910)) ),
    inference(variable_rename,[status(thm)],[f_375_1]) ).

fof(f_375_3,plain,
    ! [U_911,U_910] :
      ( U_910 = hAPP_nat_nat(suc,sK14(U_911,U_910))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_911)),U_910)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_909,sK14(U_911,U_910))],[f_375_2]) ).

cnf(f_375_4,plain,
    ( U_910 = hAPP_nat_nat(suc,sK14(U_911,U_910))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_911)),U_910)) ),
    inference(clausify,[status(thm)],[f_375_3]) ).

fof(f_376_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(F,A)),B))
      | ? [X_1] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(F,X_1)),B))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
          & is_pname(X_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_294_image__subsetI]) ).

fof(f_376_2,plain,
    ! [U_915,U_914,U_913] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(U_915,U_913)),U_914))
      | ? [U_912] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(U_915,U_912)),U_914))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_912),U_913))
          & is_pname(U_912) ) ),
    inference(variable_rename,[status(thm)],[f_376_1]) ).

fof(f_376_3,plain,
    ! [U_915,U_914,U_913] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(U_915,U_913)),U_914))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(U_915,sK15(U_915,U_914,U_913))),U_914))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK15(U_915,U_914,U_913)),U_913))
        & is_pname(sK15(U_915,U_914,U_913)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_912,sK15(U_915,U_914,U_913))],[f_376_2]) ).

cnf(f_376_4,plain,
    ( is_pname(sK15(U_915,U_914,U_913))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(U_915,U_913)),U_914)) ),
    inference(clausify,[status(thm)],[f_376_3]) ).

cnf(f_376_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK15(U_915,U_914,U_913)),U_913))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(U_915,U_913)),U_914)) ),
    inference(clausify,[status(thm)],[f_376_3]) ).

cnf(f_376_6,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(U_915,sK15(U_915,U_914,U_913))),U_914))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(U_915,U_913)),U_914)) ),
    inference(clausify,[status(thm)],[f_376_3]) ).

fof(f_377_1,plain,
    ! [X_2] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),X_2)),
    inference(fof_nnf,[status(thm)],[fact_295_order__refl]) ).

fof(f_377_2,plain,
    ! [U_916] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_916),U_916)),
    inference(variable_rename,[status(thm)],[f_377_1]) ).

cnf(f_377_3,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_916),U_916)),
    inference(clausify,[status(thm)],[f_377_2]) ).

fof(f_378_1,plain,
    ! [X_2] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_2),X_2)),
    inference(fof_nnf,[status(thm)],[fact_296_order__refl]) ).

fof(f_378_2,plain,
    ! [U_917] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_917),U_917)),
    inference(variable_rename,[status(thm)],[f_378_1]) ).

cnf(f_378_3,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_917),U_917)),
    inference(clausify,[status(thm)],[f_378_2]) ).

fof(f_379_1,plain,
    ! [X_3] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_3),X_3)),
    inference(fof_nnf,[status(thm)],[fact_297_order__refl]) ).

fof(f_379_2,plain,
    ! [U_918] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_918),U_918)),
    inference(variable_rename,[status(thm)],[f_379_1]) ).

cnf(f_379_3,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_918),U_918)),
    inference(clausify,[status(thm)],[f_379_2]) ).

fof(f_380_1,plain,
    ! [X_2] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_2),X_2)),
    inference(fof_nnf,[status(thm)],[fact_298_order__refl]) ).

fof(f_380_2,plain,
    ! [U_919] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_919),U_919)),
    inference(variable_rename,[status(thm)],[f_380_1]) ).

cnf(f_380_3,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_919),U_919)),
    inference(clausify,[status(thm)],[f_380_2]) ).

fof(f_381_1,plain,
    ! [N] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N))
        | ! [M] :
          ? [X_1] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),M))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N)) ) )
      & ( ? [M] :
          ! [X_1] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),M))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N)) ) ),
    inference(fof_nnf,[status(thm)],[fact_299_finite__nat__set__iff__bounded__le]) ).

fof(f_381_2,plain,
    ! [U_924] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_924))
        | ! [U_923] :
          ? [U_922] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_922),U_923))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_922),U_924)) ) )
      & ( ? [U_921] :
          ! [U_920] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_920),U_921))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_920),U_924)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_924)) ) ),
    inference(variable_rename,[status(thm)],[f_381_1]) ).

fof(f_381_3,plain,
    ( ! [U_926] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_926))
        | ! [U_923] :
          ? [U_922] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_922),U_923))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_922),U_926)) ) )
    & ! [U_925] :
        ( ? [U_921] :
          ! [U_920] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_920),U_921))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_920),U_925)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_925)) ) ),
    inference(miniscope,[status(thm)],[f_381_2]) ).

fof(f_381_4,plain,
    ( ! [U_926] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_926))
        | ! [U_923] :
          ? [U_922] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_922),U_923))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_922),U_926)) ) )
    & ! [U_925] :
        ( ! [U_920] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_920),sK16(U_925)))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_920),U_925)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_925)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_921,sK16(U_925))],[f_381_3]) ).

fof(f_381_5,plain,
    ( ! [U_926] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_926))
        | ! [U_923] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK17(U_926,U_923)),U_923))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK17(U_926,U_923)),U_926)) ) )
    & ! [U_925] :
        ( ! [U_920] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_920),sK16(U_925)))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_920),U_925)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_925)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_922,sK17(U_926,U_923))],[f_381_4]) ).

cnf(f_381_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_920),sK16(U_925)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_920),U_925))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_925)) ),
    inference(clausify,[status(thm)],[f_381_5]) ).

cnf(f_381_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK17(U_926,U_923)),U_926))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_926)) ),
    inference(clausify,[status(thm)],[f_381_5]) ).

cnf(f_381_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK17(U_926,U_923)),U_923))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_926)) ),
    inference(clausify,[status(thm)],[f_381_5]) ).

fof(f_382_1,plain,
    ! [P] :
      ( ~ hBOOL(P)
      | ~ hBOOL(hAPP_bool_bool(fNot,P)) ),
    inference(fof_nnf,[status(thm)],[help_fNot_1_1_U]) ).

fof(f_382_2,plain,
    ! [U_927] :
      ( ~ hBOOL(U_927)
      | ~ hBOOL(hAPP_bool_bool(fNot,U_927)) ),
    inference(variable_rename,[status(thm)],[f_382_1]) ).

cnf(f_382_3,plain,
    ( ~ hBOOL(U_927)
    | ~ hBOOL(hAPP_bool_bool(fNot,U_927)) ),
    inference(clausify,[status(thm)],[f_382_2]) ).

fof(f_383_1,plain,
    ! [P] :
      ( hBOOL(hAPP_bool_bool(fNot,P))
      | hBOOL(P) ),
    inference(fof_nnf,[status(thm)],[help_fNot_2_1_U]) ).

fof(f_383_2,plain,
    ! [U_928] :
      ( hBOOL(hAPP_bool_bool(fNot,U_928))
      | hBOOL(U_928) ),
    inference(variable_rename,[status(thm)],[f_383_1]) ).

cnf(f_383_3,plain,
    ( hBOOL(hAPP_bool_bool(fNot,U_928))
    | hBOOL(U_928) ),
    inference(clausify,[status(thm)],[f_383_2]) ).

fof(f_384_1,plain,
    ! [Q,P] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
      | ~ hBOOL(Q)
      | ~ hBOOL(P) ),
    inference(fof_nnf,[status(thm)],[help_fconj_1_1_U]) ).

fof(f_384_2,plain,
    ! [U_930,U_929] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_929),U_930))
      | ~ hBOOL(U_930)
      | ~ hBOOL(U_929) ),
    inference(variable_rename,[status(thm)],[f_384_1]) ).

fof(f_384_3,plain,
    ! [U_930] :
      ( ! [U_929] :
          ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_929),U_930))
          | ~ hBOOL(U_929) )
      | ~ hBOOL(U_930) ),
    inference(miniscope,[status(thm)],[f_384_2]) ).

cnf(f_384_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_929),U_930))
    | ~ hBOOL(U_929)
    | ~ hBOOL(U_930) ),
    inference(clausify,[status(thm)],[f_384_3]) ).

fof(f_385_1,plain,
    ! [P,Q] :
      ( hBOOL(P)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) ),
    inference(fof_nnf,[status(thm)],[help_fconj_2_1_U]) ).

fof(f_385_2,plain,
    ! [U_932,U_931] :
      ( hBOOL(U_932)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_932),U_931)) ),
    inference(variable_rename,[status(thm)],[f_385_1]) ).

fof(f_385_3,plain,
    ! [U_932] :
      ( ! [U_931] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_932),U_931))
      | hBOOL(U_932) ),
    inference(miniscope,[status(thm)],[f_385_2]) ).

cnf(f_385_4,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_932),U_931))
    | hBOOL(U_932) ),
    inference(clausify,[status(thm)],[f_385_3]) ).

fof(f_386_1,plain,
    ! [P,Q] :
      ( hBOOL(Q)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) ),
    inference(fof_nnf,[status(thm)],[help_fconj_3_1_U]) ).

fof(f_386_2,plain,
    ! [U_934,U_933] :
      ( hBOOL(U_933)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_934),U_933)) ),
    inference(variable_rename,[status(thm)],[f_386_1]) ).

cnf(f_386_3,plain,
    ( hBOOL(U_933)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_934),U_933)) ),
    inference(clausify,[status(thm)],[f_386_2]) ).

fof(f_387_1,plain,
    ! [Q,P] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q))
      | ~ hBOOL(P) ),
    inference(fof_nnf,[status(thm)],[help_fdisj_1_1_U]) ).

fof(f_387_2,plain,
    ! [U_936,U_935] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_935),U_936))
      | ~ hBOOL(U_935) ),
    inference(variable_rename,[status(thm)],[f_387_1]) ).

cnf(f_387_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_935),U_936))
    | ~ hBOOL(U_935) ),
    inference(clausify,[status(thm)],[f_387_2]) ).

fof(f_388_1,plain,
    ! [P,Q] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q))
      | ~ hBOOL(Q) ),
    inference(fof_nnf,[status(thm)],[help_fdisj_2_1_U]) ).

fof(f_388_2,plain,
    ! [U_938,U_937] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_938),U_937))
      | ~ hBOOL(U_937) ),
    inference(variable_rename,[status(thm)],[f_388_1]) ).

cnf(f_388_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_938),U_937))
    | ~ hBOOL(U_937) ),
    inference(clausify,[status(thm)],[f_388_2]) ).

fof(f_389_1,plain,
    ! [P,Q] :
      ( hBOOL(Q)
      | hBOOL(P)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) ),
    inference(fof_nnf,[status(thm)],[help_fdisj_3_1_U]) ).

fof(f_389_2,plain,
    ! [U_940,U_939] :
      ( hBOOL(U_939)
      | hBOOL(U_940)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_940),U_939)) ),
    inference(variable_rename,[status(thm)],[f_389_1]) ).

fof(f_389_3,plain,
    ! [U_940] :
      ( ! [U_939] :
          ( hBOOL(U_939)
          | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_940),U_939)) )
      | hBOOL(U_940) ),
    inference(miniscope,[status(thm)],[f_389_2]) ).

cnf(f_389_4,plain,
    ( hBOOL(U_939)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_940),U_939))
    | hBOOL(U_940) ),
    inference(clausify,[status(thm)],[f_389_3]) ).

fof(f_390_1,plain,
    ! [Q,P] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q))
      | hBOOL(P) ),
    inference(fof_nnf,[status(thm)],[help_fimplies_1_1_U]) ).

fof(f_390_2,plain,
    ! [U_942,U_941] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_941),U_942))
      | hBOOL(U_941) ),
    inference(variable_rename,[status(thm)],[f_390_1]) ).

cnf(f_390_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_941),U_942))
    | hBOOL(U_941) ),
    inference(clausify,[status(thm)],[f_390_2]) ).

fof(f_391_1,plain,
    ! [P,Q] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q))
      | ~ hBOOL(Q) ),
    inference(fof_nnf,[status(thm)],[help_fimplies_2_1_U]) ).

fof(f_391_2,plain,
    ! [U_944,U_943] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_944),U_943))
      | ~ hBOOL(U_943) ),
    inference(variable_rename,[status(thm)],[f_391_1]) ).

cnf(f_391_3,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_944),U_943))
    | ~ hBOOL(U_943) ),
    inference(clausify,[status(thm)],[f_391_2]) ).

fof(f_392_1,plain,
    ! [P,Q] :
      ( hBOOL(Q)
      | ~ hBOOL(P)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)) ),
    inference(fof_nnf,[status(thm)],[help_fimplies_3_1_U]) ).

fof(f_392_2,plain,
    ! [U_946,U_945] :
      ( hBOOL(U_945)
      | ~ hBOOL(U_946)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_946),U_945)) ),
    inference(variable_rename,[status(thm)],[f_392_1]) ).

fof(f_392_3,plain,
    ! [U_946] :
      ( ! [U_945] :
          ( hBOOL(U_945)
          | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_946),U_945)) )
      | ~ hBOOL(U_946) ),
    inference(miniscope,[status(thm)],[f_392_2]) ).

cnf(f_392_4,plain,
    ( hBOOL(U_945)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_946),U_945))
    | ~ hBOOL(U_946) ),
    inference(clausify,[status(thm)],[f_392_3]) ).

fof(f_393_1,plain,
    ! [X,Y] :
      ( X = Y
      | ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X),Y))
      | ~ is_a(Y)
      | ~ is_a(X) ),
    inference(fof_nnf,[status(thm)],[help_fequal_1_1_fequal_000t__a_T]) ).

fof(f_393_2,plain,
    ! [U_948,U_947] :
      ( U_948 = U_947
      | ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,U_948),U_947))
      | ~ is_a(U_947)
      | ~ is_a(U_948) ),
    inference(variable_rename,[status(thm)],[f_393_1]) ).

cnf(f_393_3,plain,
    ( U_948 = U_947
    | ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,U_948),U_947))
    | ~ is_a(U_947)
    | ~ is_a(U_948) ),
    inference(clausify,[status(thm)],[f_393_2]) ).

fof(f_394_1,plain,
    ! [X,Y] :
      ( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X),Y))
      | X != Y ),
    inference(fof_nnf,[status(thm)],[help_fequal_2_1_fequal_000t__a_T]) ).

fof(f_394_2,plain,
    ! [U_950,U_949] :
      ( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,U_950),U_949))
      | U_950 != U_949 ),
    inference(variable_rename,[status(thm)],[f_394_1]) ).

cnf(f_394_3,plain,
    ( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,U_950),U_949))
    | U_950 != U_949 ),
    inference(clausify,[status(thm)],[f_394_2]) ).

fof(f_395_1,plain,
    ! [X,Y] :
      ( X = Y
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)) ),
    inference(fof_nnf,[status(thm)],[help_fequal_1_1_fequal_000tc__Nat__Onat_T]) ).

fof(f_395_2,plain,
    ! [U_952,U_951] :
      ( U_952 = U_951
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_952),U_951)) ),
    inference(variable_rename,[status(thm)],[f_395_1]) ).

cnf(f_395_3,plain,
    ( U_952 = U_951
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_952),U_951)) ),
    inference(clausify,[status(thm)],[f_395_2]) ).

fof(f_396_1,plain,
    ! [X,Y] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y))
      | X != Y ),
    inference(fof_nnf,[status(thm)],[help_fequal_2_1_fequal_000tc__Nat__Onat_T]) ).

fof(f_396_2,plain,
    ! [U_954,U_953] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_954),U_953))
      | U_954 != U_953 ),
    inference(variable_rename,[status(thm)],[f_396_1]) ).

cnf(f_396_3,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_954),U_953))
    | U_954 != U_953 ),
    inference(clausify,[status(thm)],[f_396_2]) ).

fof(f_397_1,plain,
    ! [X,Y] :
      ( X = Y
      | ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X),Y))
      | ~ is_pname(Y)
      | ~ is_pname(X) ),
    inference(fof_nnf,[status(thm)],[help_fequal_1_1_fequal_000tc__Com__Opname_T]) ).

fof(f_397_2,plain,
    ! [U_956,U_955] :
      ( U_956 = U_955
      | ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,U_956),U_955))
      | ~ is_pname(U_955)
      | ~ is_pname(U_956) ),
    inference(variable_rename,[status(thm)],[f_397_1]) ).

cnf(f_397_3,plain,
    ( U_956 = U_955
    | ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,U_956),U_955))
    | ~ is_pname(U_955)
    | ~ is_pname(U_956) ),
    inference(clausify,[status(thm)],[f_397_2]) ).

fof(f_398_1,plain,
    ! [X,Y] :
      ( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X),Y))
      | X != Y ),
    inference(fof_nnf,[status(thm)],[help_fequal_2_1_fequal_000tc__Com__Opname_T]) ).

fof(f_398_2,plain,
    ! [U_958,U_957] :
      ( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,U_958),U_957))
      | U_958 != U_957 ),
    inference(variable_rename,[status(thm)],[f_398_1]) ).

cnf(f_398_3,plain,
    ( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,U_958),U_957))
    | U_958 != U_957 ),
    inference(clausify,[status(thm)],[f_398_2]) ).

fof(f_399_1,plain,
    ! [P,Q,R] : hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(P),Q),R) = hAPP_a_bool(hAPP_a_fun_a_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U]) ).

fof(f_399_2,plain,
    ! [U_961,U_960,U_959] : hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(U_961),U_960),U_959) = hAPP_a_bool(hAPP_a_fun_a_bool(U_961,U_959),U_960),
    inference(variable_rename,[status(thm)],[f_399_1]) ).

cnf(f_399_3,plain,
    hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(U_961),U_960),U_959) = hAPP_a_bool(hAPP_a_fun_a_bool(U_961,U_959),U_960),
    inference(clausify,[status(thm)],[f_399_2]) ).

fof(f_400_1,plain,
    ! [X,Y] :
      ( X = Y
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X),Y))
      | ~ is_fun_a_bool(Y)
      | ~ is_fun_a_bool(X) ),
    inference(fof_nnf,[status(thm)],[help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T]) ).

fof(f_400_2,plain,
    ! [U_963,U_962] :
      ( U_963 = U_962
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,U_963),U_962))
      | ~ is_fun_a_bool(U_962)
      | ~ is_fun_a_bool(U_963) ),
    inference(variable_rename,[status(thm)],[f_400_1]) ).

cnf(f_400_3,plain,
    ( U_963 = U_962
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,U_963),U_962))
    | ~ is_fun_a_bool(U_962)
    | ~ is_fun_a_bool(U_963) ),
    inference(clausify,[status(thm)],[f_400_2]) ).

fof(f_401_1,plain,
    ! [X,Y] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X),Y))
      | X != Y ),
    inference(fof_nnf,[status(thm)],[help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T]) ).

fof(f_401_2,plain,
    ! [U_965,U_964] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,U_965),U_964))
      | U_965 != U_964 ),
    inference(variable_rename,[status(thm)],[f_401_1]) ).

cnf(f_401_3,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,U_965),U_964))
    | U_965 != U_964 ),
    inference(clausify,[status(thm)],[f_401_2]) ).

fof(f_402_1,plain,
    ! [P,Q,R] : hAPP_a_bool(cOMBB_bool_bool_a(P,Q),R) = hAPP_bool_bool(P,hAPP_a_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U]) ).

fof(f_402_2,plain,
    ! [U_968,U_967,U_966] : hAPP_a_bool(cOMBB_bool_bool_a(U_968,U_967),U_966) = hAPP_bool_bool(U_968,hAPP_a_bool(U_967,U_966)),
    inference(variable_rename,[status(thm)],[f_402_1]) ).

cnf(f_402_3,plain,
    hAPP_a_bool(cOMBB_bool_bool_a(U_968,U_967),U_966) = hAPP_bool_bool(U_968,hAPP_a_bool(U_967,U_966)),
    inference(clausify,[status(thm)],[f_402_2]) ).

fof(f_403_1,plain,
    ! [P,Q,R] : hAPP_a_bool(cOMBS_a_bool_bool(P,Q),R) = hAPP_bool_bool(hAPP_a_fun_bool_bool(P,R),hAPP_a_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U]) ).

fof(f_403_2,plain,
    ! [U_971,U_970,U_969] : hAPP_a_bool(cOMBS_a_bool_bool(U_971,U_970),U_969) = hAPP_bool_bool(hAPP_a_fun_bool_bool(U_971,U_969),hAPP_a_bool(U_970,U_969)),
    inference(variable_rename,[status(thm)],[f_403_1]) ).

cnf(f_403_3,plain,
    hAPP_a_bool(cOMBS_a_bool_bool(U_971,U_970),U_969) = hAPP_bool_bool(hAPP_a_fun_bool_bool(U_971,U_969),hAPP_a_bool(U_970,U_969)),
    inference(clausify,[status(thm)],[f_403_2]) ).

fof(f_404_1,plain,
    ! [P,Q,R] : hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(P),Q),R) = hAPP_a_bool(hAPP_p1534023578a_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U]) ).

fof(f_404_2,plain,
    ! [U_974,U_973,U_972] : hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(U_974),U_973),U_972) = hAPP_a_bool(hAPP_p1534023578a_bool(U_974,U_972),U_973),
    inference(variable_rename,[status(thm)],[f_404_1]) ).

cnf(f_404_3,plain,
    hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(U_974),U_973),U_972) = hAPP_a_bool(hAPP_p1534023578a_bool(U_974,U_972),U_973),
    inference(clausify,[status(thm)],[f_404_2]) ).

fof(f_405_1,plain,
    ! [X,Y] :
      ( X = Y
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X),Y)) ),
    inference(fof_nnf,[status(thm)],[help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T]) ).

fof(f_405_2,plain,
    ! [U_976,U_975] :
      ( U_976 = U_975
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,U_976),U_975)) ),
    inference(variable_rename,[status(thm)],[f_405_1]) ).

cnf(f_405_3,plain,
    ( U_976 = U_975
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,U_976),U_975)) ),
    inference(clausify,[status(thm)],[f_405_2]) ).

fof(f_406_1,plain,
    ! [X,Y] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X),Y))
      | X != Y ),
    inference(fof_nnf,[status(thm)],[help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T]) ).

fof(f_406_2,plain,
    ! [U_978,U_977] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,U_978),U_977))
      | U_978 != U_977 ),
    inference(variable_rename,[status(thm)],[f_406_1]) ).

cnf(f_406_3,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,U_978),U_977))
    | U_978 != U_977 ),
    inference(clausify,[status(thm)],[f_406_2]) ).

fof(f_407_1,plain,
    ! [X,Y] :
      ( X = Y
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X),Y))
      | ~ is_fun_pname_bool(Y)
      | ~ is_fun_pname_bool(X) ),
    inference(fof_nnf,[status(thm)],[help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T]) ).

fof(f_407_2,plain,
    ! [U_980,U_979] :
      ( U_980 = U_979
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_980),U_979))
      | ~ is_fun_pname_bool(U_979)
      | ~ is_fun_pname_bool(U_980) ),
    inference(variable_rename,[status(thm)],[f_407_1]) ).

cnf(f_407_3,plain,
    ( U_980 = U_979
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_980),U_979))
    | ~ is_fun_pname_bool(U_979)
    | ~ is_fun_pname_bool(U_980) ),
    inference(clausify,[status(thm)],[f_407_2]) ).

fof(f_408_1,plain,
    ! [X,Y] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X),Y))
      | X != Y ),
    inference(fof_nnf,[status(thm)],[help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T]) ).

fof(f_408_2,plain,
    ! [U_982,U_981] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_982),U_981))
      | U_982 != U_981 ),
    inference(variable_rename,[status(thm)],[f_408_1]) ).

cnf(f_408_3,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_982),U_981))
    | U_982 != U_981 ),
    inference(clausify,[status(thm)],[f_408_2]) ).

fof(f_409_1,plain,
    ! [P,Q,R] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(P),Q),R) = hAPP_nat_bool(hAPP_n1699378549t_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U]) ).

fof(f_409_2,plain,
    ! [U_985,U_984,U_983] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(U_985),U_984),U_983) = hAPP_nat_bool(hAPP_n1699378549t_bool(U_985,U_983),U_984),
    inference(variable_rename,[status(thm)],[f_409_1]) ).

cnf(f_409_3,plain,
    hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(U_985),U_984),U_983) = hAPP_nat_bool(hAPP_n1699378549t_bool(U_985,U_983),U_984),
    inference(clausify,[status(thm)],[f_409_2]) ).

fof(f_410_1,plain,
    ! [P,Q,R] : hAPP_nat_bool(cOMBB_bool_bool_nat(P,Q),R) = hAPP_bool_bool(P,hAPP_nat_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U]) ).

fof(f_410_2,plain,
    ! [U_988,U_987,U_986] : hAPP_nat_bool(cOMBB_bool_bool_nat(U_988,U_987),U_986) = hAPP_bool_bool(U_988,hAPP_nat_bool(U_987,U_986)),
    inference(variable_rename,[status(thm)],[f_410_1]) ).

cnf(f_410_3,plain,
    hAPP_nat_bool(cOMBB_bool_bool_nat(U_988,U_987),U_986) = hAPP_bool_bool(U_988,hAPP_nat_bool(U_987,U_986)),
    inference(clausify,[status(thm)],[f_410_2]) ).

fof(f_411_1,plain,
    ! [P,Q,R] : hAPP_nat_bool(cOMBS_nat_bool_bool(P,Q),R) = hAPP_bool_bool(hAPP_n1006566506l_bool(P,R),hAPP_nat_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U]) ).

fof(f_411_2,plain,
    ! [U_991,U_990,U_989] : hAPP_nat_bool(cOMBS_nat_bool_bool(U_991,U_990),U_989) = hAPP_bool_bool(hAPP_n1006566506l_bool(U_991,U_989),hAPP_nat_bool(U_990,U_989)),
    inference(variable_rename,[status(thm)],[f_411_1]) ).

cnf(f_411_3,plain,
    hAPP_nat_bool(cOMBS_nat_bool_bool(U_991,U_990),U_989) = hAPP_bool_bool(hAPP_n1006566506l_bool(U_991,U_989),hAPP_nat_bool(U_990,U_989)),
    inference(clausify,[status(thm)],[f_411_2]) ).

fof(f_412_1,plain,
    ! [P,Q,R] : hAPP_pname_bool(cOMBB_647938656_pname(P,Q),R) = hAPP_bool_bool(P,hAPP_pname_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U]) ).

fof(f_412_2,plain,
    ! [U_994,U_993,U_992] : hAPP_pname_bool(cOMBB_647938656_pname(U_994,U_993),U_992) = hAPP_bool_bool(U_994,hAPP_pname_bool(U_993,U_992)),
    inference(variable_rename,[status(thm)],[f_412_1]) ).

cnf(f_412_3,plain,
    hAPP_pname_bool(cOMBB_647938656_pname(U_994,U_993),U_992) = hAPP_bool_bool(U_994,hAPP_pname_bool(U_993,U_992)),
    inference(clausify,[status(thm)],[f_412_2]) ).

fof(f_413_1,plain,
    ! [P,Q,R] : hAPP_pname_bool(cOMBS_568398431l_bool(P,Q),R) = hAPP_bool_bool(hAPP_p393069232l_bool(P,R),hAPP_pname_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U]) ).

fof(f_413_2,plain,
    ! [U_997,U_996,U_995] : hAPP_pname_bool(cOMBS_568398431l_bool(U_997,U_996),U_995) = hAPP_bool_bool(hAPP_p393069232l_bool(U_997,U_995),hAPP_pname_bool(U_996,U_995)),
    inference(variable_rename,[status(thm)],[f_413_1]) ).

cnf(f_413_3,plain,
    hAPP_pname_bool(cOMBS_568398431l_bool(U_997,U_996),U_995) = hAPP_bool_bool(hAPP_p393069232l_bool(U_997,U_995),hAPP_pname_bool(U_996,U_995)),
    inference(clausify,[status(thm)],[f_413_2]) ).

fof(f_414_1,plain,
    ! [P,Q,R] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(P),Q),R) = hAPP_pname_bool(hAPP_p61793385e_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U]) ).

fof(f_414_2,plain,
    ! [U_1000,U_999,U_998] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(U_1000),U_999),U_998) = hAPP_pname_bool(hAPP_p61793385e_bool(U_1000,U_998),U_999),
    inference(variable_rename,[status(thm)],[f_414_1]) ).

cnf(f_414_3,plain,
    hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(U_1000),U_999),U_998) = hAPP_pname_bool(hAPP_p61793385e_bool(U_1000,U_998),U_999),
    inference(clausify,[status(thm)],[f_414_2]) ).

fof(f_415_1,plain,
    ! [P,Q,R] : hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(P),Q),R) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo]) ).

fof(f_415_2,plain,
    ! [U_1003,U_1002,U_1001] : hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(U_1003),U_1002),U_1001) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(U_1003,U_1001),U_1002),
    inference(variable_rename,[status(thm)],[f_415_1]) ).

cnf(f_415_3,plain,
    hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(U_1003),U_1002),U_1001) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(U_1003,U_1001),U_1002),
    inference(clausify,[status(thm)],[f_415_2]) ).

fof(f_416_1,plain,
    ! [P,Q,R] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(P,Q),R) = hAPP_a_fun_a_bool(P,hAPP_pname_a(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna]) ).

fof(f_416_2,plain,
    ! [U_1006,U_1005,U_1004] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(U_1006,U_1005),U_1004) = hAPP_a_fun_a_bool(U_1006,hAPP_pname_a(U_1005,U_1004)),
    inference(variable_rename,[status(thm)],[f_416_1]) ).

cnf(f_416_3,plain,
    hAPP_p1534023578a_bool(cOMBB_1897541054_pname(U_1006,U_1005),U_1004) = hAPP_a_fun_a_bool(U_1006,hAPP_pname_a(U_1005,U_1004)),
    inference(clausify,[status(thm)],[f_416_2]) ).

fof(f_417_1,plain,
    ! [P,Q,R] : hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(P,Q),R) = hAPP_bool_bool(P,hAPP_fun_a_bool_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H]) ).

fof(f_417_2,plain,
    ! [U_1009,U_1008,U_1007] : hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(U_1009,U_1008),U_1007) = hAPP_bool_bool(U_1009,hAPP_fun_a_bool_bool(U_1008,U_1007)),
    inference(variable_rename,[status(thm)],[f_417_1]) ).

cnf(f_417_3,plain,
    hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(U_1009,U_1008),U_1007) = hAPP_bool_bool(U_1009,hAPP_fun_a_bool_bool(U_1008,U_1007)),
    inference(clausify,[status(thm)],[f_417_2]) ).

fof(f_418_1,plain,
    ! [P,Q,R] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_a_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo]) ).

fof(f_418_2,plain,
    ! [U_1012,U_1011,U_1010] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(U_1012,U_1011),U_1010) = hAPP_b589554111l_bool(U_1012,hAPP_a_bool(U_1011,U_1010)),
    inference(variable_rename,[status(thm)],[f_418_1]) ).

cnf(f_418_3,plain,
    hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(U_1012,U_1011),U_1010) = hAPP_b589554111l_bool(U_1012,hAPP_a_bool(U_1011,U_1010)),
    inference(clausify,[status(thm)],[f_418_2]) ).

fof(f_419_1,plain,
    ! [P,Q,R] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f198738859l_bool(P,R),hAPP_fun_a_bool_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_]) ).

fof(f_419_2,plain,
    ! [U_1015,U_1014,U_1013] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(U_1015,U_1014),U_1013) = hAPP_bool_bool(hAPP_f198738859l_bool(U_1015,U_1013),hAPP_fun_a_bool_bool(U_1014,U_1013)),
    inference(variable_rename,[status(thm)],[f_419_1]) ).

cnf(f_419_3,plain,
    hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(U_1015,U_1014),U_1013) = hAPP_bool_bool(hAPP_f198738859l_bool(U_1015,U_1013),hAPP_fun_a_bool_bool(U_1014,U_1013)),
    inference(clausify,[status(thm)],[f_419_2]) ).

fof(f_420_1,plain,
    ! [P,Q,R] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(P),Q),R) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_]) ).

fof(f_420_2,plain,
    ! [U_1018,U_1017,U_1016] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(U_1018),U_1017),U_1016) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(U_1018,U_1016),U_1017),
    inference(variable_rename,[status(thm)],[f_420_1]) ).

cnf(f_420_3,plain,
    hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(U_1018),U_1017),U_1016) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(U_1018,U_1016),U_1017),
    inference(clausify,[status(thm)],[f_420_2]) ).

fof(f_421_1,plain,
    ! [P,Q,R] : hAPP_f54304608l_bool(cOMBB_238756964t_bool(P,Q),R) = hAPP_bool_bool(P,hAPP_f54304608l_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On]) ).

fof(f_421_2,plain,
    ! [U_1021,U_1020,U_1019] : hAPP_f54304608l_bool(cOMBB_238756964t_bool(U_1021,U_1020),U_1019) = hAPP_bool_bool(U_1021,hAPP_f54304608l_bool(U_1020,U_1019)),
    inference(variable_rename,[status(thm)],[f_421_1]) ).

cnf(f_421_3,plain,
    hAPP_f54304608l_bool(cOMBB_238756964t_bool(U_1021,U_1020),U_1019) = hAPP_bool_bool(U_1021,hAPP_f54304608l_bool(U_1020,U_1019)),
    inference(clausify,[status(thm)],[f_421_2]) ).

fof(f_422_1,plain,
    ! [P,Q,R] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_nat_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_006]) ).

fof(f_422_2,plain,
    ! [U_1024,U_1023,U_1022] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(U_1024,U_1023),U_1022) = hAPP_b589554111l_bool(U_1024,hAPP_nat_bool(U_1023,U_1022)),
    inference(variable_rename,[status(thm)],[f_422_1]) ).

cnf(f_422_3,plain,
    hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(U_1024,U_1023),U_1022) = hAPP_b589554111l_bool(U_1024,hAPP_nat_bool(U_1023,U_1022)),
    inference(clausify,[status(thm)],[f_422_2]) ).

fof(f_423_1,plain,
    ! [P,Q,R] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f1748468828l_bool(P,R),hAPP_f54304608l_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo]) ).

fof(f_423_2,plain,
    ! [U_1027,U_1026,U_1025] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(U_1027,U_1026),U_1025) = hAPP_bool_bool(hAPP_f1748468828l_bool(U_1027,U_1025),hAPP_f54304608l_bool(U_1026,U_1025)),
    inference(variable_rename,[status(thm)],[f_423_1]) ).

cnf(f_423_3,plain,
    hAPP_f54304608l_bool(cOMBS_1187019125l_bool(U_1027,U_1026),U_1025) = hAPP_bool_bool(hAPP_f1748468828l_bool(U_1027,U_1025),hAPP_f54304608l_bool(U_1026,U_1025)),
    inference(clausify,[status(thm)],[f_423_2]) ).

fof(f_424_1,plain,
    ! [P,Q,R] : hAPP_f1664156314l_bool(cOMBB_307249310e_bool(P,Q),R) = hAPP_bool_bool(P,hAPP_f1664156314l_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op]) ).

fof(f_424_2,plain,
    ! [U_1030,U_1029,U_1028] : hAPP_f1664156314l_bool(cOMBB_307249310e_bool(U_1030,U_1029),U_1028) = hAPP_bool_bool(U_1030,hAPP_f1664156314l_bool(U_1029,U_1028)),
    inference(variable_rename,[status(thm)],[f_424_1]) ).

cnf(f_424_3,plain,
    hAPP_f1664156314l_bool(cOMBB_307249310e_bool(U_1030,U_1029),U_1028) = hAPP_bool_bool(U_1030,hAPP_f1664156314l_bool(U_1029,U_1028)),
    inference(clausify,[status(thm)],[f_424_2]) ).

fof(f_425_1,plain,
    ! [P,Q,R] : hAPP_p393069232l_bool(cOMBB_675860798_pname(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_pname_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_007]) ).

fof(f_425_2,plain,
    ! [U_1033,U_1032,U_1031] : hAPP_p393069232l_bool(cOMBB_675860798_pname(U_1033,U_1032),U_1031) = hAPP_b589554111l_bool(U_1033,hAPP_pname_bool(U_1032,U_1031)),
    inference(variable_rename,[status(thm)],[f_425_1]) ).

cnf(f_425_3,plain,
    hAPP_p393069232l_bool(cOMBB_675860798_pname(U_1033,U_1032),U_1031) = hAPP_b589554111l_bool(U_1033,hAPP_pname_bool(U_1032,U_1031)),
    inference(clausify,[status(thm)],[f_425_2]) ).

fof(f_426_1,plain,
    ! [P,Q,R] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f1476298914l_bool(P,R),hAPP_f1664156314l_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O]) ).

fof(f_426_2,plain,
    ! [U_1036,U_1035,U_1034] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(U_1036,U_1035),U_1034) = hAPP_bool_bool(hAPP_f1476298914l_bool(U_1036,U_1034),hAPP_f1664156314l_bool(U_1035,U_1034)),
    inference(variable_rename,[status(thm)],[f_426_1]) ).

cnf(f_426_3,plain,
    hAPP_f1664156314l_bool(cOMBS_350070575l_bool(U_1036,U_1035),U_1034) = hAPP_bool_bool(hAPP_f1476298914l_bool(U_1036,U_1034),hAPP_f1664156314l_bool(U_1035,U_1034)),
    inference(clausify,[status(thm)],[f_426_2]) ).

fof(f_427_1,plain,
    ! [P,Q,R] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(P),Q),R) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob]) ).

fof(f_427_2,plain,
    ! [U_1039,U_1038,U_1037] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(U_1039),U_1038),U_1037) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(U_1039,U_1037),U_1038),
    inference(variable_rename,[status(thm)],[f_427_1]) ).

cnf(f_427_3,plain,
    hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(U_1039),U_1038),U_1037) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(U_1039,U_1037),U_1038),
    inference(clausify,[status(thm)],[f_427_2]) ).

fof(f_428_1,plain,
    ! [P,Q,R] : hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(P),Q),R) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO]) ).

fof(f_428_2,plain,
    ! [U_1042,U_1041,U_1040] : hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(U_1042),U_1041),U_1040) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(U_1042,U_1040),U_1041),
    inference(variable_rename,[status(thm)],[f_428_1]) ).

cnf(f_428_3,plain,
    hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(U_1042),U_1041),U_1040) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(U_1042,U_1040),U_1041),
    inference(clausify,[status(thm)],[f_428_2]) ).

fof(f_429_1,plain,
    ! [P,Q,R] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_fun_a_bool_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_008]) ).

fof(f_429_2,plain,
    ! [U_1045,U_1044,U_1043] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(U_1045,U_1044),U_1043) = hAPP_b589554111l_bool(U_1045,hAPP_fun_a_bool_bool(U_1044,U_1043)),
    inference(variable_rename,[status(thm)],[f_429_1]) ).

cnf(f_429_3,plain,
    hAPP_f198738859l_bool(cOMBB_338059395a_bool(U_1045,U_1044),U_1043) = hAPP_b589554111l_bool(U_1045,hAPP_fun_a_bool_bool(U_1044,U_1043)),
    inference(clausify,[status(thm)],[f_429_2]) ).

fof(f_430_1,plain,
    ! [P,Q,R] : hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(P),Q),R) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_]) ).

fof(f_430_2,plain,
    ! [U_1048,U_1047,U_1046] : hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(U_1048),U_1047),U_1046) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(U_1048,U_1046),U_1047),
    inference(variable_rename,[status(thm)],[f_430_1]) ).

cnf(f_430_3,plain,
    hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(U_1048),U_1047),U_1046) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(U_1048,U_1046),U_1047),
    inference(clausify,[status(thm)],[f_430_2]) ).

fof(f_431_1,plain,
    ! [P,Q,R] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f54304608l_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009]) ).

fof(f_431_2,plain,
    ! [U_1051,U_1050,U_1049] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(U_1051,U_1050),U_1049) = hAPP_b589554111l_bool(U_1051,hAPP_f54304608l_bool(U_1050,U_1049)),
    inference(variable_rename,[status(thm)],[f_431_1]) ).

cnf(f_431_3,plain,
    hAPP_f1748468828l_bool(cOMBB_444170502t_bool(U_1051,U_1050),U_1049) = hAPP_b589554111l_bool(U_1051,hAPP_f54304608l_bool(U_1050,U_1049)),
    inference(clausify,[status(thm)],[f_431_2]) ).

fof(f_432_1,plain,
    ! [P,Q,R] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f1664156314l_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_010]) ).

fof(f_432_2,plain,
    ! [U_1054,U_1053,U_1052] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(U_1054,U_1053),U_1052) = hAPP_b589554111l_bool(U_1054,hAPP_f1664156314l_bool(U_1053,U_1052)),
    inference(variable_rename,[status(thm)],[f_432_1]) ).

cnf(f_432_3,plain,
    hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(U_1054,U_1053),U_1052) = hAPP_b589554111l_bool(U_1054,hAPP_f1664156314l_bool(U_1053,U_1052)),
    inference(clausify,[status(thm)],[f_432_2]) ).

fof(f_433_1,plain,
    ! [P,Q,R] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(P),Q),R) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It]) ).

fof(f_433_2,plain,
    ! [U_1057,U_1056,U_1055] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(U_1057),U_1056),U_1055) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(U_1057,U_1055),U_1056),
    inference(variable_rename,[status(thm)],[f_433_1]) ).

cnf(f_433_3,plain,
    hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(U_1057),U_1056),U_1055) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(U_1057,U_1055),U_1056),
    inference(clausify,[status(thm)],[f_433_2]) ).

fof(f_434_1,plain,
    ! [P,Q,R] : hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(P),Q),R) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__]) ).

fof(f_434_2,plain,
    ! [U_1060,U_1059,U_1058] : hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(U_1060),U_1059),U_1058) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(U_1060,U_1058),U_1059),
    inference(variable_rename,[status(thm)],[f_434_1]) ).

cnf(f_434_3,plain,
    hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(U_1060),U_1059),U_1058) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(U_1060,U_1058),U_1059),
    inference(clausify,[status(thm)],[f_434_2]) ).

fof(f_435_1,plain,
    ! [P,Q,R] : hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(P),Q),R) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__011]) ).

fof(f_435_2,plain,
    ! [U_1063,U_1062,U_1061] : hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(U_1063),U_1062),U_1061) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(U_1063,U_1061),U_1062),
    inference(variable_rename,[status(thm)],[f_435_1]) ).

cnf(f_435_3,plain,
    hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(U_1063),U_1062),U_1061) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(U_1063,U_1061),U_1062),
    inference(clausify,[status(thm)],[f_435_2]) ).

fof(f_436_1,plain,
    ! [P,Q,R] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(P),Q),R) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_012]) ).

fof(f_436_2,plain,
    ! [U_1066,U_1065,U_1064] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(U_1066),U_1065),U_1064) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(U_1066,U_1064),U_1065),
    inference(variable_rename,[status(thm)],[f_436_1]) ).

cnf(f_436_3,plain,
    hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(U_1066),U_1065),U_1064) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(U_1066,U_1064),U_1065),
    inference(clausify,[status(thm)],[f_436_2]) ).

fof(f_437_1,plain,
    ! [P,Q,R] : hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(P),Q),R) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool]) ).

fof(f_437_2,plain,
    ! [U_1069,U_1068,U_1067] : hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(U_1069),U_1068),U_1067) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(U_1069,U_1067),U_1068),
    inference(variable_rename,[status(thm)],[f_437_1]) ).

cnf(f_437_3,plain,
    hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(U_1069),U_1068),U_1067) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(U_1069,U_1067),U_1068),
    inference(clausify,[status(thm)],[f_437_2]) ).

fof(f_438_1,plain,
    ! [P,Q,R] : hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(P),Q),R) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H]) ).

fof(f_438_2,plain,
    ! [U_1072,U_1071,U_1070] : hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(U_1072),U_1071),U_1070) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(U_1072,U_1070),U_1071),
    inference(variable_rename,[status(thm)],[f_438_1]) ).

cnf(f_438_3,plain,
    hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(U_1072),U_1071),U_1070) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(U_1072,U_1070),U_1071),
    inference(clausify,[status(thm)],[f_438_2]) ).

fof(f_439_1,plain,
    ! [P,Q,R] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(P),Q),R) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_]) ).

fof(f_439_2,plain,
    ! [U_1075,U_1074,U_1073] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(U_1075),U_1074),U_1073) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(U_1075,U_1073),U_1074),
    inference(variable_rename,[status(thm)],[f_439_1]) ).

cnf(f_439_3,plain,
    hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(U_1075),U_1074),U_1073) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(U_1075,U_1073),U_1074),
    inference(clausify,[status(thm)],[f_439_2]) ).

fof(f_440_1,plain,
    ! [P,Q,R] : hAPP_f292226953l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(P),Q),R) = hAPP_f292226953l_bool(hAPP_f1050622307l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H]) ).

fof(f_440_2,plain,
    ! [U_1078,U_1077,U_1076] : hAPP_f292226953l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(U_1078),U_1077),U_1076) = hAPP_f292226953l_bool(hAPP_f1050622307l_bool(U_1078,U_1076),U_1077),
    inference(variable_rename,[status(thm)],[f_440_1]) ).

cnf(f_440_3,plain,
    hAPP_f292226953l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(U_1078),U_1077),U_1076) = hAPP_f292226953l_bool(hAPP_f1050622307l_bool(U_1078,U_1076),U_1077),
    inference(clausify,[status(thm)],[f_440_2]) ).

fof(f_441_1,plain,
    ! [P,Q,R] : hAPP_f937997336l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(P),Q),R) = hAPP_f937997336l_bool(hAPP_f760187903l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool]) ).

fof(f_441_2,plain,
    ! [U_1081,U_1080,U_1079] : hAPP_f937997336l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(U_1081),U_1080),U_1079) = hAPP_f937997336l_bool(hAPP_f760187903l_bool(U_1081,U_1079),U_1080),
    inference(variable_rename,[status(thm)],[f_441_1]) ).

cnf(f_441_3,plain,
    hAPP_f937997336l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(U_1081),U_1080),U_1079) = hAPP_f937997336l_bool(hAPP_f760187903l_bool(U_1081,U_1079),U_1080),
    inference(clausify,[status(thm)],[f_441_2]) ).

fof(f_442_1,plain,
    ! [P,Q,R] : hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(P),Q),R) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo]) ).

fof(f_442_2,plain,
    ! [U_1084,U_1083,U_1082] : hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(U_1084),U_1083),U_1082) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(U_1084,U_1082),U_1083),
    inference(variable_rename,[status(thm)],[f_442_1]) ).

cnf(f_442_3,plain,
    hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(U_1084),U_1083),U_1082) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(U_1084,U_1082),U_1083),
    inference(clausify,[status(thm)],[f_442_2]) ).

fof(f_443_1,plain,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
    inference(fof_nnf,[status(thm)],[conj_0]) ).

cnf(f_443_2,plain,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
    inference(clausify,[status(thm)],[f_443_1]) ).

fof(f_444_1,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
    inference(fof_nnf,[status(thm)],[conj_1]) ).

cnf(f_444_2,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
    inference(clausify,[status(thm)],[f_444_1]) ).

fof(f_445_1,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))),
    inference(fof_nnf,[status(thm)],[conj_2]) ).

cnf(f_445_2,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))),
    inference(clausify,[status(thm)],[f_445_1]) ).

fof(f_446_1,plain,
    hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)),
    inference(fof_nnf,[status(thm)],[conj_3]) ).

cnf(f_446_2,plain,
    hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)),
    inference(clausify,[status(thm)],[f_446_1]) ).

fof(f_447_1,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
    inference(fof_nnf,[status(thm)],[conj_4]) ).

cnf(f_447_2,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
    inference(clausify,[status(thm)],[f_447_1]) ).

fof(f_448_1,plain,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)),
    inference(fof_nnf,[status(thm)],[conj_5]) ).

cnf(f_448_2,plain,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)),
    inference(clausify,[status(thm)],[f_448_1]) ).

fof(f_449_1,negated_conjecture,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
    inference(negate,[status(cth)],[conj_6]) ).

fof(f_449_2,negated_conjecture,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
    inference(definitional_conversion,[status(esa)],[f_449_1]) ).

cnf(f_449_3,negated_conjecture,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))),
    inference(clausify,[status(thm)],[f_449_2]) ).

cnf(equality_1,axiom,
    Eq_x_0 = Eq_x_0,
    theory(equality,[reflexivity]) ).

cnf(equality_2,axiom,
    ( Eq_x_1 = Eq_x_0
    | Eq_x_0 != Eq_x_1 ),
    theory(equality,[symmetry]) ).

cnf(equality_3,axiom,
    ( Eq_x_0 = Eq_x_2
    | Eq_x_1 != Eq_x_2
    | Eq_x_0 != Eq_x_1 ),
    theory(equality,[transitivity]) ).

cnf(equality_4,axiom,
    ( cOMBB_bool_bool_a(Eq_x_0,Eq_x_1) = cOMBB_bool_bool_a(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_5,axiom,
    ( cOMBB_647938656_pname(Eq_x_0,Eq_x_1) = cOMBB_647938656_pname(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_6,axiom,
    ( cOMBB_2140588453a_bool(Eq_x_0,Eq_x_1) = cOMBB_2140588453a_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_7,axiom,
    ( cOMBB_307249310e_bool(Eq_x_0,Eq_x_1) = cOMBB_307249310e_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_8,axiom,
    ( cOMBS_a_bool_bool(Eq_x_0,Eq_x_1) = cOMBS_a_bool_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_9,axiom,
    ( cOMBS_568398431l_bool(Eq_x_0,Eq_x_1) = cOMBS_568398431l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_10,axiom,
    ( cOMBS_1035972772l_bool(Eq_x_0,Eq_x_1) = cOMBS_1035972772l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_11,axiom,
    ( cOMBS_350070575l_bool(Eq_x_0,Eq_x_1) = cOMBS_350070575l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_12,axiom,
    ( undefined_a(Eq_x_0) = undefined_a(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_13,axiom,
    ( undefined_pname(Eq_x_0) = undefined_pname(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_14,axiom,
    ( fun(Eq_x_0,Eq_x_1) = fun(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_15,axiom,
    ( undefined_fun_a_bool(Eq_x_0) = undefined_fun_a_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_16,axiom,
    ( undefi17486888e_bool(Eq_x_0) = undefi17486888e_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_17,axiom,
    ( undefi1699038445l_bool(Eq_x_0) = undefi1699038445l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_18,axiom,
    ( undefi64961550l_bool(Eq_x_0) = undefi64961550l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_19,axiom,
    ( collect_a(Eq_x_0) = collect_a(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_20,axiom,
    ( collect_pname(Eq_x_0) = collect_pname(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_21,axiom,
    ( collect_fun_a_bool(Eq_x_0) = collect_fun_a_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_22,axiom,
    ( collec1974731493e_bool(Eq_x_0) = collec1974731493e_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_23,axiom,
    ( image_a_a(Eq_x_0,Eq_x_1) = image_a_a(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_24,axiom,
    ( image_a_pname(Eq_x_0,Eq_x_1) = image_a_pname(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_25,axiom,
    ( image_pname_a(Eq_x_0,Eq_x_1) = image_pname_a(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_26,axiom,
    ( image_pname_pname(Eq_x_0,Eq_x_1) = image_pname_pname(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_27,axiom,
    ( image_112932426a_bool(Eq_x_0,Eq_x_1) = image_112932426a_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_28,axiom,
    ( image_47868345e_bool(Eq_x_0,Eq_x_1) = image_47868345e_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_29,axiom,
    ( image_nat_a(Eq_x_0,Eq_x_1) = image_nat_a(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_30,axiom,
    ( image_nat_pname(Eq_x_0,Eq_x_1) = image_nat_pname(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_31,axiom,
    ( image_nat_fun_a_bool(Eq_x_0,Eq_x_1) = image_nat_fun_a_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_32,axiom,
    ( image_1655916159e_bool(Eq_x_0,Eq_x_1) = image_1655916159e_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_33,axiom,
    ( image_fun_a_bool_a(Eq_x_0,Eq_x_1) = image_fun_a_bool_a(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_34,axiom,
    ( image_1854862208_pname(Eq_x_0,Eq_x_1) = image_1854862208_pname(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_35,axiom,
    ( image_876012084bool_a(Eq_x_0,Eq_x_1) = image_876012084bool_a(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_36,axiom,
    ( image_1283814551_pname(Eq_x_0,Eq_x_1) = image_1283814551_pname(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_37,axiom,
    ( image_fun_nat_bool_a(Eq_x_0,Eq_x_1) = image_fun_nat_bool_a(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_38,axiom,
    ( image_1921560913_pname(Eq_x_0,Eq_x_1) = image_1921560913_pname(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_39,axiom,
    ( image_573985017bool_a(Eq_x_0,Eq_x_1) = image_573985017bool_a(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_40,axiom,
    ( image_990671762_pname(Eq_x_0,Eq_x_1) = image_990671762_pname(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_41,axiom,
    ( image_349102846bool_a(Eq_x_0,Eq_x_1) = image_349102846bool_a(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_42,axiom,
    ( image_1705983821_pname(Eq_x_0,Eq_x_1) = image_1705983821_pname(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_43,axiom,
    ( image_526090948bool_a(Eq_x_0,Eq_x_1) = image_526090948bool_a(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_44,axiom,
    ( image_1604018183_pname(Eq_x_0,Eq_x_1) = image_1604018183_pname(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_45,axiom,
    ( insert_a(Eq_x_0,Eq_x_1) = insert_a(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_46,axiom,
    ( insert_pname(Eq_x_0,Eq_x_1) = insert_pname(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_47,axiom,
    ( insert_fun_a_bool(Eq_x_0,Eq_x_1) = insert_fun_a_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_48,axiom,
    ( insert1325755072e_bool(Eq_x_0,Eq_x_1) = insert1325755072e_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_49,axiom,
    ( hAPP_a_bool(Eq_x_0,Eq_x_1) = hAPP_a_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_50,axiom,
    ( hAPP_a_fun_a_bool(Eq_x_0,Eq_x_1) = hAPP_a_fun_a_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_51,axiom,
    ( hAPP_a93125764e_bool(Eq_x_0,Eq_x_1) = hAPP_a93125764e_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_52,axiom,
    ( hAPP_a85458249l_bool(Eq_x_0,Eq_x_1) = hAPP_a85458249l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_53,axiom,
    ( hAPP_pname_a(Eq_x_0,Eq_x_1) = hAPP_pname_a(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_54,axiom,
    ( hAPP_pname_bool(Eq_x_0,Eq_x_1) = hAPP_pname_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_55,axiom,
    ( hAPP_p1534023578a_bool(Eq_x_0,Eq_x_1) = hAPP_p1534023578a_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_56,axiom,
    ( hAPP_p61793385e_bool(Eq_x_0,Eq_x_1) = hAPP_p61793385e_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_57,axiom,
    ( hAPP_p338031245l_bool(Eq_x_0,Eq_x_1) = hAPP_p338031245l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_58,axiom,
    ( hAPP_bool_bool(Eq_x_0,Eq_x_1) = hAPP_bool_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_59,axiom,
    ( hAPP_nat_bool(Eq_x_0,Eq_x_1) = hAPP_nat_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_60,axiom,
    ( hAPP_nat_fun_a_bool(Eq_x_0,Eq_x_1) = hAPP_nat_fun_a_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_61,axiom,
    ( hAPP_n1025906991e_bool(Eq_x_0,Eq_x_1) = hAPP_n1025906991e_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_62,axiom,
    ( hAPP_fun_a_bool_bool(Eq_x_0,Eq_x_1) = hAPP_fun_a_bool_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_63,axiom,
    ( hAPP_f2050579477a_bool(Eq_x_0,Eq_x_1) = hAPP_f2050579477a_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_64,axiom,
    ( hAPP_f1631501043l_bool(Eq_x_0,Eq_x_1) = hAPP_f1631501043l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_65,axiom,
    ( hAPP_f1664156314l_bool(Eq_x_0,Eq_x_1) = hAPP_f1664156314l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_66,axiom,
    ( hAPP_f759274231e_bool(Eq_x_0,Eq_x_1) = hAPP_f759274231e_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_67,axiom,
    ( hAPP_f434788991l_bool(Eq_x_0,Eq_x_1) = hAPP_f434788991l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_68,axiom,
    ( hAPP_f54304608l_bool(Eq_x_0,Eq_x_1) = hAPP_f54304608l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_69,axiom,
    ( hAPP_f621171935l_bool(Eq_x_0,Eq_x_1) = hAPP_f621171935l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_70,axiom,
    ( hAPP_f2117159681l_bool(Eq_x_0,Eq_x_1) = hAPP_f2117159681l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_71,axiom,
    ( hAPP_f1935102916l_bool(Eq_x_0,Eq_x_1) = hAPP_f1935102916l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_72,axiom,
    ( hAPP_f559147733l_bool(Eq_x_0,Eq_x_1) = hAPP_f559147733l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_73,axiom,
    ( hAPP_f1637334154l_bool(Eq_x_0,Eq_x_1) = hAPP_f1637334154l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_74,axiom,
    ( hAPP_f292226953l_bool(Eq_x_0,Eq_x_1) = hAPP_f292226953l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_75,axiom,
    ( hAPP_f389811538l_bool(Eq_x_0,Eq_x_1) = hAPP_f389811538l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_76,axiom,
    ( hAPP_f937997336l_bool(Eq_x_0,Eq_x_1) = hAPP_f937997336l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_77,axiom,
    ( hAPP_f1363661463l_bool(Eq_x_0,Eq_x_1) = hAPP_f1363661463l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_78,axiom,
    ( hAPP_f595608956l_bool(Eq_x_0,Eq_x_1) = hAPP_f595608956l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_79,axiom,
    ( hAPP_f1295398978l_bool(Eq_x_0,Eq_x_1) = hAPP_f1295398978l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_80,axiom,
    ( p(Eq_x_0) = p(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_81,axiom,
    ( cOMBC_1693257480l_bool(Eq_x_0) = cOMBC_1693257480l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_82,axiom,
    ( hAPP_f103356543l_bool(Eq_x_0,Eq_x_1) = hAPP_f103356543l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_83,axiom,
    ( collect_fun_nat_bool(Eq_x_0) = collect_fun_nat_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_84,axiom,
    ( cOMBC_1284144636l_bool(Eq_x_0) = cOMBC_1284144636l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_85,axiom,
    ( cOMBC_1732670874l_bool(Eq_x_0) = cOMBC_1732670874l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_86,axiom,
    ( cOMBC_1269652216l_bool(Eq_x_0) = cOMBC_1269652216l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_87,axiom,
    ( hAPP_f760187903l_bool(Eq_x_0,Eq_x_1) = hAPP_f760187903l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_88,axiom,
    ( collec1874991203l_bool(Eq_x_0) = collec1874991203l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_89,axiom,
    ( cOMBC_336095980l_bool(Eq_x_0) = cOMBC_336095980l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_90,axiom,
    ( hAPP_f1759205631l_bool(Eq_x_0,Eq_x_1) = hAPP_f1759205631l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_91,axiom,
    ( collec792590109l_bool(Eq_x_0) = collec792590109l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_92,axiom,
    ( cOMBC_636888218l_bool(Eq_x_0) = cOMBC_636888218l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_93,axiom,
    ( hAPP_f1050622307l_bool(Eq_x_0,Eq_x_1) = hAPP_f1050622307l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_94,axiom,
    ( collec1635217238l_bool(Eq_x_0) = collec1635217238l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_95,axiom,
    ( cOMBC_331553030l_bool(Eq_x_0) = cOMBC_331553030l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_96,axiom,
    ( hAPP_f1434722111l_bool(Eq_x_0,Eq_x_1) = hAPP_f1434722111l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_97,axiom,
    ( collec707592106l_bool(Eq_x_0) = collec707592106l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_98,axiom,
    ( cOMBC_7971162l_bool(Eq_x_0) = cOMBC_7971162l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_99,axiom,
    ( hAPP_f510955609l_bool(Eq_x_0,Eq_x_1) = hAPP_f510955609l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_100,axiom,
    ( collec1613912337l_bool(Eq_x_0) = collec1613912337l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_101,axiom,
    ( cOMBC_595898202l_bool(Eq_x_0) = cOMBC_595898202l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_102,axiom,
    ( hAPP_f1772781669l_bool(Eq_x_0,Eq_x_1) = hAPP_f1772781669l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_103,axiom,
    ( collec1015864663l_bool(Eq_x_0) = collec1015864663l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_104,axiom,
    ( image_2089570637ol_nat(Eq_x_0,Eq_x_1) = image_2089570637ol_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_105,axiom,
    ( image_1079571347ol_nat(Eq_x_0,Eq_x_1) = image_1079571347ol_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_106,axiom,
    ( image_1802975832ol_nat(Eq_x_0,Eq_x_1) = image_1802975832ol_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_107,axiom,
    ( image_fun_a_bool_nat(Eq_x_0,Eq_x_1) = image_fun_a_bool_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_108,axiom,
    ( image_1551609309ol_nat(Eq_x_0,Eq_x_1) = image_1551609309ol_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_109,axiom,
    ( image_496248727ol_nat(Eq_x_0,Eq_x_1) = image_496248727ol_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_110,axiom,
    ( image_a_nat(Eq_x_0,Eq_x_1) = image_a_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_111,axiom,
    ( image_1607900221l_bool(Eq_x_0,Eq_x_1) = image_1607900221l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_112,axiom,
    ( image_1874789623l_bool(Eq_x_0,Eq_x_1) = image_1874789623l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_113,axiom,
    ( image_1208015684l_bool(Eq_x_0,Eq_x_1) = image_1208015684l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_114,axiom,
    ( image_26036933t_bool(Eq_x_0,Eq_x_1) = image_26036933t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_115,axiom,
    ( image_1154884483l_bool(Eq_x_0,Eq_x_1) = image_1154884483l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_116,axiom,
    ( image_1642285373l_bool(Eq_x_0,Eq_x_1) = image_1642285373l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_117,axiom,
    ( image_1420695166l_bool(Eq_x_0,Eq_x_1) = image_1420695166l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_118,axiom,
    ( image_2129980159t_bool(Eq_x_0,Eq_x_1) = image_2129980159t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_119,axiom,
    ( image_pname_nat(Eq_x_0,Eq_x_1) = image_pname_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_120,axiom,
    ( insert_nat(Eq_x_0,Eq_x_1) = insert_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_121,axiom,
    ( insert2003652156l_bool(Eq_x_0,Eq_x_1) = insert2003652156l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_122,axiom,
    ( insert1117693814l_bool(Eq_x_0,Eq_x_1) = insert1117693814l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_123,axiom,
    ( insert1457093509l_bool(Eq_x_0,Eq_x_1) = insert1457093509l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_124,axiom,
    ( insert_fun_nat_bool(Eq_x_0,Eq_x_1) = insert_fun_nat_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_125,axiom,
    ( hAPP_f22106695ol_nat(Eq_x_0,Eq_x_1) = hAPP_f22106695ol_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_126,axiom,
    ( hAPP_n1699378549t_bool(Eq_x_0,Eq_x_1) = hAPP_n1699378549t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_127,axiom,
    ( hAPP_f921600141ol_nat(Eq_x_0,Eq_x_1) = hAPP_f921600141ol_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_128,axiom,
    ( hAPP_fun_a_bool_nat(Eq_x_0,Eq_x_1) = hAPP_fun_a_bool_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_129,axiom,
    ( hAPP_f696928925ol_nat(Eq_x_0,Eq_x_1) = hAPP_f696928925ol_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_130,axiom,
    ( hAPP_f55526627ol_nat(Eq_x_0,Eq_x_1) = hAPP_f55526627ol_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_131,axiom,
    ( hAPP_f2009550088ol_nat(Eq_x_0,Eq_x_1) = hAPP_f2009550088ol_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_132,axiom,
    ( hAPP_f1690079119ol_nat(Eq_x_0,Eq_x_1) = hAPP_f1690079119ol_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_133,axiom,
    ( hAPP_f98387925ol_nat(Eq_x_0,Eq_x_1) = hAPP_f98387925ol_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_134,axiom,
    ( hAPP_f1253658590ol_nat(Eq_x_0,Eq_x_1) = hAPP_f1253658590ol_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_135,axiom,
    ( hAPP_f1951378235l_bool(Eq_x_0,Eq_x_1) = hAPP_f1951378235l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_136,axiom,
    ( hAPP_nat_nat(Eq_x_0,Eq_x_1) = hAPP_nat_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_137,axiom,
    ( hAPP_f556039215l_bool(Eq_x_0,Eq_x_1) = hAPP_f556039215l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_138,axiom,
    ( hAPP_f285962445l_bool(Eq_x_0,Eq_x_1) = hAPP_f285962445l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_139,axiom,
    ( hAPP_n215258509l_bool(Eq_x_0,Eq_x_1) = hAPP_n215258509l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_140,axiom,
    ( cOMBB_444170502t_bool(Eq_x_0,Eq_x_1) = cOMBB_444170502t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_141,axiom,
    ( cOMBS_1187019125l_bool(Eq_x_0,Eq_x_1) = cOMBS_1187019125l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_142,axiom,
    ( cOMBB_2095475776e_bool(Eq_x_0,Eq_x_1) = cOMBB_2095475776e_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_143,axiom,
    ( cOMBB_338059395a_bool(Eq_x_0,Eq_x_1) = cOMBB_338059395a_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_144,axiom,
    ( cOMBB_1972296269bool_a(Eq_x_0,Eq_x_1) = cOMBB_1972296269bool_a(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_145,axiom,
    ( cOMBB_675860798_pname(Eq_x_0,Eq_x_1) = cOMBB_675860798_pname(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_146,axiom,
    ( collect_nat(Eq_x_0) = collect_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_147,axiom,
    ( cOMBB_1015721476ol_nat(Eq_x_0,Eq_x_1) = cOMBB_1015721476ol_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_148,axiom,
    ( cOMBS_nat_bool_bool(Eq_x_0,Eq_x_1) = cOMBS_nat_bool_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_149,axiom,
    ( minus_minus_nat(Eq_x_0) = minus_minus_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_150,axiom,
    ( cOMBC_nat_nat_bool(Eq_x_0) = cOMBC_nat_nat_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_151,axiom,
    ( cOMBC_1058051404l_bool(Eq_x_0) = cOMBC_1058051404l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_152,axiom,
    ( cOMBB_1897541054_pname(Eq_x_0,Eq_x_1) = cOMBB_1897541054_pname(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_153,axiom,
    ( cOMBC_pname_a_bool(Eq_x_0) = cOMBC_pname_a_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_154,axiom,
    ( cOMBC_226598744l_bool(Eq_x_0) = cOMBC_226598744l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_155,axiom,
    ( hAPP_f800510211t_bool(Eq_x_0,Eq_x_1) = hAPP_f800510211t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_156,axiom,
    ( cOMBC_1149511130e_bool(Eq_x_0) = cOMBC_1149511130e_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_157,axiom,
    ( cOMBC_a_a_bool(Eq_x_0) = cOMBC_a_a_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_158,axiom,
    ( cOMBC_1355376034l_bool(Eq_x_0) = cOMBC_1355376034l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_159,axiom,
    ( cOMBC_1245412066l_bool(Eq_x_0) = cOMBC_1245412066l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_160,axiom,
    ( hAPP_f1246832597l_bool(Eq_x_0,Eq_x_1) = hAPP_f1246832597l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_161,axiom,
    ( cOMBC_1988546018l_bool(Eq_x_0) = cOMBC_1988546018l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_162,axiom,
    ( cOMBC_1880041174l_bool(Eq_x_0) = cOMBC_1880041174l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_163,axiom,
    ( cOMBB_bool_bool_nat(Eq_x_0,Eq_x_1) = cOMBB_bool_bool_nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_164,axiom,
    ( cOMBB_238756964t_bool(Eq_x_0,Eq_x_1) = cOMBB_238756964t_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_165,axiom,
    ( hAPP_b589554111l_bool(Eq_x_0,Eq_x_1) = hAPP_b589554111l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_166,axiom,
    ( hAPP_a_fun_bool_bool(Eq_x_0,Eq_x_1) = hAPP_a_fun_bool_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_167,axiom,
    ( hAPP_n1006566506l_bool(Eq_x_0,Eq_x_1) = hAPP_n1006566506l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_168,axiom,
    ( hAPP_p393069232l_bool(Eq_x_0,Eq_x_1) = hAPP_p393069232l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_169,axiom,
    ( hAPP_f198738859l_bool(Eq_x_0,Eq_x_1) = hAPP_f198738859l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_170,axiom,
    ( hAPP_f1748468828l_bool(Eq_x_0,Eq_x_1) = hAPP_f1748468828l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_171,axiom,
    ( hAPP_f1476298914l_bool(Eq_x_0,Eq_x_1) = hAPP_f1476298914l_bool(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_172,axiom,
    ( sK1(Eq_x_0,Eq_x_1,Eq_x_2) = sK1(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_173,axiom,
    ( sK2(Eq_x_0,Eq_x_1,Eq_x_2) = sK2(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_174,axiom,
    ( sK3(Eq_x_0,Eq_x_1,Eq_x_2) = sK3(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_175,axiom,
    ( sK4(Eq_x_0,Eq_x_1,Eq_x_2) = sK4(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_176,axiom,
    ( sK5(Eq_x_0,Eq_x_1,Eq_x_2) = sK5(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_177,axiom,
    ( sK6(Eq_x_0,Eq_x_1) = sK6(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_178,axiom,
    ( sK7(Eq_x_0,Eq_x_1,Eq_x_2) = sK7(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_179,axiom,
    ( sK8(Eq_x_0,Eq_x_1,Eq_x_2) = sK8(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_180,axiom,
    ( sK9(Eq_x_0,Eq_x_1,Eq_x_2) = sK9(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_181,axiom,
    ( sK10(Eq_x_0,Eq_x_1) = sK10(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_182,axiom,
    ( sK11(Eq_x_0,Eq_x_1) = sK11(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_183,axiom,
    ( sK12(Eq_x_0,Eq_x_1) = sK12(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_184,axiom,
    ( sK13(Eq_x_0,Eq_x_1,Eq_x_2) = sK13(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_185,axiom,
    ( sK14(Eq_x_0,Eq_x_1) = sK14(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_186,axiom,
    ( sK15(Eq_x_0,Eq_x_1,Eq_x_2) = sK15(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_187,axiom,
    ( sK16(Eq_x_0) = sK16(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_188,axiom,
    ( sK17(Eq_x_0,Eq_x_1) = sK17(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_189,axiom,
    ( is_fun_a_bool(Eq_y_0)
    | ~ is_fun_a_bool(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_190,axiom,
    ( is_fun_pname_bool(Eq_y_0)
    | ~ is_fun_pname_bool(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_191,axiom,
    ( is_fun949378684l_bool(Eq_y_0)
    | ~ is_fun949378684l_bool(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_192,axiom,
    ( is_fun1661590463l_bool(Eq_y_0)
    | ~ is_fun1661590463l_bool(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_193,axiom,
    ( is_a(Eq_y_0)
    | ~ is_a(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_194,axiom,
    ( is_pname(Eq_y_0)
    | ~ is_pname(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_195,axiom,
    ( is_bool(Eq_y_0)
    | ~ is_bool(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_196,axiom,
    ( hBOOL(Eq_y_0)
    | ~ hBOOL(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(sat_proved,plain,
    $false,
    inference(cadical,[status(thm)],[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWW473+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.03  This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04  % Command  : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37  % Computer : n026.cluster.edu
% 0.10/0.37  % Model    : x86_64 x86_64
% 0.10/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37  % Memory   : 8046.5625MB
% 0.10/0.37  % OS       : Linux 6.8.0-71-generic
% 0.10/0.37  % CPULimit : 300
% 0.10/0.37  % WCLimit  : 300
% 0.10/0.37  % DateTime : Sun Sep 20 05:43:36 UTC 2026
% 0.13/0.37  % CPUTime  : 
% 11.15/11.48  % SZS status Theorem for theBenchmark
% 11.15/11.48  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------