ConnectPP---0.7.2.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : SWW473+3 : 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 : n013.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 09:07:57 AM UTC 2026

% Result   : Theorem 46.74s 50.67s
% Output   : Proof 46.85s
% 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_1] :
      ( is_fun_a_bool(B_2_1)
     => is_fun_a_bool(cOMBB_bool_bool_a(B_1_1,B_2_1)) ),
    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_1] :
      ( is_fun_pname_bool(B_2_1)
     => is_fun_pname_bool(cOMBB_647938656_pname(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname) ).

fof(gsy_c_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t__a,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun949378684l_bool(B_1_1)
     => is_fun_a_bool(cOMBB_1273333599bool_a(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t__a) ).

fof(gsy_c_COMBK_000tc__HOL__Obool_000t__a,axiom,
    ! [B_1_1] :
      ( is_bool(B_1_1)
     => is_fun_a_bool(cOMBK_bool_a(B_1_1)) ),
    file('theBenchmark.p',gsy_c_COMBK_000tc__HOL__Obool_000t__a) ).

fof(gsy_c_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun_a_bool(B_2_1)
     => is_fun_a_bool(cOMBS_a_bool_bool(B_1_1,B_2_1)) ),
    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_1] :
      ( is_fun_pname_bool(B_2_1)
     => is_fun_pname_bool(cOMBS_568398431l_bool(B_1_1,B_2_1)) ),
    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_1] :
      ( is_fun949378684l_bool(B_2_1)
     => is_fun949378684l_bool(cOMBS_1035972772l_bool(B_1_1,B_2_1)) ),
    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_1] :
      ( is_fun1661590463l_bool(B_2_1)
     => is_fun1661590463l_bool(cOMBS_350070575l_bool(B_1_1,B_2_1)) ),
    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_Finite__Set_Ofolding__one_000t__a,axiom,
    ! [B_1_1,B_2_1] : is_bool(finite_folding_one_a(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_Finite__Set_Ofolding__one_000t__a) ).

fof(gsy_c_Finite__Set_Ofolding__one_000tc__Com__Opname,axiom,
    ! [B_1_1,B_2_1] : is_bool(finite1282449217_pname(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_Finite__Set_Ofolding__one_000tc__Com__Opname) ).

fof(gsy_c_Finite__Set_Ofolding__one_000tc__Int__Oint,axiom,
    ! [B_1_1,B_2_1] : is_bool(finite1626084323ne_int(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_Finite__Set_Ofolding__one_000tc__Int__Oint) ).

fof(gsy_c_Finite__Set_Ofolding__one_000tc__Nat__Onat,axiom,
    ! [B_1_1,B_2_1] : is_bool(finite988810631ne_nat(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_Finite__Set_Ofolding__one_000tc__Nat__Onat) ).

fof(gsy_c_Finite__Set_Ofolding__one__idem_000t__a,axiom,
    ! [B_1_1,B_2_1] : is_bool(finite1819937229idem_a(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_Finite__Set_Ofolding__one__idem_000t__a) ).

fof(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname,axiom,
    ! [B_1_1,B_2_1] : is_bool(finite89670078_pname(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname) ).

fof(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Int__Oint,axiom,
    ! [B_1_1,B_2_1] : is_bool(finite1432773856em_int(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_Finite__Set_Ofolding__one__idem_000tc__Int__Oint) ).

fof(gsy_c_Finite__Set_Ofolding__one__idem_000tc__Nat__Onat,axiom,
    ! [B_1_1,B_2_1] : is_bool(finite795500164em_nat(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_Finite__Set_Ofolding__one__idem_000tc__Nat__Onat) ).

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_Orderings_Obot__class_Obot_000tc__HOL__Obool,axiom,
    is_bool(bot_bot_bool),
    file('theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool) ).

fof(gsy_c_Orderings_Obot__class_Obot_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
    is_fun_a_bool(bot_bot_fun_a_bool),
    file('theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__fun_It__a_Mtc__HOL__Obool_J) ).

fof(gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
    is_fun_pname_bool(bot_bo844097828e_bool),
    file('theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).

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_1] :
      ( is_fun_a_bool(B_2_1)
     => is_fun_a_bool(image_a_a(B_1_1,B_2_1)) ),
    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_1] :
      ( is_fun_a_bool(B_2_1)
     => is_fun_pname_bool(image_a_pname(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_Set_Oimage_000t__a_000tc__Com__Opname) ).

fof(gsy_c_Set_Oimage_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun_a_bool(B_2_1)
     => is_fun949378684l_bool(image_a_fun_a_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_Set_Oimage_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J) ).

fof(gsy_c_Set_Oimage_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun_a_bool(B_2_1)
     => is_fun1661590463l_bool(image_819518260e_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_Set_Oimage_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).

fof(gsy_c_Set_Oimage_000tc__Com__Opname_000t__a,hypothesis,
    ! [B_1_1,B_2_1] :
      ( is_fun_pname_bool(B_2_1)
     => is_fun_a_bool(image_pname_a(B_1_1,B_2_1)) ),
    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_1] :
      ( is_fun_pname_bool(B_2_1)
     => is_fun_pname_bool(image_pname_pname(B_1_1,B_2_1)) ),
    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_1] :
      ( is_fun_pname_bool(B_2_1)
     => is_fun949378684l_bool(image_112932426a_bool(B_1_1,B_2_1)) ),
    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_1] :
      ( is_fun_pname_bool(B_2_1)
     => is_fun1661590463l_bool(image_47868345e_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_) ).

fof(gsy_c_Set_Oimage_000tc__Int__Oint_000t__a,axiom,
    ! [B_1_1,B_2_1] : is_fun_a_bool(image_int_a(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__Int__Oint_000t__a) ).

fof(gsy_c_Set_Oimage_000tc__Int__Oint_000tc__Com__Opname,axiom,
    ! [B_1_1,B_2_1] : is_fun_pname_bool(image_int_pname(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__Int__Oint_000tc__Com__Opname) ).

fof(gsy_c_Set_Oimage_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1,B_2_1] : is_fun949378684l_bool(image_int_fun_a_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J) ).

fof(gsy_c_Set_Oimage_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1,B_2_1] : is_fun1661590463l_bool(image_637364955e_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).

fof(gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a,axiom,
    ! [B_1_1,B_2_1] : is_fun_a_bool(image_nat_a(B_1_1,B_2_1)),
    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_1] : is_fun_pname_bool(image_nat_pname(B_1_1,B_2_1)),
    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_1] : is_fun949378684l_bool(image_nat_fun_a_bool(B_1_1,B_2_1)),
    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_1] : is_fun1661590463l_bool(image_1655916159e_bool(B_1_1,B_2_1)),
    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_1] :
      ( is_fun949378684l_bool(B_2_1)
     => is_fun_a_bool(image_fun_a_bool_a(B_1_1,B_2_1)) ),
    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_1] :
      ( is_fun949378684l_bool(B_2_1)
     => is_fun_pname_bool(image_1854862208_pname(B_1_1,B_2_1)) ),
    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_1] :
      ( is_fun1661590463l_bool(B_2_1)
     => is_fun_a_bool(image_876012084bool_a(B_1_1,B_2_1)) ),
    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_1] :
      ( is_fun1661590463l_bool(B_2_1)
     => is_fun_pname_bool(image_1283814551_pname(B_1_1,B_2_1)) ),
    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__Int__Oint_Mtc__HOL__Obool_J_000t__a,axiom,
    ! [B_1_1,B_2_1] : is_fun_a_bool(image_fun_int_bool_a(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000t__a) ).

fof(gsy_c_Set_Oimage_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__Com__Opname,axiom,
    ! [B_1_1,B_2_1] : is_fun_pname_bool(image_62782965_pname(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__Com__Opname) ).

fof(gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000t__a,axiom,
    ! [B_1_1,B_2_1] : is_fun_a_bool(image_fun_nat_bool_a(B_1_1,B_2_1)),
    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_1] : is_fun_pname_bool(image_1921560913_pname(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname) ).

fof(gsy_c_fFalse,axiom,
    is_bool(fFalse),
    file('theBenchmark.p',gsy_c_fFalse) ).

fof(gsy_c_fTrue,axiom,
    is_bool(fTrue),
    file('theBenchmark.p',gsy_c_fTrue) ).

fof(gsy_c_hAPP_000t__a_000t__a,axiom,
    ! [B_1_1,B_2_1] :
      ( is_a(B_2_1)
     => is_a(hAPP_a_a(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000t__a_000t__a) ).

fof(gsy_c_hAPP_000t__a_000tc__HOL__Obool,axiom,
    ! [B_1_1,B_2_1] :
      ( ( is_a(B_2_1)
        & is_fun_a_bool(B_1_1) )
     => is_bool(hAPP_a_bool(B_1_1,B_2_1)) ),
    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_1] :
      ( is_a(B_2_1)
     => is_fun_a_bool(hAPP_a_fun_a_bool(B_1_1,B_2_1)) ),
    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_1] :
      ( is_a(B_2_1)
     => is_fun_pname_bool(hAPP_a93125764e_bool(B_1_1,B_2_1)) ),
    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_1] :
      ( is_a(B_2_1)
     => is_fun949378684l_bool(hAPP_a85458249l_bool(B_1_1,B_2_1)) ),
    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_1] :
      ( is_pname(B_2_1)
     => is_a(hAPP_pname_a(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000t__a) ).

fof(gsy_c_hAPP_000tc__Com__Opname_000tc__Com__Opname,axiom,
    ! [B_1_1,B_2_1] :
      ( is_pname(B_2_1)
     => is_pname(hAPP_pname_pname(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__Com__Opname) ).

fof(gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool,axiom,
    ! [B_1_1,B_2_1] :
      ( ( is_pname(B_2_1)
        & is_fun_pname_bool(B_1_1) )
     => is_bool(hAPP_pname_bool(B_1_1,B_2_1)) ),
    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_1] :
      ( is_pname(B_2_1)
     => is_fun_a_bool(hAPP_p1534023578a_bool(B_1_1,B_2_1)) ),
    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_1] :
      ( is_pname(B_2_1)
     => is_fun_pname_bool(hAPP_p61793385e_bool(B_1_1,B_2_1)) ),
    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_1] :
      ( is_pname(B_2_1)
     => is_fun1661590463l_bool(hAPP_p338031245l_bool(B_1_1,B_2_1)) ),
    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_1] :
      ( is_bool(B_2_1)
     => is_bool(hAPP_bool_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) ).

fof(gsy_c_hAPP_000tc__Int__Oint_000t__a,axiom,
    ! [B_1_1,B_2_1] : is_a(hAPP_int_a(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Int__Oint_000t__a) ).

fof(gsy_c_hAPP_000tc__Int__Oint_000tc__HOL__Obool,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_int_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Int__Oint_000tc__HOL__Obool) ).

fof(gsy_c_hAPP_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1,B_2_1] : is_fun_a_bool(hAPP_int_fun_a_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J) ).

fof(gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
    ! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_i7355787e_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).

fof(gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL,axiom,
    ! [B_1_1,B_2_1] : is_fun949378684l_bool(hAPP_i888906320l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL) ).

fof(gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool,axiom,
    ! [B_1_1,B_2_1] : is_fun1661590463l_bool(hAPP_i1587699435l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool,hypothesis,
    ! [B_1_1,B_2_1] : is_bool(hAPP_nat_bool(B_1_1,B_2_1)),
    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_1] : is_fun_a_bool(hAPP_nat_fun_a_bool(B_1_1,B_2_1)),
    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_1] : is_fun_pname_bool(hAPP_n1025906991e_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL,axiom,
    ! [B_1_1,B_2_1] : is_fun949378684l_bool(hAPP_n1414589940l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL) ).

fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool,axiom,
    ! [B_1_1,B_2_1] : is_fun1661590463l_bool(hAPP_n850744903l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool) ).

fof(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun_a_bool(B_2_1)
     => is_a(hAPP_fun_a_bool_a(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a) ).

fof(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool,hypothesis,
    ! [B_1_1,B_2_1] :
      ( ( is_fun_a_bool(B_2_1)
        & is_fun949378684l_bool(B_1_1) )
     => is_bool(hAPP_fun_a_bool_bool(B_1_1,B_2_1)) ),
    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,hypothesis,
    ! [B_1_1,B_2_1] :
      ( is_fun_a_bool(B_2_1)
     => is_fun_a_bool(hAPP_f2050579477a_bool(B_1_1,B_2_1)) ),
    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_1] :
      ( is_fun_a_bool(B_2_1)
     => is_fun949378684l_bool(hAPP_f1631501043l_bool(B_1_1,B_2_1)) ),
    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__Com__Opname,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun_pname_bool(B_2_1)
     => is_pname(hAPP_f1297739591_pname(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opname) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool,hypothesis,
    ! [B_1_1,B_2_1] :
      ( ( is_fun_pname_bool(B_2_1)
        & is_fun1661590463l_bool(B_1_1) )
     => is_bool(hAPP_f1664156314l_bool(B_1_1,B_2_1)) ),
    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_1] :
      ( is_fun_pname_bool(B_2_1)
     => is_fun_pname_bool(hAPP_f759274231e_bool(B_1_1,B_2_1)) ),
    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_1] :
      ( is_fun_pname_bool(B_2_1)
     => is_fun1661590463l_bool(hAPP_f434788991l_bool(B_1_1,B_2_1)) ),
    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__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f448129468l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).

fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f54304608l_bool(B_1_1,B_2_1)),
    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_1] :
      ( is_fun949378684l_bool(B_2_1)
     => is_bool(hAPP_f621171935l_bool(B_1_1,B_2_1)) ),
    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___001,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun949378684l_bool(B_2_1)
     => is_fun949378684l_bool(hAPP_f2117159681l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc___001) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun1661590463l_bool(B_2_1)
     => is_bool(hAPP_f1935102916l_bool(B_1_1,B_2_1)) ),
    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_002,axiom,
    ! [B_1_1,B_2_1] :
      ( is_fun1661590463l_bool(B_2_1)
     => is_fun1661590463l_bool(hAPP_f559147733l_bool(B_1_1,B_2_1)) ),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_002) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__HOL__Obool_,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f215623910l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) ).

fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1637334154l_bool(B_1_1,B_2_1)),
    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_1] : is_bool(hAPP_f292226953l_bool(B_1_1,B_2_1)),
    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_1] : is_bool(hAPP_f389811538l_bool(B_1_1,B_2_1)),
    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__Int__Oint_Mtc__HOL__Obool_J_Mtc__HO,axiom,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1593524852l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__HO) ).

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_1] : is_bool(hAPP_f937997336l_bool(B_1_1,B_2_1)),
    file('theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HO) ).

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_mgt,axiom,
    ! [B_1_1] : is_a(mgt(B_1_1)),
    file('theBenchmark.p',gsy_v_mgt) ).

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

fof(gsy_v_wt,axiom,
    ! [B_1_1] : is_bool(wt(B_1_1)),
    file('theBenchmark.p',gsy_v_wt) ).

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_f215623910l_bool(finite1395289673t_bool,A))
     => hBOOL(hAPP_f1593524852l_bool(finite2095298929l_bool,collec1409689523l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(ord_le1848167016l_bool),A)))) ),
    file('theBenchmark.p',fact_1_finite__Collect__subsets) ).

fof(fact_2_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_2_finite__Collect__subsets) ).

fof(fact_3_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_3_finite__Collect__subsets) ).

fof(fact_4_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_4_finite__Collect__subsets) ).

fof(fact_5_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_5_finite__Collect__subsets) ).

fof(fact_6_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_6_finite__Collect__subsets) ).

fof(fact_7_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_7_finite__Collect__subsets) ).

fof(fact_8_finite__Collect__subsets,axiom,
    ! [A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(ord_le951220754t_bool),A)))) ),
    file('theBenchmark.p',fact_8_finite__Collect__subsets) ).

fof(fact_9_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
     => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1512837979t_bool(H,F_1))) ),
    file('theBenchmark.p',fact_9_finite__imageI) ).

fof(fact_10_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_10_finite__imageI) ).

fof(fact_11_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_11_finite__imageI) ).

fof(fact_12_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_12_finite__imageI) ).

fof(fact_13_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_13_finite__imageI) ).

fof(fact_14_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
     => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(H,F_1))) ),
    file('theBenchmark.p',fact_14_finite__imageI) ).

fof(fact_15_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_15_finite__imageI) ).

fof(fact_16_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_16_finite__imageI) ).

fof(fact_17_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_17_finite__imageI) ).

fof(fact_18_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1))
     => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(H,F_1))) ),
    file('theBenchmark.p',fact_18_finite__imageI) ).

fof(fact_19_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1))
     => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(H,F_1))) ),
    file('theBenchmark.p',fact_19_finite__imageI) ).

fof(fact_20_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1))
     => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(H,F_1))) ),
    file('theBenchmark.p',fact_20_finite__imageI) ).

fof(fact_21_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(H,F_1))) ),
    file('theBenchmark.p',fact_21_finite__imageI) ).

fof(fact_22_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1))
     => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(H,F_1))) ),
    file('theBenchmark.p',fact_22_finite__imageI) ).

fof(fact_23_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_23_finite__imageI) ).

fof(fact_24_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,F_1))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_62782965_pname(H,F_1))) ),
    file('theBenchmark.p',fact_24_finite__imageI) ).

fof(fact_25_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_25_finite__imageI) ).

fof(fact_26_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_26_finite__imageI) ).

fof(fact_27_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_27_finite__imageI) ).

fof(fact_28_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_28_finite__imageI) ).

fof(fact_29_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,F_1))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1431733819ol_nat(H,F_1))) ),
    file('theBenchmark.p',fact_29_finite__imageI) ).

fof(fact_30_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_30_finite__imageI) ).

fof(fact_31_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_31_finite__imageI) ).

fof(fact_32_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_32_finite__imageI) ).

fof(fact_33_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1))
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_a_int(H,F_1))) ),
    file('theBenchmark.p',fact_33_finite__imageI) ).

fof(fact_34_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,F_1))
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_2069007511ol_int(H,F_1))) ),
    file('theBenchmark.p',fact_34_finite__imageI) ).

fof(fact_35_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1))
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_1133522419ol_int(H,F_1))) ),
    file('theBenchmark.p',fact_35_finite__imageI) ).

fof(fact_36_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1))
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_41399353ol_int(H,F_1))) ),
    file('theBenchmark.p',fact_36_finite__imageI) ).

fof(fact_37_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1))
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_fun_a_bool_int(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_fun_a_bool_bool(finite_finite_a,image_pname_a(H,F_1))) ),
    file('theBenchmark.p',fact_38_finite__imageI) ).

fof(fact_39_finite__imageI,axiom,
    ! [H,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(H,F_1))) ),
    file('theBenchmark.p',fact_39_finite__imageI) ).

fof(fact_40_finite_OinsertI,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A))
     => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,A_2),A))) ),
    file('theBenchmark.p',fact_40_finite_OinsertI) ).

fof(fact_41_finite_OinsertI,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
     => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,A_2),A))) ),
    file('theBenchmark.p',fact_41_finite_OinsertI) ).

fof(fact_42_finite_OinsertI,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_2),A))) ),
    file('theBenchmark.p',fact_42_finite_OinsertI) ).

fof(fact_43_finite_OinsertI,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
     => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,A_2),A))) ),
    file('theBenchmark.p',fact_43_finite_OinsertI) ).

fof(fact_44_finite_OinsertI,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A))) ),
    file('theBenchmark.p',fact_44_finite_OinsertI) ).

fof(fact_45_finite_OinsertI,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A))) ),
    file('theBenchmark.p',fact_45_finite_OinsertI) ).

fof(fact_46_finite_OinsertI,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),A))) ),
    file('theBenchmark.p',fact_46_finite_OinsertI) ).

fof(fact_47_finite_OinsertI,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
     => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),A))) ),
    file('theBenchmark.p',fact_47_finite_OinsertI) ).

fof(fact_48_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_48_card__image__le) ).

fof(fact_49_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_49_card__image__le) ).

fof(fact_50_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_int_bool_a(F,A))),hAPP_f521865025ol_nat(finite1876863882t_bool,A))) ),
    file('theBenchmark.p',fact_50_card__image__le) ).

fof(fact_51_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_51_card__image__le) ).

fof(fact_52_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_52_card__image__le) ).

fof(fact_53_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_53_card__image__le) ).

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_f215623910l_bool(finite1395289673t_bool,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1431733819ol_nat(F,A))),hAPP_f521865025ol_nat(finite1876863882t_bool,A))) ),
    file('theBenchmark.p',fact_56_card__image__le) ).

fof(fact_57_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_57_card__image__le) ).

fof(fact_58_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_58_card__image__le) ).

fof(fact_59_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_59_card__image__le) ).

fof(fact_60_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_f957591787ol_nat(finite_card_int,image_pname_int(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A))) ),
    file('theBenchmark.p',fact_60_card__image__le) ).

fof(fact_61_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_f957591787ol_nat(finite_card_int,image_a_int(F,A))),hAPP_fun_a_bool_nat(finite_card_a,A))) ),
    file('theBenchmark.p',fact_61_card__image__le) ).

fof(fact_62_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_2069007511ol_int(F,A))),hAPP_f521865025ol_nat(finite1876863882t_bool,A))) ),
    file('theBenchmark.p',fact_62_card__image__le) ).

fof(fact_63_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_f957591787ol_nat(finite_card_int,image_1133522419ol_int(F,A))),hAPP_f696928925ol_nat(finite346522414t_bool,A))) ),
    file('theBenchmark.p',fact_63_card__image__le) ).

fof(fact_64_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_f957591787ol_nat(finite_card_int,image_41399353ol_int(F,A))),hAPP_f55526627ol_nat(finite1340463720e_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_f957591787ol_nat(finite_card_int,image_fun_a_bool_int(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_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_66_card__image__le) ).

fof(fact_67_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_67_card__image__le) ).

fof(fact_68_card__image__le,axiom,
    ! [F,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_int_pname(F,A))),hAPP_f957591787ol_nat(finite_card_int,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_fun_a_bool_nat(finite_card_a,image_pname_a(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_f54304608l_bool(finite_finite_nat,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_nat_int(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A))) ),
    file('theBenchmark.p',fact_70_card__image__le) ).

fof(fact_71_card__mono,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,A),B))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,A)),hAPP_f521865025ol_nat(finite1876863882t_bool,B))) ) ),
    file('theBenchmark.p',fact_71_card__mono) ).

fof(fact_72_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_72_card__mono) ).

fof(fact_73_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_73_card__mono) ).

fof(fact_74_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_74_card__mono) ).

fof(fact_75_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_75_card__mono) ).

fof(fact_76_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_76_card__mono) ).

fof(fact_77_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_77_card__mono) ).

fof(fact_78_card__mono,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,A)),hAPP_f957591787ol_nat(finite_card_int,B))) ) ),
    file('theBenchmark.p',fact_78_card__mono) ).

fof(fact_79_card__seteq,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,A),B))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,B)),hAPP_f521865025ol_nat(finite1876863882t_bool,A)))
         => A = B ) ) ),
    file('theBenchmark.p',fact_79_card__seteq) ).

fof(fact_80_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_80_card__seteq) ).

fof(fact_81_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_81_card__seteq) ).

fof(fact_82_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_82_card__seteq) ).

fof(fact_83_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_83_card__seteq) ).

fof(fact_84_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_84_card__seteq) ).

fof(fact_85_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_85_card__seteq) ).

fof(fact_86_card__seteq,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,B)),hAPP_f957591787ol_nat(finite_card_int,A)))
         => A = B ) ) ),
    file('theBenchmark.p',fact_86_card__seteq) ).

fof(fact_87_card__insert__le,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,A)),hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X_1),A)))) ),
    file('theBenchmark.p',fact_87_card__insert__le) ).

fof(fact_88_card__insert__le,axiom,
    ! [X_1,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,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X_1),A)))) ),
    file('theBenchmark.p',fact_88_card__insert__le) ).

fof(fact_89_card__insert__le,axiom,
    ! [X_1,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,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A)))) ),
    file('theBenchmark.p',fact_89_card__insert__le) ).

fof(fact_90_card__insert__le,axiom,
    ! [X_1,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,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X_1),A)))) ),
    file('theBenchmark.p',fact_90_card__insert__le) ).

fof(fact_91_card__insert__le,axiom,
    ! [X_1,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,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)))) ),
    file('theBenchmark.p',fact_91_card__insert__le) ).

fof(fact_92_card__insert__le,axiom,
    ! [X_1,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,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)))) ),
    file('theBenchmark.p',fact_92_card__insert__le) ).

fof(fact_93_card__insert__le,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,A)),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)))) ),
    file('theBenchmark.p',fact_93_card__insert__le) ).

fof(fact_94_card__insert__le,axiom,
    ! [X_1,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,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)))) ),
    file('theBenchmark.p',fact_94_card__insert__le) ).

fof(fact_95_card__insert__if,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A))
     => ( ( ~ hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X_1),A))
         => hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X_1),A)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,A)) )
        & ( hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X_1),A))
         => hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X_1),A)) = hAPP_f521865025ol_nat(finite1876863882t_bool,A) ) ) ),
    file('theBenchmark.p',fact_95_card__insert__if) ).

fof(fact_96_card__insert__if,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
     => ( ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_1),A))
         => hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X_1),A)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,A)) )
        & ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_1),A))
         => hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X_1),A)) = hAPP_f696928925ol_nat(finite346522414t_bool,A) ) ) ),
    file('theBenchmark.p',fact_96_card__insert__if) ).

fof(fact_97_card__insert__if,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A))
         => hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,A)) )
        & ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A))
         => hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A)) = hAPP_f55526627ol_nat(finite1340463720e_bool,A) ) ) ),
    file('theBenchmark.p',fact_97_card__insert__if) ).

fof(fact_98_card__insert__if,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
     => ( ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_1),A))
         => hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X_1),A)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,A)) )
        & ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_1),A))
         => hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X_1),A)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,A) ) ) ),
    file('theBenchmark.p',fact_98_card__insert__if) ).

fof(fact_99_card__insert__if,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
         => hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,A)) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
         => hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_f921600141ol_nat(finite_card_pname,A) ) ) ),
    file('theBenchmark.p',fact_99_card__insert__if) ).

fof(fact_100_card__insert__if,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
         => hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,A)) )
        & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
         => hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_f22106695ol_nat(finite_card_nat,A) ) ) ),
    file('theBenchmark.p',fact_100_card__insert__if) ).

fof(fact_101_card__insert__if,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => ( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
         => hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,A)) )
        & ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
         => hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_f957591787ol_nat(finite_card_int,A) ) ) ),
    file('theBenchmark.p',fact_101_card__insert__if) ).

fof(fact_102_card__insert__if,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
     => ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
         => hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),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_1),A))
         => hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_fun_a_bool_nat(finite_card_a,A) ) ) ),
    file('theBenchmark.p',fact_102_card__insert__if) ).

fof(fact_103_card__insert__disjoint,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A))
     => ( ~ hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X_1),A))
       => hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X_1),A)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,A)) ) ),
    file('theBenchmark.p',fact_103_card__insert__disjoint) ).

fof(fact_104_card__insert__disjoint,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
     => ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_1),A))
       => hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X_1),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_1,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A))
       => hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),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_1,A] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
     => ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_1),A))
       => hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X_1),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_1,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
       => hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,A)) ) ),
    file('theBenchmark.p',fact_107_card__insert__disjoint) ).

fof(fact_108_card__insert__disjoint,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
       => hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,A)) ) ),
    file('theBenchmark.p',fact_108_card__insert__disjoint) ).

fof(fact_109_card__insert__disjoint,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
       => hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,A)) ) ),
    file('theBenchmark.p',fact_109_card__insert__disjoint) ).

fof(fact_110_card__insert__disjoint,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
     => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
       => hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,A)) ) ),
    file('theBenchmark.p',fact_110_card__insert__disjoint) ).

fof(fact_111_finite__Collect__conjI,axiom,
    ! [Q_3,Pa] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Q_3)))
        | 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_3)))) ),
    file('theBenchmark.p',fact_111_finite__Collect__conjI) ).

fof(fact_112_finite__Collect__conjI,axiom,
    ! [Q_3,Pa] :
      ( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(Q_3)))
        | hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(Pa))) )
     => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,Pa),Q_3)))) ),
    file('theBenchmark.p',fact_112_finite__Collect__conjI) ).

fof(fact_113_finite__Collect__conjI,axiom,
    ! [Q_3,Pa] :
      ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Q_3)))
        | 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_3)))) ),
    file('theBenchmark.p',fact_113_finite__Collect__conjI) ).

fof(fact_114_finite__Collect__conjI,axiom,
    ! [Q_3,Pa] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_3)))
        | 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_3)))) ),
    file('theBenchmark.p',fact_114_finite__Collect__conjI) ).

fof(fact_115_finite__Collect__conjI,axiom,
    ! [Q_3,Pa] :
      ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Q_3)))
        | 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_3)))) ),
    file('theBenchmark.p',fact_115_finite__Collect__conjI) ).

fof(fact_116_finite__Collect__conjI,axiom,
    ! [Q_3,Pa] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_3)))
        | 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_3)))) ),
    file('theBenchmark.p',fact_116_finite__Collect__conjI) ).

fof(fact_117_finite__Collect__conjI,axiom,
    ! [Q_3,Pa] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_3)))
        | 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_3)))) ),
    file('theBenchmark.p',fact_117_finite__Collect__conjI) ).

fof(fact_118_finite__Collect__conjI,axiom,
    ! [Q_3,Pa] :
      ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(Q_3)))
        | hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(Pa))) )
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,Pa),Q_3)))) ),
    file('theBenchmark.p',fact_118_finite__Collect__conjI) ).

fof(fact_119_Suc__diff__le,axiom,
    ! [N,M_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_1))
     => hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_1)),N) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)) ),
    file('theBenchmark.p',fact_119_Suc__diff__le) ).

fof(fact_120_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_120_finite__Collect__le__nat) ).

fof(fact_121_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_121_card__Collect__le__nat) ).

fof(fact_122_Suc__inject,axiom,
    ! [X,Y] :
      ( hAPP_nat_nat(suc,X) = hAPP_nat_nat(suc,Y)
     => X = Y ),
    file('theBenchmark.p',fact_122_Suc__inject) ).

fof(fact_123_nat_Oinject,axiom,
    ! [Nat_3,Nat_4] :
      ( hAPP_nat_nat(suc,Nat_3) = hAPP_nat_nat(suc,Nat_4)
    <=> Nat_3 = Nat_4 ),
    file('theBenchmark.p',fact_123_nat_Oinject) ).

fof(fact_124_Suc__n__not__n,axiom,
    ! [N] : hAPP_nat_nat(suc,N) != N,
    file('theBenchmark.p',fact_124_Suc__n__not__n) ).

fof(fact_125_n__not__Suc__n,axiom,
    ! [N] : N != hAPP_nat_nat(suc,N),
    file('theBenchmark.p',fact_125_n__not__Suc__n) ).

fof(fact_126_le__antisym,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_1))
       => M_1 = N ) ),
    file('theBenchmark.p',fact_126_le__antisym) ).

fof(fact_127_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_127_le__trans) ).

fof(fact_128_eq__imp__le,axiom,
    ! [M_1,N] :
      ( M_1 = N
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) ),
    file('theBenchmark.p',fact_128_eq__imp__le) ).

fof(fact_129_nat__le__linear,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) ),
    file('theBenchmark.p',fact_129_nat__le__linear) ).

fof(fact_130_le__refl,axiom,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),N)),
    file('theBenchmark.p',fact_130_le__refl) ).

fof(fact_131_diff__commute,axiom,
    ! [I_1,J,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),J)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),K_1)),J),
    file('theBenchmark.p',fact_131_diff__commute) ).

fof(fact_132_finite__Collect__disjI,axiom,
    ! [Pa,Q_3] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,Pa),Q_3))))
    <=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Q_3)))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Pa))) ) ),
    file('theBenchmark.p',fact_132_finite__Collect__disjI) ).

fof(fact_133_finite__Collect__disjI,axiom,
    ! [Pa,Q_3] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,Pa),Q_3))))
    <=> ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(Q_3)))
        & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(Pa))) ) ),
    file('theBenchmark.p',fact_133_finite__Collect__disjI) ).

fof(fact_134_finite__Collect__disjI,axiom,
    ! [Pa,Q_3] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,Pa),Q_3))))
    <=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Q_3)))
        & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Pa))) ) ),
    file('theBenchmark.p',fact_134_finite__Collect__disjI) ).

fof(fact_135_finite__Collect__disjI,axiom,
    ! [Pa,Q_3] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,Pa),Q_3))))
    <=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_3)))
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Pa))) ) ),
    file('theBenchmark.p',fact_135_finite__Collect__disjI) ).

fof(fact_136_finite__Collect__disjI,axiom,
    ! [Pa,Q_3] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,Pa),Q_3))))
    <=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Q_3)))
        & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Pa))) ) ),
    file('theBenchmark.p',fact_136_finite__Collect__disjI) ).

fof(fact_137_finite__Collect__disjI,axiom,
    ! [Pa,Q_3] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,Pa),Q_3))))
    <=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_3)))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Pa))) ) ),
    file('theBenchmark.p',fact_137_finite__Collect__disjI) ).

fof(fact_138_finite__Collect__disjI,axiom,
    ! [Pa,Q_3] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,Pa),Q_3))))
    <=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_3)))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Pa))) ) ),
    file('theBenchmark.p',fact_138_finite__Collect__disjI) ).

fof(fact_139_finite__Collect__disjI,axiom,
    ! [Pa,Q_3] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,Pa),Q_3))))
    <=> ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(Q_3)))
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(Pa))) ) ),
    file('theBenchmark.p',fact_139_finite__Collect__disjI) ).

fof(fact_140_finite__insert,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,A_2),A)))
    <=> hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) ),
    file('theBenchmark.p',fact_140_finite__insert) ).

fof(fact_141_finite__insert,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,A_2),A)))
    <=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ),
    file('theBenchmark.p',fact_141_finite__insert) ).

fof(fact_142_finite__insert,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_2),A)))
    <=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    file('theBenchmark.p',fact_142_finite__insert) ).

fof(fact_143_finite__insert,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,A_2),A)))
    <=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) ),
    file('theBenchmark.p',fact_143_finite__insert) ).

fof(fact_144_finite__insert,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A)))
    <=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    file('theBenchmark.p',fact_144_finite__insert) ).

fof(fact_145_finite__insert,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A)))
    <=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    file('theBenchmark.p',fact_145_finite__insert) ).

fof(fact_146_finite__insert,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),A)))
    <=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    file('theBenchmark.p',fact_146_finite__insert) ).

fof(fact_147_finite__insert,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),A)))
    <=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    file('theBenchmark.p',fact_147_finite__insert) ).

fof(fact_148_finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,A),B))
     => ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B))
       => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) ) ),
    file('theBenchmark.p',fact_148_finite__subset) ).

fof(fact_149_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_149_finite__subset) ).

fof(fact_150_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_150_finite__subset) ).

fof(fact_151_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_151_finite__subset) ).

fof(fact_152_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_152_finite__subset) ).

fof(fact_153_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_153_finite__subset) ).

fof(fact_154_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_154_finite__subset) ).

fof(fact_155_finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
     => ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))
       => hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ) ),
    file('theBenchmark.p',fact_155_finite__subset) ).

fof(fact_156_rev__finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,A),B))
       => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) ) ),
    file('theBenchmark.p',fact_156_rev__finite__subset) ).

fof(fact_157_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_157_rev__finite__subset) ).

fof(fact_158_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_158_rev__finite__subset) ).

fof(fact_159_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_159_rev__finite__subset) ).

fof(fact_160_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_160_rev__finite__subset) ).

fof(fact_161_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_161_rev__finite__subset) ).

fof(fact_162_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_162_rev__finite__subset) ).

fof(fact_163_rev__finite__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
       => hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ) ),
    file('theBenchmark.p',fact_163_rev__finite__subset) ).

fof(fact_164_Suc__leD,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) ),
    file('theBenchmark.p',fact_164_Suc__leD) ).

fof(fact_165_le__SucE,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,N)))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N))
       => M_1 = hAPP_nat_nat(suc,N) ) ),
    file('theBenchmark.p',fact_165_le__SucE) ).

fof(fact_166_le__SucI,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,N))) ),
    file('theBenchmark.p',fact_166_le__SucI) ).

fof(fact_167_Suc__le__mono,axiom,
    ! [Na,M] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M)) ),
    file('theBenchmark.p',fact_167_Suc__le__mono) ).

fof(fact_168_le__Suc__eq,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,Na)))
    <=> ( M = hAPP_nat_nat(suc,Na)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) ) ),
    file('theBenchmark.p',fact_168_le__Suc__eq) ).

fof(fact_169_not__less__eq__eq,axiom,
    ! [M,Na] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M)) ),
    file('theBenchmark.p',fact_169_not__less__eq__eq) ).

fof(fact_170_Suc__n__not__le__n,axiom,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),N)),
    file('theBenchmark.p',fact_170_Suc__n__not__le__n) ).

fof(fact_171_Suc__diff__diff,axiom,
    ! [M_1,N,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_1)),N)),hAPP_nat_nat(suc,K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)),K_1),
    file('theBenchmark.p',fact_171_Suc__diff__diff) ).

fof(fact_172_diff__Suc__Suc,axiom,
    ! [M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N),
    file('theBenchmark.p',fact_172_diff__Suc__Suc) ).

fof(fact_173_le__diff__iff,axiom,
    ! [Na,K,M] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M))
     => ( 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(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,Na),K)))
        <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) ) ) ),
    file('theBenchmark.p',fact_173_le__diff__iff) ).

fof(fact_174_Nat_Odiff__diff__eq,axiom,
    ! [N,K_1,M_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N))
       => hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N) ) ),
    file('theBenchmark.p',fact_174_Nat_Odiff__diff__eq) ).

fof(fact_175_eq__diff__iff,axiom,
    ! [Na,K,M] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),Na))
       => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,Na),K)
        <=> M = Na ) ) ),
    file('theBenchmark.p',fact_175_eq__diff__iff) ).

fof(fact_176_diff__diff__cancel,axiom,
    ! [I_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),N))
     => hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),I_1)) = I_1 ),
    file('theBenchmark.p',fact_176_diff__diff__cancel) ).

fof(fact_177_diff__le__mono,axiom,
    ! [L_1,M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),L_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),L_1))) ),
    file('theBenchmark.p',fact_177_diff__le__mono) ).

fof(fact_178_diff__le__mono2,axiom,
    ! [L_1,M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_1),N)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_1),M_1))) ),
    file('theBenchmark.p',fact_178_diff__le__mono2) ).

fof(fact_179_diff__le__self,axiom,
    ! [M_1,N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)),M_1)),
    file('theBenchmark.p',fact_179_diff__le__self) ).

fof(fact_180_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_a_a(F,A)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) ) ),
    file('theBenchmark.p',fact_180_finite__surj) ).

fof(fact_181_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_fun_int_bool_a(F,A)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) ) ),
    file('theBenchmark.p',fact_181_finite__surj) ).

fof(fact_182_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_fun_nat_bool_a(F,A)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) ) ),
    file('theBenchmark.p',fact_182_finite__surj) ).

fof(fact_183_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_876012084bool_a(F,A)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) ) ),
    file('theBenchmark.p',fact_183_finite__surj) ).

fof(fact_184_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_fun_a_bool_a(F,A)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) ) ),
    file('theBenchmark.p',fact_184_finite__surj) ).

fof(fact_185_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,B),image_1512837979t_bool(F,A)))
       => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B)) ) ),
    file('theBenchmark.p',fact_185_finite__surj) ).

fof(fact_186_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B),image_2129980159t_bool(F,A)))
       => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B)) ) ),
    file('theBenchmark.p',fact_186_finite__surj) ).

fof(fact_187_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_47868345e_bool(F,A)))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) ) ),
    file('theBenchmark.p',fact_187_finite__surj) ).

fof(fact_188_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B),image_112932426a_bool(F,A)))
       => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B)) ) ),
    file('theBenchmark.p',fact_188_finite__surj) ).

fof(fact_189_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_pname_pname(F,A)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ),
    file('theBenchmark.p',fact_189_finite__surj) ).

fof(fact_190_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_nat_a(F,A)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) ) ),
    file('theBenchmark.p',fact_190_finite__surj) ).

fof(fact_191_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,B),image_1556378401t_bool(F,A)))
       => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B)) ) ),
    file('theBenchmark.p',fact_191_finite__surj) ).

fof(fact_192_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B),image_26036933t_bool(F,A)))
       => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B)) ) ),
    file('theBenchmark.p',fact_192_finite__surj) ).

fof(fact_193_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_1655916159e_bool(F,A)))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) ) ),
    file('theBenchmark.p',fact_193_finite__surj) ).

fof(fact_194_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B),image_nat_fun_a_bool(F,A)))
       => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B)) ) ),
    file('theBenchmark.p',fact_194_finite__surj) ).

fof(fact_195_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_nat_pname(F,A)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ),
    file('theBenchmark.p',fact_195_finite__surj) ).

fof(fact_196_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_int_a(F,A)))
       => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) ) ),
    file('theBenchmark.p',fact_196_finite__surj) ).

fof(fact_197_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,B),image_275383677t_bool(F,A)))
       => hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B)) ) ),
    file('theBenchmark.p',fact_197_finite__surj) ).

fof(fact_198_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B),image_892525857t_bool(F,A)))
       => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B)) ) ),
    file('theBenchmark.p',fact_198_finite__surj) ).

fof(fact_199_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_637364955e_bool(F,A)))
       => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B)) ) ),
    file('theBenchmark.p',fact_199_finite__surj) ).

fof(fact_200_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B),image_int_fun_a_bool(F,A)))
       => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B)) ) ),
    file('theBenchmark.p',fact_200_finite__surj) ).

fof(fact_201_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_int_pname(F,A)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ),
    file('theBenchmark.p',fact_201_finite__surj) ).

fof(fact_202_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_a_pname(F,A)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ),
    file('theBenchmark.p',fact_202_finite__surj) ).

fof(fact_203_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_62782965_pname(F,A)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ),
    file('theBenchmark.p',fact_203_finite__surj) ).

fof(fact_204_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1921560913_pname(F,A)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ),
    file('theBenchmark.p',fact_204_finite__surj) ).

fof(fact_205_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1283814551_pname(F,A)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ),
    file('theBenchmark.p',fact_205_finite__surj) ).

fof(fact_206_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1854862208_pname(F,A)))
       => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ) ),
    file('theBenchmark.p',fact_206_finite__surj) ).

fof(fact_207_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_a_nat(F,A)))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) ) ),
    file('theBenchmark.p',fact_207_finite__surj) ).

fof(fact_208_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_1431733819ol_nat(F,A)))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) ) ),
    file('theBenchmark.p',fact_208_finite__surj) ).

fof(fact_209_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_496248727ol_nat(F,A)))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) ) ),
    file('theBenchmark.p',fact_209_finite__surj) ).

fof(fact_210_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_1551609309ol_nat(F,A)))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) ) ),
    file('theBenchmark.p',fact_210_finite__surj) ).

fof(fact_211_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_fun_a_bool_nat(F,A)))
       => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) ) ),
    file('theBenchmark.p',fact_211_finite__surj) ).

fof(fact_212_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_a_int(F,A)))
       => hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) ) ),
    file('theBenchmark.p',fact_212_finite__surj) ).

fof(fact_213_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_2069007511ol_int(F,A)))
       => hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) ) ),
    file('theBenchmark.p',fact_213_finite__surj) ).

fof(fact_214_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_1133522419ol_int(F,A)))
       => hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) ) ),
    file('theBenchmark.p',fact_214_finite__surj) ).

fof(fact_215_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_41399353ol_int(F,A)))
       => hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) ) ),
    file('theBenchmark.p',fact_215_finite__surj) ).

fof(fact_216_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_fun_a_bool_int(F,A)))
       => hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) ) ),
    file('theBenchmark.p',fact_216_finite__surj) ).

fof(fact_217_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_217_finite__surj) ).

fof(fact_218_finite__surj,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_nat_int(F,A)))
       => hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) ) ),
    file('theBenchmark.p',fact_218_finite__surj) ).

fof(fact_219_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_fun_int_bool_a(F,A)))
         => ? [C_16] :
              ( B = image_fun_int_bool_a(F,C_16)
              & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,C_16))
              & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,C_16),A)) ) ) ) ),
    file('theBenchmark.p',fact_219_finite__subset__image) ).

fof(fact_220_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_fun_nat_bool_a(F,A)))
         => ? [C_16] :
              ( B = image_fun_nat_bool_a(F,C_16)
              & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_16))
              & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_16),A)) ) ) ) ),
    file('theBenchmark.p',fact_220_finite__subset__image) ).

fof(fact_221_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_876012084bool_a(F,A)))
         => ? [C_16] :
              ( B = image_876012084bool_a(F,C_16)
              & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_16))
              & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_16),A))
              & is_fun1661590463l_bool(C_16) ) ) ) ),
    file('theBenchmark.p',fact_221_finite__subset__image) ).

fof(fact_222_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_fun_a_bool_a(F,A)))
         => ? [C_16] :
              ( B = image_fun_a_bool_a(F,C_16)
              & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_16))
              & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_16),A))
              & is_fun949378684l_bool(C_16) ) ) ) ),
    file('theBenchmark.p',fact_222_finite__subset__image) ).

fof(fact_223_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_a_a(F,A)))
         => ? [C_16] :
              ( B = image_a_a(F,C_16)
              & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16))
              & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A))
              & is_fun_a_bool(C_16) ) ) ) ),
    file('theBenchmark.p',fact_223_finite__subset__image) ).

fof(fact_224_finite__subset__image,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,B),image_a_fun_int_bool(F,A)))
       => ? [C_16] :
            ( B = image_a_fun_int_bool(F,C_16)
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A))
            & is_fun_a_bool(C_16) ) ) ),
    file('theBenchmark.p',fact_224_finite__subset__image) ).

fof(fact_225_finite__subset__image,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B),image_a_fun_nat_bool(F,A)))
       => ? [C_16] :
            ( B = image_a_fun_nat_bool(F,C_16)
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A))
            & is_fun_a_bool(C_16) ) ) ),
    file('theBenchmark.p',fact_225_finite__subset__image) ).

fof(fact_226_finite__subset__image,axiom,
    ! [F,A,B] :
      ( is_fun1661590463l_bool(B)
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
       => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_819518260e_bool(F,A)))
         => ? [C_16] :
              ( B = image_819518260e_bool(F,C_16)
              & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16))
              & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A))
              & is_fun_a_bool(C_16) ) ) ) ),
    file('theBenchmark.p',fact_226_finite__subset__image) ).

fof(fact_227_finite__subset__image,axiom,
    ! [F,A,B] :
      ( is_fun949378684l_bool(B)
     => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))
       => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B),image_a_fun_a_bool(F,A)))
         => ? [C_16] :
              ( B = image_a_fun_a_bool(F,C_16)
              & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16))
              & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A))
              & is_fun_a_bool(C_16) ) ) ) ),
    file('theBenchmark.p',fact_227_finite__subset__image) ).

fof(fact_228_finite__subset__image,axiom,
    ! [F,A,B] :
      ( is_fun_pname_bool(B)
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_a_pname(F,A)))
         => ? [C_16] :
              ( B = image_a_pname(F,C_16)
              & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16))
              & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A))
              & is_fun_a_bool(C_16) ) ) ) ),
    file('theBenchmark.p',fact_228_finite__subset__image) ).

fof(fact_229_finite__subset__image,axiom,
    ! [F,A,B] :
      ( is_fun_pname_bool(B)
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_62782965_pname(F,A)))
         => ? [C_16] :
              ( B = image_62782965_pname(F,C_16)
              & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,C_16))
              & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,C_16),A)) ) ) ) ),
    file('theBenchmark.p',fact_229_finite__subset__image) ).

fof(fact_230_finite__subset__image,axiom,
    ! [F,A,B] :
      ( is_fun_pname_bool(B)
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1921560913_pname(F,A)))
         => ? [C_16] :
              ( B = image_1921560913_pname(F,C_16)
              & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_16))
              & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_16),A)) ) ) ) ),
    file('theBenchmark.p',fact_230_finite__subset__image) ).

fof(fact_231_finite__subset__image,axiom,
    ! [F,A,B] :
      ( is_fun_pname_bool(B)
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1283814551_pname(F,A)))
         => ? [C_16] :
              ( B = image_1283814551_pname(F,C_16)
              & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_16))
              & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_16),A))
              & is_fun1661590463l_bool(C_16) ) ) ) ),
    file('theBenchmark.p',fact_231_finite__subset__image) ).

fof(fact_232_finite__subset__image,axiom,
    ! [F,A,B] :
      ( is_fun_pname_bool(B)
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1854862208_pname(F,A)))
         => ? [C_16] :
              ( B = image_1854862208_pname(F,C_16)
              & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_16))
              & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_16),A))
              & is_fun949378684l_bool(C_16) ) ) ) ),
    file('theBenchmark.p',fact_232_finite__subset__image) ).

fof(fact_233_finite__subset__image,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_a_nat(F,A)))
       => ? [C_16] :
            ( B = image_a_nat(F,C_16)
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A))
            & is_fun_a_bool(C_16) ) ) ),
    file('theBenchmark.p',fact_233_finite__subset__image) ).

fof(fact_234_finite__subset__image,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_1431733819ol_nat(F,A)))
       => ? [C_16] :
            ( B = image_1431733819ol_nat(F,C_16)
            & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,C_16))
            & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,C_16),A)) ) ) ),
    file('theBenchmark.p',fact_234_finite__subset__image) ).

fof(fact_235_finite__subset__image,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_496248727ol_nat(F,A)))
       => ? [C_16] :
            ( B = image_496248727ol_nat(F,C_16)
            & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_16))
            & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_16),A)) ) ) ),
    file('theBenchmark.p',fact_235_finite__subset__image) ).

fof(fact_236_finite__subset__image,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_1551609309ol_nat(F,A)))
       => ? [C_16] :
            ( B = image_1551609309ol_nat(F,C_16)
            & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_16))
            & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_16),A))
            & is_fun1661590463l_bool(C_16) ) ) ),
    file('theBenchmark.p',fact_236_finite__subset__image) ).

fof(fact_237_finite__subset__image,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_fun_a_bool_nat(F,A)))
       => ? [C_16] :
            ( B = image_fun_a_bool_nat(F,C_16)
            & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_16))
            & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_16),A))
            & is_fun949378684l_bool(C_16) ) ) ),
    file('theBenchmark.p',fact_237_finite__subset__image) ).

fof(fact_238_finite__subset__image,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_pname_nat(F,A)))
       => ? [C_16] :
            ( B = image_pname_nat(F,C_16)
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A))
            & is_fun_pname_bool(C_16) ) ) ),
    file('theBenchmark.p',fact_238_finite__subset__image) ).

fof(fact_239_finite__subset__image,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_a_int(F,A)))
       => ? [C_16] :
            ( B = image_a_int(F,C_16)
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A))
            & is_fun_a_bool(C_16) ) ) ),
    file('theBenchmark.p',fact_239_finite__subset__image) ).

fof(fact_240_finite__subset__image,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_2069007511ol_int(F,A)))
       => ? [C_16] :
            ( B = image_2069007511ol_int(F,C_16)
            & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,C_16))
            & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,C_16),A)) ) ) ),
    file('theBenchmark.p',fact_240_finite__subset__image) ).

fof(fact_241_finite__subset__image,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_1133522419ol_int(F,A)))
       => ? [C_16] :
            ( B = image_1133522419ol_int(F,C_16)
            & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_16))
            & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_16),A)) ) ) ),
    file('theBenchmark.p',fact_241_finite__subset__image) ).

fof(fact_242_finite__subset__image,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_41399353ol_int(F,A)))
       => ? [C_16] :
            ( B = image_41399353ol_int(F,C_16)
            & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_16))
            & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_16),A))
            & is_fun1661590463l_bool(C_16) ) ) ),
    file('theBenchmark.p',fact_242_finite__subset__image) ).

fof(fact_243_finite__subset__image,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_fun_a_bool_int(F,A)))
       => ? [C_16] :
            ( B = image_fun_a_bool_int(F,C_16)
            & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_16))
            & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_16),A))
            & is_fun949378684l_bool(C_16) ) ) ),
    file('theBenchmark.p',fact_243_finite__subset__image) ).

fof(fact_244_finite__subset__image,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_pname_int(F,A)))
       => ? [C_16] :
            ( B = image_pname_int(F,C_16)
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A))
            & is_fun_pname_bool(C_16) ) ) ),
    file('theBenchmark.p',fact_244_finite__subset__image) ).

fof(fact_245_finite__subset__image,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,B),image_1512837979t_bool(F,A)))
       => ? [C_16] :
            ( B = image_1512837979t_bool(F,C_16)
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A))
            & is_fun_pname_bool(C_16) ) ) ),
    file('theBenchmark.p',fact_245_finite__subset__image) ).

fof(fact_246_finite__subset__image,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B),image_2129980159t_bool(F,A)))
       => ? [C_16] :
            ( B = image_2129980159t_bool(F,C_16)
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A))
            & is_fun_pname_bool(C_16) ) ) ),
    file('theBenchmark.p',fact_246_finite__subset__image) ).

fof(fact_247_finite__subset__image,axiom,
    ! [F,A,B] :
      ( is_fun1661590463l_bool(B)
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
       => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_47868345e_bool(F,A)))
         => ? [C_16] :
              ( B = image_47868345e_bool(F,C_16)
              & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16))
              & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A))
              & is_fun_pname_bool(C_16) ) ) ) ),
    file('theBenchmark.p',fact_247_finite__subset__image) ).

fof(fact_248_finite__subset__image,axiom,
    ! [F,A,B] :
      ( is_fun949378684l_bool(B)
     => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))
       => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B),image_112932426a_bool(F,A)))
         => ? [C_16] :
              ( B = image_112932426a_bool(F,C_16)
              & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16))
              & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A))
              & is_fun_pname_bool(C_16) ) ) ) ),
    file('theBenchmark.p',fact_248_finite__subset__image) ).

fof(fact_249_finite__subset__image,axiom,
    ! [F,A,B] :
      ( is_fun_pname_bool(B)
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_pname_pname(F,A)))
         => ? [C_16] :
              ( B = image_pname_pname(F,C_16)
              & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16))
              & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A))
              & is_fun_pname_bool(C_16) ) ) ) ),
    file('theBenchmark.p',fact_249_finite__subset__image) ).

fof(fact_250_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_nat_a(F,A)))
         => ? [C_16] :
              ( B = image_nat_a(F,C_16)
              & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_16))
              & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_16),A)) ) ) ) ),
    file('theBenchmark.p',fact_250_finite__subset__image) ).

fof(fact_251_finite__subset__image,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,B),image_1556378401t_bool(F,A)))
       => ? [C_16] :
            ( B = image_1556378401t_bool(F,C_16)
            & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_16))
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_16),A)) ) ) ),
    file('theBenchmark.p',fact_251_finite__subset__image) ).

fof(fact_252_finite__subset__image,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B),image_26036933t_bool(F,A)))
       => ? [C_16] :
            ( B = image_26036933t_bool(F,C_16)
            & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_16))
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_16),A)) ) ) ),
    file('theBenchmark.p',fact_252_finite__subset__image) ).

fof(fact_253_finite__subset__image,axiom,
    ! [F,A,B] :
      ( is_fun1661590463l_bool(B)
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
       => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_1655916159e_bool(F,A)))
         => ? [C_16] :
              ( B = image_1655916159e_bool(F,C_16)
              & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_16))
              & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_16),A)) ) ) ) ),
    file('theBenchmark.p',fact_253_finite__subset__image) ).

fof(fact_254_finite__subset__image,axiom,
    ! [F,A,B] :
      ( is_fun949378684l_bool(B)
     => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))
       => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B),image_nat_fun_a_bool(F,A)))
         => ? [C_16] :
              ( B = image_nat_fun_a_bool(F,C_16)
              & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_16))
              & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_16),A)) ) ) ) ),
    file('theBenchmark.p',fact_254_finite__subset__image) ).

fof(fact_255_finite__subset__image,axiom,
    ! [F,A,B] :
      ( is_fun_pname_bool(B)
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_nat_pname(F,A)))
         => ? [C_16] :
              ( B = image_nat_pname(F,C_16)
              & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_16))
              & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_16),A)) ) ) ) ),
    file('theBenchmark.p',fact_255_finite__subset__image) ).

fof(fact_256_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_int_a(F,A)))
         => ? [C_16] :
              ( B = image_int_a(F,C_16)
              & hBOOL(hAPP_f448129468l_bool(finite_finite_int,C_16))
              & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_16),A)) ) ) ) ),
    file('theBenchmark.p',fact_256_finite__subset__image) ).

fof(fact_257_finite__subset__image,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B))
     => ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,B),image_275383677t_bool(F,A)))
       => ? [C_16] :
            ( B = image_275383677t_bool(F,C_16)
            & hBOOL(hAPP_f448129468l_bool(finite_finite_int,C_16))
            & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_16),A)) ) ) ),
    file('theBenchmark.p',fact_257_finite__subset__image) ).

fof(fact_258_finite__subset__image,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B))
     => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B),image_892525857t_bool(F,A)))
       => ? [C_16] :
            ( B = image_892525857t_bool(F,C_16)
            & hBOOL(hAPP_f448129468l_bool(finite_finite_int,C_16))
            & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_16),A)) ) ) ),
    file('theBenchmark.p',fact_258_finite__subset__image) ).

fof(fact_259_finite__subset__image,axiom,
    ! [F,A,B] :
      ( is_fun1661590463l_bool(B)
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
       => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_637364955e_bool(F,A)))
         => ? [C_16] :
              ( B = image_637364955e_bool(F,C_16)
              & hBOOL(hAPP_f448129468l_bool(finite_finite_int,C_16))
              & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_16),A)) ) ) ) ),
    file('theBenchmark.p',fact_259_finite__subset__image) ).

fof(fact_260_finite__subset__image,axiom,
    ! [F,A,B] :
      ( is_fun949378684l_bool(B)
     => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))
       => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B),image_int_fun_a_bool(F,A)))
         => ? [C_16] :
              ( B = image_int_fun_a_bool(F,C_16)
              & hBOOL(hAPP_f448129468l_bool(finite_finite_int,C_16))
              & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_16),A)) ) ) ) ),
    file('theBenchmark.p',fact_260_finite__subset__image) ).

fof(fact_261_finite__subset__image,axiom,
    ! [F,A,B] :
      ( is_fun_pname_bool(B)
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
       => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_int_pname(F,A)))
         => ? [C_16] :
              ( B = image_int_pname(F,C_16)
              & hBOOL(hAPP_f448129468l_bool(finite_finite_int,C_16))
              & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_16),A)) ) ) ) ),
    file('theBenchmark.p',fact_261_finite__subset__image) ).

fof(fact_262_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_16] :
              ( B = image_pname_a(F,C_16)
              & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16))
              & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A))
              & is_fun_pname_bool(C_16) ) ) ) ),
    file('theBenchmark.p',fact_262_finite__subset__image) ).

fof(fact_263_finite__subset__image,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_nat_int(F,A)))
       => ? [C_16] :
            ( B = image_nat_int(F,C_16)
            & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_16))
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_16),A)) ) ) ),
    file('theBenchmark.p',fact_263_finite__subset__image) ).

fof(fact_264_lift__Suc__mono__le,axiom,
    ! [Na,N_3,F] :
      ( ! [N_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(F,N_1)),hAPP_n1025906991e_bool(F,hAPP_nat_nat(suc,N_1))))
     => ( 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_264_lift__Suc__mono__le) ).

fof(fact_265_lift__Suc__mono__le,axiom,
    ! [Na,N_3,F] :
      ( ! [N_1] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,N_1)),hAPP_nat_bool(F,hAPP_nat_nat(suc,N_1))))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
       => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,Na)),hAPP_nat_bool(F,N_3))) ) ),
    file('theBenchmark.p',fact_265_lift__Suc__mono__le) ).

fof(fact_266_lift__Suc__mono__le,axiom,
    ! [Na,N_3,F] :
      ( ! [N_1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(F,N_1)),hAPP_nat_fun_a_bool(F,hAPP_nat_nat(suc,N_1))))
     => ( 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_266_lift__Suc__mono__le) ).

fof(fact_267_lift__Suc__mono__le,axiom,
    ! [Na,N_3,F] :
      ( ! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,N_1)),hAPP_nat_nat(F,hAPP_nat_nat(suc,N_1))))
     => ( 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_267_lift__Suc__mono__le) ).

fof(fact_268_lift__Suc__mono__le,axiom,
    ! [Na,N_3,F] :
      ( ! [N_1] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(F,N_1)),hAPP_nat_int(F,hAPP_nat_nat(suc,N_1))))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(F,Na)),hAPP_nat_int(F,N_3))) ) ),
    file('theBenchmark.p',fact_268_lift__Suc__mono__le) ).

fof(fact_269_lift__Suc__mono__le,axiom,
    ! [Na,N_3,F] :
      ( ! [N_1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,N_1)),hAPP_n1699378549t_bool(F,hAPP_nat_nat(suc,N_1))))
     => ( 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_269_lift__Suc__mono__le) ).

fof(fact_270_lift__Suc__mono__le,axiom,
    ! [Na,N_3,F] :
      ( ! [N_1] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_n1082236369t_bool(F,N_1)),hAPP_n1082236369t_bool(F,hAPP_nat_nat(suc,N_1))))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
       => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_n1082236369t_bool(F,Na)),hAPP_n1082236369t_bool(F,N_3))) ) ),
    file('theBenchmark.p',fact_270_lift__Suc__mono__le) ).

fof(fact_271_pigeonhole__infinite,axiom,
    ! [F,A] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(F,A)))
       => ? [X_2] :
            ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,F)),hAPP_n1082236369t_bool(F,X_2))))))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ) ),
    file('theBenchmark.p',fact_271_pigeonhole__infinite) ).

fof(fact_272_pigeonhole__infinite,axiom,
    ! [F,A] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(F,A)))
       => ? [X_2] :
            ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,F)),hAPP_n1699378549t_bool(F,X_2))))))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ) ),
    file('theBenchmark.p',fact_272_pigeonhole__infinite) ).

fof(fact_273_pigeonhole__infinite,axiom,
    ! [F,A] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(F,A)))
       => ? [X_2] :
            ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,F)),hAPP_n1025906991e_bool(F,X_2))))))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ) ),
    file('theBenchmark.p',fact_273_pigeonhole__infinite) ).

fof(fact_274_pigeonhole__infinite,axiom,
    ! [F,A] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(F,A)))
       => ? [X_2] :
            ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,F)),hAPP_nat_fun_a_bool(F,X_2))))))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ) ),
    file('theBenchmark.p',fact_274_pigeonhole__infinite) ).

fof(fact_275_pigeonhole__infinite,axiom,
    ! [F,A] :
      ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(F,A)))
       => ? [X_2] :
            ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),A)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,F)),hAPP_int_a(F,X_2))))))
            & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) ) ) ),
    file('theBenchmark.p',fact_275_pigeonhole__infinite) ).

fof(fact_276_pigeonhole__infinite,axiom,
    ! [F,A] :
      ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(F,A)))
       => ? [X_2] :
            ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),A)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,F)),hAPP_i1948725293t_bool(F,X_2))))))
            & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) ) ) ),
    file('theBenchmark.p',fact_276_pigeonhole__infinite) ).

fof(fact_277_pigeonhole__infinite,axiom,
    ! [F,A] :
      ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(F,A)))
       => ? [X_2] :
            ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),A)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,F)),hAPP_i418383825t_bool(F,X_2))))))
            & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) ) ) ),
    file('theBenchmark.p',fact_277_pigeonhole__infinite) ).

fof(fact_278_pigeonhole__infinite,axiom,
    ! [F,A] :
      ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(F,A)))
       => ? [X_2] :
            ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),A)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,F)),hAPP_i7355787e_bool(F,X_2))))))
            & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) ) ) ),
    file('theBenchmark.p',fact_278_pigeonhole__infinite) ).

fof(fact_279_pigeonhole__infinite,axiom,
    ! [F,A] :
      ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(F,A)))
       => ? [X_2] :
            ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),A)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,F)),hAPP_int_fun_a_bool(F,X_2))))))
            & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) ) ) ),
    file('theBenchmark.p',fact_279_pigeonhole__infinite) ).

fof(fact_280_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_2] :
            ( ~ 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_2))))))
            & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
            & is_pname(X_2) ) ) ),
    file('theBenchmark.p',fact_280_pigeonhole__infinite) ).

fof(fact_281_pigeonhole__infinite,axiom,
    ! [F,A] :
      ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(F,A)))
       => ? [X_2] :
            ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,F)),hAPP_nat_int(F,X_2))))))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ) ),
    file('theBenchmark.p',fact_281_pigeonhole__infinite) ).

fof(fact_282_image__eqI,axiom,
    ! [A,B_3,F,X_1] :
      ( B_3 = hAPP_nat_int(F,X_1)
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
       => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_3),image_nat_int(F,A))) ) ),
    file('theBenchmark.p',fact_282_image__eqI) ).

fof(fact_283_image__eqI,axiom,
    ! [A,B_3,F,X_1] :
      ( B_3 = hAPP_pname_a(F,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,B_3),image_pname_a(F,A))) ) ),
    file('theBenchmark.p',fact_283_image__eqI) ).

fof(fact_284_equalityI,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A))
       => A = B ) ),
    file('theBenchmark.p',fact_284_equalityI) ).

fof(fact_285_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_285_equalityI) ).

fof(fact_286_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_286_equalityI) ).

fof(fact_287_subsetD,axiom,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),A))
       => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),B)) ) ),
    file('theBenchmark.p',fact_287_subsetD) ).

fof(fact_288_subsetD,axiom,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),B)) ) ),
    file('theBenchmark.p',fact_288_subsetD) ).

fof(fact_289_subsetD,axiom,
    ! [C_6,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_6),A))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),B)) ) ),
    file('theBenchmark.p',fact_289_subsetD) ).

fof(fact_290_subsetD,axiom,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),A))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),B)) ) ),
    file('theBenchmark.p',fact_290_subsetD) ).

fof(fact_291_insertCI,axiom,
    ! [B_3,A_2,B] :
      ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),B))
       => A_2 = B_3 )
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),B))) ),
    file('theBenchmark.p',fact_291_insertCI) ).

fof(fact_292_insertCI,axiom,
    ! [B_3,A_2,B] :
      ( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),B))
       => A_2 = B_3 )
     => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_3),B))) ),
    file('theBenchmark.p',fact_292_insertCI) ).

fof(fact_293_insertCI,axiom,
    ! [B_3,A_2,B] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),B))
       => A_2 = B_3 )
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_3),B))) ),
    file('theBenchmark.p',fact_293_insertCI) ).

fof(fact_294_insertCI,axiom,
    ! [B_3,A_2,B] :
      ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),B))
       => A_2 = B_3 )
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_3),B))) ),
    file('theBenchmark.p',fact_294_insertCI) ).

fof(fact_295_insertE,axiom,
    ! [A_2,B_3,A] :
      ( ( is_a(B_3)
        & is_a(A_2) )
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),A)))
       => ( A_2 != B_3
         => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A)) ) ) ),
    file('theBenchmark.p',fact_295_insertE) ).

fof(fact_296_insertE,axiom,
    ! [A_2,B_3,A] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_3),A)))
     => ( A_2 != B_3
       => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),A)) ) ),
    file('theBenchmark.p',fact_296_insertE) ).

fof(fact_297_insertE,axiom,
    ! [A_2,B_3,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_3),A)))
     => ( A_2 != B_3
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A)) ) ),
    file('theBenchmark.p',fact_297_insertE) ).

fof(fact_298_insertE,axiom,
    ! [A_2,B_3,A] :
      ( ( is_pname(B_3)
        & is_pname(A_2) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_3),A)))
       => ( A_2 != B_3
         => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A)) ) ) ),
    file('theBenchmark.p',fact_298_insertE) ).

fof(fact_299_zero__induct__lemma,axiom,
    ! [I_2,Pa,K] :
      ( hBOOL(hAPP_nat_bool(Pa,K))
     => ( ! [N_1] :
            ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_1)))
           => hBOOL(hAPP_nat_bool(Pa,N_1)) )
       => hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,K),I_2))) ) ),
    file('theBenchmark.p',fact_299_zero__induct__lemma) ).

fof(fact_300_Suc__le__D,axiom,
    ! [N,M_4] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),M_4))
     => ? [M_2] : M_4 = hAPP_nat_nat(suc,M_2) ),
    file('theBenchmark.p',fact_300_Suc__le__D) ).

fof(fact_301_order__refl,axiom,
    ! [X_1] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),X_1)),
    file('theBenchmark.p',fact_301_order__refl) ).

fof(fact_302_order__refl,axiom,
    ! [X_1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),X_1)),
    file('theBenchmark.p',fact_302_order__refl) ).

fof(fact_303_order__refl,axiom,
    ! [X_11] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_11),X_11)),
    file('theBenchmark.p',fact_303_order__refl) ).

fof(fact_304_order__refl,axiom,
    ! [X_11] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_11),X_11)),
    file('theBenchmark.p',fact_304_order__refl) ).

fof(fact_305_order__refl,axiom,
    ! [X_1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),X_1)),
    file('theBenchmark.p',fact_305_order__refl) ).

fof(fact_306_linorder__linear,axiom,
    ! [X_10,Y_9] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_9),X_10))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_10),Y_9)) ),
    file('theBenchmark.p',fact_306_linorder__linear) ).

fof(fact_307_linorder__linear,axiom,
    ! [X_10,Y_9] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_9),X_10))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_10),Y_9)) ),
    file('theBenchmark.p',fact_307_linorder__linear) ).

fof(fact_308_order__eq__iff,axiom,
    ! [X_1,Y_1] :
      ( X_1 = Y_1
    <=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),X_1))
        & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1)) ) ),
    file('theBenchmark.p',fact_308_order__eq__iff) ).

fof(fact_309_order__eq__iff,axiom,
    ! [X_1,Y_1] :
      ( X_1 = Y_1
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) ) ),
    file('theBenchmark.p',fact_309_order__eq__iff) ).

fof(fact_310_order__eq__iff,axiom,
    ! [X_1,Y_1] :
      ( X_1 = Y_1
    <=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_1),X_1))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)) ) ),
    file('theBenchmark.p',fact_310_order__eq__iff) ).

fof(fact_311_order__eq__iff,axiom,
    ! [X_1,Y_1] :
      ( X_1 = Y_1
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) ) ),
    file('theBenchmark.p',fact_311_order__eq__iff) ).

fof(fact_312_order__eq__iff,axiom,
    ! [X_1,Y_1] :
      ( ( is_fun_a_bool(Y_1)
        & is_fun_a_bool(X_1) )
     => ( X_1 = Y_1
      <=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_1),X_1))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),Y_1)) ) ) ),
    file('theBenchmark.p',fact_312_order__eq__iff) ).

fof(fact_313_order__eq__refl,axiom,
    ! [X_1,Y_1] :
      ( X_1 = Y_1
     => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1)) ),
    file('theBenchmark.p',fact_313_order__eq__refl) ).

fof(fact_314_order__eq__refl,axiom,
    ! [X_1,Y_1] :
      ( X_1 = Y_1
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) ),
    file('theBenchmark.p',fact_314_order__eq__refl) ).

fof(fact_315_order__eq__refl,axiom,
    ! [X_9,Y_8] :
      ( X_9 = Y_8
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_9),Y_8)) ),
    file('theBenchmark.p',fact_315_order__eq__refl) ).

fof(fact_316_order__eq__refl,axiom,
    ! [X_9,Y_8] :
      ( X_9 = Y_8
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_9),Y_8)) ),
    file('theBenchmark.p',fact_316_order__eq__refl) ).

fof(fact_317_order__eq__refl,axiom,
    ! [X_1,Y_1] :
      ( X_1 = Y_1
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),Y_1)) ),
    file('theBenchmark.p',fact_317_order__eq__refl) ).

fof(fact_318_order__antisym__conv,axiom,
    ! [Y_1,X_1] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),X_1))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1))
      <=> X_1 = Y_1 ) ),
    file('theBenchmark.p',fact_318_order__antisym__conv) ).

fof(fact_319_order__antisym__conv,axiom,
    ! [Y_1,X_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
      <=> X_1 = Y_1 ) ),
    file('theBenchmark.p',fact_319_order__antisym__conv) ).

fof(fact_320_order__antisym__conv,axiom,
    ! [Y_1,X_1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_1),X_1))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1))
      <=> X_1 = Y_1 ) ),
    file('theBenchmark.p',fact_320_order__antisym__conv) ).

fof(fact_321_order__antisym__conv,axiom,
    ! [Y_1,X_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
      <=> X_1 = Y_1 ) ),
    file('theBenchmark.p',fact_321_order__antisym__conv) ).

fof(fact_322_order__antisym__conv,axiom,
    ! [Y_1,X_1] :
      ( ( is_fun_a_bool(X_1)
        & is_fun_a_bool(Y_1) )
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_1),X_1))
       => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),Y_1))
        <=> X_1 = Y_1 ) ) ),
    file('theBenchmark.p',fact_322_order__antisym__conv) ).

fof(fact_323_ord__eq__le__trans,axiom,
    ! [C_6,A_2,B_3] :
      ( A_2 = B_3
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B_3),C_6))
       => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),C_6)) ) ),
    file('theBenchmark.p',fact_323_ord__eq__le__trans) ).

fof(fact_324_ord__eq__le__trans,axiom,
    ! [C_6,A_2,B_3] :
      ( A_2 = B_3
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_3),C_6))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),C_6)) ) ),
    file('theBenchmark.p',fact_324_ord__eq__le__trans) ).

fof(fact_325_ord__eq__le__trans,axiom,
    ! [C_15,A_21,B_19] :
      ( A_21 = B_19
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_19),C_15))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_21),C_15)) ) ),
    file('theBenchmark.p',fact_325_ord__eq__le__trans) ).

fof(fact_326_ord__eq__le__trans,axiom,
    ! [C_15,A_21,B_19] :
      ( A_21 = B_19
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_19),C_15))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_21),C_15)) ) ),
    file('theBenchmark.p',fact_326_ord__eq__le__trans) ).

fof(fact_327_ord__eq__le__trans,axiom,
    ! [C_6,A_2,B_3] :
      ( A_2 = B_3
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_3),C_6))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_2),C_6)) ) ),
    file('theBenchmark.p',fact_327_ord__eq__le__trans) ).

fof(fact_328_xt1_I3_J,axiom,
    ! [C_6,A_2,B_3] :
      ( A_2 = B_3
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_6),B_3))
       => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_6),A_2)) ) ),
    file('theBenchmark.p',fact_328_xt1_I3_J) ).

fof(fact_329_xt1_I3_J,axiom,
    ! [C_6,A_2,B_3] :
      ( A_2 = B_3
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_6),B_3))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_6),A_2)) ) ),
    file('theBenchmark.p',fact_329_xt1_I3_J) ).

fof(fact_330_xt1_I3_J,axiom,
    ! [C_14,A_20,B_18] :
      ( A_20 = B_18
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_14),B_18))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_14),A_20)) ) ),
    file('theBenchmark.p',fact_330_xt1_I3_J) ).

fof(fact_331_xt1_I3_J,axiom,
    ! [C_14,A_20,B_18] :
      ( A_20 = B_18
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_14),B_18))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_14),A_20)) ) ),
    file('theBenchmark.p',fact_331_xt1_I3_J) ).

fof(fact_332_xt1_I3_J,axiom,
    ! [C_6,A_2,B_3] :
      ( A_2 = B_3
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_6),B_3))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_6),A_2)) ) ),
    file('theBenchmark.p',fact_332_xt1_I3_J) ).

fof(fact_333_ord__le__eq__trans,axiom,
    ! [C_6,A_2,B_3] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_3))
     => ( B_3 = C_6
       => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),C_6)) ) ),
    file('theBenchmark.p',fact_333_ord__le__eq__trans) ).

fof(fact_334_ord__le__eq__trans,axiom,
    ! [C_6,A_2,B_3] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_3))
     => ( B_3 = C_6
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),C_6)) ) ),
    file('theBenchmark.p',fact_334_ord__le__eq__trans) ).

fof(fact_335_ord__le__eq__trans,axiom,
    ! [C_13,A_19,B_17] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_19),B_17))
     => ( B_17 = C_13
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_19),C_13)) ) ),
    file('theBenchmark.p',fact_335_ord__le__eq__trans) ).

fof(fact_336_ord__le__eq__trans,axiom,
    ! [C_13,A_19,B_17] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_19),B_17))
     => ( B_17 = C_13
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_19),C_13)) ) ),
    file('theBenchmark.p',fact_336_ord__le__eq__trans) ).

fof(fact_337_ord__le__eq__trans,axiom,
    ! [C_6,A_2,B_3] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_2),B_3))
     => ( B_3 = C_6
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_2),C_6)) ) ),
    file('theBenchmark.p',fact_337_ord__le__eq__trans) ).

fof(fact_338_xt1_I4_J,axiom,
    ! [C_6,B_3,A_2] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B_3),A_2))
     => ( B_3 = C_6
       => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_6),A_2)) ) ),
    file('theBenchmark.p',fact_338_xt1_I4_J) ).

fof(fact_339_xt1_I4_J,axiom,
    ! [C_6,B_3,A_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_3),A_2))
     => ( B_3 = C_6
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_6),A_2)) ) ),
    file('theBenchmark.p',fact_339_xt1_I4_J) ).

fof(fact_340_xt1_I4_J,axiom,
    ! [C_12,B_16,A_18] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_16),A_18))
     => ( B_16 = C_12
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_12),A_18)) ) ),
    file('theBenchmark.p',fact_340_xt1_I4_J) ).

fof(fact_341_xt1_I4_J,axiom,
    ! [C_12,B_16,A_18] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_16),A_18))
     => ( B_16 = C_12
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_12),A_18)) ) ),
    file('theBenchmark.p',fact_341_xt1_I4_J) ).

fof(fact_342_xt1_I4_J,axiom,
    ! [C_6,B_3,A_2] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_3),A_2))
     => ( B_3 = C_6
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_6),A_2)) ) ),
    file('theBenchmark.p',fact_342_xt1_I4_J) ).

fof(fact_343_order__antisym,axiom,
    ! [X_1,Y_1] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),X_1))
       => X_1 = Y_1 ) ),
    file('theBenchmark.p',fact_343_order__antisym) ).

fof(fact_344_order__antisym,axiom,
    ! [X_1,Y_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
       => X_1 = Y_1 ) ),
    file('theBenchmark.p',fact_344_order__antisym) ).

fof(fact_345_order__antisym,axiom,
    ! [X_8,Y_7] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_8),Y_7))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_7),X_8))
       => X_8 = Y_7 ) ),
    file('theBenchmark.p',fact_345_order__antisym) ).

fof(fact_346_order__antisym,axiom,
    ! [X_8,Y_7] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_8),Y_7))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_7),X_8))
       => X_8 = Y_7 ) ),
    file('theBenchmark.p',fact_346_order__antisym) ).

fof(fact_347_order__antisym,axiom,
    ! [X_1,Y_1] :
      ( ( is_fun_a_bool(Y_1)
        & is_fun_a_bool(X_1) )
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),Y_1))
       => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_1),X_1))
         => X_1 = Y_1 ) ) ),
    file('theBenchmark.p',fact_347_order__antisym) ).

fof(fact_348_order__trans,axiom,
    ! [Z_2,X_1,Y_1] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),Z_2))
       => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Z_2)) ) ),
    file('theBenchmark.p',fact_348_order__trans) ).

fof(fact_349_order__trans,axiom,
    ! [Z_2,X_1,Y_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),Z_2))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Z_2)) ) ),
    file('theBenchmark.p',fact_349_order__trans) ).

fof(fact_350_order__trans,axiom,
    ! [Z_6,X_7,Y_6] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_7),Y_6))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_6),Z_6))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_7),Z_6)) ) ),
    file('theBenchmark.p',fact_350_order__trans) ).

fof(fact_351_order__trans,axiom,
    ! [Z_6,X_7,Y_6] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_7),Y_6))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_6),Z_6))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_7),Z_6)) ) ),
    file('theBenchmark.p',fact_351_order__trans) ).

fof(fact_352_order__trans,axiom,
    ! [Z_2,X_1,Y_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),Y_1))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_1),Z_2))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),Z_2)) ) ),
    file('theBenchmark.p',fact_352_order__trans) ).

fof(fact_353_xt1_I5_J,axiom,
    ! [Y_1,X_1] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),X_1))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1))
       => X_1 = Y_1 ) ),
    file('theBenchmark.p',fact_353_xt1_I5_J) ).

fof(fact_354_xt1_I5_J,axiom,
    ! [Y_1,X_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
       => X_1 = Y_1 ) ),
    file('theBenchmark.p',fact_354_xt1_I5_J) ).

fof(fact_355_xt1_I5_J,axiom,
    ! [Y_5,X_6] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_5),X_6))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_6),Y_5))
       => X_6 = Y_5 ) ),
    file('theBenchmark.p',fact_355_xt1_I5_J) ).

fof(fact_356_xt1_I5_J,axiom,
    ! [Y_5,X_6] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_5),X_6))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_6),Y_5))
       => X_6 = Y_5 ) ),
    file('theBenchmark.p',fact_356_xt1_I5_J) ).

fof(fact_357_xt1_I5_J,axiom,
    ! [Y_1,X_1] :
      ( ( is_fun_a_bool(X_1)
        & is_fun_a_bool(Y_1) )
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_1),X_1))
       => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),Y_1))
         => X_1 = Y_1 ) ) ),
    file('theBenchmark.p',fact_357_xt1_I5_J) ).

fof(fact_358_xt1_I6_J,axiom,
    ! [Z_2,Y_1,X_1] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),X_1))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Z_2),Y_1))
       => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Z_2),X_1)) ) ),
    file('theBenchmark.p',fact_358_xt1_I6_J) ).

fof(fact_359_xt1_I6_J,axiom,
    ! [Z_2,Y_1,X_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_2),Y_1))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_2),X_1)) ) ),
    file('theBenchmark.p',fact_359_xt1_I6_J) ).

fof(fact_360_xt1_I6_J,axiom,
    ! [Z_5,Y_4,X_5] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_4),X_5))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_5),Y_4))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_5),X_5)) ) ),
    file('theBenchmark.p',fact_360_xt1_I6_J) ).

fof(fact_361_xt1_I6_J,axiom,
    ! [Z_5,Y_4,X_5] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_4),X_5))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_5),Y_4))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_5),X_5)) ) ),
    file('theBenchmark.p',fact_361_xt1_I6_J) ).

fof(fact_362_xt1_I6_J,axiom,
    ! [Z_2,Y_1,X_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_1),X_1))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Z_2),Y_1))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Z_2),X_1)) ) ),
    file('theBenchmark.p',fact_362_xt1_I6_J) ).

fof(fact_363_linorder__le__cases,axiom,
    ! [X_4,Y_3] :
      ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_4),Y_3))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_3),X_4)) ),
    file('theBenchmark.p',fact_363_linorder__le__cases) ).

fof(fact_364_linorder__le__cases,axiom,
    ! [X_4,Y_3] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_4),Y_3))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_3),X_4)) ),
    file('theBenchmark.p',fact_364_linorder__le__cases) ).

fof(fact_365_insertI1,axiom,
    ! [A_2,B] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),B))),
    file('theBenchmark.p',fact_365_insertI1) ).

fof(fact_366_insertI1,axiom,
    ! [A_2,B] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),B))),
    file('theBenchmark.p',fact_366_insertI1) ).

fof(fact_367_insertI1,axiom,
    ! [A_2,B] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B))),
    file('theBenchmark.p',fact_367_insertI1) ).

fof(fact_368_insertI1,axiom,
    ! [A_2,B] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B))),
    file('theBenchmark.p',fact_368_insertI1) ).

fof(fact_369_insert__compr,axiom,
    ! [A_2,B] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),B) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),B))),
    file('theBenchmark.p',fact_369_insert__compr) ).

fof(fact_370_insert__compr,axiom,
    ! [A_2,B] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),B) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),A_2)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),B))),
    file('theBenchmark.p',fact_370_insert__compr) ).

fof(fact_371_insert__compr,axiom,
    ! [A_2,B] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),B))),
    file('theBenchmark.p',fact_371_insert__compr) ).

fof(fact_372_insert__compr,axiom,
    ! [A_2,B] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),B))),
    file('theBenchmark.p',fact_372_insert__compr) ).

fof(fact_373_insert__Collect,axiom,
    ! [A_2,Pa] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),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_2))),Pa)),
    file('theBenchmark.p',fact_373_insert__Collect) ).

fof(fact_374_insert__Collect,axiom,
    ! [A_2,Pa] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),collect_int(Pa)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fimplies,cOMBB_bool_bool_int(fNot,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),A_2))),Pa)),
    file('theBenchmark.p',fact_374_insert__Collect) ).

fof(fact_375_insert__Collect,axiom,
    ! [A_2,Pa] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),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_2))),Pa)),
    file('theBenchmark.p',fact_375_insert__Collect) ).

fof(fact_376_mem__def,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
    <=> hBOOL(hAPP_int_bool(A,X_1)) ),
    file('theBenchmark.p',fact_376_mem__def) ).

fof(fact_377_mem__def,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
    <=> hBOOL(hAPP_nat_bool(A,X_1)) ),
    file('theBenchmark.p',fact_377_mem__def) ).

fof(fact_378_mem__def,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
    <=> hBOOL(hAPP_a_bool(A,X_1)) ),
    file('theBenchmark.p',fact_378_mem__def) ).

fof(fact_379_mem__def,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
    <=> hBOOL(hAPP_pname_bool(A,X_1)) ),
    file('theBenchmark.p',fact_379_mem__def) ).

fof(fact_380_Collect__def,axiom,
    ! [Pa] : collect_int(Pa) = Pa,
    file('theBenchmark.p',fact_380_Collect__def) ).

fof(fact_381_Collect__def,axiom,
    ! [Pa] : collect_nat(Pa) = Pa,
    file('theBenchmark.p',fact_381_Collect__def) ).

fof(fact_382_insert__absorb2,axiom,
    ! [X_1,A] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A),
    file('theBenchmark.p',fact_382_insert__absorb2) ).

fof(fact_383_insert__commute,axiom,
    ! [X_1,Y_1,A] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,Y_1),A)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,Y_1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)),
    file('theBenchmark.p',fact_383_insert__commute) ).

fof(fact_384_insert__iff,axiom,
    ! [A_2,B_3,A] :
      ( ( is_a(B_3)
        & is_a(A_2) )
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),A)))
      <=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
          | A_2 = B_3 ) ) ),
    file('theBenchmark.p',fact_384_insert__iff) ).

fof(fact_385_insert__iff,axiom,
    ! [A_2,B_3,A] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_3),A)))
    <=> ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),A))
        | A_2 = B_3 ) ),
    file('theBenchmark.p',fact_385_insert__iff) ).

fof(fact_386_insert__iff,axiom,
    ! [A_2,B_3,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_3),A)))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A))
        | A_2 = B_3 ) ),
    file('theBenchmark.p',fact_386_insert__iff) ).

fof(fact_387_insert__iff,axiom,
    ! [A_2,B_3,A] :
      ( ( is_pname(B_3)
        & is_pname(A_2) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_3),A)))
      <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A))
          | A_2 = B_3 ) ) ),
    file('theBenchmark.p',fact_387_insert__iff) ).

fof(fact_388_insert__code,axiom,
    ! [Y_1,A,X_1] :
      ( ( is_a(X_1)
        & is_a(Y_1) )
     => ( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,Y_1),A),X_1))
      <=> ( hBOOL(hAPP_a_bool(A,X_1))
          | Y_1 = X_1 ) ) ),
    file('theBenchmark.p',fact_388_insert__code) ).

fof(fact_389_insert__ident,axiom,
    ! [B,X_1,A] :
      ( ( is_fun_a_bool(A)
        & is_fun_a_bool(B) )
     => ( ~ 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))
         => ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),B)
          <=> A = B ) ) ) ),
    file('theBenchmark.p',fact_389_insert__ident) ).

fof(fact_390_insert__ident,axiom,
    ! [B,X_1,A] :
      ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
     => ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B))
       => ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B)
        <=> A = B ) ) ),
    file('theBenchmark.p',fact_390_insert__ident) ).

fof(fact_391_insert__ident,axiom,
    ! [B,X_1,A] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B))
       => ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B)
        <=> A = B ) ) ),
    file('theBenchmark.p',fact_391_insert__ident) ).

fof(fact_392_insert__ident,axiom,
    ! [B,X_1,A] :
      ( ( is_fun_pname_bool(A)
        & is_fun_pname_bool(B) )
     => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
       => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))
         => ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B)
          <=> A = B ) ) ) ),
    file('theBenchmark.p',fact_392_insert__ident) ).

fof(fact_393_insertI2,axiom,
    ! [B_3,A_2,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),B))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),B))) ),
    file('theBenchmark.p',fact_393_insertI2) ).

fof(fact_394_insertI2,axiom,
    ! [B_3,A_2,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),B))
     => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_3),B))) ),
    file('theBenchmark.p',fact_394_insertI2) ).

fof(fact_395_insertI2,axiom,
    ! [B_3,A_2,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),B))
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_3),B))) ),
    file('theBenchmark.p',fact_395_insertI2) ).

fof(fact_396_insertI2,axiom,
    ! [B_3,A_2,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),B))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_3),B))) ),
    file('theBenchmark.p',fact_396_insertI2) ).

fof(fact_397_insert__absorb,axiom,
    ! [A_2,A] :
      ( is_fun_a_bool(A)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
       => hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),A) = A ) ),
    file('theBenchmark.p',fact_397_insert__absorb) ).

fof(fact_398_insert__absorb,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),A))
     => hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),A) = A ),
    file('theBenchmark.p',fact_398_insert__absorb) ).

fof(fact_399_insert__absorb,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A))
     => hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A) = A ),
    file('theBenchmark.p',fact_399_insert__absorb) ).

fof(fact_400_insert__absorb,axiom,
    ! [A_2,A] :
      ( is_fun_pname_bool(A)
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A))
       => hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A) = A ) ),
    file('theBenchmark.p',fact_400_insert__absorb) ).

fof(fact_401_subset__refl,axiom,
    ! [A] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),A)),
    file('theBenchmark.p',fact_401_subset__refl) ).

fof(fact_402_subset__refl,axiom,
    ! [A] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),A)),
    file('theBenchmark.p',fact_402_subset__refl) ).

fof(fact_403_subset__refl,axiom,
    ! [A] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),A)),
    file('theBenchmark.p',fact_403_subset__refl) ).

fof(fact_404_set__eq__subset,axiom,
    ! [A,B] :
      ( A = B
    <=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A))
        & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) ) ),
    file('theBenchmark.p',fact_404_set__eq__subset) ).

fof(fact_405_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_405_set__eq__subset) ).

fof(fact_406_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_406_set__eq__subset) ).

fof(fact_407_equalityD1,axiom,
    ! [A,B] :
      ( A = B
     => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) ),
    file('theBenchmark.p',fact_407_equalityD1) ).

fof(fact_408_equalityD1,axiom,
    ! [A,B] :
      ( A = B
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    file('theBenchmark.p',fact_408_equalityD1) ).

fof(fact_409_equalityD1,axiom,
    ! [A,B] :
      ( A = B
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ),
    file('theBenchmark.p',fact_409_equalityD1) ).

fof(fact_410_equalityD2,axiom,
    ! [A,B] :
      ( A = B
     => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A)) ),
    file('theBenchmark.p',fact_410_equalityD2) ).

fof(fact_411_equalityD2,axiom,
    ! [A,B] :
      ( A = B
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) ),
    file('theBenchmark.p',fact_411_equalityD2) ).

fof(fact_412_equalityD2,axiom,
    ! [A,B] :
      ( A = B
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A)) ),
    file('theBenchmark.p',fact_412_equalityD2) ).

fof(fact_413_in__mono,axiom,
    ! [X_1,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
       => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B)) ) ),
    file('theBenchmark.p',fact_413_in__mono) ).

fof(fact_414_in__mono,axiom,
    ! [X_1,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) ) ),
    file('theBenchmark.p',fact_414_in__mono) ).

fof(fact_415_in__mono,axiom,
    ! [X_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,X_1),A))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B)) ) ),
    file('theBenchmark.p',fact_415_in__mono) ).

fof(fact_416_in__mono,axiom,
    ! [X_1,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) ) ),
    file('theBenchmark.p',fact_416_in__mono) ).

fof(fact_417_set__rev__mp,axiom,
    ! [B,X_1,A] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
       => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B)) ) ),
    file('theBenchmark.p',fact_417_set__rev__mp) ).

fof(fact_418_set__rev__mp,axiom,
    ! [B,X_1,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) ) ),
    file('theBenchmark.p',fact_418_set__rev__mp) ).

fof(fact_419_set__rev__mp,axiom,
    ! [B,X_1,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),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_1),B)) ) ),
    file('theBenchmark.p',fact_419_set__rev__mp) ).

fof(fact_420_set__rev__mp,axiom,
    ! [B,X_1,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) ) ),
    file('theBenchmark.p',fact_420_set__rev__mp) ).

fof(fact_421_set__mp,axiom,
    ! [X_1,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
       => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B)) ) ),
    file('theBenchmark.p',fact_421_set__mp) ).

fof(fact_422_set__mp,axiom,
    ! [X_1,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) ) ),
    file('theBenchmark.p',fact_422_set__mp) ).

fof(fact_423_set__mp,axiom,
    ! [X_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,X_1),A))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B)) ) ),
    file('theBenchmark.p',fact_423_set__mp) ).

fof(fact_424_set__mp,axiom,
    ! [X_1,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) ) ),
    file('theBenchmark.p',fact_424_set__mp) ).

fof(fact_425_subset__trans,axiom,
    ! [C_11,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),C_11))
       => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),C_11)) ) ),
    file('theBenchmark.p',fact_425_subset__trans) ).

fof(fact_426_subset__trans,axiom,
    ! [C_11,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_11))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),C_11)) ) ),
    file('theBenchmark.p',fact_426_subset__trans) ).

fof(fact_427_subset__trans,axiom,
    ! [C_11,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_11))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),C_11)) ) ),
    file('theBenchmark.p',fact_427_subset__trans) ).

fof(fact_428_equalityE,axiom,
    ! [A,B] :
      ( A = B
     => ~ ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
         => ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A)) ) ),
    file('theBenchmark.p',fact_428_equalityE) ).

fof(fact_429_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_429_equalityE) ).

fof(fact_430_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_430_equalityE) ).

fof(fact_431_image__iff,axiom,
    ! [Z_2,F,A] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Z_2),image_nat_int(F,A)))
    <=> ? [X_2] :
          ( Z_2 = hAPP_nat_int(F,X_2)
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ),
    file('theBenchmark.p',fact_431_image__iff) ).

fof(fact_432_image__iff,axiom,
    ! [Z_2,F,A] :
      ( is_a(Z_2)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,Z_2),image_pname_a(F,A)))
      <=> ? [X_2] :
            ( Z_2 = hAPP_pname_a(F,X_2)
            & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
            & is_pname(X_2) ) ) ),
    file('theBenchmark.p',fact_432_image__iff) ).

fof(fact_433_imageI,axiom,
    ! [F,X_1,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
     => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(F,X_1)),image_nat_int(F,A))) ),
    file('theBenchmark.p',fact_433_imageI) ).

fof(fact_434_imageI,axiom,
    ! [F,X_1,A] :
      ( 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)),image_pname_a(F,A))) ),
    file('theBenchmark.p',fact_434_imageI) ).

fof(fact_435_rev__image__eqI,axiom,
    ! [B_3,F,X_1,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
     => ( B_3 = hAPP_nat_int(F,X_1)
       => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_3),image_nat_int(F,A))) ) ),
    file('theBenchmark.p',fact_435_rev__image__eqI) ).

fof(fact_436_rev__image__eqI,axiom,
    ! [B_3,F,X_1,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
     => ( B_3 = hAPP_pname_a(F,X_1)
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A))) ) ),
    file('theBenchmark.p',fact_436_rev__image__eqI) ).

fof(fact_437_insert__compr__raw,axiom,
    ! [X_2,Xa] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_2),Xa) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X_2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),Xa))),
    file('theBenchmark.p',fact_437_insert__compr__raw) ).

fof(fact_438_insert__compr__raw,axiom,
    ! [X_2,Xa] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),Xa) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X_2)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),Xa))),
    file('theBenchmark.p',fact_438_insert__compr__raw) ).

fof(fact_439_insert__compr__raw,axiom,
    ! [X_2,Xa] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),Xa) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X_2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),Xa))),
    file('theBenchmark.p',fact_439_insert__compr__raw) ).

fof(fact_440_insert__compr__raw,axiom,
    ! [X_2,Xa] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),Xa) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X_2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),Xa))),
    file('theBenchmark.p',fact_440_insert__compr__raw) ).

fof(fact_441_le__fun__def,axiom,
    ! [F,G_1] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F),G_1))
    <=> ! [X_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(F,X_2)),hAPP_int_bool(G_1,X_2))) ),
    file('theBenchmark.p',fact_441_le__fun__def) ).

fof(fact_442_le__fun__def,axiom,
    ! [F,G_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G_1))
    <=> ! [X_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G_1,X_2))) ),
    file('theBenchmark.p',fact_442_le__fun__def) ).

fof(fact_443_le__fun__def,axiom,
    ! [F,G_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F),G_1))
    <=> ! [X_2] :
          ( is_a(X_2)
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(F,X_2)),hAPP_a_bool(G_1,X_2))) ) ),
    file('theBenchmark.p',fact_443_le__fun__def) ).

fof(fact_444_le__funD,axiom,
    ! [X_1,F,G_1] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F),G_1))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(F,X_1)),hAPP_int_bool(G_1,X_1))) ),
    file('theBenchmark.p',fact_444_le__funD) ).

fof(fact_445_le__funD,axiom,
    ! [X_1,F,G_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G_1))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G_1,X_1))) ),
    file('theBenchmark.p',fact_445_le__funD) ).

fof(fact_446_le__funD,axiom,
    ! [X_1,F,G_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F),G_1))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(F,X_1)),hAPP_a_bool(G_1,X_1))) ),
    file('theBenchmark.p',fact_446_le__funD) ).

fof(fact_447_le__funE,axiom,
    ! [X_1,F,G_1] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F),G_1))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(F,X_1)),hAPP_int_bool(G_1,X_1))) ),
    file('theBenchmark.p',fact_447_le__funE) ).

fof(fact_448_le__funE,axiom,
    ! [X_1,F,G_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G_1))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G_1,X_1))) ),
    file('theBenchmark.p',fact_448_le__funE) ).

fof(fact_449_le__funE,axiom,
    ! [X_1,F,G_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F),G_1))
     => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(F,X_1)),hAPP_a_bool(G_1,X_1))) ),
    file('theBenchmark.p',fact_449_le__funE) ).

fof(fact_450_subset__insertI,axiom,
    ! [B,A_2] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),B))),
    file('theBenchmark.p',fact_450_subset__insertI) ).

fof(fact_451_subset__insertI,axiom,
    ! [B,A_2] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),B))),
    file('theBenchmark.p',fact_451_subset__insertI) ).

fof(fact_452_subset__insertI,axiom,
    ! [B,A_2] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B))),
    file('theBenchmark.p',fact_452_subset__insertI) ).

fof(fact_453_insert__subset,axiom,
    ! [X_1,A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_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,X_1),B)) ) ),
    file('theBenchmark.p',fact_453_insert__subset) ).

fof(fact_454_insert__subset,axiom,
    ! [X_1,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)),B))
    <=> ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B)) ) ),
    file('theBenchmark.p',fact_454_insert__subset) ).

fof(fact_455_insert__subset,axiom,
    ! [X_1,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),B))
    <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) ) ),
    file('theBenchmark.p',fact_455_insert__subset) ).

fof(fact_456_insert__subset,axiom,
    ! [X_1,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B))
    <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) ) ),
    file('theBenchmark.p',fact_456_insert__subset) ).

fof(fact_457_subset__insert,axiom,
    ! [B,X_1,A] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),B)))
      <=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ) ),
    file('theBenchmark.p',fact_457_subset__insert) ).

fof(fact_458_subset__insert,axiom,
    ! [B,X_1,A] :
      ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B)))
      <=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) ) ),
    file('theBenchmark.p',fact_458_subset__insert) ).

fof(fact_459_subset__insert,axiom,
    ! [B,X_1,A] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B)))
      <=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ) ),
    file('theBenchmark.p',fact_459_subset__insert) ).

fof(fact_460_subset__insert,axiom,
    ! [B,X_1,A] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B)))
      <=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ) ),
    file('theBenchmark.p',fact_460_subset__insert) ).

fof(fact_461_subset__insertI2,axiom,
    ! [B_3,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),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),B))) ),
    file('theBenchmark.p',fact_461_subset__insertI2) ).

fof(fact_462_subset__insertI2,axiom,
    ! [B_3,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
     => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_3),B))) ),
    file('theBenchmark.p',fact_462_subset__insertI2) ).

fof(fact_463_subset__insertI2,axiom,
    ! [B_3,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),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_3),B))) ),
    file('theBenchmark.p',fact_463_subset__insertI2) ).

fof(fact_464_insert__mono,axiom,
    ! [A_2,C_11,D_4] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_11),D_4))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),C_11)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),D_4))) ),
    file('theBenchmark.p',fact_464_insert__mono) ).

fof(fact_465_insert__mono,axiom,
    ! [A_2,C_11,D_4] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_11),D_4))
     => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),C_11)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),D_4))) ),
    file('theBenchmark.p',fact_465_insert__mono) ).

fof(fact_466_insert__mono,axiom,
    ! [A_2,C_11,D_4] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_11),D_4))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),C_11)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),D_4))) ),
    file('theBenchmark.p',fact_466_insert__mono) ).

fof(fact_467_image__insert,axiom,
    ! [F,A_2,B] : image_nat_int(F,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(F,A_2)),image_nat_int(F,B)),
    file('theBenchmark.p',fact_467_image__insert) ).

fof(fact_468_image__insert,axiom,
    ! [F,A_2,B] : image_pname_a(F,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(F,A_2)),image_pname_a(F,B)),
    file('theBenchmark.p',fact_468_image__insert) ).

fof(fact_469_insert__image,axiom,
    ! [F,X_1,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
     => hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(F,X_1)),image_nat_int(F,A)) = image_nat_int(F,A) ),
    file('theBenchmark.p',fact_469_insert__image) ).

fof(fact_470_insert__image,axiom,
    ! [F,X_1,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
     => hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(F,X_1)),image_pname_a(F,A)) = image_pname_a(F,A) ),
    file('theBenchmark.p',fact_470_insert__image) ).

fof(fact_471_subset__image__iff,axiom,
    ! [B,F,A] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_nat_int(F,A)))
    <=> ? [AA] :
          ( B = image_nat_int(F,AA)
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,AA),A)) ) ),
    file('theBenchmark.p',fact_471_subset__image__iff) ).

fof(fact_472_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_472_subset__image__iff) ).

fof(fact_473_image__mono,axiom,
    ! [F,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
     => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(F,A)),image_nat_int(F,B))) ),
    file('theBenchmark.p',fact_473_image__mono) ).

fof(fact_474_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_474_image__mono) ).

fof(fact_475_imageE,axiom,
    ! [B_3,F,A] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_3),image_nat_int(F,A)))
     => ~ ! [X_2] :
            ( B_3 = hAPP_nat_int(F,X_2)
           => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ),
    file('theBenchmark.p',fact_475_imageE) ).

fof(fact_476_imageE,axiom,
    ! [B_3,F,A] :
      ( is_a(B_3)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
       => ~ ! [X_2] :
              ( is_pname(X_2)
             => ( B_3 = hAPP_pname_a(F,X_2)
               => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) ) ) ) ),
    file('theBenchmark.p',fact_476_imageE) ).

fof(fact_477_subsetI,axiom,
    ! [B,A] :
      ( ! [X_2] :
          ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A))
         => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),B)) )
     => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) ),
    file('theBenchmark.p',fact_477_subsetI) ).

fof(fact_478_subsetI,axiom,
    ! [B,A] :
      ( ! [X_2] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,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)) ),
    file('theBenchmark.p',fact_478_subsetI) ).

fof(fact_479_subsetI,axiom,
    ! [B,A] :
      ( ! [X_2] :
          ( is_a(X_2)
         => ( 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)) ) )
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ),
    file('theBenchmark.p',fact_479_subsetI) ).

fof(fact_480_subsetI,axiom,
    ! [B,A] :
      ( ! [X_2] :
          ( is_pname(X_2)
         => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,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)) ),
    file('theBenchmark.p',fact_480_subsetI) ).

fof(fact_481_image__subsetI,axiom,
    ! [F,B,A] :
      ( ! [X_2] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
         => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(F,X_2)),B)) )
     => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(F,A)),B)) ),
    file('theBenchmark.p',fact_481_image__subsetI) ).

fof(fact_482_image__subsetI,axiom,
    ! [F,B,A] :
      ( ! [X_2] :
          ( is_pname(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,hAPP_pname_a(F,X_2)),B)) ) )
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(F,A)),B)) ),
    file('theBenchmark.p',fact_482_image__subsetI) ).

fof(fact_483_le__funI,axiom,
    ! [F,G_1] :
      ( ! [X_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(F,X_2)),hAPP_int_bool(G_1,X_2)))
     => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F),G_1)) ),
    file('theBenchmark.p',fact_483_le__funI) ).

fof(fact_484_le__funI,axiom,
    ! [F,G_1] :
      ( ! [X_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G_1,X_2)))
     => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G_1)) ),
    file('theBenchmark.p',fact_484_le__funI) ).

fof(fact_485_le__funI,axiom,
    ! [F,G_1] :
      ( ! [X_2] :
          ( is_a(X_2)
         => hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(F,X_2)),hAPP_a_bool(G_1,X_2))) )
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F),G_1)) ),
    file('theBenchmark.p',fact_485_le__funI) ).

fof(fact_486_finite__nat__set__iff__bounded__le,axiom,
    ! [N_2] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2))
    <=> ? [M_2] :
        ! [X_2] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),N_2))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),M_2)) ) ),
    file('theBenchmark.p',fact_486_finite__nat__set__iff__bounded__le) ).

fof(fact_487_assms_I3_J,axiom,
    ! [G,C_6] :
      ( hBOOL(wt(C_6))
     => ( ! [X_2] :
            ( is_pname(X_2)
           => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),u))
             => hBOOL(hAPP_fun_a_bool_bool(p(G),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,X_2)),bot_bot_fun_a_bool))) ) )
       => hBOOL(hAPP_fun_a_bool_bool(p(G),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(C_6)),bot_bot_fun_a_bool))) ) ),
    file('theBenchmark.p',fact_487_assms_I3_J) ).

fof(fact_488_diff__eq__diff__less__eq,axiom,
    ! [A_2,B_3,C_6,D_1] :
      ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_2),B_3) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,C_6),D_1)
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),B_3))
      <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_6),D_1)) ) ),
    file('theBenchmark.p',fact_488_diff__eq__diff__less__eq) ).

fof(fact_489_less__eq__nat_Osimps_I2_J,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),Na))
    <=> hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,M)),Na)) ),
    file('theBenchmark.p',fact_489_less__eq__nat_Osimps_I2_J) ).

fof(fact_490_emptyE,axiom,
    ! [A_2] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),bot_bot_fun_int_bool)),
    file('theBenchmark.p',fact_490_emptyE) ).

fof(fact_491_emptyE,axiom,
    ! [A_2] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),bot_bot_fun_nat_bool)),
    file('theBenchmark.p',fact_491_emptyE) ).

fof(fact_492_emptyE,axiom,
    ! [A_2] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),bot_bot_fun_a_bool)),
    file('theBenchmark.p',fact_492_emptyE) ).

fof(fact_493_emptyE,axiom,
    ! [A_2] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),bot_bo844097828e_bool)),
    file('theBenchmark.p',fact_493_emptyE) ).

fof(fact_494_finite__Diff,axiom,
    ! [B,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))) ),
    file('theBenchmark.p',fact_494_finite__Diff) ).

fof(fact_495_finite__Diff,axiom,
    ! [B,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) ),
    file('theBenchmark.p',fact_495_finite__Diff) ).

fof(fact_496_finite__Diff,axiom,
    ! [B,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) ),
    file('theBenchmark.p',fact_496_finite__Diff) ).

fof(fact_497_finite_OemptyI,axiom,
    hBOOL(hAPP_f448129468l_bool(finite_finite_int,bot_bot_fun_int_bool)),
    file('theBenchmark.p',fact_497_finite_OemptyI) ).

fof(fact_498_finite_OemptyI,axiom,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)),
    file('theBenchmark.p',fact_498_finite_OemptyI) ).

fof(fact_499_finite_OemptyI,axiom,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)),
    file('theBenchmark.p',fact_499_finite_OemptyI) ).

fof(fact_500_finite_OemptyI,axiom,
    hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,bot_bot_fun_a_bool)),
    file('theBenchmark.p',fact_500_finite_OemptyI) ).

fof(fact_501_empty__subsetI,axiom,
    ! [A] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),A)),
    file('theBenchmark.p',fact_501_empty__subsetI) ).

fof(fact_502_empty__subsetI,axiom,
    ! [A] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),A)),
    file('theBenchmark.p',fact_502_empty__subsetI) ).

fof(fact_503_empty__subsetI,axiom,
    ! [A] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),A)),
    file('theBenchmark.p',fact_503_empty__subsetI) ).

fof(fact_504_equals0D,axiom,
    ! [A_2,A] :
      ( A = bot_bot_fun_int_bool
     => ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),A)) ),
    file('theBenchmark.p',fact_504_equals0D) ).

fof(fact_505_equals0D,axiom,
    ! [A_2,A] :
      ( A = bot_bot_fun_nat_bool
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A)) ),
    file('theBenchmark.p',fact_505_equals0D) ).

fof(fact_506_equals0D,axiom,
    ! [A_2,A] :
      ( A = bot_bot_fun_a_bool
     => ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A)) ),
    file('theBenchmark.p',fact_506_equals0D) ).

fof(fact_507_equals0D,axiom,
    ! [A_2,A] :
      ( A = bot_bo844097828e_bool
     => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A)) ),
    file('theBenchmark.p',fact_507_equals0D) ).

fof(fact_508_Collect__empty__eq,axiom,
    ! [Pa] :
      ( collect_int(Pa) = bot_bot_fun_int_bool
    <=> ! [X_2] : ~ hBOOL(hAPP_int_bool(Pa,X_2)) ),
    file('theBenchmark.p',fact_508_Collect__empty__eq) ).

fof(fact_509_Collect__empty__eq,axiom,
    ! [Pa] :
      ( collect_nat(Pa) = bot_bot_fun_nat_bool
    <=> ! [X_2] : ~ hBOOL(hAPP_nat_bool(Pa,X_2)) ),
    file('theBenchmark.p',fact_509_Collect__empty__eq) ).

fof(fact_510_Collect__empty__eq,axiom,
    ! [Pa] :
      ( collect_a(Pa) = bot_bot_fun_a_bool
    <=> ! [X_2] :
          ( is_a(X_2)
         => ~ hBOOL(hAPP_a_bool(Pa,X_2)) ) ),
    file('theBenchmark.p',fact_510_Collect__empty__eq) ).

fof(fact_511_Diff__cancel,axiom,
    ! [A] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),A) = bot_bot_fun_nat_bool,
    file('theBenchmark.p',fact_511_Diff__cancel) ).

fof(fact_512_Diff__cancel,axiom,
    ! [A] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),A) = bot_bot_fun_int_bool,
    file('theBenchmark.p',fact_512_Diff__cancel) ).

fof(fact_513_Diff__cancel,axiom,
    ! [A] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),A) = bot_bot_fun_a_bool,
    file('theBenchmark.p',fact_513_Diff__cancel) ).

fof(fact_514_Diff__empty,axiom,
    ! [A] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),bot_bot_fun_nat_bool) = A,
    file('theBenchmark.p',fact_514_Diff__empty) ).

fof(fact_515_Diff__empty,axiom,
    ! [A] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),bot_bot_fun_int_bool) = A,
    file('theBenchmark.p',fact_515_Diff__empty) ).

fof(fact_516_Diff__empty,axiom,
    ! [A] :
      ( is_fun_a_bool(A)
     => hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),bot_bot_fun_a_bool) = A ),
    file('theBenchmark.p',fact_516_Diff__empty) ).

fof(fact_517_empty__iff,axiom,
    ! [C_6] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),bot_bot_fun_int_bool)),
    file('theBenchmark.p',fact_517_empty__iff) ).

fof(fact_518_empty__iff,axiom,
    ! [C_6] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),bot_bot_fun_nat_bool)),
    file('theBenchmark.p',fact_518_empty__iff) ).

fof(fact_519_empty__iff,axiom,
    ! [C_6] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),bot_bot_fun_a_bool)),
    file('theBenchmark.p',fact_519_empty__iff) ).

fof(fact_520_empty__iff,axiom,
    ! [C_6] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),bot_bo844097828e_bool)),
    file('theBenchmark.p',fact_520_empty__iff) ).

fof(fact_521_empty__Collect__eq,axiom,
    ! [Pa] :
      ( bot_bot_fun_int_bool = collect_int(Pa)
    <=> ! [X_2] : ~ hBOOL(hAPP_int_bool(Pa,X_2)) ),
    file('theBenchmark.p',fact_521_empty__Collect__eq) ).

fof(fact_522_empty__Collect__eq,axiom,
    ! [Pa] :
      ( bot_bot_fun_nat_bool = collect_nat(Pa)
    <=> ! [X_2] : ~ hBOOL(hAPP_nat_bool(Pa,X_2)) ),
    file('theBenchmark.p',fact_522_empty__Collect__eq) ).

fof(fact_523_empty__Collect__eq,axiom,
    ! [Pa] :
      ( bot_bot_fun_a_bool = collect_a(Pa)
    <=> ! [X_2] :
          ( is_a(X_2)
         => ~ hBOOL(hAPP_a_bool(Pa,X_2)) ) ),
    file('theBenchmark.p',fact_523_empty__Collect__eq) ).

fof(fact_524_empty__Diff,axiom,
    ! [A] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,bot_bot_fun_nat_bool),A) = bot_bot_fun_nat_bool,
    file('theBenchmark.p',fact_524_empty__Diff) ).

fof(fact_525_empty__Diff,axiom,
    ! [A] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,bot_bot_fun_int_bool),A) = bot_bot_fun_int_bool,
    file('theBenchmark.p',fact_525_empty__Diff) ).

fof(fact_526_empty__Diff,axiom,
    ! [A] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,bot_bot_fun_a_bool),A) = bot_bot_fun_a_bool,
    file('theBenchmark.p',fact_526_empty__Diff) ).

fof(fact_527_ex__in__conv,axiom,
    ! [A] :
      ( ? [X_2] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A))
    <=> A != bot_bot_fun_int_bool ),
    file('theBenchmark.p',fact_527_ex__in__conv) ).

fof(fact_528_ex__in__conv,axiom,
    ! [A] :
      ( ? [X_2] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
    <=> A != bot_bot_fun_nat_bool ),
    file('theBenchmark.p',fact_528_ex__in__conv) ).

fof(fact_529_ex__in__conv,axiom,
    ! [A] :
      ( is_fun_a_bool(A)
     => ( ? [X_2] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
            & is_a(X_2) )
      <=> A != bot_bot_fun_a_bool ) ),
    file('theBenchmark.p',fact_529_ex__in__conv) ).

fof(fact_530_ex__in__conv,axiom,
    ! [A] :
      ( is_fun_pname_bool(A)
     => ( ? [X_2] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
            & is_pname(X_2) )
      <=> A != bot_bo844097828e_bool ) ),
    file('theBenchmark.p',fact_530_ex__in__conv) ).

fof(fact_531_all__not__in__conv,axiom,
    ! [A] :
      ( ! [X_2] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A))
    <=> A = bot_bot_fun_int_bool ),
    file('theBenchmark.p',fact_531_all__not__in__conv) ).

fof(fact_532_all__not__in__conv,axiom,
    ! [A] :
      ( ! [X_2] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
    <=> A = bot_bot_fun_nat_bool ),
    file('theBenchmark.p',fact_532_all__not__in__conv) ).

fof(fact_533_all__not__in__conv,axiom,
    ! [A] :
      ( is_fun_a_bool(A)
     => ( ! [X_2] :
            ( is_a(X_2)
           => ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A)) )
      <=> A = bot_bot_fun_a_bool ) ),
    file('theBenchmark.p',fact_533_all__not__in__conv) ).

fof(fact_534_all__not__in__conv,axiom,
    ! [A] :
      ( is_fun_pname_bool(A)
     => ( ! [X_2] :
            ( is_pname(X_2)
           => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A)) )
      <=> A = bot_bo844097828e_bool ) ),
    file('theBenchmark.p',fact_534_all__not__in__conv) ).

fof(fact_535_bot__apply,axiom,
    ! [X_1] :
      ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_1))
    <=> hBOOL(bot_bot_bool) ),
    file('theBenchmark.p',fact_535_bot__apply) ).

fof(fact_536_bot__apply,axiom,
    ! [X_1] :
      ( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X_1))
    <=> hBOOL(bot_bot_bool) ),
    file('theBenchmark.p',fact_536_bot__apply) ).

fof(fact_537_bot__apply,axiom,
    ! [X_1] :
      ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X_1))
    <=> hBOOL(bot_bot_bool) ),
    file('theBenchmark.p',fact_537_bot__apply) ).

fof(fact_538_empty__def,axiom,
    bot_bot_fun_int_bool = collect_int(cOMBK_bool_int(fFalse)),
    file('theBenchmark.p',fact_538_empty__def) ).

fof(fact_539_empty__def,axiom,
    bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse)),
    file('theBenchmark.p',fact_539_empty__def) ).

fof(fact_540_empty__def,axiom,
    bot_bot_fun_a_bool = collect_a(cOMBK_bool_a(fFalse)),
    file('theBenchmark.p',fact_540_empty__def) ).

fof(fact_541_bot__fun__def,axiom,
    ! [X_2] :
      ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_2))
    <=> hBOOL(bot_bot_bool) ),
    file('theBenchmark.p',fact_541_bot__fun__def) ).

fof(fact_542_bot__fun__def,axiom,
    ! [X_2] :
      ( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X_2))
    <=> hBOOL(bot_bot_bool) ),
    file('theBenchmark.p',fact_542_bot__fun__def) ).

fof(fact_543_bot__fun__def,axiom,
    ! [X_2] :
      ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X_2))
    <=> hBOOL(bot_bot_bool) ),
    file('theBenchmark.p',fact_543_bot__fun__def) ).

fof(fact_544_insert__Diff,axiom,
    ! [A_2,A] :
      ( is_fun_a_bool(A)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
       => hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool))) = A ) ),
    file('theBenchmark.p',fact_544_insert__Diff) ).

fof(fact_545_insert__Diff,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),A))
     => hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool))) = A ),
    file('theBenchmark.p',fact_545_insert__Diff) ).

fof(fact_546_insert__Diff,axiom,
    ! [A_2,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A))
     => hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool))) = A ),
    file('theBenchmark.p',fact_546_insert__Diff) ).

fof(fact_547_insert__Diff,axiom,
    ! [A_2,A] :
      ( is_fun_pname_bool(A)
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A))
       => hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool))) = A ) ),
    file('theBenchmark.p',fact_547_insert__Diff) ).

fof(fact_548_Diff__insert__absorb,axiom,
    ! [X_1,A] :
      ( is_fun_a_bool(A)
     => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
       => hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)) = A ) ),
    file('theBenchmark.p',fact_548_Diff__insert__absorb) ).

fof(fact_549_Diff__insert__absorb,axiom,
    ! [X_1,A] :
      ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
     => hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = A ),
    file('theBenchmark.p',fact_549_Diff__insert__absorb) ).

fof(fact_550_Diff__insert__absorb,axiom,
    ! [X_1,A] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
     => hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = A ),
    file('theBenchmark.p',fact_550_Diff__insert__absorb) ).

fof(fact_551_Diff__insert__absorb,axiom,
    ! [X_1,A] :
      ( is_fun_pname_bool(A)
     => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
       => hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = A ) ),
    file('theBenchmark.p',fact_551_Diff__insert__absorb) ).

fof(fact_552_insert__Diff__single,axiom,
    ! [A_2,A] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool))) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),A),
    file('theBenchmark.p',fact_552_insert__Diff__single) ).

fof(fact_553_insert__Diff__single,axiom,
    ! [A_2,A] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool))) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A),
    file('theBenchmark.p',fact_553_insert__Diff__single) ).

fof(fact_554_insert__Diff__single,axiom,
    ! [A_2,A] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool))) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),A),
    file('theBenchmark.p',fact_554_insert__Diff__single) ).

fof(fact_555_Diff__insert2,axiom,
    ! [A,A_2,B] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),B)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool))),B),
    file('theBenchmark.p',fact_555_Diff__insert2) ).

fof(fact_556_Diff__insert2,axiom,
    ! [A,A_2,B] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool))),B),
    file('theBenchmark.p',fact_556_Diff__insert2) ).

fof(fact_557_Diff__insert2,axiom,
    ! [A,A_2,B] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),B)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool))),B),
    file('theBenchmark.p',fact_557_Diff__insert2) ).

fof(fact_558_Diff__insert,axiom,
    ! [A,A_2,B] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),B)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool)),
    file('theBenchmark.p',fact_558_Diff__insert) ).

fof(fact_559_Diff__insert,axiom,
    ! [A,A_2,B] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool)),
    file('theBenchmark.p',fact_559_Diff__insert) ).

fof(fact_560_Diff__insert,axiom,
    ! [A,A_2,B] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),B)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool)),
    file('theBenchmark.p',fact_560_Diff__insert) ).

fof(fact_561_diff__single__insert,axiom,
    ! [A,X_1,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))),B))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),B))) ) ),
    file('theBenchmark.p',fact_561_diff__single__insert) ).

fof(fact_562_diff__single__insert,axiom,
    ! [A,X_1,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))),B))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
       => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B))) ) ),
    file('theBenchmark.p',fact_562_diff__single__insert) ).

fof(fact_563_diff__single__insert,axiom,
    ! [A,X_1,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))),B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B))) ) ),
    file('theBenchmark.p',fact_563_diff__single__insert) ).

fof(fact_564_diff__single__insert,axiom,
    ! [A,X_1,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))),B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B))) ) ),
    file('theBenchmark.p',fact_564_diff__single__insert) ).

fof(fact_565_subset__insert__iff,axiom,
    ! [A,X_1,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),B)))
    <=> ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),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_1),A))
         => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))),B)) ) ) ),
    file('theBenchmark.p',fact_565_subset__insert__iff) ).

fof(fact_566_subset__insert__iff,axiom,
    ! [A,X_1,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B)))
    <=> ( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
         => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) )
        & ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
         => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))),B)) ) ) ),
    file('theBenchmark.p',fact_566_subset__insert__iff) ).

fof(fact_567_subset__insert__iff,axiom,
    ! [A,X_1,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B)))
    <=> ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) )
        & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
         => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))),B)) ) ) ),
    file('theBenchmark.p',fact_567_subset__insert__iff) ).

fof(fact_568_subset__insert__iff,axiom,
    ! [A,X_1,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B)))
    <=> ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
         => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
         => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))),B)) ) ) ),
    file('theBenchmark.p',fact_568_subset__insert__iff) ).

fof(fact_569_finite__Diff2,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))
     => ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)))
      <=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ) ),
    file('theBenchmark.p',fact_569_finite__Diff2) ).

fof(fact_570_finite__Diff2,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
     => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)))
      <=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ) ),
    file('theBenchmark.p',fact_570_finite__Diff2) ).

fof(fact_571_finite__Diff2,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))
      <=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ) ),
    file('theBenchmark.p',fact_571_finite__Diff2) ).

fof(fact_572_insert__Diff1,axiom,
    ! [A,X_1,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
     => hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)),B) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B) ),
    file('theBenchmark.p',fact_572_insert__Diff1) ).

fof(fact_573_insert__Diff1,axiom,
    ! [A,X_1,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B))
     => hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)),B) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B) ),
    file('theBenchmark.p',fact_573_insert__Diff1) ).

fof(fact_574_insert__Diff1,axiom,
    ! [A,X_1,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B))
     => hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),B) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B) ),
    file('theBenchmark.p',fact_574_insert__Diff1) ).

fof(fact_575_insert__Diff1,axiom,
    ! [A,X_1,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))
     => hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B) ),
    file('theBenchmark.p',fact_575_insert__Diff1) ).

fof(fact_576_insert__Diff__if,axiom,
    ! [A,X_1,B] :
      ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
       => hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)),B) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)) )
      & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B))
       => hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)),B) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B) ) ),
    file('theBenchmark.p',fact_576_insert__Diff__if) ).

fof(fact_577_insert__Diff__if,axiom,
    ! [A,X_1,B] :
      ( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B))
       => hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)),B) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)) )
      & ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B))
       => hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)),B) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B) ) ),
    file('theBenchmark.p',fact_577_insert__Diff__if) ).

fof(fact_578_insert__Diff__if,axiom,
    ! [A,X_1,B] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B))
       => hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),B) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)) )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B))
       => hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),B) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B) ) ),
    file('theBenchmark.p',fact_578_insert__Diff__if) ).

fof(fact_579_insert__Diff__if,axiom,
    ! [A,X_1,B] :
      ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))
       => hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)) )
      & ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))
       => hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B) ) ),
    file('theBenchmark.p',fact_579_insert__Diff__if) ).

fof(fact_580_double__diff,axiom,
    ! [C_11,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),C_11))
       => hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,B),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,C_11),A)) = A ) ),
    file('theBenchmark.p',fact_580_double__diff) ).

fof(fact_581_double__diff,axiom,
    ! [C_11,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_11))
       => hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,B),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,C_11),A)) = A ) ),
    file('theBenchmark.p',fact_581_double__diff) ).

fof(fact_582_double__diff,axiom,
    ! [C_11,A,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),C_11))
         => hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,B),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,C_11),A)) = A ) ) ),
    file('theBenchmark.p',fact_582_double__diff) ).

fof(fact_583_Diff__mono,axiom,
    ! [D_4,B,A,C_11] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),C_11))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,D_4),B))
       => hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,C_11),D_4))) ) ),
    file('theBenchmark.p',fact_583_Diff__mono) ).

fof(fact_584_Diff__mono,axiom,
    ! [D_4,B,A,C_11] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),C_11))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,D_4),B))
       => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,C_11),D_4))) ) ),
    file('theBenchmark.p',fact_584_Diff__mono) ).

fof(fact_585_Diff__mono,axiom,
    ! [D_4,B,A,C_11] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),C_11))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,D_4),B))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,C_11),D_4))) ) ),
    file('theBenchmark.p',fact_585_Diff__mono) ).

fof(fact_586_Diff__subset,axiom,
    ! [A,B] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)),A)),
    file('theBenchmark.p',fact_586_Diff__subset) ).

fof(fact_587_Diff__subset,axiom,
    ! [A,B] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)),A)),
    file('theBenchmark.p',fact_587_Diff__subset) ).

fof(fact_588_Diff__subset,axiom,
    ! [A,B] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)),A)),
    file('theBenchmark.p',fact_588_Diff__subset) ).

fof(fact_589_singleton__inject,axiom,
    ! [A_2,B_3] :
      ( ( is_a(B_3)
        & is_a(A_2) )
     => ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),bot_bot_fun_a_bool)
       => A_2 = B_3 ) ),
    file('theBenchmark.p',fact_589_singleton__inject) ).

fof(fact_590_singleton__inject,axiom,
    ! [A_2,B_3] :
      ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_3),bot_bot_fun_nat_bool)
     => A_2 = B_3 ),
    file('theBenchmark.p',fact_590_singleton__inject) ).

fof(fact_591_singleton__inject,axiom,
    ! [A_2,B_3] :
      ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_3),bot_bot_fun_int_bool)
     => A_2 = B_3 ),
    file('theBenchmark.p',fact_591_singleton__inject) ).

fof(fact_592_singletonE,axiom,
    ! [B_3,A_2] :
      ( ( is_a(A_2)
        & is_a(B_3) )
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool)))
       => B_3 = A_2 ) ),
    file('theBenchmark.p',fact_592_singletonE) ).

fof(fact_593_singletonE,axiom,
    ! [B_3,A_2] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_3),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool)))
     => B_3 = A_2 ),
    file('theBenchmark.p',fact_593_singletonE) ).

fof(fact_594_singletonE,axiom,
    ! [B_3,A_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_3),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool)))
     => B_3 = A_2 ),
    file('theBenchmark.p',fact_594_singletonE) ).

fof(fact_595_singletonE,axiom,
    ! [B_3,A_2] :
      ( ( is_pname(A_2)
        & is_pname(B_3) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_3),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool)))
       => B_3 = A_2 ) ),
    file('theBenchmark.p',fact_595_singletonE) ).

fof(fact_596_doubleton__eq__iff,axiom,
    ! [A_2,B_3,C_6,D_1] :
      ( ( is_a(D_1)
        & is_a(C_6)
        & is_a(B_3)
        & is_a(A_2) )
     => ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),bot_bot_fun_a_bool)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,C_6),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,D_1),bot_bot_fun_a_bool))
      <=> ( ( B_3 = C_6
            & A_2 = D_1 )
          | ( B_3 = D_1
            & A_2 = C_6 ) ) ) ),
    file('theBenchmark.p',fact_596_doubleton__eq__iff) ).

fof(fact_597_doubleton__eq__iff,axiom,
    ! [A_2,B_3,C_6,D_1] :
      ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_3),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,C_6),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,D_1),bot_bot_fun_nat_bool))
    <=> ( ( B_3 = C_6
          & A_2 = D_1 )
        | ( B_3 = D_1
          & A_2 = C_6 ) ) ),
    file('theBenchmark.p',fact_597_doubleton__eq__iff) ).

fof(fact_598_doubleton__eq__iff,axiom,
    ! [A_2,B_3,C_6,D_1] :
      ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_3),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,C_6),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,D_1),bot_bot_fun_int_bool))
    <=> ( ( B_3 = C_6
          & A_2 = D_1 )
        | ( B_3 = D_1
          & A_2 = C_6 ) ) ),
    file('theBenchmark.p',fact_598_doubleton__eq__iff) ).

fof(fact_599_singleton__iff,axiom,
    ! [B_3,A_2] :
      ( ( is_a(A_2)
        & is_a(B_3) )
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool)))
      <=> B_3 = A_2 ) ),
    file('theBenchmark.p',fact_599_singleton__iff) ).

fof(fact_600_singleton__iff,axiom,
    ! [B_3,A_2] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_3),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool)))
    <=> B_3 = A_2 ),
    file('theBenchmark.p',fact_600_singleton__iff) ).

fof(fact_601_singleton__iff,axiom,
    ! [B_3,A_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_3),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool)))
    <=> B_3 = A_2 ),
    file('theBenchmark.p',fact_601_singleton__iff) ).

fof(fact_602_singleton__iff,axiom,
    ! [B_3,A_2] :
      ( ( is_pname(A_2)
        & is_pname(B_3) )
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_3),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool)))
      <=> B_3 = A_2 ) ),
    file('theBenchmark.p',fact_602_singleton__iff) ).

fof(fact_603_insert__not__empty,axiom,
    ! [A_2,A] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),A) != bot_bot_fun_a_bool,
    file('theBenchmark.p',fact_603_insert__not__empty) ).

fof(fact_604_insert__not__empty,axiom,
    ! [A_2,A] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A) != bot_bot_fun_nat_bool,
    file('theBenchmark.p',fact_604_insert__not__empty) ).

fof(fact_605_insert__not__empty,axiom,
    ! [A_2,A] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),A) != bot_bot_fun_int_bool,
    file('theBenchmark.p',fact_605_insert__not__empty) ).

fof(fact_606_empty__not__insert,axiom,
    ! [A_2,A] : bot_bot_fun_a_bool != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),A),
    file('theBenchmark.p',fact_606_empty__not__insert) ).

fof(fact_607_empty__not__insert,axiom,
    ! [A_2,A] : bot_bot_fun_nat_bool != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A),
    file('theBenchmark.p',fact_607_empty__not__insert) ).

fof(fact_608_empty__not__insert,axiom,
    ! [A_2,A] : bot_bot_fun_int_bool != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),A),
    file('theBenchmark.p',fact_608_empty__not__insert) ).

fof(fact_609_subset__empty,axiom,
    ! [A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),bot_bot_fun_nat_bool))
    <=> A = bot_bot_fun_nat_bool ),
    file('theBenchmark.p',fact_609_subset__empty) ).

fof(fact_610_subset__empty,axiom,
    ! [A] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),bot_bot_fun_int_bool))
    <=> A = bot_bot_fun_int_bool ),
    file('theBenchmark.p',fact_610_subset__empty) ).

fof(fact_611_subset__empty,axiom,
    ! [A] :
      ( is_fun_a_bool(A)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),bot_bot_fun_a_bool))
      <=> A = bot_bot_fun_a_bool ) ),
    file('theBenchmark.p',fact_611_subset__empty) ).

fof(fact_612_image__is__empty,axiom,
    ! [F,A] :
      ( image_nat_int(F,A) = bot_bot_fun_int_bool
    <=> A = bot_bot_fun_nat_bool ),
    file('theBenchmark.p',fact_612_image__is__empty) ).

fof(fact_613_image__is__empty,axiom,
    ! [F,A] :
      ( is_fun_pname_bool(A)
     => ( image_pname_a(F,A) = bot_bot_fun_a_bool
      <=> A = bot_bo844097828e_bool ) ),
    file('theBenchmark.p',fact_613_image__is__empty) ).

fof(fact_614_image__empty,axiom,
    ! [F] : image_nat_int(F,bot_bot_fun_nat_bool) = bot_bot_fun_int_bool,
    file('theBenchmark.p',fact_614_image__empty) ).

fof(fact_615_image__empty,axiom,
    ! [F] : image_pname_a(F,bot_bo844097828e_bool) = bot_bot_fun_a_bool,
    file('theBenchmark.p',fact_615_image__empty) ).

fof(fact_616_empty__is__image,axiom,
    ! [F,A] :
      ( bot_bot_fun_int_bool = image_nat_int(F,A)
    <=> A = bot_bot_fun_nat_bool ),
    file('theBenchmark.p',fact_616_empty__is__image) ).

fof(fact_617_empty__is__image,axiom,
    ! [F,A] :
      ( is_fun_pname_bool(A)
     => ( bot_bot_fun_a_bool = image_pname_a(F,A)
      <=> A = bot_bo844097828e_bool ) ),
    file('theBenchmark.p',fact_617_empty__is__image) ).

fof(fact_618_le__bot,axiom,
    ! [A_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),bot_bot_fun_nat_bool))
     => A_2 = bot_bot_fun_nat_bool ),
    file('theBenchmark.p',fact_618_le__bot) ).

fof(fact_619_le__bot,axiom,
    ! [A_2] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),bot_bot_fun_int_bool))
     => A_2 = bot_bot_fun_int_bool ),
    file('theBenchmark.p',fact_619_le__bot) ).

fof(fact_620_le__bot,axiom,
    ! [A_17] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_17),bot_bot_nat))
     => A_17 = bot_bot_nat ),
    file('theBenchmark.p',fact_620_le__bot) ).

fof(fact_621_le__bot,axiom,
    ! [A_2] :
      ( is_fun_a_bool(A_2)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_2),bot_bot_fun_a_bool))
       => A_2 = bot_bot_fun_a_bool ) ),
    file('theBenchmark.p',fact_621_le__bot) ).

fof(fact_622_bot__unique,axiom,
    ! [A_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),bot_bot_fun_nat_bool))
    <=> A_2 = bot_bot_fun_nat_bool ),
    file('theBenchmark.p',fact_622_bot__unique) ).

fof(fact_623_bot__unique,axiom,
    ! [A_2] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),bot_bot_fun_int_bool))
    <=> A_2 = bot_bot_fun_int_bool ),
    file('theBenchmark.p',fact_623_bot__unique) ).

fof(fact_624_bot__unique,axiom,
    ! [A_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_2),bot_bot_nat))
    <=> A_2 = bot_bot_nat ),
    file('theBenchmark.p',fact_624_bot__unique) ).

fof(fact_625_bot__unique,axiom,
    ! [A_2] :
      ( is_fun_a_bool(A_2)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_2),bot_bot_fun_a_bool))
      <=> A_2 = bot_bot_fun_a_bool ) ),
    file('theBenchmark.p',fact_625_bot__unique) ).

fof(fact_626_bot__least,axiom,
    ! [A_2] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),A_2)),
    file('theBenchmark.p',fact_626_bot__least) ).

fof(fact_627_bot__least,axiom,
    ! [A_2] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),A_2)),
    file('theBenchmark.p',fact_627_bot__least) ).

fof(fact_628_bot__least,axiom,
    ! [A_16] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),A_16)),
    file('theBenchmark.p',fact_628_bot__least) ).

fof(fact_629_bot__least,axiom,
    ! [A_2] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),A_2)),
    file('theBenchmark.p',fact_629_bot__least) ).

fof(fact_630_Collect__conv__if,axiom,
    ! [Pa,A_2] :
      ( ( ~ hBOOL(hAPP_a_bool(Pa,A_2))
       => collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_2)),Pa)) = bot_bot_fun_a_bool )
      & ( hBOOL(hAPP_a_bool(Pa,A_2))
       => collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_2)),Pa)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool) ) ),
    file('theBenchmark.p',fact_630_Collect__conv__if) ).

fof(fact_631_Collect__conv__if,axiom,
    ! [Pa,A_2] :
      ( ( ~ hBOOL(hAPP_int_bool(Pa,A_2))
       => collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),A_2)),Pa)) = bot_bot_fun_int_bool )
      & ( hBOOL(hAPP_int_bool(Pa,A_2))
       => collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),A_2)),Pa)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool) ) ),
    file('theBenchmark.p',fact_631_Collect__conv__if) ).

fof(fact_632_Collect__conv__if,axiom,
    ! [Pa,A_2] :
      ( ( ~ hBOOL(hAPP_nat_bool(Pa,A_2))
       => collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_2)),Pa)) = bot_bot_fun_nat_bool )
      & ( hBOOL(hAPP_nat_bool(Pa,A_2))
       => collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_2)),Pa)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool) ) ),
    file('theBenchmark.p',fact_632_Collect__conv__if) ).

fof(fact_633_Collect__conv__if2,axiom,
    ! [Pa,A_2] :
      ( ( ~ hBOOL(hAPP_a_bool(Pa,A_2))
       => collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,A_2)),Pa)) = bot_bot_fun_a_bool )
      & ( hBOOL(hAPP_a_bool(Pa,A_2))
       => collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,A_2)),Pa)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool) ) ),
    file('theBenchmark.p',fact_633_Collect__conv__if2) ).

fof(fact_634_Collect__conv__if2,axiom,
    ! [Pa,A_2] :
      ( ( ~ hBOOL(hAPP_int_bool(Pa,A_2))
       => collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,A_2)),Pa)) = bot_bot_fun_int_bool )
      & ( hBOOL(hAPP_int_bool(Pa,A_2))
       => collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,A_2)),Pa)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool) ) ),
    file('theBenchmark.p',fact_634_Collect__conv__if2) ).

fof(fact_635_Collect__conv__if2,axiom,
    ! [Pa,A_2] :
      ( ( ~ hBOOL(hAPP_nat_bool(Pa,A_2))
       => collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,A_2)),Pa)) = bot_bot_fun_nat_bool )
      & ( hBOOL(hAPP_nat_bool(Pa,A_2))
       => collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,A_2)),Pa)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool) ) ),
    file('theBenchmark.p',fact_635_Collect__conv__if2) ).

fof(fact_636_singleton__conv,axiom,
    ! [A_2] : collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_2)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool),
    file('theBenchmark.p',fact_636_singleton__conv) ).

fof(fact_637_singleton__conv,axiom,
    ! [A_2] : collect_int(hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),A_2)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool),
    file('theBenchmark.p',fact_637_singleton__conv) ).

fof(fact_638_singleton__conv,axiom,
    ! [A_2] : collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_2)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool),
    file('theBenchmark.p',fact_638_singleton__conv) ).

fof(fact_639_singleton__conv2,axiom,
    ! [A_2] : collect_a(hAPP_a_fun_a_bool(fequal_a,A_2)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool),
    file('theBenchmark.p',fact_639_singleton__conv2) ).

fof(fact_640_singleton__conv2,axiom,
    ! [A_2] : collect_int(hAPP_i1948725293t_bool(fequal_int,A_2)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool),
    file('theBenchmark.p',fact_640_singleton__conv2) ).

fof(fact_641_singleton__conv2,axiom,
    ! [A_2] : collect_nat(hAPP_n1699378549t_bool(fequal_nat,A_2)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool),
    file('theBenchmark.p',fact_641_singleton__conv2) ).

fof(fact_642_card__Suc__Diff1,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
       => hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)))) = hAPP_fun_a_bool_nat(finite_card_a,A) ) ),
    file('theBenchmark.p',fact_642_card__Suc__Diff1) ).

fof(fact_643_card__Suc__Diff1,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
       => hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))) = hAPP_f957591787ol_nat(finite_card_int,A) ) ),
    file('theBenchmark.p',fact_643_card__Suc__Diff1) ).

fof(fact_644_card__Suc__Diff1,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
       => hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))) = hAPP_f22106695ol_nat(finite_card_nat,A) ) ),
    file('theBenchmark.p',fact_644_card__Suc__Diff1) ).

fof(fact_645_card__Suc__Diff1,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
       => hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))) = hAPP_f921600141ol_nat(finite_card_pname,A) ) ),
    file('theBenchmark.p',fact_645_card__Suc__Diff1) ).

fof(fact_646_card__insert,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
     => hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)))) ),
    file('theBenchmark.p',fact_646_card__insert) ).

fof(fact_647_card__insert,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))) ),
    file('theBenchmark.p',fact_647_card__insert) ).

fof(fact_648_card__insert,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))) ),
    file('theBenchmark.p',fact_648_card__insert) ).

fof(fact_649_card__insert,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))) ),
    file('theBenchmark.p',fact_649_card__insert) ).

fof(fact_650_card__Diff1__le,axiom,
    ! [X_1,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,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)))),hAPP_fun_a_bool_nat(finite_card_a,A))) ),
    file('theBenchmark.p',fact_650_card__Diff1__le) ).

fof(fact_651_card__Diff1__le,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))),hAPP_f957591787ol_nat(finite_card_int,A))) ),
    file('theBenchmark.p',fact_651_card__Diff1__le) ).

fof(fact_652_card__Diff1__le,axiom,
    ! [X_1,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,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))),hAPP_f22106695ol_nat(finite_card_nat,A))) ),
    file('theBenchmark.p',fact_652_card__Diff1__le) ).

fof(fact_653_card__Diff1__le,axiom,
    ! [X_1,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,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))),hAPP_f921600141ol_nat(finite_card_pname,A))) ),
    file('theBenchmark.p',fact_653_card__Diff1__le) ).

fof(fact_654_finite__Diff__insert,axiom,
    ! [A,A_2,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),B))))
    <=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B))) ),
    file('theBenchmark.p',fact_654_finite__Diff__insert) ).

fof(fact_655_finite__Diff__insert,axiom,
    ! [A,A_2,B] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),B))))
    <=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))) ),
    file('theBenchmark.p',fact_655_finite__Diff__insert) ).

fof(fact_656_finite__Diff__insert,axiom,
    ! [A,A_2,B] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B))))
    <=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) ),
    file('theBenchmark.p',fact_656_finite__Diff__insert) ).

fof(fact_657_finite__Diff__insert,axiom,
    ! [A,A_2,B] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B))))
    <=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) ),
    file('theBenchmark.p',fact_657_finite__Diff__insert) ).

fof(fact_658_image__diff__subset,axiom,
    ! [F,A,B] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,image_nat_int(F,A)),image_nat_int(F,B))),image_nat_int(F,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)))),
    file('theBenchmark.p',fact_658_image__diff__subset) ).

fof(fact_659_image__diff__subset,axiom,
    ! [F,A,B] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,image_pname_a(F,A)),image_pname_a(F,B))),image_pname_a(F,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))),
    file('theBenchmark.p',fact_659_image__diff__subset) ).

fof(fact_660_subset__singletonD,axiom,
    ! [A,X_1] :
      ( is_fun_a_bool(A)
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)))
       => ( A = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)
          | A = bot_bot_fun_a_bool ) ) ),
    file('theBenchmark.p',fact_660_subset__singletonD) ).

fof(fact_661_subset__singletonD,axiom,
    ! [A,X_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))
     => ( A = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)
        | A = bot_bot_fun_nat_bool ) ),
    file('theBenchmark.p',fact_661_subset__singletonD) ).

fof(fact_662_subset__singletonD,axiom,
    ! [A,X_1] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))
     => ( A = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)
        | A = bot_bot_fun_int_bool ) ),
    file('theBenchmark.p',fact_662_subset__singletonD) ).

fof(fact_663_nat__case__Suc,axiom,
    ! [F1,F2,Nat_3] : hAPP_nat_nat(nat_case_nat(F1,F2),hAPP_nat_nat(suc,Nat_3)) = hAPP_nat_nat(F2,Nat_3),
    file('theBenchmark.p',fact_663_nat__case__Suc) ).

fof(fact_664_nat__case__Suc,axiom,
    ! [F1,F2,Nat_3] :
      ( hBOOL(hAPP_nat_bool(nat_case_bool(F1,F2),hAPP_nat_nat(suc,Nat_3)))
    <=> hBOOL(hAPP_nat_bool(F2,Nat_3)) ),
    file('theBenchmark.p',fact_664_nat__case__Suc) ).

fof(fact_665_image__constant,axiom,
    ! [C_6,X_1,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
     => image_nat_int(cOMBK_int_nat(C_6),A) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,C_6),bot_bot_fun_int_bool) ),
    file('theBenchmark.p',fact_665_image__constant) ).

fof(fact_666_image__constant,axiom,
    ! [C_6,X_1,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
     => image_pname_a(cOMBK_a_pname(C_6),A) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,C_6),bot_bot_fun_a_bool) ),
    file('theBenchmark.p',fact_666_image__constant) ).

fof(fact_667_image__constant__conv,axiom,
    ! [C_6,A] :
      ( ( A != bot_bot_fun_nat_bool
       => image_nat_int(cOMBK_int_nat(C_6),A) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,C_6),bot_bot_fun_int_bool) )
      & ( A = bot_bot_fun_nat_bool
       => image_nat_int(cOMBK_int_nat(C_6),A) = bot_bot_fun_int_bool ) ),
    file('theBenchmark.p',fact_667_image__constant__conv) ).

fof(fact_668_image__constant__conv,axiom,
    ! [C_6,A] :
      ( is_fun_pname_bool(A)
     => ( ( A != bot_bo844097828e_bool
         => image_pname_a(cOMBK_a_pname(C_6),A) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,C_6),bot_bot_fun_a_bool) )
        & ( A = bot_bo844097828e_bool
         => image_pname_a(cOMBK_a_pname(C_6),A) = bot_bot_fun_a_bool ) ) ),
    file('theBenchmark.p',fact_668_image__constant__conv) ).

fof(fact_669_diff__eq__diff__eq,axiom,
    ! [A_2,B_3,C_6,D_1] :
      ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_2),B_3) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,C_6),D_1)
     => ( A_2 = B_3
      <=> C_6 = D_1 ) ),
    file('theBenchmark.p',fact_669_diff__eq__diff__eq) ).

fof(fact_670_card__Diff__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A))
       => hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,A)),hAPP_f957591787ol_nat(finite_card_int,B)) ) ),
    file('theBenchmark.p',fact_670_card__Diff__subset) ).

fof(fact_671_card__Diff__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))
       => hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,A)),hAPP_f22106695ol_nat(finite_card_nat,B)) ) ),
    file('theBenchmark.p',fact_671_card__Diff__subset) ).

fof(fact_672_card__Diff__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,B),A))
       => hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,A)),hAPP_fun_a_bool_nat(finite_card_a,B)) ) ),
    file('theBenchmark.p',fact_672_card__Diff__subset) ).

fof(fact_673_card__Diff__subset,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
       => hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,A)),hAPP_f921600141ol_nat(finite_card_pname,B)) ) ),
    file('theBenchmark.p',fact_673_card__Diff__subset) ).

fof(fact_674_diff__card__le__card__Diff,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,A)),hAPP_f957591787ol_nat(finite_card_int,B))),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)))) ),
    file('theBenchmark.p',fact_674_diff__card__le__card__Diff) ).

fof(fact_675_diff__card__le__card__Diff,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,A)),hAPP_f22106695ol_nat(finite_card_nat,B))),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)))) ),
    file('theBenchmark.p',fact_675_diff__card__le__card__Diff) ).

fof(fact_676_diff__card__le__card__Diff,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,A)),hAPP_fun_a_bool_nat(finite_card_a,B))),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)))) ),
    file('theBenchmark.p',fact_676_diff__card__le__card__Diff) ).

fof(fact_677_diff__card__le__card__Diff,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,A)),hAPP_f921600141ol_nat(finite_card_pname,B))),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))) ),
    file('theBenchmark.p',fact_677_diff__card__le__card__Diff) ).

fof(fact_678_finite__subset__induct,axiom,
    ! [Pa,A,F_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F_1),A))
       => ( hBOOL(hAPP_fun_a_bool_bool(Pa,bot_bot_fun_a_bool))
         => ( ! [A_14,F_2] :
                ( ( is_fun_a_bool(F_2)
                  & is_a(A_14) )
               => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_2))
                 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_14),A))
                   => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_14),F_2))
                     => ( hBOOL(hAPP_fun_a_bool_bool(Pa,F_2))
                       => hBOOL(hAPP_fun_a_bool_bool(Pa,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_14),F_2))) ) ) ) ) )
           => hBOOL(hAPP_fun_a_bool_bool(Pa,F_1)) ) ) ) ),
    file('theBenchmark.p',fact_678_finite__subset__induct) ).

fof(fact_679_finite__subset__induct,axiom,
    ! [Pa,A,F_1] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F_1),A))
       => ( hBOOL(hAPP_f448129468l_bool(Pa,bot_bot_fun_int_bool))
         => ( ! [A_14,F_2] :
                ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_2))
               => ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_14),A))
                 => ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_14),F_2))
                   => ( hBOOL(hAPP_f448129468l_bool(Pa,F_2))
                     => hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_14),F_2))) ) ) ) )
           => hBOOL(hAPP_f448129468l_bool(Pa,F_1)) ) ) ) ),
    file('theBenchmark.p',fact_679_finite__subset__induct) ).

fof(fact_680_finite__subset__induct,axiom,
    ! [Pa,A,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F_1),A))
       => ( hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool))
         => ( ! [A_14,F_2] :
                ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2))
               => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_14),A))
                 => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_14),F_2))
                   => ( hBOOL(hAPP_f54304608l_bool(Pa,F_2))
                     => hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_14),F_2))) ) ) ) )
           => hBOOL(hAPP_f54304608l_bool(Pa,F_1)) ) ) ) ),
    file('theBenchmark.p',fact_680_finite__subset__induct) ).

fof(fact_681_finite__subset__induct,axiom,
    ! [Pa,A,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F_1),A))
       => ( hBOOL(hAPP_f1664156314l_bool(Pa,bot_bo844097828e_bool))
         => ( ! [A_14,F_2] :
                ( ( is_fun_pname_bool(F_2)
                  & is_pname(A_14) )
               => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_2))
                 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_14),A))
                   => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_14),F_2))
                     => ( hBOOL(hAPP_f1664156314l_bool(Pa,F_2))
                       => hBOOL(hAPP_f1664156314l_bool(Pa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_14),F_2))) ) ) ) ) )
           => hBOOL(hAPP_f1664156314l_bool(Pa,F_1)) ) ) ) ),
    file('theBenchmark.p',fact_681_finite__subset__induct) ).

fof(fact_682_assms_I2_J,axiom,
    ! [Pn,G] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,Pn)),G)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(the_com(body(Pn)))),bot_bot_fun_a_bool)))
     => hBOOL(hAPP_fun_a_bool_bool(p(G),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,Pn)),bot_bot_fun_a_bool))) ),
    file('theBenchmark.p',fact_682_assms_I2_J) ).

fof(fact_683_finite__empty__induct,axiom,
    ! [Pa,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
     => ( hBOOL(hAPP_fun_a_bool_bool(Pa,A))
       => ( ! [A_14,A_15] :
              ( ( is_fun_a_bool(A_15)
                & is_a(A_14) )
             => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_15))
               => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_14),A_15))
                 => ( hBOOL(hAPP_fun_a_bool_bool(Pa,A_15))
                   => hBOOL(hAPP_fun_a_bool_bool(Pa,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A_15),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_14),bot_bot_fun_a_bool)))) ) ) ) )
         => hBOOL(hAPP_fun_a_bool_bool(Pa,bot_bot_fun_a_bool)) ) ) ),
    file('theBenchmark.p',fact_683_finite__empty__induct) ).

fof(fact_684_finite__empty__induct,axiom,
    ! [Pa,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => ( hBOOL(hAPP_f448129468l_bool(Pa,A))
       => ( ! [A_14,A_15] :
              ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_15))
             => ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_14),A_15))
               => ( hBOOL(hAPP_f448129468l_bool(Pa,A_15))
                 => hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_15),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_14),bot_bot_fun_int_bool)))) ) ) )
         => hBOOL(hAPP_f448129468l_bool(Pa,bot_bot_fun_int_bool)) ) ) ),
    file('theBenchmark.p',fact_684_finite__empty__induct) ).

fof(fact_685_finite__empty__induct,axiom,
    ! [Pa,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => ( hBOOL(hAPP_f54304608l_bool(Pa,A))
       => ( ! [A_14,A_15] :
              ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_15))
             => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_14),A_15))
               => ( hBOOL(hAPP_f54304608l_bool(Pa,A_15))
                 => hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_15),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_14),bot_bot_fun_nat_bool)))) ) ) )
         => hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool)) ) ) ),
    file('theBenchmark.p',fact_685_finite__empty__induct) ).

fof(fact_686_finite__empty__induct,axiom,
    ! [Pa,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f1664156314l_bool(Pa,A))
       => ( ! [A_14,A_15] :
              ( ( is_fun_pname_bool(A_15)
                & is_pname(A_14) )
             => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_15))
               => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_14),A_15))
                 => ( hBOOL(hAPP_f1664156314l_bool(Pa,A_15))
                   => hBOOL(hAPP_f1664156314l_bool(Pa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_15),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_14),bot_bo844097828e_bool)))) ) ) ) )
         => hBOOL(hAPP_f1664156314l_bool(Pa,bot_bo844097828e_bool)) ) ) ),
    file('theBenchmark.p',fact_686_finite__empty__induct) ).

fof(fact_687_finite__induct,axiom,
    ! [Pa,F_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1))
     => ( hBOOL(hAPP_fun_a_bool_bool(Pa,bot_bot_fun_a_bool))
       => ( ! [X_2,F_2] :
              ( ( is_fun_a_bool(F_2)
                & is_a(X_2) )
             => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_2))
               => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),F_2))
                 => ( hBOOL(hAPP_fun_a_bool_bool(Pa,F_2))
                   => hBOOL(hAPP_fun_a_bool_bool(Pa,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_2),F_2))) ) ) ) )
         => hBOOL(hAPP_fun_a_bool_bool(Pa,F_1)) ) ) ),
    file('theBenchmark.p',fact_687_finite__induct) ).

fof(fact_688_finite__induct,axiom,
    ! [Pa,F_1] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1))
     => ( hBOOL(hAPP_f448129468l_bool(Pa,bot_bot_fun_int_bool))
       => ( ! [X_2,F_2] :
              ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_2))
             => ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),F_2))
               => ( hBOOL(hAPP_f448129468l_bool(Pa,F_2))
                 => hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),F_2))) ) ) )
         => hBOOL(hAPP_f448129468l_bool(Pa,F_1)) ) ) ),
    file('theBenchmark.p',fact_688_finite__induct) ).

fof(fact_689_finite__induct,axiom,
    ! [Pa,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
     => ( hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool))
       => ( ! [X_2,F_2] :
              ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2))
             => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),F_2))
               => ( hBOOL(hAPP_f54304608l_bool(Pa,F_2))
                 => hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),F_2))) ) ) )
         => hBOOL(hAPP_f54304608l_bool(Pa,F_1)) ) ) ),
    file('theBenchmark.p',fact_689_finite__induct) ).

fof(fact_690_finite__induct,axiom,
    ! [Pa,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
     => ( hBOOL(hAPP_f1664156314l_bool(Pa,bot_bo844097828e_bool))
       => ( ! [X_2,F_2] :
              ( ( is_fun_pname_bool(F_2)
                & is_pname(X_2) )
             => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_2))
               => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),F_2))
                 => ( hBOOL(hAPP_f1664156314l_bool(Pa,F_2))
                   => hBOOL(hAPP_f1664156314l_bool(Pa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),F_2))) ) ) ) )
         => hBOOL(hAPP_f1664156314l_bool(Pa,F_1)) ) ) ),
    file('theBenchmark.p',fact_690_finite__induct) ).

fof(fact_691_finite_Osimps,axiom,
    ! [A_2] :
      ( is_fun_a_bool(A_2)
     => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_2))
      <=> ( ? [A_15,A_14] :
              ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_15))
              & A_2 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_14),A_15)
              & is_a(A_14)
              & is_fun_a_bool(A_15) )
          | A_2 = bot_bot_fun_a_bool ) ) ),
    file('theBenchmark.p',fact_691_finite_Osimps) ).

fof(fact_692_finite_Osimps,axiom,
    ! [A_2] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
    <=> ( ? [A_15,A_14] :
            ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_15))
            & A_2 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_14),A_15) )
        | A_2 = bot_bot_fun_int_bool ) ),
    file('theBenchmark.p',fact_692_finite_Osimps) ).

fof(fact_693_finite_Osimps,axiom,
    ! [A_2] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
    <=> ( ? [A_15,A_14] :
            ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_15))
            & A_2 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_14),A_15) )
        | A_2 = bot_bot_fun_nat_bool ) ),
    file('theBenchmark.p',fact_693_finite_Osimps) ).

fof(fact_694_finite_Osimps,axiom,
    ! [A_2] :
      ( is_fun_pname_bool(A_2)
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_2))
      <=> ( ? [A_15,A_14] :
              ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_15))
              & A_2 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_14),A_15)
              & is_pname(A_14)
              & is_fun_pname_bool(A_15) )
          | A_2 = bot_bo844097828e_bool ) ) ),
    file('theBenchmark.p',fact_694_finite_Osimps) ).

fof(fact_695_finite__less__ub,axiom,
    ! [U,F] :
      ( ! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(F,N_1)))
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,F)),U)))) ),
    file('theBenchmark.p',fact_695_finite__less__ub) ).

fof(fact_696_the__elem__eq,axiom,
    ! [X_1] :
      ( is_a(X_1)
     => hAPP_fun_a_bool_a(the_elem_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)) = X_1 ),
    file('theBenchmark.p',fact_696_the__elem__eq) ).

fof(fact_697_the__elem__eq,axiom,
    ! [X_1] : hAPP_f22106695ol_nat(the_elem_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = X_1,
    file('theBenchmark.p',fact_697_the__elem__eq) ).

fof(fact_698_the__elem__eq,axiom,
    ! [X_1] : hAPP_f1594865479ol_int(the_elem_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = X_1,
    file('theBenchmark.p',fact_698_the__elem__eq) ).

fof(fact_699_nonempty__iff,axiom,
    ! [A] :
      ( is_fun_a_bool(A)
     => ( A != bot_bot_fun_a_bool
      <=> ? [X_2,B_15] :
            ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B_15))
            & A = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_2),B_15)
            & is_fun_a_bool(B_15)
            & is_a(X_2) ) ) ),
    file('theBenchmark.p',fact_699_nonempty__iff) ).

fof(fact_700_nonempty__iff,axiom,
    ! [A] :
      ( A != bot_bot_fun_int_bool
    <=> ? [X_2,B_15] :
          ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),B_15))
          & A = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),B_15) ) ),
    file('theBenchmark.p',fact_700_nonempty__iff) ).

fof(fact_701_nonempty__iff,axiom,
    ! [A] :
      ( A != bot_bot_fun_nat_bool
    <=> ? [X_2,B_15] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_15))
          & A = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),B_15) ) ),
    file('theBenchmark.p',fact_701_nonempty__iff) ).

fof(fact_702_nonempty__iff,axiom,
    ! [A] :
      ( is_fun_pname_bool(A)
     => ( A != bot_bo844097828e_bool
      <=> ? [X_2,B_15] :
            ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B_15))
            & A = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),B_15)
            & is_fun_pname_bool(B_15)
            & is_pname(X_2) ) ) ),
    file('theBenchmark.p',fact_702_nonempty__iff) ).

fof(fact_703_assms_I4_J,axiom,
    ! [Pn] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Pn),u))
     => hBOOL(wt(the_com(body(Pn)))) ),
    file('theBenchmark.p',fact_703_assms_I4_J) ).

fof(fact_704_DiffE,axiom,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)))
     => ~ ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),A))
         => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),B)) ) ),
    file('theBenchmark.p',fact_704_DiffE) ).

fof(fact_705_DiffE,axiom,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)))
     => ~ ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),A))
         => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),B)) ) ),
    file('theBenchmark.p',fact_705_DiffE) ).

fof(fact_706_DiffE,axiom,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)))
     => ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),A))
         => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),B)) ) ),
    file('theBenchmark.p',fact_706_DiffE) ).

fof(fact_707_DiffE,axiom,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))
     => ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),A))
         => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),B)) ) ),
    file('theBenchmark.p',fact_707_DiffE) ).

fof(fact_708_DiffI,axiom,
    ! [B,C_6,A] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),A))
     => ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),B))
       => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))) ) ),
    file('theBenchmark.p',fact_708_DiffI) ).

fof(fact_709_DiffI,axiom,
    ! [B,C_6,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),A))
     => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),B))
       => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) ) ),
    file('theBenchmark.p',fact_709_DiffI) ).

fof(fact_710_DiffI,axiom,
    ! [B,C_6,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),A))
     => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),B))
       => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B))) ) ),
    file('theBenchmark.p',fact_710_DiffI) ).

fof(fact_711_DiffI,axiom,
    ! [B,C_6,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),A))
     => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),B))
       => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) ) ),
    file('theBenchmark.p',fact_711_DiffI) ).

fof(fact_712_DiffD2,axiom,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)))
     => ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),B)) ),
    file('theBenchmark.p',fact_712_DiffD2) ).

fof(fact_713_DiffD2,axiom,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)))
     => ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),B)) ),
    file('theBenchmark.p',fact_713_DiffD2) ).

fof(fact_714_DiffD2,axiom,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)))
     => ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),B)) ),
    file('theBenchmark.p',fact_714_DiffD2) ).

fof(fact_715_DiffD2,axiom,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))
     => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),B)) ),
    file('theBenchmark.p',fact_715_DiffD2) ).

fof(fact_716_DiffD1,axiom,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)))
     => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),A)) ),
    file('theBenchmark.p',fact_716_DiffD1) ).

fof(fact_717_DiffD1,axiom,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)))
     => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),A)) ),
    file('theBenchmark.p',fact_717_DiffD1) ).

fof(fact_718_DiffD1,axiom,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)))
     => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),A)) ),
    file('theBenchmark.p',fact_718_DiffD1) ).

fof(fact_719_DiffD1,axiom,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))
     => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),A)) ),
    file('theBenchmark.p',fact_719_DiffD1) ).

fof(fact_720_Diff__iff,axiom,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)))
    <=> ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),B))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),A)) ) ),
    file('theBenchmark.p',fact_720_Diff__iff) ).

fof(fact_721_Diff__iff,axiom,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)))
    <=> ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),B))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),A)) ) ),
    file('theBenchmark.p',fact_721_Diff__iff) ).

fof(fact_722_Diff__iff,axiom,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)))
    <=> ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),B))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),A)) ) ),
    file('theBenchmark.p',fact_722_Diff__iff) ).

fof(fact_723_Diff__iff,axiom,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))
    <=> ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),B))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),A)) ) ),
    file('theBenchmark.p',fact_723_Diff__iff) ).

fof(fact_724_set__diff__eq,axiom,
    ! [A,B] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),A)),cOMBB_bool_bool_int(fNot,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),B)))),
    file('theBenchmark.p',fact_724_set__diff__eq) ).

fof(fact_725_set__diff__eq,axiom,
    ! [A,B] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A)),cOMBB_bool_bool_nat(fNot,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),B)))),
    file('theBenchmark.p',fact_725_set__diff__eq) ).

fof(fact_726_set__diff__eq,axiom,
    ! [A,B] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A)),cOMBB_bool_bool_a(fNot,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),B)))),
    file('theBenchmark.p',fact_726_set__diff__eq) ).

fof(fact_727_set__diff__eq,axiom,
    ! [A,B] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A)),cOMBB_647938656_pname(fNot,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),B)))),
    file('theBenchmark.p',fact_727_set__diff__eq) ).

fof(fact_728_folding__one_Oinsert__remove,axiom,
    ! [X_1,A,F,F_1] :
      ( is_a(X_1)
     => ( hBOOL(finite_folding_one_a(F,F_1))
       => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
         => ( ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)) != bot_bot_fun_a_bool
             => hAPP_fun_a_bool_a(F_1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_a_a(hAPP_a_fun_a_a(F,X_1),hAPP_fun_a_bool_a(F_1,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)))) )
            & ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)) = bot_bot_fun_a_bool
             => hAPP_fun_a_bool_a(F_1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = X_1 ) ) ) ) ),
    file('theBenchmark.p',fact_728_folding__one_Oinsert__remove) ).

fof(fact_729_folding__one_Oinsert__remove,axiom,
    ! [X_1,A,F,F_1] :
      ( hBOOL(finite1626084323ne_int(F,F_1))
     => ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
       => ( ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) != bot_bot_fun_int_bool
           => hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))) )
          & ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = bot_bot_fun_int_bool
           => hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = X_1 ) ) ) ),
    file('theBenchmark.p',fact_729_folding__one_Oinsert__remove) ).

fof(fact_730_folding__one_Oinsert__remove,axiom,
    ! [X_1,A,F,F_1] :
      ( hBOOL(finite988810631ne_nat(F,F_1))
     => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
       => ( ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool
           => hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))) )
          & ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool
           => hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = X_1 ) ) ) ),
    file('theBenchmark.p',fact_730_folding__one_Oinsert__remove) ).

fof(fact_731_folding__one_Oinsert__remove,axiom,
    ! [X_1,A,F,F_1] :
      ( is_pname(X_1)
     => ( hBOOL(finite1282449217_pname(F,F_1))
       => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
         => ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) != bot_bo844097828e_bool
             => hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))) )
            & ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = bot_bo844097828e_bool
             => hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = X_1 ) ) ) ) ),
    file('theBenchmark.p',fact_731_folding__one_Oinsert__remove) ).

fof(fact_732_folding__one_Oremove,axiom,
    ! [X_1,A,F,F_1] :
      ( is_a(X_1)
     => ( hBOOL(finite_folding_one_a(F,F_1))
       => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
         => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
           => ( ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)) != bot_bot_fun_a_bool
               => hAPP_fun_a_bool_a(F_1,A) = hAPP_a_a(hAPP_a_fun_a_a(F,X_1),hAPP_fun_a_bool_a(F_1,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)))) )
              & ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)) = bot_bot_fun_a_bool
               => hAPP_fun_a_bool_a(F_1,A) = X_1 ) ) ) ) ) ),
    file('theBenchmark.p',fact_732_folding__one_Oremove) ).

fof(fact_733_folding__one_Oremove,axiom,
    ! [X_1,A,F,F_1] :
      ( hBOOL(finite1626084323ne_int(F,F_1))
     => ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
       => ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
         => ( ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) != bot_bot_fun_int_bool
             => hAPP_f1594865479ol_int(F_1,A) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))) )
            & ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = bot_bot_fun_int_bool
             => hAPP_f1594865479ol_int(F_1,A) = X_1 ) ) ) ) ),
    file('theBenchmark.p',fact_733_folding__one_Oremove) ).

fof(fact_734_folding__one_Oremove,axiom,
    ! [X_1,A,F,F_1] :
      ( hBOOL(finite988810631ne_nat(F,F_1))
     => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
       => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
         => ( ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool
             => hAPP_f22106695ol_nat(F_1,A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))) )
            & ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool
             => hAPP_f22106695ol_nat(F_1,A) = X_1 ) ) ) ) ),
    file('theBenchmark.p',fact_734_folding__one_Oremove) ).

fof(fact_735_folding__one_Oremove,axiom,
    ! [X_1,A,F,F_1] :
      ( is_pname(X_1)
     => ( hBOOL(finite1282449217_pname(F,F_1))
       => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
         => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
           => ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) != bot_bo844097828e_bool
               => hAPP_f1297739591_pname(F_1,A) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))) )
              & ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = bot_bo844097828e_bool
               => hAPP_f1297739591_pname(F_1,A) = X_1 ) ) ) ) ) ),
    file('theBenchmark.p',fact_735_folding__one_Oremove) ).

fof(fact_736_card__Diff__singleton__if,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
     => ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
         => hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))) = hAPP_fun_a_bool_nat(finite_card_a,A) )
        & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
         => hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,A)),one_one_nat) ) ) ),
    file('theBenchmark.p',fact_736_card__Diff__singleton__if) ).

fof(fact_737_card__Diff__singleton__if,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => ( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
         => hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))) = hAPP_f957591787ol_nat(finite_card_int,A) )
        & ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
         => hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,A)),one_one_nat) ) ) ),
    file('theBenchmark.p',fact_737_card__Diff__singleton__if) ).

fof(fact_738_card__Diff__singleton__if,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
         => hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) = hAPP_f22106695ol_nat(finite_card_nat,A) )
        & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
         => hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,A)),one_one_nat) ) ) ),
    file('theBenchmark.p',fact_738_card__Diff__singleton__if) ).

fof(fact_739_card__Diff__singleton__if,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
         => hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))) = hAPP_f921600141ol_nat(finite_card_pname,A) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
         => hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,A)),one_one_nat) ) ) ),
    file('theBenchmark.p',fact_739_card__Diff__singleton__if) ).

fof(fact_740_card__Diff__singleton,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
       => hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,A)),one_one_nat) ) ),
    file('theBenchmark.p',fact_740_card__Diff__singleton) ).

fof(fact_741_card__Diff__singleton,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
       => hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,A)),one_one_nat) ) ),
    file('theBenchmark.p',fact_741_card__Diff__singleton) ).

fof(fact_742_card__Diff__singleton,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
       => hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,A)),one_one_nat) ) ),
    file('theBenchmark.p',fact_742_card__Diff__singleton) ).

fof(fact_743_card__Diff__singleton,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
       => hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,A)),one_one_nat) ) ),
    file('theBenchmark.p',fact_743_card__Diff__singleton) ).

fof(fact_744_one__reorient,axiom,
    ! [X_1] :
      ( one_one_int = X_1
    <=> X_1 = one_one_int ),
    file('theBenchmark.p',fact_744_one__reorient) ).

fof(fact_745_one__reorient,axiom,
    ! [X_1] :
      ( one_one_nat = X_1
    <=> X_1 = one_one_nat ),
    file('theBenchmark.p',fact_745_one__reorient) ).

fof(fact_746_diff__Suc__1,axiom,
    ! [N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,N)),one_one_nat) = N,
    file('theBenchmark.p',fact_746_diff__Suc__1) ).

fof(fact_747_diff__Suc__eq__diff__pred,axiom,
    ! [M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),one_one_nat)),N),
    file('theBenchmark.p',fact_747_diff__Suc__eq__diff__pred) ).

fof(fact_748_folding__one_Osingleton,axiom,
    ! [X_1,F,F_1] :
      ( is_a(X_1)
     => ( hBOOL(finite_folding_one_a(F,F_1))
       => hAPP_fun_a_bool_a(F_1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)) = X_1 ) ),
    file('theBenchmark.p',fact_748_folding__one_Osingleton) ).

fof(fact_749_folding__one_Osingleton,axiom,
    ! [X_1,F,F_1] :
      ( hBOOL(finite988810631ne_nat(F,F_1))
     => hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = X_1 ),
    file('theBenchmark.p',fact_749_folding__one_Osingleton) ).

fof(fact_750_folding__one_Osingleton,axiom,
    ! [X_1,F,F_1] :
      ( hBOOL(finite1626084323ne_int(F,F_1))
     => hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = X_1 ),
    file('theBenchmark.p',fact_750_folding__one_Osingleton) ).

fof(fact_751_card__Diff__insert,axiom,
    ! [B,A_2,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
       => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),B))
         => hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),B))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B))),one_one_nat) ) ) ),
    file('theBenchmark.p',fact_751_card__Diff__insert) ).

fof(fact_752_card__Diff__insert,axiom,
    ! [B,A_2,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),A))
       => ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),B))
         => hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),B))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))),one_one_nat) ) ) ),
    file('theBenchmark.p',fact_752_card__Diff__insert) ).

fof(fact_753_card__Diff__insert,axiom,
    ! [B,A_2,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A))
       => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),B))
         => hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))),one_one_nat) ) ) ),
    file('theBenchmark.p',fact_753_card__Diff__insert) ).

fof(fact_754_card__Diff__insert,axiom,
    ! [B,A_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A))
       => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),B))
         => hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))),one_one_nat) ) ) ),
    file('theBenchmark.p',fact_754_card__Diff__insert) ).

fof(fact_755_folding__one_Oinsert,axiom,
    ! [X_1,A,F,F_1] :
      ( is_fun_a_bool(A)
     => ( hBOOL(finite_folding_one_a(F,F_1))
       => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
         => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
           => ( A != bot_bot_fun_a_bool
             => hAPP_fun_a_bool_a(F_1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_a_a(hAPP_a_fun_a_a(F,X_1),hAPP_fun_a_bool_a(F_1,A)) ) ) ) ) ),
    file('theBenchmark.p',fact_755_folding__one_Oinsert) ).

fof(fact_756_folding__one_Oinsert,axiom,
    ! [X_1,A,F,F_1] :
      ( hBOOL(finite1626084323ne_int(F,F_1))
     => ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
       => ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
         => ( A != bot_bot_fun_int_bool
           => hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,A)) ) ) ) ),
    file('theBenchmark.p',fact_756_folding__one_Oinsert) ).

fof(fact_757_folding__one_Oinsert,axiom,
    ! [X_1,A,F,F_1] :
      ( hBOOL(finite988810631ne_nat(F,F_1))
     => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
       => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
         => ( A != bot_bot_fun_nat_bool
           => hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,A)) ) ) ) ),
    file('theBenchmark.p',fact_757_folding__one_Oinsert) ).

fof(fact_758_folding__one_Oinsert,axiom,
    ! [X_1,A,F,F_1] :
      ( is_fun_pname_bool(A)
     => ( hBOOL(finite1282449217_pname(F,F_1))
       => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
         => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
           => ( A != bot_bo844097828e_bool
             => hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(F_1,A)) ) ) ) ) ),
    file('theBenchmark.p',fact_758_folding__one_Oinsert) ).

fof(fact_759_folding__one_Oclosed,axiom,
    ! [A,F,F_1] :
      ( is_fun_a_bool(A)
     => ( hBOOL(finite_folding_one_a(F,F_1))
       => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
         => ( A != bot_bot_fun_a_bool
           => ( ! [X_2,Y_2] :
                  ( ( is_a(Y_2)
                    & is_a(X_2) )
                 => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_a_a(hAPP_a_fun_a_a(F,X_2),Y_2)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,Y_2),bot_bot_fun_a_bool)))) )
             => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_fun_a_bool_a(F_1,A)),A)) ) ) ) ) ),
    file('theBenchmark.p',fact_759_folding__one_Oclosed) ).

fof(fact_760_folding__one_Oclosed,axiom,
    ! [A,F,F_1] :
      ( hBOOL(finite1626084323ne_int(F,F_1))
     => ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
       => ( A != bot_bot_fun_int_bool
         => ( ! [X_2,Y_2] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(F,X_2),Y_2)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Y_2),bot_bot_fun_int_bool))))
           => hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_f1594865479ol_int(F_1,A)),A)) ) ) ) ),
    file('theBenchmark.p',fact_760_folding__one_Oclosed) ).

fof(fact_761_folding__one_Oclosed,axiom,
    ! [A,F,F_1] :
      ( hBOOL(finite988810631ne_nat(F,F_1))
     => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
       => ( A != bot_bot_fun_nat_bool
         => ( ! [X_2,Y_2] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_2),Y_2)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_2),bot_bot_fun_nat_bool))))
           => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f22106695ol_nat(F_1,A)),A)) ) ) ) ),
    file('theBenchmark.p',fact_761_folding__one_Oclosed) ).

fof(fact_762_folding__one_Oclosed,axiom,
    ! [A,F,F_1] :
      ( is_fun_pname_bool(A)
     => ( hBOOL(finite1282449217_pname(F,F_1))
       => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
         => ( A != bot_bo844097828e_bool
           => ( ! [X_2,Y_2] :
                  ( ( is_pname(Y_2)
                    & is_pname(X_2) )
                 => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),Y_2)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_2),bot_bo844097828e_bool)))) )
             => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(F_1,A)),A)) ) ) ) ) ),
    file('theBenchmark.p',fact_762_folding__one_Oclosed) ).

fof(fact_763_card_Oremove,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
     => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
       => hAPP_fun_a_bool_nat(finite_card_a,A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)))) ) ),
    file('theBenchmark.p',fact_763_card_Oremove) ).

fof(fact_764_card_Oremove,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
       => hAPP_f957591787ol_nat(finite_card_int,A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))) ) ),
    file('theBenchmark.p',fact_764_card_Oremove) ).

fof(fact_765_card_Oremove,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
       => hAPP_f22106695ol_nat(finite_card_nat,A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))) ) ),
    file('theBenchmark.p',fact_765_card_Oremove) ).

fof(fact_766_card_Oremove,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
       => hAPP_f921600141ol_nat(finite_card_pname,A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))) ) ),
    file('theBenchmark.p',fact_766_card_Oremove) ).

fof(fact_767_card_Oinsert__remove,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
     => hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)))) ),
    file('theBenchmark.p',fact_767_card_Oinsert__remove) ).

fof(fact_768_card_Oinsert__remove,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
     => hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))) ),
    file('theBenchmark.p',fact_768_card_Oinsert__remove) ).

fof(fact_769_card_Oinsert__remove,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
     => hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))) ),
    file('theBenchmark.p',fact_769_card_Oinsert__remove) ).

fof(fact_770_card_Oinsert__remove,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
     => hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))) ),
    file('theBenchmark.p',fact_770_card_Oinsert__remove) ).

fof(fact_771_folding__one__idem_Osubset__idem,axiom,
    ! [B,A,F,F_1] :
      ( hBOOL(finite1432773856em_int(F,F_1))
     => ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
       => ( B != bot_bot_fun_int_bool
         => ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A))
           => hAPP_int_int(hAPP_int_fun_int_int(F,hAPP_f1594865479ol_int(F_1,B)),hAPP_f1594865479ol_int(F_1,A)) = hAPP_f1594865479ol_int(F_1,A) ) ) ) ),
    file('theBenchmark.p',fact_771_folding__one__idem_Osubset__idem) ).

fof(fact_772_folding__one__idem_Osubset__idem,axiom,
    ! [B,A,F,F_1] :
      ( hBOOL(finite795500164em_nat(F,F_1))
     => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
       => ( B != bot_bot_fun_nat_bool
         => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))
           => hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,hAPP_f22106695ol_nat(F_1,B)),hAPP_f22106695ol_nat(F_1,A)) = hAPP_f22106695ol_nat(F_1,A) ) ) ) ),
    file('theBenchmark.p',fact_772_folding__one__idem_Osubset__idem) ).

fof(fact_773_folding__one__idem_Osubset__idem,axiom,
    ! [B,A,F,F_1] :
      ( is_fun_pname_bool(B)
     => ( hBOOL(finite89670078_pname(F,F_1))
       => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
         => ( B != bot_bo844097828e_bool
           => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
             => hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(F_1,B)),hAPP_f1297739591_pname(F_1,A)) = hAPP_f1297739591_pname(F_1,A) ) ) ) ) ),
    file('theBenchmark.p',fact_773_folding__one__idem_Osubset__idem) ).

fof(fact_774_folding__one__idem_Osubset__idem,axiom,
    ! [B,A,F,F_1] :
      ( is_fun_a_bool(B)
     => ( hBOOL(finite1819937229idem_a(F,F_1))
       => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
         => ( B != bot_bot_fun_a_bool
           => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A))
             => hAPP_a_a(hAPP_a_fun_a_a(F,hAPP_fun_a_bool_a(F_1,B)),hAPP_fun_a_bool_a(F_1,A)) = hAPP_fun_a_bool_a(F_1,A) ) ) ) ) ),
    file('theBenchmark.p',fact_774_folding__one__idem_Osubset__idem) ).

fof(fact_775_folding__one__idem_Oinsert__idem,axiom,
    ! [X_1,A,F,F_1] :
      ( is_fun_a_bool(A)
     => ( hBOOL(finite1819937229idem_a(F,F_1))
       => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
         => ( A != bot_bot_fun_a_bool
           => hAPP_fun_a_bool_a(F_1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_a_a(hAPP_a_fun_a_a(F,X_1),hAPP_fun_a_bool_a(F_1,A)) ) ) ) ),
    file('theBenchmark.p',fact_775_folding__one__idem_Oinsert__idem) ).

fof(fact_776_folding__one__idem_Oinsert__idem,axiom,
    ! [X_1,A,F,F_1] :
      ( hBOOL(finite1432773856em_int(F,F_1))
     => ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
       => ( A != bot_bot_fun_int_bool
         => hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,A)) ) ) ),
    file('theBenchmark.p',fact_776_folding__one__idem_Oinsert__idem) ).

fof(fact_777_folding__one__idem_Oinsert__idem,axiom,
    ! [X_1,A,F,F_1] :
      ( hBOOL(finite795500164em_nat(F,F_1))
     => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
       => ( A != bot_bot_fun_nat_bool
         => hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,A)) ) ) ),
    file('theBenchmark.p',fact_777_folding__one__idem_Oinsert__idem) ).

fof(fact_778_folding__one__idem_Oinsert__idem,axiom,
    ! [X_1,A,F,F_1] :
      ( is_fun_pname_bool(A)
     => ( hBOOL(finite89670078_pname(F,F_1))
       => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
         => ( A != bot_bo844097828e_bool
           => hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(F_1,A)) ) ) ) ),
    file('theBenchmark.p',fact_778_folding__one__idem_Oinsert__idem) ).

fof(fact_779_finite__ne__induct,axiom,
    ! [Pa,F_1] :
      ( is_fun_a_bool(F_1)
     => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1))
       => ( F_1 != bot_bot_fun_a_bool
         => ( ! [X_2] :
                ( is_a(X_2)
               => hBOOL(hAPP_fun_a_bool_bool(Pa,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_2),bot_bot_fun_a_bool))) )
           => ( ! [X_2,F_2] :
                  ( ( is_fun_a_bool(F_2)
                    & is_a(X_2) )
                 => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_2))
                   => ( F_2 != bot_bot_fun_a_bool
                     => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),F_2))
                       => ( hBOOL(hAPP_fun_a_bool_bool(Pa,F_2))
                         => hBOOL(hAPP_fun_a_bool_bool(Pa,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_2),F_2))) ) ) ) ) )
             => hBOOL(hAPP_fun_a_bool_bool(Pa,F_1)) ) ) ) ) ),
    file('theBenchmark.p',fact_779_finite__ne__induct) ).

fof(fact_780_finite__ne__induct,axiom,
    ! [Pa,F_1] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1))
     => ( F_1 != bot_bot_fun_int_bool
       => ( ! [X_2] : hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),bot_bot_fun_int_bool)))
         => ( ! [X_2,F_2] :
                ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_2))
               => ( F_2 != bot_bot_fun_int_bool
                 => ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),F_2))
                   => ( hBOOL(hAPP_f448129468l_bool(Pa,F_2))
                     => hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),F_2))) ) ) ) )
           => hBOOL(hAPP_f448129468l_bool(Pa,F_1)) ) ) ) ),
    file('theBenchmark.p',fact_780_finite__ne__induct) ).

fof(fact_781_finite__ne__induct,axiom,
    ! [Pa,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
     => ( F_1 != bot_bot_fun_nat_bool
       => ( ! [X_2] : hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),bot_bot_fun_nat_bool)))
         => ( ! [X_2,F_2] :
                ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2))
               => ( F_2 != bot_bot_fun_nat_bool
                 => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),F_2))
                   => ( hBOOL(hAPP_f54304608l_bool(Pa,F_2))
                     => hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),F_2))) ) ) ) )
           => hBOOL(hAPP_f54304608l_bool(Pa,F_1)) ) ) ) ),
    file('theBenchmark.p',fact_781_finite__ne__induct) ).

fof(fact_782_finite__ne__induct,axiom,
    ! [Pa,F_1] :
      ( is_fun_pname_bool(F_1)
     => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
       => ( F_1 != bot_bo844097828e_bool
         => ( ! [X_2] :
                ( is_pname(X_2)
               => hBOOL(hAPP_f1664156314l_bool(Pa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),bot_bo844097828e_bool))) )
           => ( ! [X_2,F_2] :
                  ( ( is_fun_pname_bool(F_2)
                    & is_pname(X_2) )
                 => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_2))
                   => ( F_2 != bot_bo844097828e_bool
                     => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),F_2))
                       => ( hBOOL(hAPP_f1664156314l_bool(Pa,F_2))
                         => hBOOL(hAPP_f1664156314l_bool(Pa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),F_2))) ) ) ) ) )
             => hBOOL(hAPP_f1664156314l_bool(Pa,F_1)) ) ) ) ) ),
    file('theBenchmark.p',fact_782_finite__ne__induct) ).

fof(fact_783_the__elem__def,axiom,
    ! [X_3] : hAPP_fun_a_bool_a(the_elem_a,X_3) = hAPP_fun_a_bool_a(the_a,cOMBB_1273333599bool_a(hAPP_f1631501043l_bool(fequal_fun_a_bool,X_3),hAPP_f1038053735a_bool(cOMBC_394484100a_bool(insert_a),bot_bot_fun_a_bool))),
    file('theBenchmark.p',fact_783_the__elem__def) ).

fof(fact_784_the__elem__def,axiom,
    ! [X_3] : hAPP_f22106695ol_nat(the_elem_nat,X_3) = hAPP_f22106695ol_nat(the_nat,cOMBB_955900739ol_nat(hAPP_f103356543l_bool(fequal_fun_nat_bool,X_3),hAPP_f1570313510t_bool(cOMBC_178881787t_bool(insert_nat),bot_bot_fun_nat_bool))),
    file('theBenchmark.p',fact_784_the__elem__def) ).

fof(fact_785_the__elem__def,axiom,
    ! [X_3] : hAPP_f1594865479ol_int(the_elem_int,X_3) = hAPP_f1594865479ol_int(the_int,cOMBB_1418110531ol_int(hAPP_f284875647l_bool(fequal_fun_int_bool,X_3),hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(insert_int),bot_bot_fun_int_bool))),
    file('theBenchmark.p',fact_785_the__elem__def) ).

fof(fact_786_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [A_13,B_14,C_10] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_13),B_14)),C_10) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_13),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_14),C_10)),
    file('theBenchmark.p',fact_786_ab__semigroup__add__class_Oadd__ac_I1_J) ).

fof(fact_787_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [A_13,B_14,C_10] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),B_14)),C_10) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_14),C_10)),
    file('theBenchmark.p',fact_787_ab__semigroup__add__class_Oadd__ac_I1_J) ).

fof(fact_788_add__left__cancel,axiom,
    ! [A_2,B_3,C_6] :
      ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),B_3) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),C_6)
    <=> B_3 = C_6 ),
    file('theBenchmark.p',fact_788_add__left__cancel) ).

fof(fact_789_add__left__cancel,axiom,
    ! [A_2,B_3,C_6] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_2),B_3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_2),C_6)
    <=> B_3 = C_6 ),
    file('theBenchmark.p',fact_789_add__left__cancel) ).

fof(fact_790_add__right__cancel,axiom,
    ! [B_3,A_2,C_6] :
      ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_3),A_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_6),A_2)
    <=> B_3 = C_6 ),
    file('theBenchmark.p',fact_790_add__right__cancel) ).

fof(fact_791_add__right__cancel,axiom,
    ! [B_3,A_2,C_6] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),A_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_6),A_2)
    <=> B_3 = C_6 ),
    file('theBenchmark.p',fact_791_add__right__cancel) ).

fof(fact_792_add__left__imp__eq,axiom,
    ! [A_12,B_13,C_9] :
      ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_12),B_13) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_12),C_9)
     => B_13 = C_9 ),
    file('theBenchmark.p',fact_792_add__left__imp__eq) ).

fof(fact_793_add__left__imp__eq,axiom,
    ! [A_12,B_13,C_9] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),B_13) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),C_9)
     => B_13 = C_9 ),
    file('theBenchmark.p',fact_793_add__left__imp__eq) ).

fof(fact_794_add__imp__eq,axiom,
    ! [A_11,B_12,C_8] :
      ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_11),B_12) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_11),C_8)
     => B_12 = C_8 ),
    file('theBenchmark.p',fact_794_add__imp__eq) ).

fof(fact_795_add__imp__eq,axiom,
    ! [A_11,B_12,C_8] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_11),B_12) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_11),C_8)
     => B_12 = C_8 ),
    file('theBenchmark.p',fact_795_add__imp__eq) ).

fof(fact_796_add__right__imp__eq,axiom,
    ! [B_11,A_10,C_7] :
      ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_11),A_10) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_7),A_10)
     => B_11 = C_7 ),
    file('theBenchmark.p',fact_796_add__right__imp__eq) ).

fof(fact_797_add__right__imp__eq,axiom,
    ! [B_11,A_10,C_7] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_11),A_10) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_7),A_10)
     => B_11 = C_7 ),
    file('theBenchmark.p',fact_797_add__right__imp__eq) ).

fof(fact_798_nat__add__commute,axiom,
    ! [M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M_1),
    file('theBenchmark.p',fact_798_nat__add__commute) ).

fof(fact_799_nat__add__left__commute,axiom,
    ! [X,Y,Z] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),Z)),
    file('theBenchmark.p',fact_799_nat__add__left__commute) ).

fof(fact_800_nat__add__assoc,axiom,
    ! [M_1,N,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),K_1)),
    file('theBenchmark.p',fact_800_nat__add__assoc) ).

fof(fact_801_nat__add__left__cancel,axiom,
    ! [K,M,Na] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)
    <=> M = Na ),
    file('theBenchmark.p',fact_801_nat__add__left__cancel) ).

fof(fact_802_nat__add__right__cancel,axiom,
    ! [M,K,Na] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Na),K)
    <=> M = Na ),
    file('theBenchmark.p',fact_802_nat__add__right__cancel) ).

fof(fact_803_add__le__cancel__right,axiom,
    ! [A_2,C_6,B_3] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),C_6)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_3),C_6)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),B_3)) ),
    file('theBenchmark.p',fact_803_add__le__cancel__right) ).

fof(fact_804_add__le__cancel__right,axiom,
    ! [A_2,C_6,B_3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_2),C_6)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),C_6)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_2),B_3)) ),
    file('theBenchmark.p',fact_804_add__le__cancel__right) ).

fof(fact_805_add__le__cancel__left,axiom,
    ! [C_6,A_2,B_3] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_6),A_2)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_6),B_3)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),B_3)) ),
    file('theBenchmark.p',fact_805_add__le__cancel__left) ).

fof(fact_806_add__le__cancel__left,axiom,
    ! [C_6,A_2,B_3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_6),A_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_6),B_3)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_2),B_3)) ),
    file('theBenchmark.p',fact_806_add__le__cancel__left) ).

fof(fact_807_add__right__mono,axiom,
    ! [C_5,A_9,B_10] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_9),B_10))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_9),C_5)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_10),C_5))) ),
    file('theBenchmark.p',fact_807_add__right__mono) ).

fof(fact_808_add__right__mono,axiom,
    ! [C_5,A_9,B_10] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_9),B_10))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_9),C_5)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_10),C_5))) ),
    file('theBenchmark.p',fact_808_add__right__mono) ).

fof(fact_809_add__left__mono,axiom,
    ! [C_4,A_8,B_9] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_8),B_9))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_4),A_8)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_4),B_9))) ),
    file('theBenchmark.p',fact_809_add__left__mono) ).

fof(fact_810_add__left__mono,axiom,
    ! [C_4,A_8,B_9] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_8),B_9))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_4),A_8)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_4),B_9))) ),
    file('theBenchmark.p',fact_810_add__left__mono) ).

fof(fact_811_add__mono,axiom,
    ! [C_3,D_3,A_7,B_8] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_7),B_8))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_3),D_3))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_7),C_3)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_8),D_3))) ) ),
    file('theBenchmark.p',fact_811_add__mono) ).

fof(fact_812_add__mono,axiom,
    ! [C_3,D_3,A_7,B_8] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_7),B_8))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_3),D_3))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_7),C_3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_8),D_3))) ) ),
    file('theBenchmark.p',fact_812_add__mono) ).

fof(fact_813_add__le__imp__le__right,axiom,
    ! [A_6,C_2,B_7] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_6),C_2)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_7),C_2)))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_6),B_7)) ),
    file('theBenchmark.p',fact_813_add__le__imp__le__right) ).

fof(fact_814_add__le__imp__le__right,axiom,
    ! [A_6,C_2,B_7] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_6),C_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_7),C_2)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_6),B_7)) ),
    file('theBenchmark.p',fact_814_add__le__imp__le__right) ).

fof(fact_815_add__le__imp__le__left,axiom,
    ! [C_1,A_5,B_6] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_1),A_5)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_1),B_6)))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_5),B_6)) ),
    file('theBenchmark.p',fact_815_add__le__imp__le__left) ).

fof(fact_816_add__le__imp__le__left,axiom,
    ! [C_1,A_5,B_6] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_1),A_5)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_1),B_6)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_5),B_6)) ),
    file('theBenchmark.p',fact_816_add__le__imp__le__left) ).

fof(fact_817_diff__add__cancel,axiom,
    ! [A_4,B_5] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_4),B_5)),B_5) = A_4,
    file('theBenchmark.p',fact_817_diff__add__cancel) ).

fof(fact_818_add__diff__cancel,axiom,
    ! [A_3,B_4] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_3),B_4)),B_4) = A_3,
    file('theBenchmark.p',fact_818_add__diff__cancel) ).

fof(fact_819_add__Suc__right,axiom,
    ! [M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N)),
    file('theBenchmark.p',fact_819_add__Suc__right) ).

fof(fact_820_add__Suc,axiom,
    ! [M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_1)),N) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N)),
    file('theBenchmark.p',fact_820_add__Suc) ).

fof(fact_821_add__Suc__shift,axiom,
    ! [M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_1)),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(suc,N)),
    file('theBenchmark.p',fact_821_add__Suc__shift) ).

fof(fact_822_le__add2,axiom,
    ! [N,M_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N))),
    file('theBenchmark.p',fact_822_le__add2) ).

fof(fact_823_le__add1,axiom,
    ! [N,M_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M_1))),
    file('theBenchmark.p',fact_823_le__add1) ).

fof(fact_824_le__iff__add,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
    <=> ? [K_2] : Na = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K_2) ),
    file('theBenchmark.p',fact_824_le__iff__add) ).

fof(fact_825_nat__add__left__cancel__le,axiom,
    ! [K,M,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) ),
    file('theBenchmark.p',fact_825_nat__add__left__cancel__le) ).

fof(fact_826_trans__le__add1,axiom,
    ! [M_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,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),M_1))) ),
    file('theBenchmark.p',fact_826_trans__le__add1) ).

fof(fact_827_trans__le__add2,axiom,
    ! [M_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,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),J))) ),
    file('theBenchmark.p',fact_827_trans__le__add2) ).

fof(fact_828_add__le__mono1,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,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K_1))) ),
    file('theBenchmark.p',fact_828_add__le__mono1) ).

fof(fact_829_add__le__mono,axiom,
    ! [K_1,L_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,K_1),L_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),L_1))) ) ),
    file('theBenchmark.p',fact_829_add__le__mono) ).

fof(fact_830_add__leD2,axiom,
    ! [M_1,K_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N)) ),
    file('theBenchmark.p',fact_830_add__leD2) ).

fof(fact_831_add__leD1,axiom,
    ! [M_1,K_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) ),
    file('theBenchmark.p',fact_831_add__leD1) ).

fof(fact_832_add__leE,axiom,
    ! [M_1,K_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),N))
     => ~ ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N))
         => ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N)) ) ),
    file('theBenchmark.p',fact_832_add__leE) ).

fof(fact_833_diff__add__inverse2,axiom,
    ! [M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N)),N) = M_1,
    file('theBenchmark.p',fact_833_diff__add__inverse2) ).

fof(fact_834_diff__add__inverse,axiom,
    ! [N,M_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M_1)),N) = M_1,
    file('theBenchmark.p',fact_834_diff__add__inverse) ).

fof(fact_835_diff__diff__left,axiom,
    ! [I_1,J,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),J)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K_1)),
    file('theBenchmark.p',fact_835_diff__diff__left) ).

fof(fact_836_diff__cancel,axiom,
    ! [K_1,M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N),
    file('theBenchmark.p',fact_836_diff__cancel) ).

fof(fact_837_diff__cancel2,axiom,
    ! [M_1,K_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N),
    file('theBenchmark.p',fact_837_diff__cancel2) ).

fof(fact_838_diff__diff__right,axiom,
    ! [I_1,K_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J))
     => hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),J) ),
    file('theBenchmark.p',fact_838_diff__diff__right) ).

fof(fact_839_le__diff__conv,axiom,
    ! [J_1,K,I_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K)),I_2))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K))) ),
    file('theBenchmark.p',fact_839_le__diff__conv) ).

fof(fact_840_le__add__diff,axiom,
    ! [M_1,K_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M_1)),K_1))) ),
    file('theBenchmark.p',fact_840_le__add__diff) ).

fof(fact_841_le__add__diff__inverse,axiom,
    ! [N,M_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_1))
     => hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)) = M_1 ),
    file('theBenchmark.p',fact_841_le__add__diff__inverse) ).

fof(fact_842_add__diff__assoc,axiom,
    ! [I_1,K_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J))
     => hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),K_1) ),
    file('theBenchmark.p',fact_842_add__diff__assoc) ).

fof(fact_843_le__diff__conv2,axiom,
    ! [I_2,K,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K)),J_1)) ) ),
    file('theBenchmark.p',fact_843_le__diff__conv2) ).

fof(fact_844_le__add__diff__inverse2,axiom,
    ! [N,M_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_1))
     => hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)),N) = M_1 ),
    file('theBenchmark.p',fact_844_le__add__diff__inverse2) ).

fof(fact_845_le__imp__diff__is__add,axiom,
    ! [K,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
     => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),I_2) = K
      <=> J_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),I_2) ) ),
    file('theBenchmark.p',fact_845_le__imp__diff__is__add) ).

fof(fact_846_diff__add__assoc,axiom,
    ! [I_1,K_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J))
     => hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)) ),
    file('theBenchmark.p',fact_846_diff__add__assoc) ).

fof(fact_847_add__diff__assoc2,axiom,
    ! [I_1,K_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J))
     => hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)),I_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),I_1)),K_1) ),
    file('theBenchmark.p',fact_847_add__diff__assoc2) ).

fof(fact_848_diff__add__assoc2,axiom,
    ! [I_1,K_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J))
     => hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),I_1)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)),I_1) ),
    file('theBenchmark.p',fact_848_diff__add__assoc2) ).

fof(fact_849_Suc__eq__plus1__left,axiom,
    ! [N] : hAPP_nat_nat(suc,N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N),
    file('theBenchmark.p',fact_849_Suc__eq__plus1__left) ).

fof(fact_850_Suc__eq__plus1,axiom,
    ! [N] : hAPP_nat_nat(suc,N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat),
    file('theBenchmark.p',fact_850_Suc__eq__plus1) ).

fof(fact_851_diff__Suc__diff__eq1,axiom,
    ! [M_1,K_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J))
     => hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),hAPP_nat_nat(suc,J)) ),
    file('theBenchmark.p',fact_851_diff__Suc__diff__eq1) ).

fof(fact_852_diff__Suc__diff__eq2,axiom,
    ! [M_1,K_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J))
     => hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1))),M_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,J)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),M_1)) ),
    file('theBenchmark.p',fact_852_diff__Suc__diff__eq2) ).

fof(fact_853_termination__basic__simps_I4_J,axiom,
    ! [Y,X,Z] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Z))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ),
    file('theBenchmark.p',fact_853_termination__basic__simps_I4_J) ).

fof(fact_854_termination__basic__simps_I3_J,axiom,
    ! [Z,X,Y] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ),
    file('theBenchmark.p',fact_854_termination__basic__simps_I3_J) ).

fof(fact_855_lessI,axiom,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,N))),
    file('theBenchmark.p',fact_855_lessI) ).

fof(fact_856_Suc__mono,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N))) ),
    file('theBenchmark.p',fact_856_Suc__mono) ).

fof(fact_857_finite__Collect__less__nat,axiom,
    ! [K] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),K)))),
    file('theBenchmark.p',fact_857_finite__Collect__less__nat) ).

fof(fact_858_less__not__refl,axiom,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N)),
    file('theBenchmark.p',fact_858_less__not__refl) ).

fof(fact_859_nat__neq__iff,axiom,
    ! [M,Na] :
      ( M != Na
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) ) ),
    file('theBenchmark.p',fact_859_nat__neq__iff) ).

fof(fact_860_linorder__neqE__nat,axiom,
    ! [X,Y] :
      ( X != Y
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y),X)) ) ),
    file('theBenchmark.p',fact_860_linorder__neqE__nat) ).

fof(fact_861_less__irrefl__nat,axiom,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N)),
    file('theBenchmark.p',fact_861_less__irrefl__nat) ).

fof(fact_862_less__not__refl2,axiom,
    ! [N,M_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M_1))
     => M_1 != N ),
    file('theBenchmark.p',fact_862_less__not__refl2) ).

fof(fact_863_less__not__refl3,axiom,
    ! [S,T] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T))
     => S != T ),
    file('theBenchmark.p',fact_863_less__not__refl3) ).

fof(fact_864_nat__less__cases,axiom,
    ! [Pa,M,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M)) )
     => ( ( M = Na
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M)) )
       => ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M))
           => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M)) )
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M)) ) ) ),
    file('theBenchmark.p',fact_864_nat__less__cases) ).

fof(fact_865_not__less__eq,axiom,
    ! [M,Na] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M))) ),
    file('theBenchmark.p',fact_865_not__less__eq) ).

fof(fact_866_less__Suc__eq,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,Na)))
    <=> ( M = Na
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) ) ),
    file('theBenchmark.p',fact_866_less__Suc__eq) ).

fof(fact_867_Suc__less__eq,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) ),
    file('theBenchmark.p',fact_867_Suc__less__eq) ).

fof(fact_868_not__less__less__Suc__eq,axiom,
    ! [Na,M] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M)))
      <=> Na = M ) ),
    file('theBenchmark.p',fact_868_not__less__less__Suc__eq) ).

fof(fact_869_less__antisym,axiom,
    ! [N,M_1] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,M_1)))
       => M_1 = N ) ),
    file('theBenchmark.p',fact_869_less__antisym) ).

fof(fact_870_less__SucI,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N))) ),
    file('theBenchmark.p',fact_870_less__SucI) ).

fof(fact_871_Suc__lessI,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N))
     => ( hAPP_nat_nat(suc,M_1) != N
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),N)) ) ),
    file('theBenchmark.p',fact_871_Suc__lessI) ).

fof(fact_872_less__trans__Suc,axiom,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_1)),K_1)) ) ),
    file('theBenchmark.p',fact_872_less__trans__Suc) ).

fof(fact_873_less__SucE,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N)))
     => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N))
       => M_1 = N ) ),
    file('theBenchmark.p',fact_873_less__SucE) ).

fof(fact_874_Suc__lessD,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) ),
    file('theBenchmark.p',fact_874_Suc__lessD) ).

fof(fact_875_Suc__less__SucD,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N)))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) ),
    file('theBenchmark.p',fact_875_Suc__less__SucD) ).

fof(fact_876_not__add__less1,axiom,
    ! [I_1,J] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),I_1)),
    file('theBenchmark.p',fact_876_not__add__less1) ).

fof(fact_877_not__add__less2,axiom,
    ! [J,I_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),I_1)),I_1)),
    file('theBenchmark.p',fact_877_not__add__less2) ).

fof(fact_878_nat__add__left__cancel__less,axiom,
    ! [K,M,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) ),
    file('theBenchmark.p',fact_878_nat__add__left__cancel__less) ).

fof(fact_879_trans__less__add1,axiom,
    ! [M_1,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),M_1))) ),
    file('theBenchmark.p',fact_879_trans__less__add1) ).

fof(fact_880_trans__less__add2,axiom,
    ! [M_1,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),J))) ),
    file('theBenchmark.p',fact_880_trans__less__add2) ).

fof(fact_881_add__less__mono1,axiom,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K_1))) ),
    file('theBenchmark.p',fact_881_add__less__mono1) ).

fof(fact_882_add__less__mono,axiom,
    ! [K_1,L_1,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),L_1))) ) ),
    file('theBenchmark.p',fact_882_add__less__mono) ).

fof(fact_883_less__add__eq__less,axiom,
    ! [M_1,N,K_1,L_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L_1))
     => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),L_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N)
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) ) ),
    file('theBenchmark.p',fact_883_less__add__eq__less) ).

fof(fact_884_add__lessD1,axiom,
    ! [I_1,J,K_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),K_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),K_1)) ),
    file('theBenchmark.p',fact_884_add__lessD1) ).

fof(fact_885_termination__basic__simps_I1_J,axiom,
    ! [Z,X,Y] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ),
    file('theBenchmark.p',fact_885_termination__basic__simps_I1_J) ).

fof(fact_886_termination__basic__simps_I2_J,axiom,
    ! [Y,X,Z] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Z))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z))) ),
    file('theBenchmark.p',fact_886_termination__basic__simps_I2_J) ).

fof(fact_887_nat__less__le,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
    <=> ( M != Na
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) ) ),
    file('theBenchmark.p',fact_887_nat__less__le) ).

fof(fact_888_le__eq__less__or__eq,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
    <=> ( M = Na
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) ) ),
    file('theBenchmark.p',fact_888_le__eq__less__or__eq) ).

fof(fact_889_less__imp__le__nat,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) ),
    file('theBenchmark.p',fact_889_less__imp__le__nat) ).

fof(fact_890_le__neq__implies__less,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N))
     => ( M_1 != N
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) ) ),
    file('theBenchmark.p',fact_890_le__neq__implies__less) ).

fof(fact_891_less__or__eq__imp__le,axiom,
    ! [M_1,N] :
      ( ( M_1 = N
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) ),
    file('theBenchmark.p',fact_891_less__or__eq__imp__le) ).

fof(fact_892_termination__basic__simps_I5_J,axiom,
    ! [X,Y] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y)) ),
    file('theBenchmark.p',fact_892_termination__basic__simps_I5_J) ).

fof(fact_893_less__imp__diff__less,axiom,
    ! [N,J,K_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K_1))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),N)),K_1)) ),
    file('theBenchmark.p',fact_893_less__imp__diff__less) ).

fof(fact_894_diff__less__mono2,axiom,
    ! [L_1,M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),L_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_1),N)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_1),M_1))) ) ),
    file('theBenchmark.p',fact_894_diff__less__mono2) ).

fof(fact_895_finite__nat__set__iff__bounded,axiom,
    ! [N_2] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2))
    <=> ? [M_2] :
        ! [X_2] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),N_2))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),M_2)) ) ),
    file('theBenchmark.p',fact_895_finite__nat__set__iff__bounded) ).

fof(fact_896_card__Collect__less__nat,axiom,
    ! [Na] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),Na))) = Na,
    file('theBenchmark.p',fact_896_card__Collect__less__nat) ).

fof(fact_897_finite__M__bounded__by__nat,axiom,
    ! [Pa,I_2] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,Pa),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),I_2))))),
    file('theBenchmark.p',fact_897_finite__M__bounded__by__nat) ).

fof(fact_898_less__add__Suc1,axiom,
    ! [I_1,M_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),M_1)))),
    file('theBenchmark.p',fact_898_less__add__Suc1) ).

fof(fact_899_less__add__Suc2,axiom,
    ! [I_1,M_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),I_1)))),
    file('theBenchmark.p',fact_899_less__add__Suc2) ).

fof(fact_900_less__iff__Suc__add,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
    <=> ? [K_2] : Na = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K_2)) ),
    file('theBenchmark.p',fact_900_less__iff__Suc__add) ).

fof(fact_901_less__eq__Suc__le,axiom,
    ! [Na,M] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M)) ),
    file('theBenchmark.p',fact_901_less__eq__Suc__le) ).

fof(fact_902_less__Suc__eq__le,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) ),
    file('theBenchmark.p',fact_902_less__Suc__eq__le) ).

fof(fact_903_Suc__le__eq,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),Na))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) ),
    file('theBenchmark.p',fact_903_Suc__le__eq) ).

fof(fact_904_le__imp__less__Suc,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N))) ),
    file('theBenchmark.p',fact_904_le__imp__less__Suc) ).

fof(fact_905_Suc__leI,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),N)) ),
    file('theBenchmark.p',fact_905_Suc__leI) ).

fof(fact_906_le__less__Suc__eq,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M)))
      <=> Na = M ) ),
    file('theBenchmark.p',fact_906_le__less__Suc__eq) ).

fof(fact_907_Suc__le__lessD,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) ),
    file('theBenchmark.p',fact_907_Suc__le__lessD) ).

fof(fact_908_diff__less__Suc,axiom,
    ! [M_1,N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)),hAPP_nat_nat(suc,M_1))),
    file('theBenchmark.p',fact_908_diff__less__Suc) ).

fof(fact_909_less__diff__conv,axiom,
    ! [I_2,J_1,K] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K)),J_1)) ),
    file('theBenchmark.p',fact_909_less__diff__conv) ).

fof(fact_910_add__diff__inverse,axiom,
    ! [M_1,N] :
      ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N))
     => hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)) = M_1 ),
    file('theBenchmark.p',fact_910_add__diff__inverse) ).

fof(fact_911_diff__less__mono,axiom,
    ! [C,A_1,B_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_1),B_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C),A_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,A_1),C)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,B_2),C))) ) ),
    file('theBenchmark.p',fact_911_diff__less__mono) ).

fof(fact_912_less__diff__iff,axiom,
    ! [Na,K,M] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),Na))
       => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,Na),K)))
        <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) ) ) ),
    file('theBenchmark.p',fact_912_less__diff__iff) ).

fof(fact_913_less__eq__Suc__le__raw,axiom,
    ! [X_2] : hAPP_n1699378549t_bool(ord_less_nat,X_2) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X_2)),
    file('theBenchmark.p',fact_913_less__eq__Suc__le__raw) ).

fof(fact_914_mono__nat__linear__lb,axiom,
    ! [M,K,F] :
      ( ! [M_2,N_1] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,M_2)),hAPP_nat_nat(F,N_1))) )
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(F,M)),K)),hAPP_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K)))) ),
    file('theBenchmark.p',fact_914_mono__nat__linear__lb) ).

fof(fact_915_inc__induct,axiom,
    ! [Pa,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
     => ( hBOOL(hAPP_nat_bool(Pa,J_1))
       => ( ! [I] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_1))
             => ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,I)))
               => hBOOL(hAPP_nat_bool(Pa,I)) ) )
         => hBOOL(hAPP_nat_bool(Pa,I_2)) ) ) ),
    file('theBenchmark.p',fact_915_inc__induct) ).

fof(fact_916_less__imp__Suc__add,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N))
     => ? [K_2] : N = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_2)) ),
    file('theBenchmark.p',fact_916_less__imp__Suc__add) ).

fof(fact_917_bounded__nat__set__is__finite,axiom,
    ! [Na,N_2] :
      ( ! [X_2] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),N_2))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Na)) )
     => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2)) ),
    file('theBenchmark.p',fact_917_bounded__nat__set__is__finite) ).

fof(fact_918_less__mono__imp__le__mono,axiom,
    ! [I_2,J_1,F] :
      ( ! [I,J_2] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2))
         => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,I)),hAPP_nat_nat(F,J_2))) )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I_2)),hAPP_nat_nat(F,J_1))) ) ),
    file('theBenchmark.p',fact_918_less__mono__imp__le__mono) ).

fof(fact_919_lessE,axiom,
    ! [I_1,K_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),K_1))
     => ( K_1 != hAPP_nat_nat(suc,I_1)
       => ~ ! [J_2] :
              ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_2))
             => K_1 != hAPP_nat_nat(suc,J_2) ) ) ),
    file('theBenchmark.p',fact_919_lessE) ).

fof(fact_920_Suc__lessE,axiom,
    ! [I_1,K_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_1)),K_1))
     => ~ ! [J_2] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_2))
           => K_1 != hAPP_nat_nat(suc,J_2) ) ),
    file('theBenchmark.p',fact_920_Suc__lessE) ).

fof(fact_921_less__zeroE,axiom,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)),
    file('theBenchmark.p',fact_921_less__zeroE) ).

fof(fact_922_le0,axiom,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N)),
    file('theBenchmark.p',fact_922_le0) ).

fof(fact_923_zero__less__Suc,axiom,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N))),
    file('theBenchmark.p',fact_923_zero__less__Suc) ).

fof(fact_924_le__0__eq,axiom,
    ! [Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),zero_zero_nat))
    <=> Na = zero_zero_nat ),
    file('theBenchmark.p',fact_924_le__0__eq) ).

fof(fact_925_less__eq__nat_Osimps_I1_J,axiom,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N)),
    file('theBenchmark.p',fact_925_less__eq__nat_Osimps_I1_J) ).

fof(fact_926_diffs0__imp__equal,axiom,
    ! [M_1,N] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N) = zero_zero_nat
     => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),M_1) = zero_zero_nat
       => M_1 = N ) ),
    file('theBenchmark.p',fact_926_diffs0__imp__equal) ).

fof(fact_927_diff__self__eq__0,axiom,
    ! [M_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),M_1) = zero_zero_nat,
    file('theBenchmark.p',fact_927_diff__self__eq__0) ).

fof(fact_928_minus__nat_Odiff__0,axiom,
    ! [M_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),zero_zero_nat) = M_1,
    file('theBenchmark.p',fact_928_minus__nat_Odiff__0) ).

fof(fact_929_diff__0__eq__0,axiom,
    ! [N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),N) = zero_zero_nat,
    file('theBenchmark.p',fact_929_diff__0__eq__0) ).

fof(fact_930_bot__nat__def,axiom,
    bot_bot_nat = zero_zero_nat,
    file('theBenchmark.p',fact_930_bot__nat__def) ).

fof(fact_931_add__eq__self__zero,axiom,
    ! [M_1,N] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N) = M_1
     => N = zero_zero_nat ),
    file('theBenchmark.p',fact_931_add__eq__self__zero) ).

fof(fact_932_add__is__0,axiom,
    ! [M,Na] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),Na) = zero_zero_nat
    <=> ( Na = zero_zero_nat
        & M = zero_zero_nat ) ),
    file('theBenchmark.p',fact_932_add__is__0) ).

fof(fact_933_Nat_Oadd__0__right,axiom,
    ! [M_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),zero_zero_nat) = M_1,
    file('theBenchmark.p',fact_933_Nat_Oadd__0__right) ).

fof(fact_934_plus__nat_Oadd__0,axiom,
    ! [N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),N) = N,
    file('theBenchmark.p',fact_934_plus__nat_Oadd__0) ).

fof(fact_935_gr0I,axiom,
    ! [N] :
      ( N != zero_zero_nat
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) ),
    file('theBenchmark.p',fact_935_gr0I) ).

fof(fact_936_gr__implies__not0,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N))
     => N != zero_zero_nat ),
    file('theBenchmark.p',fact_936_gr__implies__not0) ).

fof(fact_937_less__nat__zero__code,axiom,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)),
    file('theBenchmark.p',fact_937_less__nat__zero__code) ).

fof(fact_938_neq0__conv,axiom,
    ! [Na] :
      ( Na != zero_zero_nat
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)) ),
    file('theBenchmark.p',fact_938_neq0__conv) ).

fof(fact_939_not__less0,axiom,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)),
    file('theBenchmark.p',fact_939_not__less0) ).

fof(fact_940_Suc__neq__Zero,axiom,
    ! [M_1] : hAPP_nat_nat(suc,M_1) != zero_zero_nat,
    file('theBenchmark.p',fact_940_Suc__neq__Zero) ).

fof(fact_941_Zero__neq__Suc,axiom,
    ! [M_1] : zero_zero_nat != hAPP_nat_nat(suc,M_1),
    file('theBenchmark.p',fact_941_Zero__neq__Suc) ).

fof(fact_942_nat_Osimps_I3_J,axiom,
    ! [Nat_2] : hAPP_nat_nat(suc,Nat_2) != zero_zero_nat,
    file('theBenchmark.p',fact_942_nat_Osimps_I3_J) ).

fof(fact_943_Suc__not__Zero,axiom,
    ! [M_1] : hAPP_nat_nat(suc,M_1) != zero_zero_nat,
    file('theBenchmark.p',fact_943_Suc__not__Zero) ).

fof(fact_944_nat_Osimps_I2_J,axiom,
    ! [Nat_1] : zero_zero_nat != hAPP_nat_nat(suc,Nat_1),
    file('theBenchmark.p',fact_944_nat_Osimps_I2_J) ).

fof(fact_945_Zero__not__Suc,axiom,
    ! [M_1] : zero_zero_nat != hAPP_nat_nat(suc,M_1),
    file('theBenchmark.p',fact_945_Zero__not__Suc) ).

fof(fact_946_gr0__conv__Suc,axiom,
    ! [Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na))
    <=> ? [M_2] : Na = hAPP_nat_nat(suc,M_2) ),
    file('theBenchmark.p',fact_946_gr0__conv__Suc) ).

fof(fact_947_less__Suc0,axiom,
    ! [Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,zero_zero_nat)))
    <=> Na = zero_zero_nat ),
    file('theBenchmark.p',fact_947_less__Suc0) ).

fof(fact_948_less__Suc__eq__0__disj,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,Na)))
    <=> ( ? [J_2] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),Na))
            & M = hAPP_nat_nat(suc,J_2) )
        | M = zero_zero_nat ) ),
    file('theBenchmark.p',fact_948_less__Suc__eq__0__disj) ).

fof(fact_949_one__is__add,axiom,
    ! [M,Na] :
      ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),Na)
    <=> ( ( Na = hAPP_nat_nat(suc,zero_zero_nat)
          & M = zero_zero_nat )
        | ( Na = zero_zero_nat
          & M = hAPP_nat_nat(suc,zero_zero_nat) ) ) ),
    file('theBenchmark.p',fact_949_one__is__add) ).

fof(fact_950_add__is__1,axiom,
    ! [M,Na] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),Na) = hAPP_nat_nat(suc,zero_zero_nat)
    <=> ( ( Na = hAPP_nat_nat(suc,zero_zero_nat)
          & M = zero_zero_nat )
        | ( Na = zero_zero_nat
          & M = hAPP_nat_nat(suc,zero_zero_nat) ) ) ),
    file('theBenchmark.p',fact_950_add__is__1) ).

fof(fact_951_add__gr__0,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),Na)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M)) ) ),
    file('theBenchmark.p',fact_951_add__gr__0) ).

fof(fact_952_zero__less__diff,axiom,
    ! [Na,M] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,Na),M)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) ),
    file('theBenchmark.p',fact_952_zero__less__diff) ).

fof(fact_953_diff__less,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)),M_1)) ) ),
    file('theBenchmark.p',fact_953_diff__less) ).

fof(fact_954_diff__add__0,axiom,
    ! [N,M_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M_1)) = zero_zero_nat,
    file('theBenchmark.p',fact_954_diff__add__0) ).

fof(fact_955_diff__is__0__eq,axiom,
    ! [M,Na] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),Na) = zero_zero_nat
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) ),
    file('theBenchmark.p',fact_955_diff__is__0__eq) ).

fof(fact_956_diff__is__0__eq_H,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N))
     => hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N) = zero_zero_nat ),
    file('theBenchmark.p',fact_956_diff__is__0__eq_H) ).

fof(fact_957_One__nat__def,axiom,
    one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
    file('theBenchmark.p',fact_957_One__nat__def) ).

fof(fact_958_diff__Suc,axiom,
    ! [M,Na] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),hAPP_nat_nat(suc,Na)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),Na)),
    file('theBenchmark.p',fact_958_diff__Suc) ).

fof(fact_959_Suc__pred,axiom,
    ! [N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
     => hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(suc,zero_zero_nat))) = N ),
    file('theBenchmark.p',fact_959_Suc__pred) ).

fof(fact_960_diff__Suc__less,axiom,
    ! [I_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
     => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(suc,I_1))),N)) ),
    file('theBenchmark.p',fact_960_diff__Suc__less) ).

fof(fact_961_nat__diff__split,axiom,
    ! [Pa,A_2,B_3] :
      ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,A_2),B_3)))
    <=> ( ! [D_2] :
            ( A_2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),D_2)
           => hBOOL(hAPP_nat_bool(Pa,D_2)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_3))
         => hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) ) ) ),
    file('theBenchmark.p',fact_961_nat__diff__split) ).

fof(fact_962_nat__diff__split__asm,axiom,
    ! [Pa,A_2,B_3] :
      ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,A_2),B_3)))
    <=> ~ ( ? [D_2] :
              ( ~ hBOOL(hAPP_nat_bool(Pa,D_2))
              & A_2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),D_2) )
          | ( ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_3)) ) ) ),
    file('theBenchmark.p',fact_962_nat__diff__split__asm) ).

fof(fact_963_card__less__Suc,axiom,
    ! [I_2,M_3] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3))
     => hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),M_3)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),I_2))))) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),M_3)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,I_2))))) ),
    file('theBenchmark.p',fact_963_card__less__Suc) ).

fof(fact_964_card__less,axiom,
    ! [I_2,M_3] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3))
     => hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),M_3)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,I_2))))) != zero_zero_nat ),
    file('theBenchmark.p',fact_964_card__less) ).

fof(fact_965_card__less__Suc2,axiom,
    ! [I_2,M_3] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3))
     => hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),M_3)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),I_2)))) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),M_3)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,I_2))))) ),
    file('theBenchmark.p',fact_965_card__less__Suc2) ).

fof(fact_966_Suc__diff__1,axiom,
    ! [N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
     => hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),one_one_nat)) = N ),
    file('theBenchmark.p',fact_966_Suc__diff__1) ).

fof(fact_967_Suc__pred_H,axiom,
    ! [N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
     => N = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),one_one_nat)) ),
    file('theBenchmark.p',fact_967_Suc__pred_H) ).

fof(fact_968_add__eq__if,axiom,
    ! [N,M_1] :
      ( ( M_1 != zero_zero_nat
       => hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),one_one_nat)),N)) )
      & ( M_1 = zero_zero_nat
       => hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N) = N ) ),
    file('theBenchmark.p',fact_968_add__eq__if) ).

fof(fact_969_ex__least__nat__less,axiom,
    ! [Na,Pa] :
      ( ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
     => ( hBOOL(hAPP_nat_bool(Pa,Na))
       => ? [K_2] :
            ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),one_one_nat)))
            & ! [I] :
                ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),K_2))
               => ~ hBOOL(hAPP_nat_bool(Pa,I)) )
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),Na)) ) ) ),
    file('theBenchmark.p',fact_969_ex__least__nat__less) ).

fof(fact_970_ex__least__nat__le,axiom,
    ! [Na,Pa] :
      ( ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
     => ( hBOOL(hAPP_nat_bool(Pa,Na))
       => ? [K_2] :
            ( hBOOL(hAPP_nat_bool(Pa,K_2))
            & ! [I] :
                ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K_2))
               => ~ hBOOL(hAPP_nat_bool(Pa,I)) )
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),Na)) ) ) ),
    file('theBenchmark.p',fact_970_ex__least__nat__le) ).

fof(fact_971_less__imp__add__positive,axiom,
    ! [I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J))
     => ? [K_2] :
          ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_2) = J
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2)) ) ),
    file('theBenchmark.p',fact_971_less__imp__add__positive) ).

fof(fact_972_gr0__implies__Suc,axiom,
    ! [N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
     => ? [M_2] : N = hAPP_nat_nat(suc,M_2) ),
    file('theBenchmark.p',fact_972_gr0__implies__Suc) ).

fof(fact_973_nat_Oexhaust,axiom,
    ! [Y] :
      ( Y != zero_zero_nat
     => ~ ! [Nat] : Y != hAPP_nat_nat(suc,Nat) ),
    file('theBenchmark.p',fact_973_nat_Oexhaust) ).

fof(fact_974_zero__induct,axiom,
    ! [Pa,K] :
      ( hBOOL(hAPP_nat_bool(Pa,K))
     => ( ! [N_1] :
            ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_1)))
           => hBOOL(hAPP_nat_bool(Pa,N_1)) )
       => hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) ) ),
    file('theBenchmark.p',fact_974_zero__induct) ).

fof(fact_975_not0__implies__Suc,axiom,
    ! [N] :
      ( N != zero_zero_nat
     => ? [M_2] : N = hAPP_nat_nat(suc,M_2) ),
    file('theBenchmark.p',fact_975_not0__implies__Suc) ).

fof(fact_976_nat__induct,axiom,
    ! [Na,Pa] :
      ( hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
     => ( ! [N_1] :
            ( hBOOL(hAPP_nat_bool(Pa,N_1))
           => hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_1))) )
       => hBOOL(hAPP_nat_bool(Pa,Na)) ) ),
    file('theBenchmark.p',fact_976_nat__induct) ).

fof(fact_977_expand__Suc,axiom,
    ! [V] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(V)))
     => number_number_of_nat(V) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,number_number_of_nat(V)),one_one_nat)) ),
    file('theBenchmark.p',fact_977_expand__Suc) ).

fof(fact_978_mult__0,axiom,
    ! [N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),N) = zero_zero_nat,
    file('theBenchmark.p',fact_978_mult__0) ).

fof(fact_979_mult__0__right,axiom,
    ! [M_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),zero_zero_nat) = zero_zero_nat,
    file('theBenchmark.p',fact_979_mult__0__right) ).

fof(fact_980_mult__is__0,axiom,
    ! [M,Na] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na) = zero_zero_nat
    <=> ( Na = zero_zero_nat
        | M = zero_zero_nat ) ),
    file('theBenchmark.p',fact_980_mult__is__0) ).

fof(fact_981_mult__cancel1,axiom,
    ! [K,M,Na] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na)
    <=> ( K = zero_zero_nat
        | M = Na ) ),
    file('theBenchmark.p',fact_981_mult__cancel1) ).

fof(fact_982_mult__cancel2,axiom,
    ! [M,K,Na] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Na),K)
    <=> ( K = zero_zero_nat
        | M = Na ) ),
    file('theBenchmark.p',fact_982_mult__cancel2) ).

fof(fact_983_Suc__mult__cancel1,axiom,
    ! [K,M,Na] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),Na)
    <=> M = Na ),
    file('theBenchmark.p',fact_983_Suc__mult__cancel1) ).

fof(fact_984_add__mult__distrib,axiom,
    ! [M_1,N,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),K_1)),
    file('theBenchmark.p',fact_984_add__mult__distrib) ).

fof(fact_985_add__mult__distrib2,axiom,
    ! [K_1,M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N)),
    file('theBenchmark.p',fact_985_add__mult__distrib2) ).

fof(fact_986_mult__le__mono,axiom,
    ! [K_1,L_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,K_1),L_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),L_1))) ) ),
    file('theBenchmark.p',fact_986_mult__le__mono) ).

fof(fact_987_mult__le__mono2,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,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),I_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),J))) ),
    file('theBenchmark.p',fact_987_mult__le__mono2) ).

fof(fact_988_mult__le__mono1,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,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),K_1))) ),
    file('theBenchmark.p',fact_988_mult__le__mono1) ).

fof(fact_989_le__cube,axiom,
    ! [M_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),M_1)))),
    file('theBenchmark.p',fact_989_le__cube) ).

fof(fact_990_le__square,axiom,
    ! [M_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),M_1))),
    file('theBenchmark.p',fact_990_le__square) ).

fof(fact_991_diff__mult__distrib,axiom,
    ! [M_1,N,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),K_1)),
    file('theBenchmark.p',fact_991_diff__mult__distrib) ).

fof(fact_992_diff__mult__distrib2,axiom,
    ! [K_1,M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N)),
    file('theBenchmark.p',fact_992_diff__mult__distrib2) ).

fof(fact_993_nat__mult__eq__1__iff,axiom,
    ! [M,Na] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na) = one_one_nat
    <=> ( Na = one_one_nat
        & M = one_one_nat ) ),
    file('theBenchmark.p',fact_993_nat__mult__eq__1__iff) ).

fof(fact_994_nat__mult__1__right,axiom,
    ! [N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),one_one_nat) = N,
    file('theBenchmark.p',fact_994_nat__mult__1__right) ).

fof(fact_995_nat__1__eq__mult__iff,axiom,
    ! [M,Na] :
      ( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na)
    <=> ( Na = one_one_nat
        & M = one_one_nat ) ),
    file('theBenchmark.p',fact_995_nat__1__eq__mult__iff) ).

fof(fact_996_nat__mult__1,axiom,
    ! [N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),N) = N,
    file('theBenchmark.p',fact_996_nat__mult__1) ).

fof(fact_997_mult__eq__1__iff,axiom,
    ! [M,Na] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na) = hAPP_nat_nat(suc,zero_zero_nat)
    <=> ( Na = hAPP_nat_nat(suc,zero_zero_nat)
        & M = hAPP_nat_nat(suc,zero_zero_nat) ) ),
    file('theBenchmark.p',fact_997_mult__eq__1__iff) ).

fof(fact_998_mult__less__mono2,axiom,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),I_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),J))) ) ),
    file('theBenchmark.p',fact_998_mult__less__mono2) ).

fof(fact_999_mult__less__mono1,axiom,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),K_1))) ) ),
    file('theBenchmark.p',fact_999_mult__less__mono1) ).

fof(fact_1000_mult__less__cancel2,axiom,
    ! [M,K,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Na),K)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) ) ),
    file('theBenchmark.p',fact_1000_mult__less__cancel2) ).

fof(fact_1001_mult__less__cancel1,axiom,
    ! [K,M,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) ) ),
    file('theBenchmark.p',fact_1001_mult__less__cancel1) ).

fof(fact_1002_nat__0__less__mult__iff,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M)) ) ),
    file('theBenchmark.p',fact_1002_nat__0__less__mult__iff) ).

fof(fact_1003_Suc__mult__less__cancel1,axiom,
    ! [K,M,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) ),
    file('theBenchmark.p',fact_1003_Suc__mult__less__cancel1) ).

fof(fact_1004_mult__Suc__right,axiom,
    ! [M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N)),
    file('theBenchmark.p',fact_1004_mult__Suc__right) ).

fof(fact_1005_mult__Suc,axiom,
    ! [M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,M_1)),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N)),
    file('theBenchmark.p',fact_1005_mult__Suc) ).

fof(fact_1006_Suc__mult__le__cancel1,axiom,
    ! [K,M,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) ),
    file('theBenchmark.p',fact_1006_Suc__mult__le__cancel1) ).

fof(fact_1007_mult__eq__self__implies__10,axiom,
    ! [M_1,N] :
      ( M_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N)
     => ( M_1 = zero_zero_nat
        | N = one_one_nat ) ),
    file('theBenchmark.p',fact_1007_mult__eq__self__implies__10) ).

fof(fact_1008_n__less__m__mult__n,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N))) ) ),
    file('theBenchmark.p',fact_1008_n__less__m__mult__n) ).

fof(fact_1009_n__less__n__mult__m,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),M_1))) ) ),
    file('theBenchmark.p',fact_1009_n__less__n__mult__m) ).

fof(fact_1010_one__less__mult,axiom,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N))) ) ),
    file('theBenchmark.p',fact_1010_one__less__mult) ).

fof(fact_1011_one__le__mult__iff,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),Na))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),M)) ) ),
    file('theBenchmark.p',fact_1011_one__le__mult__iff) ).

fof(fact_1012_mult__le__cancel1,axiom,
    ! [K,M,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) ) ),
    file('theBenchmark.p',fact_1012_mult__le__cancel1) ).

fof(fact_1013_mult__le__cancel2,axiom,
    ! [M,K,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Na),K)))
    <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
       => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) ) ),
    file('theBenchmark.p',fact_1013_mult__le__cancel2) ).

fof(fact_1014_mult__eq__if,axiom,
    ! [N,M_1] :
      ( ( M_1 != zero_zero_nat
       => hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),one_one_nat)),N)) )
      & ( M_1 = zero_zero_nat
       => hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N) = zero_zero_nat ) ),
    file('theBenchmark.p',fact_1014_mult__eq__if) ).

fof(fact_1015_nat__less__add__iff2,axiom,
    ! [U,M,Na,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),I_2)),U)),Na))) ) ),
    file('theBenchmark.p',fact_1015_nat__less__add__iff2) ).

fof(fact_1016_nat__mult__commute,axiom,
    ! [M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),M_1),
    file('theBenchmark.p',fact_1016_nat__mult__commute) ).

fof(fact_1017_nat__mult__assoc,axiom,
    ! [M_1,N,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),K_1)),
    file('theBenchmark.p',fact_1017_nat__mult__assoc) ).

fof(fact_1018_less__number__of__int__code,axiom,
    ! [K,L] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(K)),number_number_of_int(L)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L)) ),
    file('theBenchmark.p',fact_1018_less__number__of__int__code) ).

fof(fact_1019_zmult__1,axiom,
    ! [Z] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),Z) = Z,
    file('theBenchmark.p',fact_1019_zmult__1) ).

fof(fact_1020_zmult__1__right,axiom,
    ! [Z] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z),one_one_int) = Z,
    file('theBenchmark.p',fact_1020_zmult__1__right) ).

fof(fact_1021_zmult__commute,axiom,
    ! [Z,W] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z),W) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Z),
    file('theBenchmark.p',fact_1021_zmult__commute) ).

fof(fact_1022_times__numeral__code_I5_J,axiom,
    ! [V,W] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,number_number_of_int(V)),number_number_of_int(W)) = number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V),W)),
    file('theBenchmark.p',fact_1022_times__numeral__code_I5_J) ).

fof(fact_1023_zmult__assoc,axiom,
    ! [Z1,Z2,Z3] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),Z2)),Z3) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z2),Z3)),
    file('theBenchmark.p',fact_1023_zmult__assoc) ).

fof(fact_1024_less__eq__number__of__int__code,axiom,
    ! [K,L] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(K)),number_number_of_int(L)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L)) ),
    file('theBenchmark.p',fact_1024_less__eq__number__of__int__code) ).

fof(fact_1025_zdiff__zmult__distrib,axiom,
    ! [Z1,Z2,W] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z1),Z2)),W) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),W)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z2),W)),
    file('theBenchmark.p',fact_1025_zdiff__zmult__distrib) ).

fof(fact_1026_zdiff__zmult__distrib2,axiom,
    ! [W,Z1,Z2] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z1),Z2)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Z1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Z2)),
    file('theBenchmark.p',fact_1026_zdiff__zmult__distrib2) ).

fof(fact_1027_zadd__zmult__distrib2,axiom,
    ! [W,Z1,Z2] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),Z2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Z1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Z2)),
    file('theBenchmark.p',fact_1027_zadd__zmult__distrib2) ).

fof(fact_1028_plus__numeral__code_I9_J,axiom,
    ! [V,W] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,number_number_of_int(V)),number_number_of_int(W)) = number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V),W)),
    file('theBenchmark.p',fact_1028_plus__numeral__code_I9_J) ).

fof(fact_1029_zadd__zmult__distrib,axiom,
    ! [Z1,Z2,W] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),Z2)),W) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),W)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z2),W)),
    file('theBenchmark.p',fact_1029_zadd__zmult__distrib) ).

fof(fact_1030_zmult__zless__mono2,axiom,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),J))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),K_1))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_1),I_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_1),J))) ) ),
    file('theBenchmark.p',fact_1030_zmult__zless__mono2) ).

fof(fact_1031_pos__zmult__eq__1__iff,axiom,
    ! [Na,M] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M))
     => ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M),Na) = one_one_int
      <=> ( Na = one_one_int
          & M = one_one_int ) ) ),
    file('theBenchmark.p',fact_1031_pos__zmult__eq__1__iff) ).

fof(fact_1032_odd__nonzero,axiom,
    ! [Z] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),Z)),Z) != zero_zero_int,
    file('theBenchmark.p',fact_1032_odd__nonzero) ).

fof(fact_1033_zadd__0__right,axiom,
    ! [Z] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z),zero_zero_int) = Z,
    file('theBenchmark.p',fact_1033_zadd__0__right) ).

fof(fact_1034_zadd__0,axiom,
    ! [Z] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),Z) = Z,
    file('theBenchmark.p',fact_1034_zadd__0) ).

fof(fact_1035_int__0__less__1,axiom,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
    file('theBenchmark.p',fact_1035_int__0__less__1) ).

fof(fact_1036_int__one__le__iff__zero__less,axiom,
    ! [Z_2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Z_2))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2)) ),
    file('theBenchmark.p',fact_1036_int__one__le__iff__zero__less) ).

fof(fact_1037_less__bin__lemma,axiom,
    ! [K,L] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K),L)),zero_zero_int)) ),
    file('theBenchmark.p',fact_1037_less__bin__lemma) ).

fof(fact_1038_le__imp__0__less,axiom,
    ! [Z] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),Z))) ),
    file('theBenchmark.p',fact_1038_le__imp__0__less) ).

fof(fact_1039_odd__less__0,axiom,
    ! [Z_2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),Z_2)),Z_2)),zero_zero_int))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_2),zero_zero_int)) ),
    file('theBenchmark.p',fact_1039_odd__less__0) ).

fof(fact_1040_zadd__left__mono,axiom,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),J))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_1),I_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_1),J))) ),
    file('theBenchmark.p',fact_1040_zadd__left__mono) ).

fof(fact_1041_zadd__assoc,axiom,
    ! [Z1,Z2,Z3] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),Z2)),Z3) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z2),Z3)),
    file('theBenchmark.p',fact_1041_zadd__assoc) ).

fof(fact_1042_zadd__left__commute,axiom,
    ! [X,Y,Z] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Y),Z)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Y),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),Z)),
    file('theBenchmark.p',fact_1042_zadd__left__commute) ).

fof(fact_1043_zadd__commute,axiom,
    ! [Z,W] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z),W) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W),Z),
    file('theBenchmark.p',fact_1043_zadd__commute) ).

fof(fact_1044_zle__refl,axiom,
    ! [W] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),W)),
    file('theBenchmark.p',fact_1044_zle__refl) ).

fof(fact_1045_zle__linear,axiom,
    ! [Z,W] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),Z))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z),W)) ),
    file('theBenchmark.p',fact_1045_zle__linear) ).

fof(fact_1046_zle__trans,axiom,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),J))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,J),K_1))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),K_1)) ) ),
    file('theBenchmark.p',fact_1046_zle__trans) ).

fof(fact_1047_zle__antisym,axiom,
    ! [Z,W] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z),W))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),Z))
       => Z = W ) ),
    file('theBenchmark.p',fact_1047_zle__antisym) ).

fof(fact_1048_zle__diff1__eq,axiom,
    ! [W_1,Z_2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z_2),one_one_int)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ),
    file('theBenchmark.p',fact_1048_zle__diff1__eq) ).

fof(fact_1049_zless__linear,axiom,
    ! [X,Y] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y),X))
      | X = Y
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X),Y)) ),
    file('theBenchmark.p',fact_1049_zless__linear) ).

fof(fact_1050_zless__le,axiom,
    ! [Z_2,W_1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_2),W_1))
    <=> ( Z_2 != W_1
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_2),W_1)) ) ),
    file('theBenchmark.p',fact_1050_zless__le) ).

fof(fact_1051_zadd__strict__right__mono,axiom,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),J))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I_1),K_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,J),K_1))) ),
    file('theBenchmark.p',fact_1051_zadd__strict__right__mono) ).

fof(fact_1052_zadd__zless__mono,axiom,
    ! [Z_4,Z,W_2,W] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_2),W))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_4),Z))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_2),Z_4)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W),Z))) ) ),
    file('theBenchmark.p',fact_1052_zadd__zless__mono) ).

fof(fact_1053_zle__add1__eq__le,axiom,
    ! [W_1,Z_2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_2),one_one_int)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),Z_2)) ),
    file('theBenchmark.p',fact_1053_zle__add1__eq__le) ).

fof(fact_1054_add1__zle__eq,axiom,
    ! [W_1,Z_2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_1),one_one_int)),Z_2))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ),
    file('theBenchmark.p',fact_1054_add1__zle__eq) ).

fof(fact_1055_zless__imp__add1__zle,axiom,
    ! [W,Z] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),Z))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W),one_one_int)),Z)) ),
    file('theBenchmark.p',fact_1055_zless__imp__add1__zle) ).

fof(fact_1056_zless__add1__eq,axiom,
    ! [W_1,Z_2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_2),one_one_int)))
    <=> ( W_1 = Z_2
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) ),
    file('theBenchmark.p',fact_1056_zless__add1__eq) ).

fof(fact_1057_nat__mult__eq__cancel__disj,axiom,
    ! [K,M,Na] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na)
    <=> ( M = Na
        | K = zero_zero_nat ) ),
    file('theBenchmark.p',fact_1057_nat__mult__eq__cancel__disj) ).

fof(fact_1058_left__add__mult__distrib,axiom,
    ! [I_1,U_1,J,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),U_1)),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),U_1)),K_1),
    file('theBenchmark.p',fact_1058_left__add__mult__distrib) ).

fof(fact_1059_nat__mult__eq__cancel1,axiom,
    ! [M,Na,K] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
     => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na)
      <=> M = Na ) ),
    file('theBenchmark.p',fact_1059_nat__mult__eq__cancel1) ).

fof(fact_1060_nat__mult__less__cancel1,axiom,
    ! [M,Na,K] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) ) ),
    file('theBenchmark.p',fact_1060_nat__mult__less__cancel1) ).

fof(fact_1061_nat__mult__le__cancel1,axiom,
    ! [M,Na,K] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) ) ),
    file('theBenchmark.p',fact_1061_nat__mult__le__cancel1) ).

fof(fact_1062_nat__le__add__iff1,axiom,
    ! [U,M,Na,J_1,I_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),I_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_2),J_1)),U)),M)),Na)) ) ),
    file('theBenchmark.p',fact_1062_nat__le__add__iff1) ).

fof(fact_1063_nat__diff__add__eq1,axiom,
    ! [U_1,M_1,N,J,I_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),I_1))
     => hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U_1)),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),U_1)),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),J)),U_1)),M_1)),N) ),
    file('theBenchmark.p',fact_1063_nat__diff__add__eq1) ).

fof(fact_1064_nat__eq__add__iff1,axiom,
    ! [U,M,Na,J_1,I_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),I_2))
     => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na)
      <=> hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_2),J_1)),U)),M) = Na ) ),
    file('theBenchmark.p',fact_1064_nat__eq__add__iff1) ).

fof(fact_1065_nat__le__add__iff2,axiom,
    ! [U,M,Na,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),I_2)),U)),Na))) ) ),
    file('theBenchmark.p',fact_1065_nat__le__add__iff2) ).

fof(fact_1066_nat__diff__add__eq2,axiom,
    ! [U_1,M_1,N,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J))
     => hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U_1)),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),U_1)),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),I_1)),U_1)),N)) ),
    file('theBenchmark.p',fact_1066_nat__diff__add__eq2) ).

fof(fact_1067_nat__eq__add__iff2,axiom,
    ! [U,M,Na,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
     => ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na)
      <=> M = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),I_2)),U)),Na) ) ),
    file('theBenchmark.p',fact_1067_nat__eq__add__iff2) ).

fof(fact_1068_nat__less__add__iff1,axiom,
    ! [U,M,Na,J_1,I_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),I_2))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na)))
      <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_2),J_1)),U)),M)),Na)) ) ),
    file('theBenchmark.p',fact_1068_nat__less__add__iff1) ).

fof(fact_1069_zdiv__mono2__neg__lemma,axiom,
    ! [B_2,Q_2,R_2,B_1,Q_1,R_1] :
      ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),Q_2)),R_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_1)
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_1)),zero_zero_int))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_2),B_2))
         => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1))
           => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1))
             => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_1),B_2))
               => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),Q_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_1069_zdiv__mono2__neg__lemma) ).

fof(fact_1070_unique__quotient__lemma__neg,axiom,
    ! [B_2,Q_1,R_1,Q_2,R_2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),Q_1)),R_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),Q_2)),R_2)))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,R_2),zero_zero_int))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_2),R_2))
         => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_2),R_1))
           => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_2),Q_1)) ) ) ) ),
    file('theBenchmark.p',fact_1070_unique__quotient__lemma__neg) ).

fof(fact_1071_number__of__is__id,axiom,
    ! [K_1] : number_number_of_int(K_1) = K_1,
    file('theBenchmark.p',fact_1071_number__of__is__id) ).

fof(fact_1072_int__0__neq__1,axiom,
    zero_zero_int != one_one_int,
    file('theBenchmark.p',fact_1072_int__0__neq__1) ).

fof(fact_1073_self__quotient__aux1,axiom,
    ! [R_2,Q_2,A_1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_1))
     => ( A_1 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,R_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_1),Q_2))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_2),A_1))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Q_2)) ) ) ),
    file('theBenchmark.p',fact_1073_self__quotient__aux1) ).

fof(fact_1074_self__quotient__aux2,axiom,
    ! [R_2,Q_2,A_1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_1))
     => ( A_1 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,R_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_1),Q_2))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_2))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_2),one_one_int)) ) ) ),
    file('theBenchmark.p',fact_1074_self__quotient__aux2) ).

fof(fact_1075_q__pos__lemma,axiom,
    ! [B_1,Q_1,R_1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_1)))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B_1))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Q_1)) ) ) ),
    file('theBenchmark.p',fact_1075_q__pos__lemma) ).

fof(fact_1076_q__neg__lemma,axiom,
    ! [B_1,Q_1,R_1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_1)),zero_zero_int))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),zero_zero_int)) ) ) ),
    file('theBenchmark.p',fact_1076_q__neg__lemma) ).

fof(fact_1077_unique__quotient__lemma,axiom,
    ! [B_2,Q_1,R_1,Q_2,R_2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),Q_1)),R_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),Q_2)),R_2)))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B_2))
         => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_2),B_2))
           => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),Q_2)) ) ) ) ),
    file('theBenchmark.p',fact_1077_unique__quotient__lemma) ).

fof(fact_1078_zdiv__mono2__lemma,axiom,
    ! [B_2,Q_2,R_2,B_1,Q_1,R_1] :
      ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),Q_2)),R_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_1)
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_1)))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B_1))
         => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_2))
           => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1))
             => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_1),B_2))
               => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_2),Q_1)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_1078_zdiv__mono2__lemma) ).

fof(fact_1079_int__less__induct,axiom,
    ! [Pa,I_2,K] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_2),K))
     => ( hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K),one_one_int)))
       => ( ! [I] :
              ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I),K))
             => ( hBOOL(hAPP_int_bool(Pa,I))
               => hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,I),one_one_int))) ) )
         => hBOOL(hAPP_int_bool(Pa,I_2)) ) ) ),
    file('theBenchmark.p',fact_1079_int__less__induct) ).

fof(fact_1080_int__le__induct,axiom,
    ! [Pa,I_2,K] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_2),K))
     => ( hBOOL(hAPP_int_bool(Pa,K))
       => ( ! [I] :
              ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I),K))
             => ( hBOOL(hAPP_int_bool(Pa,I))
               => hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,I),one_one_int))) ) )
         => hBOOL(hAPP_int_bool(Pa,I_2)) ) ) ),
    file('theBenchmark.p',fact_1080_int__le__induct) ).

fof(fact_1081_int__gr__induct,axiom,
    ! [Pa,K,I_2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),I_2))
     => ( hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K),one_one_int)))
       => ( ! [I] :
              ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),I))
             => ( hBOOL(hAPP_int_bool(Pa,I))
               => hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I),one_one_int))) ) )
         => hBOOL(hAPP_int_bool(Pa,I_2)) ) ) ),
    file('theBenchmark.p',fact_1081_int__gr__induct) ).

fof(fact_1082_int__ge__induct,axiom,
    ! [Pa,K,I_2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),I_2))
     => ( hBOOL(hAPP_int_bool(Pa,K))
       => ( ! [I] :
              ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),I))
             => ( hBOOL(hAPP_int_bool(Pa,I))
               => hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I),one_one_int))) ) )
         => hBOOL(hAPP_int_bool(Pa,I_2)) ) ) ),
    file('theBenchmark.p',fact_1082_int__ge__induct) ).

fof(fact_1083_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
    ! [Y,X] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X),Y))) ) ),
    file('theBenchmark.p',fact_1083_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).

fof(fact_1084_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)),
    file('theBenchmark.p',fact_1084_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).

fof(fact_1085_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
    ! [Y,X] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),Y))) ) ),
    file('theBenchmark.p',fact_1085_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).

fof(fact_1086_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
    file('theBenchmark.p',fact_1086_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).

fof(fact_1087_transfer__nat__int__set__cong,axiom,
    ! [P_1,Pa] :
      ( ! [X_2] :
          ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2))
         => ( hBOOL(hAPP_int_bool(Pa,X_2))
          <=> hBOOL(hAPP_int_bool(P_1,X_2)) ) )
     => collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),Pa)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),P_1)) ),
    file('theBenchmark.p',fact_1087_transfer__nat__int__set__cong) ).

fof(fact_1088_decr__mult__lemma,axiom,
    ! [K,Pa,D_1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1))
     => ( ! [X_2] :
            ( hBOOL(hAPP_int_bool(Pa,X_2))
           => hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),D_1))) )
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K))
         => ! [X_2] :
              ( hBOOL(hAPP_int_bool(Pa,X_2))
             => hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K),D_1)))) ) ) ) ),
    file('theBenchmark.p',fact_1088_decr__mult__lemma) ).

fof(fact_1089_conj__le__cong,axiom,
    ! [P_1,Pa,X_1] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1))
       => ( hBOOL(Pa)
        <=> hBOOL(P_1) ) )
     => ( ( hBOOL(Pa)
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) )
      <=> ( hBOOL(P_1)
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) ) ) ),
    file('theBenchmark.p',fact_1089_conj__le__cong) ).

fof(fact_1090_imp__le__cong,axiom,
    ! [P_1,Pa,X_1] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1))
       => ( hBOOL(Pa)
        <=> hBOOL(P_1) ) )
     => ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1))
         => hBOOL(Pa) )
      <=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1))
         => hBOOL(P_1) ) ) ),
    file('theBenchmark.p',fact_1090_imp__le__cong) ).

fof(fact_1091_incr__mult__lemma,axiom,
    ! [K,Pa,D_1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1))
     => ( ! [X_2] :
            ( hBOOL(hAPP_int_bool(Pa,X_2))
           => hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),D_1))) )
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K))
         => ! [X_2] :
              ( hBOOL(hAPP_int_bool(Pa,X_2))
             => hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K),D_1)))) ) ) ) ),
    file('theBenchmark.p',fact_1091_incr__mult__lemma) ).

fof(fact_1092_int__induct,axiom,
    ! [I_2,Pa,K] :
      ( hBOOL(hAPP_int_bool(Pa,K))
     => ( ! [I] :
            ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),I))
           => ( hBOOL(hAPP_int_bool(Pa,I))
             => hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I),one_one_int))) ) )
       => ( ! [I] :
              ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I),K))
             => ( hBOOL(hAPP_int_bool(Pa,I))
               => hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,I),one_one_int))) ) )
         => hBOOL(hAPP_int_bool(Pa,I_2)) ) ) ),
    file('theBenchmark.p',fact_1092_int__induct) ).

fof(fact_1093_minusinfinity,axiom,
    ! [Pa,P1,D_1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1))
     => ( ! [X_2,K_2] :
            ( hBOOL(hAPP_int_bool(P1,X_2))
          <=> hBOOL(hAPP_int_bool(P1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),D_1)))) )
       => ( ? [Z_3] :
            ! [X_2] :
              ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),Z_3))
             => ( hBOOL(hAPP_int_bool(Pa,X_2))
              <=> hBOOL(hAPP_int_bool(P1,X_2)) ) )
         => ( ? [X1] : hBOOL(hAPP_int_bool(P1,X1))
           => ? [X1] : hBOOL(hAPP_int_bool(Pa,X1)) ) ) ) ),
    file('theBenchmark.p',fact_1093_minusinfinity) ).

fof(fact_1094_plusinfinity,axiom,
    ! [Pa,P_1,D_1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1))
     => ( ! [X_2,K_2] :
            ( hBOOL(hAPP_int_bool(P_1,X_2))
          <=> hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),D_1)))) )
       => ( ? [Z_3] :
            ! [X_2] :
              ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_3),X_2))
             => ( hBOOL(hAPP_int_bool(Pa,X_2))
              <=> hBOOL(hAPP_int_bool(P_1,X_2)) ) )
         => ( ? [X1] : hBOOL(hAPP_int_bool(P_1,X1))
           => ? [X1] : hBOOL(hAPP_int_bool(Pa,X1)) ) ) ) ),
    file('theBenchmark.p',fact_1094_plusinfinity) ).

fof(fact_1095_tsub__def,axiom,
    ! [Y,X] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),X))
       => hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X),Y) = zero_zero_int )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),X))
       => hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X),Y) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Y) ) ),
    file('theBenchmark.p',fact_1095_tsub__def) ).

fof(fact_1096_zero__zle__int,axiom,
    ! [N] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,N))),
    file('theBenchmark.p',fact_1096_zero__zle__int) ).

fof(fact_1097_int__less__0__conv,axiom,
    ! [K_1] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,K_1)),zero_zero_int)),
    file('theBenchmark.p',fact_1097_int__less__0__conv) ).

fof(fact_1098_int__1,axiom,
    hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int,
    file('theBenchmark.p',fact_1098_int__1) ).

fof(fact_1099_int__0,axiom,
    hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
    file('theBenchmark.p',fact_1099_int__0) ).

fof(fact_1100_int__eq__0__conv,axiom,
    ! [Na] :
      ( hAPP_nat_int(semiri1621563631at_int,Na) = zero_zero_int
    <=> Na = zero_zero_nat ),
    file('theBenchmark.p',fact_1100_int__eq__0__conv) ).

fof(fact_1101_zless__int,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) ),
    file('theBenchmark.p',fact_1101_zless__int) ).

fof(fact_1102_zle__int,axiom,
    ! [M,Na] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) ),
    file('theBenchmark.p',fact_1102_zle__int) ).

fof(fact_1103_zadd__int,axiom,
    ! [M_1,N] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N)),
    file('theBenchmark.p',fact_1103_zadd__int) ).

fof(fact_1104_zadd__int__left,axiom,
    ! [M_1,N,Z] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,N)),Z)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N))),Z),
    file('theBenchmark.p',fact_1104_zadd__int__left) ).

fof(fact_1105_zle__iff__zadd,axiom,
    ! [W_1,Z_2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),Z_2))
    <=> ? [N_1] : Z_2 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_1),hAPP_nat_int(semiri1621563631at_int,N_1)) ),
    file('theBenchmark.p',fact_1105_zle__iff__zadd) ).

fof(fact_1106_zmult__int,axiom,
    ! [M_1,N] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N)),
    file('theBenchmark.p',fact_1106_zmult__int) ).

fof(fact_1107_int__mult,axiom,
    ! [M_1,N] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N)),
    file('theBenchmark.p',fact_1107_int__mult) ).

fof(fact_1108_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
    ! [X,Y] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X)),hAPP_nat_int(semiri1621563631at_int,Y)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X),Y)),
    file('theBenchmark.p',fact_1108_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).

fof(fact_1109_transfer__int__nat__relations_I2_J,axiom,
    ! [X_1,Y_1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_1)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) ),
    file('theBenchmark.p',fact_1109_transfer__int__nat__relations_I2_J) ).

fof(fact_1110_transfer__int__nat__relations_I3_J,axiom,
    ! [X_1,Y_1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_1)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) ),
    file('theBenchmark.p',fact_1110_transfer__int__nat__relations_I3_J) ).

fof(fact_1111_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
    ! [X,Y] : hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,hAPP_nat_int(semiri1621563631at_int,X)),hAPP_nat_int(semiri1621563631at_int,Y)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X),Y)),
    file('theBenchmark.p',fact_1111_Nat__Transfer_Otransfer__int__nat__functions_I3_J) ).

fof(fact_1112_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
    ! [X,Y] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X)),hAPP_nat_int(semiri1621563631at_int,Y)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),Y)),
    file('theBenchmark.p',fact_1112_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).

fof(fact_1113_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
    ! [A] : hAPP_f22106695ol_nat(finite_card_nat,A) = hAPP_f957591787ol_nat(finite_card_int,image_nat_int(semiri1621563631at_int,A)),
    file('theBenchmark.p',fact_1113_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) ).

fof(fact_1114_transfer__nat__int__set__relations_I1_J,axiom,
    ! [A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
    <=> hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,A))) ),
    file('theBenchmark.p',fact_1114_transfer__nat__int__set__relations_I1_J) ).

fof(fact_1115_transfer__int__nat__numerals_I2_J,axiom,
    one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
    file('theBenchmark.p',fact_1115_transfer__int__nat__numerals_I2_J) ).

fof(fact_1116_transfer__int__nat__numerals_I1_J,axiom,
    zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
    file('theBenchmark.p',fact_1116_transfer__int__nat__numerals_I1_J) ).

fof(fact_1117_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
    ! [Pa] : collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),Pa)) = image_nat_int(semiri1621563631at_int,collect_nat(cOMBB_int_bool_nat(Pa,semiri1621563631at_int))),
    file('theBenchmark.p',fact_1117_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J) ).

fof(fact_1118_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
    ! [Z] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z))),
    file('theBenchmark.p',fact_1118_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).

fof(fact_1119_transfer__int__nat__quantifiers_I2_J,axiom,
    ! [Pa] :
      ( ? [X_2] :
          ( hBOOL(hAPP_int_bool(Pa,X_2))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) )
    <=> ? [X_2] : hBOOL(hAPP_int_bool(Pa,hAPP_nat_int(semiri1621563631at_int,X_2))) ),
    file('theBenchmark.p',fact_1119_transfer__int__nat__quantifiers_I2_J) ).

fof(fact_1120_transfer__int__nat__quantifiers_I1_J,axiom,
    ! [Pa] :
      ( ! [X_2] :
          ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2))
         => hBOOL(hAPP_int_bool(Pa,X_2)) )
    <=> ! [X_2] : hBOOL(hAPP_int_bool(Pa,hAPP_nat_int(semiri1621563631at_int,X_2))) ),
    file('theBenchmark.p',fact_1120_transfer__int__nat__quantifiers_I1_J) ).

fof(fact_1121_int__le__0__conv,axiom,
    ! [Na] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,Na)),zero_zero_int))
    <=> Na = zero_zero_nat ),
    file('theBenchmark.p',fact_1121_int__le__0__conv) ).

fof(fact_1122_int__Suc0__eq__1,axiom,
    hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,zero_zero_nat)) = one_one_int,
    file('theBenchmark.p',fact_1122_int__Suc0__eq__1) ).

fof(fact_1123_zless__iff__Suc__zadd,axiom,
    ! [W_1,Z_2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2))
    <=> ? [N_1] : Z_2 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_1),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,N_1))) ),
    file('theBenchmark.p',fact_1123_zless__iff__Suc__zadd) ).

fof(fact_1124_int__Suc,axiom,
    ! [M_1] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M_1)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,M_1)),
    file('theBenchmark.p',fact_1124_int__Suc) ).

fof(fact_1125_zdiff__int,axiom,
    ! [N,M_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_1))
     => hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)) ),
    file('theBenchmark.p',fact_1125_zdiff__int) ).

fof(fact_1126_zero__less__int__conv,axiom,
    ! [Na] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Na)))
    <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)) ),
    file('theBenchmark.p',fact_1126_zero__less__int__conv) ).

fof(fact_1127_zmult__zless__mono2__lemma,axiom,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),J))
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,K_1)),I_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,K_1)),J))) ) ),
    file('theBenchmark.p',fact_1127_zmult__zless__mono2__lemma) ).

fof(fact_1128_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
    ! [Y,X] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X))
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y))
       => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X),Y))) ) ),
    file('theBenchmark.p',fact_1128_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).

fof(fact_1129_zdiff__int__split,axiom,
    ! [Pa,X_1,Y_1] :
      ( hBOOL(hAPP_int_bool(Pa,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X_1),Y_1))))
    <=> ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
         => hBOOL(hAPP_int_bool(Pa,zero_zero_int)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
         => hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_1)))) ) ) ),
    file('theBenchmark.p',fact_1129_zdiff__int__split) ).

fof(fact_1130_tsub__eq,axiom,
    ! [Y,X] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),X))
     => hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X),Y) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Y) ),
    file('theBenchmark.p',fact_1130_tsub__eq) ).

fof(fact_1131_zero__less__imp__eq__int,axiom,
    ! [K_1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),K_1))
     => ? [N_1] :
          ( K_1 = hAPP_nat_int(semiri1621563631at_int,N_1)
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) ) ),
    file('theBenchmark.p',fact_1131_zero__less__imp__eq__int) ).

fof(fact_1132_int__int__eq,axiom,
    ! [M,Na] :
      ( hAPP_nat_int(semiri1621563631at_int,M) = hAPP_nat_int(semiri1621563631at_int,Na)
    <=> M = Na ),
    file('theBenchmark.p',fact_1132_int__int__eq) ).

fof(fact_1133_transfer__nat__int__set__relations_I4_J,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
    <=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,A)),image_nat_int(semiri1621563631at_int,B))) ),
    file('theBenchmark.p',fact_1133_transfer__nat__int__set__relations_I4_J) ).

fof(fact_1134_transfer__nat__int__set__relations_I5_J,axiom,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
    <=> hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,A)),image_nat_int(semiri1621563631at_int,B))) ),
    file('theBenchmark.p',fact_1134_transfer__nat__int__set__relations_I5_J) ).

fof(fact_1135_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
    bot_bot_fun_int_bool = image_nat_int(semiri1621563631at_int,bot_bot_fun_nat_bool),
    file('theBenchmark.p',fact_1135_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J) ).

fof(fact_1136_transfer__nat__int__set__relations_I3_J,axiom,
    ! [A,B] :
      ( A = B
    <=> image_nat_int(semiri1621563631at_int,A) = image_nat_int(semiri1621563631at_int,B) ),
    file('theBenchmark.p',fact_1136_transfer__nat__int__set__relations_I3_J) ).

fof(fact_1137_transfer__nat__int__set__relations_I2_J,axiom,
    ! [X_1,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
    <=> hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,X_1)),image_nat_int(semiri1621563631at_int,A))) ),
    file('theBenchmark.p',fact_1137_transfer__nat__int__set__relations_I2_J) ).

fof(fact_1138_int__if__cong,axiom,
    ! [X_1,Y_1,Pa] :
      ( ( ~ hBOOL(Pa)
       => hAPP_nat_int(semiri1621563631at_int,Y_1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(Pa),X_1),Y_1)) )
      & ( hBOOL(Pa)
       => hAPP_nat_int(semiri1621563631at_int,X_1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(Pa),X_1),Y_1)) ) ),
    file('theBenchmark.p',fact_1138_int__if__cong) ).

fof(fact_1139_transfer__int__nat__relations_I1_J,axiom,
    ! [X_1,Y_1] :
      ( hAPP_nat_int(semiri1621563631at_int,X_1) = hAPP_nat_int(semiri1621563631at_int,Y_1)
    <=> X_1 = Y_1 ),
    file('theBenchmark.p',fact_1139_transfer__int__nat__relations_I1_J) ).

fof(fact_1140_nonneg__int__cases,axiom,
    ! [K_1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K_1))
     => ~ ! [N_1] : K_1 != hAPP_nat_int(semiri1621563631at_int,N_1) ),
    file('theBenchmark.p',fact_1140_nonneg__int__cases) ).

fof(fact_1141_nonneg__eq__int,axiom,
    ! [Z] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z))
     => ~ ! [M_2] : Z != hAPP_nat_int(semiri1621563631at_int,M_2) ),
    file('theBenchmark.p',fact_1141_nonneg__eq__int) ).

fof(fact_1142_zero__le__imp__eq__int,axiom,
    ! [K_1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K_1))
     => ? [N_1] : K_1 = hAPP_nat_int(semiri1621563631at_int,N_1) ),
    file('theBenchmark.p',fact_1142_zero__le__imp__eq__int) ).

fof(fact_1143_int__diff__cases,axiom,
    ! [Z] :
      ~ ! [M_2,N_1] : Z != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,M_2)),hAPP_nat_int(semiri1621563631at_int,N_1)),
    file('theBenchmark.p',fact_1143_int__diff__cases) ).

fof(fact_1144_decr__lemma,axiom,
    ! [X,Z,D] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Z))),one_one_int)),D))),Z)) ),
    file('theBenchmark.p',fact_1144_decr__lemma) ).

fof(fact_1145_zabs__less__one__iff,axiom,
    ! [Z_2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(Z_2)),one_one_int))
    <=> Z_2 = zero_zero_int ),
    file('theBenchmark.p',fact_1145_zabs__less__one__iff) ).

fof(fact_1146_neg__def,axiom,
    ! [Z_1] :
      ( hBOOL(hAPP_int_bool(nat_neg,Z_1))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_1),zero_zero_int)) ),
    file('theBenchmark.p',fact_1146_neg__def) ).

fof(fact_1147_not__neg__eq__ge__0,axiom,
    ! [X_1] :
      ( ~ hBOOL(hAPP_int_bool(nat_neg,X_1))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) ),
    file('theBenchmark.p',fact_1147_not__neg__eq__ge__0) ).

fof(fact_1148_not__neg__1,axiom,
    ~ hBOOL(hAPP_int_bool(nat_neg,one_one_int)),
    file('theBenchmark.p',fact_1148_not__neg__1) ).

fof(fact_1149_not__neg__0,axiom,
    ~ hBOOL(hAPP_int_bool(nat_neg,zero_zero_int)),
    file('theBenchmark.p',fact_1149_not__neg__0) ).

fof(fact_1150_abs__zmult__eq__1,axiom,
    ! [M_1,N] :
      ( abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M_1),N)) = one_one_int
     => abs_abs_int(M_1) = one_one_int ),
    file('theBenchmark.p',fact_1150_abs__zmult__eq__1) ).

fof(fact_1151_not__neg__int,axiom,
    ! [N] : ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_nat_int(semiri1621563631at_int,N))),
    file('theBenchmark.p',fact_1151_not__neg__int) ).

fof(fact_1152_abs__int__eq,axiom,
    ! [M_1] : abs_abs_int(hAPP_nat_int(semiri1621563631at_int,M_1)) = hAPP_nat_int(semiri1621563631at_int,M_1),
    file('theBenchmark.p',fact_1152_abs__int__eq) ).

fof(fact_1153_neg__imp__number__of__eq__0,axiom,
    ! [V] :
      ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V)))
     => number_number_of_nat(V) = zero_zero_nat ),
    file('theBenchmark.p',fact_1153_neg__imp__number__of__eq__0) ).

fof(fact_1154_eq__nat__number__of,axiom,
    ! [V_3,V_2] :
      ( number_number_of_nat(V_3) = number_number_of_nat(V_2)
    <=> ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_3)))
         => ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_2)))
             => V_3 = V_2 )
            & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_2)))
             => number_number_of_int(V_3) = zero_zero_int ) ) )
        & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_3)))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(V_2)),zero_zero_int)) ) ) ),
    file('theBenchmark.p',fact_1154_eq__nat__number__of) ).

fof(fact_1155_nat__number__of__add__left,axiom,
    ! [V_1,K_1,V] :
      ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V)))
       => ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_1)))
           => hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V_1)),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V),V_1))),K_1) )
          & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_1)))
           => hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V_1)),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V)),K_1) ) ) )
      & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V)))
       => hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V_1)),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V_1)),K_1) ) ),
    file('theBenchmark.p',fact_1155_nat__number__of__add__left) ).

fof(fact_1156_int__nat__number__of,axiom,
    ! [V] :
      ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V)))
       => hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(V)) = number_number_of_int(V) )
      & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V)))
       => hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(V)) = zero_zero_int ) ),
    file('theBenchmark.p',fact_1156_int__nat__number__of) ).

fof(fact_1157_incr__lemma,axiom,
    ! [Z,X,D] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D))
     => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Z))),one_one_int)),D)))) ),
    file('theBenchmark.p',fact_1157_incr__lemma) ).

fof(fact_1158_int__val__lemma,axiom,
    ! [K,F,Na] :
      ( ! [I] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),Na))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),one_one_nat))),hAPP_nat_int(F,I)))),one_one_int)) )
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(F,zero_zero_nat)),K))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),hAPP_nat_int(F,Na)))
         => ? [I] :
              ( hAPP_nat_int(F,I) = K
              & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),Na)) ) ) ) ),
    file('theBenchmark.p',fact_1158_int__val__lemma) ).

fof(fact_1159_nat0__intermed__int__val,axiom,
    ! [K,F,Na] :
      ( ! [I] :
          ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),Na))
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),one_one_nat))),hAPP_nat_int(F,I)))),one_one_int)) )
     => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(F,zero_zero_nat)),K))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),hAPP_nat_int(F,Na)))
         => ? [I] :
              ( hAPP_nat_int(F,I) = K
              & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),Na)) ) ) ) ),
    file('theBenchmark.p',fact_1159_nat0__intermed__int__val) ).

fof(fact_1160_nat__intermed__int__val,axiom,
    ! [K,F,Na,M] :
      ( ! [I] :
          ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),Na))
            & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),I)) )
         => hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),one_one_nat))),hAPP_nat_int(F,I)))),one_one_int)) )
     => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
       => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(F,M)),K))
         => ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),hAPP_nat_int(F,Na)))
           => ? [I] :
                ( hAPP_nat_int(F,I) = K
                & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),Na))
                & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),I)) ) ) ) ) ),
    file('theBenchmark.p',fact_1160_nat__intermed__int__val) ).

fof(fact_1161_Suc__nat__number__of__add,axiom,
    ! [N,V] :
      ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V)))
       => hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V)),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(succ(V))),N) )
      & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V)))
       => hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V)),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N) ) ),
    file('theBenchmark.p',fact_1161_Suc__nat__number__of__add) ).

fof(fact_1162_succ__def,axiom,
    ! [K_1] : succ(K_1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_1),one_one_int),
    file('theBenchmark.p',fact_1162_succ__def) ).

fof(fact_1163_Suc__nat__number__of,axiom,
    ! [V] :
      ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V)))
       => hAPP_nat_nat(suc,number_number_of_nat(V)) = number_number_of_nat(succ(V)) )
      & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V)))
       => hAPP_nat_nat(suc,number_number_of_nat(V)) = one_one_nat ) ),
    file('theBenchmark.p',fact_1163_Suc__nat__number__of) ).

fof(fact_1164_nat__number__of__Bit1,axiom,
    ! [W] :
      ( ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(W)))
       => number_number_of_nat(bit1(W)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(W)),number_number_of_nat(W))) )
      & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(W)))
       => number_number_of_nat(bit1(W)) = zero_zero_nat ) ),
    file('theBenchmark.p',fact_1164_nat__number__of__Bit1) ).

fof(fact_1165_nat__1__add__number__of,axiom,
    ! [V] :
      ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls))
       => hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(V)) = number_number_of_nat(succ(V)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls))
       => hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(V)) = one_one_nat ) ),
    file('theBenchmark.p',fact_1165_nat__1__add__number__of) ).

fof(fact_1166_succ__Pls,axiom,
    succ(pls) = bit1(pls),
    file('theBenchmark.p',fact_1166_succ__Pls) ).

fof(fact_1167_neg__number__of__Bit1,axiom,
    ! [W_1] :
      ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(W_1))))
    <=> hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(W_1))) ),
    file('theBenchmark.p',fact_1167_neg__number__of__Bit1) ).

fof(fact_1168_not__neg__number__of__Pls,axiom,
    ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(pls))),
    file('theBenchmark.p',fact_1168_not__neg__number__of__Pls) ).

fof(fact_1169_transfer__int__nat__numerals_I4_J,axiom,
    number_number_of_int(bit1(bit1(pls))) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(bit1(bit1(pls)))),
    file('theBenchmark.p',fact_1169_transfer__int__nat__numerals_I4_J) ).

fof(fact_1170_numeral__1__eq__Suc__0,axiom,
    number_number_of_nat(bit1(pls)) = hAPP_nat_nat(suc,zero_zero_nat),
    file('theBenchmark.p',fact_1170_numeral__1__eq__Suc__0) ).

fof(fact_1171_numeral__3__eq__3,axiom,
    number_number_of_nat(bit1(bit1(pls))) = hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))),
    file('theBenchmark.p',fact_1171_numeral__3__eq__3) ).

fof(fact_1172_Suc3__eq__add__3,axiom,
    ! [N] : hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,N))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(bit1(bit1(pls)))),N),
    file('theBenchmark.p',fact_1172_Suc3__eq__add__3) ).

fof(fact_1173_Numeral1__eq1__nat,axiom,
    one_one_nat = number_number_of_nat(bit1(pls)),
    file('theBenchmark.p',fact_1173_Numeral1__eq1__nat) ).

fof(fact_1174_nat__numeral__1__eq__1,axiom,
    number_number_of_nat(bit1(pls)) = one_one_nat,
    file('theBenchmark.p',fact_1174_nat__numeral__1__eq__1) ).

fof(fact_1175_one__is__num__one,axiom,
    one_one_int = number_number_of_int(bit1(pls)),
    file('theBenchmark.p',fact_1175_one__is__num__one) ).

fof(fact_1176_zero__is__num__zero,axiom,
    zero_zero_int = number_number_of_int(pls),
    file('theBenchmark.p',fact_1176_zero__is__num__zero) ).

fof(fact_1177_Bit1__def,axiom,
    ! [K_1] : bit1(K_1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_1)),K_1),
    file('theBenchmark.p',fact_1177_Bit1__def) ).

fof(fact_1178_nat__number__of__Pls,axiom,
    number_number_of_nat(pls) = zero_zero_nat,
    file('theBenchmark.p',fact_1178_nat__number__of__Pls) ).

fof(fact_1179_semiring__norm_I113_J,axiom,
    zero_zero_nat = number_number_of_nat(pls),
    file('theBenchmark.p',fact_1179_semiring__norm_I113_J) ).

fof(fact_1180_Pls__def,axiom,
    pls = zero_zero_int,
    file('theBenchmark.p',fact_1180_Pls__def) ).

fof(fact_1181_rel__simps_I51_J,axiom,
    ! [K,L] :
      ( bit1(K) = bit1(L)
    <=> K = L ),
    file('theBenchmark.p',fact_1181_rel__simps_I51_J) ).

fof(fact_1182_rel__simps_I46_J,axiom,
    ! [K_1] : bit1(K_1) != pls,
    file('theBenchmark.p',fact_1182_rel__simps_I46_J) ).

fof(fact_1183_rel__simps_I39_J,axiom,
    ! [L_1] : pls != bit1(L_1),
    file('theBenchmark.p',fact_1183_rel__simps_I39_J) ).

fof(fact_1184_diff__bin__simps_I1_J,axiom,
    ! [K_1] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K_1),pls) = K_1,
    file('theBenchmark.p',fact_1184_diff__bin__simps_I1_J) ).

fof(fact_1185_add__Pls,axiom,
    ! [K_1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),K_1) = K_1,
    file('theBenchmark.p',fact_1185_add__Pls) ).

fof(fact_1186_add__Pls__right,axiom,
    ! [K_1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_1),pls) = K_1,
    file('theBenchmark.p',fact_1186_add__Pls__right) ).

fof(fact_1187_mult__Pls,axiom,
    ! [W] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,pls),W) = pls,
    file('theBenchmark.p',fact_1187_mult__Pls) ).

fof(fact_1188_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(bit1(pls))))),
    file('theBenchmark.p',fact_1188_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).

fof(fact_1189_rel__simps_I19_J,axiom,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls)),
    file('theBenchmark.p',fact_1189_rel__simps_I19_J) ).

fof(fact_1190_rel__simps_I22_J,axiom,
    ! [K] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(K)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),K)) ),
    file('theBenchmark.p',fact_1190_rel__simps_I22_J) ).

fof(fact_1191_rel__simps_I34_J,axiom,
    ! [K,L] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K)),bit1(L)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L)) ),
    file('theBenchmark.p',fact_1191_rel__simps_I34_J) ).

fof(fact_1192_less__eq__int__code_I16_J,axiom,
    ! [K1,K2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K1)),bit1(K2)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K1),K2)) ),
    file('theBenchmark.p',fact_1192_less__eq__int__code_I16_J) ).

fof(fact_1193_rel__simps_I2_J,axiom,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
    file('theBenchmark.p',fact_1193_rel__simps_I2_J) ).

fof(fact_1194_rel__simps_I12_J,axiom,
    ! [K] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K)),pls))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),pls)) ),
    file('theBenchmark.p',fact_1194_rel__simps_I12_J) ).

fof(fact_1195_rel__simps_I17_J,axiom,
    ! [K,L] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K)),bit1(L)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L)) ),
    file('theBenchmark.p',fact_1195_rel__simps_I17_J) ).

fof(fact_1196_less__int__code_I16_J,axiom,
    ! [K1,K2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K1)),bit1(K2)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K1),K2)) ),
    file('theBenchmark.p',fact_1196_less__int__code_I16_J) ).

fof(fact_1197_rel__simps_I29_J,axiom,
    ! [K] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K)),pls))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),pls)) ),
    file('theBenchmark.p',fact_1197_rel__simps_I29_J) ).

fof(fact_1198_rel__simps_I5_J,axiom,
    ! [K] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(K)))
    <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),K)) ),
    file('theBenchmark.p',fact_1198_rel__simps_I5_J) ).

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_fFalse_1_1_U,axiom,
    ~ hBOOL(fFalse),
    file('theBenchmark.p',help_fFalse_1_1_U) ).

fof(help_fFalse_1_1_T,axiom,
    ! [P] :
      ( is_bool(P)
     => ( P = fFalse
        | P = fTrue ) ),
    file('theBenchmark.p',help_fFalse_1_1_T) ).

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_If_1_1_If_000tc__Nat__Onat_T,axiom,
    ! [X,Y] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fTrue),X),Y) = X,
    file('theBenchmark.p',help_If_1_1_If_000tc__Nat__Onat_T) ).

fof(help_If_2_1_If_000tc__Nat__Onat_T,axiom,
    ! [X,Y] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fFalse),X),Y) = Y,
    file('theBenchmark.p',help_If_2_1_If_000tc__Nat__Onat_T) ).

fof(help_If_3_1_If_000tc__Nat__Onat_T,axiom,
    ! [P] :
      ( is_bool(P)
     => ( P = fFalse
        | P = fTrue ) ),
    file('theBenchmark.p',help_If_3_1_If_000tc__Nat__Onat_T) ).

fof(help_COMBI_1_1_COMBI_000tc__Nat__Onat_U,axiom,
    ! [P] : hAPP_nat_nat(cOMBI_nat,P) = P,
    file('theBenchmark.p',help_COMBI_1_1_COMBI_000tc__Nat__Onat_U) ).

fof(help_fequal_1_1_fequal_000tc__Int__Oint_T,axiom,
    ! [X,Y] :
      ( X = Y
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X),Y)) ),
    file('theBenchmark.p',help_fequal_1_1_fequal_000tc__Int__Oint_T) ).

fof(help_fequal_2_1_fequal_000tc__Int__Oint_T,axiom,
    ! [X,Y] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X),Y))
      | X != Y ),
    file('theBenchmark.p',help_fequal_2_1_fequal_000tc__Int__Oint_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_COMBK_1_1_COMBK_000tc__HOL__Obool_000t__a_U,axiom,
    ! [P,Q] :
      ( is_bool(P)
     => hAPP_a_bool(cOMBK_bool_a(P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000t__a_U) ).

fof(help_COMBK_1_1_COMBK_000t__a_000tc__Com__Opname_U,axiom,
    ! [P,Q] :
      ( is_a(P)
     => hAPP_pname_a(cOMBK_a_pname(P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000t__a_000tc__Com__Opname_U) ).

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_COMBK_1_1_COMBK_000tc__Int__Oint_000tc__Nat__Onat_U,axiom,
    ! [P,Q] : hAPP_nat_int(cOMBK_int_nat(P),Q) = P,
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Int__Oint_000tc__Nat__Onat_U) ).

fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Int__Oint_U,axiom,
    ! [P,Q] :
      ( is_bool(P)
     => hAPP_int_bool(cOMBK_bool_int(P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Int__Oint_U) ).

fof(help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
    ! [P,Q] :
      ( is_bool(P)
     => hAPP_nat_bool(cOMBK_bool_nat(P),Q) = P ),
    file('theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_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_COMBC_1_1_COMBC_000tc__Int__Oint_000t__a_000tc__HOL__Obool_U,axiom,
    ! [P,Q,R] : hAPP_int_bool(hAPP_a_fun_int_bool(cOMBC_int_a_bool(P),Q),R) = hAPP_a_bool(hAPP_int_fun_a_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000t__a_000tc__HOL__Obool_U) ).

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__Int__Oint_Mtc__HOL__Obool_J_T,axiom,
    ! [X,Y] :
      ( X = Y
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X),Y)) ),
    file('theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T) ).

fof(help_fequal_2_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T,axiom,
    ! [X,Y] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X),Y))
      | X != Y ),
    file('theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T) ).

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_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
    ! [P,Q,R] : hAPP_nat_bool(cOMBB_int_bool_nat(P,Q),R) = hAPP_int_bool(P,hAPP_nat_int(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__HOL__Obool_000tc__Nat__Onat_U) ).

fof(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U,axiom,
    ! [P,Q,R] : hAPP_int_bool(hAPP_i1948725293t_bool(cOMBC_int_int_bool(P),Q),R) = hAPP_int_bool(hAPP_i1948725293t_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U) ).

fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Int__Oint_000tc__HOL__Obool_U,axiom,
    ! [P,Q,R] : hAPP_nat_bool(hAPP_i418383825t_bool(cOMBC_nat_int_bool(P),Q),R) = hAPP_int_bool(hAPP_n1082236369t_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Int__Oint_000tc__HOL__Obool_U) ).

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__Int__Oint_U,axiom,
    ! [P,Q,R] : hAPP_int_bool(cOMBB_bool_bool_int(P,Q),R) = hAPP_bool_bool(P,hAPP_int_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Int__Oint_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__Int__Oint_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
    ! [P,Q,R] : hAPP_int_bool(cOMBS_int_bool_bool(P,Q),R) = hAPP_bool_bool(hAPP_i68813070l_bool(P,R),hAPP_int_bool(Q,R)),
    file('theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__HOL__Obool_000tc__HOL__Obool_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_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Int__Oint,axiom,
    ! [P,Q,R] : hAPP_int_fun_a_bool(cOMBB_375279840ol_int(P,Q),R) = hAPP_a_fun_a_bool(P,hAPP_int_a(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Int__Oint) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t__,axiom,
    ! [P,Q,R] : hAPP_a_bool(cOMBB_1273333599bool_a(P,Q),R) = hAPP_fun_a_bool_bool(P,hAPP_a_fun_a_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t__) ).

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_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__,axiom,
    ! [P,Q,R] : hAPP_int_bool(hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(P),Q),R) = hAPP_fun_a_bool_bool(hAPP_i888906320l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__) ).

fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__,axiom,
    ! [P,Q,R] : hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(P),Q),R) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__) ).

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_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_,axiom,
    ! [P,Q,R] : hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(P,Q),R) = hAPP_i1948725293t_bool(P,hAPP_nat_int(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_) ).

fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
    ! [P,Q,R] : hAPP_n1699378549t_bool(cOMBB_800536526ol_nat(P,Q),R) = hAPP_n1699378549t_bool(P,hAPP_nat_nat(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).

fof(help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a,axiom,
    ! [P,Q,R] : hAPP_a_fun_a_bool(hAPP_f1038053735a_bool(cOMBC_394484100a_bool(P),Q),R) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obo,axiom,
    ! [P,Q,R] : hAPP_int_bool(cOMBB_1418110531ol_int(P,Q),R) = hAPP_f448129468l_bool(P,hAPP_i1948725293t_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obo) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo,axiom,
    ! [P,Q,R] : hAPP_nat_bool(cOMBB_955900739ol_nat(P,Q),R) = hAPP_f54304608l_bool(P,hAPP_n1699378549t_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) ).

fof(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_,axiom,
    ! [P,Q,R] : hAPP_int_bool(hAPP_f1805168059t_bool(cOMBC_94739984l_bool(P),Q),R) = hAPP_f448129468l_bool(hAPP_i2112223885l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_) ).

fof(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
    ! [P,Q,R] : hAPP_int_bool(hAPP_f183368031t_bool(cOMBC_1848398772l_bool(P),Q),R) = hAPP_f54304608l_bool(hAPP_i1718399025l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).

fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_,axiom,
    ! [P,Q,R] : hAPP_nat_bool(hAPP_f274826591t_bool(cOMBC_620423604l_bool(P),Q),R) = hAPP_f448129468l_bool(hAPP_n609083369l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_) ).

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__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_003,axiom,
    ! [P,Q,R] : hAPP_i68813070l_bool(cOMBB_1652995168ol_int(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_int_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_003) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_004,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_004) ).

fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obo,axiom,
    ! [P,Q,R] : hAPP_f448129468l_bool(cOMBS_1912792529l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f1721100032l_bool(P,R),hAPP_f448129468l_bool(Q,R)),
    file('theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obo) ).

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_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo,axiom,
    ! [P,Q,R] : hAPP_int_bool(hAPP_f449020825t_bool(cOMBC_316919022l_bool(P),Q),R) = hAPP_f1664156314l_bool(hAPP_i1587699435l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) ).

fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo,axiom,
    ! [P,Q,R] : hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(P),Q),R) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_005,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_005) ).

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_006,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_006) ).

fof(help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO,axiom,
    ! [P,Q,R] : hAPP_n215258509l_bool(cOMBB_1146692694ol_nat(P,Q),R) = hAPP_n215258509l_bool(P,hAPP_nat_nat(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO) ).

fof(help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool__007,axiom,
    ! [P,Q,R] : hAPP_i1948725293t_bool(hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(P),Q),R) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool__007) ).

fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__008,axiom,
    ! [P,Q,R] : hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBC_178881787t_bool(P),Q),R) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__008) ).

fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc_,axiom,
    ! [P,Q,R] : hAPP_f448129468l_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(P),Q),R) = hAPP_f448129468l_bool(hAPP_f284875647l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).

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_f1721100032l_bool(cOMBB_1974511970t_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f448129468l_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_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_010) ).

fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_011,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_011) ).

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_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__,axiom,
    ! [P,Q,R] : hAPP_i888906320l_bool(cOMBB_313729068ol_int(P,Q),R) = hAPP_f1631501043l_bool(P,hAPP_int_fun_a_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___012,axiom,
    ! [P,Q,R] : hAPP_n1414589940l_bool(cOMBB_1823939024ol_nat(P,Q),R) = hAPP_f1631501043l_bool(P,hAPP_nat_fun_a_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___012) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc_,axiom,
    ! [P,Q,R] : hAPP_i2112223885l_bool(cOMBB_1761098400ol_int(P,Q),R) = hAPP_f284875647l_bool(P,hAPP_i1948725293t_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc__013,axiom,
    ! [P,Q,R] : hAPP_n609083369l_bool(cOMBB_1123824708ol_nat(P,Q),R) = hAPP_f284875647l_bool(P,hAPP_n1082236369t_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc__013) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_,axiom,
    ! [P,Q,R] : hAPP_i1718399025l_bool(cOMBB_516767136ol_int(P,Q),R) = hAPP_f103356543l_bool(P,hAPP_i418383825t_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__014,axiom,
    ! [P,Q,R] : hAPP_n215258509l_bool(cOMBB_2026977092ol_nat(P,Q),R) = hAPP_f103356543l_bool(P,hAPP_n1699378549t_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__014) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It,axiom,
    ! [P,Q,R] : hAPP_i1587699435l_bool(cOMBB_607112096ol_int(P,Q),R) = hAPP_f434788991l_bool(P,hAPP_i7355787e_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).

fof(help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_015,axiom,
    ! [P,Q,R] : hAPP_n850744903l_bool(cOMBB_2117322052ol_nat(P,Q),R) = hAPP_f434788991l_bool(P,hAPP_n1025906991e_bool(Q,R)),
    file('theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_015) ).

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__Int__Oint_Mtc__HOL__Obool_J_Mtc__H,axiom,
    ! [P,Q,R] : hAPP_f215623910l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(P),Q),R) = hAPP_f215623910l_bool(hAPP_f317860125l_bool(P,R),Q),
    file('theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__H) ).

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(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(hAPP_nat_fun_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,hAPP_f2050579477a_bool(hAPP_a1206381875a_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_1] :
      ( is_fun_a_bool(cOMBB_bool_bool_a(B_1_1,B_2_1))
      | ~ is_fun_a_bool(B_2_1) ),
    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]) ).

fof(f_1_3,plain,
    ! [U_1,U_0] :
      ( is_fun_a_bool(cOMBB_bool_bool_a(U_1,U_0))
      | ~ is_fun_a_bool(U_0) ),
    inference(definitional_conversion,[status(esa)],[f_1_2]) ).

cnf(f_1_4,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_3]) ).

fof(f_2_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun_pname_bool(cOMBB_647938656_pname(B_1_1,B_2_1))
      | ~ is_fun_pname_bool(B_2_1) ),
    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]) ).

fof(f_2_3,plain,
    ! [U_2,U_3] :
      ( is_fun_pname_bool(cOMBB_647938656_pname(U_3,U_2))
      | ~ is_fun_pname_bool(U_2) ),
    inference(definitional_conversion,[status(esa)],[f_2_2]) ).

cnf(f_2_4,plain,
    ( is_fun_pname_bool(cOMBB_647938656_pname(U_3,U_2))
    | ~ is_fun_pname_bool(U_2) ),
    inference(clausify,[status(thm)],[f_2_3]) ).

fof(f_3_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun_a_bool(cOMBB_1273333599bool_a(B_1_1,B_2_1))
      | ~ is_fun949378684l_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t__a]) ).

fof(f_3_2,plain,
    ! [U_5,U_4] :
      ( is_fun_a_bool(cOMBB_1273333599bool_a(U_5,U_4))
      | ~ is_fun949378684l_bool(U_5) ),
    inference(variable_rename,[status(thm)],[f_3_1]) ).

fof(f_3_3,plain,
    ! [U_5] :
      ( ! [U_4] : is_fun_a_bool(cOMBB_1273333599bool_a(U_5,U_4))
      | ~ is_fun949378684l_bool(U_5) ),
    inference(miniscope,[status(thm)],[f_3_2]) ).

fof(f_3_4,plain,
    ! [U_4,U_5] :
      ( is_fun_a_bool(cOMBB_1273333599bool_a(U_5,U_4))
      | ~ is_fun949378684l_bool(U_5) ),
    inference(definitional_conversion,[status(esa)],[f_3_3]) ).

cnf(f_3_5,plain,
    ( is_fun_a_bool(cOMBB_1273333599bool_a(U_5,U_4))
    | ~ is_fun949378684l_bool(U_5) ),
    inference(clausify,[status(thm)],[f_3_4]) ).

fof(f_4_1,plain,
    ! [B_1_1] :
      ( is_fun_a_bool(cOMBK_bool_a(B_1_1))
      | ~ is_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_COMBK_000tc__HOL__Obool_000t__a]) ).

fof(f_4_2,plain,
    ! [U_6] :
      ( is_fun_a_bool(cOMBK_bool_a(U_6))
      | ~ is_bool(U_6) ),
    inference(variable_rename,[status(thm)],[f_4_1]) ).

fof(f_4_3,plain,
    ! [U_6] :
      ( is_fun_a_bool(cOMBK_bool_a(U_6))
      | ~ is_bool(U_6) ),
    inference(definitional_conversion,[status(esa)],[f_4_2]) ).

cnf(f_4_4,plain,
    ( is_fun_a_bool(cOMBK_bool_a(U_6))
    | ~ is_bool(U_6) ),
    inference(clausify,[status(thm)],[f_4_3]) ).

fof(f_5_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun_a_bool(cOMBS_a_bool_bool(B_1_1,B_2_1))
      | ~ is_fun_a_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool]) ).

fof(f_5_2,plain,
    ! [U_8,U_7] :
      ( is_fun_a_bool(cOMBS_a_bool_bool(U_8,U_7))
      | ~ is_fun_a_bool(U_7) ),
    inference(variable_rename,[status(thm)],[f_5_1]) ).

fof(f_5_3,plain,
    ! [U_7,U_8] :
      ( is_fun_a_bool(cOMBS_a_bool_bool(U_8,U_7))
      | ~ is_fun_a_bool(U_7) ),
    inference(definitional_conversion,[status(esa)],[f_5_2]) ).

cnf(f_5_4,plain,
    ( is_fun_a_bool(cOMBS_a_bool_bool(U_8,U_7))
    | ~ is_fun_a_bool(U_7) ),
    inference(clausify,[status(thm)],[f_5_3]) ).

fof(f_6_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun_pname_bool(cOMBS_568398431l_bool(B_1_1,B_2_1))
      | ~ is_fun_pname_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool]) ).

fof(f_6_2,plain,
    ! [U_10,U_9] :
      ( is_fun_pname_bool(cOMBS_568398431l_bool(U_10,U_9))
      | ~ is_fun_pname_bool(U_9) ),
    inference(variable_rename,[status(thm)],[f_6_1]) ).

fof(f_6_3,plain,
    ! [U_9,U_10] :
      ( is_fun_pname_bool(cOMBS_568398431l_bool(U_10,U_9))
      | ~ is_fun_pname_bool(U_9) ),
    inference(definitional_conversion,[status(esa)],[f_6_2]) ).

cnf(f_6_4,plain,
    ( is_fun_pname_bool(cOMBS_568398431l_bool(U_10,U_9))
    | ~ is_fun_pname_bool(U_9) ),
    inference(clausify,[status(thm)],[f_6_3]) ).

fof(f_7_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun949378684l_bool(cOMBS_1035972772l_bool(B_1_1,B_2_1))
      | ~ is_fun949378684l_bool(B_2_1) ),
    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_12,U_11] :
      ( is_fun949378684l_bool(cOMBS_1035972772l_bool(U_12,U_11))
      | ~ is_fun949378684l_bool(U_11) ),
    inference(variable_rename,[status(thm)],[f_7_1]) ).

fof(f_7_3,plain,
    ! [U_11,U_12] :
      ( is_fun949378684l_bool(cOMBS_1035972772l_bool(U_12,U_11))
      | ~ is_fun949378684l_bool(U_11) ),
    inference(definitional_conversion,[status(esa)],[f_7_2]) ).

cnf(f_7_4,plain,
    ( is_fun949378684l_bool(cOMBS_1035972772l_bool(U_12,U_11))
    | ~ is_fun949378684l_bool(U_11) ),
    inference(clausify,[status(thm)],[f_7_3]) ).

fof(f_8_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1661590463l_bool(cOMBS_350070575l_bool(B_1_1,B_2_1))
      | ~ is_fun1661590463l_bool(B_2_1) ),
    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_14,U_13] :
      ( is_fun1661590463l_bool(cOMBS_350070575l_bool(U_14,U_13))
      | ~ is_fun1661590463l_bool(U_13) ),
    inference(variable_rename,[status(thm)],[f_8_1]) ).

fof(f_8_3,plain,
    ! [U_13,U_14] :
      ( is_fun1661590463l_bool(cOMBS_350070575l_bool(U_14,U_13))
      | ~ is_fun1661590463l_bool(U_13) ),
    inference(definitional_conversion,[status(esa)],[f_8_2]) ).

cnf(f_8_4,plain,
    ( is_fun1661590463l_bool(cOMBS_350070575l_bool(U_14,U_13))
    | ~ is_fun1661590463l_bool(U_13) ),
    inference(clausify,[status(thm)],[f_8_3]) ).

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

fof(f_9_2,plain,
    is_fun949378684l_bool(finite_finite_a),
    inference(definitional_conversion,[status(esa)],[f_9_1]) ).

cnf(f_9_3,plain,
    is_fun949378684l_bool(finite_finite_a),
    inference(clausify,[status(thm)],[f_9_2]) ).

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

fof(f_10_2,plain,
    is_fun1661590463l_bool(finite_finite_pname),
    inference(definitional_conversion,[status(esa)],[f_10_1]) ).

cnf(f_10_3,plain,
    is_fun1661590463l_bool(finite_finite_pname),
    inference(clausify,[status(thm)],[f_10_2]) ).

fof(f_11_1,plain,
    ! [B_1_1,B_2_1] : is_bool(finite_folding_one_a(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Finite__Set_Ofolding__one_000t__a]) ).

fof(f_11_2,plain,
    ! [U_16,U_15] : is_bool(finite_folding_one_a(U_16,U_15)),
    inference(variable_rename,[status(thm)],[f_11_1]) ).

fof(f_11_3,plain,
    ! [U_15,U_16] : is_bool(finite_folding_one_a(U_16,U_15)),
    inference(definitional_conversion,[status(esa)],[f_11_2]) ).

cnf(f_11_4,plain,
    is_bool(finite_folding_one_a(U_16,U_15)),
    inference(clausify,[status(thm)],[f_11_3]) ).

fof(f_12_1,plain,
    ! [B_1_1,B_2_1] : is_bool(finite1282449217_pname(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Finite__Set_Ofolding__one_000tc__Com__Opname]) ).

fof(f_12_2,plain,
    ! [U_18,U_17] : is_bool(finite1282449217_pname(U_18,U_17)),
    inference(variable_rename,[status(thm)],[f_12_1]) ).

fof(f_12_3,plain,
    ! [U_17,U_18] : is_bool(finite1282449217_pname(U_18,U_17)),
    inference(definitional_conversion,[status(esa)],[f_12_2]) ).

cnf(f_12_4,plain,
    is_bool(finite1282449217_pname(U_18,U_17)),
    inference(clausify,[status(thm)],[f_12_3]) ).

fof(f_13_1,plain,
    ! [B_1_1,B_2_1] : is_bool(finite1626084323ne_int(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Finite__Set_Ofolding__one_000tc__Int__Oint]) ).

fof(f_13_2,plain,
    ! [U_20,U_19] : is_bool(finite1626084323ne_int(U_20,U_19)),
    inference(variable_rename,[status(thm)],[f_13_1]) ).

fof(f_13_3,plain,
    ! [U_19,U_20] : is_bool(finite1626084323ne_int(U_20,U_19)),
    inference(definitional_conversion,[status(esa)],[f_13_2]) ).

cnf(f_13_4,plain,
    is_bool(finite1626084323ne_int(U_20,U_19)),
    inference(clausify,[status(thm)],[f_13_3]) ).

fof(f_14_1,plain,
    ! [B_1_1,B_2_1] : is_bool(finite988810631ne_nat(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Finite__Set_Ofolding__one_000tc__Nat__Onat]) ).

fof(f_14_2,plain,
    ! [U_22,U_21] : is_bool(finite988810631ne_nat(U_22,U_21)),
    inference(variable_rename,[status(thm)],[f_14_1]) ).

fof(f_14_3,plain,
    ! [U_21,U_22] : is_bool(finite988810631ne_nat(U_22,U_21)),
    inference(definitional_conversion,[status(esa)],[f_14_2]) ).

cnf(f_14_4,plain,
    is_bool(finite988810631ne_nat(U_22,U_21)),
    inference(clausify,[status(thm)],[f_14_3]) ).

fof(f_15_1,plain,
    ! [B_1_1,B_2_1] : is_bool(finite1819937229idem_a(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Finite__Set_Ofolding__one__idem_000t__a]) ).

fof(f_15_2,plain,
    ! [U_24,U_23] : is_bool(finite1819937229idem_a(U_24,U_23)),
    inference(variable_rename,[status(thm)],[f_15_1]) ).

fof(f_15_3,plain,
    ! [U_23,U_24] : is_bool(finite1819937229idem_a(U_24,U_23)),
    inference(definitional_conversion,[status(esa)],[f_15_2]) ).

cnf(f_15_4,plain,
    is_bool(finite1819937229idem_a(U_24,U_23)),
    inference(clausify,[status(thm)],[f_15_3]) ).

fof(f_16_1,plain,
    ! [B_1_1,B_2_1] : is_bool(finite89670078_pname(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname]) ).

fof(f_16_2,plain,
    ! [U_26,U_25] : is_bool(finite89670078_pname(U_26,U_25)),
    inference(variable_rename,[status(thm)],[f_16_1]) ).

fof(f_16_3,plain,
    ! [U_25,U_26] : is_bool(finite89670078_pname(U_26,U_25)),
    inference(definitional_conversion,[status(esa)],[f_16_2]) ).

cnf(f_16_4,plain,
    is_bool(finite89670078_pname(U_26,U_25)),
    inference(clausify,[status(thm)],[f_16_3]) ).

fof(f_17_1,plain,
    ! [B_1_1,B_2_1] : is_bool(finite1432773856em_int(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Finite__Set_Ofolding__one__idem_000tc__Int__Oint]) ).

fof(f_17_2,plain,
    ! [U_28,U_27] : is_bool(finite1432773856em_int(U_28,U_27)),
    inference(variable_rename,[status(thm)],[f_17_1]) ).

fof(f_17_3,plain,
    ! [U_27,U_28] : is_bool(finite1432773856em_int(U_28,U_27)),
    inference(definitional_conversion,[status(esa)],[f_17_2]) ).

cnf(f_17_4,plain,
    is_bool(finite1432773856em_int(U_28,U_27)),
    inference(clausify,[status(thm)],[f_17_3]) ).

fof(f_18_1,plain,
    ! [B_1_1,B_2_1] : is_bool(finite795500164em_nat(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Finite__Set_Ofolding__one__idem_000tc__Nat__Onat]) ).

fof(f_18_2,plain,
    ! [U_30,U_29] : is_bool(finite795500164em_nat(U_30,U_29)),
    inference(variable_rename,[status(thm)],[f_18_1]) ).

fof(f_18_3,plain,
    ! [U_29,U_30] : is_bool(finite795500164em_nat(U_30,U_29)),
    inference(definitional_conversion,[status(esa)],[f_18_2]) ).

cnf(f_18_4,plain,
    is_bool(finite795500164em_nat(U_30,U_29)),
    inference(clausify,[status(thm)],[f_18_3]) ).

fof(f_19_1,plain,
    is_a(undefined_a(x_a)),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000t__a]) ).

fof(f_19_2,plain,
    is_a(undefined_a(x_a)),
    inference(definitional_conversion,[status(esa)],[f_19_1]) ).

cnf(f_19_3,plain,
    is_a(undefined_a(x_a)),
    inference(clausify,[status(thm)],[f_19_2]) ).

fof(f_20_1,plain,
    is_pname(undefined_pname(pname)),
    inference(fof_nnf,[status(thm)],[gsy_c_HOL_Oundefined_000tc__Com__Opname]) ).

fof(f_20_2,plain,
    is_pname(undefined_pname(pname)),
    inference(definitional_conversion,[status(esa)],[f_20_1]) ).

cnf(f_20_3,plain,
    is_pname(undefined_pname(pname)),
    inference(clausify,[status(thm)],[f_20_2]) ).

fof(f_21_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]) ).

fof(f_21_2,plain,
    is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool))),
    inference(definitional_conversion,[status(esa)],[f_21_1]) ).

cnf(f_21_3,plain,
    is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool))),
    inference(clausify,[status(thm)],[f_21_2]) ).

fof(f_22_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]) ).

fof(f_22_2,plain,
    is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))),
    inference(definitional_conversion,[status(esa)],[f_22_1]) ).

cnf(f_22_3,plain,
    is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))),
    inference(clausify,[status(thm)],[f_22_2]) ).

fof(f_23_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]) ).

fof(f_23_2,plain,
    is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))),
    inference(definitional_conversion,[status(esa)],[f_23_1]) ).

cnf(f_23_3,plain,
    is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))),
    inference(clausify,[status(thm)],[f_23_2]) ).

fof(f_24_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_]) ).

fof(f_24_2,plain,
    is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))),
    inference(definitional_conversion,[status(esa)],[f_24_1]) ).

cnf(f_24_3,plain,
    is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))),
    inference(clausify,[status(thm)],[f_24_2]) ).

fof(f_25_1,plain,
    is_bool(bot_bot_bool),
    inference(fof_nnf,[status(thm)],[gsy_c_Orderings_Obot__class_Obot_000tc__HOL__Obool]) ).

fof(f_25_2,plain,
    is_bool(bot_bot_bool),
    inference(definitional_conversion,[status(esa)],[f_25_1]) ).

cnf(f_25_3,plain,
    is_bool(bot_bot_bool),
    inference(clausify,[status(thm)],[f_25_2]) ).

fof(f_26_1,plain,
    is_fun_a_bool(bot_bot_fun_a_bool),
    inference(fof_nnf,[status(thm)],[gsy_c_Orderings_Obot__class_Obot_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).

fof(f_26_2,plain,
    is_fun_a_bool(bot_bot_fun_a_bool),
    inference(definitional_conversion,[status(esa)],[f_26_1]) ).

cnf(f_26_3,plain,
    is_fun_a_bool(bot_bot_fun_a_bool),
    inference(clausify,[status(thm)],[f_26_2]) ).

fof(f_27_1,plain,
    is_fun_pname_bool(bot_bo844097828e_bool),
    inference(fof_nnf,[status(thm)],[gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).

fof(f_27_2,plain,
    is_fun_pname_bool(bot_bo844097828e_bool),
    inference(definitional_conversion,[status(esa)],[f_27_1]) ).

cnf(f_27_3,plain,
    is_fun_pname_bool(bot_bo844097828e_bool),
    inference(clausify,[status(thm)],[f_27_2]) ).

fof(f_28_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_28_2,plain,
    ! [U_31] :
      ( is_fun_a_bool(collect_a(U_31))
      | ~ is_fun_a_bool(U_31) ),
    inference(variable_rename,[status(thm)],[f_28_1]) ).

fof(f_28_3,plain,
    ! [U_31] :
      ( is_fun_a_bool(collect_a(U_31))
      | ~ is_fun_a_bool(U_31) ),
    inference(definitional_conversion,[status(esa)],[f_28_2]) ).

cnf(f_28_4,plain,
    ( is_fun_a_bool(collect_a(U_31))
    | ~ is_fun_a_bool(U_31) ),
    inference(clausify,[status(thm)],[f_28_3]) ).

fof(f_29_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_29_2,plain,
    ! [U_32] :
      ( is_fun_pname_bool(collect_pname(U_32))
      | ~ is_fun_pname_bool(U_32) ),
    inference(variable_rename,[status(thm)],[f_29_1]) ).

fof(f_29_3,plain,
    ! [U_32] :
      ( is_fun_pname_bool(collect_pname(U_32))
      | ~ is_fun_pname_bool(U_32) ),
    inference(definitional_conversion,[status(esa)],[f_29_2]) ).

cnf(f_29_4,plain,
    ( is_fun_pname_bool(collect_pname(U_32))
    | ~ is_fun_pname_bool(U_32) ),
    inference(clausify,[status(thm)],[f_29_3]) ).

fof(f_30_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_30_2,plain,
    ! [U_33] :
      ( is_fun949378684l_bool(collect_fun_a_bool(U_33))
      | ~ is_fun949378684l_bool(U_33) ),
    inference(variable_rename,[status(thm)],[f_30_1]) ).

fof(f_30_3,plain,
    ! [U_33] :
      ( is_fun949378684l_bool(collect_fun_a_bool(U_33))
      | ~ is_fun949378684l_bool(U_33) ),
    inference(definitional_conversion,[status(esa)],[f_30_2]) ).

cnf(f_30_4,plain,
    ( is_fun949378684l_bool(collect_fun_a_bool(U_33))
    | ~ is_fun949378684l_bool(U_33) ),
    inference(clausify,[status(thm)],[f_30_3]) ).

fof(f_31_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_31_2,plain,
    ! [U_34] :
      ( is_fun1661590463l_bool(collec1974731493e_bool(U_34))
      | ~ is_fun1661590463l_bool(U_34) ),
    inference(variable_rename,[status(thm)],[f_31_1]) ).

fof(f_31_3,plain,
    ! [U_34] :
      ( is_fun1661590463l_bool(collec1974731493e_bool(U_34))
      | ~ is_fun1661590463l_bool(U_34) ),
    inference(definitional_conversion,[status(esa)],[f_31_2]) ).

cnf(f_31_4,plain,
    ( is_fun1661590463l_bool(collec1974731493e_bool(U_34))
    | ~ is_fun1661590463l_bool(U_34) ),
    inference(clausify,[status(thm)],[f_31_3]) ).

fof(f_32_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun_a_bool(image_a_a(B_1_1,B_2_1))
      | ~ is_fun_a_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000t__a_000t__a]) ).

fof(f_32_2,plain,
    ! [U_36,U_35] :
      ( is_fun_a_bool(image_a_a(U_36,U_35))
      | ~ is_fun_a_bool(U_35) ),
    inference(variable_rename,[status(thm)],[f_32_1]) ).

fof(f_32_3,plain,
    ! [U_36,U_35] :
      ( is_fun_a_bool(image_a_a(U_36,U_35))
      | ~ is_fun_a_bool(U_35) ),
    inference(definitional_conversion,[status(esa)],[f_32_2]) ).

cnf(f_32_4,plain,
    ( is_fun_a_bool(image_a_a(U_36,U_35))
    | ~ is_fun_a_bool(U_35) ),
    inference(clausify,[status(thm)],[f_32_3]) ).

fof(f_33_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun_pname_bool(image_a_pname(B_1_1,B_2_1))
      | ~ is_fun_a_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000t__a_000tc__Com__Opname]) ).

fof(f_33_2,plain,
    ! [U_38,U_37] :
      ( is_fun_pname_bool(image_a_pname(U_38,U_37))
      | ~ is_fun_a_bool(U_37) ),
    inference(variable_rename,[status(thm)],[f_33_1]) ).

fof(f_33_3,plain,
    ! [U_37,U_38] :
      ( is_fun_pname_bool(image_a_pname(U_38,U_37))
      | ~ is_fun_a_bool(U_37) ),
    inference(definitional_conversion,[status(esa)],[f_33_2]) ).

cnf(f_33_4,plain,
    ( is_fun_pname_bool(image_a_pname(U_38,U_37))
    | ~ is_fun_a_bool(U_37) ),
    inference(clausify,[status(thm)],[f_33_3]) ).

fof(f_34_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun949378684l_bool(image_a_fun_a_bool(B_1_1,B_2_1))
      | ~ is_fun_a_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).

fof(f_34_2,plain,
    ! [U_40,U_39] :
      ( is_fun949378684l_bool(image_a_fun_a_bool(U_40,U_39))
      | ~ is_fun_a_bool(U_39) ),
    inference(variable_rename,[status(thm)],[f_34_1]) ).

fof(f_34_3,plain,
    ! [U_39,U_40] :
      ( is_fun949378684l_bool(image_a_fun_a_bool(U_40,U_39))
      | ~ is_fun_a_bool(U_39) ),
    inference(definitional_conversion,[status(esa)],[f_34_2]) ).

cnf(f_34_4,plain,
    ( is_fun949378684l_bool(image_a_fun_a_bool(U_40,U_39))
    | ~ is_fun_a_bool(U_39) ),
    inference(clausify,[status(thm)],[f_34_3]) ).

fof(f_35_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1661590463l_bool(image_819518260e_bool(B_1_1,B_2_1))
      | ~ is_fun_a_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).

fof(f_35_2,plain,
    ! [U_42,U_41] :
      ( is_fun1661590463l_bool(image_819518260e_bool(U_42,U_41))
      | ~ is_fun_a_bool(U_41) ),
    inference(variable_rename,[status(thm)],[f_35_1]) ).

fof(f_35_3,plain,
    ! [U_41,U_42] :
      ( is_fun1661590463l_bool(image_819518260e_bool(U_42,U_41))
      | ~ is_fun_a_bool(U_41) ),
    inference(definitional_conversion,[status(esa)],[f_35_2]) ).

cnf(f_35_4,plain,
    ( is_fun1661590463l_bool(image_819518260e_bool(U_42,U_41))
    | ~ is_fun_a_bool(U_41) ),
    inference(clausify,[status(thm)],[f_35_3]) ).

fof(f_36_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun_a_bool(image_pname_a(B_1_1,B_2_1))
      | ~ is_fun_pname_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Com__Opname_000t__a]) ).

fof(f_36_2,plain,
    ! [U_44,U_43] :
      ( is_fun_a_bool(image_pname_a(U_44,U_43))
      | ~ is_fun_pname_bool(U_43) ),
    inference(variable_rename,[status(thm)],[f_36_1]) ).

fof(f_36_3,plain,
    ! [U_43,U_44] :
      ( is_fun_a_bool(image_pname_a(U_44,U_43))
      | ~ is_fun_pname_bool(U_43) ),
    inference(definitional_conversion,[status(esa)],[f_36_2]) ).

cnf(f_36_4,plain,
    ( is_fun_a_bool(image_pname_a(U_44,U_43))
    | ~ is_fun_pname_bool(U_43) ),
    inference(clausify,[status(thm)],[f_36_3]) ).

fof(f_37_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun_pname_bool(image_pname_pname(B_1_1,B_2_1))
      | ~ is_fun_pname_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname]) ).

fof(f_37_2,plain,
    ! [U_46,U_45] :
      ( is_fun_pname_bool(image_pname_pname(U_46,U_45))
      | ~ is_fun_pname_bool(U_45) ),
    inference(variable_rename,[status(thm)],[f_37_1]) ).

fof(f_37_3,plain,
    ! [U_45,U_46] :
      ( is_fun_pname_bool(image_pname_pname(U_46,U_45))
      | ~ is_fun_pname_bool(U_45) ),
    inference(definitional_conversion,[status(esa)],[f_37_2]) ).

cnf(f_37_4,plain,
    ( is_fun_pname_bool(image_pname_pname(U_46,U_45))
    | ~ is_fun_pname_bool(U_45) ),
    inference(clausify,[status(thm)],[f_37_3]) ).

fof(f_38_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun949378684l_bool(image_112932426a_bool(B_1_1,B_2_1))
      | ~ is_fun_pname_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).

fof(f_38_2,plain,
    ! [U_48,U_47] :
      ( is_fun949378684l_bool(image_112932426a_bool(U_48,U_47))
      | ~ is_fun_pname_bool(U_47) ),
    inference(variable_rename,[status(thm)],[f_38_1]) ).

fof(f_38_3,plain,
    ! [U_47,U_48] :
      ( is_fun949378684l_bool(image_112932426a_bool(U_48,U_47))
      | ~ is_fun_pname_bool(U_47) ),
    inference(definitional_conversion,[status(esa)],[f_38_2]) ).

cnf(f_38_4,plain,
    ( is_fun949378684l_bool(image_112932426a_bool(U_48,U_47))
    | ~ is_fun_pname_bool(U_47) ),
    inference(clausify,[status(thm)],[f_38_3]) ).

fof(f_39_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1661590463l_bool(image_47868345e_bool(B_1_1,B_2_1))
      | ~ is_fun_pname_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_]) ).

fof(f_39_2,plain,
    ! [U_50,U_49] :
      ( is_fun1661590463l_bool(image_47868345e_bool(U_50,U_49))
      | ~ is_fun_pname_bool(U_49) ),
    inference(variable_rename,[status(thm)],[f_39_1]) ).

fof(f_39_3,plain,
    ! [U_49,U_50] :
      ( is_fun1661590463l_bool(image_47868345e_bool(U_50,U_49))
      | ~ is_fun_pname_bool(U_49) ),
    inference(definitional_conversion,[status(esa)],[f_39_2]) ).

cnf(f_39_4,plain,
    ( is_fun1661590463l_bool(image_47868345e_bool(U_50,U_49))
    | ~ is_fun_pname_bool(U_49) ),
    inference(clausify,[status(thm)],[f_39_3]) ).

fof(f_40_1,plain,
    ! [B_1_1,B_2_1] : is_fun_a_bool(image_int_a(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Int__Oint_000t__a]) ).

fof(f_40_2,plain,
    ! [U_52,U_51] : is_fun_a_bool(image_int_a(U_52,U_51)),
    inference(variable_rename,[status(thm)],[f_40_1]) ).

fof(f_40_3,plain,
    ! [U_51,U_52] : is_fun_a_bool(image_int_a(U_52,U_51)),
    inference(definitional_conversion,[status(esa)],[f_40_2]) ).

cnf(f_40_4,plain,
    is_fun_a_bool(image_int_a(U_52,U_51)),
    inference(clausify,[status(thm)],[f_40_3]) ).

fof(f_41_1,plain,
    ! [B_1_1,B_2_1] : is_fun_pname_bool(image_int_pname(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Int__Oint_000tc__Com__Opname]) ).

fof(f_41_2,plain,
    ! [U_54,U_53] : is_fun_pname_bool(image_int_pname(U_54,U_53)),
    inference(variable_rename,[status(thm)],[f_41_1]) ).

fof(f_41_3,plain,
    ! [U_53,U_54] : is_fun_pname_bool(image_int_pname(U_54,U_53)),
    inference(definitional_conversion,[status(esa)],[f_41_2]) ).

cnf(f_41_4,plain,
    is_fun_pname_bool(image_int_pname(U_54,U_53)),
    inference(clausify,[status(thm)],[f_41_3]) ).

fof(f_42_1,plain,
    ! [B_1_1,B_2_1] : is_fun949378684l_bool(image_int_fun_a_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).

fof(f_42_2,plain,
    ! [U_56,U_55] : is_fun949378684l_bool(image_int_fun_a_bool(U_56,U_55)),
    inference(variable_rename,[status(thm)],[f_42_1]) ).

fof(f_42_3,plain,
    ! [U_55,U_56] : is_fun949378684l_bool(image_int_fun_a_bool(U_56,U_55)),
    inference(definitional_conversion,[status(esa)],[f_42_2]) ).

cnf(f_42_4,plain,
    is_fun949378684l_bool(image_int_fun_a_bool(U_56,U_55)),
    inference(clausify,[status(thm)],[f_42_3]) ).

fof(f_43_1,plain,
    ! [B_1_1,B_2_1] : is_fun1661590463l_bool(image_637364955e_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).

fof(f_43_2,plain,
    ! [U_58,U_57] : is_fun1661590463l_bool(image_637364955e_bool(U_58,U_57)),
    inference(variable_rename,[status(thm)],[f_43_1]) ).

fof(f_43_3,plain,
    ! [U_57,U_58] : is_fun1661590463l_bool(image_637364955e_bool(U_58,U_57)),
    inference(definitional_conversion,[status(esa)],[f_43_2]) ).

cnf(f_43_4,plain,
    is_fun1661590463l_bool(image_637364955e_bool(U_58,U_57)),
    inference(clausify,[status(thm)],[f_43_3]) ).

fof(f_44_1,plain,
    ! [B_1_1,B_2_1] : is_fun_a_bool(image_nat_a(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a]) ).

fof(f_44_2,plain,
    ! [U_60,U_59] : is_fun_a_bool(image_nat_a(U_60,U_59)),
    inference(variable_rename,[status(thm)],[f_44_1]) ).

fof(f_44_3,plain,
    ! [U_59,U_60] : is_fun_a_bool(image_nat_a(U_60,U_59)),
    inference(definitional_conversion,[status(esa)],[f_44_2]) ).

cnf(f_44_4,plain,
    is_fun_a_bool(image_nat_a(U_60,U_59)),
    inference(clausify,[status(thm)],[f_44_3]) ).

fof(f_45_1,plain,
    ! [B_1_1,B_2_1] : is_fun_pname_bool(image_nat_pname(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname]) ).

fof(f_45_2,plain,
    ! [U_62,U_61] : is_fun_pname_bool(image_nat_pname(U_62,U_61)),
    inference(variable_rename,[status(thm)],[f_45_1]) ).

fof(f_45_3,plain,
    ! [U_61,U_62] : is_fun_pname_bool(image_nat_pname(U_62,U_61)),
    inference(definitional_conversion,[status(esa)],[f_45_2]) ).

cnf(f_45_4,plain,
    is_fun_pname_bool(image_nat_pname(U_62,U_61)),
    inference(clausify,[status(thm)],[f_45_3]) ).

fof(f_46_1,plain,
    ! [B_1_1,B_2_1] : is_fun949378684l_bool(image_nat_fun_a_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).

fof(f_46_2,plain,
    ! [U_64,U_63] : is_fun949378684l_bool(image_nat_fun_a_bool(U_64,U_63)),
    inference(variable_rename,[status(thm)],[f_46_1]) ).

fof(f_46_3,plain,
    ! [U_63,U_64] : is_fun949378684l_bool(image_nat_fun_a_bool(U_64,U_63)),
    inference(definitional_conversion,[status(esa)],[f_46_2]) ).

cnf(f_46_4,plain,
    is_fun949378684l_bool(image_nat_fun_a_bool(U_64,U_63)),
    inference(clausify,[status(thm)],[f_46_3]) ).

fof(f_47_1,plain,
    ! [B_1_1,B_2_1] : is_fun1661590463l_bool(image_1655916159e_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).

fof(f_47_2,plain,
    ! [U_66,U_65] : is_fun1661590463l_bool(image_1655916159e_bool(U_66,U_65)),
    inference(variable_rename,[status(thm)],[f_47_1]) ).

fof(f_47_3,plain,
    ! [U_65,U_66] : is_fun1661590463l_bool(image_1655916159e_bool(U_66,U_65)),
    inference(definitional_conversion,[status(esa)],[f_47_2]) ).

cnf(f_47_4,plain,
    is_fun1661590463l_bool(image_1655916159e_bool(U_66,U_65)),
    inference(clausify,[status(thm)],[f_47_3]) ).

fof(f_48_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun_a_bool(image_fun_a_bool_a(B_1_1,B_2_1))
      | ~ is_fun949378684l_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a]) ).

fof(f_48_2,plain,
    ! [U_68,U_67] :
      ( is_fun_a_bool(image_fun_a_bool_a(U_68,U_67))
      | ~ is_fun949378684l_bool(U_67) ),
    inference(variable_rename,[status(thm)],[f_48_1]) ).

fof(f_48_3,plain,
    ! [U_67,U_68] :
      ( is_fun_a_bool(image_fun_a_bool_a(U_68,U_67))
      | ~ is_fun949378684l_bool(U_67) ),
    inference(definitional_conversion,[status(esa)],[f_48_2]) ).

cnf(f_48_4,plain,
    ( is_fun_a_bool(image_fun_a_bool_a(U_68,U_67))
    | ~ is_fun949378684l_bool(U_67) ),
    inference(clausify,[status(thm)],[f_48_3]) ).

fof(f_49_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun_pname_bool(image_1854862208_pname(B_1_1,B_2_1))
      | ~ is_fun949378684l_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname]) ).

fof(f_49_2,plain,
    ! [U_70,U_69] :
      ( is_fun_pname_bool(image_1854862208_pname(U_70,U_69))
      | ~ is_fun949378684l_bool(U_69) ),
    inference(variable_rename,[status(thm)],[f_49_1]) ).

fof(f_49_3,plain,
    ! [U_69,U_70] :
      ( is_fun_pname_bool(image_1854862208_pname(U_70,U_69))
      | ~ is_fun949378684l_bool(U_69) ),
    inference(definitional_conversion,[status(esa)],[f_49_2]) ).

cnf(f_49_4,plain,
    ( is_fun_pname_bool(image_1854862208_pname(U_70,U_69))
    | ~ is_fun949378684l_bool(U_69) ),
    inference(clausify,[status(thm)],[f_49_3]) ).

fof(f_50_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun_a_bool(image_876012084bool_a(B_1_1,B_2_1))
      | ~ is_fun1661590463l_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000t__a]) ).

fof(f_50_2,plain,
    ! [U_72,U_71] :
      ( is_fun_a_bool(image_876012084bool_a(U_72,U_71))
      | ~ is_fun1661590463l_bool(U_71) ),
    inference(variable_rename,[status(thm)],[f_50_1]) ).

fof(f_50_3,plain,
    ! [U_71,U_72] :
      ( is_fun_a_bool(image_876012084bool_a(U_72,U_71))
      | ~ is_fun1661590463l_bool(U_71) ),
    inference(definitional_conversion,[status(esa)],[f_50_2]) ).

cnf(f_50_4,plain,
    ( is_fun_a_bool(image_876012084bool_a(U_72,U_71))
    | ~ is_fun1661590463l_bool(U_71) ),
    inference(clausify,[status(thm)],[f_50_3]) ).

fof(f_51_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun_pname_bool(image_1283814551_pname(B_1_1,B_2_1))
      | ~ is_fun1661590463l_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opnam]) ).

fof(f_51_2,plain,
    ! [U_74,U_73] :
      ( is_fun_pname_bool(image_1283814551_pname(U_74,U_73))
      | ~ is_fun1661590463l_bool(U_73) ),
    inference(variable_rename,[status(thm)],[f_51_1]) ).

fof(f_51_3,plain,
    ! [U_73,U_74] :
      ( is_fun_pname_bool(image_1283814551_pname(U_74,U_73))
      | ~ is_fun1661590463l_bool(U_73) ),
    inference(definitional_conversion,[status(esa)],[f_51_2]) ).

cnf(f_51_4,plain,
    ( is_fun_pname_bool(image_1283814551_pname(U_74,U_73))
    | ~ is_fun1661590463l_bool(U_73) ),
    inference(clausify,[status(thm)],[f_51_3]) ).

fof(f_52_1,plain,
    ! [B_1_1,B_2_1] : is_fun_a_bool(image_fun_int_bool_a(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000t__a]) ).

fof(f_52_2,plain,
    ! [U_76,U_75] : is_fun_a_bool(image_fun_int_bool_a(U_76,U_75)),
    inference(variable_rename,[status(thm)],[f_52_1]) ).

fof(f_52_3,plain,
    ! [U_75,U_76] : is_fun_a_bool(image_fun_int_bool_a(U_76,U_75)),
    inference(definitional_conversion,[status(esa)],[f_52_2]) ).

cnf(f_52_4,plain,
    is_fun_a_bool(image_fun_int_bool_a(U_76,U_75)),
    inference(clausify,[status(thm)],[f_52_3]) ).

fof(f_53_1,plain,
    ! [B_1_1,B_2_1] : is_fun_pname_bool(image_62782965_pname(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__Com__Opname]) ).

fof(f_53_2,plain,
    ! [U_78,U_77] : is_fun_pname_bool(image_62782965_pname(U_78,U_77)),
    inference(variable_rename,[status(thm)],[f_53_1]) ).

fof(f_53_3,plain,
    ! [U_77,U_78] : is_fun_pname_bool(image_62782965_pname(U_78,U_77)),
    inference(definitional_conversion,[status(esa)],[f_53_2]) ).

cnf(f_53_4,plain,
    is_fun_pname_bool(image_62782965_pname(U_78,U_77)),
    inference(clausify,[status(thm)],[f_53_3]) ).

fof(f_54_1,plain,
    ! [B_1_1,B_2_1] : is_fun_a_bool(image_fun_nat_bool_a(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000t__a]) ).

fof(f_54_2,plain,
    ! [U_80,U_79] : is_fun_a_bool(image_fun_nat_bool_a(U_80,U_79)),
    inference(variable_rename,[status(thm)],[f_54_1]) ).

fof(f_54_3,plain,
    ! [U_79,U_80] : is_fun_a_bool(image_fun_nat_bool_a(U_80,U_79)),
    inference(definitional_conversion,[status(esa)],[f_54_2]) ).

cnf(f_54_4,plain,
    is_fun_a_bool(image_fun_nat_bool_a(U_80,U_79)),
    inference(clausify,[status(thm)],[f_54_3]) ).

fof(f_55_1,plain,
    ! [B_1_1,B_2_1] : is_fun_pname_bool(image_1921560913_pname(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname]) ).

fof(f_55_2,plain,
    ! [U_82,U_81] : is_fun_pname_bool(image_1921560913_pname(U_82,U_81)),
    inference(variable_rename,[status(thm)],[f_55_1]) ).

fof(f_55_3,plain,
    ! [U_81,U_82] : is_fun_pname_bool(image_1921560913_pname(U_82,U_81)),
    inference(definitional_conversion,[status(esa)],[f_55_2]) ).

cnf(f_55_4,plain,
    is_fun_pname_bool(image_1921560913_pname(U_82,U_81)),
    inference(clausify,[status(thm)],[f_55_3]) ).

fof(f_56_1,plain,
    is_bool(fFalse),
    inference(fof_nnf,[status(thm)],[gsy_c_fFalse]) ).

fof(f_56_2,plain,
    is_bool(fFalse),
    inference(definitional_conversion,[status(esa)],[f_56_1]) ).

cnf(f_56_3,plain,
    is_bool(fFalse),
    inference(clausify,[status(thm)],[f_56_2]) ).

fof(f_57_1,plain,
    is_bool(fTrue),
    inference(fof_nnf,[status(thm)],[gsy_c_fTrue]) ).

fof(f_57_2,plain,
    is_bool(fTrue),
    inference(definitional_conversion,[status(esa)],[f_57_1]) ).

cnf(f_57_3,plain,
    is_bool(fTrue),
    inference(clausify,[status(thm)],[f_57_2]) ).

fof(f_58_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_a(hAPP_a_a(B_1_1,B_2_1))
      | ~ is_a(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000t__a_000t__a]) ).

fof(f_58_2,plain,
    ! [U_84,U_83] :
      ( is_a(hAPP_a_a(U_84,U_83))
      | ~ is_a(U_83) ),
    inference(variable_rename,[status(thm)],[f_58_1]) ).

fof(f_58_3,plain,
    ! [U_84,U_83] :
      ( is_a(hAPP_a_a(U_84,U_83))
      | ~ is_a(U_83) ),
    inference(definitional_conversion,[status(esa)],[f_58_2]) ).

cnf(f_58_4,plain,
    ( is_a(hAPP_a_a(U_84,U_83))
    | ~ is_a(U_83) ),
    inference(clausify,[status(thm)],[f_58_3]) ).

fof(f_59_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_a_bool(B_1_1,B_2_1))
      | ~ is_a(B_2_1)
      | ~ is_fun_a_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000t__a_000tc__HOL__Obool]) ).

fof(f_59_2,plain,
    ! [U_86,U_85] :
      ( is_bool(hAPP_a_bool(U_86,U_85))
      | ~ is_a(U_85)
      | ~ is_fun_a_bool(U_86) ),
    inference(variable_rename,[status(thm)],[f_59_1]) ).

fof(f_59_3,plain,
    ! [U_86,U_85] :
      ( is_bool(hAPP_a_bool(U_86,U_85))
      | ~ is_a(U_85)
      | ~ is_fun_a_bool(U_86) ),
    inference(definitional_conversion,[status(esa)],[f_59_2]) ).

cnf(f_59_4,plain,
    ( is_bool(hAPP_a_bool(U_86,U_85))
    | ~ is_a(U_85)
    | ~ is_fun_a_bool(U_86) ),
    inference(clausify,[status(thm)],[f_59_3]) ).

fof(f_60_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun_a_bool(hAPP_a_fun_a_bool(B_1_1,B_2_1))
      | ~ is_a(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).

fof(f_60_2,plain,
    ! [U_88,U_87] :
      ( is_fun_a_bool(hAPP_a_fun_a_bool(U_88,U_87))
      | ~ is_a(U_87) ),
    inference(variable_rename,[status(thm)],[f_60_1]) ).

fof(f_60_3,plain,
    ! [U_88,U_87] :
      ( is_fun_a_bool(hAPP_a_fun_a_bool(U_88,U_87))
      | ~ is_a(U_87) ),
    inference(definitional_conversion,[status(esa)],[f_60_2]) ).

cnf(f_60_4,plain,
    ( is_fun_a_bool(hAPP_a_fun_a_bool(U_88,U_87))
    | ~ is_a(U_87) ),
    inference(clausify,[status(thm)],[f_60_3]) ).

fof(f_61_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun_pname_bool(hAPP_a93125764e_bool(B_1_1,B_2_1))
      | ~ is_a(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).

fof(f_61_2,plain,
    ! [U_90,U_89] :
      ( is_fun_pname_bool(hAPP_a93125764e_bool(U_90,U_89))
      | ~ is_a(U_89) ),
    inference(variable_rename,[status(thm)],[f_61_1]) ).

fof(f_61_3,plain,
    ! [U_89,U_90] :
      ( is_fun_pname_bool(hAPP_a93125764e_bool(U_90,U_89))
      | ~ is_a(U_89) ),
    inference(definitional_conversion,[status(esa)],[f_61_2]) ).

cnf(f_61_4,plain,
    ( is_fun_pname_bool(hAPP_a93125764e_bool(U_90,U_89))
    | ~ is_a(U_89) ),
    inference(clausify,[status(thm)],[f_61_3]) ).

fof(f_62_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun949378684l_bool(hAPP_a85458249l_bool(B_1_1,B_2_1))
      | ~ is_a(B_2_1) ),
    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_62_2,plain,
    ! [U_92,U_91] :
      ( is_fun949378684l_bool(hAPP_a85458249l_bool(U_92,U_91))
      | ~ is_a(U_91) ),
    inference(variable_rename,[status(thm)],[f_62_1]) ).

fof(f_62_3,plain,
    ! [U_91,U_92] :
      ( is_fun949378684l_bool(hAPP_a85458249l_bool(U_92,U_91))
      | ~ is_a(U_91) ),
    inference(definitional_conversion,[status(esa)],[f_62_2]) ).

cnf(f_62_4,plain,
    ( is_fun949378684l_bool(hAPP_a85458249l_bool(U_92,U_91))
    | ~ is_a(U_91) ),
    inference(clausify,[status(thm)],[f_62_3]) ).

fof(f_63_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_a(hAPP_pname_a(B_1_1,B_2_1))
      | ~ is_pname(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000t__a]) ).

fof(f_63_2,plain,
    ! [U_94,U_93] :
      ( is_a(hAPP_pname_a(U_94,U_93))
      | ~ is_pname(U_93) ),
    inference(variable_rename,[status(thm)],[f_63_1]) ).

fof(f_63_3,plain,
    ! [U_94,U_93] :
      ( is_a(hAPP_pname_a(U_94,U_93))
      | ~ is_pname(U_93) ),
    inference(definitional_conversion,[status(esa)],[f_63_2]) ).

cnf(f_63_4,plain,
    ( is_a(hAPP_pname_a(U_94,U_93))
    | ~ is_pname(U_93) ),
    inference(clausify,[status(thm)],[f_63_3]) ).

fof(f_64_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_pname(hAPP_pname_pname(B_1_1,B_2_1))
      | ~ is_pname(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000tc__Com__Opname]) ).

fof(f_64_2,plain,
    ! [U_96,U_95] :
      ( is_pname(hAPP_pname_pname(U_96,U_95))
      | ~ is_pname(U_95) ),
    inference(variable_rename,[status(thm)],[f_64_1]) ).

fof(f_64_3,plain,
    ! [U_96,U_95] :
      ( is_pname(hAPP_pname_pname(U_96,U_95))
      | ~ is_pname(U_95) ),
    inference(definitional_conversion,[status(esa)],[f_64_2]) ).

cnf(f_64_4,plain,
    ( is_pname(hAPP_pname_pname(U_96,U_95))
    | ~ is_pname(U_95) ),
    inference(clausify,[status(thm)],[f_64_3]) ).

fof(f_65_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_pname_bool(B_1_1,B_2_1))
      | ~ is_pname(B_2_1)
      | ~ is_fun_pname_bool(B_1_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool]) ).

fof(f_65_2,plain,
    ! [U_98,U_97] :
      ( is_bool(hAPP_pname_bool(U_98,U_97))
      | ~ is_pname(U_97)
      | ~ is_fun_pname_bool(U_98) ),
    inference(variable_rename,[status(thm)],[f_65_1]) ).

fof(f_65_3,plain,
    ! [U_97,U_98] :
      ( is_bool(hAPP_pname_bool(U_98,U_97))
      | ~ is_pname(U_97)
      | ~ is_fun_pname_bool(U_98) ),
    inference(definitional_conversion,[status(esa)],[f_65_2]) ).

cnf(f_65_4,plain,
    ( is_bool(hAPP_pname_bool(U_98,U_97))
    | ~ is_pname(U_97)
    | ~ is_fun_pname_bool(U_98) ),
    inference(clausify,[status(thm)],[f_65_3]) ).

fof(f_66_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun_a_bool(hAPP_p1534023578a_bool(B_1_1,B_2_1))
      | ~ is_pname(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).

fof(f_66_2,plain,
    ! [U_100,U_99] :
      ( is_fun_a_bool(hAPP_p1534023578a_bool(U_100,U_99))
      | ~ is_pname(U_99) ),
    inference(variable_rename,[status(thm)],[f_66_1]) ).

fof(f_66_3,plain,
    ! [U_100,U_99] :
      ( is_fun_a_bool(hAPP_p1534023578a_bool(U_100,U_99))
      | ~ is_pname(U_99) ),
    inference(definitional_conversion,[status(esa)],[f_66_2]) ).

cnf(f_66_4,plain,
    ( is_fun_a_bool(hAPP_p1534023578a_bool(U_100,U_99))
    | ~ is_pname(U_99) ),
    inference(clausify,[status(thm)],[f_66_3]) ).

fof(f_67_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun_pname_bool(hAPP_p61793385e_bool(B_1_1,B_2_1))
      | ~ is_pname(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).

fof(f_67_2,plain,
    ! [U_102,U_101] :
      ( is_fun_pname_bool(hAPP_p61793385e_bool(U_102,U_101))
      | ~ is_pname(U_101) ),
    inference(variable_rename,[status(thm)],[f_67_1]) ).

fof(f_67_3,plain,
    ! [U_102,U_101] :
      ( is_fun_pname_bool(hAPP_p61793385e_bool(U_102,U_101))
      | ~ is_pname(U_101) ),
    inference(definitional_conversion,[status(esa)],[f_67_2]) ).

cnf(f_67_4,plain,
    ( is_fun_pname_bool(hAPP_p61793385e_bool(U_102,U_101))
    | ~ is_pname(U_101) ),
    inference(clausify,[status(thm)],[f_67_3]) ).

fof(f_68_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1661590463l_bool(hAPP_p338031245l_bool(B_1_1,B_2_1))
      | ~ is_pname(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo]) ).

fof(f_68_2,plain,
    ! [U_104,U_103] :
      ( is_fun1661590463l_bool(hAPP_p338031245l_bool(U_104,U_103))
      | ~ is_pname(U_103) ),
    inference(variable_rename,[status(thm)],[f_68_1]) ).

fof(f_68_3,plain,
    ! [U_103,U_104] :
      ( is_fun1661590463l_bool(hAPP_p338031245l_bool(U_104,U_103))
      | ~ is_pname(U_103) ),
    inference(definitional_conversion,[status(esa)],[f_68_2]) ).

cnf(f_68_4,plain,
    ( is_fun1661590463l_bool(hAPP_p338031245l_bool(U_104,U_103))
    | ~ is_pname(U_103) ),
    inference(clausify,[status(thm)],[f_68_3]) ).

fof(f_69_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_bool_bool(B_1_1,B_2_1))
      | ~ is_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool]) ).

fof(f_69_2,plain,
    ! [U_106,U_105] :
      ( is_bool(hAPP_bool_bool(U_106,U_105))
      | ~ is_bool(U_105) ),
    inference(variable_rename,[status(thm)],[f_69_1]) ).

fof(f_69_3,plain,
    ! [U_105,U_106] :
      ( is_bool(hAPP_bool_bool(U_106,U_105))
      | ~ is_bool(U_105) ),
    inference(definitional_conversion,[status(esa)],[f_69_2]) ).

cnf(f_69_4,plain,
    ( is_bool(hAPP_bool_bool(U_106,U_105))
    | ~ is_bool(U_105) ),
    inference(clausify,[status(thm)],[f_69_3]) ).

fof(f_70_1,plain,
    ! [B_1_1,B_2_1] : is_a(hAPP_int_a(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Int__Oint_000t__a]) ).

fof(f_70_2,plain,
    ! [U_108,U_107] : is_a(hAPP_int_a(U_108,U_107)),
    inference(variable_rename,[status(thm)],[f_70_1]) ).

fof(f_70_3,plain,
    ! [U_107,U_108] : is_a(hAPP_int_a(U_108,U_107)),
    inference(definitional_conversion,[status(esa)],[f_70_2]) ).

cnf(f_70_4,plain,
    is_a(hAPP_int_a(U_108,U_107)),
    inference(clausify,[status(thm)],[f_70_3]) ).

fof(f_71_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_int_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Int__Oint_000tc__HOL__Obool]) ).

fof(f_71_2,plain,
    ! [U_110,U_109] : is_bool(hAPP_int_bool(U_110,U_109)),
    inference(variable_rename,[status(thm)],[f_71_1]) ).

fof(f_71_3,plain,
    ! [U_109,U_110] : is_bool(hAPP_int_bool(U_110,U_109)),
    inference(definitional_conversion,[status(esa)],[f_71_2]) ).

cnf(f_71_4,plain,
    is_bool(hAPP_int_bool(U_110,U_109)),
    inference(clausify,[status(thm)],[f_71_3]) ).

fof(f_72_1,plain,
    ! [B_1_1,B_2_1] : is_fun_a_bool(hAPP_int_fun_a_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).

fof(f_72_2,plain,
    ! [U_112,U_111] : is_fun_a_bool(hAPP_int_fun_a_bool(U_112,U_111)),
    inference(variable_rename,[status(thm)],[f_72_1]) ).

fof(f_72_3,plain,
    ! [U_111,U_112] : is_fun_a_bool(hAPP_int_fun_a_bool(U_112,U_111)),
    inference(definitional_conversion,[status(esa)],[f_72_2]) ).

cnf(f_72_4,plain,
    is_fun_a_bool(hAPP_int_fun_a_bool(U_112,U_111)),
    inference(clausify,[status(thm)],[f_72_3]) ).

fof(f_73_1,plain,
    ! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_i7355787e_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).

fof(f_73_2,plain,
    ! [U_114,U_113] : is_fun_pname_bool(hAPP_i7355787e_bool(U_114,U_113)),
    inference(variable_rename,[status(thm)],[f_73_1]) ).

fof(f_73_3,plain,
    ! [U_113,U_114] : is_fun_pname_bool(hAPP_i7355787e_bool(U_114,U_113)),
    inference(definitional_conversion,[status(esa)],[f_73_2]) ).

cnf(f_73_4,plain,
    is_fun_pname_bool(hAPP_i7355787e_bool(U_114,U_113)),
    inference(clausify,[status(thm)],[f_73_3]) ).

fof(f_74_1,plain,
    ! [B_1_1,B_2_1] : is_fun949378684l_bool(hAPP_i888906320l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL]) ).

fof(f_74_2,plain,
    ! [U_116,U_115] : is_fun949378684l_bool(hAPP_i888906320l_bool(U_116,U_115)),
    inference(variable_rename,[status(thm)],[f_74_1]) ).

fof(f_74_3,plain,
    ! [U_115,U_116] : is_fun949378684l_bool(hAPP_i888906320l_bool(U_116,U_115)),
    inference(definitional_conversion,[status(esa)],[f_74_2]) ).

cnf(f_74_4,plain,
    is_fun949378684l_bool(hAPP_i888906320l_bool(U_116,U_115)),
    inference(clausify,[status(thm)],[f_74_3]) ).

fof(f_75_1,plain,
    ! [B_1_1,B_2_1] : is_fun1661590463l_bool(hAPP_i1587699435l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Int__Oint_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool]) ).

fof(f_75_2,plain,
    ! [U_118,U_117] : is_fun1661590463l_bool(hAPP_i1587699435l_bool(U_118,U_117)),
    inference(variable_rename,[status(thm)],[f_75_1]) ).

fof(f_75_3,plain,
    ! [U_117,U_118] : is_fun1661590463l_bool(hAPP_i1587699435l_bool(U_118,U_117)),
    inference(definitional_conversion,[status(esa)],[f_75_2]) ).

cnf(f_75_4,plain,
    is_fun1661590463l_bool(hAPP_i1587699435l_bool(U_118,U_117)),
    inference(clausify,[status(thm)],[f_75_3]) ).

fof(f_76_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_nat_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool]) ).

fof(f_76_2,plain,
    ! [U_120,U_119] : is_bool(hAPP_nat_bool(U_120,U_119)),
    inference(variable_rename,[status(thm)],[f_76_1]) ).

fof(f_76_3,plain,
    ! [U_119,U_120] : is_bool(hAPP_nat_bool(U_120,U_119)),
    inference(definitional_conversion,[status(esa)],[f_76_2]) ).

cnf(f_76_4,plain,
    is_bool(hAPP_nat_bool(U_120,U_119)),
    inference(clausify,[status(thm)],[f_76_3]) ).

fof(f_77_1,plain,
    ! [B_1_1,B_2_1] : is_fun_a_bool(hAPP_nat_fun_a_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J]) ).

fof(f_77_2,plain,
    ! [U_122,U_121] : is_fun_a_bool(hAPP_nat_fun_a_bool(U_122,U_121)),
    inference(variable_rename,[status(thm)],[f_77_1]) ).

fof(f_77_3,plain,
    ! [U_121,U_122] : is_fun_a_bool(hAPP_nat_fun_a_bool(U_122,U_121)),
    inference(definitional_conversion,[status(esa)],[f_77_2]) ).

cnf(f_77_4,plain,
    is_fun_a_bool(hAPP_nat_fun_a_bool(U_122,U_121)),
    inference(clausify,[status(thm)],[f_77_3]) ).

fof(f_78_1,plain,
    ! [B_1_1,B_2_1] : is_fun_pname_bool(hAPP_n1025906991e_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J]) ).

fof(f_78_2,plain,
    ! [U_124,U_123] : is_fun_pname_bool(hAPP_n1025906991e_bool(U_124,U_123)),
    inference(variable_rename,[status(thm)],[f_78_1]) ).

fof(f_78_3,plain,
    ! [U_123,U_124] : is_fun_pname_bool(hAPP_n1025906991e_bool(U_124,U_123)),
    inference(definitional_conversion,[status(esa)],[f_78_2]) ).

cnf(f_78_4,plain,
    is_fun_pname_bool(hAPP_n1025906991e_bool(U_124,U_123)),
    inference(clausify,[status(thm)],[f_78_3]) ).

fof(f_79_1,plain,
    ! [B_1_1,B_2_1] : is_fun949378684l_bool(hAPP_n1414589940l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL]) ).

fof(f_79_2,plain,
    ! [U_126,U_125] : is_fun949378684l_bool(hAPP_n1414589940l_bool(U_126,U_125)),
    inference(variable_rename,[status(thm)],[f_79_1]) ).

fof(f_79_3,plain,
    ! [U_125,U_126] : is_fun949378684l_bool(hAPP_n1414589940l_bool(U_126,U_125)),
    inference(definitional_conversion,[status(esa)],[f_79_2]) ).

cnf(f_79_4,plain,
    is_fun949378684l_bool(hAPP_n1414589940l_bool(U_126,U_125)),
    inference(clausify,[status(thm)],[f_79_3]) ).

fof(f_80_1,plain,
    ! [B_1_1,B_2_1] : is_fun1661590463l_bool(hAPP_n850744903l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool]) ).

fof(f_80_2,plain,
    ! [U_128,U_127] : is_fun1661590463l_bool(hAPP_n850744903l_bool(U_128,U_127)),
    inference(variable_rename,[status(thm)],[f_80_1]) ).

fof(f_80_3,plain,
    ! [U_127,U_128] : is_fun1661590463l_bool(hAPP_n850744903l_bool(U_128,U_127)),
    inference(definitional_conversion,[status(esa)],[f_80_2]) ).

cnf(f_80_4,plain,
    is_fun1661590463l_bool(hAPP_n850744903l_bool(U_128,U_127)),
    inference(clausify,[status(thm)],[f_80_3]) ).

fof(f_81_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_a(hAPP_fun_a_bool_a(B_1_1,B_2_1))
      | ~ is_fun_a_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a]) ).

fof(f_81_2,plain,
    ! [U_130,U_129] :
      ( is_a(hAPP_fun_a_bool_a(U_130,U_129))
      | ~ is_fun_a_bool(U_129) ),
    inference(variable_rename,[status(thm)],[f_81_1]) ).

fof(f_81_3,plain,
    ! [U_129,U_130] :
      ( is_a(hAPP_fun_a_bool_a(U_130,U_129))
      | ~ is_fun_a_bool(U_129) ),
    inference(definitional_conversion,[status(esa)],[f_81_2]) ).

cnf(f_81_4,plain,
    ( is_a(hAPP_fun_a_bool_a(U_130,U_129))
    | ~ is_fun_a_bool(U_129) ),
    inference(clausify,[status(thm)],[f_81_3]) ).

fof(f_82_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_fun_a_bool_bool(B_1_1,B_2_1))
      | ~ is_fun_a_bool(B_2_1)
      | ~ 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_82_2,plain,
    ! [U_132,U_131] :
      ( is_bool(hAPP_fun_a_bool_bool(U_132,U_131))
      | ~ is_fun_a_bool(U_131)
      | ~ is_fun949378684l_bool(U_132) ),
    inference(variable_rename,[status(thm)],[f_82_1]) ).

fof(f_82_3,plain,
    ! [U_131,U_132] :
      ( is_bool(hAPP_fun_a_bool_bool(U_132,U_131))
      | ~ is_fun_a_bool(U_131)
      | ~ is_fun949378684l_bool(U_132) ),
    inference(definitional_conversion,[status(esa)],[f_82_2]) ).

cnf(f_82_4,plain,
    ( is_bool(hAPP_fun_a_bool_bool(U_132,U_131))
    | ~ is_fun_a_bool(U_131)
    | ~ is_fun949378684l_bool(U_132) ),
    inference(clausify,[status(thm)],[f_82_3]) ).

fof(f_83_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun_a_bool(hAPP_f2050579477a_bool(B_1_1,B_2_1))
      | ~ is_fun_a_bool(B_2_1) ),
    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_83_2,plain,
    ! [U_134,U_133] :
      ( is_fun_a_bool(hAPP_f2050579477a_bool(U_134,U_133))
      | ~ is_fun_a_bool(U_133) ),
    inference(variable_rename,[status(thm)],[f_83_1]) ).

fof(f_83_3,plain,
    ! [U_134,U_133] :
      ( is_fun_a_bool(hAPP_f2050579477a_bool(U_134,U_133))
      | ~ is_fun_a_bool(U_133) ),
    inference(definitional_conversion,[status(esa)],[f_83_2]) ).

cnf(f_83_4,plain,
    ( is_fun_a_bool(hAPP_f2050579477a_bool(U_134,U_133))
    | ~ is_fun_a_bool(U_133) ),
    inference(clausify,[status(thm)],[f_83_3]) ).

fof(f_84_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun949378684l_bool(hAPP_f1631501043l_bool(B_1_1,B_2_1))
      | ~ is_fun_a_bool(B_2_1) ),
    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_84_2,plain,
    ! [U_136,U_135] :
      ( is_fun949378684l_bool(hAPP_f1631501043l_bool(U_136,U_135))
      | ~ is_fun_a_bool(U_135) ),
    inference(variable_rename,[status(thm)],[f_84_1]) ).

fof(f_84_3,plain,
    ! [U_135,U_136] :
      ( is_fun949378684l_bool(hAPP_f1631501043l_bool(U_136,U_135))
      | ~ is_fun_a_bool(U_135) ),
    inference(definitional_conversion,[status(esa)],[f_84_2]) ).

cnf(f_84_4,plain,
    ( is_fun949378684l_bool(hAPP_f1631501043l_bool(U_136,U_135))
    | ~ is_fun_a_bool(U_135) ),
    inference(clausify,[status(thm)],[f_84_3]) ).

fof(f_85_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_pname(hAPP_f1297739591_pname(B_1_1,B_2_1))
      | ~ is_fun_pname_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opname]) ).

fof(f_85_2,plain,
    ! [U_138,U_137] :
      ( is_pname(hAPP_f1297739591_pname(U_138,U_137))
      | ~ is_fun_pname_bool(U_137) ),
    inference(variable_rename,[status(thm)],[f_85_1]) ).

fof(f_85_3,plain,
    ! [U_137,U_138] :
      ( is_pname(hAPP_f1297739591_pname(U_138,U_137))
      | ~ is_fun_pname_bool(U_137) ),
    inference(definitional_conversion,[status(esa)],[f_85_2]) ).

cnf(f_85_4,plain,
    ( is_pname(hAPP_f1297739591_pname(U_138,U_137))
    | ~ is_fun_pname_bool(U_137) ),
    inference(clausify,[status(thm)],[f_85_3]) ).

fof(f_86_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_f1664156314l_bool(B_1_1,B_2_1))
      | ~ is_fun_pname_bool(B_2_1)
      | ~ 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_86_2,plain,
    ! [U_140,U_139] :
      ( is_bool(hAPP_f1664156314l_bool(U_140,U_139))
      | ~ is_fun_pname_bool(U_139)
      | ~ is_fun1661590463l_bool(U_140) ),
    inference(variable_rename,[status(thm)],[f_86_1]) ).

fof(f_86_3,plain,
    ! [U_139,U_140] :
      ( is_bool(hAPP_f1664156314l_bool(U_140,U_139))
      | ~ is_fun_pname_bool(U_139)
      | ~ is_fun1661590463l_bool(U_140) ),
    inference(definitional_conversion,[status(esa)],[f_86_2]) ).

cnf(f_86_4,plain,
    ( is_bool(hAPP_f1664156314l_bool(U_140,U_139))
    | ~ is_fun_pname_bool(U_139)
    | ~ is_fun1661590463l_bool(U_140) ),
    inference(clausify,[status(thm)],[f_86_3]) ).

fof(f_87_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun_pname_bool(hAPP_f759274231e_bool(B_1_1,B_2_1))
      | ~ is_fun_pname_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op]) ).

fof(f_87_2,plain,
    ! [U_142,U_141] :
      ( is_fun_pname_bool(hAPP_f759274231e_bool(U_142,U_141))
      | ~ is_fun_pname_bool(U_141) ),
    inference(variable_rename,[status(thm)],[f_87_1]) ).

fof(f_87_3,plain,
    ! [U_142,U_141] :
      ( is_fun_pname_bool(hAPP_f759274231e_bool(U_142,U_141))
      | ~ is_fun_pname_bool(U_141) ),
    inference(definitional_conversion,[status(esa)],[f_87_2]) ).

cnf(f_87_4,plain,
    ( is_fun_pname_bool(hAPP_f759274231e_bool(U_142,U_141))
    | ~ is_fun_pname_bool(U_141) ),
    inference(clausify,[status(thm)],[f_87_3]) ).

fof(f_88_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1661590463l_bool(hAPP_f434788991l_bool(B_1_1,B_2_1))
      | ~ is_fun_pname_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc]) ).

fof(f_88_2,plain,
    ! [U_144,U_143] :
      ( is_fun1661590463l_bool(hAPP_f434788991l_bool(U_144,U_143))
      | ~ is_fun_pname_bool(U_143) ),
    inference(variable_rename,[status(thm)],[f_88_1]) ).

fof(f_88_3,plain,
    ! [U_143,U_144] :
      ( is_fun1661590463l_bool(hAPP_f434788991l_bool(U_144,U_143))
      | ~ is_fun_pname_bool(U_143) ),
    inference(definitional_conversion,[status(esa)],[f_88_2]) ).

cnf(f_88_4,plain,
    ( is_fun1661590463l_bool(hAPP_f434788991l_bool(U_144,U_143))
    | ~ is_fun_pname_bool(U_143) ),
    inference(clausify,[status(thm)],[f_88_3]) ).

fof(f_89_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f448129468l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obool]) ).

fof(f_89_2,plain,
    ! [U_146,U_145] : is_bool(hAPP_f448129468l_bool(U_146,U_145)),
    inference(variable_rename,[status(thm)],[f_89_1]) ).

fof(f_89_3,plain,
    ! [U_145,U_146] : is_bool(hAPP_f448129468l_bool(U_146,U_145)),
    inference(definitional_conversion,[status(esa)],[f_89_2]) ).

cnf(f_89_4,plain,
    is_bool(hAPP_f448129468l_bool(U_146,U_145)),
    inference(clausify,[status(thm)],[f_89_3]) ).

fof(f_90_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f54304608l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool]) ).

fof(f_90_2,plain,
    ! [U_148,U_147] : is_bool(hAPP_f54304608l_bool(U_148,U_147)),
    inference(variable_rename,[status(thm)],[f_90_1]) ).

fof(f_90_3,plain,
    ! [U_147,U_148] : is_bool(hAPP_f54304608l_bool(U_148,U_147)),
    inference(definitional_conversion,[status(esa)],[f_90_2]) ).

cnf(f_90_4,plain,
    is_bool(hAPP_f54304608l_bool(U_148,U_147)),
    inference(clausify,[status(thm)],[f_90_3]) ).

fof(f_91_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_f621171935l_bool(B_1_1,B_2_1))
      | ~ is_fun949378684l_bool(B_2_1) ),
    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_91_2,plain,
    ! [U_150,U_149] :
      ( is_bool(hAPP_f621171935l_bool(U_150,U_149))
      | ~ is_fun949378684l_bool(U_149) ),
    inference(variable_rename,[status(thm)],[f_91_1]) ).

fof(f_91_3,plain,
    ! [U_149,U_150] :
      ( is_bool(hAPP_f621171935l_bool(U_150,U_149))
      | ~ is_fun949378684l_bool(U_149) ),
    inference(definitional_conversion,[status(esa)],[f_91_2]) ).

cnf(f_91_4,plain,
    ( is_bool(hAPP_f621171935l_bool(U_150,U_149))
    | ~ is_fun949378684l_bool(U_149) ),
    inference(clausify,[status(thm)],[f_91_3]) ).

fof(f_92_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun949378684l_bool(hAPP_f2117159681l_bool(B_1_1,B_2_1))
      | ~ is_fun949378684l_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc___001]) ).

fof(f_92_2,plain,
    ! [U_152,U_151] :
      ( is_fun949378684l_bool(hAPP_f2117159681l_bool(U_152,U_151))
      | ~ is_fun949378684l_bool(U_151) ),
    inference(variable_rename,[status(thm)],[f_92_1]) ).

fof(f_92_3,plain,
    ! [U_151,U_152] :
      ( is_fun949378684l_bool(hAPP_f2117159681l_bool(U_152,U_151))
      | ~ is_fun949378684l_bool(U_151) ),
    inference(definitional_conversion,[status(esa)],[f_92_2]) ).

cnf(f_92_4,plain,
    ( is_fun949378684l_bool(hAPP_f2117159681l_bool(U_152,U_151))
    | ~ is_fun949378684l_bool(U_151) ),
    inference(clausify,[status(thm)],[f_92_3]) ).

fof(f_93_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_bool(hAPP_f1935102916l_bool(B_1_1,B_2_1))
      | ~ is_fun1661590463l_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo]) ).

fof(f_93_2,plain,
    ! [U_154,U_153] :
      ( is_bool(hAPP_f1935102916l_bool(U_154,U_153))
      | ~ is_fun1661590463l_bool(U_153) ),
    inference(variable_rename,[status(thm)],[f_93_1]) ).

fof(f_93_3,plain,
    ! [U_153,U_154] :
      ( is_bool(hAPP_f1935102916l_bool(U_154,U_153))
      | ~ is_fun1661590463l_bool(U_153) ),
    inference(definitional_conversion,[status(esa)],[f_93_2]) ).

cnf(f_93_4,plain,
    ( is_bool(hAPP_f1935102916l_bool(U_154,U_153))
    | ~ is_fun1661590463l_bool(U_153) ),
    inference(clausify,[status(thm)],[f_93_3]) ).

fof(f_94_1,plain,
    ! [B_1_1,B_2_1] :
      ( is_fun1661590463l_bool(hAPP_f559147733l_bool(B_1_1,B_2_1))
      | ~ is_fun1661590463l_bool(B_2_1) ),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_002]) ).

fof(f_94_2,plain,
    ! [U_156,U_155] :
      ( is_fun1661590463l_bool(hAPP_f559147733l_bool(U_156,U_155))
      | ~ is_fun1661590463l_bool(U_155) ),
    inference(variable_rename,[status(thm)],[f_94_1]) ).

fof(f_94_3,plain,
    ! [U_155,U_156] :
      ( is_fun1661590463l_bool(hAPP_f559147733l_bool(U_156,U_155))
      | ~ is_fun1661590463l_bool(U_155) ),
    inference(definitional_conversion,[status(esa)],[f_94_2]) ).

cnf(f_94_4,plain,
    ( is_fun1661590463l_bool(hAPP_f559147733l_bool(U_156,U_155))
    | ~ is_fun1661590463l_bool(U_155) ),
    inference(clausify,[status(thm)],[f_94_3]) ).

fof(f_95_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f215623910l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__HOL__Obool_]) ).

fof(f_95_2,plain,
    ! [U_158,U_157] : is_bool(hAPP_f215623910l_bool(U_158,U_157)),
    inference(variable_rename,[status(thm)],[f_95_1]) ).

fof(f_95_3,plain,
    ! [U_157,U_158] : is_bool(hAPP_f215623910l_bool(U_158,U_157)),
    inference(definitional_conversion,[status(esa)],[f_95_2]) ).

cnf(f_95_4,plain,
    is_bool(hAPP_f215623910l_bool(U_158,U_157)),
    inference(clausify,[status(thm)],[f_95_3]) ).

fof(f_96_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1637334154l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_]) ).

fof(f_96_2,plain,
    ! [U_160,U_159] : is_bool(hAPP_f1637334154l_bool(U_160,U_159)),
    inference(variable_rename,[status(thm)],[f_96_1]) ).

fof(f_96_3,plain,
    ! [U_159,U_160] : is_bool(hAPP_f1637334154l_bool(U_160,U_159)),
    inference(definitional_conversion,[status(esa)],[f_96_2]) ).

cnf(f_96_4,plain,
    is_bool(hAPP_f1637334154l_bool(U_160,U_159)),
    inference(clausify,[status(thm)],[f_96_3]) ).

fof(f_97_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f292226953l_bool(B_1_1,B_2_1)),
    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_97_2,plain,
    ! [U_162,U_161] : is_bool(hAPP_f292226953l_bool(U_162,U_161)),
    inference(variable_rename,[status(thm)],[f_97_1]) ).

fof(f_97_3,plain,
    ! [U_161,U_162] : is_bool(hAPP_f292226953l_bool(U_162,U_161)),
    inference(definitional_conversion,[status(esa)],[f_97_2]) ).

cnf(f_97_4,plain,
    is_bool(hAPP_f292226953l_bool(U_162,U_161)),
    inference(clausify,[status(thm)],[f_97_3]) ).

fof(f_98_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f389811538l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__]) ).

fof(f_98_2,plain,
    ! [U_164,U_163] : is_bool(hAPP_f389811538l_bool(U_164,U_163)),
    inference(variable_rename,[status(thm)],[f_98_1]) ).

fof(f_98_3,plain,
    ! [U_163,U_164] : is_bool(hAPP_f389811538l_bool(U_164,U_163)),
    inference(definitional_conversion,[status(esa)],[f_98_2]) ).

cnf(f_98_4,plain,
    is_bool(hAPP_f389811538l_bool(U_164,U_163)),
    inference(clausify,[status(thm)],[f_98_3]) ).

fof(f_99_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f1593524852l_bool(B_1_1,B_2_1)),
    inference(fof_nnf,[status(thm)],[gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__HO]) ).

fof(f_99_2,plain,
    ! [U_166,U_165] : is_bool(hAPP_f1593524852l_bool(U_166,U_165)),
    inference(variable_rename,[status(thm)],[f_99_1]) ).

fof(f_99_3,plain,
    ! [U_165,U_166] : is_bool(hAPP_f1593524852l_bool(U_166,U_165)),
    inference(definitional_conversion,[status(esa)],[f_99_2]) ).

cnf(f_99_4,plain,
    is_bool(hAPP_f1593524852l_bool(U_166,U_165)),
    inference(clausify,[status(thm)],[f_99_3]) ).

fof(f_100_1,plain,
    ! [B_1_1,B_2_1] : is_bool(hAPP_f937997336l_bool(B_1_1,B_2_1)),
    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_100_2,plain,
    ! [U_168,U_167] : is_bool(hAPP_f937997336l_bool(U_168,U_167)),
    inference(variable_rename,[status(thm)],[f_100_1]) ).

fof(f_100_3,plain,
    ! [U_167,U_168] : is_bool(hAPP_f937997336l_bool(U_168,U_167)),
    inference(definitional_conversion,[status(esa)],[f_100_2]) ).

cnf(f_100_4,plain,
    is_bool(hAPP_f937997336l_bool(U_168,U_167)),
    inference(clausify,[status(thm)],[f_100_3]) ).

fof(f_101_1,plain,
    is_fun_a_bool(g),
    inference(fof_nnf,[status(thm)],[gsy_v_G]) ).

fof(f_101_2,plain,
    is_fun_a_bool(g),
    inference(definitional_conversion,[status(esa)],[f_101_1]) ).

cnf(f_101_3,plain,
    is_fun_a_bool(g),
    inference(clausify,[status(thm)],[f_101_2]) ).

fof(f_102_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_102_2,plain,
    ! [U_169] :
      ( is_fun949378684l_bool(p(U_169))
      | ~ is_fun_a_bool(U_169) ),
    inference(variable_rename,[status(thm)],[f_102_1]) ).

fof(f_102_3,plain,
    ! [U_169] :
      ( is_fun949378684l_bool(p(U_169))
      | ~ is_fun_a_bool(U_169) ),
    inference(definitional_conversion,[status(esa)],[f_102_2]) ).

cnf(f_102_4,plain,
    ( is_fun949378684l_bool(p(U_169))
    | ~ is_fun_a_bool(U_169) ),
    inference(clausify,[status(thm)],[f_102_3]) ).

fof(f_103_1,plain,
    is_fun_pname_bool(u),
    inference(fof_nnf,[status(thm)],[gsy_v_U]) ).

fof(f_103_2,plain,
    is_fun_pname_bool(u),
    inference(definitional_conversion,[status(esa)],[f_103_1]) ).

cnf(f_103_3,plain,
    is_fun_pname_bool(u),
    inference(clausify,[status(thm)],[f_103_2]) ).

fof(f_104_1,plain,
    ! [B_1_1] : is_a(mgt(B_1_1)),
    inference(fof_nnf,[status(thm)],[gsy_v_mgt]) ).

fof(f_104_2,plain,
    ! [U_170] : is_a(mgt(U_170)),
    inference(variable_rename,[status(thm)],[f_104_1]) ).

fof(f_104_3,plain,
    ! [U_170] : is_a(mgt(U_170)),
    inference(definitional_conversion,[status(esa)],[f_104_2]) ).

cnf(f_104_4,plain,
    is_a(mgt(U_170)),
    inference(clausify,[status(thm)],[f_104_3]) ).

fof(f_105_1,plain,
    is_pname(pn),
    inference(fof_nnf,[status(thm)],[gsy_v_pn]) ).

fof(f_105_2,plain,
    is_pname(pn),
    inference(definitional_conversion,[status(esa)],[f_105_1]) ).

cnf(f_105_3,plain,
    is_pname(pn),
    inference(clausify,[status(thm)],[f_105_2]) ).

fof(f_106_1,plain,
    ! [B_1_1] : is_bool(wt(B_1_1)),
    inference(fof_nnf,[status(thm)],[gsy_v_wt]) ).

fof(f_106_2,plain,
    ! [U_171] : is_bool(wt(U_171)),
    inference(variable_rename,[status(thm)],[f_106_1]) ).

fof(f_106_3,plain,
    ! [U_171] : is_bool(wt(U_171)),
    inference(definitional_conversion,[status(esa)],[f_106_2]) ).

cnf(f_106_4,plain,
    is_bool(wt(U_171)),
    inference(clausify,[status(thm)],[f_106_3]) ).

fof(f_107_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_107_2,plain,
    ! [U_173,U_172] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(U_172),U_173))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_173),U_172)) ),
    inference(variable_rename,[status(thm)],[f_107_1]) ).

fof(f_107_3,plain,
    ! [U_172,U_173] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(U_172),U_173))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_173),U_172)) ),
    inference(definitional_conversion,[status(esa)],[f_107_2]) ).

cnf(f_107_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(p(U_172),U_173))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_173),U_172)) ),
    inference(clausify,[status(thm)],[f_107_3]) ).

fof(f_108_1,plain,
    ! [A] :
      ( hBOOL(hAPP_f1593524852l_bool(finite2095298929l_bool,collec1409689523l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(ord_le1848167016l_bool),A))))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_1_finite__Collect__subsets]) ).

fof(f_108_2,plain,
    ! [U_174] :
      ( hBOOL(hAPP_f1593524852l_bool(finite2095298929l_bool,collec1409689523l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(ord_le1848167016l_bool),U_174))))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_174)) ),
    inference(variable_rename,[status(thm)],[f_108_1]) ).

fof(f_108_3,plain,
    ! [U_174] :
      ( hBOOL(hAPP_f1593524852l_bool(finite2095298929l_bool,collec1409689523l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(ord_le1848167016l_bool),U_174))))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_174)) ),
    inference(definitional_conversion,[status(esa)],[f_108_2]) ).

cnf(f_108_4,plain,
    ( hBOOL(hAPP_f1593524852l_bool(finite2095298929l_bool,collec1409689523l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(ord_le1848167016l_bool),U_174))))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_174)) ),
    inference(clausify,[status(thm)],[f_108_3]) ).

fof(f_109_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_2_finite__Collect__subsets]) ).

fof(f_109_2,plain,
    ! [U_175] :
      ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),U_175))))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_175)) ),
    inference(variable_rename,[status(thm)],[f_109_1]) ).

fof(f_109_3,plain,
    ! [U_175] :
      ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),U_175))))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_175)) ),
    inference(definitional_conversion,[status(esa)],[f_109_2]) ).

cnf(f_109_4,plain,
    ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),U_175))))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_175)) ),
    inference(clausify,[status(thm)],[f_109_3]) ).

fof(f_110_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_3_finite__Collect__subsets]) ).

fof(f_110_2,plain,
    ! [U_176] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),U_176))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_176)) ),
    inference(variable_rename,[status(thm)],[f_110_1]) ).

fof(f_110_3,plain,
    ! [U_176] :
      ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),U_176))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_176)) ),
    inference(definitional_conversion,[status(esa)],[f_110_2]) ).

cnf(f_110_4,plain,
    ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),U_176))))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_176)) ),
    inference(clausify,[status(thm)],[f_110_3]) ).

fof(f_111_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_4_finite__Collect__subsets]) ).

fof(f_111_2,plain,
    ! [U_177] :
      ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),U_177))))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_177)) ),
    inference(variable_rename,[status(thm)],[f_111_1]) ).

fof(f_111_3,plain,
    ! [U_177] :
      ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),U_177))))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_177)) ),
    inference(definitional_conversion,[status(esa)],[f_111_2]) ).

cnf(f_111_4,plain,
    ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),U_177))))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_177)) ),
    inference(clausify,[status(thm)],[f_111_3]) ).

fof(f_112_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_5_finite__Collect__subsets]) ).

fof(f_112_2,plain,
    ! [U_178] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),U_178))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_178)) ),
    inference(variable_rename,[status(thm)],[f_112_1]) ).

fof(f_112_3,plain,
    ! [U_178] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),U_178))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_178)) ),
    inference(definitional_conversion,[status(esa)],[f_112_2]) ).

cnf(f_112_4,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),U_178))))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_178)) ),
    inference(clausify,[status(thm)],[f_112_3]) ).

fof(f_113_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_6_finite__Collect__subsets]) ).

fof(f_113_2,plain,
    ! [U_179] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),U_179))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_179)) ),
    inference(variable_rename,[status(thm)],[f_113_1]) ).

fof(f_113_3,plain,
    ! [U_179] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),U_179))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_179)) ),
    inference(definitional_conversion,[status(esa)],[f_113_2]) ).

cnf(f_113_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),U_179))))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_179)) ),
    inference(clausify,[status(thm)],[f_113_3]) ).

fof(f_114_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_7_finite__Collect__subsets]) ).

fof(f_114_2,plain,
    ! [U_180] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),U_180))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_180)) ),
    inference(variable_rename,[status(thm)],[f_114_1]) ).

fof(f_114_3,plain,
    ! [U_180] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),U_180))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_180)) ),
    inference(definitional_conversion,[status(esa)],[f_114_2]) ).

cnf(f_114_4,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),U_180))))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_180)) ),
    inference(clausify,[status(thm)],[f_114_3]) ).

fof(f_115_1,plain,
    ! [A] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(ord_le951220754t_bool),A))))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_8_finite__Collect__subsets]) ).

fof(f_115_2,plain,
    ! [U_181] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(ord_le951220754t_bool),U_181))))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_181)) ),
    inference(variable_rename,[status(thm)],[f_115_1]) ).

fof(f_115_3,plain,
    ! [U_181] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(ord_le951220754t_bool),U_181))))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_181)) ),
    inference(definitional_conversion,[status(esa)],[f_115_2]) ).

cnf(f_115_4,plain,
    ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(ord_le951220754t_bool),U_181))))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_181)) ),
    inference(clausify,[status(thm)],[f_115_3]) ).

fof(f_116_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1512837979t_bool(H,F_1)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_9_finite__imageI]) ).

fof(f_116_2,plain,
    ! [U_183,U_182] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1512837979t_bool(U_183,U_182)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_182)) ),
    inference(variable_rename,[status(thm)],[f_116_1]) ).

fof(f_116_3,plain,
    ! [U_182,U_183] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1512837979t_bool(U_183,U_182)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_182)) ),
    inference(definitional_conversion,[status(esa)],[f_116_2]) ).

cnf(f_116_4,plain,
    ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1512837979t_bool(U_183,U_182)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_182)) ),
    inference(clausify,[status(thm)],[f_116_3]) ).

fof(f_117_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_10_finite__imageI]) ).

fof(f_117_2,plain,
    ! [U_185,U_184] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(U_185,U_184)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_184)) ),
    inference(variable_rename,[status(thm)],[f_117_1]) ).

fof(f_117_3,plain,
    ! [U_184,U_185] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(U_185,U_184)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_184)) ),
    inference(definitional_conversion,[status(esa)],[f_117_2]) ).

cnf(f_117_4,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(U_185,U_184)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_184)) ),
    inference(clausify,[status(thm)],[f_117_3]) ).

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_11_finite__imageI]) ).

fof(f_118_2,plain,
    ! [U_187,U_186] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(U_187,U_186)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_186)) ),
    inference(variable_rename,[status(thm)],[f_118_1]) ).

fof(f_118_3,plain,
    ! [U_186,U_187] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(U_187,U_186)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_186)) ),
    inference(definitional_conversion,[status(esa)],[f_118_2]) ).

cnf(f_118_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(U_187,U_186)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_186)) ),
    inference(clausify,[status(thm)],[f_118_3]) ).

fof(f_119_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_12_finite__imageI]) ).

fof(f_119_2,plain,
    ! [U_189,U_188] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(U_189,U_188)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_188)) ),
    inference(variable_rename,[status(thm)],[f_119_1]) ).

fof(f_119_3,plain,
    ! [U_188,U_189] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(U_189,U_188)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_188)) ),
    inference(definitional_conversion,[status(esa)],[f_119_2]) ).

cnf(f_119_4,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(U_189,U_188)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_188)) ),
    inference(clausify,[status(thm)],[f_119_3]) ).

fof(f_120_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_13_finite__imageI]) ).

fof(f_120_2,plain,
    ! [U_191,U_190] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(U_191,U_190)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_190)) ),
    inference(variable_rename,[status(thm)],[f_120_1]) ).

fof(f_120_3,plain,
    ! [U_190,U_191] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(U_191,U_190)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_190)) ),
    inference(definitional_conversion,[status(esa)],[f_120_2]) ).

cnf(f_120_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(U_191,U_190)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_190)) ),
    inference(clausify,[status(thm)],[f_120_3]) ).

fof(f_121_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(H,F_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_14_finite__imageI]) ).

fof(f_121_2,plain,
    ! [U_193,U_192] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(U_193,U_192)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_192)) ),
    inference(variable_rename,[status(thm)],[f_121_1]) ).

fof(f_121_3,plain,
    ! [U_192,U_193] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(U_193,U_192)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_192)) ),
    inference(definitional_conversion,[status(esa)],[f_121_2]) ).

cnf(f_121_4,plain,
    ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(U_193,U_192)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_192)) ),
    inference(clausify,[status(thm)],[f_121_3]) ).

fof(f_122_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_15_finite__imageI]) ).

fof(f_122_2,plain,
    ! [U_195,U_194] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(U_195,U_194)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_194)) ),
    inference(variable_rename,[status(thm)],[f_122_1]) ).

fof(f_122_3,plain,
    ! [U_194,U_195] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(U_195,U_194)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_194)) ),
    inference(definitional_conversion,[status(esa)],[f_122_2]) ).

cnf(f_122_4,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(U_195,U_194)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_194)) ),
    inference(clausify,[status(thm)],[f_122_3]) ).

fof(f_123_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_16_finite__imageI]) ).

fof(f_123_2,plain,
    ! [U_197,U_196] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(U_197,U_196)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_196)) ),
    inference(variable_rename,[status(thm)],[f_123_1]) ).

fof(f_123_3,plain,
    ! [U_196,U_197] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(U_197,U_196)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_196)) ),
    inference(definitional_conversion,[status(esa)],[f_123_2]) ).

cnf(f_123_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(U_197,U_196)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_196)) ),
    inference(clausify,[status(thm)],[f_123_3]) ).

fof(f_124_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_17_finite__imageI]) ).

fof(f_124_2,plain,
    ! [U_199,U_198] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(U_199,U_198)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_198)) ),
    inference(variable_rename,[status(thm)],[f_124_1]) ).

fof(f_124_3,plain,
    ! [U_198,U_199] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(U_199,U_198)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_198)) ),
    inference(definitional_conversion,[status(esa)],[f_124_2]) ).

cnf(f_124_4,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(U_199,U_198)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_198)) ),
    inference(clausify,[status(thm)],[f_124_3]) ).

fof(f_125_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(H,F_1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_18_finite__imageI]) ).

fof(f_125_2,plain,
    ! [U_201,U_200] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(U_201,U_200)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_200)) ),
    inference(variable_rename,[status(thm)],[f_125_1]) ).

fof(f_125_3,plain,
    ! [U_200,U_201] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(U_201,U_200)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_200)) ),
    inference(definitional_conversion,[status(esa)],[f_125_2]) ).

cnf(f_125_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(U_201,U_200)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_200)) ),
    inference(clausify,[status(thm)],[f_125_3]) ).

fof(f_126_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(H,F_1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_19_finite__imageI]) ).

fof(f_126_2,plain,
    ! [U_203,U_202] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(U_203,U_202)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_202)) ),
    inference(variable_rename,[status(thm)],[f_126_1]) ).

fof(f_126_3,plain,
    ! [U_202,U_203] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(U_203,U_202)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_202)) ),
    inference(definitional_conversion,[status(esa)],[f_126_2]) ).

cnf(f_126_4,plain,
    ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(U_203,U_202)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_202)) ),
    inference(clausify,[status(thm)],[f_126_3]) ).

fof(f_127_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(H,F_1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_20_finite__imageI]) ).

fof(f_127_2,plain,
    ! [U_205,U_204] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(U_205,U_204)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_204)) ),
    inference(variable_rename,[status(thm)],[f_127_1]) ).

fof(f_127_3,plain,
    ! [U_204,U_205] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(U_205,U_204)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_204)) ),
    inference(definitional_conversion,[status(esa)],[f_127_2]) ).

cnf(f_127_4,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(U_205,U_204)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_204)) ),
    inference(clausify,[status(thm)],[f_127_3]) ).

fof(f_128_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(H,F_1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_21_finite__imageI]) ).

fof(f_128_2,plain,
    ! [U_207,U_206] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(U_207,U_206)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_206)) ),
    inference(variable_rename,[status(thm)],[f_128_1]) ).

fof(f_128_3,plain,
    ! [U_206,U_207] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(U_207,U_206)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_206)) ),
    inference(definitional_conversion,[status(esa)],[f_128_2]) ).

cnf(f_128_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(U_207,U_206)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_206)) ),
    inference(clausify,[status(thm)],[f_128_3]) ).

fof(f_129_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(H,F_1)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_22_finite__imageI]) ).

fof(f_129_2,plain,
    ! [U_209,U_208] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(U_209,U_208)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_208)) ),
    inference(variable_rename,[status(thm)],[f_129_1]) ).

fof(f_129_3,plain,
    ! [U_208,U_209] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(U_209,U_208)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_208)) ),
    inference(definitional_conversion,[status(esa)],[f_129_2]) ).

cnf(f_129_4,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(U_209,U_208)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_208)) ),
    inference(clausify,[status(thm)],[f_129_3]) ).

fof(f_130_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_23_finite__imageI]) ).

fof(f_130_2,plain,
    ! [U_211,U_210] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(U_211,U_210)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_210)) ),
    inference(variable_rename,[status(thm)],[f_130_1]) ).

fof(f_130_3,plain,
    ! [U_211,U_210] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(U_211,U_210)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_210)) ),
    inference(definitional_conversion,[status(esa)],[f_130_2]) ).

cnf(f_130_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(U_211,U_210)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_210)) ),
    inference(clausify,[status(thm)],[f_130_3]) ).

fof(f_131_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_62782965_pname(H,F_1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_24_finite__imageI]) ).

fof(f_131_2,plain,
    ! [U_213,U_212] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_62782965_pname(U_213,U_212)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_212)) ),
    inference(variable_rename,[status(thm)],[f_131_1]) ).

fof(f_131_3,plain,
    ! [U_212,U_213] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_62782965_pname(U_213,U_212)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_212)) ),
    inference(definitional_conversion,[status(esa)],[f_131_2]) ).

cnf(f_131_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_62782965_pname(U_213,U_212)))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_212)) ),
    inference(clausify,[status(thm)],[f_131_3]) ).

fof(f_132_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_25_finite__imageI]) ).

fof(f_132_2,plain,
    ! [U_215,U_214] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(U_215,U_214)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_214)) ),
    inference(variable_rename,[status(thm)],[f_132_1]) ).

fof(f_132_3,plain,
    ! [U_214,U_215] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(U_215,U_214)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_214)) ),
    inference(definitional_conversion,[status(esa)],[f_132_2]) ).

cnf(f_132_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(U_215,U_214)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_214)) ),
    inference(clausify,[status(thm)],[f_132_3]) ).

fof(f_133_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_26_finite__imageI]) ).

fof(f_133_2,plain,
    ! [U_217,U_216] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(U_217,U_216)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_216)) ),
    inference(variable_rename,[status(thm)],[f_133_1]) ).

fof(f_133_3,plain,
    ! [U_216,U_217] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(U_217,U_216)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_216)) ),
    inference(definitional_conversion,[status(esa)],[f_133_2]) ).

cnf(f_133_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(U_217,U_216)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_216)) ),
    inference(clausify,[status(thm)],[f_133_3]) ).

fof(f_134_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_27_finite__imageI]) ).

fof(f_134_2,plain,
    ! [U_219,U_218] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(U_219,U_218)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_218)) ),
    inference(variable_rename,[status(thm)],[f_134_1]) ).

fof(f_134_3,plain,
    ! [U_218,U_219] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(U_219,U_218)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_218)) ),
    inference(definitional_conversion,[status(esa)],[f_134_2]) ).

cnf(f_134_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(U_219,U_218)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_218)) ),
    inference(clausify,[status(thm)],[f_134_3]) ).

fof(f_135_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_28_finite__imageI]) ).

fof(f_135_2,plain,
    ! [U_221,U_220] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(U_221,U_220)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_220)) ),
    inference(variable_rename,[status(thm)],[f_135_1]) ).

fof(f_135_3,plain,
    ! [U_220,U_221] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(U_221,U_220)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_220)) ),
    inference(definitional_conversion,[status(esa)],[f_135_2]) ).

cnf(f_135_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(U_221,U_220)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_220)) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

fof(f_136_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1431733819ol_nat(H,F_1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_29_finite__imageI]) ).

fof(f_136_2,plain,
    ! [U_223,U_222] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1431733819ol_nat(U_223,U_222)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_222)) ),
    inference(variable_rename,[status(thm)],[f_136_1]) ).

fof(f_136_3,plain,
    ! [U_222,U_223] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1431733819ol_nat(U_223,U_222)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_222)) ),
    inference(definitional_conversion,[status(esa)],[f_136_2]) ).

cnf(f_136_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1431733819ol_nat(U_223,U_222)))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_222)) ),
    inference(clausify,[status(thm)],[f_136_3]) ).

fof(f_137_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_30_finite__imageI]) ).

fof(f_137_2,plain,
    ! [U_225,U_224] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(U_225,U_224)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_224)) ),
    inference(variable_rename,[status(thm)],[f_137_1]) ).

fof(f_137_3,plain,
    ! [U_224,U_225] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(U_225,U_224)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_224)) ),
    inference(definitional_conversion,[status(esa)],[f_137_2]) ).

cnf(f_137_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(U_225,U_224)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_224)) ),
    inference(clausify,[status(thm)],[f_137_3]) ).

fof(f_138_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_31_finite__imageI]) ).

fof(f_138_2,plain,
    ! [U_227,U_226] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(U_227,U_226)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_226)) ),
    inference(variable_rename,[status(thm)],[f_138_1]) ).

fof(f_138_3,plain,
    ! [U_226,U_227] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(U_227,U_226)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_226)) ),
    inference(definitional_conversion,[status(esa)],[f_138_2]) ).

cnf(f_138_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(U_227,U_226)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_226)) ),
    inference(clausify,[status(thm)],[f_138_3]) ).

fof(f_139_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_32_finite__imageI]) ).

fof(f_139_2,plain,
    ! [U_229,U_228] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(U_229,U_228)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_228)) ),
    inference(variable_rename,[status(thm)],[f_139_1]) ).

fof(f_139_3,plain,
    ! [U_228,U_229] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(U_229,U_228)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_228)) ),
    inference(definitional_conversion,[status(esa)],[f_139_2]) ).

cnf(f_139_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(U_229,U_228)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_228)) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

fof(f_140_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_a_int(H,F_1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_33_finite__imageI]) ).

fof(f_140_2,plain,
    ! [U_231,U_230] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_a_int(U_231,U_230)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_230)) ),
    inference(variable_rename,[status(thm)],[f_140_1]) ).

fof(f_140_3,plain,
    ! [U_230,U_231] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_a_int(U_231,U_230)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_230)) ),
    inference(definitional_conversion,[status(esa)],[f_140_2]) ).

cnf(f_140_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_a_int(U_231,U_230)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_230)) ),
    inference(clausify,[status(thm)],[f_140_3]) ).

fof(f_141_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_2069007511ol_int(H,F_1)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_34_finite__imageI]) ).

fof(f_141_2,plain,
    ! [U_233,U_232] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_2069007511ol_int(U_233,U_232)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_232)) ),
    inference(variable_rename,[status(thm)],[f_141_1]) ).

fof(f_141_3,plain,
    ! [U_232,U_233] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_2069007511ol_int(U_233,U_232)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_232)) ),
    inference(definitional_conversion,[status(esa)],[f_141_2]) ).

cnf(f_141_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_2069007511ol_int(U_233,U_232)))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_232)) ),
    inference(clausify,[status(thm)],[f_141_3]) ).

fof(f_142_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_1133522419ol_int(H,F_1)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_35_finite__imageI]) ).

fof(f_142_2,plain,
    ! [U_235,U_234] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_1133522419ol_int(U_235,U_234)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_234)) ),
    inference(variable_rename,[status(thm)],[f_142_1]) ).

fof(f_142_3,plain,
    ! [U_234,U_235] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_1133522419ol_int(U_235,U_234)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_234)) ),
    inference(definitional_conversion,[status(esa)],[f_142_2]) ).

cnf(f_142_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_1133522419ol_int(U_235,U_234)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_234)) ),
    inference(clausify,[status(thm)],[f_142_3]) ).

fof(f_143_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_41399353ol_int(H,F_1)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_36_finite__imageI]) ).

fof(f_143_2,plain,
    ! [U_237,U_236] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_41399353ol_int(U_237,U_236)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_236)) ),
    inference(variable_rename,[status(thm)],[f_143_1]) ).

fof(f_143_3,plain,
    ! [U_236,U_237] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_41399353ol_int(U_237,U_236)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_236)) ),
    inference(definitional_conversion,[status(esa)],[f_143_2]) ).

cnf(f_143_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_41399353ol_int(U_237,U_236)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_236)) ),
    inference(clausify,[status(thm)],[f_143_3]) ).

fof(f_144_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_fun_a_bool_int(H,F_1)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_37_finite__imageI]) ).

fof(f_144_2,plain,
    ! [U_239,U_238] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_fun_a_bool_int(U_239,U_238)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_238)) ),
    inference(variable_rename,[status(thm)],[f_144_1]) ).

fof(f_144_3,plain,
    ! [U_238,U_239] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_fun_a_bool_int(U_239,U_238)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_238)) ),
    inference(definitional_conversion,[status(esa)],[f_144_2]) ).

cnf(f_144_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_fun_a_bool_int(U_239,U_238)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_238)) ),
    inference(clausify,[status(thm)],[f_144_3]) ).

fof(f_145_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_38_finite__imageI]) ).

fof(f_145_2,plain,
    ! [U_241,U_240] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(U_241,U_240)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_240)) ),
    inference(variable_rename,[status(thm)],[f_145_1]) ).

fof(f_145_3,plain,
    ! [U_240,U_241] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(U_241,U_240)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_240)) ),
    inference(definitional_conversion,[status(esa)],[f_145_2]) ).

cnf(f_145_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(U_241,U_240)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_240)) ),
    inference(clausify,[status(thm)],[f_145_3]) ).

fof(f_146_1,plain,
    ! [H,F_1] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(H,F_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_39_finite__imageI]) ).

fof(f_146_2,plain,
    ! [U_243,U_242] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(U_243,U_242)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_242)) ),
    inference(variable_rename,[status(thm)],[f_146_1]) ).

fof(f_146_3,plain,
    ! [U_242,U_243] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(U_243,U_242)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_242)) ),
    inference(definitional_conversion,[status(esa)],[f_146_2]) ).

cnf(f_146_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(U_243,U_242)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_242)) ),
    inference(clausify,[status(thm)],[f_146_3]) ).

fof(f_147_1,plain,
    ! [A_2,A] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,A_2),A)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_40_finite_OinsertI]) ).

fof(f_147_2,plain,
    ! [U_245,U_244] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,U_245),U_244)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_244)) ),
    inference(variable_rename,[status(thm)],[f_147_1]) ).

fof(f_147_3,plain,
    ! [U_244,U_245] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,U_245),U_244)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_244)) ),
    inference(definitional_conversion,[status(esa)],[f_147_2]) ).

cnf(f_147_4,plain,
    ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,U_245),U_244)))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_244)) ),
    inference(clausify,[status(thm)],[f_147_3]) ).

fof(f_148_1,plain,
    ! [A_2,A] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,A_2),A)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_41_finite_OinsertI]) ).

fof(f_148_2,plain,
    ! [U_247,U_246] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,U_247),U_246)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_246)) ),
    inference(variable_rename,[status(thm)],[f_148_1]) ).

fof(f_148_3,plain,
    ! [U_246,U_247] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,U_247),U_246)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_246)) ),
    inference(definitional_conversion,[status(esa)],[f_148_2]) ).

cnf(f_148_4,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,U_247),U_246)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_246)) ),
    inference(clausify,[status(thm)],[f_148_3]) ).

fof(f_149_1,plain,
    ! [A_2,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_2),A)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_42_finite_OinsertI]) ).

fof(f_149_2,plain,
    ! [U_249,U_248] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,U_249),U_248)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_248)) ),
    inference(variable_rename,[status(thm)],[f_149_1]) ).

fof(f_149_3,plain,
    ! [U_248,U_249] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,U_249),U_248)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_248)) ),
    inference(definitional_conversion,[status(esa)],[f_149_2]) ).

cnf(f_149_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,U_249),U_248)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_248)) ),
    inference(clausify,[status(thm)],[f_149_3]) ).

fof(f_150_1,plain,
    ! [A_2,A] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,A_2),A)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_43_finite_OinsertI]) ).

fof(f_150_2,plain,
    ! [U_251,U_250] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,U_251),U_250)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_250)) ),
    inference(variable_rename,[status(thm)],[f_150_1]) ).

fof(f_150_3,plain,
    ! [U_250,U_251] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,U_251),U_250)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_250)) ),
    inference(definitional_conversion,[status(esa)],[f_150_2]) ).

cnf(f_150_4,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,U_251),U_250)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_250)) ),
    inference(clausify,[status(thm)],[f_150_3]) ).

fof(f_151_1,plain,
    ! [A_2,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_44_finite_OinsertI]) ).

fof(f_151_2,plain,
    ! [U_253,U_252] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_253),U_252)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_252)) ),
    inference(variable_rename,[status(thm)],[f_151_1]) ).

fof(f_151_3,plain,
    ! [U_252,U_253] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_253),U_252)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_252)) ),
    inference(definitional_conversion,[status(esa)],[f_151_2]) ).

cnf(f_151_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_253),U_252)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_252)) ),
    inference(clausify,[status(thm)],[f_151_3]) ).

fof(f_152_1,plain,
    ! [A_2,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_45_finite_OinsertI]) ).

fof(f_152_2,plain,
    ! [U_255,U_254] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_255),U_254)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_254)) ),
    inference(variable_rename,[status(thm)],[f_152_1]) ).

fof(f_152_3,plain,
    ! [U_254,U_255] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_255),U_254)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_254)) ),
    inference(definitional_conversion,[status(esa)],[f_152_2]) ).

cnf(f_152_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_255),U_254)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_254)) ),
    inference(clausify,[status(thm)],[f_152_3]) ).

fof(f_153_1,plain,
    ! [A_2,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),A)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_46_finite_OinsertI]) ).

fof(f_153_2,plain,
    ! [U_257,U_256] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_257),U_256)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_256)) ),
    inference(variable_rename,[status(thm)],[f_153_1]) ).

fof(f_153_3,plain,
    ! [U_256,U_257] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_257),U_256)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_256)) ),
    inference(definitional_conversion,[status(esa)],[f_153_2]) ).

cnf(f_153_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_257),U_256)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_256)) ),
    inference(clausify,[status(thm)],[f_153_3]) ).

fof(f_154_1,plain,
    ! [A_2,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),A)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_47_finite_OinsertI]) ).

fof(f_154_2,plain,
    ! [U_259,U_258] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_259),U_258)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_258)) ),
    inference(variable_rename,[status(thm)],[f_154_1]) ).

fof(f_154_3,plain,
    ! [U_258,U_259] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_259),U_258)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_258)) ),
    inference(definitional_conversion,[status(esa)],[f_154_2]) ).

cnf(f_154_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_259),U_258)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_258)) ),
    inference(clausify,[status(thm)],[f_154_3]) ).

fof(f_155_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_48_card__image__le]) ).

fof(f_155_2,plain,
    ! [U_261,U_260] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(U_261,U_260))),hAPP_f921600141ol_nat(finite_card_pname,U_260)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_260)) ),
    inference(variable_rename,[status(thm)],[f_155_1]) ).

fof(f_155_3,plain,
    ! [U_260,U_261] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(U_261,U_260))),hAPP_f921600141ol_nat(finite_card_pname,U_260)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_260)) ),
    inference(definitional_conversion,[status(esa)],[f_155_2]) ).

cnf(f_155_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(U_261,U_260))),hAPP_f921600141ol_nat(finite_card_pname,U_260)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_260)) ),
    inference(clausify,[status(thm)],[f_155_3]) ).

fof(f_156_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_49_card__image__le]) ).

fof(f_156_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_156_1]) ).

fof(f_156_3,plain,
    ! [U_262,U_263] :
      ( 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(definitional_conversion,[status(esa)],[f_156_2]) ).

cnf(f_156_4,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_156_3]) ).

fof(f_157_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_int_bool_a(F,A))),hAPP_f521865025ol_nat(finite1876863882t_bool,A)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_50_card__image__le]) ).

fof(f_157_2,plain,
    ! [U_265,U_264] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_int_bool_a(U_265,U_264))),hAPP_f521865025ol_nat(finite1876863882t_bool,U_264)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_264)) ),
    inference(variable_rename,[status(thm)],[f_157_1]) ).

fof(f_157_3,plain,
    ! [U_264,U_265] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_int_bool_a(U_265,U_264))),hAPP_f521865025ol_nat(finite1876863882t_bool,U_264)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_264)) ),
    inference(definitional_conversion,[status(esa)],[f_157_2]) ).

cnf(f_157_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_int_bool_a(U_265,U_264))),hAPP_f521865025ol_nat(finite1876863882t_bool,U_264)))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_264)) ),
    inference(clausify,[status(thm)],[f_157_3]) ).

fof(f_158_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_51_card__image__le]) ).

fof(f_158_2,plain,
    ! [U_267,U_266] :
      ( 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_267,U_266))),hAPP_f696928925ol_nat(finite346522414t_bool,U_266)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_266)) ),
    inference(variable_rename,[status(thm)],[f_158_1]) ).

fof(f_158_3,plain,
    ! [U_266,U_267] :
      ( 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_267,U_266))),hAPP_f696928925ol_nat(finite346522414t_bool,U_266)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_266)) ),
    inference(definitional_conversion,[status(esa)],[f_158_2]) ).

cnf(f_158_4,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_267,U_266))),hAPP_f696928925ol_nat(finite346522414t_bool,U_266)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_266)) ),
    inference(clausify,[status(thm)],[f_158_3]) ).

fof(f_159_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_52_card__image__le]) ).

fof(f_159_2,plain,
    ! [U_269,U_268] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(U_269,U_268))),hAPP_f55526627ol_nat(finite1340463720e_bool,U_268)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_268)) ),
    inference(variable_rename,[status(thm)],[f_159_1]) ).

fof(f_159_3,plain,
    ! [U_268,U_269] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(U_269,U_268))),hAPP_f55526627ol_nat(finite1340463720e_bool,U_268)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_268)) ),
    inference(definitional_conversion,[status(esa)],[f_159_2]) ).

cnf(f_159_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(U_269,U_268))),hAPP_f55526627ol_nat(finite1340463720e_bool,U_268)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_268)) ),
    inference(clausify,[status(thm)],[f_159_3]) ).

fof(f_160_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_53_card__image__le]) ).

fof(f_160_2,plain,
    ! [U_271,U_270] :
      ( 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_271,U_270))),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_270)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_270)) ),
    inference(variable_rename,[status(thm)],[f_160_1]) ).

fof(f_160_3,plain,
    ! [U_270,U_271] :
      ( 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_271,U_270))),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_270)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_270)) ),
    inference(definitional_conversion,[status(esa)],[f_160_2]) ).

cnf(f_160_4,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_271,U_270))),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_270)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_270)) ),
    inference(clausify,[status(thm)],[f_160_3]) ).

fof(f_161_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_161_2,plain,
    ! [U_273,U_272] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(U_273,U_272))),hAPP_f921600141ol_nat(finite_card_pname,U_272)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_272)) ),
    inference(variable_rename,[status(thm)],[f_161_1]) ).

fof(f_161_3,plain,
    ! [U_272,U_273] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(U_273,U_272))),hAPP_f921600141ol_nat(finite_card_pname,U_272)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_272)) ),
    inference(definitional_conversion,[status(esa)],[f_161_2]) ).

cnf(f_161_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(U_273,U_272))),hAPP_f921600141ol_nat(finite_card_pname,U_272)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_272)) ),
    inference(clausify,[status(thm)],[f_161_3]) ).

fof(f_162_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_162_2,plain,
    ! [U_275,U_274] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(U_275,U_274))),hAPP_fun_a_bool_nat(finite_card_a,U_274)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_274)) ),
    inference(variable_rename,[status(thm)],[f_162_1]) ).

fof(f_162_3,plain,
    ! [U_274,U_275] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(U_275,U_274))),hAPP_fun_a_bool_nat(finite_card_a,U_274)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_274)) ),
    inference(definitional_conversion,[status(esa)],[f_162_2]) ).

cnf(f_162_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(U_275,U_274))),hAPP_fun_a_bool_nat(finite_card_a,U_274)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_274)) ),
    inference(clausify,[status(thm)],[f_162_3]) ).

fof(f_163_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1431733819ol_nat(F,A))),hAPP_f521865025ol_nat(finite1876863882t_bool,A)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_56_card__image__le]) ).

fof(f_163_2,plain,
    ! [U_277,U_276] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1431733819ol_nat(U_277,U_276))),hAPP_f521865025ol_nat(finite1876863882t_bool,U_276)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_276)) ),
    inference(variable_rename,[status(thm)],[f_163_1]) ).

fof(f_163_3,plain,
    ! [U_277,U_276] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1431733819ol_nat(U_277,U_276))),hAPP_f521865025ol_nat(finite1876863882t_bool,U_276)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_276)) ),
    inference(definitional_conversion,[status(esa)],[f_163_2]) ).

cnf(f_163_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1431733819ol_nat(U_277,U_276))),hAPP_f521865025ol_nat(finite1876863882t_bool,U_276)))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_276)) ),
    inference(clausify,[status(thm)],[f_163_3]) ).

fof(f_164_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_57_card__image__le]) ).

fof(f_164_2,plain,
    ! [U_279,U_278] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(U_279,U_278))),hAPP_f696928925ol_nat(finite346522414t_bool,U_278)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_278)) ),
    inference(variable_rename,[status(thm)],[f_164_1]) ).

fof(f_164_3,plain,
    ! [U_278,U_279] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(U_279,U_278))),hAPP_f696928925ol_nat(finite346522414t_bool,U_278)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_278)) ),
    inference(definitional_conversion,[status(esa)],[f_164_2]) ).

cnf(f_164_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(U_279,U_278))),hAPP_f696928925ol_nat(finite346522414t_bool,U_278)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_278)) ),
    inference(clausify,[status(thm)],[f_164_3]) ).

fof(f_165_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_58_card__image__le]) ).

fof(f_165_2,plain,
    ! [U_281,U_280] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(U_281,U_280))),hAPP_f55526627ol_nat(finite1340463720e_bool,U_280)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_280)) ),
    inference(variable_rename,[status(thm)],[f_165_1]) ).

fof(f_165_3,plain,
    ! [U_280,U_281] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(U_281,U_280))),hAPP_f55526627ol_nat(finite1340463720e_bool,U_280)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_280)) ),
    inference(definitional_conversion,[status(esa)],[f_165_2]) ).

cnf(f_165_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(U_281,U_280))),hAPP_f55526627ol_nat(finite1340463720e_bool,U_280)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_280)) ),
    inference(clausify,[status(thm)],[f_165_3]) ).

fof(f_166_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_59_card__image__le]) ).

fof(f_166_2,plain,
    ! [U_283,U_282] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(U_283,U_282))),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_282)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_282)) ),
    inference(variable_rename,[status(thm)],[f_166_1]) ).

fof(f_166_3,plain,
    ! [U_282,U_283] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(U_283,U_282))),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_282)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_282)) ),
    inference(definitional_conversion,[status(esa)],[f_166_2]) ).

cnf(f_166_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(U_283,U_282))),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_282)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_282)) ),
    inference(clausify,[status(thm)],[f_166_3]) ).

fof(f_167_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_pname_int(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_60_card__image__le]) ).

fof(f_167_2,plain,
    ! [U_285,U_284] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_pname_int(U_285,U_284))),hAPP_f921600141ol_nat(finite_card_pname,U_284)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_284)) ),
    inference(variable_rename,[status(thm)],[f_167_1]) ).

fof(f_167_3,plain,
    ! [U_284,U_285] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_pname_int(U_285,U_284))),hAPP_f921600141ol_nat(finite_card_pname,U_284)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_284)) ),
    inference(definitional_conversion,[status(esa)],[f_167_2]) ).

cnf(f_167_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_pname_int(U_285,U_284))),hAPP_f921600141ol_nat(finite_card_pname,U_284)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_284)) ),
    inference(clausify,[status(thm)],[f_167_3]) ).

fof(f_168_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_a_int(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_61_card__image__le]) ).

fof(f_168_2,plain,
    ! [U_287,U_286] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_a_int(U_287,U_286))),hAPP_fun_a_bool_nat(finite_card_a,U_286)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_286)) ),
    inference(variable_rename,[status(thm)],[f_168_1]) ).

fof(f_168_3,plain,
    ! [U_286,U_287] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_a_int(U_287,U_286))),hAPP_fun_a_bool_nat(finite_card_a,U_286)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_286)) ),
    inference(definitional_conversion,[status(esa)],[f_168_2]) ).

cnf(f_168_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_a_int(U_287,U_286))),hAPP_fun_a_bool_nat(finite_card_a,U_286)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_286)) ),
    inference(clausify,[status(thm)],[f_168_3]) ).

fof(f_169_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_2069007511ol_int(F,A))),hAPP_f521865025ol_nat(finite1876863882t_bool,A)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_62_card__image__le]) ).

fof(f_169_2,plain,
    ! [U_289,U_288] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_2069007511ol_int(U_289,U_288))),hAPP_f521865025ol_nat(finite1876863882t_bool,U_288)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_288)) ),
    inference(variable_rename,[status(thm)],[f_169_1]) ).

fof(f_169_3,plain,
    ! [U_288,U_289] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_2069007511ol_int(U_289,U_288))),hAPP_f521865025ol_nat(finite1876863882t_bool,U_288)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_288)) ),
    inference(definitional_conversion,[status(esa)],[f_169_2]) ).

cnf(f_169_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_2069007511ol_int(U_289,U_288))),hAPP_f521865025ol_nat(finite1876863882t_bool,U_288)))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_288)) ),
    inference(clausify,[status(thm)],[f_169_3]) ).

fof(f_170_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_1133522419ol_int(F,A))),hAPP_f696928925ol_nat(finite346522414t_bool,A)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_63_card__image__le]) ).

fof(f_170_2,plain,
    ! [U_291,U_290] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_1133522419ol_int(U_291,U_290))),hAPP_f696928925ol_nat(finite346522414t_bool,U_290)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_290)) ),
    inference(variable_rename,[status(thm)],[f_170_1]) ).

fof(f_170_3,plain,
    ! [U_290,U_291] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_1133522419ol_int(U_291,U_290))),hAPP_f696928925ol_nat(finite346522414t_bool,U_290)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_290)) ),
    inference(definitional_conversion,[status(esa)],[f_170_2]) ).

cnf(f_170_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_1133522419ol_int(U_291,U_290))),hAPP_f696928925ol_nat(finite346522414t_bool,U_290)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_290)) ),
    inference(clausify,[status(thm)],[f_170_3]) ).

fof(f_171_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_41399353ol_int(F,A))),hAPP_f55526627ol_nat(finite1340463720e_bool,A)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_64_card__image__le]) ).

fof(f_171_2,plain,
    ! [U_293,U_292] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_41399353ol_int(U_293,U_292))),hAPP_f55526627ol_nat(finite1340463720e_bool,U_292)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_292)) ),
    inference(variable_rename,[status(thm)],[f_171_1]) ).

fof(f_171_3,plain,
    ! [U_292,U_293] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_41399353ol_int(U_293,U_292))),hAPP_f55526627ol_nat(finite1340463720e_bool,U_292)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_292)) ),
    inference(definitional_conversion,[status(esa)],[f_171_2]) ).

cnf(f_171_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_41399353ol_int(U_293,U_292))),hAPP_f55526627ol_nat(finite1340463720e_bool,U_292)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_292)) ),
    inference(clausify,[status(thm)],[f_171_3]) ).

fof(f_172_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_fun_a_bool_int(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_172_2,plain,
    ! [U_295,U_294] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_fun_a_bool_int(U_295,U_294))),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_294)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_294)) ),
    inference(variable_rename,[status(thm)],[f_172_1]) ).

fof(f_172_3,plain,
    ! [U_294,U_295] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_fun_a_bool_int(U_295,U_294))),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_294)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_294)) ),
    inference(definitional_conversion,[status(esa)],[f_172_2]) ).

cnf(f_172_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_fun_a_bool_int(U_295,U_294))),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_294)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_294)) ),
    inference(clausify,[status(thm)],[f_172_3]) ).

fof(f_173_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_66_card__image__le]) ).

fof(f_173_2,plain,
    ! [U_297,U_296] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(U_297,U_296))),hAPP_fun_a_bool_nat(finite_card_a,U_296)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_296)) ),
    inference(variable_rename,[status(thm)],[f_173_1]) ).

fof(f_173_3,plain,
    ! [U_296,U_297] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(U_297,U_296))),hAPP_fun_a_bool_nat(finite_card_a,U_296)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_296)) ),
    inference(definitional_conversion,[status(esa)],[f_173_2]) ).

cnf(f_173_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(U_297,U_296))),hAPP_fun_a_bool_nat(finite_card_a,U_296)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_296)) ),
    inference(clausify,[status(thm)],[f_173_3]) ).

fof(f_174_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_67_card__image__le]) ).

fof(f_174_2,plain,
    ! [U_299,U_298] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(U_299,U_298))),hAPP_f22106695ol_nat(finite_card_nat,U_298)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_298)) ),
    inference(variable_rename,[status(thm)],[f_174_1]) ).

fof(f_174_3,plain,
    ! [U_298,U_299] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(U_299,U_298))),hAPP_f22106695ol_nat(finite_card_nat,U_298)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_298)) ),
    inference(definitional_conversion,[status(esa)],[f_174_2]) ).

cnf(f_174_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(U_299,U_298))),hAPP_f22106695ol_nat(finite_card_nat,U_298)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_298)) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

fof(f_175_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_int_pname(F,A))),hAPP_f957591787ol_nat(finite_card_int,A)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_68_card__image__le]) ).

fof(f_175_2,plain,
    ! [U_301,U_300] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_int_pname(U_301,U_300))),hAPP_f957591787ol_nat(finite_card_int,U_300)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_300)) ),
    inference(variable_rename,[status(thm)],[f_175_1]) ).

fof(f_175_3,plain,
    ! [U_300,U_301] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_int_pname(U_301,U_300))),hAPP_f957591787ol_nat(finite_card_int,U_300)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_300)) ),
    inference(definitional_conversion,[status(esa)],[f_175_2]) ).

cnf(f_175_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_int_pname(U_301,U_300))),hAPP_f957591787ol_nat(finite_card_int,U_300)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_300)) ),
    inference(clausify,[status(thm)],[f_175_3]) ).

fof(f_176_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_69_card__image__le]) ).

fof(f_176_2,plain,
    ! [U_303,U_302] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(U_303,U_302))),hAPP_f921600141ol_nat(finite_card_pname,U_302)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_302)) ),
    inference(variable_rename,[status(thm)],[f_176_1]) ).

fof(f_176_3,plain,
    ! [U_302,U_303] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(U_303,U_302))),hAPP_f921600141ol_nat(finite_card_pname,U_302)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_302)) ),
    inference(definitional_conversion,[status(esa)],[f_176_2]) ).

cnf(f_176_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(U_303,U_302))),hAPP_f921600141ol_nat(finite_card_pname,U_302)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_302)) ),
    inference(clausify,[status(thm)],[f_176_3]) ).

fof(f_177_1,plain,
    ! [F,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_nat_int(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_70_card__image__le]) ).

fof(f_177_2,plain,
    ! [U_305,U_304] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_nat_int(U_305,U_304))),hAPP_f22106695ol_nat(finite_card_nat,U_304)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_304)) ),
    inference(variable_rename,[status(thm)],[f_177_1]) ).

fof(f_177_3,plain,
    ! [U_304,U_305] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_nat_int(U_305,U_304))),hAPP_f22106695ol_nat(finite_card_nat,U_304)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_304)) ),
    inference(definitional_conversion,[status(esa)],[f_177_2]) ).

cnf(f_177_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,image_nat_int(U_305,U_304))),hAPP_f22106695ol_nat(finite_card_nat,U_304)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_304)) ),
    inference(clausify,[status(thm)],[f_177_3]) ).

fof(f_178_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,A)),hAPP_f521865025ol_nat(finite1876863882t_bool,B)))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,A),B))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B)) ),
    inference(fof_nnf,[status(thm)],[fact_71_card__mono]) ).

fof(f_178_2,plain,
    ! [U_307,U_306] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,U_307)),hAPP_f521865025ol_nat(finite1876863882t_bool,U_306)))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_307),U_306))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_306)) ),
    inference(variable_rename,[status(thm)],[f_178_1]) ).

fof(f_178_3,plain,
    ! [U_306,U_307] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,U_307)),hAPP_f521865025ol_nat(finite1876863882t_bool,U_306)))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_307),U_306))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_306)) ),
    inference(definitional_conversion,[status(esa)],[f_178_2]) ).

cnf(f_178_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,U_307)),hAPP_f521865025ol_nat(finite1876863882t_bool,U_306)))
    | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_307),U_306))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_306)) ),
    inference(clausify,[status(thm)],[f_178_3]) ).

fof(f_179_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_72_card__mono]) ).

fof(f_179_2,plain,
    ! [U_309,U_308] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,U_309)),hAPP_f696928925ol_nat(finite346522414t_bool,U_308)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_309),U_308))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_308)) ),
    inference(variable_rename,[status(thm)],[f_179_1]) ).

fof(f_179_3,plain,
    ! [U_308,U_309] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,U_309)),hAPP_f696928925ol_nat(finite346522414t_bool,U_308)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_309),U_308))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_308)) ),
    inference(definitional_conversion,[status(esa)],[f_179_2]) ).

cnf(f_179_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,U_309)),hAPP_f696928925ol_nat(finite346522414t_bool,U_308)))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_309),U_308))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_308)) ),
    inference(clausify,[status(thm)],[f_179_3]) ).

fof(f_180_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_73_card__mono]) ).

fof(f_180_2,plain,
    ! [U_311,U_310] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,U_311)),hAPP_f55526627ol_nat(finite1340463720e_bool,U_310)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_311),U_310))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_310)) ),
    inference(variable_rename,[status(thm)],[f_180_1]) ).

fof(f_180_3,plain,
    ! [U_310,U_311] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,U_311)),hAPP_f55526627ol_nat(finite1340463720e_bool,U_310)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_311),U_310))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_310)) ),
    inference(definitional_conversion,[status(esa)],[f_180_2]) ).

cnf(f_180_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,U_311)),hAPP_f55526627ol_nat(finite1340463720e_bool,U_310)))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_311),U_310))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_310)) ),
    inference(clausify,[status(thm)],[f_180_3]) ).

fof(f_181_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_74_card__mono]) ).

fof(f_181_2,plain,
    ! [U_313,U_312] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_313)),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_312)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_313),U_312))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_312)) ),
    inference(variable_rename,[status(thm)],[f_181_1]) ).

fof(f_181_3,plain,
    ! [U_313,U_312] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_313)),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_312)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_313),U_312))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_312)) ),
    inference(definitional_conversion,[status(esa)],[f_181_2]) ).

cnf(f_181_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_313)),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_312)))
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_313),U_312))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_312)) ),
    inference(clausify,[status(thm)],[f_181_3]) ).

fof(f_182_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_75_card__mono]) ).

fof(f_182_2,plain,
    ! [U_315,U_314] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,U_315)),hAPP_f921600141ol_nat(finite_card_pname,U_314)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_315),U_314))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_314)) ),
    inference(variable_rename,[status(thm)],[f_182_1]) ).

fof(f_182_3,plain,
    ! [U_314,U_315] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,U_315)),hAPP_f921600141ol_nat(finite_card_pname,U_314)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_315),U_314))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_314)) ),
    inference(definitional_conversion,[status(esa)],[f_182_2]) ).

cnf(f_182_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,U_315)),hAPP_f921600141ol_nat(finite_card_pname,U_314)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_315),U_314))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_314)) ),
    inference(clausify,[status(thm)],[f_182_3]) ).

fof(f_183_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_76_card__mono]) ).

fof(f_183_2,plain,
    ! [U_317,U_316] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,U_317)),hAPP_fun_a_bool_nat(finite_card_a,U_316)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_317),U_316))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_316)) ),
    inference(variable_rename,[status(thm)],[f_183_1]) ).

fof(f_183_3,plain,
    ! [U_316,U_317] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,U_317)),hAPP_fun_a_bool_nat(finite_card_a,U_316)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_317),U_316))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_316)) ),
    inference(definitional_conversion,[status(esa)],[f_183_2]) ).

cnf(f_183_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,U_317)),hAPP_fun_a_bool_nat(finite_card_a,U_316)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_317),U_316))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_316)) ),
    inference(clausify,[status(thm)],[f_183_3]) ).

fof(f_184_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_77_card__mono]) ).

fof(f_184_2,plain,
    ! [U_319,U_318] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,U_319)),hAPP_f22106695ol_nat(finite_card_nat,U_318)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_319),U_318))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_318)) ),
    inference(variable_rename,[status(thm)],[f_184_1]) ).

fof(f_184_3,plain,
    ! [U_318,U_319] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,U_319)),hAPP_f22106695ol_nat(finite_card_nat,U_318)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_319),U_318))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_318)) ),
    inference(definitional_conversion,[status(esa)],[f_184_2]) ).

cnf(f_184_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,U_319)),hAPP_f22106695ol_nat(finite_card_nat,U_318)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_319),U_318))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_318)) ),
    inference(clausify,[status(thm)],[f_184_3]) ).

fof(f_185_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,A)),hAPP_f957591787ol_nat(finite_card_int,B)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) ),
    inference(fof_nnf,[status(thm)],[fact_78_card__mono]) ).

fof(f_185_2,plain,
    ! [U_321,U_320] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,U_321)),hAPP_f957591787ol_nat(finite_card_int,U_320)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_321),U_320))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_320)) ),
    inference(variable_rename,[status(thm)],[f_185_1]) ).

fof(f_185_3,plain,
    ! [U_320,U_321] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,U_321)),hAPP_f957591787ol_nat(finite_card_int,U_320)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_321),U_320))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_320)) ),
    inference(definitional_conversion,[status(esa)],[f_185_2]) ).

cnf(f_185_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,U_321)),hAPP_f957591787ol_nat(finite_card_int,U_320)))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_321),U_320))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_320)) ),
    inference(clausify,[status(thm)],[f_185_3]) ).

fof(f_186_1,plain,
    ! [A,B] :
      ( A = B
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,B)),hAPP_f521865025ol_nat(finite1876863882t_bool,A)))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,A),B))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B)) ),
    inference(fof_nnf,[status(thm)],[fact_79_card__seteq]) ).

fof(f_186_2,plain,
    ! [U_323,U_322] :
      ( U_323 = U_322
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,U_322)),hAPP_f521865025ol_nat(finite1876863882t_bool,U_323)))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_323),U_322))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_322)) ),
    inference(variable_rename,[status(thm)],[f_186_1]) ).

fof(f_186_3,plain,
    ! [U_322,U_323] :
      ( U_323 = U_322
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,U_322)),hAPP_f521865025ol_nat(finite1876863882t_bool,U_323)))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_323),U_322))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_322)) ),
    inference(definitional_conversion,[status(esa)],[f_186_2]) ).

cnf(f_186_4,plain,
    ( U_323 = U_322
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,U_322)),hAPP_f521865025ol_nat(finite1876863882t_bool,U_323)))
    | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_323),U_322))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_322)) ),
    inference(clausify,[status(thm)],[f_186_3]) ).

fof(f_187_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_80_card__seteq]) ).

fof(f_187_2,plain,
    ! [U_325,U_324] :
      ( U_325 = U_324
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,U_324)),hAPP_f696928925ol_nat(finite346522414t_bool,U_325)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_325),U_324))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_324)) ),
    inference(variable_rename,[status(thm)],[f_187_1]) ).

fof(f_187_3,plain,
    ! [U_324,U_325] :
      ( U_325 = U_324
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,U_324)),hAPP_f696928925ol_nat(finite346522414t_bool,U_325)))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_325),U_324))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_324)) ),
    inference(definitional_conversion,[status(esa)],[f_187_2]) ).

cnf(f_187_4,plain,
    ( U_325 = U_324
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,U_324)),hAPP_f696928925ol_nat(finite346522414t_bool,U_325)))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_325),U_324))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_324)) ),
    inference(clausify,[status(thm)],[f_187_3]) ).

fof(f_188_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_81_card__seteq]) ).

fof(f_188_2,plain,
    ! [U_327,U_326] :
      ( U_327 = U_326
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,U_326)),hAPP_f55526627ol_nat(finite1340463720e_bool,U_327)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_327),U_326))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_326))
      | ~ is_fun1661590463l_bool(U_326)
      | ~ is_fun1661590463l_bool(U_327) ),
    inference(variable_rename,[status(thm)],[f_188_1]) ).

fof(f_188_3,plain,
    ! [U_326,U_327] :
      ( U_327 = U_326
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,U_326)),hAPP_f55526627ol_nat(finite1340463720e_bool,U_327)))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_327),U_326))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_326))
      | ~ is_fun1661590463l_bool(U_326)
      | ~ is_fun1661590463l_bool(U_327) ),
    inference(definitional_conversion,[status(esa)],[f_188_2]) ).

cnf(f_188_4,plain,
    ( U_327 = U_326
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,U_326)),hAPP_f55526627ol_nat(finite1340463720e_bool,U_327)))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_327),U_326))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_326))
    | ~ is_fun1661590463l_bool(U_326)
    | ~ is_fun1661590463l_bool(U_327) ),
    inference(clausify,[status(thm)],[f_188_3]) ).

fof(f_189_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_82_card__seteq]) ).

fof(f_189_2,plain,
    ! [U_329,U_328] :
      ( U_329 = U_328
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_328)),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_329)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_329),U_328))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_328))
      | ~ is_fun949378684l_bool(U_328)
      | ~ is_fun949378684l_bool(U_329) ),
    inference(variable_rename,[status(thm)],[f_189_1]) ).

fof(f_189_3,plain,
    ! [U_328,U_329] :
      ( U_329 = U_328
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_328)),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_329)))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_329),U_328))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_328))
      | ~ is_fun949378684l_bool(U_328)
      | ~ is_fun949378684l_bool(U_329) ),
    inference(definitional_conversion,[status(esa)],[f_189_2]) ).

cnf(f_189_4,plain,
    ( U_329 = U_328
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_328)),hAPP_f2009550088ol_nat(finite1306199131a_bool,U_329)))
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_329),U_328))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_328))
    | ~ is_fun949378684l_bool(U_328)
    | ~ is_fun949378684l_bool(U_329) ),
    inference(clausify,[status(thm)],[f_189_3]) ).

fof(f_190_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_83_card__seteq]) ).

fof(f_190_2,plain,
    ! [U_331,U_330] :
      ( U_331 = U_330
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,U_330)),hAPP_f921600141ol_nat(finite_card_pname,U_331)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_331),U_330))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_330))
      | ~ is_fun_pname_bool(U_330)
      | ~ is_fun_pname_bool(U_331) ),
    inference(variable_rename,[status(thm)],[f_190_1]) ).

fof(f_190_3,plain,
    ! [U_331,U_330] :
      ( U_331 = U_330
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,U_330)),hAPP_f921600141ol_nat(finite_card_pname,U_331)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_331),U_330))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_330))
      | ~ is_fun_pname_bool(U_330)
      | ~ is_fun_pname_bool(U_331) ),
    inference(definitional_conversion,[status(esa)],[f_190_2]) ).

cnf(f_190_4,plain,
    ( U_331 = U_330
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,U_330)),hAPP_f921600141ol_nat(finite_card_pname,U_331)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_331),U_330))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_330))
    | ~ is_fun_pname_bool(U_330)
    | ~ is_fun_pname_bool(U_331) ),
    inference(clausify,[status(thm)],[f_190_3]) ).

fof(f_191_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_84_card__seteq]) ).

fof(f_191_2,plain,
    ! [U_333,U_332] :
      ( U_333 = U_332
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,U_332)),hAPP_fun_a_bool_nat(finite_card_a,U_333)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_333),U_332))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_332))
      | ~ is_fun_a_bool(U_332)
      | ~ is_fun_a_bool(U_333) ),
    inference(variable_rename,[status(thm)],[f_191_1]) ).

fof(f_191_3,plain,
    ! [U_332,U_333] :
      ( U_333 = U_332
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,U_332)),hAPP_fun_a_bool_nat(finite_card_a,U_333)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_333),U_332))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_332))
      | ~ is_fun_a_bool(U_332)
      | ~ is_fun_a_bool(U_333) ),
    inference(definitional_conversion,[status(esa)],[f_191_2]) ).

cnf(f_191_4,plain,
    ( U_333 = U_332
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,U_332)),hAPP_fun_a_bool_nat(finite_card_a,U_333)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_333),U_332))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_332))
    | ~ is_fun_a_bool(U_332)
    | ~ is_fun_a_bool(U_333) ),
    inference(clausify,[status(thm)],[f_191_3]) ).

fof(f_192_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_85_card__seteq]) ).

fof(f_192_2,plain,
    ! [U_335,U_334] :
      ( U_335 = U_334
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,U_334)),hAPP_f22106695ol_nat(finite_card_nat,U_335)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_335),U_334))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_334)) ),
    inference(variable_rename,[status(thm)],[f_192_1]) ).

fof(f_192_3,plain,
    ! [U_335,U_334] :
      ( U_335 = U_334
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,U_334)),hAPP_f22106695ol_nat(finite_card_nat,U_335)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_335),U_334))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_334)) ),
    inference(definitional_conversion,[status(esa)],[f_192_2]) ).

cnf(f_192_4,plain,
    ( U_335 = U_334
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,U_334)),hAPP_f22106695ol_nat(finite_card_nat,U_335)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_335),U_334))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_334)) ),
    inference(clausify,[status(thm)],[f_192_3]) ).

fof(f_193_1,plain,
    ! [A,B] :
      ( A = B
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,B)),hAPP_f957591787ol_nat(finite_card_int,A)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) ),
    inference(fof_nnf,[status(thm)],[fact_86_card__seteq]) ).

fof(f_193_2,plain,
    ! [U_337,U_336] :
      ( U_337 = U_336
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,U_336)),hAPP_f957591787ol_nat(finite_card_int,U_337)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_337),U_336))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_336)) ),
    inference(variable_rename,[status(thm)],[f_193_1]) ).

fof(f_193_3,plain,
    ! [U_336,U_337] :
      ( U_337 = U_336
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,U_336)),hAPP_f957591787ol_nat(finite_card_int,U_337)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_337),U_336))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_336)) ),
    inference(definitional_conversion,[status(esa)],[f_193_2]) ).

cnf(f_193_4,plain,
    ( U_337 = U_336
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,U_336)),hAPP_f957591787ol_nat(finite_card_int,U_337)))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_337),U_336))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_336)) ),
    inference(clausify,[status(thm)],[f_193_3]) ).

fof(f_194_1,plain,
    ! [X_1,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,A)),hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X_1),A))))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_87_card__insert__le]) ).

fof(f_194_2,plain,
    ! [U_339,U_338] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,U_338)),hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,U_339),U_338))))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_338)) ),
    inference(variable_rename,[status(thm)],[f_194_1]) ).

fof(f_194_3,plain,
    ! [U_338,U_339] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,U_338)),hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,U_339),U_338))))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_338)) ),
    inference(definitional_conversion,[status(esa)],[f_194_2]) ).

cnf(f_194_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f521865025ol_nat(finite1876863882t_bool,U_338)),hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,U_339),U_338))))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_338)) ),
    inference(clausify,[status(thm)],[f_194_3]) ).

fof(f_195_1,plain,
    ! [X_1,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,A)),hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X_1),A))))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_88_card__insert__le]) ).

fof(f_195_2,plain,
    ! [U_341,U_340] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,U_340)),hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,U_341),U_340))))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_340)) ),
    inference(variable_rename,[status(thm)],[f_195_1]) ).

fof(f_195_3,plain,
    ! [U_340,U_341] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,U_340)),hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,U_341),U_340))))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_340)) ),
    inference(definitional_conversion,[status(esa)],[f_195_2]) ).

cnf(f_195_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,U_340)),hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,U_341),U_340))))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_340)) ),
    inference(clausify,[status(thm)],[f_195_3]) ).

fof(f_196_1,plain,
    ! [X_1,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,A)),hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_89_card__insert__le]) ).

fof(f_196_2,plain,
    ! [U_343,U_342] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,U_342)),hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,U_343),U_342))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_342)) ),
    inference(variable_rename,[status(thm)],[f_196_1]) ).

fof(f_196_3,plain,
    ! [U_342,U_343] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,U_342)),hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,U_343),U_342))))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_342)) ),
    inference(definitional_conversion,[status(esa)],[f_196_2]) ).

cnf(f_196_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,U_342)),hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,U_343),U_342))))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_342)) ),
    inference(clausify,[status(thm)],[f_196_3]) ).

fof(f_197_1,plain,
    ! [X_1,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,A)),hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X_1),A))))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_90_card__insert__le]) ).

fof(f_197_2,plain,
    ! [U_345,U_344] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_344)),hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,U_345),U_344))))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_344)) ),
    inference(variable_rename,[status(thm)],[f_197_1]) ).

fof(f_197_3,plain,
    ! [U_344,U_345] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_344)),hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,U_345),U_344))))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_344)) ),
    inference(definitional_conversion,[status(esa)],[f_197_2]) ).

cnf(f_197_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_344)),hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,U_345),U_344))))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_344)) ),
    inference(clausify,[status(thm)],[f_197_3]) ).

fof(f_198_1,plain,
    ! [X_1,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,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_91_card__insert__le]) ).

fof(f_198_2,plain,
    ! [U_347,U_346] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,U_346)),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_347),U_346))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_346)) ),
    inference(variable_rename,[status(thm)],[f_198_1]) ).

fof(f_198_3,plain,
    ! [U_346,U_347] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,U_346)),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_347),U_346))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_346)) ),
    inference(definitional_conversion,[status(esa)],[f_198_2]) ).

cnf(f_198_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,U_346)),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_347),U_346))))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_346)) ),
    inference(clausify,[status(thm)],[f_198_3]) ).

fof(f_199_1,plain,
    ! [X_1,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,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_92_card__insert__le]) ).

fof(f_199_2,plain,
    ! [U_349,U_348] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,U_348)),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_349),U_348))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_348)) ),
    inference(variable_rename,[status(thm)],[f_199_1]) ).

fof(f_199_3,plain,
    ! [U_348,U_349] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,U_348)),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_349),U_348))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_348)) ),
    inference(definitional_conversion,[status(esa)],[f_199_2]) ).

cnf(f_199_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,U_348)),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_349),U_348))))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_348)) ),
    inference(clausify,[status(thm)],[f_199_3]) ).

fof(f_200_1,plain,
    ! [X_1,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,A)),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A))))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_93_card__insert__le]) ).

fof(f_200_2,plain,
    ! [U_351,U_350] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,U_350)),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_351),U_350))))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_350)) ),
    inference(variable_rename,[status(thm)],[f_200_1]) ).

fof(f_200_3,plain,
    ! [U_350,U_351] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,U_350)),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_351),U_350))))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_350)) ),
    inference(definitional_conversion,[status(esa)],[f_200_2]) ).

cnf(f_200_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,U_350)),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_351),U_350))))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_350)) ),
    inference(clausify,[status(thm)],[f_200_3]) ).

fof(f_201_1,plain,
    ! [X_1,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,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_94_card__insert__le]) ).

fof(f_201_2,plain,
    ! [U_353,U_352] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,U_352)),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_353),U_352))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_352)) ),
    inference(variable_rename,[status(thm)],[f_201_1]) ).

fof(f_201_3,plain,
    ! [U_353,U_352] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,U_352)),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_353),U_352))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_352)) ),
    inference(definitional_conversion,[status(esa)],[f_201_2]) ).

cnf(f_201_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,U_352)),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_353),U_352))))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_352)) ),
    inference(clausify,[status(thm)],[f_201_3]) ).

fof(f_202_1,plain,
    ! [X_1,A] :
      ( ( ( hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X_1),A)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,A))
          | hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X_1),A)) )
        & ( hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X_1),A)) = hAPP_f521865025ol_nat(finite1876863882t_bool,A)
          | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X_1),A)) ) )
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_95_card__insert__if]) ).

fof(f_202_2,plain,
    ! [U_355,U_354] :
      ( ( ( hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,U_355),U_354)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,U_354))
          | hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,U_355),U_354)) )
        & ( hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,U_355),U_354)) = hAPP_f521865025ol_nat(finite1876863882t_bool,U_354)
          | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,U_355),U_354)) ) )
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_354)) ),
    inference(variable_rename,[status(thm)],[f_202_1]) ).

fof(f_202_3,plain,
    ( ! [U_354,U_355] :
        ( hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,U_355),U_354)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,U_354))
        | hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,U_355),U_354))
        | ~ sP0(U_354,U_355) )
    & ! [U_354,U_355] :
        ( hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,U_355),U_354)) = hAPP_f521865025ol_nat(finite1876863882t_bool,U_354)
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,U_355),U_354))
        | ~ sP0(U_354,U_355) )
    & ! [U_354,U_355] :
        ( sP0(U_354,U_355)
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_354)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_202_2]) ).

cnf(f_202_4,plain,
    ( sP0(U_354,U_355)
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_354)) ),
    inference(clausify,[status(thm)],[f_202_3]) ).

cnf(f_202_5,plain,
    ( hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,U_355),U_354)) = hAPP_f521865025ol_nat(finite1876863882t_bool,U_354)
    | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,U_355),U_354))
    | ~ sP0(U_354,U_355) ),
    inference(clausify,[status(thm)],[f_202_3]) ).

cnf(f_202_6,plain,
    ( hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,U_355),U_354)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,U_354))
    | hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,U_355),U_354))
    | ~ sP0(U_354,U_355) ),
    inference(clausify,[status(thm)],[f_202_3]) ).

fof(f_203_1,plain,
    ! [X_1,A] :
      ( ( ( hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X_1),A)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,A))
          | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_1),A)) )
        & ( hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X_1),A)) = hAPP_f696928925ol_nat(finite346522414t_bool,A)
          | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_1),A)) ) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_96_card__insert__if]) ).

fof(f_203_2,plain,
    ! [U_357,U_356] :
      ( ( ( hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,U_357),U_356)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,U_356))
          | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_357),U_356)) )
        & ( hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,U_357),U_356)) = hAPP_f696928925ol_nat(finite346522414t_bool,U_356)
          | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_357),U_356)) ) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_356)) ),
    inference(variable_rename,[status(thm)],[f_203_1]) ).

fof(f_203_3,plain,
    ( ! [U_357,U_356] :
        ( hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,U_357),U_356)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,U_356))
        | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_357),U_356))
        | ~ sP1(U_357,U_356) )
    & ! [U_357,U_356] :
        ( hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,U_357),U_356)) = hAPP_f696928925ol_nat(finite346522414t_bool,U_356)
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_357),U_356))
        | ~ sP1(U_357,U_356) )
    & ! [U_357,U_356] :
        ( sP1(U_357,U_356)
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_356)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_203_2]) ).

cnf(f_203_4,plain,
    ( sP1(U_357,U_356)
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_356)) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

cnf(f_203_5,plain,
    ( hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,U_357),U_356)) = hAPP_f696928925ol_nat(finite346522414t_bool,U_356)
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_357),U_356))
    | ~ sP1(U_357,U_356) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

cnf(f_203_6,plain,
    ( hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,U_357),U_356)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,U_356))
    | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_357),U_356))
    | ~ sP1(U_357,U_356) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

fof(f_204_1,plain,
    ! [X_1,A] :
      ( ( ( hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,A))
          | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A)) )
        & ( hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A)) = hAPP_f55526627ol_nat(finite1340463720e_bool,A)
          | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A)) ) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_97_card__insert__if]) ).

fof(f_204_2,plain,
    ! [U_359,U_358] :
      ( ( ( hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,U_359),U_358)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,U_358))
          | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_359),U_358)) )
        & ( hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,U_359),U_358)) = hAPP_f55526627ol_nat(finite1340463720e_bool,U_358)
          | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_359),U_358)) ) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_358)) ),
    inference(variable_rename,[status(thm)],[f_204_1]) ).

fof(f_204_3,plain,
    ( ! [U_359,U_358] :
        ( hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,U_359),U_358)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,U_358))
        | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_359),U_358))
        | ~ sP2(U_359,U_358) )
    & ! [U_359,U_358] :
        ( hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,U_359),U_358)) = hAPP_f55526627ol_nat(finite1340463720e_bool,U_358)
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_359),U_358))
        | ~ sP2(U_359,U_358) )
    & ! [U_359,U_358] :
        ( sP2(U_359,U_358)
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_358)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_204_2]) ).

cnf(f_204_4,plain,
    ( sP2(U_359,U_358)
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_358)) ),
    inference(clausify,[status(thm)],[f_204_3]) ).

cnf(f_204_5,plain,
    ( hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,U_359),U_358)) = hAPP_f55526627ol_nat(finite1340463720e_bool,U_358)
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_359),U_358))
    | ~ sP2(U_359,U_358) ),
    inference(clausify,[status(thm)],[f_204_3]) ).

cnf(f_204_6,plain,
    ( hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,U_359),U_358)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,U_358))
    | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_359),U_358))
    | ~ sP2(U_359,U_358) ),
    inference(clausify,[status(thm)],[f_204_3]) ).

fof(f_205_1,plain,
    ! [X_1,A] :
      ( ( ( hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X_1),A)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,A))
          | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_1),A)) )
        & ( hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X_1),A)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,A)
          | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_1),A)) ) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_98_card__insert__if]) ).

fof(f_205_2,plain,
    ! [U_361,U_360] :
      ( ( ( hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,U_361),U_360)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_360))
          | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_361),U_360)) )
        & ( hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,U_361),U_360)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,U_360)
          | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_361),U_360)) ) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_360)) ),
    inference(variable_rename,[status(thm)],[f_205_1]) ).

fof(f_205_3,plain,
    ( ! [U_361,U_360] :
        ( hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,U_361),U_360)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_360))
        | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_361),U_360))
        | ~ sP3(U_361,U_360) )
    & ! [U_361,U_360] :
        ( hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,U_361),U_360)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,U_360)
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_361),U_360))
        | ~ sP3(U_361,U_360) )
    & ! [U_361,U_360] :
        ( sP3(U_361,U_360)
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_360)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_205_2]) ).

cnf(f_205_4,plain,
    ( sP3(U_361,U_360)
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_360)) ),
    inference(clausify,[status(thm)],[f_205_3]) ).

cnf(f_205_5,plain,
    ( hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,U_361),U_360)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,U_360)
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_361),U_360))
    | ~ sP3(U_361,U_360) ),
    inference(clausify,[status(thm)],[f_205_3]) ).

cnf(f_205_6,plain,
    ( hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,U_361),U_360)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_360))
    | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_361),U_360))
    | ~ sP3(U_361,U_360) ),
    inference(clausify,[status(thm)],[f_205_3]) ).

fof(f_206_1,plain,
    ! [X_1,A] :
      ( ( ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,A))
          | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) )
        & ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_f921600141ol_nat(finite_card_pname,A)
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) ) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_99_card__insert__if]) ).

fof(f_206_2,plain,
    ! [U_363,U_362] :
      ( ( ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_363),U_362)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,U_362))
          | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_363),U_362)) )
        & ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_363),U_362)) = hAPP_f921600141ol_nat(finite_card_pname,U_362)
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_363),U_362)) ) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_362)) ),
    inference(variable_rename,[status(thm)],[f_206_1]) ).

fof(f_206_3,plain,
    ( ! [U_363,U_362] :
        ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_363),U_362)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,U_362))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_363),U_362))
        | ~ sP4(U_363,U_362) )
    & ! [U_363,U_362] :
        ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_363),U_362)) = hAPP_f921600141ol_nat(finite_card_pname,U_362)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_363),U_362))
        | ~ sP4(U_363,U_362) )
    & ! [U_363,U_362] :
        ( sP4(U_363,U_362)
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_362)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_206_2]) ).

cnf(f_206_4,plain,
    ( sP4(U_363,U_362)
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_362)) ),
    inference(clausify,[status(thm)],[f_206_3]) ).

cnf(f_206_5,plain,
    ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_363),U_362)) = hAPP_f921600141ol_nat(finite_card_pname,U_362)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_363),U_362))
    | ~ sP4(U_363,U_362) ),
    inference(clausify,[status(thm)],[f_206_3]) ).

cnf(f_206_6,plain,
    ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_363),U_362)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,U_362))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_363),U_362))
    | ~ sP4(U_363,U_362) ),
    inference(clausify,[status(thm)],[f_206_3]) ).

fof(f_207_1,plain,
    ! [X_1,A] :
      ( ( ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,A))
          | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) )
        & ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_f22106695ol_nat(finite_card_nat,A)
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_100_card__insert__if]) ).

fof(f_207_2,plain,
    ! [U_365,U_364] :
      ( ( ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_365),U_364)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,U_364))
          | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_365),U_364)) )
        & ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_365),U_364)) = hAPP_f22106695ol_nat(finite_card_nat,U_364)
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_365),U_364)) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_364)) ),
    inference(variable_rename,[status(thm)],[f_207_1]) ).

fof(f_207_3,plain,
    ( ! [U_364,U_365] :
        ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_365),U_364)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,U_364))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_365),U_364))
        | ~ sP5(U_364,U_365) )
    & ! [U_364,U_365] :
        ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_365),U_364)) = hAPP_f22106695ol_nat(finite_card_nat,U_364)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_365),U_364))
        | ~ sP5(U_364,U_365) )
    & ! [U_364,U_365] :
        ( sP5(U_364,U_365)
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_364)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_207_2]) ).

cnf(f_207_4,plain,
    ( sP5(U_364,U_365)
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_364)) ),
    inference(clausify,[status(thm)],[f_207_3]) ).

cnf(f_207_5,plain,
    ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_365),U_364)) = hAPP_f22106695ol_nat(finite_card_nat,U_364)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_365),U_364))
    | ~ sP5(U_364,U_365) ),
    inference(clausify,[status(thm)],[f_207_3]) ).

cnf(f_207_6,plain,
    ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_365),U_364)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,U_364))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_365),U_364))
    | ~ sP5(U_364,U_365) ),
    inference(clausify,[status(thm)],[f_207_3]) ).

fof(f_208_1,plain,
    ! [X_1,A] :
      ( ( ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,A))
          | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) )
        & ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_f957591787ol_nat(finite_card_int,A)
          | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) ) )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_101_card__insert__if]) ).

fof(f_208_2,plain,
    ! [U_367,U_366] :
      ( ( ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_367),U_366)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,U_366))
          | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_367),U_366)) )
        & ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_367),U_366)) = hAPP_f957591787ol_nat(finite_card_int,U_366)
          | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_367),U_366)) ) )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_366)) ),
    inference(variable_rename,[status(thm)],[f_208_1]) ).

fof(f_208_3,plain,
    ( ! [U_366,U_367] :
        ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_367),U_366)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,U_366))
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_367),U_366))
        | ~ sP6(U_366,U_367) )
    & ! [U_366,U_367] :
        ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_367),U_366)) = hAPP_f957591787ol_nat(finite_card_int,U_366)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_367),U_366))
        | ~ sP6(U_366,U_367) )
    & ! [U_366,U_367] :
        ( sP6(U_366,U_367)
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_366)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_208_2]) ).

cnf(f_208_4,plain,
    ( sP6(U_366,U_367)
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_366)) ),
    inference(clausify,[status(thm)],[f_208_3]) ).

cnf(f_208_5,plain,
    ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_367),U_366)) = hAPP_f957591787ol_nat(finite_card_int,U_366)
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_367),U_366))
    | ~ sP6(U_366,U_367) ),
    inference(clausify,[status(thm)],[f_208_3]) ).

cnf(f_208_6,plain,
    ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_367),U_366)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,U_366))
    | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_367),U_366))
    | ~ sP6(U_366,U_367) ),
    inference(clausify,[status(thm)],[f_208_3]) ).

fof(f_209_1,plain,
    ! [X_1,A] :
      ( ( ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),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_1),A)) )
        & ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_fun_a_bool_nat(finite_card_a,A)
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) ) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_102_card__insert__if]) ).

fof(f_209_2,plain,
    ! [U_369,U_368] :
      ( ( ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_369),U_368)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,U_368))
          | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_369),U_368)) )
        & ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_369),U_368)) = hAPP_fun_a_bool_nat(finite_card_a,U_368)
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_369),U_368)) ) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_368)) ),
    inference(variable_rename,[status(thm)],[f_209_1]) ).

fof(f_209_3,plain,
    ( ! [U_368,U_369] :
        ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_369),U_368)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,U_368))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_369),U_368))
        | ~ sP7(U_368,U_369) )
    & ! [U_368,U_369] :
        ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_369),U_368)) = hAPP_fun_a_bool_nat(finite_card_a,U_368)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_369),U_368))
        | ~ sP7(U_368,U_369) )
    & ! [U_368,U_369] :
        ( sP7(U_368,U_369)
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_368)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_209_2]) ).

cnf(f_209_4,plain,
    ( sP7(U_368,U_369)
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_368)) ),
    inference(clausify,[status(thm)],[f_209_3]) ).

cnf(f_209_5,plain,
    ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_369),U_368)) = hAPP_fun_a_bool_nat(finite_card_a,U_368)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_369),U_368))
    | ~ sP7(U_368,U_369) ),
    inference(clausify,[status(thm)],[f_209_3]) ).

cnf(f_209_6,plain,
    ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_369),U_368)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,U_368))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_369),U_368))
    | ~ sP7(U_368,U_369) ),
    inference(clausify,[status(thm)],[f_209_3]) ).

fof(f_210_1,plain,
    ! [X_1,A] :
      ( hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,X_1),A)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,A))
      | hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,X_1),A))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_103_card__insert__disjoint]) ).

fof(f_210_2,plain,
    ! [U_371,U_370] :
      ( hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,U_371),U_370)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,U_370))
      | hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,U_371),U_370))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_370)) ),
    inference(variable_rename,[status(thm)],[f_210_1]) ).

fof(f_210_3,plain,
    ! [U_370,U_371] :
      ( hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,U_371),U_370)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,U_370))
      | hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,U_371),U_370))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_370)) ),
    inference(definitional_conversion,[status(esa)],[f_210_2]) ).

cnf(f_210_4,plain,
    ( hAPP_f521865025ol_nat(finite1876863882t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,U_371),U_370)) = hAPP_nat_nat(suc,hAPP_f521865025ol_nat(finite1876863882t_bool,U_370))
    | hBOOL(hAPP_f215623910l_bool(hAPP_f628503027l_bool(member_fun_int_bool,U_371),U_370))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_370)) ),
    inference(clausify,[status(thm)],[f_210_3]) ).

fof(f_211_1,plain,
    ! [X_1,A] :
      ( hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,X_1),A)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,A))
      | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_1),A))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_104_card__insert__disjoint]) ).

fof(f_211_2,plain,
    ! [U_373,U_372] :
      ( hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,U_373),U_372)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,U_372))
      | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_373),U_372))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_372)) ),
    inference(variable_rename,[status(thm)],[f_211_1]) ).

fof(f_211_3,plain,
    ! [U_373,U_372] :
      ( hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,U_373),U_372)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,U_372))
      | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_373),U_372))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_372)) ),
    inference(definitional_conversion,[status(esa)],[f_211_2]) ).

cnf(f_211_4,plain,
    ( hAPP_f696928925ol_nat(finite346522414t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,U_373),U_372)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,U_372))
    | hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,U_373),U_372))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_372)) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

fof(f_212_1,plain,
    ! [X_1,A] :
      ( hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,X_1),A)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,A))
      | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_1),A))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_105_card__insert__disjoint]) ).

fof(f_212_2,plain,
    ! [U_375,U_374] :
      ( hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,U_375),U_374)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,U_374))
      | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_375),U_374))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_374)) ),
    inference(variable_rename,[status(thm)],[f_212_1]) ).

fof(f_212_3,plain,
    ! [U_374,U_375] :
      ( hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,U_375),U_374)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,U_374))
      | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_375),U_374))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_374)) ),
    inference(definitional_conversion,[status(esa)],[f_212_2]) ).

cnf(f_212_4,plain,
    ( hAPP_f55526627ol_nat(finite1340463720e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,U_375),U_374)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,U_374))
    | hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,U_375),U_374))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_374)) ),
    inference(clausify,[status(thm)],[f_212_3]) ).

fof(f_213_1,plain,
    ! [X_1,A] :
      ( hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,X_1),A)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,A))
      | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_1),A))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_106_card__insert__disjoint]) ).

fof(f_213_2,plain,
    ! [U_377,U_376] :
      ( hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,U_377),U_376)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_376))
      | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_377),U_376))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_376)) ),
    inference(variable_rename,[status(thm)],[f_213_1]) ).

fof(f_213_3,plain,
    ! [U_376,U_377] :
      ( hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,U_377),U_376)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_376))
      | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_377),U_376))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_376)) ),
    inference(definitional_conversion,[status(esa)],[f_213_2]) ).

cnf(f_213_4,plain,
    ( hAPP_f2009550088ol_nat(finite1306199131a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,U_377),U_376)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,U_376))
    | hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,U_377),U_376))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_376)) ),
    inference(clausify,[status(thm)],[f_213_3]) ).

fof(f_214_1,plain,
    ! [X_1,A] :
      ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,A))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_107_card__insert__disjoint]) ).

fof(f_214_2,plain,
    ! [U_379,U_378] :
      ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_379),U_378)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,U_378))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_379),U_378))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_378)) ),
    inference(variable_rename,[status(thm)],[f_214_1]) ).

fof(f_214_3,plain,
    ! [U_379,U_378] :
      ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_379),U_378)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,U_378))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_379),U_378))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_378)) ),
    inference(definitional_conversion,[status(esa)],[f_214_2]) ).

cnf(f_214_4,plain,
    ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_379),U_378)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,U_378))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_379),U_378))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_378)) ),
    inference(clausify,[status(thm)],[f_214_3]) ).

fof(f_215_1,plain,
    ! [X_1,A] :
      ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,A))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_108_card__insert__disjoint]) ).

fof(f_215_2,plain,
    ! [U_381,U_380] :
      ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_381),U_380)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,U_380))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_381),U_380))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_380)) ),
    inference(variable_rename,[status(thm)],[f_215_1]) ).

fof(f_215_3,plain,
    ! [U_380,U_381] :
      ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_381),U_380)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,U_380))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_381),U_380))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_380)) ),
    inference(definitional_conversion,[status(esa)],[f_215_2]) ).

cnf(f_215_4,plain,
    ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_381),U_380)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,U_380))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_381),U_380))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_380)) ),
    inference(clausify,[status(thm)],[f_215_3]) ).

fof(f_216_1,plain,
    ! [X_1,A] :
      ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,A))
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_109_card__insert__disjoint]) ).

fof(f_216_2,plain,
    ! [U_383,U_382] :
      ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_383),U_382)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,U_382))
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_383),U_382))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_382)) ),
    inference(variable_rename,[status(thm)],[f_216_1]) ).

fof(f_216_3,plain,
    ! [U_383,U_382] :
      ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_383),U_382)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,U_382))
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_383),U_382))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_382)) ),
    inference(definitional_conversion,[status(esa)],[f_216_2]) ).

cnf(f_216_4,plain,
    ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_383),U_382)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,U_382))
    | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_383),U_382))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_382)) ),
    inference(clausify,[status(thm)],[f_216_3]) ).

fof(f_217_1,plain,
    ! [X_1,A] :
      ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),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_1),A))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_110_card__insert__disjoint]) ).

fof(f_217_2,plain,
    ! [U_385,U_384] :
      ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_385),U_384)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,U_384))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_385),U_384))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_384)) ),
    inference(variable_rename,[status(thm)],[f_217_1]) ).

fof(f_217_3,plain,
    ! [U_384,U_385] :
      ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_385),U_384)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,U_384))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_385),U_384))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_384)) ),
    inference(definitional_conversion,[status(esa)],[f_217_2]) ).

cnf(f_217_4,plain,
    ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_385),U_384)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,U_384))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_385),U_384))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_384)) ),
    inference(clausify,[status(thm)],[f_217_3]) ).

fof(f_218_1,plain,
    ! [Q_3,Pa] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,Pa),Q_3))))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Q_3)))
        & ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Pa))) ) ),
    inference(fof_nnf,[status(thm)],[fact_111_finite__Collect__conjI]) ).

fof(f_218_2,plain,
    ! [U_387,U_386] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,U_386),U_387))))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_387)))
        & ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_386))) ) ),
    inference(variable_rename,[status(thm)],[f_218_1]) ).

fof(f_218_3,plain,
    ( ! [U_386,U_387] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_387)))
        | ~ sP8(U_386,U_387) )
    & ! [U_386,U_387] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_386)))
        | ~ sP8(U_386,U_387) )
    & ! [U_386,U_387] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,U_386),U_387))))
        | sP8(U_386,U_387) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_218_2]) ).

cnf(f_218_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,U_386),U_387))))
    | sP8(U_386,U_387) ),
    inference(clausify,[status(thm)],[f_218_3]) ).

cnf(f_218_5,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_386)))
    | ~ sP8(U_386,U_387) ),
    inference(clausify,[status(thm)],[f_218_3]) ).

cnf(f_218_6,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_387)))
    | ~ sP8(U_386,U_387) ),
    inference(clausify,[status(thm)],[f_218_3]) ).

fof(f_219_1,plain,
    ! [Q_3,Pa] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,Pa),Q_3))))
      | ( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(Q_3)))
        & ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(Pa))) ) ),
    inference(fof_nnf,[status(thm)],[fact_112_finite__Collect__conjI]) ).

fof(f_219_2,plain,
    ! [U_389,U_388] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,U_388),U_389))))
      | ( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(U_389)))
        & ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(U_388))) ) ),
    inference(variable_rename,[status(thm)],[f_219_1]) ).

fof(f_219_3,plain,
    ( ! [U_388,U_389] :
        ( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(U_389)))
        | ~ sP9(U_388,U_389) )
    & ! [U_388,U_389] :
        ( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(U_388)))
        | ~ sP9(U_388,U_389) )
    & ! [U_388,U_389] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,U_388),U_389))))
        | sP9(U_388,U_389) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_219_2]) ).

cnf(f_219_4,plain,
    ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fconj,U_388),U_389))))
    | sP9(U_388,U_389) ),
    inference(clausify,[status(thm)],[f_219_3]) ).

cnf(f_219_5,plain,
    ( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(U_388)))
    | ~ sP9(U_388,U_389) ),
    inference(clausify,[status(thm)],[f_219_3]) ).

cnf(f_219_6,plain,
    ( ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(U_389)))
    | ~ sP9(U_388,U_389) ),
    inference(clausify,[status(thm)],[f_219_3]) ).

fof(f_220_1,plain,
    ! [Q_3,Pa] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,Pa),Q_3))))
      | ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Q_3)))
        & ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Pa))) ) ),
    inference(fof_nnf,[status(thm)],[fact_113_finite__Collect__conjI]) ).

fof(f_220_2,plain,
    ! [U_391,U_390] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,U_390),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_390))) ) ),
    inference(variable_rename,[status(thm)],[f_220_1]) ).

fof(f_220_3,plain,
    ( ! [U_390,U_391] :
        ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_391)))
        | ~ sP10(U_390,U_391) )
    & ! [U_390,U_391] :
        ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_390)))
        | ~ sP10(U_390,U_391) )
    & ! [U_390,U_391] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,U_390),U_391))))
        | sP10(U_390,U_391) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_220_2]) ).

cnf(f_220_4,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,U_390),U_391))))
    | sP10(U_390,U_391) ),
    inference(clausify,[status(thm)],[f_220_3]) ).

cnf(f_220_5,plain,
    ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_390)))
    | ~ sP10(U_390,U_391) ),
    inference(clausify,[status(thm)],[f_220_3]) ).

cnf(f_220_6,plain,
    ( ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_391)))
    | ~ sP10(U_390,U_391) ),
    inference(clausify,[status(thm)],[f_220_3]) ).

fof(f_221_1,plain,
    ! [Q_3,Pa] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,Pa),Q_3))))
      | ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_3)))
        & ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Pa))) ) ),
    inference(fof_nnf,[status(thm)],[fact_114_finite__Collect__conjI]) ).

fof(f_221_2,plain,
    ! [U_393,U_392] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,U_392),U_393))))
      | ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_393)))
        & ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_392))) ) ),
    inference(variable_rename,[status(thm)],[f_221_1]) ).

fof(f_221_3,plain,
    ( ! [U_392,U_393] :
        ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_393)))
        | ~ sP11(U_392,U_393) )
    & ! [U_392,U_393] :
        ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_392)))
        | ~ sP11(U_392,U_393) )
    & ! [U_392,U_393] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,U_392),U_393))))
        | sP11(U_392,U_393) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11])],[f_221_2]) ).

cnf(f_221_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,U_392),U_393))))
    | sP11(U_392,U_393) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_5,plain,
    ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_392)))
    | ~ sP11(U_392,U_393) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

cnf(f_221_6,plain,
    ( ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_393)))
    | ~ sP11(U_392,U_393) ),
    inference(clausify,[status(thm)],[f_221_3]) ).

fof(f_222_1,plain,
    ! [Q_3,Pa] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,Pa),Q_3))))
      | ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Q_3)))
        & ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Pa))) ) ),
    inference(fof_nnf,[status(thm)],[fact_115_finite__Collect__conjI]) ).

fof(f_222_2,plain,
    ! [U_395,U_394] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,U_394),U_395))))
      | ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_395)))
        & ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_394))) ) ),
    inference(variable_rename,[status(thm)],[f_222_1]) ).

fof(f_222_3,plain,
    ( ! [U_394,U_395] :
        ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_395)))
        | ~ sP12(U_394,U_395) )
    & ! [U_394,U_395] :
        ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_394)))
        | ~ sP12(U_394,U_395) )
    & ! [U_394,U_395] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,U_394),U_395))))
        | sP12(U_394,U_395) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12])],[f_222_2]) ).

cnf(f_222_4,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,U_394),U_395))))
    | sP12(U_394,U_395) ),
    inference(clausify,[status(thm)],[f_222_3]) ).

cnf(f_222_5,plain,
    ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_394)))
    | ~ sP12(U_394,U_395) ),
    inference(clausify,[status(thm)],[f_222_3]) ).

cnf(f_222_6,plain,
    ( ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_395)))
    | ~ sP12(U_394,U_395) ),
    inference(clausify,[status(thm)],[f_222_3]) ).

fof(f_223_1,plain,
    ! [Q_3,Pa] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,Pa),Q_3))))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_3)))
        & ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Pa))) ) ),
    inference(fof_nnf,[status(thm)],[fact_116_finite__Collect__conjI]) ).

fof(f_223_2,plain,
    ! [U_397,U_396] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,U_396),U_397))))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_397)))
        & ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_396))) ) ),
    inference(variable_rename,[status(thm)],[f_223_1]) ).

fof(f_223_3,plain,
    ( ! [U_396,U_397] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_397)))
        | ~ sP13(U_396,U_397) )
    & ! [U_396,U_397] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_396)))
        | ~ sP13(U_396,U_397) )
    & ! [U_396,U_397] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,U_396),U_397))))
        | sP13(U_396,U_397) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13])],[f_223_2]) ).

cnf(f_223_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,U_396),U_397))))
    | sP13(U_396,U_397) ),
    inference(clausify,[status(thm)],[f_223_3]) ).

cnf(f_223_5,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_396)))
    | ~ sP13(U_396,U_397) ),
    inference(clausify,[status(thm)],[f_223_3]) ).

cnf(f_223_6,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_397)))
    | ~ sP13(U_396,U_397) ),
    inference(clausify,[status(thm)],[f_223_3]) ).

fof(f_224_1,plain,
    ! [Q_3,Pa] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,Pa),Q_3))))
      | ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_3)))
        & ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Pa))) ) ),
    inference(fof_nnf,[status(thm)],[fact_117_finite__Collect__conjI]) ).

fof(f_224_2,plain,
    ! [U_399,U_398] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,U_398),U_399))))
      | ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_399)))
        & ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_398))) ) ),
    inference(variable_rename,[status(thm)],[f_224_1]) ).

fof(f_224_3,plain,
    ( ! [U_398,U_399] :
        ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_399)))
        | ~ sP14(U_398,U_399) )
    & ! [U_398,U_399] :
        ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_398)))
        | ~ sP14(U_398,U_399) )
    & ! [U_398,U_399] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,U_398),U_399))))
        | sP14(U_398,U_399) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14])],[f_224_2]) ).

cnf(f_224_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,U_398),U_399))))
    | sP14(U_398,U_399) ),
    inference(clausify,[status(thm)],[f_224_3]) ).

cnf(f_224_5,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_398)))
    | ~ sP14(U_398,U_399) ),
    inference(clausify,[status(thm)],[f_224_3]) ).

cnf(f_224_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_399)))
    | ~ sP14(U_398,U_399) ),
    inference(clausify,[status(thm)],[f_224_3]) ).

fof(f_225_1,plain,
    ! [Q_3,Pa] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,Pa),Q_3))))
      | ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(Q_3)))
        & ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(Pa))) ) ),
    inference(fof_nnf,[status(thm)],[fact_118_finite__Collect__conjI]) ).

fof(f_225_2,plain,
    ! [U_401,U_400] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,U_400),U_401))))
      | ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(U_401)))
        & ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(U_400))) ) ),
    inference(variable_rename,[status(thm)],[f_225_1]) ).

fof(f_225_3,plain,
    ( ! [U_400,U_401] :
        ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(U_401)))
        | ~ sP15(U_400,U_401) )
    & ! [U_400,U_401] :
        ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(U_400)))
        | ~ sP15(U_400,U_401) )
    & ! [U_400,U_401] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,U_400),U_401))))
        | sP15(U_400,U_401) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP15])],[f_225_2]) ).

cnf(f_225_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,U_400),U_401))))
    | sP15(U_400,U_401) ),
    inference(clausify,[status(thm)],[f_225_3]) ).

cnf(f_225_5,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(U_400)))
    | ~ sP15(U_400,U_401) ),
    inference(clausify,[status(thm)],[f_225_3]) ).

cnf(f_225_6,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(U_401)))
    | ~ sP15(U_400,U_401) ),
    inference(clausify,[status(thm)],[f_225_3]) ).

fof(f_226_1,plain,
    ! [N,M_1] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_1)),N) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_119_Suc__diff__le]) ).

fof(f_226_2,plain,
    ! [U_403,U_402] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,U_402)),U_403) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_402),U_403))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_403),U_402)) ),
    inference(variable_rename,[status(thm)],[f_226_1]) ).

fof(f_226_3,plain,
    ! [U_402,U_403] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,U_402)),U_403) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_402),U_403))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_403),U_402)) ),
    inference(definitional_conversion,[status(esa)],[f_226_2]) ).

cnf(f_226_4,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,U_402)),U_403) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_402),U_403))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_403),U_402)) ),
    inference(clausify,[status(thm)],[f_226_3]) ).

fof(f_227_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_120_finite__Collect__le__nat]) ).

fof(f_227_2,plain,
    ! [U_404] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),U_404)))),
    inference(variable_rename,[status(thm)],[f_227_1]) ).

fof(f_227_3,plain,
    ! [U_404] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),U_404)))),
    inference(definitional_conversion,[status(esa)],[f_227_2]) ).

cnf(f_227_4,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),U_404)))),
    inference(clausify,[status(thm)],[f_227_3]) ).

fof(f_228_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_121_card__Collect__le__nat]) ).

fof(f_228_2,plain,
    ! [U_405] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),U_405))) = hAPP_nat_nat(suc,U_405),
    inference(variable_rename,[status(thm)],[f_228_1]) ).

fof(f_228_3,plain,
    ! [U_405] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),U_405))) = hAPP_nat_nat(suc,U_405),
    inference(definitional_conversion,[status(esa)],[f_228_2]) ).

cnf(f_228_4,plain,
    hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),U_405))) = hAPP_nat_nat(suc,U_405),
    inference(clausify,[status(thm)],[f_228_3]) ).

fof(f_229_1,plain,
    ! [X,Y] :
      ( X = Y
      | hAPP_nat_nat(suc,X) != hAPP_nat_nat(suc,Y) ),
    inference(fof_nnf,[status(thm)],[fact_122_Suc__inject]) ).

fof(f_229_2,plain,
    ! [U_407,U_406] :
      ( U_407 = U_406
      | hAPP_nat_nat(suc,U_407) != hAPP_nat_nat(suc,U_406) ),
    inference(variable_rename,[status(thm)],[f_229_1]) ).

fof(f_229_3,plain,
    ! [U_406,U_407] :
      ( U_407 = U_406
      | hAPP_nat_nat(suc,U_407) != hAPP_nat_nat(suc,U_406) ),
    inference(definitional_conversion,[status(esa)],[f_229_2]) ).

cnf(f_229_4,plain,
    ( U_407 = U_406
    | hAPP_nat_nat(suc,U_407) != hAPP_nat_nat(suc,U_406) ),
    inference(clausify,[status(thm)],[f_229_3]) ).

fof(f_230_1,plain,
    ! [Nat_3,Nat_4] :
      ( ( hAPP_nat_nat(suc,Nat_3) = hAPP_nat_nat(suc,Nat_4)
        | Nat_3 != Nat_4 )
      & ( Nat_3 = Nat_4
        | hAPP_nat_nat(suc,Nat_3) != hAPP_nat_nat(suc,Nat_4) ) ),
    inference(fof_nnf,[status(thm)],[fact_123_nat_Oinject]) ).

fof(f_230_2,plain,
    ! [U_409,U_408] :
      ( ( hAPP_nat_nat(suc,U_409) = hAPP_nat_nat(suc,U_408)
        | U_409 != U_408 )
      & ( U_409 = U_408
        | hAPP_nat_nat(suc,U_409) != hAPP_nat_nat(suc,U_408) ) ),
    inference(variable_rename,[status(thm)],[f_230_1]) ).

fof(f_230_3,plain,
    ( ! [U_413,U_411] :
        ( hAPP_nat_nat(suc,U_413) = hAPP_nat_nat(suc,U_411)
        | U_413 != U_411 )
    & ! [U_412,U_410] :
        ( U_412 = U_410
        | hAPP_nat_nat(suc,U_412) != hAPP_nat_nat(suc,U_410) ) ),
    inference(miniscope,[status(thm)],[f_230_2]) ).

fof(f_230_4,plain,
    ( ! [U_411,U_413] :
        ( hAPP_nat_nat(suc,U_413) = hAPP_nat_nat(suc,U_411)
        | U_413 != U_411 )
    & ! [U_412,U_410] :
        ( U_412 = U_410
        | hAPP_nat_nat(suc,U_412) != hAPP_nat_nat(suc,U_410) ) ),
    inference(definitional_conversion,[status(esa)],[f_230_3]) ).

cnf(f_230_5,plain,
    ( U_412 = U_410
    | hAPP_nat_nat(suc,U_412) != hAPP_nat_nat(suc,U_410) ),
    inference(clausify,[status(thm)],[f_230_4]) ).

cnf(f_230_6,plain,
    ( hAPP_nat_nat(suc,U_413) = hAPP_nat_nat(suc,U_411)
    | U_413 != U_411 ),
    inference(clausify,[status(thm)],[f_230_4]) ).

fof(f_231_1,plain,
    ! [N] : hAPP_nat_nat(suc,N) != N,
    inference(fof_nnf,[status(thm)],[fact_124_Suc__n__not__n]) ).

fof(f_231_2,plain,
    ! [U_414] : hAPP_nat_nat(suc,U_414) != U_414,
    inference(variable_rename,[status(thm)],[f_231_1]) ).

fof(f_231_3,plain,
    ! [U_414] : hAPP_nat_nat(suc,U_414) != U_414,
    inference(definitional_conversion,[status(esa)],[f_231_2]) ).

cnf(f_231_4,plain,
    hAPP_nat_nat(suc,U_414) != U_414,
    inference(clausify,[status(thm)],[f_231_3]) ).

fof(f_232_1,plain,
    ! [N] : N != hAPP_nat_nat(suc,N),
    inference(fof_nnf,[status(thm)],[fact_125_n__not__Suc__n]) ).

fof(f_232_2,plain,
    ! [U_415] : U_415 != hAPP_nat_nat(suc,U_415),
    inference(variable_rename,[status(thm)],[f_232_1]) ).

fof(f_232_3,plain,
    ! [U_415] : U_415 != hAPP_nat_nat(suc,U_415),
    inference(definitional_conversion,[status(esa)],[f_232_2]) ).

cnf(f_232_4,plain,
    U_415 != hAPP_nat_nat(suc,U_415),
    inference(clausify,[status(thm)],[f_232_3]) ).

fof(f_233_1,plain,
    ! [M_1,N] :
      ( M_1 = N
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_126_le__antisym]) ).

fof(f_233_2,plain,
    ! [U_417,U_416] :
      ( U_417 = U_416
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_416),U_417))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_417),U_416)) ),
    inference(variable_rename,[status(thm)],[f_233_1]) ).

fof(f_233_3,plain,
    ! [U_416,U_417] :
      ( U_417 = U_416
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_416),U_417))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_417),U_416)) ),
    inference(definitional_conversion,[status(esa)],[f_233_2]) ).

cnf(f_233_4,plain,
    ( U_417 = U_416
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_416),U_417))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_417),U_416)) ),
    inference(clausify,[status(thm)],[f_233_3]) ).

fof(f_234_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_127_le__trans]) ).

fof(f_234_2,plain,
    ! [U_420,U_419,U_418] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_419),U_420))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_418),U_420))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_419),U_418)) ),
    inference(variable_rename,[status(thm)],[f_234_1]) ).

fof(f_234_3,plain,
    ! [U_418,U_419,U_420] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_419),U_420))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_418),U_420))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_419),U_418)) ),
    inference(definitional_conversion,[status(esa)],[f_234_2]) ).

cnf(f_234_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_419),U_420))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_418),U_420))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_419),U_418)) ),
    inference(clausify,[status(thm)],[f_234_3]) ).

fof(f_235_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N))
      | M_1 != N ),
    inference(fof_nnf,[status(thm)],[fact_128_eq__imp__le]) ).

fof(f_235_2,plain,
    ! [U_422,U_421] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_422),U_421))
      | U_422 != U_421 ),
    inference(variable_rename,[status(thm)],[f_235_1]) ).

fof(f_235_3,plain,
    ! [U_422,U_421] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_422),U_421))
      | U_422 != U_421 ),
    inference(definitional_conversion,[status(esa)],[f_235_2]) ).

cnf(f_235_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_422),U_421))
    | U_422 != U_421 ),
    inference(clausify,[status(thm)],[f_235_3]) ).

fof(f_236_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_1))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_129_nat__le__linear]) ).

fof(f_236_2,plain,
    ! [U_424,U_423] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_423),U_424))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_424),U_423)) ),
    inference(variable_rename,[status(thm)],[f_236_1]) ).

fof(f_236_3,plain,
    ! [U_423,U_424] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_423),U_424))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_424),U_423)) ),
    inference(definitional_conversion,[status(esa)],[f_236_2]) ).

cnf(f_236_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_423),U_424))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_424),U_423)) ),
    inference(clausify,[status(thm)],[f_236_3]) ).

fof(f_237_1,plain,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),N)),
    inference(fof_nnf,[status(thm)],[fact_130_le__refl]) ).

fof(f_237_2,plain,
    ! [U_425] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_425),U_425)),
    inference(variable_rename,[status(thm)],[f_237_1]) ).

fof(f_237_3,plain,
    ! [U_425] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_425),U_425)),
    inference(definitional_conversion,[status(esa)],[f_237_2]) ).

cnf(f_237_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_425),U_425)),
    inference(clausify,[status(thm)],[f_237_3]) ).

fof(f_238_1,plain,
    ! [I_1,J,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),J)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),K_1)),J),
    inference(fof_nnf,[status(thm)],[fact_131_diff__commute]) ).

fof(f_238_2,plain,
    ! [U_428,U_427,U_426] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_428),U_427)),U_426) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_428),U_426)),U_427),
    inference(variable_rename,[status(thm)],[f_238_1]) ).

fof(f_238_3,plain,
    ! [U_426,U_427,U_428] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_428),U_427)),U_426) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_428),U_426)),U_427),
    inference(definitional_conversion,[status(esa)],[f_238_2]) ).

cnf(f_238_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_428),U_427)),U_426) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_428),U_426)),U_427),
    inference(clausify,[status(thm)],[f_238_3]) ).

fof(f_239_1,plain,
    ! [Pa,Q_3] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,Pa),Q_3))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Q_3)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Pa))) )
      & ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Q_3)))
          & 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_3)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_132_finite__Collect__disjI]) ).

fof(f_239_2,plain,
    ! [U_430,U_429] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,U_430),U_429))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_429)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_430))) )
      & ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_429)))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_430))) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,U_430),U_429)))) ) ),
    inference(variable_rename,[status(thm)],[f_239_1]) ).

fof(f_239_3,plain,
    ( ! [U_434,U_432] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,U_434),U_432))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_432)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_434))) )
    & ! [U_433,U_431] :
        ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_431)))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_433))) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,U_433),U_431)))) ) ),
    inference(miniscope,[status(thm)],[f_239_2]) ).

fof(f_239_4,plain,
    ( ! [U_433,U_431] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_431)))
        | ~ sP16(U_433,U_431) )
    & ! [U_433,U_431] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_433)))
        | ~ sP16(U_433,U_431) )
    & ! [U_434,U_432] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,U_434),U_432))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_432)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_434))) )
    & ! [U_433,U_431] :
        ( sP16(U_433,U_431)
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,U_433),U_431)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16])],[f_239_3]) ).

cnf(f_239_5,plain,
    ( sP16(U_433,U_431)
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,U_433),U_431)))) ),
    inference(clausify,[status(thm)],[f_239_4]) ).

cnf(f_239_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,U_434),U_432))))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_432)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_434))) ),
    inference(clausify,[status(thm)],[f_239_4]) ).

cnf(f_239_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_433)))
    | ~ sP16(U_433,U_431) ),
    inference(clausify,[status(thm)],[f_239_4]) ).

cnf(f_239_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(U_431)))
    | ~ sP16(U_433,U_431) ),
    inference(clausify,[status(thm)],[f_239_4]) ).

fof(f_240_1,plain,
    ! [Pa,Q_3] :
      ( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,Pa),Q_3))))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(Q_3)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(Pa))) )
      & ( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(Q_3)))
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(Pa))) )
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,Pa),Q_3)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_133_finite__Collect__disjI]) ).

fof(f_240_2,plain,
    ! [U_436,U_435] :
      ( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,U_436),U_435))))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(U_435)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(U_436))) )
      & ( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(U_435)))
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(U_436))) )
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,U_436),U_435)))) ) ),
    inference(variable_rename,[status(thm)],[f_240_1]) ).

fof(f_240_3,plain,
    ( ! [U_440,U_438] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,U_440),U_438))))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(U_438)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(U_440))) )
    & ! [U_439,U_437] :
        ( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(U_437)))
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(U_439))) )
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,U_439),U_437)))) ) ),
    inference(miniscope,[status(thm)],[f_240_2]) ).

fof(f_240_4,plain,
    ( ! [U_437,U_439] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(U_437)))
        | ~ sP17(U_437,U_439) )
    & ! [U_437,U_439] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(U_439)))
        | ~ sP17(U_437,U_439) )
    & ! [U_438,U_440] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,U_440),U_438))))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(U_438)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(U_440))) )
    & ! [U_437,U_439] :
        ( sP17(U_437,U_439)
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,U_439),U_437)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17])],[f_240_3]) ).

cnf(f_240_5,plain,
    ( sP17(U_437,U_439)
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,U_439),U_437)))) ),
    inference(clausify,[status(thm)],[f_240_4]) ).

cnf(f_240_6,plain,
    ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(cOMBS_1912792529l_bool(cOMBB_1974511970t_bool(fdisj,U_440),U_438))))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(U_438)))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(U_440))) ),
    inference(clausify,[status(thm)],[f_240_4]) ).

cnf(f_240_7,plain,
    ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(U_439)))
    | ~ sP17(U_437,U_439) ),
    inference(clausify,[status(thm)],[f_240_4]) ).

cnf(f_240_8,plain,
    ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,collect_fun_int_bool(U_437)))
    | ~ sP17(U_437,U_439) ),
    inference(clausify,[status(thm)],[f_240_4]) ).

fof(f_241_1,plain,
    ! [Pa,Q_3] :
      ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,Pa),Q_3))))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Q_3)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Pa))) )
      & ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Q_3)))
          & 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_3)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_134_finite__Collect__disjI]) ).

fof(f_241_2,plain,
    ! [U_442,U_441] :
      ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,U_442),U_441))))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_441)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_442))) )
      & ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_441)))
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_442))) )
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,U_442),U_441)))) ) ),
    inference(variable_rename,[status(thm)],[f_241_1]) ).

fof(f_241_3,plain,
    ( ! [U_446,U_444] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,U_446),U_444))))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_444)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_446))) )
    & ! [U_445,U_443] :
        ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_443)))
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_445))) )
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,U_445),U_443)))) ) ),
    inference(miniscope,[status(thm)],[f_241_2]) ).

fof(f_241_4,plain,
    ( ! [U_445,U_443] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_443)))
        | ~ sP18(U_445,U_443) )
    & ! [U_445,U_443] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_445)))
        | ~ sP18(U_445,U_443) )
    & ! [U_444,U_446] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,U_446),U_444))))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_444)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_446))) )
    & ! [U_445,U_443] :
        ( sP18(U_445,U_443)
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,U_445),U_443)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18])],[f_241_3]) ).

cnf(f_241_5,plain,
    ( sP18(U_445,U_443)
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,U_445),U_443)))) ),
    inference(clausify,[status(thm)],[f_241_4]) ).

cnf(f_241_6,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,U_446),U_444))))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_444)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_446))) ),
    inference(clausify,[status(thm)],[f_241_4]) ).

cnf(f_241_7,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_445)))
    | ~ sP18(U_445,U_443) ),
    inference(clausify,[status(thm)],[f_241_4]) ).

cnf(f_241_8,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(U_443)))
    | ~ sP18(U_445,U_443) ),
    inference(clausify,[status(thm)],[f_241_4]) ).

fof(f_242_1,plain,
    ! [Pa,Q_3] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,Pa),Q_3))))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_3)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Pa))) )
      & ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_3)))
          & 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_3)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_135_finite__Collect__disjI]) ).

fof(f_242_2,plain,
    ! [U_448,U_447] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_448),U_447))))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_447)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_448))) )
      & ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_447)))
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_448))) )
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_448),U_447)))) ) ),
    inference(variable_rename,[status(thm)],[f_242_1]) ).

fof(f_242_3,plain,
    ( ! [U_452,U_450] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_452),U_450))))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_450)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_452))) )
    & ! [U_451,U_449] :
        ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_449)))
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_451))) )
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_451),U_449)))) ) ),
    inference(miniscope,[status(thm)],[f_242_2]) ).

fof(f_242_4,plain,
    ( ! [U_449,U_451] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_449)))
        | ~ sP19(U_449,U_451) )
    & ! [U_449,U_451] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_451)))
        | ~ sP19(U_449,U_451) )
    & ! [U_450,U_452] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_452),U_450))))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_450)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_452))) )
    & ! [U_449,U_451] :
        ( sP19(U_449,U_451)
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_451),U_449)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19])],[f_242_3]) ).

cnf(f_242_5,plain,
    ( sP19(U_449,U_451)
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_451),U_449)))) ),
    inference(clausify,[status(thm)],[f_242_4]) ).

cnf(f_242_6,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,U_452),U_450))))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_450)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_452))) ),
    inference(clausify,[status(thm)],[f_242_4]) ).

cnf(f_242_7,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_451)))
    | ~ sP19(U_449,U_451) ),
    inference(clausify,[status(thm)],[f_242_4]) ).

cnf(f_242_8,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(U_449)))
    | ~ sP19(U_449,U_451) ),
    inference(clausify,[status(thm)],[f_242_4]) ).

fof(f_243_1,plain,
    ! [Pa,Q_3] :
      ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,Pa),Q_3))))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Q_3)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Pa))) )
      & ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Q_3)))
          & 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_3)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_136_finite__Collect__disjI]) ).

fof(f_243_2,plain,
    ! [U_454,U_453] :
      ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,U_454),U_453))))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_453)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_454))) )
      & ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_453)))
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_454))) )
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,U_454),U_453)))) ) ),
    inference(variable_rename,[status(thm)],[f_243_1]) ).

fof(f_243_3,plain,
    ( ! [U_458,U_456] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,U_458),U_456))))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_456)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_458))) )
    & ! [U_457,U_455] :
        ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_455)))
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_457))) )
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,U_457),U_455)))) ) ),
    inference(miniscope,[status(thm)],[f_243_2]) ).

fof(f_243_4,plain,
    ( ! [U_455,U_457] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_455)))
        | ~ sP20(U_455,U_457) )
    & ! [U_455,U_457] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_457)))
        | ~ sP20(U_455,U_457) )
    & ! [U_456,U_458] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,U_458),U_456))))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_456)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_458))) )
    & ! [U_455,U_457] :
        ( sP20(U_455,U_457)
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,U_457),U_455)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP20])],[f_243_3]) ).

cnf(f_243_5,plain,
    ( sP20(U_455,U_457)
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,U_457),U_455)))) ),
    inference(clausify,[status(thm)],[f_243_4]) ).

cnf(f_243_6,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,U_458),U_456))))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_456)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_458))) ),
    inference(clausify,[status(thm)],[f_243_4]) ).

cnf(f_243_7,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_457)))
    | ~ sP20(U_455,U_457) ),
    inference(clausify,[status(thm)],[f_243_4]) ).

cnf(f_243_8,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(U_455)))
    | ~ sP20(U_455,U_457) ),
    inference(clausify,[status(thm)],[f_243_4]) ).

fof(f_244_1,plain,
    ! [Pa,Q_3] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,Pa),Q_3))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_3)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Pa))) )
      & ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_3)))
          & 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_3)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_137_finite__Collect__disjI]) ).

fof(f_244_2,plain,
    ! [U_460,U_459] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_460),U_459))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_459)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_460))) )
      & ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_459)))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_460))) )
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_460),U_459)))) ) ),
    inference(variable_rename,[status(thm)],[f_244_1]) ).

fof(f_244_3,plain,
    ( ! [U_464,U_462] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_464),U_462))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_462)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_464))) )
    & ! [U_463,U_461] :
        ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_461)))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_463))) )
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_463),U_461)))) ) ),
    inference(miniscope,[status(thm)],[f_244_2]) ).

fof(f_244_4,plain,
    ( ! [U_461,U_463] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_461)))
        | ~ sP21(U_461,U_463) )
    & ! [U_461,U_463] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_463)))
        | ~ sP21(U_461,U_463) )
    & ! [U_462,U_464] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_464),U_462))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_462)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_464))) )
    & ! [U_461,U_463] :
        ( sP21(U_461,U_463)
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_463),U_461)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP21])],[f_244_3]) ).

cnf(f_244_5,plain,
    ( sP21(U_461,U_463)
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_463),U_461)))) ),
    inference(clausify,[status(thm)],[f_244_4]) ).

cnf(f_244_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,U_464),U_462))))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_462)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_464))) ),
    inference(clausify,[status(thm)],[f_244_4]) ).

cnf(f_244_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_463)))
    | ~ sP21(U_461,U_463) ),
    inference(clausify,[status(thm)],[f_244_4]) ).

cnf(f_244_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(U_461)))
    | ~ sP21(U_461,U_463) ),
    inference(clausify,[status(thm)],[f_244_4]) ).

fof(f_245_1,plain,
    ! [Pa,Q_3] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,Pa),Q_3))))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_3)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Pa))) )
      & ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_3)))
          & 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_3)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_138_finite__Collect__disjI]) ).

fof(f_245_2,plain,
    ! [U_466,U_465] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,U_466),U_465))))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_465)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_466))) )
      & ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_465)))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_466))) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,U_466),U_465)))) ) ),
    inference(variable_rename,[status(thm)],[f_245_1]) ).

fof(f_245_3,plain,
    ( ! [U_470,U_468] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,U_470),U_468))))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_468)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_470))) )
    & ! [U_469,U_467] :
        ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_467)))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_469))) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,U_469),U_467)))) ) ),
    inference(miniscope,[status(thm)],[f_245_2]) ).

fof(f_245_4,plain,
    ( ! [U_469,U_467] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_467)))
        | ~ sP22(U_469,U_467) )
    & ! [U_469,U_467] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_469)))
        | ~ sP22(U_469,U_467) )
    & ! [U_468,U_470] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,U_470),U_468))))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_468)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_470))) )
    & ! [U_469,U_467] :
        ( sP22(U_469,U_467)
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,U_469),U_467)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP22])],[f_245_3]) ).

cnf(f_245_5,plain,
    ( sP22(U_469,U_467)
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,U_469),U_467)))) ),
    inference(clausify,[status(thm)],[f_245_4]) ).

cnf(f_245_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,U_470),U_468))))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_468)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_470))) ),
    inference(clausify,[status(thm)],[f_245_4]) ).

cnf(f_245_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_469)))
    | ~ sP22(U_469,U_467) ),
    inference(clausify,[status(thm)],[f_245_4]) ).

cnf(f_245_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(U_467)))
    | ~ sP22(U_469,U_467) ),
    inference(clausify,[status(thm)],[f_245_4]) ).

fof(f_246_1,plain,
    ! [Pa,Q_3] :
      ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,Pa),Q_3))))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(Q_3)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(Pa))) )
      & ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(Q_3)))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(Pa))) )
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,Pa),Q_3)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_139_finite__Collect__disjI]) ).

fof(f_246_2,plain,
    ! [U_472,U_471] :
      ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,U_472),U_471))))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(U_471)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(U_472))) )
      & ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(U_471)))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(U_472))) )
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,U_472),U_471)))) ) ),
    inference(variable_rename,[status(thm)],[f_246_1]) ).

fof(f_246_3,plain,
    ( ! [U_476,U_474] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,U_476),U_474))))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(U_474)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(U_476))) )
    & ! [U_475,U_473] :
        ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(U_473)))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(U_475))) )
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,U_475),U_473)))) ) ),
    inference(miniscope,[status(thm)],[f_246_2]) ).

fof(f_246_4,plain,
    ( ! [U_475,U_473] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(U_473)))
        | ~ sP23(U_475,U_473) )
    & ! [U_475,U_473] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(U_475)))
        | ~ sP23(U_475,U_473) )
    & ! [U_474,U_476] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,U_476),U_474))))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(U_474)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(U_476))) )
    & ! [U_475,U_473] :
        ( sP23(U_475,U_473)
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,U_475),U_473)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP23])],[f_246_3]) ).

cnf(f_246_5,plain,
    ( sP23(U_475,U_473)
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,U_475),U_473)))) ),
    inference(clausify,[status(thm)],[f_246_4]) ).

cnf(f_246_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,U_476),U_474))))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(U_474)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(U_476))) ),
    inference(clausify,[status(thm)],[f_246_4]) ).

cnf(f_246_7,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(U_475)))
    | ~ sP23(U_475,U_473) ),
    inference(clausify,[status(thm)],[f_246_4]) ).

cnf(f_246_8,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(U_473)))
    | ~ sP23(U_475,U_473) ),
    inference(clausify,[status(thm)],[f_246_4]) ).

fof(f_247_1,plain,
    ! [A_2,A] :
      ( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,A_2),A)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) )
      & ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,A_2),A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_140_finite__insert]) ).

fof(f_247_2,plain,
    ! [U_478,U_477] :
      ( ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,U_478),U_477)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_477)) )
      & ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_477))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,U_478),U_477))) ) ),
    inference(variable_rename,[status(thm)],[f_247_1]) ).

fof(f_247_3,plain,
    ( ! [U_482,U_480] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,U_482),U_480)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_480)) )
    & ! [U_481,U_479] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_479))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,U_481),U_479))) ) ),
    inference(miniscope,[status(thm)],[f_247_2]) ).

fof(f_247_4,plain,
    ( ! [U_482,U_480] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,U_482),U_480)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_480)) )
    & ! [U_481,U_479] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_479))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,U_481),U_479))) ) ),
    inference(definitional_conversion,[status(esa)],[f_247_3]) ).

cnf(f_247_5,plain,
    ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_479))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,U_481),U_479))) ),
    inference(clausify,[status(thm)],[f_247_4]) ).

cnf(f_247_6,plain,
    ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,hAPP_f1948010709l_bool(hAPP_f587666462l_bool(insert_fun_int_bool,U_482),U_480)))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_480)) ),
    inference(clausify,[status(thm)],[f_247_4]) ).

fof(f_248_1,plain,
    ! [A_2,A] :
      ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,A_2),A)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) )
      & ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,A_2),A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_141_finite__insert]) ).

fof(f_248_2,plain,
    ! [U_484,U_483] :
      ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,U_484),U_483)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_483)) )
      & ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_483))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,U_484),U_483))) ) ),
    inference(variable_rename,[status(thm)],[f_248_1]) ).

fof(f_248_3,plain,
    ( ! [U_488,U_486] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,U_488),U_486)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_486)) )
    & ! [U_487,U_485] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_485))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,U_487),U_485))) ) ),
    inference(miniscope,[status(thm)],[f_248_2]) ).

fof(f_248_4,plain,
    ( ! [U_486,U_488] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,U_488),U_486)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_486)) )
    & ! [U_487,U_485] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_485))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,U_487),U_485))) ) ),
    inference(definitional_conversion,[status(esa)],[f_248_3]) ).

cnf(f_248_5,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_485))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,U_487),U_485))) ),
    inference(clausify,[status(thm)],[f_248_4]) ).

cnf(f_248_6,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,hAPP_f1246832597l_bool(hAPP_f633452666l_bool(insert_fun_nat_bool,U_488),U_486)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_486)) ),
    inference(clausify,[status(thm)],[f_248_4]) ).

fof(f_249_1,plain,
    ! [A_2,A] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_2),A)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) )
      & ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,A_2),A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_142_finite__insert]) ).

fof(f_249_2,plain,
    ! [U_490,U_489] :
      ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,U_490),U_489)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_489)) )
      & ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_489))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,U_490),U_489))) ) ),
    inference(variable_rename,[status(thm)],[f_249_1]) ).

fof(f_249_3,plain,
    ( ! [U_494,U_492] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,U_494),U_492)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_492)) )
    & ! [U_493,U_491] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_491))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,U_493),U_491))) ) ),
    inference(miniscope,[status(thm)],[f_249_2]) ).

fof(f_249_4,plain,
    ( ! [U_492,U_494] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,U_494),U_492)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_492)) )
    & ! [U_493,U_491] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_491))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,U_493),U_491))) ) ),
    inference(definitional_conversion,[status(esa)],[f_249_3]) ).

cnf(f_249_5,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_491))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,U_493),U_491))) ),
    inference(clausify,[status(thm)],[f_249_4]) ).

cnf(f_249_6,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,hAPP_f559147733l_bool(hAPP_f1320879424l_bool(insert1325755072e_bool,U_494),U_492)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_492)) ),
    inference(clausify,[status(thm)],[f_249_4]) ).

fof(f_250_1,plain,
    ! [A_2,A] :
      ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,A_2),A)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) )
      & ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,A_2),A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_143_finite__insert]) ).

fof(f_250_2,plain,
    ! [U_496,U_495] :
      ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,U_496),U_495)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_495)) )
      & ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_495))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,U_496),U_495))) ) ),
    inference(variable_rename,[status(thm)],[f_250_1]) ).

fof(f_250_3,plain,
    ( ! [U_500,U_498] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,U_500),U_498)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_498)) )
    & ! [U_499,U_497] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_497))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,U_499),U_497))) ) ),
    inference(miniscope,[status(thm)],[f_250_2]) ).

fof(f_250_4,plain,
    ( ! [U_498,U_500] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,U_500),U_498)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_498)) )
    & ! [U_499,U_497] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_497))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,U_499),U_497))) ) ),
    inference(definitional_conversion,[status(esa)],[f_250_3]) ).

cnf(f_250_5,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_497))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,U_499),U_497))) ),
    inference(clausify,[status(thm)],[f_250_4]) ).

cnf(f_250_6,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,hAPP_f2117159681l_bool(hAPP_f1531278575l_bool(insert_fun_a_bool,U_500),U_498)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_498)) ),
    inference(clausify,[status(thm)],[f_250_4]) ).

fof(f_251_1,plain,
    ! [A_2,A] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) )
      & ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_144_finite__insert]) ).

fof(f_251_2,plain,
    ! [U_502,U_501] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_502),U_501)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_501)) )
      & ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_501))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_502),U_501))) ) ),
    inference(variable_rename,[status(thm)],[f_251_1]) ).

fof(f_251_3,plain,
    ( ! [U_506,U_504] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_506),U_504)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_504)) )
    & ! [U_505,U_503] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_503))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_505),U_503))) ) ),
    inference(miniscope,[status(thm)],[f_251_2]) ).

fof(f_251_4,plain,
    ( ! [U_504,U_506] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_506),U_504)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_504)) )
    & ! [U_505,U_503] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_503))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_505),U_503))) ) ),
    inference(definitional_conversion,[status(esa)],[f_251_3]) ).

cnf(f_251_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_503))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_505),U_503))) ),
    inference(clausify,[status(thm)],[f_251_4]) ).

cnf(f_251_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_506),U_504)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_504)) ),
    inference(clausify,[status(thm)],[f_251_4]) ).

fof(f_252_1,plain,
    ! [A_2,A] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) )
      & ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_145_finite__insert]) ).

fof(f_252_2,plain,
    ! [U_508,U_507] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_508),U_507)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_507)) )
      & ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_507))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_508),U_507))) ) ),
    inference(variable_rename,[status(thm)],[f_252_1]) ).

fof(f_252_3,plain,
    ( ! [U_512,U_510] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_512),U_510)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_510)) )
    & ! [U_511,U_509] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_509))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_511),U_509))) ) ),
    inference(miniscope,[status(thm)],[f_252_2]) ).

fof(f_252_4,plain,
    ( ! [U_510,U_512] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_512),U_510)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_510)) )
    & ! [U_511,U_509] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_509))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_511),U_509))) ) ),
    inference(definitional_conversion,[status(esa)],[f_252_3]) ).

cnf(f_252_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_509))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_511),U_509))) ),
    inference(clausify,[status(thm)],[f_252_4]) ).

cnf(f_252_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_512),U_510)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_510)) ),
    inference(clausify,[status(thm)],[f_252_4]) ).

fof(f_253_1,plain,
    ! [A_2,A] :
      ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),A)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) )
      & ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_146_finite__insert]) ).

fof(f_253_2,plain,
    ! [U_514,U_513] :
      ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_514),U_513)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_513)) )
      & ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_513))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_514),U_513))) ) ),
    inference(variable_rename,[status(thm)],[f_253_1]) ).

fof(f_253_3,plain,
    ( ! [U_518,U_516] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_518),U_516)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_516)) )
    & ! [U_517,U_515] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_515))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_517),U_515))) ) ),
    inference(miniscope,[status(thm)],[f_253_2]) ).

fof(f_253_4,plain,
    ( ! [U_516,U_518] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_518),U_516)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_516)) )
    & ! [U_517,U_515] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_515))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_517),U_515))) ) ),
    inference(definitional_conversion,[status(esa)],[f_253_3]) ).

cnf(f_253_5,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_515))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_517),U_515))) ),
    inference(clausify,[status(thm)],[f_253_4]) ).

cnf(f_253_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_518),U_516)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_516)) ),
    inference(clausify,[status(thm)],[f_253_4]) ).

fof(f_254_1,plain,
    ! [A_2,A] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),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,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_147_finite__insert]) ).

fof(f_254_2,plain,
    ! [U_520,U_519] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_520),U_519)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_519)) )
      & ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_519))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_520),U_519))) ) ),
    inference(variable_rename,[status(thm)],[f_254_1]) ).

fof(f_254_3,plain,
    ( ! [U_524,U_522] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_524),U_522)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_522)) )
    & ! [U_523,U_521] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_521))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_523),U_521))) ) ),
    inference(miniscope,[status(thm)],[f_254_2]) ).

fof(f_254_4,plain,
    ( ! [U_522,U_524] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_524),U_522)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_522)) )
    & ! [U_523,U_521] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_521))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_523),U_521))) ) ),
    inference(definitional_conversion,[status(esa)],[f_254_3]) ).

cnf(f_254_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_521))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_523),U_521))) ),
    inference(clausify,[status(thm)],[f_254_4]) ).

cnf(f_254_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_524),U_522)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_522)) ),
    inference(clausify,[status(thm)],[f_254_4]) ).

fof(f_255_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_148_finite__subset]) ).

fof(f_255_2,plain,
    ! [U_526,U_525] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_526))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_525))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_526),U_525)) ),
    inference(variable_rename,[status(thm)],[f_255_1]) ).

fof(f_255_3,plain,
    ! [U_525,U_526] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_526))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_525))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_526),U_525)) ),
    inference(definitional_conversion,[status(esa)],[f_255_2]) ).

cnf(f_255_4,plain,
    ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_526))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_525))
    | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_526),U_525)) ),
    inference(clausify,[status(thm)],[f_255_3]) ).

fof(f_256_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_149_finite__subset]) ).

fof(f_256_2,plain,
    ! [U_528,U_527] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_528))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_527))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_528),U_527)) ),
    inference(variable_rename,[status(thm)],[f_256_1]) ).

fof(f_256_3,plain,
    ! [U_528,U_527] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_528))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_527))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_528),U_527)) ),
    inference(definitional_conversion,[status(esa)],[f_256_2]) ).

cnf(f_256_4,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_528))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_527))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_528),U_527)) ),
    inference(clausify,[status(thm)],[f_256_3]) ).

fof(f_257_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_150_finite__subset]) ).

fof(f_257_2,plain,
    ! [U_530,U_529] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_530))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_529))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_530),U_529)) ),
    inference(variable_rename,[status(thm)],[f_257_1]) ).

fof(f_257_3,plain,
    ! [U_530,U_529] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_530))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_529))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_530),U_529)) ),
    inference(definitional_conversion,[status(esa)],[f_257_2]) ).

cnf(f_257_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_530))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_529))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_530),U_529)) ),
    inference(clausify,[status(thm)],[f_257_3]) ).

fof(f_258_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_151_finite__subset]) ).

fof(f_258_2,plain,
    ! [U_532,U_531] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_532))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_531))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_532),U_531)) ),
    inference(variable_rename,[status(thm)],[f_258_1]) ).

fof(f_258_3,plain,
    ! [U_532,U_531] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_532))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_531))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_532),U_531)) ),
    inference(definitional_conversion,[status(esa)],[f_258_2]) ).

cnf(f_258_4,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_532))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_531))
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_532),U_531)) ),
    inference(clausify,[status(thm)],[f_258_3]) ).

fof(f_259_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_152_finite__subset]) ).

fof(f_259_2,plain,
    ! [U_534,U_533] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_534))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_533))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_534),U_533)) ),
    inference(variable_rename,[status(thm)],[f_259_1]) ).

fof(f_259_3,plain,
    ! [U_534,U_533] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_534))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_533))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_534),U_533)) ),
    inference(definitional_conversion,[status(esa)],[f_259_2]) ).

cnf(f_259_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_534))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_533))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_534),U_533)) ),
    inference(clausify,[status(thm)],[f_259_3]) ).

fof(f_260_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_153_finite__subset]) ).

fof(f_260_2,plain,
    ! [U_536,U_535] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_536))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_535))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_536),U_535)) ),
    inference(variable_rename,[status(thm)],[f_260_1]) ).

fof(f_260_3,plain,
    ! [U_535,U_536] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_536))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_535))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_536),U_535)) ),
    inference(definitional_conversion,[status(esa)],[f_260_2]) ).

cnf(f_260_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_536))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_535))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_536),U_535)) ),
    inference(clausify,[status(thm)],[f_260_3]) ).

fof(f_261_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_154_finite__subset]) ).

fof(f_261_2,plain,
    ! [U_538,U_537] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_538))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_537))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_538),U_537)) ),
    inference(variable_rename,[status(thm)],[f_261_1]) ).

fof(f_261_3,plain,
    ! [U_538,U_537] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_538))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_537))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_538),U_537)) ),
    inference(definitional_conversion,[status(esa)],[f_261_2]) ).

cnf(f_261_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_538))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_537))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_538),U_537)) ),
    inference(clausify,[status(thm)],[f_261_3]) ).

fof(f_262_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_155_finite__subset]) ).

fof(f_262_2,plain,
    ! [U_540,U_539] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_540))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_539))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_540),U_539)) ),
    inference(variable_rename,[status(thm)],[f_262_1]) ).

fof(f_262_3,plain,
    ! [U_540,U_539] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_540))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_539))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_540),U_539)) ),
    inference(definitional_conversion,[status(esa)],[f_262_2]) ).

cnf(f_262_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_540))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_539))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_540),U_539)) ),
    inference(clausify,[status(thm)],[f_262_3]) ).

fof(f_263_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,A),B))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B)) ),
    inference(fof_nnf,[status(thm)],[fact_156_rev__finite__subset]) ).

fof(f_263_2,plain,
    ! [U_542,U_541] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_542))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_542),U_541))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_541)) ),
    inference(variable_rename,[status(thm)],[f_263_1]) ).

fof(f_263_3,plain,
    ! [U_541,U_542] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_542))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_542),U_541))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_541)) ),
    inference(definitional_conversion,[status(esa)],[f_263_2]) ).

cnf(f_263_4,plain,
    ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_542))
    | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_542),U_541))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_541)) ),
    inference(clausify,[status(thm)],[f_263_3]) ).

fof(f_264_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_157_rev__finite__subset]) ).

fof(f_264_2,plain,
    ! [U_544,U_543] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_544))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_544),U_543))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_543)) ),
    inference(variable_rename,[status(thm)],[f_264_1]) ).

fof(f_264_3,plain,
    ! [U_543,U_544] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_544))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_544),U_543))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_543)) ),
    inference(definitional_conversion,[status(esa)],[f_264_2]) ).

cnf(f_264_4,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_544))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_544),U_543))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_543)) ),
    inference(clausify,[status(thm)],[f_264_3]) ).

fof(f_265_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_158_rev__finite__subset]) ).

fof(f_265_2,plain,
    ! [U_546,U_545] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_546))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_546),U_545))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_545)) ),
    inference(variable_rename,[status(thm)],[f_265_1]) ).

fof(f_265_3,plain,
    ! [U_545,U_546] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_546))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_546),U_545))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_545)) ),
    inference(definitional_conversion,[status(esa)],[f_265_2]) ).

cnf(f_265_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_546))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_546),U_545))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_545)) ),
    inference(clausify,[status(thm)],[f_265_3]) ).

fof(f_266_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_159_rev__finite__subset]) ).

fof(f_266_2,plain,
    ! [U_548,U_547] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_548))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_548),U_547))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_547)) ),
    inference(variable_rename,[status(thm)],[f_266_1]) ).

fof(f_266_3,plain,
    ! [U_547,U_548] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_548))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_548),U_547))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_547)) ),
    inference(definitional_conversion,[status(esa)],[f_266_2]) ).

cnf(f_266_4,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_548))
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_548),U_547))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_547)) ),
    inference(clausify,[status(thm)],[f_266_3]) ).

fof(f_267_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_160_rev__finite__subset]) ).

fof(f_267_2,plain,
    ! [U_550,U_549] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_550))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_550),U_549))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_549)) ),
    inference(variable_rename,[status(thm)],[f_267_1]) ).

fof(f_267_3,plain,
    ! [U_549,U_550] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_550))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_550),U_549))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_549)) ),
    inference(definitional_conversion,[status(esa)],[f_267_2]) ).

cnf(f_267_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_550))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_550),U_549))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_549)) ),
    inference(clausify,[status(thm)],[f_267_3]) ).

fof(f_268_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_161_rev__finite__subset]) ).

fof(f_268_2,plain,
    ! [U_552,U_551] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_552))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_552),U_551))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_551)) ),
    inference(variable_rename,[status(thm)],[f_268_1]) ).

fof(f_268_3,plain,
    ! [U_551,U_552] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_552))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_552),U_551))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_551)) ),
    inference(definitional_conversion,[status(esa)],[f_268_2]) ).

cnf(f_268_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_552))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_552),U_551))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_551)) ),
    inference(clausify,[status(thm)],[f_268_3]) ).

fof(f_269_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_162_rev__finite__subset]) ).

fof(f_269_2,plain,
    ! [U_554,U_553] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_554))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_554),U_553))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_553)) ),
    inference(variable_rename,[status(thm)],[f_269_1]) ).

fof(f_269_3,plain,
    ! [U_553,U_554] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_554))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_554),U_553))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_553)) ),
    inference(definitional_conversion,[status(esa)],[f_269_2]) ).

cnf(f_269_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_554))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_554),U_553))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_553)) ),
    inference(clausify,[status(thm)],[f_269_3]) ).

fof(f_270_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) ),
    inference(fof_nnf,[status(thm)],[fact_163_rev__finite__subset]) ).

fof(f_270_2,plain,
    ! [U_556,U_555] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_556))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_556),U_555))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_555)) ),
    inference(variable_rename,[status(thm)],[f_270_1]) ).

fof(f_270_3,plain,
    ! [U_555,U_556] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_556))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_556),U_555))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_555)) ),
    inference(definitional_conversion,[status(esa)],[f_270_2]) ).

cnf(f_270_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_556))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_556),U_555))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_555)) ),
    inference(clausify,[status(thm)],[f_270_3]) ).

fof(f_271_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_164_Suc__leD]) ).

fof(f_271_2,plain,
    ! [U_558,U_557] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_558),U_557))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_558)),U_557)) ),
    inference(variable_rename,[status(thm)],[f_271_1]) ).

fof(f_271_3,plain,
    ! [U_557,U_558] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_558),U_557))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_558)),U_557)) ),
    inference(definitional_conversion,[status(esa)],[f_271_2]) ).

cnf(f_271_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_558),U_557))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_558)),U_557)) ),
    inference(clausify,[status(thm)],[f_271_3]) ).

fof(f_272_1,plain,
    ! [M_1,N] :
      ( M_1 = hAPP_nat_nat(suc,N)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,N))) ),
    inference(fof_nnf,[status(thm)],[fact_165_le__SucE]) ).

fof(f_272_2,plain,
    ! [U_560,U_559] :
      ( U_560 = hAPP_nat_nat(suc,U_559)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_560),U_559))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_560),hAPP_nat_nat(suc,U_559))) ),
    inference(variable_rename,[status(thm)],[f_272_1]) ).

fof(f_272_3,plain,
    ! [U_559,U_560] :
      ( U_560 = hAPP_nat_nat(suc,U_559)
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_560),U_559))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_560),hAPP_nat_nat(suc,U_559))) ),
    inference(definitional_conversion,[status(esa)],[f_272_2]) ).

cnf(f_272_4,plain,
    ( U_560 = hAPP_nat_nat(suc,U_559)
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_560),U_559))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_560),hAPP_nat_nat(suc,U_559))) ),
    inference(clausify,[status(thm)],[f_272_3]) ).

fof(f_273_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(suc,N)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_166_le__SucI]) ).

fof(f_273_2,plain,
    ! [U_562,U_561] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_562),hAPP_nat_nat(suc,U_561)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_562),U_561)) ),
    inference(variable_rename,[status(thm)],[f_273_1]) ).

fof(f_273_3,plain,
    ! [U_561,U_562] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_562),hAPP_nat_nat(suc,U_561)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_562),U_561)) ),
    inference(definitional_conversion,[status(esa)],[f_273_2]) ).

cnf(f_273_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_562),hAPP_nat_nat(suc,U_561)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_562),U_561)) ),
    inference(clausify,[status(thm)],[f_273_3]) ).

fof(f_274_1,plain,
    ! [Na,M] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M))) ) ),
    inference(fof_nnf,[status(thm)],[fact_167_Suc__le__mono]) ).

fof(f_274_2,plain,
    ! [U_564,U_563] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_564)),hAPP_nat_nat(suc,U_563)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_564),U_563)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_564),U_563))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_564)),hAPP_nat_nat(suc,U_563))) ) ),
    inference(variable_rename,[status(thm)],[f_274_1]) ).

fof(f_274_3,plain,
    ( ! [U_568,U_566] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_568)),hAPP_nat_nat(suc,U_566)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_568),U_566)) )
    & ! [U_567,U_565] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_567),U_565))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_567)),hAPP_nat_nat(suc,U_565))) ) ),
    inference(miniscope,[status(thm)],[f_274_2]) ).

fof(f_274_4,plain,
    ( ! [U_566,U_568] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_568)),hAPP_nat_nat(suc,U_566)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_568),U_566)) )
    & ! [U_567,U_565] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_567),U_565))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_567)),hAPP_nat_nat(suc,U_565))) ) ),
    inference(definitional_conversion,[status(esa)],[f_274_3]) ).

cnf(f_274_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_567),U_565))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_567)),hAPP_nat_nat(suc,U_565))) ),
    inference(clausify,[status(thm)],[f_274_4]) ).

cnf(f_274_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_568)),hAPP_nat_nat(suc,U_566)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_568),U_566)) ),
    inference(clausify,[status(thm)],[f_274_4]) ).

fof(f_275_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,Na)))
        | ( M != hAPP_nat_nat(suc,Na)
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) ) )
      & ( M = hAPP_nat_nat(suc,Na)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_168_le__Suc__eq]) ).

fof(f_275_2,plain,
    ! [U_570,U_569] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_570),hAPP_nat_nat(suc,U_569)))
        | ( U_570 != hAPP_nat_nat(suc,U_569)
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_570),U_569)) ) )
      & ( U_570 = hAPP_nat_nat(suc,U_569)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_570),U_569))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_570),hAPP_nat_nat(suc,U_569))) ) ),
    inference(variable_rename,[status(thm)],[f_275_1]) ).

fof(f_275_3,plain,
    ( ! [U_574,U_572] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_574),hAPP_nat_nat(suc,U_572)))
        | ( U_574 != hAPP_nat_nat(suc,U_572)
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_574),U_572)) ) )
    & ! [U_573,U_571] :
        ( U_573 = hAPP_nat_nat(suc,U_571)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_573),U_571))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_573),hAPP_nat_nat(suc,U_571))) ) ),
    inference(miniscope,[status(thm)],[f_275_2]) ).

fof(f_275_4,plain,
    ( ! [U_574,U_572] :
        ( U_574 != hAPP_nat_nat(suc,U_572)
        | ~ sP24(U_574,U_572) )
    & ! [U_574,U_572] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_574),U_572))
        | ~ sP24(U_574,U_572) )
    & ! [U_574,U_572] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_574),hAPP_nat_nat(suc,U_572)))
        | sP24(U_574,U_572) )
    & ! [U_573,U_571] :
        ( U_573 = hAPP_nat_nat(suc,U_571)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_573),U_571))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_573),hAPP_nat_nat(suc,U_571))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP24])],[f_275_3]) ).

cnf(f_275_5,plain,
    ( U_573 = hAPP_nat_nat(suc,U_571)
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_573),U_571))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_573),hAPP_nat_nat(suc,U_571))) ),
    inference(clausify,[status(thm)],[f_275_4]) ).

cnf(f_275_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_574),hAPP_nat_nat(suc,U_572)))
    | sP24(U_574,U_572) ),
    inference(clausify,[status(thm)],[f_275_4]) ).

cnf(f_275_7,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_574),U_572))
    | ~ sP24(U_574,U_572) ),
    inference(clausify,[status(thm)],[f_275_4]) ).

cnf(f_275_8,plain,
    ( U_574 != hAPP_nat_nat(suc,U_572)
    | ~ sP24(U_574,U_572) ),
    inference(clausify,[status(thm)],[f_275_4]) ).

fof(f_276_1,plain,
    ! [M,Na] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_169_not__less__eq__eq]) ).

fof(f_276_2,plain,
    ! [U_576,U_575] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_576),U_575))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_575)),U_576)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_575)),U_576))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_576),U_575)) ) ),
    inference(variable_rename,[status(thm)],[f_276_1]) ).

fof(f_276_3,plain,
    ( ! [U_580,U_578] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_580),U_578))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_578)),U_580)) )
    & ! [U_579,U_577] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_577)),U_579))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_579),U_577)) ) ),
    inference(miniscope,[status(thm)],[f_276_2]) ).

fof(f_276_4,plain,
    ( ! [U_578,U_580] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_580),U_578))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_578)),U_580)) )
    & ! [U_579,U_577] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_577)),U_579))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_579),U_577)) ) ),
    inference(definitional_conversion,[status(esa)],[f_276_3]) ).

cnf(f_276_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_577)),U_579))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_579),U_577)) ),
    inference(clausify,[status(thm)],[f_276_4]) ).

cnf(f_276_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_580),U_578))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_578)),U_580)) ),
    inference(clausify,[status(thm)],[f_276_4]) ).

fof(f_277_1,plain,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),N)),
    inference(fof_nnf,[status(thm)],[fact_170_Suc__n__not__le__n]) ).

fof(f_277_2,plain,
    ! [U_581] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_581)),U_581)),
    inference(variable_rename,[status(thm)],[f_277_1]) ).

fof(f_277_3,plain,
    ! [U_581] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_581)),U_581)),
    inference(definitional_conversion,[status(esa)],[f_277_2]) ).

cnf(f_277_4,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_581)),U_581)),
    inference(clausify,[status(thm)],[f_277_3]) ).

fof(f_278_1,plain,
    ! [M_1,N,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_1)),N)),hAPP_nat_nat(suc,K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)),K_1),
    inference(fof_nnf,[status(thm)],[fact_171_Suc__diff__diff]) ).

fof(f_278_2,plain,
    ! [U_584,U_583,U_582] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,U_584)),U_583)),hAPP_nat_nat(suc,U_582)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_584),U_583)),U_582),
    inference(variable_rename,[status(thm)],[f_278_1]) ).

fof(f_278_3,plain,
    ! [U_582,U_583,U_584] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,U_584)),U_583)),hAPP_nat_nat(suc,U_582)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_584),U_583)),U_582),
    inference(definitional_conversion,[status(esa)],[f_278_2]) ).

cnf(f_278_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,U_584)),U_583)),hAPP_nat_nat(suc,U_582)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_584),U_583)),U_582),
    inference(clausify,[status(thm)],[f_278_3]) ).

fof(f_279_1,plain,
    ! [M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N),
    inference(fof_nnf,[status(thm)],[fact_172_diff__Suc__Suc]) ).

fof(f_279_2,plain,
    ! [U_586,U_585] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,U_586)),hAPP_nat_nat(suc,U_585)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_586),U_585),
    inference(variable_rename,[status(thm)],[f_279_1]) ).

fof(f_279_3,plain,
    ! [U_585,U_586] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,U_586)),hAPP_nat_nat(suc,U_585)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_586),U_585),
    inference(definitional_conversion,[status(esa)],[f_279_2]) ).

cnf(f_279_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,U_586)),hAPP_nat_nat(suc,U_585)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_586),U_585),
    inference(clausify,[status(thm)],[f_279_3]) ).

fof(f_280_1,plain,
    ! [Na,K,M] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,Na),K)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_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)) ),
    inference(fof_nnf,[status(thm)],[fact_173_le__diff__iff]) ).

fof(f_280_2,plain,
    ! [U_589,U_588,U_587] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_587),U_588)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_589),U_588)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_587),U_589)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_587),U_589))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_587),U_588)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_589),U_588))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_588),U_589))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_588),U_587)) ),
    inference(variable_rename,[status(thm)],[f_280_1]) ).

fof(f_280_3,plain,
    ( ! [U_587,U_588,U_589] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_587),U_588)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_589),U_588)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_587),U_589))
        | ~ sP25(U_587,U_588,U_589) )
    & ! [U_587,U_588,U_589] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_587),U_589))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_587),U_588)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_589),U_588)))
        | ~ sP25(U_587,U_588,U_589) )
    & ! [U_587,U_588,U_589] :
        ( sP25(U_587,U_588,U_589)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_588),U_589))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_588),U_587)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP25])],[f_280_2]) ).

cnf(f_280_4,plain,
    ( sP25(U_587,U_588,U_589)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_588),U_589))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_588),U_587)) ),
    inference(clausify,[status(thm)],[f_280_3]) ).

cnf(f_280_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_587),U_589))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_587),U_588)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_589),U_588)))
    | ~ sP25(U_587,U_588,U_589) ),
    inference(clausify,[status(thm)],[f_280_3]) ).

cnf(f_280_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_587),U_588)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_589),U_588)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_587),U_589))
    | ~ sP25(U_587,U_588,U_589) ),
    inference(clausify,[status(thm)],[f_280_3]) ).

fof(f_281_1,plain,
    ! [N,K_1,M_1] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_174_Nat_Odiff__diff__eq]) ).

fof(f_281_2,plain,
    ! [U_592,U_591,U_590] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_590),U_591)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_592),U_591)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_590),U_592)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_591),U_592))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_591),U_590)) ),
    inference(variable_rename,[status(thm)],[f_281_1]) ).

fof(f_281_3,plain,
    ! [U_591,U_592,U_590] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_590),U_591)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_592),U_591)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_590),U_592)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_591),U_592))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_591),U_590)) ),
    inference(definitional_conversion,[status(esa)],[f_281_2]) ).

cnf(f_281_4,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_590),U_591)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_592),U_591)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_590),U_592)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_591),U_592))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_591),U_590)) ),
    inference(clausify,[status(thm)],[f_281_3]) ).

fof(f_282_1,plain,
    ! [Na,K,M] :
      ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,Na),K)
          | M != Na )
        & ( M = Na
          | hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K) != hAPP_nat_nat(hAPP_nat_fun_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)) ),
    inference(fof_nnf,[status(thm)],[fact_175_eq__diff__iff]) ).

fof(f_282_2,plain,
    ! [U_595,U_594,U_593] :
      ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_593),U_594) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_595),U_594)
          | U_593 != U_595 )
        & ( U_593 = U_595
          | hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_593),U_594) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_595),U_594) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_594),U_595))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_594),U_593)) ),
    inference(variable_rename,[status(thm)],[f_282_1]) ).

fof(f_282_3,plain,
    ( ! [U_594,U_593,U_595] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_593),U_594) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_595),U_594)
        | U_593 != U_595
        | ~ sP26(U_594,U_593,U_595) )
    & ! [U_594,U_593,U_595] :
        ( U_593 = U_595
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_593),U_594) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_595),U_594)
        | ~ sP26(U_594,U_593,U_595) )
    & ! [U_594,U_593,U_595] :
        ( sP26(U_594,U_593,U_595)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_594),U_595))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_594),U_593)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP26])],[f_282_2]) ).

cnf(f_282_4,plain,
    ( sP26(U_594,U_593,U_595)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_594),U_595))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_594),U_593)) ),
    inference(clausify,[status(thm)],[f_282_3]) ).

cnf(f_282_5,plain,
    ( U_593 = U_595
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_593),U_594) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_595),U_594)
    | ~ sP26(U_594,U_593,U_595) ),
    inference(clausify,[status(thm)],[f_282_3]) ).

cnf(f_282_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_593),U_594) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_595),U_594)
    | U_593 != U_595
    | ~ sP26(U_594,U_593,U_595) ),
    inference(clausify,[status(thm)],[f_282_3]) ).

fof(f_283_1,plain,
    ! [I_1,N] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),I_1)) = I_1
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_176_diff__diff__cancel]) ).

fof(f_283_2,plain,
    ! [U_597,U_596] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_596),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_596),U_597)) = U_597
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_597),U_596)) ),
    inference(variable_rename,[status(thm)],[f_283_1]) ).

fof(f_283_3,plain,
    ! [U_597,U_596] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_596),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_596),U_597)) = U_597
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_597),U_596)) ),
    inference(definitional_conversion,[status(esa)],[f_283_2]) ).

cnf(f_283_4,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_596),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_596),U_597)) = U_597
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_597),U_596)) ),
    inference(clausify,[status(thm)],[f_283_3]) ).

fof(f_284_1,plain,
    ! [L_1,M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),L_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),L_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_177_diff__le__mono]) ).

fof(f_284_2,plain,
    ! [U_600,U_599,U_598] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_599),U_600)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_598),U_600)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_599),U_598)) ),
    inference(variable_rename,[status(thm)],[f_284_1]) ).

fof(f_284_3,plain,
    ! [U_598,U_599,U_600] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_599),U_600)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_598),U_600)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_599),U_598)) ),
    inference(definitional_conversion,[status(esa)],[f_284_2]) ).

cnf(f_284_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_599),U_600)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_598),U_600)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_599),U_598)) ),
    inference(clausify,[status(thm)],[f_284_3]) ).

fof(f_285_1,plain,
    ! [L_1,M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_1),N)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_1),M_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_178_diff__le__mono2]) ).

fof(f_285_2,plain,
    ! [U_603,U_602,U_601] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_603),U_601)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_603),U_602)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_602),U_601)) ),
    inference(variable_rename,[status(thm)],[f_285_1]) ).

fof(f_285_3,plain,
    ! [U_601,U_602,U_603] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_603),U_601)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_603),U_602)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_602),U_601)) ),
    inference(definitional_conversion,[status(esa)],[f_285_2]) ).

cnf(f_285_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_603),U_601)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_603),U_602)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_602),U_601)) ),
    inference(clausify,[status(thm)],[f_285_3]) ).

fof(f_286_1,plain,
    ! [M_1,N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)),M_1)),
    inference(fof_nnf,[status(thm)],[fact_179_diff__le__self]) ).

fof(f_286_2,plain,
    ! [U_605,U_604] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_605),U_604)),U_605)),
    inference(variable_rename,[status(thm)],[f_286_1]) ).

fof(f_286_3,plain,
    ! [U_604,U_605] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_605),U_604)),U_605)),
    inference(definitional_conversion,[status(esa)],[f_286_2]) ).

cnf(f_286_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_605),U_604)),U_605)),
    inference(clausify,[status(thm)],[f_286_3]) ).

fof(f_287_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_a_a(F,A)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_180_finite__surj]) ).

fof(f_287_2,plain,
    ! [U_608,U_607,U_606] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_608))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_608),image_a_a(U_607,U_606)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_606)) ),
    inference(variable_rename,[status(thm)],[f_287_1]) ).

fof(f_287_3,plain,
    ! [U_606,U_607,U_608] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_608))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_608),image_a_a(U_607,U_606)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_606)) ),
    inference(definitional_conversion,[status(esa)],[f_287_2]) ).

cnf(f_287_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_608))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_608),image_a_a(U_607,U_606)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_606)) ),
    inference(clausify,[status(thm)],[f_287_3]) ).

fof(f_288_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_fun_int_bool_a(F,A)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_181_finite__surj]) ).

fof(f_288_2,plain,
    ! [U_611,U_610,U_609] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_611))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_611),image_fun_int_bool_a(U_610,U_609)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_609)) ),
    inference(variable_rename,[status(thm)],[f_288_1]) ).

fof(f_288_3,plain,
    ! [U_610,U_609,U_611] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_611))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_611),image_fun_int_bool_a(U_610,U_609)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_609)) ),
    inference(definitional_conversion,[status(esa)],[f_288_2]) ).

cnf(f_288_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_611))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_611),image_fun_int_bool_a(U_610,U_609)))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_609)) ),
    inference(clausify,[status(thm)],[f_288_3]) ).

fof(f_289_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_fun_nat_bool_a(F,A)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_182_finite__surj]) ).

fof(f_289_2,plain,
    ! [U_614,U_613,U_612] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_614))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_614),image_fun_nat_bool_a(U_613,U_612)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_612)) ),
    inference(variable_rename,[status(thm)],[f_289_1]) ).

fof(f_289_3,plain,
    ! [U_612,U_613,U_614] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_614))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_614),image_fun_nat_bool_a(U_613,U_612)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_612)) ),
    inference(definitional_conversion,[status(esa)],[f_289_2]) ).

cnf(f_289_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_614))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_614),image_fun_nat_bool_a(U_613,U_612)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_612)) ),
    inference(clausify,[status(thm)],[f_289_3]) ).

fof(f_290_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_876012084bool_a(F,A)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_183_finite__surj]) ).

fof(f_290_2,plain,
    ! [U_617,U_616,U_615] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_617))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_617),image_876012084bool_a(U_616,U_615)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_615)) ),
    inference(variable_rename,[status(thm)],[f_290_1]) ).

fof(f_290_3,plain,
    ! [U_615,U_616,U_617] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_617))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_617),image_876012084bool_a(U_616,U_615)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_615)) ),
    inference(definitional_conversion,[status(esa)],[f_290_2]) ).

cnf(f_290_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_617))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_617),image_876012084bool_a(U_616,U_615)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_615)) ),
    inference(clausify,[status(thm)],[f_290_3]) ).

fof(f_291_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_fun_a_bool_a(F,A)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_184_finite__surj]) ).

fof(f_291_2,plain,
    ! [U_620,U_619,U_618] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_620))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_620),image_fun_a_bool_a(U_619,U_618)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_618)) ),
    inference(variable_rename,[status(thm)],[f_291_1]) ).

fof(f_291_3,plain,
    ! [U_618,U_619,U_620] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_620))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_620),image_fun_a_bool_a(U_619,U_618)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_618)) ),
    inference(definitional_conversion,[status(esa)],[f_291_2]) ).

cnf(f_291_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_620))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_620),image_fun_a_bool_a(U_619,U_618)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_618)) ),
    inference(clausify,[status(thm)],[f_291_3]) ).

fof(f_292_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,B),image_1512837979t_bool(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_185_finite__surj]) ).

fof(f_292_2,plain,
    ! [U_623,U_622,U_621] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_623))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_623),image_1512837979t_bool(U_622,U_621)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_621)) ),
    inference(variable_rename,[status(thm)],[f_292_1]) ).

fof(f_292_3,plain,
    ! [U_621,U_622,U_623] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_623))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_623),image_1512837979t_bool(U_622,U_621)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_621)) ),
    inference(definitional_conversion,[status(esa)],[f_292_2]) ).

cnf(f_292_4,plain,
    ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_623))
    | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_623),image_1512837979t_bool(U_622,U_621)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_621)) ),
    inference(clausify,[status(thm)],[f_292_3]) ).

fof(f_293_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B),image_2129980159t_bool(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_186_finite__surj]) ).

fof(f_293_2,plain,
    ! [U_626,U_625,U_624] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_626))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_626),image_2129980159t_bool(U_625,U_624)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_624)) ),
    inference(variable_rename,[status(thm)],[f_293_1]) ).

fof(f_293_3,plain,
    ! [U_624,U_625,U_626] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_626))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_626),image_2129980159t_bool(U_625,U_624)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_624)) ),
    inference(definitional_conversion,[status(esa)],[f_293_2]) ).

cnf(f_293_4,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_626))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_626),image_2129980159t_bool(U_625,U_624)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_624)) ),
    inference(clausify,[status(thm)],[f_293_3]) ).

fof(f_294_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_47868345e_bool(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_187_finite__surj]) ).

fof(f_294_2,plain,
    ! [U_629,U_628,U_627] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_629))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_629),image_47868345e_bool(U_628,U_627)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_627)) ),
    inference(variable_rename,[status(thm)],[f_294_1]) ).

fof(f_294_3,plain,
    ! [U_627,U_628,U_629] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_629))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_629),image_47868345e_bool(U_628,U_627)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_627)) ),
    inference(definitional_conversion,[status(esa)],[f_294_2]) ).

cnf(f_294_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_629))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_629),image_47868345e_bool(U_628,U_627)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_627)) ),
    inference(clausify,[status(thm)],[f_294_3]) ).

fof(f_295_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B),image_112932426a_bool(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_188_finite__surj]) ).

fof(f_295_2,plain,
    ! [U_632,U_631,U_630] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_632))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_632),image_112932426a_bool(U_631,U_630)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_630)) ),
    inference(variable_rename,[status(thm)],[f_295_1]) ).

fof(f_295_3,plain,
    ! [U_630,U_631,U_632] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_632))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_632),image_112932426a_bool(U_631,U_630)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_630)) ),
    inference(definitional_conversion,[status(esa)],[f_295_2]) ).

cnf(f_295_4,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_632))
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_632),image_112932426a_bool(U_631,U_630)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_630)) ),
    inference(clausify,[status(thm)],[f_295_3]) ).

fof(f_296_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_pname_pname(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_189_finite__surj]) ).

fof(f_296_2,plain,
    ! [U_635,U_634,U_633] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_635))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_635),image_pname_pname(U_634,U_633)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_633)) ),
    inference(variable_rename,[status(thm)],[f_296_1]) ).

fof(f_296_3,plain,
    ! [U_633,U_634,U_635] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_635))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_635),image_pname_pname(U_634,U_633)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_633)) ),
    inference(definitional_conversion,[status(esa)],[f_296_2]) ).

cnf(f_296_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_635))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_635),image_pname_pname(U_634,U_633)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_633)) ),
    inference(clausify,[status(thm)],[f_296_3]) ).

fof(f_297_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_nat_a(F,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_190_finite__surj]) ).

fof(f_297_2,plain,
    ! [U_638,U_637,U_636] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_638))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_638),image_nat_a(U_637,U_636)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_636)) ),
    inference(variable_rename,[status(thm)],[f_297_1]) ).

fof(f_297_3,plain,
    ! [U_636,U_637,U_638] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_638))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_638),image_nat_a(U_637,U_636)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_636)) ),
    inference(definitional_conversion,[status(esa)],[f_297_2]) ).

cnf(f_297_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_638))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_638),image_nat_a(U_637,U_636)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_636)) ),
    inference(clausify,[status(thm)],[f_297_3]) ).

fof(f_298_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,B),image_1556378401t_bool(F,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_191_finite__surj]) ).

fof(f_298_2,plain,
    ! [U_641,U_640,U_639] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_641))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_641),image_1556378401t_bool(U_640,U_639)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_639)) ),
    inference(variable_rename,[status(thm)],[f_298_1]) ).

fof(f_298_3,plain,
    ! [U_639,U_640,U_641] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_641))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_641),image_1556378401t_bool(U_640,U_639)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_639)) ),
    inference(definitional_conversion,[status(esa)],[f_298_2]) ).

cnf(f_298_4,plain,
    ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_641))
    | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_641),image_1556378401t_bool(U_640,U_639)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_639)) ),
    inference(clausify,[status(thm)],[f_298_3]) ).

fof(f_299_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B),image_26036933t_bool(F,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_192_finite__surj]) ).

fof(f_299_2,plain,
    ! [U_644,U_643,U_642] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_644))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_644),image_26036933t_bool(U_643,U_642)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_642)) ),
    inference(variable_rename,[status(thm)],[f_299_1]) ).

fof(f_299_3,plain,
    ! [U_642,U_643,U_644] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_644))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_644),image_26036933t_bool(U_643,U_642)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_642)) ),
    inference(definitional_conversion,[status(esa)],[f_299_2]) ).

cnf(f_299_4,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_644))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_644),image_26036933t_bool(U_643,U_642)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_642)) ),
    inference(clausify,[status(thm)],[f_299_3]) ).

fof(f_300_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_1655916159e_bool(F,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_193_finite__surj]) ).

fof(f_300_2,plain,
    ! [U_647,U_646,U_645] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_647))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_647),image_1655916159e_bool(U_646,U_645)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_645)) ),
    inference(variable_rename,[status(thm)],[f_300_1]) ).

fof(f_300_3,plain,
    ! [U_645,U_646,U_647] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_647))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_647),image_1655916159e_bool(U_646,U_645)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_645)) ),
    inference(definitional_conversion,[status(esa)],[f_300_2]) ).

cnf(f_300_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_647))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_647),image_1655916159e_bool(U_646,U_645)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_645)) ),
    inference(clausify,[status(thm)],[f_300_3]) ).

fof(f_301_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B),image_nat_fun_a_bool(F,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_194_finite__surj]) ).

fof(f_301_2,plain,
    ! [U_650,U_649,U_648] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_650))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_650),image_nat_fun_a_bool(U_649,U_648)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_648)) ),
    inference(variable_rename,[status(thm)],[f_301_1]) ).

fof(f_301_3,plain,
    ! [U_648,U_649,U_650] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_650))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_650),image_nat_fun_a_bool(U_649,U_648)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_648)) ),
    inference(definitional_conversion,[status(esa)],[f_301_2]) ).

cnf(f_301_4,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_650))
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_650),image_nat_fun_a_bool(U_649,U_648)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_648)) ),
    inference(clausify,[status(thm)],[f_301_3]) ).

fof(f_302_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_nat_pname(F,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_195_finite__surj]) ).

fof(f_302_2,plain,
    ! [U_653,U_652,U_651] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_653))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_653),image_nat_pname(U_652,U_651)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_651)) ),
    inference(variable_rename,[status(thm)],[f_302_1]) ).

fof(f_302_3,plain,
    ! [U_652,U_651,U_653] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_653))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_653),image_nat_pname(U_652,U_651)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_651)) ),
    inference(definitional_conversion,[status(esa)],[f_302_2]) ).

cnf(f_302_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_653))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_653),image_nat_pname(U_652,U_651)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_651)) ),
    inference(clausify,[status(thm)],[f_302_3]) ).

fof(f_303_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_int_a(F,A)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_196_finite__surj]) ).

fof(f_303_2,plain,
    ! [U_656,U_655,U_654] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_656))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_656),image_int_a(U_655,U_654)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_654)) ),
    inference(variable_rename,[status(thm)],[f_303_1]) ).

fof(f_303_3,plain,
    ! [U_655,U_654,U_656] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_656))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_656),image_int_a(U_655,U_654)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_654)) ),
    inference(definitional_conversion,[status(esa)],[f_303_2]) ).

cnf(f_303_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_656))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_656),image_int_a(U_655,U_654)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_654)) ),
    inference(clausify,[status(thm)],[f_303_3]) ).

fof(f_304_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,B),image_275383677t_bool(F,A)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_197_finite__surj]) ).

fof(f_304_2,plain,
    ! [U_659,U_658,U_657] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_659))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_659),image_275383677t_bool(U_658,U_657)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_657)) ),
    inference(variable_rename,[status(thm)],[f_304_1]) ).

fof(f_304_3,plain,
    ! [U_657,U_658,U_659] :
      ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_659))
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_659),image_275383677t_bool(U_658,U_657)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_657)) ),
    inference(definitional_conversion,[status(esa)],[f_304_2]) ).

cnf(f_304_4,plain,
    ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_659))
    | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_659),image_275383677t_bool(U_658,U_657)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_657)) ),
    inference(clausify,[status(thm)],[f_304_3]) ).

fof(f_305_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B),image_892525857t_bool(F,A)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_198_finite__surj]) ).

fof(f_305_2,plain,
    ! [U_662,U_661,U_660] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_662))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_662),image_892525857t_bool(U_661,U_660)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_660)) ),
    inference(variable_rename,[status(thm)],[f_305_1]) ).

fof(f_305_3,plain,
    ! [U_660,U_661,U_662] :
      ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_662))
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_662),image_892525857t_bool(U_661,U_660)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_660)) ),
    inference(definitional_conversion,[status(esa)],[f_305_2]) ).

cnf(f_305_4,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_662))
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_662),image_892525857t_bool(U_661,U_660)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_660)) ),
    inference(clausify,[status(thm)],[f_305_3]) ).

fof(f_306_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_637364955e_bool(F,A)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_199_finite__surj]) ).

fof(f_306_2,plain,
    ! [U_665,U_664,U_663] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_665))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_665),image_637364955e_bool(U_664,U_663)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_663)) ),
    inference(variable_rename,[status(thm)],[f_306_1]) ).

fof(f_306_3,plain,
    ! [U_663,U_664,U_665] :
      ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_665))
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_665),image_637364955e_bool(U_664,U_663)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_663)) ),
    inference(definitional_conversion,[status(esa)],[f_306_2]) ).

cnf(f_306_4,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_665))
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_665),image_637364955e_bool(U_664,U_663)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_663)) ),
    inference(clausify,[status(thm)],[f_306_3]) ).

fof(f_307_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B),image_int_fun_a_bool(F,A)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_200_finite__surj]) ).

fof(f_307_2,plain,
    ! [U_668,U_667,U_666] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_668))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_668),image_int_fun_a_bool(U_667,U_666)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_666)) ),
    inference(variable_rename,[status(thm)],[f_307_1]) ).

fof(f_307_3,plain,
    ! [U_666,U_667,U_668] :
      ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_668))
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_668),image_int_fun_a_bool(U_667,U_666)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_666)) ),
    inference(definitional_conversion,[status(esa)],[f_307_2]) ).

cnf(f_307_4,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_668))
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_668),image_int_fun_a_bool(U_667,U_666)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_666)) ),
    inference(clausify,[status(thm)],[f_307_3]) ).

fof(f_308_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_int_pname(F,A)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_201_finite__surj]) ).

fof(f_308_2,plain,
    ! [U_671,U_670,U_669] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_671))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_671),image_int_pname(U_670,U_669)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_669)) ),
    inference(variable_rename,[status(thm)],[f_308_1]) ).

fof(f_308_3,plain,
    ! [U_670,U_669,U_671] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_671))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_671),image_int_pname(U_670,U_669)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_669)) ),
    inference(definitional_conversion,[status(esa)],[f_308_2]) ).

cnf(f_308_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_671))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_671),image_int_pname(U_670,U_669)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_669)) ),
    inference(clausify,[status(thm)],[f_308_3]) ).

fof(f_309_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_a_pname(F,A)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_202_finite__surj]) ).

fof(f_309_2,plain,
    ! [U_674,U_673,U_672] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_674))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_674),image_a_pname(U_673,U_672)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_672)) ),
    inference(variable_rename,[status(thm)],[f_309_1]) ).

fof(f_309_3,plain,
    ! [U_672,U_673,U_674] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_674))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_674),image_a_pname(U_673,U_672)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_672)) ),
    inference(definitional_conversion,[status(esa)],[f_309_2]) ).

cnf(f_309_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_674))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_674),image_a_pname(U_673,U_672)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_672)) ),
    inference(clausify,[status(thm)],[f_309_3]) ).

fof(f_310_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_62782965_pname(F,A)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_203_finite__surj]) ).

fof(f_310_2,plain,
    ! [U_677,U_676,U_675] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_677))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_677),image_62782965_pname(U_676,U_675)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_675)) ),
    inference(variable_rename,[status(thm)],[f_310_1]) ).

fof(f_310_3,plain,
    ! [U_676,U_675,U_677] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_677))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_677),image_62782965_pname(U_676,U_675)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_675)) ),
    inference(definitional_conversion,[status(esa)],[f_310_2]) ).

cnf(f_310_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_677))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_677),image_62782965_pname(U_676,U_675)))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_675)) ),
    inference(clausify,[status(thm)],[f_310_3]) ).

fof(f_311_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1921560913_pname(F,A)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_204_finite__surj]) ).

fof(f_311_2,plain,
    ! [U_680,U_679,U_678] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_680))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_680),image_1921560913_pname(U_679,U_678)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_678)) ),
    inference(variable_rename,[status(thm)],[f_311_1]) ).

fof(f_311_3,plain,
    ! [U_678,U_679,U_680] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_680))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_680),image_1921560913_pname(U_679,U_678)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_678)) ),
    inference(definitional_conversion,[status(esa)],[f_311_2]) ).

cnf(f_311_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_680))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_680),image_1921560913_pname(U_679,U_678)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_678)) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

fof(f_312_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1283814551_pname(F,A)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_205_finite__surj]) ).

fof(f_312_2,plain,
    ! [U_683,U_682,U_681] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_683))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_683),image_1283814551_pname(U_682,U_681)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_681)) ),
    inference(variable_rename,[status(thm)],[f_312_1]) ).

fof(f_312_3,plain,
    ! [U_681,U_682,U_683] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_683))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_683),image_1283814551_pname(U_682,U_681)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_681)) ),
    inference(definitional_conversion,[status(esa)],[f_312_2]) ).

cnf(f_312_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_683))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_683),image_1283814551_pname(U_682,U_681)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_681)) ),
    inference(clausify,[status(thm)],[f_312_3]) ).

fof(f_313_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1854862208_pname(F,A)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_206_finite__surj]) ).

fof(f_313_2,plain,
    ! [U_686,U_685,U_684] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_686))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_686),image_1854862208_pname(U_685,U_684)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_684)) ),
    inference(variable_rename,[status(thm)],[f_313_1]) ).

fof(f_313_3,plain,
    ! [U_684,U_685,U_686] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_686))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_686),image_1854862208_pname(U_685,U_684)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_684)) ),
    inference(definitional_conversion,[status(esa)],[f_313_2]) ).

cnf(f_313_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_686))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_686),image_1854862208_pname(U_685,U_684)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_684)) ),
    inference(clausify,[status(thm)],[f_313_3]) ).

fof(f_314_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_a_nat(F,A)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_207_finite__surj]) ).

fof(f_314_2,plain,
    ! [U_689,U_688,U_687] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_689))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_689),image_a_nat(U_688,U_687)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_687)) ),
    inference(variable_rename,[status(thm)],[f_314_1]) ).

fof(f_314_3,plain,
    ! [U_687,U_688,U_689] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_689))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_689),image_a_nat(U_688,U_687)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_687)) ),
    inference(definitional_conversion,[status(esa)],[f_314_2]) ).

cnf(f_314_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_689))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_689),image_a_nat(U_688,U_687)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_687)) ),
    inference(clausify,[status(thm)],[f_314_3]) ).

fof(f_315_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_1431733819ol_nat(F,A)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_208_finite__surj]) ).

fof(f_315_2,plain,
    ! [U_692,U_691,U_690] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_692))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_692),image_1431733819ol_nat(U_691,U_690)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_690)) ),
    inference(variable_rename,[status(thm)],[f_315_1]) ).

fof(f_315_3,plain,
    ! [U_691,U_690,U_692] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_692))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_692),image_1431733819ol_nat(U_691,U_690)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_690)) ),
    inference(definitional_conversion,[status(esa)],[f_315_2]) ).

cnf(f_315_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_692))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_692),image_1431733819ol_nat(U_691,U_690)))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_690)) ),
    inference(clausify,[status(thm)],[f_315_3]) ).

fof(f_316_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_496248727ol_nat(F,A)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_209_finite__surj]) ).

fof(f_316_2,plain,
    ! [U_695,U_694,U_693] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_695))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_695),image_496248727ol_nat(U_694,U_693)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_693)) ),
    inference(variable_rename,[status(thm)],[f_316_1]) ).

fof(f_316_3,plain,
    ! [U_693,U_694,U_695] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_695))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_695),image_496248727ol_nat(U_694,U_693)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_693)) ),
    inference(definitional_conversion,[status(esa)],[f_316_2]) ).

cnf(f_316_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_695))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_695),image_496248727ol_nat(U_694,U_693)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_693)) ),
    inference(clausify,[status(thm)],[f_316_3]) ).

fof(f_317_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_1551609309ol_nat(F,A)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_210_finite__surj]) ).

fof(f_317_2,plain,
    ! [U_698,U_697,U_696] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_698))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_698),image_1551609309ol_nat(U_697,U_696)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_696)) ),
    inference(variable_rename,[status(thm)],[f_317_1]) ).

fof(f_317_3,plain,
    ! [U_696,U_697,U_698] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_698))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_698),image_1551609309ol_nat(U_697,U_696)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_696)) ),
    inference(definitional_conversion,[status(esa)],[f_317_2]) ).

cnf(f_317_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_698))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_698),image_1551609309ol_nat(U_697,U_696)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_696)) ),
    inference(clausify,[status(thm)],[f_317_3]) ).

fof(f_318_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_fun_a_bool_nat(F,A)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_211_finite__surj]) ).

fof(f_318_2,plain,
    ! [U_701,U_700,U_699] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_701))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_701),image_fun_a_bool_nat(U_700,U_699)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_699)) ),
    inference(variable_rename,[status(thm)],[f_318_1]) ).

fof(f_318_3,plain,
    ! [U_699,U_700,U_701] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_701))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_701),image_fun_a_bool_nat(U_700,U_699)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_699)) ),
    inference(definitional_conversion,[status(esa)],[f_318_2]) ).

cnf(f_318_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_701))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_701),image_fun_a_bool_nat(U_700,U_699)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_699)) ),
    inference(clausify,[status(thm)],[f_318_3]) ).

fof(f_319_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_a_int(F,A)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_212_finite__surj]) ).

fof(f_319_2,plain,
    ! [U_704,U_703,U_702] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_704))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_704),image_a_int(U_703,U_702)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_702)) ),
    inference(variable_rename,[status(thm)],[f_319_1]) ).

fof(f_319_3,plain,
    ! [U_703,U_702,U_704] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_704))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_704),image_a_int(U_703,U_702)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_702)) ),
    inference(definitional_conversion,[status(esa)],[f_319_2]) ).

cnf(f_319_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_704))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_704),image_a_int(U_703,U_702)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_702)) ),
    inference(clausify,[status(thm)],[f_319_3]) ).

fof(f_320_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_2069007511ol_int(F,A)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_213_finite__surj]) ).

fof(f_320_2,plain,
    ! [U_707,U_706,U_705] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_707))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_707),image_2069007511ol_int(U_706,U_705)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_705)) ),
    inference(variable_rename,[status(thm)],[f_320_1]) ).

fof(f_320_3,plain,
    ! [U_706,U_705,U_707] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_707))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_707),image_2069007511ol_int(U_706,U_705)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_705)) ),
    inference(definitional_conversion,[status(esa)],[f_320_2]) ).

cnf(f_320_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_707))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_707),image_2069007511ol_int(U_706,U_705)))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_705)) ),
    inference(clausify,[status(thm)],[f_320_3]) ).

fof(f_321_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_1133522419ol_int(F,A)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_214_finite__surj]) ).

fof(f_321_2,plain,
    ! [U_710,U_709,U_708] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_710))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_710),image_1133522419ol_int(U_709,U_708)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_708)) ),
    inference(variable_rename,[status(thm)],[f_321_1]) ).

fof(f_321_3,plain,
    ! [U_708,U_709,U_710] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_710))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_710),image_1133522419ol_int(U_709,U_708)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_708)) ),
    inference(definitional_conversion,[status(esa)],[f_321_2]) ).

cnf(f_321_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_710))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_710),image_1133522419ol_int(U_709,U_708)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_708)) ),
    inference(clausify,[status(thm)],[f_321_3]) ).

fof(f_322_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_41399353ol_int(F,A)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_215_finite__surj]) ).

fof(f_322_2,plain,
    ! [U_713,U_712,U_711] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_713))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_713),image_41399353ol_int(U_712,U_711)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_711)) ),
    inference(variable_rename,[status(thm)],[f_322_1]) ).

fof(f_322_3,plain,
    ! [U_711,U_712,U_713] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_713))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_713),image_41399353ol_int(U_712,U_711)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_711)) ),
    inference(definitional_conversion,[status(esa)],[f_322_2]) ).

cnf(f_322_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_713))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_713),image_41399353ol_int(U_712,U_711)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_711)) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

fof(f_323_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_fun_a_bool_int(F,A)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) ),
    inference(fof_nnf,[status(thm)],[fact_216_finite__surj]) ).

fof(f_323_2,plain,
    ! [U_716,U_715,U_714] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_716))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_716),image_fun_a_bool_int(U_715,U_714)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_714)) ),
    inference(variable_rename,[status(thm)],[f_323_1]) ).

fof(f_323_3,plain,
    ! [U_714,U_715,U_716] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_716))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_716),image_fun_a_bool_int(U_715,U_714)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_714)) ),
    inference(definitional_conversion,[status(esa)],[f_323_2]) ).

cnf(f_323_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_716))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_716),image_fun_a_bool_int(U_715,U_714)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_714)) ),
    inference(clausify,[status(thm)],[f_323_3]) ).

fof(f_324_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_217_finite__surj]) ).

fof(f_324_2,plain,
    ! [U_719,U_718,U_717] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_719))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_719),image_pname_a(U_718,U_717)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_717)) ),
    inference(variable_rename,[status(thm)],[f_324_1]) ).

fof(f_324_3,plain,
    ! [U_717,U_718,U_719] :
      ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_719))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_719),image_pname_a(U_718,U_717)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_717)) ),
    inference(definitional_conversion,[status(esa)],[f_324_2]) ).

cnf(f_324_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_719))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_719),image_pname_a(U_718,U_717)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_717)) ),
    inference(clausify,[status(thm)],[f_324_3]) ).

fof(f_325_1,plain,
    ! [B,F,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,B))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_nat_int(F,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_218_finite__surj]) ).

fof(f_325_2,plain,
    ! [U_722,U_721,U_720] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_722))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_722),image_nat_int(U_721,U_720)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_720)) ),
    inference(variable_rename,[status(thm)],[f_325_1]) ).

fof(f_325_3,plain,
    ! [U_720,U_721,U_722] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_722))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_722),image_nat_int(U_721,U_720)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_720)) ),
    inference(definitional_conversion,[status(esa)],[f_325_2]) ).

cnf(f_325_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_722))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_722),image_nat_int(U_721,U_720)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_720)) ),
    inference(clausify,[status(thm)],[f_325_3]) ).

fof(f_326_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_fun_int_bool_a(F,C_16)
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,C_16))
          & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,C_16),A)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_fun_int_bool_a(F,A)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))
      | ~ is_fun_a_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_219_finite__subset__image]) ).

fof(f_326_2,plain,
    ! [U_726,U_725,U_724] :
      ( ? [U_723] :
          ( U_724 = image_fun_int_bool_a(U_726,U_723)
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_723))
          & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_723),U_725)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_724),image_fun_int_bool_a(U_726,U_725)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_724))
      | ~ is_fun_a_bool(U_724) ),
    inference(variable_rename,[status(thm)],[f_326_1]) ).

fof(f_326_3,plain,
    ! [U_726,U_725,U_724] :
      ( ( U_724 = image_fun_int_bool_a(U_726,sK1(U_726,U_725,U_724))
        & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK1(U_726,U_725,U_724)))
        & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK1(U_726,U_725,U_724)),U_725)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_724),image_fun_int_bool_a(U_726,U_725)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_724))
      | ~ is_fun_a_bool(U_724) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_723,sK1(U_726,U_725,U_724))],[f_326_2]) ).

fof(f_326_4,plain,
    ( ! [U_724,U_725,U_726] :
        ( U_724 = image_fun_int_bool_a(U_726,sK1(U_726,U_725,U_724))
        | ~ sP27(U_724,U_725,U_726) )
    & ! [U_724,U_725,U_726] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK1(U_726,U_725,U_724)))
        | ~ sP27(U_724,U_725,U_726) )
    & ! [U_724,U_725,U_726] :
        ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK1(U_726,U_725,U_724)),U_725))
        | ~ sP27(U_724,U_725,U_726) )
    & ! [U_724,U_725,U_726] :
        ( sP27(U_724,U_725,U_726)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_724),image_fun_int_bool_a(U_726,U_725)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_724))
        | ~ is_fun_a_bool(U_724) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP27])],[f_326_3]) ).

cnf(f_326_5,plain,
    ( sP27(U_724,U_725,U_726)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_724),image_fun_int_bool_a(U_726,U_725)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_724))
    | ~ is_fun_a_bool(U_724) ),
    inference(clausify,[status(thm)],[f_326_4]) ).

cnf(f_326_6,plain,
    ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK1(U_726,U_725,U_724)),U_725))
    | ~ sP27(U_724,U_725,U_726) ),
    inference(clausify,[status(thm)],[f_326_4]) ).

cnf(f_326_7,plain,
    ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK1(U_726,U_725,U_724)))
    | ~ sP27(U_724,U_725,U_726) ),
    inference(clausify,[status(thm)],[f_326_4]) ).

cnf(f_326_8,plain,
    ( U_724 = image_fun_int_bool_a(U_726,sK1(U_726,U_725,U_724))
    | ~ sP27(U_724,U_725,U_726) ),
    inference(clausify,[status(thm)],[f_326_4]) ).

fof(f_327_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_fun_nat_bool_a(F,C_16)
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_16))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_16),A)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_fun_nat_bool_a(F,A)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))
      | ~ is_fun_a_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_220_finite__subset__image]) ).

fof(f_327_2,plain,
    ! [U_730,U_729,U_728] :
      ( ? [U_727] :
          ( U_728 = image_fun_nat_bool_a(U_730,U_727)
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_727))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_727),U_729)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_728),image_fun_nat_bool_a(U_730,U_729)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_728))
      | ~ is_fun_a_bool(U_728) ),
    inference(variable_rename,[status(thm)],[f_327_1]) ).

fof(f_327_3,plain,
    ! [U_730,U_729,U_728] :
      ( ( U_728 = image_fun_nat_bool_a(U_730,sK2(U_730,U_729,U_728))
        & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK2(U_730,U_729,U_728)))
        & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK2(U_730,U_729,U_728)),U_729)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_728),image_fun_nat_bool_a(U_730,U_729)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_728))
      | ~ is_fun_a_bool(U_728) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_727,sK2(U_730,U_729,U_728))],[f_327_2]) ).

fof(f_327_4,plain,
    ( ! [U_728,U_730,U_729] :
        ( U_728 = image_fun_nat_bool_a(U_730,sK2(U_730,U_729,U_728))
        | ~ sP28(U_728,U_730,U_729) )
    & ! [U_728,U_730,U_729] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK2(U_730,U_729,U_728)))
        | ~ sP28(U_728,U_730,U_729) )
    & ! [U_728,U_730,U_729] :
        ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK2(U_730,U_729,U_728)),U_729))
        | ~ sP28(U_728,U_730,U_729) )
    & ! [U_728,U_730,U_729] :
        ( sP28(U_728,U_730,U_729)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_728),image_fun_nat_bool_a(U_730,U_729)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_728))
        | ~ is_fun_a_bool(U_728) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP28])],[f_327_3]) ).

cnf(f_327_5,plain,
    ( sP28(U_728,U_730,U_729)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_728),image_fun_nat_bool_a(U_730,U_729)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_728))
    | ~ is_fun_a_bool(U_728) ),
    inference(clausify,[status(thm)],[f_327_4]) ).

cnf(f_327_6,plain,
    ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK2(U_730,U_729,U_728)),U_729))
    | ~ sP28(U_728,U_730,U_729) ),
    inference(clausify,[status(thm)],[f_327_4]) ).

cnf(f_327_7,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK2(U_730,U_729,U_728)))
    | ~ sP28(U_728,U_730,U_729) ),
    inference(clausify,[status(thm)],[f_327_4]) ).

cnf(f_327_8,plain,
    ( U_728 = image_fun_nat_bool_a(U_730,sK2(U_730,U_729,U_728))
    | ~ sP28(U_728,U_730,U_729) ),
    inference(clausify,[status(thm)],[f_327_4]) ).

fof(f_328_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_876012084bool_a(F,C_16)
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_16))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_16),A))
          & is_fun1661590463l_bool(C_16) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_876012084bool_a(F,A)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))
      | ~ is_fun_a_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_221_finite__subset__image]) ).

fof(f_328_2,plain,
    ! [U_734,U_733,U_732] :
      ( ? [U_731] :
          ( U_732 = image_876012084bool_a(U_734,U_731)
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_731))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_731),U_733))
          & is_fun1661590463l_bool(U_731) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_732),image_876012084bool_a(U_734,U_733)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_732))
      | ~ is_fun_a_bool(U_732) ),
    inference(variable_rename,[status(thm)],[f_328_1]) ).

fof(f_328_3,plain,
    ! [U_734,U_733,U_732] :
      ( ( U_732 = image_876012084bool_a(U_734,sK3(U_734,U_733,U_732))
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK3(U_734,U_733,U_732)))
        & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK3(U_734,U_733,U_732)),U_733))
        & is_fun1661590463l_bool(sK3(U_734,U_733,U_732)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_732),image_876012084bool_a(U_734,U_733)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_732))
      | ~ is_fun_a_bool(U_732) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_731,sK3(U_734,U_733,U_732))],[f_328_2]) ).

fof(f_328_4,plain,
    ( ! [U_734,U_732,U_733] :
        ( U_732 = image_876012084bool_a(U_734,sK3(U_734,U_733,U_732))
        | ~ sP29(U_734,U_732,U_733) )
    & ! [U_734,U_732,U_733] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK3(U_734,U_733,U_732)))
        | ~ sP29(U_734,U_732,U_733) )
    & ! [U_734,U_732,U_733] :
        ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK3(U_734,U_733,U_732)),U_733))
        | ~ sP29(U_734,U_732,U_733) )
    & ! [U_734,U_732,U_733] :
        ( is_fun1661590463l_bool(sK3(U_734,U_733,U_732))
        | ~ sP29(U_734,U_732,U_733) )
    & ! [U_734,U_732,U_733] :
        ( sP29(U_734,U_732,U_733)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_732),image_876012084bool_a(U_734,U_733)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_732))
        | ~ is_fun_a_bool(U_732) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP29])],[f_328_3]) ).

cnf(f_328_5,plain,
    ( sP29(U_734,U_732,U_733)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_732),image_876012084bool_a(U_734,U_733)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_732))
    | ~ is_fun_a_bool(U_732) ),
    inference(clausify,[status(thm)],[f_328_4]) ).

cnf(f_328_6,plain,
    ( is_fun1661590463l_bool(sK3(U_734,U_733,U_732))
    | ~ sP29(U_734,U_732,U_733) ),
    inference(clausify,[status(thm)],[f_328_4]) ).

cnf(f_328_7,plain,
    ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK3(U_734,U_733,U_732)),U_733))
    | ~ sP29(U_734,U_732,U_733) ),
    inference(clausify,[status(thm)],[f_328_4]) ).

cnf(f_328_8,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK3(U_734,U_733,U_732)))
    | ~ sP29(U_734,U_732,U_733) ),
    inference(clausify,[status(thm)],[f_328_4]) ).

cnf(f_328_9,plain,
    ( U_732 = image_876012084bool_a(U_734,sK3(U_734,U_733,U_732))
    | ~ sP29(U_734,U_732,U_733) ),
    inference(clausify,[status(thm)],[f_328_4]) ).

fof(f_329_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_fun_a_bool_a(F,C_16)
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_16))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_16),A))
          & is_fun949378684l_bool(C_16) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_fun_a_bool_a(F,A)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))
      | ~ is_fun_a_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_222_finite__subset__image]) ).

fof(f_329_2,plain,
    ! [U_738,U_737,U_736] :
      ( ? [U_735] :
          ( U_736 = image_fun_a_bool_a(U_738,U_735)
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_735))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_735),U_737))
          & is_fun949378684l_bool(U_735) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_736),image_fun_a_bool_a(U_738,U_737)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_736))
      | ~ is_fun_a_bool(U_736) ),
    inference(variable_rename,[status(thm)],[f_329_1]) ).

fof(f_329_3,plain,
    ! [U_738,U_737,U_736] :
      ( ( U_736 = image_fun_a_bool_a(U_738,sK4(U_738,U_737,U_736))
        & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK4(U_738,U_737,U_736)))
        & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK4(U_738,U_737,U_736)),U_737))
        & is_fun949378684l_bool(sK4(U_738,U_737,U_736)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_736),image_fun_a_bool_a(U_738,U_737)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_736))
      | ~ is_fun_a_bool(U_736) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_735,sK4(U_738,U_737,U_736))],[f_329_2]) ).

fof(f_329_4,plain,
    ( ! [U_736,U_738,U_737] :
        ( U_736 = image_fun_a_bool_a(U_738,sK4(U_738,U_737,U_736))
        | ~ sP30(U_736,U_738,U_737) )
    & ! [U_736,U_738,U_737] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK4(U_738,U_737,U_736)))
        | ~ sP30(U_736,U_738,U_737) )
    & ! [U_736,U_738,U_737] :
        ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK4(U_738,U_737,U_736)),U_737))
        | ~ sP30(U_736,U_738,U_737) )
    & ! [U_736,U_738,U_737] :
        ( is_fun949378684l_bool(sK4(U_738,U_737,U_736))
        | ~ sP30(U_736,U_738,U_737) )
    & ! [U_736,U_738,U_737] :
        ( sP30(U_736,U_738,U_737)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_736),image_fun_a_bool_a(U_738,U_737)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_736))
        | ~ is_fun_a_bool(U_736) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP30])],[f_329_3]) ).

cnf(f_329_5,plain,
    ( sP30(U_736,U_738,U_737)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_736),image_fun_a_bool_a(U_738,U_737)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_736))
    | ~ is_fun_a_bool(U_736) ),
    inference(clausify,[status(thm)],[f_329_4]) ).

cnf(f_329_6,plain,
    ( is_fun949378684l_bool(sK4(U_738,U_737,U_736))
    | ~ sP30(U_736,U_738,U_737) ),
    inference(clausify,[status(thm)],[f_329_4]) ).

cnf(f_329_7,plain,
    ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK4(U_738,U_737,U_736)),U_737))
    | ~ sP30(U_736,U_738,U_737) ),
    inference(clausify,[status(thm)],[f_329_4]) ).

cnf(f_329_8,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK4(U_738,U_737,U_736)))
    | ~ sP30(U_736,U_738,U_737) ),
    inference(clausify,[status(thm)],[f_329_4]) ).

cnf(f_329_9,plain,
    ( U_736 = image_fun_a_bool_a(U_738,sK4(U_738,U_737,U_736))
    | ~ sP30(U_736,U_738,U_737) ),
    inference(clausify,[status(thm)],[f_329_4]) ).

fof(f_330_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_a_a(F,C_16)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A))
          & is_fun_a_bool(C_16) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_a_a(F,A)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))
      | ~ is_fun_a_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_223_finite__subset__image]) ).

fof(f_330_2,plain,
    ! [U_742,U_741,U_740] :
      ( ? [U_739] :
          ( U_740 = image_a_a(U_742,U_739)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_739))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_739),U_741))
          & is_fun_a_bool(U_739) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_740),image_a_a(U_742,U_741)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_740))
      | ~ is_fun_a_bool(U_740) ),
    inference(variable_rename,[status(thm)],[f_330_1]) ).

fof(f_330_3,plain,
    ! [U_742,U_741,U_740] :
      ( ( U_740 = image_a_a(U_742,sK5(U_742,U_741,U_740))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK5(U_742,U_741,U_740)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK5(U_742,U_741,U_740)),U_741))
        & is_fun_a_bool(sK5(U_742,U_741,U_740)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_740),image_a_a(U_742,U_741)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_740))
      | ~ is_fun_a_bool(U_740) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_739,sK5(U_742,U_741,U_740))],[f_330_2]) ).

fof(f_330_4,plain,
    ( ! [U_741,U_740,U_742] :
        ( U_740 = image_a_a(U_742,sK5(U_742,U_741,U_740))
        | ~ sP31(U_741,U_740,U_742) )
    & ! [U_741,U_740,U_742] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK5(U_742,U_741,U_740)))
        | ~ sP31(U_741,U_740,U_742) )
    & ! [U_741,U_740,U_742] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK5(U_742,U_741,U_740)),U_741))
        | ~ sP31(U_741,U_740,U_742) )
    & ! [U_741,U_740,U_742] :
        ( is_fun_a_bool(sK5(U_742,U_741,U_740))
        | ~ sP31(U_741,U_740,U_742) )
    & ! [U_741,U_740,U_742] :
        ( sP31(U_741,U_740,U_742)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_740),image_a_a(U_742,U_741)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_740))
        | ~ is_fun_a_bool(U_740) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP31])],[f_330_3]) ).

cnf(f_330_5,plain,
    ( sP31(U_741,U_740,U_742)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_740),image_a_a(U_742,U_741)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_740))
    | ~ is_fun_a_bool(U_740) ),
    inference(clausify,[status(thm)],[f_330_4]) ).

cnf(f_330_6,plain,
    ( is_fun_a_bool(sK5(U_742,U_741,U_740))
    | ~ sP31(U_741,U_740,U_742) ),
    inference(clausify,[status(thm)],[f_330_4]) ).

cnf(f_330_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK5(U_742,U_741,U_740)),U_741))
    | ~ sP31(U_741,U_740,U_742) ),
    inference(clausify,[status(thm)],[f_330_4]) ).

cnf(f_330_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK5(U_742,U_741,U_740)))
    | ~ sP31(U_741,U_740,U_742) ),
    inference(clausify,[status(thm)],[f_330_4]) ).

cnf(f_330_9,plain,
    ( U_740 = image_a_a(U_742,sK5(U_742,U_741,U_740))
    | ~ sP31(U_741,U_740,U_742) ),
    inference(clausify,[status(thm)],[f_330_4]) ).

fof(f_331_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_a_fun_int_bool(F,C_16)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A))
          & is_fun_a_bool(C_16) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,B),image_a_fun_int_bool(F,A)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B)) ),
    inference(fof_nnf,[status(thm)],[fact_224_finite__subset__image]) ).

fof(f_331_2,plain,
    ! [U_746,U_745,U_744] :
      ( ? [U_743] :
          ( U_744 = image_a_fun_int_bool(U_746,U_743)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_743))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_743),U_745))
          & is_fun_a_bool(U_743) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_744),image_a_fun_int_bool(U_746,U_745)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_744)) ),
    inference(variable_rename,[status(thm)],[f_331_1]) ).

fof(f_331_3,plain,
    ! [U_746,U_745,U_744] :
      ( ( U_744 = image_a_fun_int_bool(U_746,sK6(U_746,U_745,U_744))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK6(U_746,U_745,U_744)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK6(U_746,U_745,U_744)),U_745))
        & is_fun_a_bool(sK6(U_746,U_745,U_744)) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_744),image_a_fun_int_bool(U_746,U_745)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_744)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_743,sK6(U_746,U_745,U_744))],[f_331_2]) ).

fof(f_331_4,plain,
    ( ! [U_745,U_744,U_746] :
        ( U_744 = image_a_fun_int_bool(U_746,sK6(U_746,U_745,U_744))
        | ~ sP32(U_745,U_744,U_746) )
    & ! [U_745,U_744,U_746] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK6(U_746,U_745,U_744)))
        | ~ sP32(U_745,U_744,U_746) )
    & ! [U_745,U_744,U_746] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK6(U_746,U_745,U_744)),U_745))
        | ~ sP32(U_745,U_744,U_746) )
    & ! [U_745,U_744,U_746] :
        ( is_fun_a_bool(sK6(U_746,U_745,U_744))
        | ~ sP32(U_745,U_744,U_746) )
    & ! [U_745,U_744,U_746] :
        ( sP32(U_745,U_744,U_746)
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_744),image_a_fun_int_bool(U_746,U_745)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_744)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP32])],[f_331_3]) ).

cnf(f_331_5,plain,
    ( sP32(U_745,U_744,U_746)
    | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_744),image_a_fun_int_bool(U_746,U_745)))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_744)) ),
    inference(clausify,[status(thm)],[f_331_4]) ).

cnf(f_331_6,plain,
    ( is_fun_a_bool(sK6(U_746,U_745,U_744))
    | ~ sP32(U_745,U_744,U_746) ),
    inference(clausify,[status(thm)],[f_331_4]) ).

cnf(f_331_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK6(U_746,U_745,U_744)),U_745))
    | ~ sP32(U_745,U_744,U_746) ),
    inference(clausify,[status(thm)],[f_331_4]) ).

cnf(f_331_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK6(U_746,U_745,U_744)))
    | ~ sP32(U_745,U_744,U_746) ),
    inference(clausify,[status(thm)],[f_331_4]) ).

cnf(f_331_9,plain,
    ( U_744 = image_a_fun_int_bool(U_746,sK6(U_746,U_745,U_744))
    | ~ sP32(U_745,U_744,U_746) ),
    inference(clausify,[status(thm)],[f_331_4]) ).

fof(f_332_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_a_fun_nat_bool(F,C_16)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A))
          & is_fun_a_bool(C_16) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B),image_a_fun_nat_bool(F,A)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B)) ),
    inference(fof_nnf,[status(thm)],[fact_225_finite__subset__image]) ).

fof(f_332_2,plain,
    ! [U_750,U_749,U_748] :
      ( ? [U_747] :
          ( U_748 = image_a_fun_nat_bool(U_750,U_747)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_747))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_747),U_749))
          & is_fun_a_bool(U_747) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_748),image_a_fun_nat_bool(U_750,U_749)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_748)) ),
    inference(variable_rename,[status(thm)],[f_332_1]) ).

fof(f_332_3,plain,
    ! [U_750,U_749,U_748] :
      ( ( U_748 = image_a_fun_nat_bool(U_750,sK7(U_750,U_749,U_748))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK7(U_750,U_749,U_748)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK7(U_750,U_749,U_748)),U_749))
        & is_fun_a_bool(sK7(U_750,U_749,U_748)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_748),image_a_fun_nat_bool(U_750,U_749)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_748)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_747,sK7(U_750,U_749,U_748))],[f_332_2]) ).

fof(f_332_4,plain,
    ( ! [U_749,U_748,U_750] :
        ( U_748 = image_a_fun_nat_bool(U_750,sK7(U_750,U_749,U_748))
        | ~ sP33(U_749,U_748,U_750) )
    & ! [U_749,U_748,U_750] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK7(U_750,U_749,U_748)))
        | ~ sP33(U_749,U_748,U_750) )
    & ! [U_749,U_748,U_750] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK7(U_750,U_749,U_748)),U_749))
        | ~ sP33(U_749,U_748,U_750) )
    & ! [U_749,U_748,U_750] :
        ( is_fun_a_bool(sK7(U_750,U_749,U_748))
        | ~ sP33(U_749,U_748,U_750) )
    & ! [U_749,U_748,U_750] :
        ( sP33(U_749,U_748,U_750)
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_748),image_a_fun_nat_bool(U_750,U_749)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_748)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP33])],[f_332_3]) ).

cnf(f_332_5,plain,
    ( sP33(U_749,U_748,U_750)
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_748),image_a_fun_nat_bool(U_750,U_749)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_748)) ),
    inference(clausify,[status(thm)],[f_332_4]) ).

cnf(f_332_6,plain,
    ( is_fun_a_bool(sK7(U_750,U_749,U_748))
    | ~ sP33(U_749,U_748,U_750) ),
    inference(clausify,[status(thm)],[f_332_4]) ).

cnf(f_332_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK7(U_750,U_749,U_748)),U_749))
    | ~ sP33(U_749,U_748,U_750) ),
    inference(clausify,[status(thm)],[f_332_4]) ).

cnf(f_332_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK7(U_750,U_749,U_748)))
    | ~ sP33(U_749,U_748,U_750) ),
    inference(clausify,[status(thm)],[f_332_4]) ).

cnf(f_332_9,plain,
    ( U_748 = image_a_fun_nat_bool(U_750,sK7(U_750,U_749,U_748))
    | ~ sP33(U_749,U_748,U_750) ),
    inference(clausify,[status(thm)],[f_332_4]) ).

fof(f_333_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_819518260e_bool(F,C_16)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A))
          & is_fun_a_bool(C_16) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_819518260e_bool(F,A)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
      | ~ is_fun1661590463l_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_226_finite__subset__image]) ).

fof(f_333_2,plain,
    ! [U_754,U_753,U_752] :
      ( ? [U_751] :
          ( U_752 = image_819518260e_bool(U_754,U_751)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_751))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_751),U_753))
          & is_fun_a_bool(U_751) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_752),image_819518260e_bool(U_754,U_753)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_752))
      | ~ is_fun1661590463l_bool(U_752) ),
    inference(variable_rename,[status(thm)],[f_333_1]) ).

fof(f_333_3,plain,
    ! [U_754,U_753,U_752] :
      ( ( U_752 = image_819518260e_bool(U_754,sK8(U_754,U_753,U_752))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK8(U_754,U_753,U_752)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK8(U_754,U_753,U_752)),U_753))
        & is_fun_a_bool(sK8(U_754,U_753,U_752)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_752),image_819518260e_bool(U_754,U_753)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_752))
      | ~ is_fun1661590463l_bool(U_752) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_751,sK8(U_754,U_753,U_752))],[f_333_2]) ).

fof(f_333_4,plain,
    ( ! [U_753,U_752,U_754] :
        ( U_752 = image_819518260e_bool(U_754,sK8(U_754,U_753,U_752))
        | ~ sP34(U_753,U_752,U_754) )
    & ! [U_753,U_752,U_754] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK8(U_754,U_753,U_752)))
        | ~ sP34(U_753,U_752,U_754) )
    & ! [U_753,U_752,U_754] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK8(U_754,U_753,U_752)),U_753))
        | ~ sP34(U_753,U_752,U_754) )
    & ! [U_753,U_752,U_754] :
        ( is_fun_a_bool(sK8(U_754,U_753,U_752))
        | ~ sP34(U_753,U_752,U_754) )
    & ! [U_753,U_752,U_754] :
        ( sP34(U_753,U_752,U_754)
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_752),image_819518260e_bool(U_754,U_753)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_752))
        | ~ is_fun1661590463l_bool(U_752) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP34])],[f_333_3]) ).

cnf(f_333_5,plain,
    ( sP34(U_753,U_752,U_754)
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_752),image_819518260e_bool(U_754,U_753)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_752))
    | ~ is_fun1661590463l_bool(U_752) ),
    inference(clausify,[status(thm)],[f_333_4]) ).

cnf(f_333_6,plain,
    ( is_fun_a_bool(sK8(U_754,U_753,U_752))
    | ~ sP34(U_753,U_752,U_754) ),
    inference(clausify,[status(thm)],[f_333_4]) ).

cnf(f_333_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK8(U_754,U_753,U_752)),U_753))
    | ~ sP34(U_753,U_752,U_754) ),
    inference(clausify,[status(thm)],[f_333_4]) ).

cnf(f_333_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK8(U_754,U_753,U_752)))
    | ~ sP34(U_753,U_752,U_754) ),
    inference(clausify,[status(thm)],[f_333_4]) ).

cnf(f_333_9,plain,
    ( U_752 = image_819518260e_bool(U_754,sK8(U_754,U_753,U_752))
    | ~ sP34(U_753,U_752,U_754) ),
    inference(clausify,[status(thm)],[f_333_4]) ).

fof(f_334_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_a_fun_a_bool(F,C_16)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A))
          & is_fun_a_bool(C_16) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B),image_a_fun_a_bool(F,A)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))
      | ~ is_fun949378684l_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_227_finite__subset__image]) ).

fof(f_334_2,plain,
    ! [U_758,U_757,U_756] :
      ( ? [U_755] :
          ( U_756 = image_a_fun_a_bool(U_758,U_755)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_755))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_755),U_757))
          & is_fun_a_bool(U_755) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_756),image_a_fun_a_bool(U_758,U_757)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_756))
      | ~ is_fun949378684l_bool(U_756) ),
    inference(variable_rename,[status(thm)],[f_334_1]) ).

fof(f_334_3,plain,
    ! [U_758,U_757,U_756] :
      ( ( U_756 = image_a_fun_a_bool(U_758,sK9(U_758,U_757,U_756))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK9(U_758,U_757,U_756)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK9(U_758,U_757,U_756)),U_757))
        & is_fun_a_bool(sK9(U_758,U_757,U_756)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_756),image_a_fun_a_bool(U_758,U_757)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_756))
      | ~ is_fun949378684l_bool(U_756) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_755,sK9(U_758,U_757,U_756))],[f_334_2]) ).

fof(f_334_4,plain,
    ( ! [U_758,U_757,U_756] :
        ( U_756 = image_a_fun_a_bool(U_758,sK9(U_758,U_757,U_756))
        | ~ sP35(U_758,U_757,U_756) )
    & ! [U_758,U_757,U_756] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK9(U_758,U_757,U_756)))
        | ~ sP35(U_758,U_757,U_756) )
    & ! [U_758,U_757,U_756] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK9(U_758,U_757,U_756)),U_757))
        | ~ sP35(U_758,U_757,U_756) )
    & ! [U_758,U_757,U_756] :
        ( is_fun_a_bool(sK9(U_758,U_757,U_756))
        | ~ sP35(U_758,U_757,U_756) )
    & ! [U_758,U_757,U_756] :
        ( sP35(U_758,U_757,U_756)
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_756),image_a_fun_a_bool(U_758,U_757)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_756))
        | ~ is_fun949378684l_bool(U_756) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP35])],[f_334_3]) ).

cnf(f_334_5,plain,
    ( sP35(U_758,U_757,U_756)
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_756),image_a_fun_a_bool(U_758,U_757)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_756))
    | ~ is_fun949378684l_bool(U_756) ),
    inference(clausify,[status(thm)],[f_334_4]) ).

cnf(f_334_6,plain,
    ( is_fun_a_bool(sK9(U_758,U_757,U_756))
    | ~ sP35(U_758,U_757,U_756) ),
    inference(clausify,[status(thm)],[f_334_4]) ).

cnf(f_334_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK9(U_758,U_757,U_756)),U_757))
    | ~ sP35(U_758,U_757,U_756) ),
    inference(clausify,[status(thm)],[f_334_4]) ).

cnf(f_334_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK9(U_758,U_757,U_756)))
    | ~ sP35(U_758,U_757,U_756) ),
    inference(clausify,[status(thm)],[f_334_4]) ).

cnf(f_334_9,plain,
    ( U_756 = image_a_fun_a_bool(U_758,sK9(U_758,U_757,U_756))
    | ~ sP35(U_758,U_757,U_756) ),
    inference(clausify,[status(thm)],[f_334_4]) ).

fof(f_335_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_a_pname(F,C_16)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A))
          & is_fun_a_bool(C_16) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_a_pname(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ is_fun_pname_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_228_finite__subset__image]) ).

fof(f_335_2,plain,
    ! [U_762,U_761,U_760] :
      ( ? [U_759] :
          ( U_760 = image_a_pname(U_762,U_759)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_759))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_759),U_761))
          & is_fun_a_bool(U_759) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_760),image_a_pname(U_762,U_761)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_760))
      | ~ is_fun_pname_bool(U_760) ),
    inference(variable_rename,[status(thm)],[f_335_1]) ).

fof(f_335_3,plain,
    ! [U_762,U_761,U_760] :
      ( ( U_760 = image_a_pname(U_762,sK10(U_762,U_761,U_760))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK10(U_762,U_761,U_760)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK10(U_762,U_761,U_760)),U_761))
        & is_fun_a_bool(sK10(U_762,U_761,U_760)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_760),image_a_pname(U_762,U_761)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_760))
      | ~ is_fun_pname_bool(U_760) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_759,sK10(U_762,U_761,U_760))],[f_335_2]) ).

fof(f_335_4,plain,
    ( ! [U_760,U_762,U_761] :
        ( U_760 = image_a_pname(U_762,sK10(U_762,U_761,U_760))
        | ~ sP36(U_760,U_762,U_761) )
    & ! [U_760,U_762,U_761] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK10(U_762,U_761,U_760)))
        | ~ sP36(U_760,U_762,U_761) )
    & ! [U_760,U_762,U_761] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK10(U_762,U_761,U_760)),U_761))
        | ~ sP36(U_760,U_762,U_761) )
    & ! [U_760,U_762,U_761] :
        ( is_fun_a_bool(sK10(U_762,U_761,U_760))
        | ~ sP36(U_760,U_762,U_761) )
    & ! [U_760,U_762,U_761] :
        ( sP36(U_760,U_762,U_761)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_760),image_a_pname(U_762,U_761)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_760))
        | ~ is_fun_pname_bool(U_760) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP36])],[f_335_3]) ).

cnf(f_335_5,plain,
    ( sP36(U_760,U_762,U_761)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_760),image_a_pname(U_762,U_761)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_760))
    | ~ is_fun_pname_bool(U_760) ),
    inference(clausify,[status(thm)],[f_335_4]) ).

cnf(f_335_6,plain,
    ( is_fun_a_bool(sK10(U_762,U_761,U_760))
    | ~ sP36(U_760,U_762,U_761) ),
    inference(clausify,[status(thm)],[f_335_4]) ).

cnf(f_335_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK10(U_762,U_761,U_760)),U_761))
    | ~ sP36(U_760,U_762,U_761) ),
    inference(clausify,[status(thm)],[f_335_4]) ).

cnf(f_335_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK10(U_762,U_761,U_760)))
    | ~ sP36(U_760,U_762,U_761) ),
    inference(clausify,[status(thm)],[f_335_4]) ).

cnf(f_335_9,plain,
    ( U_760 = image_a_pname(U_762,sK10(U_762,U_761,U_760))
    | ~ sP36(U_760,U_762,U_761) ),
    inference(clausify,[status(thm)],[f_335_4]) ).

fof(f_336_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_62782965_pname(F,C_16)
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,C_16))
          & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,C_16),A)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_62782965_pname(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ is_fun_pname_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_229_finite__subset__image]) ).

fof(f_336_2,plain,
    ! [U_766,U_765,U_764] :
      ( ? [U_763] :
          ( U_764 = image_62782965_pname(U_766,U_763)
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_763))
          & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_763),U_765)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_764),image_62782965_pname(U_766,U_765)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_764))
      | ~ is_fun_pname_bool(U_764) ),
    inference(variable_rename,[status(thm)],[f_336_1]) ).

fof(f_336_3,plain,
    ! [U_766,U_765,U_764] :
      ( ( U_764 = image_62782965_pname(U_766,sK11(U_766,U_765,U_764))
        & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK11(U_766,U_765,U_764)))
        & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK11(U_766,U_765,U_764)),U_765)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_764),image_62782965_pname(U_766,U_765)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_764))
      | ~ is_fun_pname_bool(U_764) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_763,sK11(U_766,U_765,U_764))],[f_336_2]) ).

fof(f_336_4,plain,
    ( ! [U_766,U_764,U_765] :
        ( U_764 = image_62782965_pname(U_766,sK11(U_766,U_765,U_764))
        | ~ sP37(U_766,U_764,U_765) )
    & ! [U_766,U_764,U_765] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK11(U_766,U_765,U_764)))
        | ~ sP37(U_766,U_764,U_765) )
    & ! [U_766,U_764,U_765] :
        ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK11(U_766,U_765,U_764)),U_765))
        | ~ sP37(U_766,U_764,U_765) )
    & ! [U_766,U_764,U_765] :
        ( sP37(U_766,U_764,U_765)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_764),image_62782965_pname(U_766,U_765)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_764))
        | ~ is_fun_pname_bool(U_764) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP37])],[f_336_3]) ).

cnf(f_336_5,plain,
    ( sP37(U_766,U_764,U_765)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_764),image_62782965_pname(U_766,U_765)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_764))
    | ~ is_fun_pname_bool(U_764) ),
    inference(clausify,[status(thm)],[f_336_4]) ).

cnf(f_336_6,plain,
    ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK11(U_766,U_765,U_764)),U_765))
    | ~ sP37(U_766,U_764,U_765) ),
    inference(clausify,[status(thm)],[f_336_4]) ).

cnf(f_336_7,plain,
    ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK11(U_766,U_765,U_764)))
    | ~ sP37(U_766,U_764,U_765) ),
    inference(clausify,[status(thm)],[f_336_4]) ).

cnf(f_336_8,plain,
    ( U_764 = image_62782965_pname(U_766,sK11(U_766,U_765,U_764))
    | ~ sP37(U_766,U_764,U_765) ),
    inference(clausify,[status(thm)],[f_336_4]) ).

fof(f_337_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_1921560913_pname(F,C_16)
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_16))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_16),A)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1921560913_pname(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ is_fun_pname_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_230_finite__subset__image]) ).

fof(f_337_2,plain,
    ! [U_770,U_769,U_768] :
      ( ? [U_767] :
          ( U_768 = image_1921560913_pname(U_770,U_767)
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_767))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_767),U_769)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_768),image_1921560913_pname(U_770,U_769)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_768))
      | ~ is_fun_pname_bool(U_768) ),
    inference(variable_rename,[status(thm)],[f_337_1]) ).

fof(f_337_3,plain,
    ! [U_770,U_769,U_768] :
      ( ( U_768 = image_1921560913_pname(U_770,sK12(U_770,U_769,U_768))
        & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK12(U_770,U_769,U_768)))
        & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK12(U_770,U_769,U_768)),U_769)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_768),image_1921560913_pname(U_770,U_769)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_768))
      | ~ is_fun_pname_bool(U_768) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_767,sK12(U_770,U_769,U_768))],[f_337_2]) ).

fof(f_337_4,plain,
    ( ! [U_769,U_770,U_768] :
        ( U_768 = image_1921560913_pname(U_770,sK12(U_770,U_769,U_768))
        | ~ sP38(U_769,U_770,U_768) )
    & ! [U_769,U_770,U_768] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK12(U_770,U_769,U_768)))
        | ~ sP38(U_769,U_770,U_768) )
    & ! [U_769,U_770,U_768] :
        ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK12(U_770,U_769,U_768)),U_769))
        | ~ sP38(U_769,U_770,U_768) )
    & ! [U_769,U_770,U_768] :
        ( sP38(U_769,U_770,U_768)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_768),image_1921560913_pname(U_770,U_769)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_768))
        | ~ is_fun_pname_bool(U_768) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP38])],[f_337_3]) ).

cnf(f_337_5,plain,
    ( sP38(U_769,U_770,U_768)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_768),image_1921560913_pname(U_770,U_769)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_768))
    | ~ is_fun_pname_bool(U_768) ),
    inference(clausify,[status(thm)],[f_337_4]) ).

cnf(f_337_6,plain,
    ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK12(U_770,U_769,U_768)),U_769))
    | ~ sP38(U_769,U_770,U_768) ),
    inference(clausify,[status(thm)],[f_337_4]) ).

cnf(f_337_7,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK12(U_770,U_769,U_768)))
    | ~ sP38(U_769,U_770,U_768) ),
    inference(clausify,[status(thm)],[f_337_4]) ).

cnf(f_337_8,plain,
    ( U_768 = image_1921560913_pname(U_770,sK12(U_770,U_769,U_768))
    | ~ sP38(U_769,U_770,U_768) ),
    inference(clausify,[status(thm)],[f_337_4]) ).

fof(f_338_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_1283814551_pname(F,C_16)
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_16))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_16),A))
          & is_fun1661590463l_bool(C_16) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1283814551_pname(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ is_fun_pname_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_231_finite__subset__image]) ).

fof(f_338_2,plain,
    ! [U_774,U_773,U_772] :
      ( ? [U_771] :
          ( U_772 = image_1283814551_pname(U_774,U_771)
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_771))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_771),U_773))
          & is_fun1661590463l_bool(U_771) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_772),image_1283814551_pname(U_774,U_773)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_772))
      | ~ is_fun_pname_bool(U_772) ),
    inference(variable_rename,[status(thm)],[f_338_1]) ).

fof(f_338_3,plain,
    ! [U_774,U_773,U_772] :
      ( ( U_772 = image_1283814551_pname(U_774,sK13(U_774,U_773,U_772))
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK13(U_774,U_773,U_772)))
        & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK13(U_774,U_773,U_772)),U_773))
        & is_fun1661590463l_bool(sK13(U_774,U_773,U_772)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_772),image_1283814551_pname(U_774,U_773)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_772))
      | ~ is_fun_pname_bool(U_772) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_771,sK13(U_774,U_773,U_772))],[f_338_2]) ).

fof(f_338_4,plain,
    ( ! [U_773,U_774,U_772] :
        ( U_772 = image_1283814551_pname(U_774,sK13(U_774,U_773,U_772))
        | ~ sP39(U_773,U_774,U_772) )
    & ! [U_773,U_774,U_772] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK13(U_774,U_773,U_772)))
        | ~ sP39(U_773,U_774,U_772) )
    & ! [U_773,U_774,U_772] :
        ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK13(U_774,U_773,U_772)),U_773))
        | ~ sP39(U_773,U_774,U_772) )
    & ! [U_773,U_774,U_772] :
        ( is_fun1661590463l_bool(sK13(U_774,U_773,U_772))
        | ~ sP39(U_773,U_774,U_772) )
    & ! [U_773,U_774,U_772] :
        ( sP39(U_773,U_774,U_772)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_772),image_1283814551_pname(U_774,U_773)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_772))
        | ~ is_fun_pname_bool(U_772) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP39])],[f_338_3]) ).

cnf(f_338_5,plain,
    ( sP39(U_773,U_774,U_772)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_772),image_1283814551_pname(U_774,U_773)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_772))
    | ~ is_fun_pname_bool(U_772) ),
    inference(clausify,[status(thm)],[f_338_4]) ).

cnf(f_338_6,plain,
    ( is_fun1661590463l_bool(sK13(U_774,U_773,U_772))
    | ~ sP39(U_773,U_774,U_772) ),
    inference(clausify,[status(thm)],[f_338_4]) ).

cnf(f_338_7,plain,
    ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK13(U_774,U_773,U_772)),U_773))
    | ~ sP39(U_773,U_774,U_772) ),
    inference(clausify,[status(thm)],[f_338_4]) ).

cnf(f_338_8,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK13(U_774,U_773,U_772)))
    | ~ sP39(U_773,U_774,U_772) ),
    inference(clausify,[status(thm)],[f_338_4]) ).

cnf(f_338_9,plain,
    ( U_772 = image_1283814551_pname(U_774,sK13(U_774,U_773,U_772))
    | ~ sP39(U_773,U_774,U_772) ),
    inference(clausify,[status(thm)],[f_338_4]) ).

fof(f_339_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_1854862208_pname(F,C_16)
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_16))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_16),A))
          & is_fun949378684l_bool(C_16) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_1854862208_pname(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ is_fun_pname_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_232_finite__subset__image]) ).

fof(f_339_2,plain,
    ! [U_778,U_777,U_776] :
      ( ? [U_775] :
          ( U_776 = image_1854862208_pname(U_778,U_775)
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_775))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_775),U_777))
          & is_fun949378684l_bool(U_775) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_776),image_1854862208_pname(U_778,U_777)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_776))
      | ~ is_fun_pname_bool(U_776) ),
    inference(variable_rename,[status(thm)],[f_339_1]) ).

fof(f_339_3,plain,
    ! [U_778,U_777,U_776] :
      ( ( U_776 = image_1854862208_pname(U_778,sK14(U_778,U_777,U_776))
        & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK14(U_778,U_777,U_776)))
        & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK14(U_778,U_777,U_776)),U_777))
        & is_fun949378684l_bool(sK14(U_778,U_777,U_776)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_776),image_1854862208_pname(U_778,U_777)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_776))
      | ~ is_fun_pname_bool(U_776) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_775,sK14(U_778,U_777,U_776))],[f_339_2]) ).

fof(f_339_4,plain,
    ( ! [U_776,U_777,U_778] :
        ( U_776 = image_1854862208_pname(U_778,sK14(U_778,U_777,U_776))
        | ~ sP40(U_776,U_777,U_778) )
    & ! [U_776,U_777,U_778] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK14(U_778,U_777,U_776)))
        | ~ sP40(U_776,U_777,U_778) )
    & ! [U_776,U_777,U_778] :
        ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK14(U_778,U_777,U_776)),U_777))
        | ~ sP40(U_776,U_777,U_778) )
    & ! [U_776,U_777,U_778] :
        ( is_fun949378684l_bool(sK14(U_778,U_777,U_776))
        | ~ sP40(U_776,U_777,U_778) )
    & ! [U_776,U_777,U_778] :
        ( sP40(U_776,U_777,U_778)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_776),image_1854862208_pname(U_778,U_777)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_776))
        | ~ is_fun_pname_bool(U_776) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP40])],[f_339_3]) ).

cnf(f_339_5,plain,
    ( sP40(U_776,U_777,U_778)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_776),image_1854862208_pname(U_778,U_777)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_776))
    | ~ is_fun_pname_bool(U_776) ),
    inference(clausify,[status(thm)],[f_339_4]) ).

cnf(f_339_6,plain,
    ( is_fun949378684l_bool(sK14(U_778,U_777,U_776))
    | ~ sP40(U_776,U_777,U_778) ),
    inference(clausify,[status(thm)],[f_339_4]) ).

cnf(f_339_7,plain,
    ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK14(U_778,U_777,U_776)),U_777))
    | ~ sP40(U_776,U_777,U_778) ),
    inference(clausify,[status(thm)],[f_339_4]) ).

cnf(f_339_8,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK14(U_778,U_777,U_776)))
    | ~ sP40(U_776,U_777,U_778) ),
    inference(clausify,[status(thm)],[f_339_4]) ).

cnf(f_339_9,plain,
    ( U_776 = image_1854862208_pname(U_778,sK14(U_778,U_777,U_776))
    | ~ sP40(U_776,U_777,U_778) ),
    inference(clausify,[status(thm)],[f_339_4]) ).

fof(f_340_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_a_nat(F,C_16)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A))
          & is_fun_a_bool(C_16) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_a_nat(F,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) ),
    inference(fof_nnf,[status(thm)],[fact_233_finite__subset__image]) ).

fof(f_340_2,plain,
    ! [U_782,U_781,U_780] :
      ( ? [U_779] :
          ( U_780 = image_a_nat(U_782,U_779)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_779))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_779),U_781))
          & is_fun_a_bool(U_779) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_780),image_a_nat(U_782,U_781)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_780)) ),
    inference(variable_rename,[status(thm)],[f_340_1]) ).

fof(f_340_3,plain,
    ! [U_782,U_781,U_780] :
      ( ( U_780 = image_a_nat(U_782,sK15(U_782,U_781,U_780))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK15(U_782,U_781,U_780)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK15(U_782,U_781,U_780)),U_781))
        & is_fun_a_bool(sK15(U_782,U_781,U_780)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_780),image_a_nat(U_782,U_781)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_780)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_779,sK15(U_782,U_781,U_780))],[f_340_2]) ).

fof(f_340_4,plain,
    ( ! [U_782,U_781,U_780] :
        ( U_780 = image_a_nat(U_782,sK15(U_782,U_781,U_780))
        | ~ sP41(U_782,U_781,U_780) )
    & ! [U_782,U_781,U_780] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK15(U_782,U_781,U_780)))
        | ~ sP41(U_782,U_781,U_780) )
    & ! [U_782,U_781,U_780] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK15(U_782,U_781,U_780)),U_781))
        | ~ sP41(U_782,U_781,U_780) )
    & ! [U_782,U_781,U_780] :
        ( is_fun_a_bool(sK15(U_782,U_781,U_780))
        | ~ sP41(U_782,U_781,U_780) )
    & ! [U_782,U_781,U_780] :
        ( sP41(U_782,U_781,U_780)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_780),image_a_nat(U_782,U_781)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_780)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP41])],[f_340_3]) ).

cnf(f_340_5,plain,
    ( sP41(U_782,U_781,U_780)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_780),image_a_nat(U_782,U_781)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_780)) ),
    inference(clausify,[status(thm)],[f_340_4]) ).

cnf(f_340_6,plain,
    ( is_fun_a_bool(sK15(U_782,U_781,U_780))
    | ~ sP41(U_782,U_781,U_780) ),
    inference(clausify,[status(thm)],[f_340_4]) ).

cnf(f_340_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK15(U_782,U_781,U_780)),U_781))
    | ~ sP41(U_782,U_781,U_780) ),
    inference(clausify,[status(thm)],[f_340_4]) ).

cnf(f_340_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK15(U_782,U_781,U_780)))
    | ~ sP41(U_782,U_781,U_780) ),
    inference(clausify,[status(thm)],[f_340_4]) ).

cnf(f_340_9,plain,
    ( U_780 = image_a_nat(U_782,sK15(U_782,U_781,U_780))
    | ~ sP41(U_782,U_781,U_780) ),
    inference(clausify,[status(thm)],[f_340_4]) ).

fof(f_341_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_1431733819ol_nat(F,C_16)
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,C_16))
          & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,C_16),A)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_1431733819ol_nat(F,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) ),
    inference(fof_nnf,[status(thm)],[fact_234_finite__subset__image]) ).

fof(f_341_2,plain,
    ! [U_786,U_785,U_784] :
      ( ? [U_783] :
          ( U_784 = image_1431733819ol_nat(U_786,U_783)
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_783))
          & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_783),U_785)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_784),image_1431733819ol_nat(U_786,U_785)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_784)) ),
    inference(variable_rename,[status(thm)],[f_341_1]) ).

fof(f_341_3,plain,
    ! [U_786,U_785,U_784] :
      ( ( U_784 = image_1431733819ol_nat(U_786,sK16(U_786,U_785,U_784))
        & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK16(U_786,U_785,U_784)))
        & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK16(U_786,U_785,U_784)),U_785)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_784),image_1431733819ol_nat(U_786,U_785)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_784)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_783,sK16(U_786,U_785,U_784))],[f_341_2]) ).

fof(f_341_4,plain,
    ( ! [U_785,U_784,U_786] :
        ( U_784 = image_1431733819ol_nat(U_786,sK16(U_786,U_785,U_784))
        | ~ sP42(U_785,U_784,U_786) )
    & ! [U_785,U_784,U_786] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK16(U_786,U_785,U_784)))
        | ~ sP42(U_785,U_784,U_786) )
    & ! [U_785,U_784,U_786] :
        ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK16(U_786,U_785,U_784)),U_785))
        | ~ sP42(U_785,U_784,U_786) )
    & ! [U_785,U_784,U_786] :
        ( sP42(U_785,U_784,U_786)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_784),image_1431733819ol_nat(U_786,U_785)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_784)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP42])],[f_341_3]) ).

cnf(f_341_5,plain,
    ( sP42(U_785,U_784,U_786)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_784),image_1431733819ol_nat(U_786,U_785)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_784)) ),
    inference(clausify,[status(thm)],[f_341_4]) ).

cnf(f_341_6,plain,
    ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK16(U_786,U_785,U_784)),U_785))
    | ~ sP42(U_785,U_784,U_786) ),
    inference(clausify,[status(thm)],[f_341_4]) ).

cnf(f_341_7,plain,
    ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK16(U_786,U_785,U_784)))
    | ~ sP42(U_785,U_784,U_786) ),
    inference(clausify,[status(thm)],[f_341_4]) ).

cnf(f_341_8,plain,
    ( U_784 = image_1431733819ol_nat(U_786,sK16(U_786,U_785,U_784))
    | ~ sP42(U_785,U_784,U_786) ),
    inference(clausify,[status(thm)],[f_341_4]) ).

fof(f_342_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_496248727ol_nat(F,C_16)
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_16))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_16),A)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_496248727ol_nat(F,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) ),
    inference(fof_nnf,[status(thm)],[fact_235_finite__subset__image]) ).

fof(f_342_2,plain,
    ! [U_790,U_789,U_788] :
      ( ? [U_787] :
          ( U_788 = image_496248727ol_nat(U_790,U_787)
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_787))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_787),U_789)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_788),image_496248727ol_nat(U_790,U_789)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_788)) ),
    inference(variable_rename,[status(thm)],[f_342_1]) ).

fof(f_342_3,plain,
    ! [U_790,U_789,U_788] :
      ( ( U_788 = image_496248727ol_nat(U_790,sK17(U_790,U_789,U_788))
        & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK17(U_790,U_789,U_788)))
        & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK17(U_790,U_789,U_788)),U_789)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_788),image_496248727ol_nat(U_790,U_789)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_788)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_787,sK17(U_790,U_789,U_788))],[f_342_2]) ).

fof(f_342_4,plain,
    ( ! [U_789,U_790,U_788] :
        ( U_788 = image_496248727ol_nat(U_790,sK17(U_790,U_789,U_788))
        | ~ sP43(U_789,U_790,U_788) )
    & ! [U_789,U_790,U_788] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK17(U_790,U_789,U_788)))
        | ~ sP43(U_789,U_790,U_788) )
    & ! [U_789,U_790,U_788] :
        ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK17(U_790,U_789,U_788)),U_789))
        | ~ sP43(U_789,U_790,U_788) )
    & ! [U_789,U_790,U_788] :
        ( sP43(U_789,U_790,U_788)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_788),image_496248727ol_nat(U_790,U_789)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_788)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP43])],[f_342_3]) ).

cnf(f_342_5,plain,
    ( sP43(U_789,U_790,U_788)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_788),image_496248727ol_nat(U_790,U_789)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_788)) ),
    inference(clausify,[status(thm)],[f_342_4]) ).

cnf(f_342_6,plain,
    ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK17(U_790,U_789,U_788)),U_789))
    | ~ sP43(U_789,U_790,U_788) ),
    inference(clausify,[status(thm)],[f_342_4]) ).

cnf(f_342_7,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK17(U_790,U_789,U_788)))
    | ~ sP43(U_789,U_790,U_788) ),
    inference(clausify,[status(thm)],[f_342_4]) ).

cnf(f_342_8,plain,
    ( U_788 = image_496248727ol_nat(U_790,sK17(U_790,U_789,U_788))
    | ~ sP43(U_789,U_790,U_788) ),
    inference(clausify,[status(thm)],[f_342_4]) ).

fof(f_343_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_1551609309ol_nat(F,C_16)
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_16))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_16),A))
          & is_fun1661590463l_bool(C_16) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_1551609309ol_nat(F,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) ),
    inference(fof_nnf,[status(thm)],[fact_236_finite__subset__image]) ).

fof(f_343_2,plain,
    ! [U_794,U_793,U_792] :
      ( ? [U_791] :
          ( U_792 = image_1551609309ol_nat(U_794,U_791)
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_791))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_791),U_793))
          & is_fun1661590463l_bool(U_791) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_792),image_1551609309ol_nat(U_794,U_793)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_792)) ),
    inference(variable_rename,[status(thm)],[f_343_1]) ).

fof(f_343_3,plain,
    ! [U_794,U_793,U_792] :
      ( ( U_792 = image_1551609309ol_nat(U_794,sK18(U_794,U_793,U_792))
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK18(U_794,U_793,U_792)))
        & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK18(U_794,U_793,U_792)),U_793))
        & is_fun1661590463l_bool(sK18(U_794,U_793,U_792)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_792),image_1551609309ol_nat(U_794,U_793)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_792)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_791,sK18(U_794,U_793,U_792))],[f_343_2]) ).

fof(f_343_4,plain,
    ( ! [U_793,U_792,U_794] :
        ( U_792 = image_1551609309ol_nat(U_794,sK18(U_794,U_793,U_792))
        | ~ sP44(U_793,U_792,U_794) )
    & ! [U_793,U_792,U_794] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK18(U_794,U_793,U_792)))
        | ~ sP44(U_793,U_792,U_794) )
    & ! [U_793,U_792,U_794] :
        ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK18(U_794,U_793,U_792)),U_793))
        | ~ sP44(U_793,U_792,U_794) )
    & ! [U_793,U_792,U_794] :
        ( is_fun1661590463l_bool(sK18(U_794,U_793,U_792))
        | ~ sP44(U_793,U_792,U_794) )
    & ! [U_793,U_792,U_794] :
        ( sP44(U_793,U_792,U_794)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_792),image_1551609309ol_nat(U_794,U_793)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_792)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP44])],[f_343_3]) ).

cnf(f_343_5,plain,
    ( sP44(U_793,U_792,U_794)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_792),image_1551609309ol_nat(U_794,U_793)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_792)) ),
    inference(clausify,[status(thm)],[f_343_4]) ).

cnf(f_343_6,plain,
    ( is_fun1661590463l_bool(sK18(U_794,U_793,U_792))
    | ~ sP44(U_793,U_792,U_794) ),
    inference(clausify,[status(thm)],[f_343_4]) ).

cnf(f_343_7,plain,
    ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK18(U_794,U_793,U_792)),U_793))
    | ~ sP44(U_793,U_792,U_794) ),
    inference(clausify,[status(thm)],[f_343_4]) ).

cnf(f_343_8,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK18(U_794,U_793,U_792)))
    | ~ sP44(U_793,U_792,U_794) ),
    inference(clausify,[status(thm)],[f_343_4]) ).

cnf(f_343_9,plain,
    ( U_792 = image_1551609309ol_nat(U_794,sK18(U_794,U_793,U_792))
    | ~ sP44(U_793,U_792,U_794) ),
    inference(clausify,[status(thm)],[f_343_4]) ).

fof(f_344_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_fun_a_bool_nat(F,C_16)
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_16))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_16),A))
          & is_fun949378684l_bool(C_16) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_fun_a_bool_nat(F,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) ),
    inference(fof_nnf,[status(thm)],[fact_237_finite__subset__image]) ).

fof(f_344_2,plain,
    ! [U_798,U_797,U_796] :
      ( ? [U_795] :
          ( U_796 = image_fun_a_bool_nat(U_798,U_795)
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_795))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_795),U_797))
          & is_fun949378684l_bool(U_795) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_796),image_fun_a_bool_nat(U_798,U_797)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_796)) ),
    inference(variable_rename,[status(thm)],[f_344_1]) ).

fof(f_344_3,plain,
    ! [U_798,U_797,U_796] :
      ( ( U_796 = image_fun_a_bool_nat(U_798,sK19(U_798,U_797,U_796))
        & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK19(U_798,U_797,U_796)))
        & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK19(U_798,U_797,U_796)),U_797))
        & is_fun949378684l_bool(sK19(U_798,U_797,U_796)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_796),image_fun_a_bool_nat(U_798,U_797)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_796)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_795,sK19(U_798,U_797,U_796))],[f_344_2]) ).

fof(f_344_4,plain,
    ( ! [U_797,U_796,U_798] :
        ( U_796 = image_fun_a_bool_nat(U_798,sK19(U_798,U_797,U_796))
        | ~ sP45(U_797,U_796,U_798) )
    & ! [U_797,U_796,U_798] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK19(U_798,U_797,U_796)))
        | ~ sP45(U_797,U_796,U_798) )
    & ! [U_797,U_796,U_798] :
        ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK19(U_798,U_797,U_796)),U_797))
        | ~ sP45(U_797,U_796,U_798) )
    & ! [U_797,U_796,U_798] :
        ( is_fun949378684l_bool(sK19(U_798,U_797,U_796))
        | ~ sP45(U_797,U_796,U_798) )
    & ! [U_797,U_796,U_798] :
        ( sP45(U_797,U_796,U_798)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_796),image_fun_a_bool_nat(U_798,U_797)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_796)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP45])],[f_344_3]) ).

cnf(f_344_5,plain,
    ( sP45(U_797,U_796,U_798)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_796),image_fun_a_bool_nat(U_798,U_797)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_796)) ),
    inference(clausify,[status(thm)],[f_344_4]) ).

cnf(f_344_6,plain,
    ( is_fun949378684l_bool(sK19(U_798,U_797,U_796))
    | ~ sP45(U_797,U_796,U_798) ),
    inference(clausify,[status(thm)],[f_344_4]) ).

cnf(f_344_7,plain,
    ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK19(U_798,U_797,U_796)),U_797))
    | ~ sP45(U_797,U_796,U_798) ),
    inference(clausify,[status(thm)],[f_344_4]) ).

cnf(f_344_8,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK19(U_798,U_797,U_796)))
    | ~ sP45(U_797,U_796,U_798) ),
    inference(clausify,[status(thm)],[f_344_4]) ).

cnf(f_344_9,plain,
    ( U_796 = image_fun_a_bool_nat(U_798,sK19(U_798,U_797,U_796))
    | ~ sP45(U_797,U_796,U_798) ),
    inference(clausify,[status(thm)],[f_344_4]) ).

fof(f_345_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_pname_nat(F,C_16)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A))
          & is_fun_pname_bool(C_16) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),image_pname_nat(F,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) ),
    inference(fof_nnf,[status(thm)],[fact_238_finite__subset__image]) ).

fof(f_345_2,plain,
    ! [U_802,U_801,U_800] :
      ( ? [U_799] :
          ( U_800 = image_pname_nat(U_802,U_799)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_799))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_799),U_801))
          & is_fun_pname_bool(U_799) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_800),image_pname_nat(U_802,U_801)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_800)) ),
    inference(variable_rename,[status(thm)],[f_345_1]) ).

fof(f_345_3,plain,
    ! [U_802,U_801,U_800] :
      ( ( U_800 = image_pname_nat(U_802,sK20(U_802,U_801,U_800))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK20(U_802,U_801,U_800)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK20(U_802,U_801,U_800)),U_801))
        & is_fun_pname_bool(sK20(U_802,U_801,U_800)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_800),image_pname_nat(U_802,U_801)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_800)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_799,sK20(U_802,U_801,U_800))],[f_345_2]) ).

fof(f_345_4,plain,
    ( ! [U_801,U_800,U_802] :
        ( U_800 = image_pname_nat(U_802,sK20(U_802,U_801,U_800))
        | ~ sP46(U_801,U_800,U_802) )
    & ! [U_801,U_800,U_802] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK20(U_802,U_801,U_800)))
        | ~ sP46(U_801,U_800,U_802) )
    & ! [U_801,U_800,U_802] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK20(U_802,U_801,U_800)),U_801))
        | ~ sP46(U_801,U_800,U_802) )
    & ! [U_801,U_800,U_802] :
        ( is_fun_pname_bool(sK20(U_802,U_801,U_800))
        | ~ sP46(U_801,U_800,U_802) )
    & ! [U_801,U_800,U_802] :
        ( sP46(U_801,U_800,U_802)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_800),image_pname_nat(U_802,U_801)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_800)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP46])],[f_345_3]) ).

cnf(f_345_5,plain,
    ( sP46(U_801,U_800,U_802)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_800),image_pname_nat(U_802,U_801)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_800)) ),
    inference(clausify,[status(thm)],[f_345_4]) ).

cnf(f_345_6,plain,
    ( is_fun_pname_bool(sK20(U_802,U_801,U_800))
    | ~ sP46(U_801,U_800,U_802) ),
    inference(clausify,[status(thm)],[f_345_4]) ).

cnf(f_345_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK20(U_802,U_801,U_800)),U_801))
    | ~ sP46(U_801,U_800,U_802) ),
    inference(clausify,[status(thm)],[f_345_4]) ).

cnf(f_345_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK20(U_802,U_801,U_800)))
    | ~ sP46(U_801,U_800,U_802) ),
    inference(clausify,[status(thm)],[f_345_4]) ).

cnf(f_345_9,plain,
    ( U_800 = image_pname_nat(U_802,sK20(U_802,U_801,U_800))
    | ~ sP46(U_801,U_800,U_802) ),
    inference(clausify,[status(thm)],[f_345_4]) ).

fof(f_346_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_a_int(F,C_16)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,C_16))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_16),A))
          & is_fun_a_bool(C_16) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_a_int(F,A)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) ),
    inference(fof_nnf,[status(thm)],[fact_239_finite__subset__image]) ).

fof(f_346_2,plain,
    ! [U_806,U_805,U_804] :
      ( ? [U_803] :
          ( U_804 = image_a_int(U_806,U_803)
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_803))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_803),U_805))
          & is_fun_a_bool(U_803) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_804),image_a_int(U_806,U_805)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_804)) ),
    inference(variable_rename,[status(thm)],[f_346_1]) ).

fof(f_346_3,plain,
    ! [U_806,U_805,U_804] :
      ( ( U_804 = image_a_int(U_806,sK21(U_806,U_805,U_804))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK21(U_806,U_805,U_804)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK21(U_806,U_805,U_804)),U_805))
        & is_fun_a_bool(sK21(U_806,U_805,U_804)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_804),image_a_int(U_806,U_805)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_804)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_803,sK21(U_806,U_805,U_804))],[f_346_2]) ).

fof(f_346_4,plain,
    ( ! [U_804,U_805,U_806] :
        ( U_804 = image_a_int(U_806,sK21(U_806,U_805,U_804))
        | ~ sP47(U_804,U_805,U_806) )
    & ! [U_804,U_805,U_806] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK21(U_806,U_805,U_804)))
        | ~ sP47(U_804,U_805,U_806) )
    & ! [U_804,U_805,U_806] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK21(U_806,U_805,U_804)),U_805))
        | ~ sP47(U_804,U_805,U_806) )
    & ! [U_804,U_805,U_806] :
        ( is_fun_a_bool(sK21(U_806,U_805,U_804))
        | ~ sP47(U_804,U_805,U_806) )
    & ! [U_804,U_805,U_806] :
        ( sP47(U_804,U_805,U_806)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_804),image_a_int(U_806,U_805)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_804)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP47])],[f_346_3]) ).

cnf(f_346_5,plain,
    ( sP47(U_804,U_805,U_806)
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_804),image_a_int(U_806,U_805)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_804)) ),
    inference(clausify,[status(thm)],[f_346_4]) ).

cnf(f_346_6,plain,
    ( is_fun_a_bool(sK21(U_806,U_805,U_804))
    | ~ sP47(U_804,U_805,U_806) ),
    inference(clausify,[status(thm)],[f_346_4]) ).

cnf(f_346_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,sK21(U_806,U_805,U_804)),U_805))
    | ~ sP47(U_804,U_805,U_806) ),
    inference(clausify,[status(thm)],[f_346_4]) ).

cnf(f_346_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK21(U_806,U_805,U_804)))
    | ~ sP47(U_804,U_805,U_806) ),
    inference(clausify,[status(thm)],[f_346_4]) ).

cnf(f_346_9,plain,
    ( U_804 = image_a_int(U_806,sK21(U_806,U_805,U_804))
    | ~ sP47(U_804,U_805,U_806) ),
    inference(clausify,[status(thm)],[f_346_4]) ).

fof(f_347_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_2069007511ol_int(F,C_16)
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,C_16))
          & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,C_16),A)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_2069007511ol_int(F,A)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) ),
    inference(fof_nnf,[status(thm)],[fact_240_finite__subset__image]) ).

fof(f_347_2,plain,
    ! [U_810,U_809,U_808] :
      ( ? [U_807] :
          ( U_808 = image_2069007511ol_int(U_810,U_807)
          & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_807))
          & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_807),U_809)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_808),image_2069007511ol_int(U_810,U_809)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_808)) ),
    inference(variable_rename,[status(thm)],[f_347_1]) ).

fof(f_347_3,plain,
    ! [U_810,U_809,U_808] :
      ( ( U_808 = image_2069007511ol_int(U_810,sK22(U_810,U_809,U_808))
        & hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK22(U_810,U_809,U_808)))
        & hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK22(U_810,U_809,U_808)),U_809)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_808),image_2069007511ol_int(U_810,U_809)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_808)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_807,sK22(U_810,U_809,U_808))],[f_347_2]) ).

fof(f_347_4,plain,
    ( ! [U_809,U_808,U_810] :
        ( U_808 = image_2069007511ol_int(U_810,sK22(U_810,U_809,U_808))
        | ~ sP48(U_809,U_808,U_810) )
    & ! [U_809,U_808,U_810] :
        ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK22(U_810,U_809,U_808)))
        | ~ sP48(U_809,U_808,U_810) )
    & ! [U_809,U_808,U_810] :
        ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK22(U_810,U_809,U_808)),U_809))
        | ~ sP48(U_809,U_808,U_810) )
    & ! [U_809,U_808,U_810] :
        ( sP48(U_809,U_808,U_810)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_808),image_2069007511ol_int(U_810,U_809)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_808)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP48])],[f_347_3]) ).

cnf(f_347_5,plain,
    ( sP48(U_809,U_808,U_810)
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_808),image_2069007511ol_int(U_810,U_809)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_808)) ),
    inference(clausify,[status(thm)],[f_347_4]) ).

cnf(f_347_6,plain,
    ( hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,sK22(U_810,U_809,U_808)),U_809))
    | ~ sP48(U_809,U_808,U_810) ),
    inference(clausify,[status(thm)],[f_347_4]) ).

cnf(f_347_7,plain,
    ( hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,sK22(U_810,U_809,U_808)))
    | ~ sP48(U_809,U_808,U_810) ),
    inference(clausify,[status(thm)],[f_347_4]) ).

cnf(f_347_8,plain,
    ( U_808 = image_2069007511ol_int(U_810,sK22(U_810,U_809,U_808))
    | ~ sP48(U_809,U_808,U_810) ),
    inference(clausify,[status(thm)],[f_347_4]) ).

fof(f_348_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_1133522419ol_int(F,C_16)
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,C_16))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,C_16),A)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_1133522419ol_int(F,A)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) ),
    inference(fof_nnf,[status(thm)],[fact_241_finite__subset__image]) ).

fof(f_348_2,plain,
    ! [U_814,U_813,U_812] :
      ( ? [U_811] :
          ( U_812 = image_1133522419ol_int(U_814,U_811)
          & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_811))
          & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_811),U_813)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_812),image_1133522419ol_int(U_814,U_813)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_812)) ),
    inference(variable_rename,[status(thm)],[f_348_1]) ).

fof(f_348_3,plain,
    ! [U_814,U_813,U_812] :
      ( ( U_812 = image_1133522419ol_int(U_814,sK23(U_814,U_813,U_812))
        & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK23(U_814,U_813,U_812)))
        & hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK23(U_814,U_813,U_812)),U_813)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_812),image_1133522419ol_int(U_814,U_813)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_812)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_811,sK23(U_814,U_813,U_812))],[f_348_2]) ).

fof(f_348_4,plain,
    ( ! [U_813,U_814,U_812] :
        ( U_812 = image_1133522419ol_int(U_814,sK23(U_814,U_813,U_812))
        | ~ sP49(U_813,U_814,U_812) )
    & ! [U_813,U_814,U_812] :
        ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK23(U_814,U_813,U_812)))
        | ~ sP49(U_813,U_814,U_812) )
    & ! [U_813,U_814,U_812] :
        ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK23(U_814,U_813,U_812)),U_813))
        | ~ sP49(U_813,U_814,U_812) )
    & ! [U_813,U_814,U_812] :
        ( sP49(U_813,U_814,U_812)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_812),image_1133522419ol_int(U_814,U_813)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_812)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP49])],[f_348_3]) ).

cnf(f_348_5,plain,
    ( sP49(U_813,U_814,U_812)
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_812),image_1133522419ol_int(U_814,U_813)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_812)) ),
    inference(clausify,[status(thm)],[f_348_4]) ).

cnf(f_348_6,plain,
    ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,sK23(U_814,U_813,U_812)),U_813))
    | ~ sP49(U_813,U_814,U_812) ),
    inference(clausify,[status(thm)],[f_348_4]) ).

cnf(f_348_7,plain,
    ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,sK23(U_814,U_813,U_812)))
    | ~ sP49(U_813,U_814,U_812) ),
    inference(clausify,[status(thm)],[f_348_4]) ).

cnf(f_348_8,plain,
    ( U_812 = image_1133522419ol_int(U_814,sK23(U_814,U_813,U_812))
    | ~ sP49(U_813,U_814,U_812) ),
    inference(clausify,[status(thm)],[f_348_4]) ).

fof(f_349_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_41399353ol_int(F,C_16)
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,C_16))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,C_16),A))
          & is_fun1661590463l_bool(C_16) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_41399353ol_int(F,A)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) ),
    inference(fof_nnf,[status(thm)],[fact_242_finite__subset__image]) ).

fof(f_349_2,plain,
    ! [U_818,U_817,U_816] :
      ( ? [U_815] :
          ( U_816 = image_41399353ol_int(U_818,U_815)
          & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_815))
          & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_815),U_817))
          & is_fun1661590463l_bool(U_815) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_816),image_41399353ol_int(U_818,U_817)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_816)) ),
    inference(variable_rename,[status(thm)],[f_349_1]) ).

fof(f_349_3,plain,
    ! [U_818,U_817,U_816] :
      ( ( U_816 = image_41399353ol_int(U_818,sK24(U_818,U_817,U_816))
        & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK24(U_818,U_817,U_816)))
        & hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK24(U_818,U_817,U_816)),U_817))
        & is_fun1661590463l_bool(sK24(U_818,U_817,U_816)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_816),image_41399353ol_int(U_818,U_817)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_816)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_815,sK24(U_818,U_817,U_816))],[f_349_2]) ).

fof(f_349_4,plain,
    ( ! [U_817,U_818,U_816] :
        ( U_816 = image_41399353ol_int(U_818,sK24(U_818,U_817,U_816))
        | ~ sP50(U_817,U_818,U_816) )
    & ! [U_817,U_818,U_816] :
        ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK24(U_818,U_817,U_816)))
        | ~ sP50(U_817,U_818,U_816) )
    & ! [U_817,U_818,U_816] :
        ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK24(U_818,U_817,U_816)),U_817))
        | ~ sP50(U_817,U_818,U_816) )
    & ! [U_817,U_818,U_816] :
        ( is_fun1661590463l_bool(sK24(U_818,U_817,U_816))
        | ~ sP50(U_817,U_818,U_816) )
    & ! [U_817,U_818,U_816] :
        ( sP50(U_817,U_818,U_816)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_816),image_41399353ol_int(U_818,U_817)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_816)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP50])],[f_349_3]) ).

cnf(f_349_5,plain,
    ( sP50(U_817,U_818,U_816)
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_816),image_41399353ol_int(U_818,U_817)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_816)) ),
    inference(clausify,[status(thm)],[f_349_4]) ).

cnf(f_349_6,plain,
    ( is_fun1661590463l_bool(sK24(U_818,U_817,U_816))
    | ~ sP50(U_817,U_818,U_816) ),
    inference(clausify,[status(thm)],[f_349_4]) ).

cnf(f_349_7,plain,
    ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,sK24(U_818,U_817,U_816)),U_817))
    | ~ sP50(U_817,U_818,U_816) ),
    inference(clausify,[status(thm)],[f_349_4]) ).

cnf(f_349_8,plain,
    ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,sK24(U_818,U_817,U_816)))
    | ~ sP50(U_817,U_818,U_816) ),
    inference(clausify,[status(thm)],[f_349_4]) ).

cnf(f_349_9,plain,
    ( U_816 = image_41399353ol_int(U_818,sK24(U_818,U_817,U_816))
    | ~ sP50(U_817,U_818,U_816) ),
    inference(clausify,[status(thm)],[f_349_4]) ).

fof(f_350_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_fun_a_bool_int(F,C_16)
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,C_16))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,C_16),A))
          & is_fun949378684l_bool(C_16) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_fun_a_bool_int(F,A)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) ),
    inference(fof_nnf,[status(thm)],[fact_243_finite__subset__image]) ).

fof(f_350_2,plain,
    ! [U_822,U_821,U_820] :
      ( ? [U_819] :
          ( U_820 = image_fun_a_bool_int(U_822,U_819)
          & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_819))
          & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_819),U_821))
          & is_fun949378684l_bool(U_819) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_820),image_fun_a_bool_int(U_822,U_821)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_820)) ),
    inference(variable_rename,[status(thm)],[f_350_1]) ).

fof(f_350_3,plain,
    ! [U_822,U_821,U_820] :
      ( ( U_820 = image_fun_a_bool_int(U_822,sK25(U_822,U_821,U_820))
        & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK25(U_822,U_821,U_820)))
        & hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK25(U_822,U_821,U_820)),U_821))
        & is_fun949378684l_bool(sK25(U_822,U_821,U_820)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_820),image_fun_a_bool_int(U_822,U_821)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_820)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_819,sK25(U_822,U_821,U_820))],[f_350_2]) ).

fof(f_350_4,plain,
    ( ! [U_821,U_820,U_822] :
        ( U_820 = image_fun_a_bool_int(U_822,sK25(U_822,U_821,U_820))
        | ~ sP51(U_821,U_820,U_822) )
    & ! [U_821,U_820,U_822] :
        ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK25(U_822,U_821,U_820)))
        | ~ sP51(U_821,U_820,U_822) )
    & ! [U_821,U_820,U_822] :
        ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK25(U_822,U_821,U_820)),U_821))
        | ~ sP51(U_821,U_820,U_822) )
    & ! [U_821,U_820,U_822] :
        ( is_fun949378684l_bool(sK25(U_822,U_821,U_820))
        | ~ sP51(U_821,U_820,U_822) )
    & ! [U_821,U_820,U_822] :
        ( sP51(U_821,U_820,U_822)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_820),image_fun_a_bool_int(U_822,U_821)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_820)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP51])],[f_350_3]) ).

cnf(f_350_5,plain,
    ( sP51(U_821,U_820,U_822)
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_820),image_fun_a_bool_int(U_822,U_821)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_820)) ),
    inference(clausify,[status(thm)],[f_350_4]) ).

cnf(f_350_6,plain,
    ( is_fun949378684l_bool(sK25(U_822,U_821,U_820))
    | ~ sP51(U_821,U_820,U_822) ),
    inference(clausify,[status(thm)],[f_350_4]) ).

cnf(f_350_7,plain,
    ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,sK25(U_822,U_821,U_820)),U_821))
    | ~ sP51(U_821,U_820,U_822) ),
    inference(clausify,[status(thm)],[f_350_4]) ).

cnf(f_350_8,plain,
    ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,sK25(U_822,U_821,U_820)))
    | ~ sP51(U_821,U_820,U_822) ),
    inference(clausify,[status(thm)],[f_350_4]) ).

cnf(f_350_9,plain,
    ( U_820 = image_fun_a_bool_int(U_822,sK25(U_822,U_821,U_820))
    | ~ sP51(U_821,U_820,U_822) ),
    inference(clausify,[status(thm)],[f_350_4]) ).

fof(f_351_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_pname_int(F,C_16)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A))
          & is_fun_pname_bool(C_16) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_pname_int(F,A)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) ),
    inference(fof_nnf,[status(thm)],[fact_244_finite__subset__image]) ).

fof(f_351_2,plain,
    ! [U_826,U_825,U_824] :
      ( ? [U_823] :
          ( U_824 = image_pname_int(U_826,U_823)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_823))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_823),U_825))
          & is_fun_pname_bool(U_823) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_824),image_pname_int(U_826,U_825)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_824)) ),
    inference(variable_rename,[status(thm)],[f_351_1]) ).

fof(f_351_3,plain,
    ! [U_826,U_825,U_824] :
      ( ( U_824 = image_pname_int(U_826,sK26(U_826,U_825,U_824))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK26(U_826,U_825,U_824)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK26(U_826,U_825,U_824)),U_825))
        & is_fun_pname_bool(sK26(U_826,U_825,U_824)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_824),image_pname_int(U_826,U_825)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_824)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_823,sK26(U_826,U_825,U_824))],[f_351_2]) ).

fof(f_351_4,plain,
    ( ! [U_825,U_824,U_826] :
        ( U_824 = image_pname_int(U_826,sK26(U_826,U_825,U_824))
        | ~ sP52(U_825,U_824,U_826) )
    & ! [U_825,U_824,U_826] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK26(U_826,U_825,U_824)))
        | ~ sP52(U_825,U_824,U_826) )
    & ! [U_825,U_824,U_826] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK26(U_826,U_825,U_824)),U_825))
        | ~ sP52(U_825,U_824,U_826) )
    & ! [U_825,U_824,U_826] :
        ( is_fun_pname_bool(sK26(U_826,U_825,U_824))
        | ~ sP52(U_825,U_824,U_826) )
    & ! [U_825,U_824,U_826] :
        ( sP52(U_825,U_824,U_826)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_824),image_pname_int(U_826,U_825)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_824)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP52])],[f_351_3]) ).

cnf(f_351_5,plain,
    ( sP52(U_825,U_824,U_826)
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_824),image_pname_int(U_826,U_825)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_824)) ),
    inference(clausify,[status(thm)],[f_351_4]) ).

cnf(f_351_6,plain,
    ( is_fun_pname_bool(sK26(U_826,U_825,U_824))
    | ~ sP52(U_825,U_824,U_826) ),
    inference(clausify,[status(thm)],[f_351_4]) ).

cnf(f_351_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK26(U_826,U_825,U_824)),U_825))
    | ~ sP52(U_825,U_824,U_826) ),
    inference(clausify,[status(thm)],[f_351_4]) ).

cnf(f_351_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK26(U_826,U_825,U_824)))
    | ~ sP52(U_825,U_824,U_826) ),
    inference(clausify,[status(thm)],[f_351_4]) ).

cnf(f_351_9,plain,
    ( U_824 = image_pname_int(U_826,sK26(U_826,U_825,U_824))
    | ~ sP52(U_825,U_824,U_826) ),
    inference(clausify,[status(thm)],[f_351_4]) ).

fof(f_352_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_1512837979t_bool(F,C_16)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A))
          & is_fun_pname_bool(C_16) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,B),image_1512837979t_bool(F,A)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B)) ),
    inference(fof_nnf,[status(thm)],[fact_245_finite__subset__image]) ).

fof(f_352_2,plain,
    ! [U_830,U_829,U_828] :
      ( ? [U_827] :
          ( U_828 = image_1512837979t_bool(U_830,U_827)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_827))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_827),U_829))
          & is_fun_pname_bool(U_827) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_828),image_1512837979t_bool(U_830,U_829)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_828)) ),
    inference(variable_rename,[status(thm)],[f_352_1]) ).

fof(f_352_3,plain,
    ! [U_830,U_829,U_828] :
      ( ( U_828 = image_1512837979t_bool(U_830,sK27(U_830,U_829,U_828))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK27(U_830,U_829,U_828)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK27(U_830,U_829,U_828)),U_829))
        & is_fun_pname_bool(sK27(U_830,U_829,U_828)) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_828),image_1512837979t_bool(U_830,U_829)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_828)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_827,sK27(U_830,U_829,U_828))],[f_352_2]) ).

fof(f_352_4,plain,
    ( ! [U_828,U_829,U_830] :
        ( U_828 = image_1512837979t_bool(U_830,sK27(U_830,U_829,U_828))
        | ~ sP53(U_828,U_829,U_830) )
    & ! [U_828,U_829,U_830] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK27(U_830,U_829,U_828)))
        | ~ sP53(U_828,U_829,U_830) )
    & ! [U_828,U_829,U_830] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK27(U_830,U_829,U_828)),U_829))
        | ~ sP53(U_828,U_829,U_830) )
    & ! [U_828,U_829,U_830] :
        ( is_fun_pname_bool(sK27(U_830,U_829,U_828))
        | ~ sP53(U_828,U_829,U_830) )
    & ! [U_828,U_829,U_830] :
        ( sP53(U_828,U_829,U_830)
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_828),image_1512837979t_bool(U_830,U_829)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_828)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP53])],[f_352_3]) ).

cnf(f_352_5,plain,
    ( sP53(U_828,U_829,U_830)
    | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_828),image_1512837979t_bool(U_830,U_829)))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_828)) ),
    inference(clausify,[status(thm)],[f_352_4]) ).

cnf(f_352_6,plain,
    ( is_fun_pname_bool(sK27(U_830,U_829,U_828))
    | ~ sP53(U_828,U_829,U_830) ),
    inference(clausify,[status(thm)],[f_352_4]) ).

cnf(f_352_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK27(U_830,U_829,U_828)),U_829))
    | ~ sP53(U_828,U_829,U_830) ),
    inference(clausify,[status(thm)],[f_352_4]) ).

cnf(f_352_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK27(U_830,U_829,U_828)))
    | ~ sP53(U_828,U_829,U_830) ),
    inference(clausify,[status(thm)],[f_352_4]) ).

cnf(f_352_9,plain,
    ( U_828 = image_1512837979t_bool(U_830,sK27(U_830,U_829,U_828))
    | ~ sP53(U_828,U_829,U_830) ),
    inference(clausify,[status(thm)],[f_352_4]) ).

fof(f_353_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_2129980159t_bool(F,C_16)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A))
          & is_fun_pname_bool(C_16) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B),image_2129980159t_bool(F,A)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B)) ),
    inference(fof_nnf,[status(thm)],[fact_246_finite__subset__image]) ).

fof(f_353_2,plain,
    ! [U_834,U_833,U_832] :
      ( ? [U_831] :
          ( U_832 = image_2129980159t_bool(U_834,U_831)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_831))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_831),U_833))
          & is_fun_pname_bool(U_831) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_832),image_2129980159t_bool(U_834,U_833)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_832)) ),
    inference(variable_rename,[status(thm)],[f_353_1]) ).

fof(f_353_3,plain,
    ! [U_834,U_833,U_832] :
      ( ( U_832 = image_2129980159t_bool(U_834,sK28(U_834,U_833,U_832))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK28(U_834,U_833,U_832)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK28(U_834,U_833,U_832)),U_833))
        & is_fun_pname_bool(sK28(U_834,U_833,U_832)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_832),image_2129980159t_bool(U_834,U_833)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_832)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_831,sK28(U_834,U_833,U_832))],[f_353_2]) ).

fof(f_353_4,plain,
    ( ! [U_833,U_832,U_834] :
        ( U_832 = image_2129980159t_bool(U_834,sK28(U_834,U_833,U_832))
        | ~ sP54(U_833,U_832,U_834) )
    & ! [U_833,U_832,U_834] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK28(U_834,U_833,U_832)))
        | ~ sP54(U_833,U_832,U_834) )
    & ! [U_833,U_832,U_834] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK28(U_834,U_833,U_832)),U_833))
        | ~ sP54(U_833,U_832,U_834) )
    & ! [U_833,U_832,U_834] :
        ( is_fun_pname_bool(sK28(U_834,U_833,U_832))
        | ~ sP54(U_833,U_832,U_834) )
    & ! [U_833,U_832,U_834] :
        ( sP54(U_833,U_832,U_834)
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_832),image_2129980159t_bool(U_834,U_833)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_832)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP54])],[f_353_3]) ).

cnf(f_353_5,plain,
    ( sP54(U_833,U_832,U_834)
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_832),image_2129980159t_bool(U_834,U_833)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_832)) ),
    inference(clausify,[status(thm)],[f_353_4]) ).

cnf(f_353_6,plain,
    ( is_fun_pname_bool(sK28(U_834,U_833,U_832))
    | ~ sP54(U_833,U_832,U_834) ),
    inference(clausify,[status(thm)],[f_353_4]) ).

cnf(f_353_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK28(U_834,U_833,U_832)),U_833))
    | ~ sP54(U_833,U_832,U_834) ),
    inference(clausify,[status(thm)],[f_353_4]) ).

cnf(f_353_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK28(U_834,U_833,U_832)))
    | ~ sP54(U_833,U_832,U_834) ),
    inference(clausify,[status(thm)],[f_353_4]) ).

cnf(f_353_9,plain,
    ( U_832 = image_2129980159t_bool(U_834,sK28(U_834,U_833,U_832))
    | ~ sP54(U_833,U_832,U_834) ),
    inference(clausify,[status(thm)],[f_353_4]) ).

fof(f_354_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_47868345e_bool(F,C_16)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A))
          & is_fun_pname_bool(C_16) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_47868345e_bool(F,A)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
      | ~ is_fun1661590463l_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_247_finite__subset__image]) ).

fof(f_354_2,plain,
    ! [U_838,U_837,U_836] :
      ( ? [U_835] :
          ( U_836 = image_47868345e_bool(U_838,U_835)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_835))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_835),U_837))
          & is_fun_pname_bool(U_835) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_836),image_47868345e_bool(U_838,U_837)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_836))
      | ~ is_fun1661590463l_bool(U_836) ),
    inference(variable_rename,[status(thm)],[f_354_1]) ).

fof(f_354_3,plain,
    ! [U_838,U_837,U_836] :
      ( ( U_836 = image_47868345e_bool(U_838,sK29(U_838,U_837,U_836))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK29(U_838,U_837,U_836)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK29(U_838,U_837,U_836)),U_837))
        & is_fun_pname_bool(sK29(U_838,U_837,U_836)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_836),image_47868345e_bool(U_838,U_837)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_836))
      | ~ is_fun1661590463l_bool(U_836) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_835,sK29(U_838,U_837,U_836))],[f_354_2]) ).

fof(f_354_4,plain,
    ( ! [U_836,U_837,U_838] :
        ( U_836 = image_47868345e_bool(U_838,sK29(U_838,U_837,U_836))
        | ~ sP55(U_836,U_837,U_838) )
    & ! [U_836,U_837,U_838] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK29(U_838,U_837,U_836)))
        | ~ sP55(U_836,U_837,U_838) )
    & ! [U_836,U_837,U_838] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK29(U_838,U_837,U_836)),U_837))
        | ~ sP55(U_836,U_837,U_838) )
    & ! [U_836,U_837,U_838] :
        ( is_fun_pname_bool(sK29(U_838,U_837,U_836))
        | ~ sP55(U_836,U_837,U_838) )
    & ! [U_836,U_837,U_838] :
        ( sP55(U_836,U_837,U_838)
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_836),image_47868345e_bool(U_838,U_837)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_836))
        | ~ is_fun1661590463l_bool(U_836) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP55])],[f_354_3]) ).

cnf(f_354_5,plain,
    ( sP55(U_836,U_837,U_838)
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_836),image_47868345e_bool(U_838,U_837)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_836))
    | ~ is_fun1661590463l_bool(U_836) ),
    inference(clausify,[status(thm)],[f_354_4]) ).

cnf(f_354_6,plain,
    ( is_fun_pname_bool(sK29(U_838,U_837,U_836))
    | ~ sP55(U_836,U_837,U_838) ),
    inference(clausify,[status(thm)],[f_354_4]) ).

cnf(f_354_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK29(U_838,U_837,U_836)),U_837))
    | ~ sP55(U_836,U_837,U_838) ),
    inference(clausify,[status(thm)],[f_354_4]) ).

cnf(f_354_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK29(U_838,U_837,U_836)))
    | ~ sP55(U_836,U_837,U_838) ),
    inference(clausify,[status(thm)],[f_354_4]) ).

cnf(f_354_9,plain,
    ( U_836 = image_47868345e_bool(U_838,sK29(U_838,U_837,U_836))
    | ~ sP55(U_836,U_837,U_838) ),
    inference(clausify,[status(thm)],[f_354_4]) ).

fof(f_355_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_112932426a_bool(F,C_16)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A))
          & is_fun_pname_bool(C_16) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B),image_112932426a_bool(F,A)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))
      | ~ is_fun949378684l_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_248_finite__subset__image]) ).

fof(f_355_2,plain,
    ! [U_842,U_841,U_840] :
      ( ? [U_839] :
          ( U_840 = image_112932426a_bool(U_842,U_839)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_839))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_839),U_841))
          & is_fun_pname_bool(U_839) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_840),image_112932426a_bool(U_842,U_841)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_840))
      | ~ is_fun949378684l_bool(U_840) ),
    inference(variable_rename,[status(thm)],[f_355_1]) ).

fof(f_355_3,plain,
    ! [U_842,U_841,U_840] :
      ( ( U_840 = image_112932426a_bool(U_842,sK30(U_842,U_841,U_840))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK30(U_842,U_841,U_840)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK30(U_842,U_841,U_840)),U_841))
        & is_fun_pname_bool(sK30(U_842,U_841,U_840)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_840),image_112932426a_bool(U_842,U_841)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_840))
      | ~ is_fun949378684l_bool(U_840) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_839,sK30(U_842,U_841,U_840))],[f_355_2]) ).

fof(f_355_4,plain,
    ( ! [U_841,U_842,U_840] :
        ( U_840 = image_112932426a_bool(U_842,sK30(U_842,U_841,U_840))
        | ~ sP56(U_841,U_842,U_840) )
    & ! [U_841,U_842,U_840] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK30(U_842,U_841,U_840)))
        | ~ sP56(U_841,U_842,U_840) )
    & ! [U_841,U_842,U_840] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK30(U_842,U_841,U_840)),U_841))
        | ~ sP56(U_841,U_842,U_840) )
    & ! [U_841,U_842,U_840] :
        ( is_fun_pname_bool(sK30(U_842,U_841,U_840))
        | ~ sP56(U_841,U_842,U_840) )
    & ! [U_841,U_842,U_840] :
        ( sP56(U_841,U_842,U_840)
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_840),image_112932426a_bool(U_842,U_841)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_840))
        | ~ is_fun949378684l_bool(U_840) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP56])],[f_355_3]) ).

cnf(f_355_5,plain,
    ( sP56(U_841,U_842,U_840)
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_840),image_112932426a_bool(U_842,U_841)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_840))
    | ~ is_fun949378684l_bool(U_840) ),
    inference(clausify,[status(thm)],[f_355_4]) ).

cnf(f_355_6,plain,
    ( is_fun_pname_bool(sK30(U_842,U_841,U_840))
    | ~ sP56(U_841,U_842,U_840) ),
    inference(clausify,[status(thm)],[f_355_4]) ).

cnf(f_355_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK30(U_842,U_841,U_840)),U_841))
    | ~ sP56(U_841,U_842,U_840) ),
    inference(clausify,[status(thm)],[f_355_4]) ).

cnf(f_355_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK30(U_842,U_841,U_840)))
    | ~ sP56(U_841,U_842,U_840) ),
    inference(clausify,[status(thm)],[f_355_4]) ).

cnf(f_355_9,plain,
    ( U_840 = image_112932426a_bool(U_842,sK30(U_842,U_841,U_840))
    | ~ sP56(U_841,U_842,U_840) ),
    inference(clausify,[status(thm)],[f_355_4]) ).

fof(f_356_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_pname_pname(F,C_16)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A))
          & is_fun_pname_bool(C_16) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_pname_pname(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ is_fun_pname_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_249_finite__subset__image]) ).

fof(f_356_2,plain,
    ! [U_846,U_845,U_844] :
      ( ? [U_843] :
          ( U_844 = image_pname_pname(U_846,U_843)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_843))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_843),U_845))
          & is_fun_pname_bool(U_843) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_844),image_pname_pname(U_846,U_845)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_844))
      | ~ is_fun_pname_bool(U_844) ),
    inference(variable_rename,[status(thm)],[f_356_1]) ).

fof(f_356_3,plain,
    ! [U_846,U_845,U_844] :
      ( ( U_844 = image_pname_pname(U_846,sK31(U_846,U_845,U_844))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK31(U_846,U_845,U_844)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK31(U_846,U_845,U_844)),U_845))
        & is_fun_pname_bool(sK31(U_846,U_845,U_844)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_844),image_pname_pname(U_846,U_845)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_844))
      | ~ is_fun_pname_bool(U_844) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_843,sK31(U_846,U_845,U_844))],[f_356_2]) ).

fof(f_356_4,plain,
    ( ! [U_844,U_845,U_846] :
        ( U_844 = image_pname_pname(U_846,sK31(U_846,U_845,U_844))
        | ~ sP57(U_844,U_845,U_846) )
    & ! [U_844,U_845,U_846] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK31(U_846,U_845,U_844)))
        | ~ sP57(U_844,U_845,U_846) )
    & ! [U_844,U_845,U_846] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK31(U_846,U_845,U_844)),U_845))
        | ~ sP57(U_844,U_845,U_846) )
    & ! [U_844,U_845,U_846] :
        ( is_fun_pname_bool(sK31(U_846,U_845,U_844))
        | ~ sP57(U_844,U_845,U_846) )
    & ! [U_844,U_845,U_846] :
        ( sP57(U_844,U_845,U_846)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_844),image_pname_pname(U_846,U_845)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_844))
        | ~ is_fun_pname_bool(U_844) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP57])],[f_356_3]) ).

cnf(f_356_5,plain,
    ( sP57(U_844,U_845,U_846)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_844),image_pname_pname(U_846,U_845)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_844))
    | ~ is_fun_pname_bool(U_844) ),
    inference(clausify,[status(thm)],[f_356_4]) ).

cnf(f_356_6,plain,
    ( is_fun_pname_bool(sK31(U_846,U_845,U_844))
    | ~ sP57(U_844,U_845,U_846) ),
    inference(clausify,[status(thm)],[f_356_4]) ).

cnf(f_356_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK31(U_846,U_845,U_844)),U_845))
    | ~ sP57(U_844,U_845,U_846) ),
    inference(clausify,[status(thm)],[f_356_4]) ).

cnf(f_356_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK31(U_846,U_845,U_844)))
    | ~ sP57(U_844,U_845,U_846) ),
    inference(clausify,[status(thm)],[f_356_4]) ).

cnf(f_356_9,plain,
    ( U_844 = image_pname_pname(U_846,sK31(U_846,U_845,U_844))
    | ~ sP57(U_844,U_845,U_846) ),
    inference(clausify,[status(thm)],[f_356_4]) ).

fof(f_357_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_nat_a(F,C_16)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_16))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_16),A)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_nat_a(F,A)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))
      | ~ is_fun_a_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_250_finite__subset__image]) ).

fof(f_357_2,plain,
    ! [U_850,U_849,U_848] :
      ( ? [U_847] :
          ( U_848 = image_nat_a(U_850,U_847)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_847))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_847),U_849)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_848),image_nat_a(U_850,U_849)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_848))
      | ~ is_fun_a_bool(U_848) ),
    inference(variable_rename,[status(thm)],[f_357_1]) ).

fof(f_357_3,plain,
    ! [U_850,U_849,U_848] :
      ( ( U_848 = image_nat_a(U_850,sK32(U_850,U_849,U_848))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK32(U_850,U_849,U_848)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK32(U_850,U_849,U_848)),U_849)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_848),image_nat_a(U_850,U_849)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_848))
      | ~ is_fun_a_bool(U_848) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_847,sK32(U_850,U_849,U_848))],[f_357_2]) ).

fof(f_357_4,plain,
    ( ! [U_849,U_848,U_850] :
        ( U_848 = image_nat_a(U_850,sK32(U_850,U_849,U_848))
        | ~ sP58(U_849,U_848,U_850) )
    & ! [U_849,U_848,U_850] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK32(U_850,U_849,U_848)))
        | ~ sP58(U_849,U_848,U_850) )
    & ! [U_849,U_848,U_850] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK32(U_850,U_849,U_848)),U_849))
        | ~ sP58(U_849,U_848,U_850) )
    & ! [U_849,U_848,U_850] :
        ( sP58(U_849,U_848,U_850)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_848),image_nat_a(U_850,U_849)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_848))
        | ~ is_fun_a_bool(U_848) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP58])],[f_357_3]) ).

cnf(f_357_5,plain,
    ( sP58(U_849,U_848,U_850)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_848),image_nat_a(U_850,U_849)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_848))
    | ~ is_fun_a_bool(U_848) ),
    inference(clausify,[status(thm)],[f_357_4]) ).

cnf(f_357_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK32(U_850,U_849,U_848)),U_849))
    | ~ sP58(U_849,U_848,U_850) ),
    inference(clausify,[status(thm)],[f_357_4]) ).

cnf(f_357_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK32(U_850,U_849,U_848)))
    | ~ sP58(U_849,U_848,U_850) ),
    inference(clausify,[status(thm)],[f_357_4]) ).

cnf(f_357_8,plain,
    ( U_848 = image_nat_a(U_850,sK32(U_850,U_849,U_848))
    | ~ sP58(U_849,U_848,U_850) ),
    inference(clausify,[status(thm)],[f_357_4]) ).

fof(f_358_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_1556378401t_bool(F,C_16)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_16))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_16),A)) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,B),image_1556378401t_bool(F,A)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B)) ),
    inference(fof_nnf,[status(thm)],[fact_251_finite__subset__image]) ).

fof(f_358_2,plain,
    ! [U_854,U_853,U_852] :
      ( ? [U_851] :
          ( U_852 = image_1556378401t_bool(U_854,U_851)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_851))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_851),U_853)) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_852),image_1556378401t_bool(U_854,U_853)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_852)) ),
    inference(variable_rename,[status(thm)],[f_358_1]) ).

fof(f_358_3,plain,
    ! [U_854,U_853,U_852] :
      ( ( U_852 = image_1556378401t_bool(U_854,sK33(U_854,U_853,U_852))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK33(U_854,U_853,U_852)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK33(U_854,U_853,U_852)),U_853)) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_852),image_1556378401t_bool(U_854,U_853)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_852)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_851,sK33(U_854,U_853,U_852))],[f_358_2]) ).

fof(f_358_4,plain,
    ( ! [U_853,U_854,U_852] :
        ( U_852 = image_1556378401t_bool(U_854,sK33(U_854,U_853,U_852))
        | ~ sP59(U_853,U_854,U_852) )
    & ! [U_853,U_854,U_852] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK33(U_854,U_853,U_852)))
        | ~ sP59(U_853,U_854,U_852) )
    & ! [U_853,U_854,U_852] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK33(U_854,U_853,U_852)),U_853))
        | ~ sP59(U_853,U_854,U_852) )
    & ! [U_853,U_854,U_852] :
        ( sP59(U_853,U_854,U_852)
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_852),image_1556378401t_bool(U_854,U_853)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_852)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP59])],[f_358_3]) ).

cnf(f_358_5,plain,
    ( sP59(U_853,U_854,U_852)
    | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_852),image_1556378401t_bool(U_854,U_853)))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_852)) ),
    inference(clausify,[status(thm)],[f_358_4]) ).

cnf(f_358_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK33(U_854,U_853,U_852)),U_853))
    | ~ sP59(U_853,U_854,U_852) ),
    inference(clausify,[status(thm)],[f_358_4]) ).

cnf(f_358_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK33(U_854,U_853,U_852)))
    | ~ sP59(U_853,U_854,U_852) ),
    inference(clausify,[status(thm)],[f_358_4]) ).

cnf(f_358_8,plain,
    ( U_852 = image_1556378401t_bool(U_854,sK33(U_854,U_853,U_852))
    | ~ sP59(U_853,U_854,U_852) ),
    inference(clausify,[status(thm)],[f_358_4]) ).

fof(f_359_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_26036933t_bool(F,C_16)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_16))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_16),A)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B),image_26036933t_bool(F,A)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B)) ),
    inference(fof_nnf,[status(thm)],[fact_252_finite__subset__image]) ).

fof(f_359_2,plain,
    ! [U_858,U_857,U_856] :
      ( ? [U_855] :
          ( U_856 = image_26036933t_bool(U_858,U_855)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_855))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_855),U_857)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_856),image_26036933t_bool(U_858,U_857)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_856)) ),
    inference(variable_rename,[status(thm)],[f_359_1]) ).

fof(f_359_3,plain,
    ! [U_858,U_857,U_856] :
      ( ( U_856 = image_26036933t_bool(U_858,sK34(U_858,U_857,U_856))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK34(U_858,U_857,U_856)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK34(U_858,U_857,U_856)),U_857)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_856),image_26036933t_bool(U_858,U_857)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_856)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_855,sK34(U_858,U_857,U_856))],[f_359_2]) ).

fof(f_359_4,plain,
    ( ! [U_857,U_858,U_856] :
        ( U_856 = image_26036933t_bool(U_858,sK34(U_858,U_857,U_856))
        | ~ sP60(U_857,U_858,U_856) )
    & ! [U_857,U_858,U_856] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK34(U_858,U_857,U_856)))
        | ~ sP60(U_857,U_858,U_856) )
    & ! [U_857,U_858,U_856] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK34(U_858,U_857,U_856)),U_857))
        | ~ sP60(U_857,U_858,U_856) )
    & ! [U_857,U_858,U_856] :
        ( sP60(U_857,U_858,U_856)
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_856),image_26036933t_bool(U_858,U_857)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_856)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP60])],[f_359_3]) ).

cnf(f_359_5,plain,
    ( sP60(U_857,U_858,U_856)
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_856),image_26036933t_bool(U_858,U_857)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_856)) ),
    inference(clausify,[status(thm)],[f_359_4]) ).

cnf(f_359_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK34(U_858,U_857,U_856)),U_857))
    | ~ sP60(U_857,U_858,U_856) ),
    inference(clausify,[status(thm)],[f_359_4]) ).

cnf(f_359_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK34(U_858,U_857,U_856)))
    | ~ sP60(U_857,U_858,U_856) ),
    inference(clausify,[status(thm)],[f_359_4]) ).

cnf(f_359_8,plain,
    ( U_856 = image_26036933t_bool(U_858,sK34(U_858,U_857,U_856))
    | ~ sP60(U_857,U_858,U_856) ),
    inference(clausify,[status(thm)],[f_359_4]) ).

fof(f_360_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_1655916159e_bool(F,C_16)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_16))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_16),A)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_1655916159e_bool(F,A)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
      | ~ is_fun1661590463l_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_253_finite__subset__image]) ).

fof(f_360_2,plain,
    ! [U_862,U_861,U_860] :
      ( ? [U_859] :
          ( U_860 = image_1655916159e_bool(U_862,U_859)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_859))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_859),U_861)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_860),image_1655916159e_bool(U_862,U_861)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_860))
      | ~ is_fun1661590463l_bool(U_860) ),
    inference(variable_rename,[status(thm)],[f_360_1]) ).

fof(f_360_3,plain,
    ! [U_862,U_861,U_860] :
      ( ( U_860 = image_1655916159e_bool(U_862,sK35(U_862,U_861,U_860))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK35(U_862,U_861,U_860)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK35(U_862,U_861,U_860)),U_861)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_860),image_1655916159e_bool(U_862,U_861)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_860))
      | ~ is_fun1661590463l_bool(U_860) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_859,sK35(U_862,U_861,U_860))],[f_360_2]) ).

fof(f_360_4,plain,
    ( ! [U_861,U_860,U_862] :
        ( U_860 = image_1655916159e_bool(U_862,sK35(U_862,U_861,U_860))
        | ~ sP61(U_861,U_860,U_862) )
    & ! [U_861,U_860,U_862] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK35(U_862,U_861,U_860)))
        | ~ sP61(U_861,U_860,U_862) )
    & ! [U_861,U_860,U_862] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK35(U_862,U_861,U_860)),U_861))
        | ~ sP61(U_861,U_860,U_862) )
    & ! [U_861,U_860,U_862] :
        ( sP61(U_861,U_860,U_862)
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_860),image_1655916159e_bool(U_862,U_861)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_860))
        | ~ is_fun1661590463l_bool(U_860) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP61])],[f_360_3]) ).

cnf(f_360_5,plain,
    ( sP61(U_861,U_860,U_862)
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_860),image_1655916159e_bool(U_862,U_861)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_860))
    | ~ is_fun1661590463l_bool(U_860) ),
    inference(clausify,[status(thm)],[f_360_4]) ).

cnf(f_360_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK35(U_862,U_861,U_860)),U_861))
    | ~ sP61(U_861,U_860,U_862) ),
    inference(clausify,[status(thm)],[f_360_4]) ).

cnf(f_360_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK35(U_862,U_861,U_860)))
    | ~ sP61(U_861,U_860,U_862) ),
    inference(clausify,[status(thm)],[f_360_4]) ).

cnf(f_360_8,plain,
    ( U_860 = image_1655916159e_bool(U_862,sK35(U_862,U_861,U_860))
    | ~ sP61(U_861,U_860,U_862) ),
    inference(clausify,[status(thm)],[f_360_4]) ).

fof(f_361_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_nat_fun_a_bool(F,C_16)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_16))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_16),A)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B),image_nat_fun_a_bool(F,A)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))
      | ~ is_fun949378684l_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_254_finite__subset__image]) ).

fof(f_361_2,plain,
    ! [U_866,U_865,U_864] :
      ( ? [U_863] :
          ( U_864 = image_nat_fun_a_bool(U_866,U_863)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_863))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_863),U_865)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_864),image_nat_fun_a_bool(U_866,U_865)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_864))
      | ~ is_fun949378684l_bool(U_864) ),
    inference(variable_rename,[status(thm)],[f_361_1]) ).

fof(f_361_3,plain,
    ! [U_866,U_865,U_864] :
      ( ( U_864 = image_nat_fun_a_bool(U_866,sK36(U_866,U_865,U_864))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK36(U_866,U_865,U_864)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK36(U_866,U_865,U_864)),U_865)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_864),image_nat_fun_a_bool(U_866,U_865)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_864))
      | ~ is_fun949378684l_bool(U_864) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_863,sK36(U_866,U_865,U_864))],[f_361_2]) ).

fof(f_361_4,plain,
    ( ! [U_865,U_864,U_866] :
        ( U_864 = image_nat_fun_a_bool(U_866,sK36(U_866,U_865,U_864))
        | ~ sP62(U_865,U_864,U_866) )
    & ! [U_865,U_864,U_866] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK36(U_866,U_865,U_864)))
        | ~ sP62(U_865,U_864,U_866) )
    & ! [U_865,U_864,U_866] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK36(U_866,U_865,U_864)),U_865))
        | ~ sP62(U_865,U_864,U_866) )
    & ! [U_865,U_864,U_866] :
        ( sP62(U_865,U_864,U_866)
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_864),image_nat_fun_a_bool(U_866,U_865)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_864))
        | ~ is_fun949378684l_bool(U_864) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP62])],[f_361_3]) ).

cnf(f_361_5,plain,
    ( sP62(U_865,U_864,U_866)
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_864),image_nat_fun_a_bool(U_866,U_865)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_864))
    | ~ is_fun949378684l_bool(U_864) ),
    inference(clausify,[status(thm)],[f_361_4]) ).

cnf(f_361_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK36(U_866,U_865,U_864)),U_865))
    | ~ sP62(U_865,U_864,U_866) ),
    inference(clausify,[status(thm)],[f_361_4]) ).

cnf(f_361_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK36(U_866,U_865,U_864)))
    | ~ sP62(U_865,U_864,U_866) ),
    inference(clausify,[status(thm)],[f_361_4]) ).

cnf(f_361_8,plain,
    ( U_864 = image_nat_fun_a_bool(U_866,sK36(U_866,U_865,U_864))
    | ~ sP62(U_865,U_864,U_866) ),
    inference(clausify,[status(thm)],[f_361_4]) ).

fof(f_362_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_nat_pname(F,C_16)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_16))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_16),A)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_nat_pname(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ is_fun_pname_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_255_finite__subset__image]) ).

fof(f_362_2,plain,
    ! [U_870,U_869,U_868] :
      ( ? [U_867] :
          ( U_868 = image_nat_pname(U_870,U_867)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_867))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_867),U_869)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_868),image_nat_pname(U_870,U_869)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_868))
      | ~ is_fun_pname_bool(U_868) ),
    inference(variable_rename,[status(thm)],[f_362_1]) ).

fof(f_362_3,plain,
    ! [U_870,U_869,U_868] :
      ( ( U_868 = image_nat_pname(U_870,sK37(U_870,U_869,U_868))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK37(U_870,U_869,U_868)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK37(U_870,U_869,U_868)),U_869)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_868),image_nat_pname(U_870,U_869)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_868))
      | ~ is_fun_pname_bool(U_868) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_867,sK37(U_870,U_869,U_868))],[f_362_2]) ).

fof(f_362_4,plain,
    ( ! [U_869,U_870,U_868] :
        ( U_868 = image_nat_pname(U_870,sK37(U_870,U_869,U_868))
        | ~ sP63(U_869,U_870,U_868) )
    & ! [U_869,U_870,U_868] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK37(U_870,U_869,U_868)))
        | ~ sP63(U_869,U_870,U_868) )
    & ! [U_869,U_870,U_868] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK37(U_870,U_869,U_868)),U_869))
        | ~ sP63(U_869,U_870,U_868) )
    & ! [U_869,U_870,U_868] :
        ( sP63(U_869,U_870,U_868)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_868),image_nat_pname(U_870,U_869)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_868))
        | ~ is_fun_pname_bool(U_868) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP63])],[f_362_3]) ).

cnf(f_362_5,plain,
    ( sP63(U_869,U_870,U_868)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_868),image_nat_pname(U_870,U_869)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_868))
    | ~ is_fun_pname_bool(U_868) ),
    inference(clausify,[status(thm)],[f_362_4]) ).

cnf(f_362_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK37(U_870,U_869,U_868)),U_869))
    | ~ sP63(U_869,U_870,U_868) ),
    inference(clausify,[status(thm)],[f_362_4]) ).

cnf(f_362_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK37(U_870,U_869,U_868)))
    | ~ sP63(U_869,U_870,U_868) ),
    inference(clausify,[status(thm)],[f_362_4]) ).

cnf(f_362_8,plain,
    ( U_868 = image_nat_pname(U_870,sK37(U_870,U_869,U_868))
    | ~ sP63(U_869,U_870,U_868) ),
    inference(clausify,[status(thm)],[f_362_4]) ).

fof(f_363_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_int_a(F,C_16)
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,C_16))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_16),A)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_int_a(F,A)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))
      | ~ is_fun_a_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_256_finite__subset__image]) ).

fof(f_363_2,plain,
    ! [U_874,U_873,U_872] :
      ( ? [U_871] :
          ( U_872 = image_int_a(U_874,U_871)
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_871))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_871),U_873)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_872),image_int_a(U_874,U_873)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_872))
      | ~ is_fun_a_bool(U_872) ),
    inference(variable_rename,[status(thm)],[f_363_1]) ).

fof(f_363_3,plain,
    ! [U_874,U_873,U_872] :
      ( ( U_872 = image_int_a(U_874,sK38(U_874,U_873,U_872))
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK38(U_874,U_873,U_872)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK38(U_874,U_873,U_872)),U_873)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_872),image_int_a(U_874,U_873)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_872))
      | ~ is_fun_a_bool(U_872) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_871,sK38(U_874,U_873,U_872))],[f_363_2]) ).

fof(f_363_4,plain,
    ( ! [U_873,U_874,U_872] :
        ( U_872 = image_int_a(U_874,sK38(U_874,U_873,U_872))
        | ~ sP64(U_873,U_874,U_872) )
    & ! [U_873,U_874,U_872] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK38(U_874,U_873,U_872)))
        | ~ sP64(U_873,U_874,U_872) )
    & ! [U_873,U_874,U_872] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK38(U_874,U_873,U_872)),U_873))
        | ~ sP64(U_873,U_874,U_872) )
    & ! [U_873,U_874,U_872] :
        ( sP64(U_873,U_874,U_872)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_872),image_int_a(U_874,U_873)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_872))
        | ~ is_fun_a_bool(U_872) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP64])],[f_363_3]) ).

cnf(f_363_5,plain,
    ( sP64(U_873,U_874,U_872)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_872),image_int_a(U_874,U_873)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_872))
    | ~ is_fun_a_bool(U_872) ),
    inference(clausify,[status(thm)],[f_363_4]) ).

cnf(f_363_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK38(U_874,U_873,U_872)),U_873))
    | ~ sP64(U_873,U_874,U_872) ),
    inference(clausify,[status(thm)],[f_363_4]) ).

cnf(f_363_7,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK38(U_874,U_873,U_872)))
    | ~ sP64(U_873,U_874,U_872) ),
    inference(clausify,[status(thm)],[f_363_4]) ).

cnf(f_363_8,plain,
    ( U_872 = image_int_a(U_874,sK38(U_874,U_873,U_872))
    | ~ sP64(U_873,U_874,U_872) ),
    inference(clausify,[status(thm)],[f_363_4]) ).

fof(f_364_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_275383677t_bool(F,C_16)
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,C_16))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_16),A)) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,B),image_275383677t_bool(F,A)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,B)) ),
    inference(fof_nnf,[status(thm)],[fact_257_finite__subset__image]) ).

fof(f_364_2,plain,
    ! [U_878,U_877,U_876] :
      ( ? [U_875] :
          ( U_876 = image_275383677t_bool(U_878,U_875)
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_875))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_875),U_877)) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_876),image_275383677t_bool(U_878,U_877)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_876)) ),
    inference(variable_rename,[status(thm)],[f_364_1]) ).

fof(f_364_3,plain,
    ! [U_878,U_877,U_876] :
      ( ( U_876 = image_275383677t_bool(U_878,sK39(U_878,U_877,U_876))
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK39(U_878,U_877,U_876)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK39(U_878,U_877,U_876)),U_877)) )
      | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_876),image_275383677t_bool(U_878,U_877)))
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_876)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_875,sK39(U_878,U_877,U_876))],[f_364_2]) ).

fof(f_364_4,plain,
    ( ! [U_877,U_878,U_876] :
        ( U_876 = image_275383677t_bool(U_878,sK39(U_878,U_877,U_876))
        | ~ sP65(U_877,U_878,U_876) )
    & ! [U_877,U_878,U_876] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK39(U_878,U_877,U_876)))
        | ~ sP65(U_877,U_878,U_876) )
    & ! [U_877,U_878,U_876] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK39(U_878,U_877,U_876)),U_877))
        | ~ sP65(U_877,U_878,U_876) )
    & ! [U_877,U_878,U_876] :
        ( sP65(U_877,U_878,U_876)
        | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_876),image_275383677t_bool(U_878,U_877)))
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_876)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP65])],[f_364_3]) ).

cnf(f_364_5,plain,
    ( sP65(U_877,U_878,U_876)
    | ~ hBOOL(hAPP_f215623910l_bool(hAPP_f317860125l_bool(ord_le1848167016l_bool,U_876),image_275383677t_bool(U_878,U_877)))
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,U_876)) ),
    inference(clausify,[status(thm)],[f_364_4]) ).

cnf(f_364_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK39(U_878,U_877,U_876)),U_877))
    | ~ sP65(U_877,U_878,U_876) ),
    inference(clausify,[status(thm)],[f_364_4]) ).

cnf(f_364_7,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK39(U_878,U_877,U_876)))
    | ~ sP65(U_877,U_878,U_876) ),
    inference(clausify,[status(thm)],[f_364_4]) ).

cnf(f_364_8,plain,
    ( U_876 = image_275383677t_bool(U_878,sK39(U_878,U_877,U_876))
    | ~ sP65(U_877,U_878,U_876) ),
    inference(clausify,[status(thm)],[f_364_4]) ).

fof(f_365_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_892525857t_bool(F,C_16)
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,C_16))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_16),A)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,B),image_892525857t_bool(F,A)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B)) ),
    inference(fof_nnf,[status(thm)],[fact_258_finite__subset__image]) ).

fof(f_365_2,plain,
    ! [U_882,U_881,U_880] :
      ( ? [U_879] :
          ( U_880 = image_892525857t_bool(U_882,U_879)
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_879))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_879),U_881)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_880),image_892525857t_bool(U_882,U_881)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_880)) ),
    inference(variable_rename,[status(thm)],[f_365_1]) ).

fof(f_365_3,plain,
    ! [U_882,U_881,U_880] :
      ( ( U_880 = image_892525857t_bool(U_882,sK40(U_882,U_881,U_880))
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK40(U_882,U_881,U_880)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK40(U_882,U_881,U_880)),U_881)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_880),image_892525857t_bool(U_882,U_881)))
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_880)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_879,sK40(U_882,U_881,U_880))],[f_365_2]) ).

fof(f_365_4,plain,
    ( ! [U_881,U_882,U_880] :
        ( U_880 = image_892525857t_bool(U_882,sK40(U_882,U_881,U_880))
        | ~ sP66(U_881,U_882,U_880) )
    & ! [U_881,U_882,U_880] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK40(U_882,U_881,U_880)))
        | ~ sP66(U_881,U_882,U_880) )
    & ! [U_881,U_882,U_880] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK40(U_882,U_881,U_880)),U_881))
        | ~ sP66(U_881,U_882,U_880) )
    & ! [U_881,U_882,U_880] :
        ( sP66(U_881,U_882,U_880)
        | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_880),image_892525857t_bool(U_882,U_881)))
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_880)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP66])],[f_365_3]) ).

cnf(f_365_5,plain,
    ( sP66(U_881,U_882,U_880)
    | ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,U_880),image_892525857t_bool(U_882,U_881)))
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,U_880)) ),
    inference(clausify,[status(thm)],[f_365_4]) ).

cnf(f_365_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK40(U_882,U_881,U_880)),U_881))
    | ~ sP66(U_881,U_882,U_880) ),
    inference(clausify,[status(thm)],[f_365_4]) ).

cnf(f_365_7,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK40(U_882,U_881,U_880)))
    | ~ sP66(U_881,U_882,U_880) ),
    inference(clausify,[status(thm)],[f_365_4]) ).

cnf(f_365_8,plain,
    ( U_880 = image_892525857t_bool(U_882,sK40(U_882,U_881,U_880))
    | ~ sP66(U_881,U_882,U_880) ),
    inference(clausify,[status(thm)],[f_365_4]) ).

fof(f_366_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_637364955e_bool(F,C_16)
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,C_16))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_16),A)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,B),image_637364955e_bool(F,A)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
      | ~ is_fun1661590463l_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_259_finite__subset__image]) ).

fof(f_366_2,plain,
    ! [U_886,U_885,U_884] :
      ( ? [U_883] :
          ( U_884 = image_637364955e_bool(U_886,U_883)
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_883))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_883),U_885)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_884),image_637364955e_bool(U_886,U_885)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_884))
      | ~ is_fun1661590463l_bool(U_884) ),
    inference(variable_rename,[status(thm)],[f_366_1]) ).

fof(f_366_3,plain,
    ! [U_886,U_885,U_884] :
      ( ( U_884 = image_637364955e_bool(U_886,sK41(U_886,U_885,U_884))
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK41(U_886,U_885,U_884)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK41(U_886,U_885,U_884)),U_885)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_884),image_637364955e_bool(U_886,U_885)))
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_884))
      | ~ is_fun1661590463l_bool(U_884) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_883,sK41(U_886,U_885,U_884))],[f_366_2]) ).

fof(f_366_4,plain,
    ( ! [U_885,U_884,U_886] :
        ( U_884 = image_637364955e_bool(U_886,sK41(U_886,U_885,U_884))
        | ~ sP67(U_885,U_884,U_886) )
    & ! [U_885,U_884,U_886] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK41(U_886,U_885,U_884)))
        | ~ sP67(U_885,U_884,U_886) )
    & ! [U_885,U_884,U_886] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK41(U_886,U_885,U_884)),U_885))
        | ~ sP67(U_885,U_884,U_886) )
    & ! [U_885,U_884,U_886] :
        ( sP67(U_885,U_884,U_886)
        | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_884),image_637364955e_bool(U_886,U_885)))
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_884))
        | ~ is_fun1661590463l_bool(U_884) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP67])],[f_366_3]) ).

cnf(f_366_5,plain,
    ( sP67(U_885,U_884,U_886)
    | ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,U_884),image_637364955e_bool(U_886,U_885)))
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,U_884))
    | ~ is_fun1661590463l_bool(U_884) ),
    inference(clausify,[status(thm)],[f_366_4]) ).

cnf(f_366_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK41(U_886,U_885,U_884)),U_885))
    | ~ sP67(U_885,U_884,U_886) ),
    inference(clausify,[status(thm)],[f_366_4]) ).

cnf(f_366_7,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK41(U_886,U_885,U_884)))
    | ~ sP67(U_885,U_884,U_886) ),
    inference(clausify,[status(thm)],[f_366_4]) ).

cnf(f_366_8,plain,
    ( U_884 = image_637364955e_bool(U_886,sK41(U_886,U_885,U_884))
    | ~ sP67(U_885,U_884,U_886) ),
    inference(clausify,[status(thm)],[f_366_4]) ).

fof(f_367_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_int_fun_a_bool(F,C_16)
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,C_16))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_16),A)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,B),image_int_fun_a_bool(F,A)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))
      | ~ is_fun949378684l_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_260_finite__subset__image]) ).

fof(f_367_2,plain,
    ! [U_890,U_889,U_888] :
      ( ? [U_887] :
          ( U_888 = image_int_fun_a_bool(U_890,U_887)
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_887))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_887),U_889)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_888),image_int_fun_a_bool(U_890,U_889)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_888))
      | ~ is_fun949378684l_bool(U_888) ),
    inference(variable_rename,[status(thm)],[f_367_1]) ).

fof(f_367_3,plain,
    ! [U_890,U_889,U_888] :
      ( ( U_888 = image_int_fun_a_bool(U_890,sK42(U_890,U_889,U_888))
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK42(U_890,U_889,U_888)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK42(U_890,U_889,U_888)),U_889)) )
      | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_888),image_int_fun_a_bool(U_890,U_889)))
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_888))
      | ~ is_fun949378684l_bool(U_888) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_887,sK42(U_890,U_889,U_888))],[f_367_2]) ).

fof(f_367_4,plain,
    ( ! [U_888,U_889,U_890] :
        ( U_888 = image_int_fun_a_bool(U_890,sK42(U_890,U_889,U_888))
        | ~ sP68(U_888,U_889,U_890) )
    & ! [U_888,U_889,U_890] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK42(U_890,U_889,U_888)))
        | ~ sP68(U_888,U_889,U_890) )
    & ! [U_888,U_889,U_890] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK42(U_890,U_889,U_888)),U_889))
        | ~ sP68(U_888,U_889,U_890) )
    & ! [U_888,U_889,U_890] :
        ( sP68(U_888,U_889,U_890)
        | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_888),image_int_fun_a_bool(U_890,U_889)))
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_888))
        | ~ is_fun949378684l_bool(U_888) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP68])],[f_367_3]) ).

cnf(f_367_5,plain,
    ( sP68(U_888,U_889,U_890)
    | ~ hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,U_888),image_int_fun_a_bool(U_890,U_889)))
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,U_888))
    | ~ is_fun949378684l_bool(U_888) ),
    inference(clausify,[status(thm)],[f_367_4]) ).

cnf(f_367_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK42(U_890,U_889,U_888)),U_889))
    | ~ sP68(U_888,U_889,U_890) ),
    inference(clausify,[status(thm)],[f_367_4]) ).

cnf(f_367_7,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK42(U_890,U_889,U_888)))
    | ~ sP68(U_888,U_889,U_890) ),
    inference(clausify,[status(thm)],[f_367_4]) ).

cnf(f_367_8,plain,
    ( U_888 = image_int_fun_a_bool(U_890,sK42(U_890,U_889,U_888))
    | ~ sP68(U_888,U_889,U_890) ),
    inference(clausify,[status(thm)],[f_367_4]) ).

fof(f_368_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_int_pname(F,C_16)
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,C_16))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_16),A)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),image_int_pname(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
      | ~ is_fun_pname_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_261_finite__subset__image]) ).

fof(f_368_2,plain,
    ! [U_894,U_893,U_892] :
      ( ? [U_891] :
          ( U_892 = image_int_pname(U_894,U_891)
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_891))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_891),U_893)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_892),image_int_pname(U_894,U_893)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_892))
      | ~ is_fun_pname_bool(U_892) ),
    inference(variable_rename,[status(thm)],[f_368_1]) ).

fof(f_368_3,plain,
    ! [U_894,U_893,U_892] :
      ( ( U_892 = image_int_pname(U_894,sK43(U_894,U_893,U_892))
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK43(U_894,U_893,U_892)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK43(U_894,U_893,U_892)),U_893)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_892),image_int_pname(U_894,U_893)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_892))
      | ~ is_fun_pname_bool(U_892) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_891,sK43(U_894,U_893,U_892))],[f_368_2]) ).

fof(f_368_4,plain,
    ( ! [U_892,U_894,U_893] :
        ( U_892 = image_int_pname(U_894,sK43(U_894,U_893,U_892))
        | ~ sP69(U_892,U_894,U_893) )
    & ! [U_892,U_894,U_893] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK43(U_894,U_893,U_892)))
        | ~ sP69(U_892,U_894,U_893) )
    & ! [U_892,U_894,U_893] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK43(U_894,U_893,U_892)),U_893))
        | ~ sP69(U_892,U_894,U_893) )
    & ! [U_892,U_894,U_893] :
        ( sP69(U_892,U_894,U_893)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_892),image_int_pname(U_894,U_893)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_892))
        | ~ is_fun_pname_bool(U_892) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP69])],[f_368_3]) ).

cnf(f_368_5,plain,
    ( sP69(U_892,U_894,U_893)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_892),image_int_pname(U_894,U_893)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_892))
    | ~ is_fun_pname_bool(U_892) ),
    inference(clausify,[status(thm)],[f_368_4]) ).

cnf(f_368_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,sK43(U_894,U_893,U_892)),U_893))
    | ~ sP69(U_892,U_894,U_893) ),
    inference(clausify,[status(thm)],[f_368_4]) ).

cnf(f_368_7,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK43(U_894,U_893,U_892)))
    | ~ sP69(U_892,U_894,U_893) ),
    inference(clausify,[status(thm)],[f_368_4]) ).

cnf(f_368_8,plain,
    ( U_892 = image_int_pname(U_894,sK43(U_894,U_893,U_892))
    | ~ sP69(U_892,U_894,U_893) ),
    inference(clausify,[status(thm)],[f_368_4]) ).

fof(f_369_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_pname_a(F,C_16)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_16))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_16),A))
          & is_fun_pname_bool(C_16) )
      | ~ 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_262_finite__subset__image]) ).

fof(f_369_2,plain,
    ! [U_898,U_897,U_896] :
      ( ? [U_895] :
          ( U_896 = image_pname_a(U_898,U_895)
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_895))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_895),U_897))
          & is_fun_pname_bool(U_895) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_896),image_pname_a(U_898,U_897)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_896))
      | ~ is_fun_a_bool(U_896) ),
    inference(variable_rename,[status(thm)],[f_369_1]) ).

fof(f_369_3,plain,
    ! [U_898,U_897,U_896] :
      ( ( U_896 = image_pname_a(U_898,sK44(U_898,U_897,U_896))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK44(U_898,U_897,U_896)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK44(U_898,U_897,U_896)),U_897))
        & is_fun_pname_bool(sK44(U_898,U_897,U_896)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_896),image_pname_a(U_898,U_897)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_896))
      | ~ is_fun_a_bool(U_896) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_895,sK44(U_898,U_897,U_896))],[f_369_2]) ).

fof(f_369_4,plain,
    ( ! [U_896,U_897,U_898] :
        ( U_896 = image_pname_a(U_898,sK44(U_898,U_897,U_896))
        | ~ sP70(U_896,U_897,U_898) )
    & ! [U_896,U_897,U_898] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK44(U_898,U_897,U_896)))
        | ~ sP70(U_896,U_897,U_898) )
    & ! [U_896,U_897,U_898] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK44(U_898,U_897,U_896)),U_897))
        | ~ sP70(U_896,U_897,U_898) )
    & ! [U_896,U_897,U_898] :
        ( is_fun_pname_bool(sK44(U_898,U_897,U_896))
        | ~ sP70(U_896,U_897,U_898) )
    & ! [U_896,U_897,U_898] :
        ( sP70(U_896,U_897,U_898)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_896),image_pname_a(U_898,U_897)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_896))
        | ~ is_fun_a_bool(U_896) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP70])],[f_369_3]) ).

cnf(f_369_5,plain,
    ( sP70(U_896,U_897,U_898)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_896),image_pname_a(U_898,U_897)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_896))
    | ~ is_fun_a_bool(U_896) ),
    inference(clausify,[status(thm)],[f_369_4]) ).

cnf(f_369_6,plain,
    ( is_fun_pname_bool(sK44(U_898,U_897,U_896))
    | ~ sP70(U_896,U_897,U_898) ),
    inference(clausify,[status(thm)],[f_369_4]) ).

cnf(f_369_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK44(U_898,U_897,U_896)),U_897))
    | ~ sP70(U_896,U_897,U_898) ),
    inference(clausify,[status(thm)],[f_369_4]) ).

cnf(f_369_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK44(U_898,U_897,U_896)))
    | ~ sP70(U_896,U_897,U_898) ),
    inference(clausify,[status(thm)],[f_369_4]) ).

cnf(f_369_9,plain,
    ( U_896 = image_pname_a(U_898,sK44(U_898,U_897,U_896))
    | ~ sP70(U_896,U_897,U_898) ),
    inference(clausify,[status(thm)],[f_369_4]) ).

fof(f_370_1,plain,
    ! [F,A,B] :
      ( ? [C_16] :
          ( B = image_nat_int(F,C_16)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,C_16))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_16),A)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_nat_int(F,A)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) ),
    inference(fof_nnf,[status(thm)],[fact_263_finite__subset__image]) ).

fof(f_370_2,plain,
    ! [U_902,U_901,U_900] :
      ( ? [U_899] :
          ( U_900 = image_nat_int(U_902,U_899)
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_899))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_899),U_901)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_900),image_nat_int(U_902,U_901)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_900)) ),
    inference(variable_rename,[status(thm)],[f_370_1]) ).

fof(f_370_3,plain,
    ! [U_902,U_901,U_900] :
      ( ( U_900 = image_nat_int(U_902,sK45(U_902,U_901,U_900))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK45(U_902,U_901,U_900)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK45(U_902,U_901,U_900)),U_901)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_900),image_nat_int(U_902,U_901)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_900)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_899,sK45(U_902,U_901,U_900))],[f_370_2]) ).

fof(f_370_4,plain,
    ( ! [U_901,U_900,U_902] :
        ( U_900 = image_nat_int(U_902,sK45(U_902,U_901,U_900))
        | ~ sP71(U_901,U_900,U_902) )
    & ! [U_901,U_900,U_902] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK45(U_902,U_901,U_900)))
        | ~ sP71(U_901,U_900,U_902) )
    & ! [U_901,U_900,U_902] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK45(U_902,U_901,U_900)),U_901))
        | ~ sP71(U_901,U_900,U_902) )
    & ! [U_901,U_900,U_902] :
        ( sP71(U_901,U_900,U_902)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_900),image_nat_int(U_902,U_901)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_900)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP71])],[f_370_3]) ).

cnf(f_370_5,plain,
    ( sP71(U_901,U_900,U_902)
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_900),image_nat_int(U_902,U_901)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_900)) ),
    inference(clausify,[status(thm)],[f_370_4]) ).

cnf(f_370_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK45(U_902,U_901,U_900)),U_901))
    | ~ sP71(U_901,U_900,U_902) ),
    inference(clausify,[status(thm)],[f_370_4]) ).

cnf(f_370_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK45(U_902,U_901,U_900)))
    | ~ sP71(U_901,U_900,U_902) ),
    inference(clausify,[status(thm)],[f_370_4]) ).

cnf(f_370_8,plain,
    ( U_900 = image_nat_int(U_902,sK45(U_902,U_901,U_900))
    | ~ sP71(U_901,U_900,U_902) ),
    inference(clausify,[status(thm)],[f_370_4]) ).

fof(f_371_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_1] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(F,N_1)),hAPP_n1025906991e_bool(F,hAPP_nat_nat(suc,N_1)))) ),
    inference(fof_nnf,[status(thm)],[fact_264_lift__Suc__mono__le]) ).

fof(f_371_2,plain,
    ! [U_906,U_905,U_904] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(U_904,U_906)),hAPP_n1025906991e_bool(U_904,U_905)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_906),U_905))
      | ? [U_903] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(U_904,U_903)),hAPP_n1025906991e_bool(U_904,hAPP_nat_nat(suc,U_903)))) ),
    inference(variable_rename,[status(thm)],[f_371_1]) ).

fof(f_371_3,plain,
    ! [U_906,U_905,U_904] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(U_904,U_906)),hAPP_n1025906991e_bool(U_904,U_905)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_906),U_905))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(U_904,sK46(U_906,U_905,U_904))),hAPP_n1025906991e_bool(U_904,hAPP_nat_nat(suc,sK46(U_906,U_905,U_904))))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_903,sK46(U_906,U_905,U_904))],[f_371_2]) ).

fof(f_371_4,plain,
    ! [U_904,U_905,U_906] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(U_904,U_906)),hAPP_n1025906991e_bool(U_904,U_905)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_906),U_905))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(U_904,sK46(U_906,U_905,U_904))),hAPP_n1025906991e_bool(U_904,hAPP_nat_nat(suc,sK46(U_906,U_905,U_904))))) ),
    inference(definitional_conversion,[status(esa)],[f_371_3]) ).

cnf(f_371_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(U_904,U_906)),hAPP_n1025906991e_bool(U_904,U_905)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_906),U_905))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(U_904,sK46(U_906,U_905,U_904))),hAPP_n1025906991e_bool(U_904,hAPP_nat_nat(suc,sK46(U_906,U_905,U_904))))) ),
    inference(clausify,[status(thm)],[f_371_4]) ).

fof(f_372_1,plain,
    ! [Na,N_3,F] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,Na)),hAPP_nat_bool(F,N_3)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
      | ? [N_1] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,N_1)),hAPP_nat_bool(F,hAPP_nat_nat(suc,N_1)))) ),
    inference(fof_nnf,[status(thm)],[fact_265_lift__Suc__mono__le]) ).

fof(f_372_2,plain,
    ! [U_910,U_909,U_908] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_908,U_910)),hAPP_nat_bool(U_908,U_909)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_910),U_909))
      | ? [U_907] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_908,U_907)),hAPP_nat_bool(U_908,hAPP_nat_nat(suc,U_907)))) ),
    inference(variable_rename,[status(thm)],[f_372_1]) ).

fof(f_372_3,plain,
    ! [U_910,U_909,U_908] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_908,U_910)),hAPP_nat_bool(U_908,U_909)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_910),U_909))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_908,sK47(U_910,U_909,U_908))),hAPP_nat_bool(U_908,hAPP_nat_nat(suc,sK47(U_910,U_909,U_908))))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_907,sK47(U_910,U_909,U_908))],[f_372_2]) ).

fof(f_372_4,plain,
    ! [U_908,U_909,U_910] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_908,U_910)),hAPP_nat_bool(U_908,U_909)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_910),U_909))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_908,sK47(U_910,U_909,U_908))),hAPP_nat_bool(U_908,hAPP_nat_nat(suc,sK47(U_910,U_909,U_908))))) ),
    inference(definitional_conversion,[status(esa)],[f_372_3]) ).

cnf(f_372_5,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_908,U_910)),hAPP_nat_bool(U_908,U_909)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_910),U_909))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_908,sK47(U_910,U_909,U_908))),hAPP_nat_bool(U_908,hAPP_nat_nat(suc,sK47(U_910,U_909,U_908))))) ),
    inference(clausify,[status(thm)],[f_372_4]) ).

fof(f_373_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_1] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(F,N_1)),hAPP_nat_fun_a_bool(F,hAPP_nat_nat(suc,N_1)))) ),
    inference(fof_nnf,[status(thm)],[fact_266_lift__Suc__mono__le]) ).

fof(f_373_2,plain,
    ! [U_914,U_913,U_912] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(U_912,U_914)),hAPP_nat_fun_a_bool(U_912,U_913)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_914),U_913))
      | ? [U_911] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(U_912,U_911)),hAPP_nat_fun_a_bool(U_912,hAPP_nat_nat(suc,U_911)))) ),
    inference(variable_rename,[status(thm)],[f_373_1]) ).

fof(f_373_3,plain,
    ! [U_914,U_913,U_912] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(U_912,U_914)),hAPP_nat_fun_a_bool(U_912,U_913)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_914),U_913))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(U_912,sK48(U_914,U_913,U_912))),hAPP_nat_fun_a_bool(U_912,hAPP_nat_nat(suc,sK48(U_914,U_913,U_912))))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_911,sK48(U_914,U_913,U_912))],[f_373_2]) ).

fof(f_373_4,plain,
    ! [U_912,U_913,U_914] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(U_912,U_914)),hAPP_nat_fun_a_bool(U_912,U_913)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_914),U_913))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(U_912,sK48(U_914,U_913,U_912))),hAPP_nat_fun_a_bool(U_912,hAPP_nat_nat(suc,sK48(U_914,U_913,U_912))))) ),
    inference(definitional_conversion,[status(esa)],[f_373_3]) ).

cnf(f_373_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(U_912,U_914)),hAPP_nat_fun_a_bool(U_912,U_913)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_914),U_913))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(U_912,sK48(U_914,U_913,U_912))),hAPP_nat_fun_a_bool(U_912,hAPP_nat_nat(suc,sK48(U_914,U_913,U_912))))) ),
    inference(clausify,[status(thm)],[f_373_4]) ).

fof(f_374_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_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,N_1)),hAPP_nat_nat(F,hAPP_nat_nat(suc,N_1)))) ),
    inference(fof_nnf,[status(thm)],[fact_267_lift__Suc__mono__le]) ).

fof(f_374_2,plain,
    ! [U_918,U_917,U_916] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_916,U_918)),hAPP_nat_nat(U_916,U_917)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_918),U_917))
      | ? [U_915] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_916,U_915)),hAPP_nat_nat(U_916,hAPP_nat_nat(suc,U_915)))) ),
    inference(variable_rename,[status(thm)],[f_374_1]) ).

fof(f_374_3,plain,
    ! [U_918,U_917,U_916] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_916,U_918)),hAPP_nat_nat(U_916,U_917)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_918),U_917))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_916,sK49(U_918,U_917,U_916))),hAPP_nat_nat(U_916,hAPP_nat_nat(suc,sK49(U_918,U_917,U_916))))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_915,sK49(U_918,U_917,U_916))],[f_374_2]) ).

fof(f_374_4,plain,
    ! [U_916,U_917,U_918] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_916,U_918)),hAPP_nat_nat(U_916,U_917)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_918),U_917))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_916,sK49(U_918,U_917,U_916))),hAPP_nat_nat(U_916,hAPP_nat_nat(suc,sK49(U_918,U_917,U_916))))) ),
    inference(definitional_conversion,[status(esa)],[f_374_3]) ).

cnf(f_374_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_916,U_918)),hAPP_nat_nat(U_916,U_917)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_918),U_917))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_916,sK49(U_918,U_917,U_916))),hAPP_nat_nat(U_916,hAPP_nat_nat(suc,sK49(U_918,U_917,U_916))))) ),
    inference(clausify,[status(thm)],[f_374_4]) ).

fof(f_375_1,plain,
    ! [Na,N_3,F] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(F,Na)),hAPP_nat_int(F,N_3)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
      | ? [N_1] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(F,N_1)),hAPP_nat_int(F,hAPP_nat_nat(suc,N_1)))) ),
    inference(fof_nnf,[status(thm)],[fact_268_lift__Suc__mono__le]) ).

fof(f_375_2,plain,
    ! [U_922,U_921,U_920] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(U_920,U_922)),hAPP_nat_int(U_920,U_921)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_922),U_921))
      | ? [U_919] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(U_920,U_919)),hAPP_nat_int(U_920,hAPP_nat_nat(suc,U_919)))) ),
    inference(variable_rename,[status(thm)],[f_375_1]) ).

fof(f_375_3,plain,
    ! [U_922,U_921,U_920] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(U_920,U_922)),hAPP_nat_int(U_920,U_921)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_922),U_921))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(U_920,sK50(U_922,U_921,U_920))),hAPP_nat_int(U_920,hAPP_nat_nat(suc,sK50(U_922,U_921,U_920))))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_919,sK50(U_922,U_921,U_920))],[f_375_2]) ).

fof(f_375_4,plain,
    ! [U_920,U_921,U_922] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(U_920,U_922)),hAPP_nat_int(U_920,U_921)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_922),U_921))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(U_920,sK50(U_922,U_921,U_920))),hAPP_nat_int(U_920,hAPP_nat_nat(suc,sK50(U_922,U_921,U_920))))) ),
    inference(definitional_conversion,[status(esa)],[f_375_3]) ).

cnf(f_375_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(U_920,U_922)),hAPP_nat_int(U_920,U_921)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_922),U_921))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(U_920,sK50(U_922,U_921,U_920))),hAPP_nat_int(U_920,hAPP_nat_nat(suc,sK50(U_922,U_921,U_920))))) ),
    inference(clausify,[status(thm)],[f_375_4]) ).

fof(f_376_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_1] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,N_1)),hAPP_n1699378549t_bool(F,hAPP_nat_nat(suc,N_1)))) ),
    inference(fof_nnf,[status(thm)],[fact_269_lift__Suc__mono__le]) ).

fof(f_376_2,plain,
    ! [U_926,U_925,U_924] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_924,U_926)),hAPP_n1699378549t_bool(U_924,U_925)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_926),U_925))
      | ? [U_923] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_924,U_923)),hAPP_n1699378549t_bool(U_924,hAPP_nat_nat(suc,U_923)))) ),
    inference(variable_rename,[status(thm)],[f_376_1]) ).

fof(f_376_3,plain,
    ! [U_926,U_925,U_924] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_924,U_926)),hAPP_n1699378549t_bool(U_924,U_925)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_926),U_925))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_924,sK51(U_926,U_925,U_924))),hAPP_n1699378549t_bool(U_924,hAPP_nat_nat(suc,sK51(U_926,U_925,U_924))))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_923,sK51(U_926,U_925,U_924))],[f_376_2]) ).

fof(f_376_4,plain,
    ! [U_924,U_925,U_926] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_924,U_926)),hAPP_n1699378549t_bool(U_924,U_925)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_926),U_925))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_924,sK51(U_926,U_925,U_924))),hAPP_n1699378549t_bool(U_924,hAPP_nat_nat(suc,sK51(U_926,U_925,U_924))))) ),
    inference(definitional_conversion,[status(esa)],[f_376_3]) ).

cnf(f_376_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_924,U_926)),hAPP_n1699378549t_bool(U_924,U_925)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_926),U_925))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(U_924,sK51(U_926,U_925,U_924))),hAPP_n1699378549t_bool(U_924,hAPP_nat_nat(suc,sK51(U_926,U_925,U_924))))) ),
    inference(clausify,[status(thm)],[f_376_4]) ).

fof(f_377_1,plain,
    ! [Na,N_3,F] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_n1082236369t_bool(F,Na)),hAPP_n1082236369t_bool(F,N_3)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
      | ? [N_1] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_n1082236369t_bool(F,N_1)),hAPP_n1082236369t_bool(F,hAPP_nat_nat(suc,N_1)))) ),
    inference(fof_nnf,[status(thm)],[fact_270_lift__Suc__mono__le]) ).

fof(f_377_2,plain,
    ! [U_930,U_929,U_928] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_n1082236369t_bool(U_928,U_930)),hAPP_n1082236369t_bool(U_928,U_929)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_930),U_929))
      | ? [U_927] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_n1082236369t_bool(U_928,U_927)),hAPP_n1082236369t_bool(U_928,hAPP_nat_nat(suc,U_927)))) ),
    inference(variable_rename,[status(thm)],[f_377_1]) ).

fof(f_377_3,plain,
    ! [U_930,U_929,U_928] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_n1082236369t_bool(U_928,U_930)),hAPP_n1082236369t_bool(U_928,U_929)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_930),U_929))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_n1082236369t_bool(U_928,sK52(U_930,U_929,U_928))),hAPP_n1082236369t_bool(U_928,hAPP_nat_nat(suc,sK52(U_930,U_929,U_928))))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_927,sK52(U_930,U_929,U_928))],[f_377_2]) ).

fof(f_377_4,plain,
    ! [U_928,U_929,U_930] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_n1082236369t_bool(U_928,U_930)),hAPP_n1082236369t_bool(U_928,U_929)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_930),U_929))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_n1082236369t_bool(U_928,sK52(U_930,U_929,U_928))),hAPP_n1082236369t_bool(U_928,hAPP_nat_nat(suc,sK52(U_930,U_929,U_928))))) ),
    inference(definitional_conversion,[status(esa)],[f_377_3]) ).

cnf(f_377_5,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_n1082236369t_bool(U_928,U_930)),hAPP_n1082236369t_bool(U_928,U_929)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_930),U_929))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_n1082236369t_bool(U_928,sK52(U_930,U_929,U_928))),hAPP_n1082236369t_bool(U_928,hAPP_nat_nat(suc,sK52(U_930,U_929,U_928))))) ),
    inference(clausify,[status(thm)],[f_377_4]) ).

fof(f_378_1,plain,
    ! [F,A] :
      ( ? [X_2] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,F)),hAPP_n1082236369t_bool(F,X_2))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) )
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(F,A)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_271_pigeonhole__infinite]) ).

fof(f_378_2,plain,
    ! [U_933,U_932] :
      ( ? [U_931] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_932)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,U_933)),hAPP_n1082236369t_bool(U_933,U_931))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_931),U_932)) )
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(U_933,U_932)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_932)) ),
    inference(variable_rename,[status(thm)],[f_378_1]) ).

fof(f_378_3,plain,
    ! [U_933,U_932] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_932)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,U_933)),hAPP_n1082236369t_bool(U_933,sK53(U_933,U_932)))))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK53(U_933,U_932)),U_932)) )
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(U_933,U_932)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_932)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_931,sK53(U_933,U_932))],[f_378_2]) ).

fof(f_378_4,plain,
    ( ! [U_932,U_933] :
        ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_932)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,U_933)),hAPP_n1082236369t_bool(U_933,sK53(U_933,U_932)))))))
        | ~ sP72(U_932,U_933) )
    & ! [U_932,U_933] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK53(U_933,U_932)),U_932))
        | ~ sP72(U_932,U_933) )
    & ! [U_932,U_933] :
        ( sP72(U_932,U_933)
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(U_933,U_932)))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_932)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP72])],[f_378_3]) ).

cnf(f_378_5,plain,
    ( sP72(U_932,U_933)
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_1556378401t_bool(U_933,U_932)))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_932)) ),
    inference(clausify,[status(thm)],[f_378_4]) ).

cnf(f_378_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK53(U_933,U_932)),U_932))
    | ~ sP72(U_932,U_933) ),
    inference(clausify,[status(thm)],[f_378_4]) ).

cnf(f_378_7,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_932)),hAPP_f274826591t_bool(cOMBC_620423604l_bool(cOMBB_1123824708ol_nat(fequal_fun_int_bool,U_933)),hAPP_n1082236369t_bool(U_933,sK53(U_933,U_932)))))))
    | ~ sP72(U_932,U_933) ),
    inference(clausify,[status(thm)],[f_378_4]) ).

fof(f_379_1,plain,
    ! [F,A] :
      ( ? [X_2] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,F)),hAPP_n1699378549t_bool(F,X_2))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(F,A)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_272_pigeonhole__infinite]) ).

fof(f_379_2,plain,
    ! [U_936,U_935] :
      ( ? [U_934] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_935)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,U_936)),hAPP_n1699378549t_bool(U_936,U_934))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_934),U_935)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(U_936,U_935)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_935)) ),
    inference(variable_rename,[status(thm)],[f_379_1]) ).

fof(f_379_3,plain,
    ! [U_936,U_935] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_935)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,U_936)),hAPP_n1699378549t_bool(U_936,sK54(U_936,U_935)))))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK54(U_936,U_935)),U_935)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(U_936,U_935)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_935)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_934,sK54(U_936,U_935))],[f_379_2]) ).

fof(f_379_4,plain,
    ( ! [U_935,U_936] :
        ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_935)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,U_936)),hAPP_n1699378549t_bool(U_936,sK54(U_936,U_935)))))))
        | ~ sP73(U_935,U_936) )
    & ! [U_935,U_936] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK54(U_936,U_935)),U_935))
        | ~ sP73(U_935,U_936) )
    & ! [U_935,U_936] :
        ( sP73(U_935,U_936)
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(U_936,U_935)))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_935)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP73])],[f_379_3]) ).

cnf(f_379_5,plain,
    ( sP73(U_935,U_936)
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(U_936,U_935)))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_935)) ),
    inference(clausify,[status(thm)],[f_379_4]) ).

cnf(f_379_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK54(U_936,U_935)),U_935))
    | ~ sP73(U_935,U_936) ),
    inference(clausify,[status(thm)],[f_379_4]) ).

cnf(f_379_7,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_935)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_2026977092ol_nat(fequal_fun_nat_bool,U_936)),hAPP_n1699378549t_bool(U_936,sK54(U_936,U_935)))))))
    | ~ sP73(U_935,U_936) ),
    inference(clausify,[status(thm)],[f_379_4]) ).

fof(f_380_1,plain,
    ! [F,A] :
      ( ? [X_2] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,F)),hAPP_n1025906991e_bool(F,X_2))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(F,A)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_273_pigeonhole__infinite]) ).

fof(f_380_2,plain,
    ! [U_939,U_938] :
      ( ? [U_937] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_938)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,U_939)),hAPP_n1025906991e_bool(U_939,U_937))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_937),U_938)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(U_939,U_938)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_938)) ),
    inference(variable_rename,[status(thm)],[f_380_1]) ).

fof(f_380_3,plain,
    ! [U_939,U_938] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_938)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,U_939)),hAPP_n1025906991e_bool(U_939,sK55(U_939,U_938)))))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK55(U_939,U_938)),U_938)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(U_939,U_938)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_938)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_937,sK55(U_939,U_938))],[f_380_2]) ).

fof(f_380_4,plain,
    ( ! [U_939,U_938] :
        ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_938)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,U_939)),hAPP_n1025906991e_bool(U_939,sK55(U_939,U_938)))))))
        | ~ sP74(U_939,U_938) )
    & ! [U_939,U_938] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK55(U_939,U_938)),U_938))
        | ~ sP74(U_939,U_938) )
    & ! [U_939,U_938] :
        ( sP74(U_939,U_938)
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(U_939,U_938)))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_938)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP74])],[f_380_3]) ).

cnf(f_380_5,plain,
    ( sP74(U_939,U_938)
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(U_939,U_938)))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_938)) ),
    inference(clausify,[status(thm)],[f_380_4]) ).

cnf(f_380_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK55(U_939,U_938)),U_938))
    | ~ sP74(U_939,U_938) ),
    inference(clausify,[status(thm)],[f_380_4]) ).

cnf(f_380_7,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_938)),hAPP_f1066163005t_bool(cOMBC_386238098l_bool(cOMBB_2117322052ol_nat(fequal533582459e_bool,U_939)),hAPP_n1025906991e_bool(U_939,sK55(U_939,U_938)))))))
    | ~ sP74(U_939,U_938) ),
    inference(clausify,[status(thm)],[f_380_4]) ).

fof(f_381_1,plain,
    ! [F,A] :
      ( ? [X_2] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,F)),hAPP_nat_fun_a_bool(F,X_2))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(F,A)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_274_pigeonhole__infinite]) ).

fof(f_381_2,plain,
    ! [U_942,U_941] :
      ( ? [U_940] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_941)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,U_942)),hAPP_nat_fun_a_bool(U_942,U_940))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_940),U_941)) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(U_942,U_941)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_941)) ),
    inference(variable_rename,[status(thm)],[f_381_1]) ).

fof(f_381_3,plain,
    ! [U_942,U_941] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_941)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,U_942)),hAPP_nat_fun_a_bool(U_942,sK56(U_942,U_941)))))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK56(U_942,U_941)),U_941)) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(U_942,U_941)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_941)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_940,sK56(U_942,U_941))],[f_381_2]) ).

fof(f_381_4,plain,
    ( ! [U_941,U_942] :
        ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_941)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,U_942)),hAPP_nat_fun_a_bool(U_942,sK56(U_942,U_941)))))))
        | ~ sP75(U_941,U_942) )
    & ! [U_941,U_942] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK56(U_942,U_941)),U_941))
        | ~ sP75(U_941,U_942) )
    & ! [U_941,U_942] :
        ( sP75(U_941,U_942)
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(U_942,U_941)))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_941)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP75])],[f_381_3]) ).

cnf(f_381_5,plain,
    ( sP75(U_941,U_942)
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(U_942,U_941)))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_941)) ),
    inference(clausify,[status(thm)],[f_381_4]) ).

cnf(f_381_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK56(U_942,U_941)),U_941))
    | ~ sP75(U_941,U_942) ),
    inference(clausify,[status(thm)],[f_381_4]) ).

cnf(f_381_7,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_941)),hAPP_f282463732t_bool(cOMBC_1928494297l_bool(cOMBB_1823939024ol_nat(fequal_fun_a_bool,U_942)),hAPP_nat_fun_a_bool(U_942,sK56(U_942,U_941)))))))
    | ~ sP75(U_941,U_942) ),
    inference(clausify,[status(thm)],[f_381_4]) ).

fof(f_382_1,plain,
    ! [F,A] :
      ( ? [X_2] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),A)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,F)),hAPP_int_a(F,X_2))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(F,A)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_275_pigeonhole__infinite]) ).

fof(f_382_2,plain,
    ! [U_945,U_944] :
      ( ? [U_943] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_944)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,U_945)),hAPP_int_a(U_945,U_943))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_943),U_944)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(U_945,U_944)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_944)) ),
    inference(variable_rename,[status(thm)],[f_382_1]) ).

fof(f_382_3,plain,
    ! [U_945,U_944] :
      ( ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_944)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,U_945)),hAPP_int_a(U_945,sK57(U_945,U_944)))))))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK57(U_945,U_944)),U_944)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(U_945,U_944)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_944)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_943,sK57(U_945,U_944))],[f_382_2]) ).

fof(f_382_4,plain,
    ( ! [U_944,U_945] :
        ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_944)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,U_945)),hAPP_int_a(U_945,sK57(U_945,U_944)))))))
        | ~ sP76(U_944,U_945) )
    & ! [U_944,U_945] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK57(U_945,U_944)),U_944))
        | ~ sP76(U_944,U_945) )
    & ! [U_944,U_945] :
        ( sP76(U_944,U_945)
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(U_945,U_944)))
        | hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_944)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP76])],[f_382_3]) ).

cnf(f_382_5,plain,
    ( sP76(U_944,U_945)
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_int_a(U_945,U_944)))
    | hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_944)) ),
    inference(clausify,[status(thm)],[f_382_4]) ).

cnf(f_382_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK57(U_945,U_944)),U_944))
    | ~ sP76(U_944,U_945) ),
    inference(clausify,[status(thm)],[f_382_4]) ).

cnf(f_382_7,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_944)),hAPP_a_fun_int_bool(cOMBC_int_a_bool(cOMBB_375279840ol_int(fequal_a,U_945)),hAPP_int_a(U_945,sK57(U_945,U_944)))))))
    | ~ sP76(U_944,U_945) ),
    inference(clausify,[status(thm)],[f_382_4]) ).

fof(f_383_1,plain,
    ! [F,A] :
      ( ? [X_2] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),A)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,F)),hAPP_i1948725293t_bool(F,X_2))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) )
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(F,A)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_276_pigeonhole__infinite]) ).

fof(f_383_2,plain,
    ! [U_948,U_947] :
      ( ? [U_946] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_947)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,U_948)),hAPP_i1948725293t_bool(U_948,U_946))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_946),U_947)) )
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(U_948,U_947)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_947)) ),
    inference(variable_rename,[status(thm)],[f_383_1]) ).

fof(f_383_3,plain,
    ! [U_948,U_947] :
      ( ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_947)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,U_948)),hAPP_i1948725293t_bool(U_948,sK58(U_948,U_947)))))))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK58(U_948,U_947)),U_947)) )
      | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(U_948,U_947)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_947)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_946,sK58(U_948,U_947))],[f_383_2]) ).

fof(f_383_4,plain,
    ( ! [U_947,U_948] :
        ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_947)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,U_948)),hAPP_i1948725293t_bool(U_948,sK58(U_948,U_947)))))))
        | ~ sP77(U_947,U_948) )
    & ! [U_947,U_948] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK58(U_948,U_947)),U_947))
        | ~ sP77(U_947,U_948) )
    & ! [U_947,U_948] :
        ( sP77(U_947,U_948)
        | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(U_948,U_947)))
        | hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_947)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP77])],[f_383_3]) ).

cnf(f_383_5,plain,
    ( sP77(U_947,U_948)
    | ~ hBOOL(hAPP_f215623910l_bool(finite1395289673t_bool,image_275383677t_bool(U_948,U_947)))
    | hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_947)) ),
    inference(clausify,[status(thm)],[f_383_4]) ).

cnf(f_383_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK58(U_948,U_947)),U_947))
    | ~ sP77(U_947,U_948) ),
    inference(clausify,[status(thm)],[f_383_4]) ).

cnf(f_383_7,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_947)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(cOMBB_1761098400ol_int(fequal_fun_int_bool,U_948)),hAPP_i1948725293t_bool(U_948,sK58(U_948,U_947)))))))
    | ~ sP77(U_947,U_948) ),
    inference(clausify,[status(thm)],[f_383_4]) ).

fof(f_384_1,plain,
    ! [F,A] :
      ( ? [X_2] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),A)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,F)),hAPP_i418383825t_bool(F,X_2))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(F,A)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_277_pigeonhole__infinite]) ).

fof(f_384_2,plain,
    ! [U_951,U_950] :
      ( ? [U_949] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_950)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,U_951)),hAPP_i418383825t_bool(U_951,U_949))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_949),U_950)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(U_951,U_950)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_950)) ),
    inference(variable_rename,[status(thm)],[f_384_1]) ).

fof(f_384_3,plain,
    ! [U_951,U_950] :
      ( ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_950)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,U_951)),hAPP_i418383825t_bool(U_951,sK59(U_951,U_950)))))))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK59(U_951,U_950)),U_950)) )
      | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(U_951,U_950)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_950)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_949,sK59(U_951,U_950))],[f_384_2]) ).

fof(f_384_4,plain,
    ( ! [U_951,U_950] :
        ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_950)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,U_951)),hAPP_i418383825t_bool(U_951,sK59(U_951,U_950)))))))
        | ~ sP78(U_951,U_950) )
    & ! [U_951,U_950] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK59(U_951,U_950)),U_950))
        | ~ sP78(U_951,U_950) )
    & ! [U_951,U_950] :
        ( sP78(U_951,U_950)
        | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(U_951,U_950)))
        | hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_950)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP78])],[f_384_3]) ).

cnf(f_384_5,plain,
    ( sP78(U_951,U_950)
    | ~ hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_892525857t_bool(U_951,U_950)))
    | hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_950)) ),
    inference(clausify,[status(thm)],[f_384_4]) ).

cnf(f_384_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK59(U_951,U_950)),U_950))
    | ~ sP78(U_951,U_950) ),
    inference(clausify,[status(thm)],[f_384_4]) ).

cnf(f_384_7,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_950)),hAPP_f183368031t_bool(cOMBC_1848398772l_bool(cOMBB_516767136ol_int(fequal_fun_nat_bool,U_951)),hAPP_i418383825t_bool(U_951,sK59(U_951,U_950)))))))
    | ~ sP78(U_951,U_950) ),
    inference(clausify,[status(thm)],[f_384_4]) ).

fof(f_385_1,plain,
    ! [F,A] :
      ( ? [X_2] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),A)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,F)),hAPP_i7355787e_bool(F,X_2))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(F,A)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_278_pigeonhole__infinite]) ).

fof(f_385_2,plain,
    ! [U_954,U_953] :
      ( ? [U_952] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_953)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,U_954)),hAPP_i7355787e_bool(U_954,U_952))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_952),U_953)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(U_954,U_953)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_953)) ),
    inference(variable_rename,[status(thm)],[f_385_1]) ).

fof(f_385_3,plain,
    ! [U_954,U_953] :
      ( ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_953)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,U_954)),hAPP_i7355787e_bool(U_954,sK60(U_954,U_953)))))))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK60(U_954,U_953)),U_953)) )
      | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(U_954,U_953)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_953)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_952,sK60(U_954,U_953))],[f_385_2]) ).

fof(f_385_4,plain,
    ( ! [U_953,U_954] :
        ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_953)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,U_954)),hAPP_i7355787e_bool(U_954,sK60(U_954,U_953)))))))
        | ~ sP79(U_953,U_954) )
    & ! [U_953,U_954] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK60(U_954,U_953)),U_953))
        | ~ sP79(U_953,U_954) )
    & ! [U_953,U_954] :
        ( sP79(U_953,U_954)
        | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(U_954,U_953)))
        | hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_953)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP79])],[f_385_3]) ).

cnf(f_385_5,plain,
    ( sP79(U_953,U_954)
    | ~ hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_637364955e_bool(U_954,U_953)))
    | hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_953)) ),
    inference(clausify,[status(thm)],[f_385_4]) ).

cnf(f_385_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK60(U_954,U_953)),U_953))
    | ~ sP79(U_953,U_954) ),
    inference(clausify,[status(thm)],[f_385_4]) ).

cnf(f_385_7,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_953)),hAPP_f449020825t_bool(cOMBC_316919022l_bool(cOMBB_607112096ol_int(fequal533582459e_bool,U_954)),hAPP_i7355787e_bool(U_954,sK60(U_954,U_953)))))))
    | ~ sP79(U_953,U_954) ),
    inference(clausify,[status(thm)],[f_385_4]) ).

fof(f_386_1,plain,
    ! [F,A] :
      ( ? [X_2] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),A)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,F)),hAPP_int_fun_a_bool(F,X_2))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(F,A)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_279_pigeonhole__infinite]) ).

fof(f_386_2,plain,
    ! [U_957,U_956] :
      ( ? [U_955] :
          ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_956)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,U_957)),hAPP_int_fun_a_bool(U_957,U_955))))))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_955),U_956)) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(U_957,U_956)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_956)) ),
    inference(variable_rename,[status(thm)],[f_386_1]) ).

fof(f_386_3,plain,
    ! [U_957,U_956] :
      ( ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_956)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,U_957)),hAPP_int_fun_a_bool(U_957,sK61(U_957,U_956)))))))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK61(U_957,U_956)),U_956)) )
      | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(U_957,U_956)))
      | hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_956)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_955,sK61(U_957,U_956))],[f_386_2]) ).

fof(f_386_4,plain,
    ( ! [U_956,U_957] :
        ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_956)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,U_957)),hAPP_int_fun_a_bool(U_957,sK61(U_957,U_956)))))))
        | ~ sP80(U_956,U_957) )
    & ! [U_956,U_957] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK61(U_957,U_956)),U_956))
        | ~ sP80(U_956,U_957) )
    & ! [U_956,U_957] :
        ( sP80(U_956,U_957)
        | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(U_957,U_956)))
        | hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_956)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP80])],[f_386_3]) ).

cnf(f_386_5,plain,
    ( sP80(U_956,U_957)
    | ~ hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_int_fun_a_bool(U_957,U_956)))
    | hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_956)) ),
    inference(clausify,[status(thm)],[f_386_4]) ).

cnf(f_386_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK61(U_957,U_956)),U_956))
    | ~ sP80(U_956,U_957) ),
    inference(clausify,[status(thm)],[f_386_4]) ).

cnf(f_386_7,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_956)),hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(cOMBB_313729068ol_int(fequal_fun_a_bool,U_957)),hAPP_int_fun_a_bool(U_957,sK61(U_957,U_956)))))))
    | ~ sP80(U_956,U_957) ),
    inference(clausify,[status(thm)],[f_386_4]) ).

fof(f_387_1,plain,
    ! [F,A] :
      ( ? [X_2] :
          ( ~ 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_2))))))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
          & is_pname(X_2) )
      | ~ 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_280_pigeonhole__infinite]) ).

fof(f_387_2,plain,
    ! [U_960,U_959] :
      ( ? [U_958] :
          ( ~ 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_959)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,U_960)),hAPP_pname_a(U_960,U_958))))))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_958),U_959))
          & is_pname(U_958) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(U_960,U_959)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_959)) ),
    inference(variable_rename,[status(thm)],[f_387_1]) ).

fof(f_387_3,plain,
    ! [U_960,U_959] :
      ( ( ~ 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_959)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,U_960)),hAPP_pname_a(U_960,sK62(U_960,U_959)))))))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK62(U_960,U_959)),U_959))
        & is_pname(sK62(U_960,U_959)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(U_960,U_959)))
      | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_959)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_958,sK62(U_960,U_959))],[f_387_2]) ).

fof(f_387_4,plain,
    ( ! [U_959,U_960] :
        ( ~ 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_959)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,U_960)),hAPP_pname_a(U_960,sK62(U_960,U_959)))))))
        | ~ sP81(U_959,U_960) )
    & ! [U_959,U_960] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK62(U_960,U_959)),U_959))
        | ~ sP81(U_959,U_960) )
    & ! [U_959,U_960] :
        ( is_pname(sK62(U_960,U_959))
        | ~ sP81(U_959,U_960) )
    & ! [U_959,U_960] :
        ( sP81(U_959,U_960)
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(U_960,U_959)))
        | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_959)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP81])],[f_387_3]) ).

cnf(f_387_5,plain,
    ( sP81(U_959,U_960)
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(U_960,U_959)))
    | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_959)) ),
    inference(clausify,[status(thm)],[f_387_4]) ).

cnf(f_387_6,plain,
    ( is_pname(sK62(U_960,U_959))
    | ~ sP81(U_959,U_960) ),
    inference(clausify,[status(thm)],[f_387_4]) ).

cnf(f_387_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK62(U_960,U_959)),U_959))
    | ~ sP81(U_959,U_960) ),
    inference(clausify,[status(thm)],[f_387_4]) ).

cnf(f_387_8,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_959)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,U_960)),hAPP_pname_a(U_960,sK62(U_960,U_959)))))))
    | ~ sP81(U_959,U_960) ),
    inference(clausify,[status(thm)],[f_387_4]) ).

fof(f_388_1,plain,
    ! [F,A] :
      ( ? [X_2] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,F)),hAPP_nat_int(F,X_2))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(F,A)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_281_pigeonhole__infinite]) ).

fof(f_388_2,plain,
    ! [U_963,U_962] :
      ( ? [U_961] :
          ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_962)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,U_963)),hAPP_nat_int(U_963,U_961))))))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_961),U_962)) )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(U_963,U_962)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_962)) ),
    inference(variable_rename,[status(thm)],[f_388_1]) ).

fof(f_388_3,plain,
    ! [U_963,U_962] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_962)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,U_963)),hAPP_nat_int(U_963,sK63(U_963,U_962)))))))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK63(U_963,U_962)),U_962)) )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(U_963,U_962)))
      | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_962)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_961,sK63(U_963,U_962))],[f_388_2]) ).

fof(f_388_4,plain,
    ( ! [U_962,U_963] :
        ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_962)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,U_963)),hAPP_nat_int(U_963,sK63(U_963,U_962)))))))
        | ~ sP82(U_962,U_963) )
    & ! [U_962,U_963] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK63(U_963,U_962)),U_962))
        | ~ sP82(U_962,U_963) )
    & ! [U_962,U_963] :
        ( sP82(U_962,U_963)
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(U_963,U_962)))
        | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_962)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP82])],[f_388_3]) ).

cnf(f_388_5,plain,
    ( sP82(U_962,U_963)
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(U_963,U_962)))
    | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_962)) ),
    inference(clausify,[status(thm)],[f_388_4]) ).

cnf(f_388_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK63(U_963,U_962)),U_962))
    | ~ sP82(U_962,U_963) ),
    inference(clausify,[status(thm)],[f_388_4]) ).

cnf(f_388_7,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_962)),hAPP_i418383825t_bool(cOMBC_nat_int_bool(cOMBB_1628441366ol_nat(fequal_int,U_963)),hAPP_nat_int(U_963,sK63(U_963,U_962)))))))
    | ~ sP82(U_962,U_963) ),
    inference(clausify,[status(thm)],[f_388_4]) ).

fof(f_389_1,plain,
    ! [A,B_3,F,X_1] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_3),image_nat_int(F,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
      | B_3 != hAPP_nat_int(F,X_1) ),
    inference(fof_nnf,[status(thm)],[fact_282_image__eqI]) ).

fof(f_389_2,plain,
    ! [U_967,U_966,U_965,U_964] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_966),image_nat_int(U_965,U_967)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_964),U_967))
      | U_966 != hAPP_nat_int(U_965,U_964) ),
    inference(variable_rename,[status(thm)],[f_389_1]) ).

fof(f_389_3,plain,
    ! [U_967,U_966,U_964,U_965] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_966),image_nat_int(U_965,U_967)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_964),U_967))
      | U_966 != hAPP_nat_int(U_965,U_964) ),
    inference(definitional_conversion,[status(esa)],[f_389_2]) ).

cnf(f_389_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_966),image_nat_int(U_965,U_967)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_964),U_967))
    | U_966 != hAPP_nat_int(U_965,U_964) ),
    inference(clausify,[status(thm)],[f_389_3]) ).

fof(f_390_1,plain,
    ! [A,B_3,F,X_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
      | B_3 != hAPP_pname_a(F,X_1) ),
    inference(fof_nnf,[status(thm)],[fact_283_image__eqI]) ).

fof(f_390_2,plain,
    ! [U_971,U_970,U_969,U_968] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_970),image_pname_a(U_969,U_971)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_968),U_971))
      | U_970 != hAPP_pname_a(U_969,U_968) ),
    inference(variable_rename,[status(thm)],[f_390_1]) ).

fof(f_390_3,plain,
    ! [U_969,U_968,U_970,U_971] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_970),image_pname_a(U_969,U_971)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_968),U_971))
      | U_970 != hAPP_pname_a(U_969,U_968) ),
    inference(definitional_conversion,[status(esa)],[f_390_2]) ).

cnf(f_390_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_970),image_pname_a(U_969,U_971)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_968),U_971))
    | U_970 != hAPP_pname_a(U_969,U_968) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

fof(f_391_1,plain,
    ! [A,B] :
      ( A = B
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_284_equalityI]) ).

fof(f_391_2,plain,
    ! [U_973,U_972] :
      ( U_973 = U_972
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_972),U_973))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_973),U_972)) ),
    inference(variable_rename,[status(thm)],[f_391_1]) ).

fof(f_391_3,plain,
    ! [U_973,U_972] :
      ( U_973 = U_972
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_972),U_973))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_973),U_972)) ),
    inference(definitional_conversion,[status(esa)],[f_391_2]) ).

cnf(f_391_4,plain,
    ( U_973 = U_972
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_972),U_973))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_973),U_972)) ),
    inference(clausify,[status(thm)],[f_391_3]) ).

fof(f_392_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_285_equalityI]) ).

fof(f_392_2,plain,
    ! [U_975,U_974] :
      ( U_975 = U_974
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_974),U_975))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_975),U_974)) ),
    inference(variable_rename,[status(thm)],[f_392_1]) ).

fof(f_392_3,plain,
    ! [U_974,U_975] :
      ( U_975 = U_974
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_974),U_975))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_975),U_974)) ),
    inference(definitional_conversion,[status(esa)],[f_392_2]) ).

cnf(f_392_4,plain,
    ( U_975 = U_974
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_974),U_975))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_975),U_974)) ),
    inference(clausify,[status(thm)],[f_392_3]) ).

fof(f_393_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_286_equalityI]) ).

fof(f_393_2,plain,
    ! [U_977,U_976] :
      ( U_977 = U_976
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_976),U_977))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_977),U_976))
      | ~ is_fun_a_bool(U_976)
      | ~ is_fun_a_bool(U_977) ),
    inference(variable_rename,[status(thm)],[f_393_1]) ).

fof(f_393_3,plain,
    ! [U_976,U_977] :
      ( U_977 = U_976
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_976),U_977))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_977),U_976))
      | ~ is_fun_a_bool(U_976)
      | ~ is_fun_a_bool(U_977) ),
    inference(definitional_conversion,[status(esa)],[f_393_2]) ).

cnf(f_393_4,plain,
    ( U_977 = U_976
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_976),U_977))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_977),U_976))
    | ~ is_fun_a_bool(U_976)
    | ~ is_fun_a_bool(U_977) ),
    inference(clausify,[status(thm)],[f_393_3]) ).

fof(f_394_1,plain,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),B))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),A))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_287_subsetD]) ).

fof(f_394_2,plain,
    ! [U_980,U_979,U_978] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_980),U_978))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_980),U_979))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_979),U_978)) ),
    inference(variable_rename,[status(thm)],[f_394_1]) ).

fof(f_394_3,plain,
    ! [U_980,U_978,U_979] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_980),U_978))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_980),U_979))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_979),U_978)) ),
    inference(definitional_conversion,[status(esa)],[f_394_2]) ).

cnf(f_394_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_980),U_978))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_980),U_979))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_979),U_978)) ),
    inference(clausify,[status(thm)],[f_394_3]) ).

fof(f_395_1,plain,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),A))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_288_subsetD]) ).

fof(f_395_2,plain,
    ! [U_983,U_982,U_981] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_983),U_981))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_983),U_982))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_982),U_981)) ),
    inference(variable_rename,[status(thm)],[f_395_1]) ).

fof(f_395_3,plain,
    ! [U_981,U_982,U_983] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_983),U_981))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_983),U_982))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_982),U_981)) ),
    inference(definitional_conversion,[status(esa)],[f_395_2]) ).

cnf(f_395_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_983),U_981))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_983),U_982))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_982),U_981)) ),
    inference(clausify,[status(thm)],[f_395_3]) ).

fof(f_396_1,plain,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),B))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),A))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_289_subsetD]) ).

fof(f_396_2,plain,
    ! [U_986,U_985,U_984] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_986),U_984))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_986),U_985))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_985),U_984)) ),
    inference(variable_rename,[status(thm)],[f_396_1]) ).

fof(f_396_3,plain,
    ! [U_984,U_985,U_986] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_986),U_984))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_986),U_985))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_985),U_984)) ),
    inference(definitional_conversion,[status(esa)],[f_396_2]) ).

cnf(f_396_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_986),U_984))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_986),U_985))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_985),U_984)) ),
    inference(clausify,[status(thm)],[f_396_3]) ).

fof(f_397_1,plain,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_290_subsetD]) ).

fof(f_397_2,plain,
    ! [U_989,U_988,U_987] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_989),U_987))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_989),U_988))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_988),U_987)) ),
    inference(variable_rename,[status(thm)],[f_397_1]) ).

fof(f_397_3,plain,
    ! [U_987,U_988,U_989] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_989),U_987))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_989),U_988))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_988),U_987)) ),
    inference(definitional_conversion,[status(esa)],[f_397_2]) ).

cnf(f_397_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_989),U_987))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_989),U_988))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_988),U_987)) ),
    inference(clausify,[status(thm)],[f_397_3]) ).

fof(f_398_1,plain,
    ! [B_3,A_2,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),B)))
      | ( A_2 != B_3
        & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_291_insertCI]) ).

fof(f_398_2,plain,
    ! [U_992,U_991,U_990] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_991),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_992),U_990)))
      | ( U_991 != U_992
        & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_991),U_990)) ) ),
    inference(variable_rename,[status(thm)],[f_398_1]) ).

fof(f_398_3,plain,
    ( ! [U_990,U_991,U_992] :
        ( U_991 != U_992
        | ~ sP83(U_990,U_991,U_992) )
    & ! [U_990,U_991,U_992] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_991),U_990))
        | ~ sP83(U_990,U_991,U_992) )
    & ! [U_990,U_991,U_992] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_991),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_992),U_990)))
        | sP83(U_990,U_991,U_992) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP83])],[f_398_2]) ).

cnf(f_398_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_991),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_992),U_990)))
    | sP83(U_990,U_991,U_992) ),
    inference(clausify,[status(thm)],[f_398_3]) ).

cnf(f_398_5,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_991),U_990))
    | ~ sP83(U_990,U_991,U_992) ),
    inference(clausify,[status(thm)],[f_398_3]) ).

cnf(f_398_6,plain,
    ( U_991 != U_992
    | ~ sP83(U_990,U_991,U_992) ),
    inference(clausify,[status(thm)],[f_398_3]) ).

fof(f_399_1,plain,
    ! [B_3,A_2,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_3),B)))
      | ( A_2 != B_3
        & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_292_insertCI]) ).

fof(f_399_2,plain,
    ! [U_995,U_994,U_993] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_994),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_995),U_993)))
      | ( U_994 != U_995
        & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_994),U_993)) ) ),
    inference(variable_rename,[status(thm)],[f_399_1]) ).

fof(f_399_3,plain,
    ( ! [U_994,U_993,U_995] :
        ( U_994 != U_995
        | ~ sP84(U_994,U_993,U_995) )
    & ! [U_994,U_993,U_995] :
        ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_994),U_993))
        | ~ sP84(U_994,U_993,U_995) )
    & ! [U_994,U_993,U_995] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_994),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_995),U_993)))
        | sP84(U_994,U_993,U_995) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP84])],[f_399_2]) ).

cnf(f_399_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_994),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_995),U_993)))
    | sP84(U_994,U_993,U_995) ),
    inference(clausify,[status(thm)],[f_399_3]) ).

cnf(f_399_5,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_994),U_993))
    | ~ sP84(U_994,U_993,U_995) ),
    inference(clausify,[status(thm)],[f_399_3]) ).

cnf(f_399_6,plain,
    ( U_994 != U_995
    | ~ sP84(U_994,U_993,U_995) ),
    inference(clausify,[status(thm)],[f_399_3]) ).

fof(f_400_1,plain,
    ! [B_3,A_2,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_3),B)))
      | ( A_2 != B_3
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_293_insertCI]) ).

fof(f_400_2,plain,
    ! [U_998,U_997,U_996] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_997),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_998),U_996)))
      | ( U_997 != U_998
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_997),U_996)) ) ),
    inference(variable_rename,[status(thm)],[f_400_1]) ).

fof(f_400_3,plain,
    ( ! [U_996,U_997,U_998] :
        ( U_997 != U_998
        | ~ sP85(U_996,U_997,U_998) )
    & ! [U_996,U_997,U_998] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_997),U_996))
        | ~ sP85(U_996,U_997,U_998) )
    & ! [U_996,U_997,U_998] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_997),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_998),U_996)))
        | sP85(U_996,U_997,U_998) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP85])],[f_400_2]) ).

cnf(f_400_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_997),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_998),U_996)))
    | sP85(U_996,U_997,U_998) ),
    inference(clausify,[status(thm)],[f_400_3]) ).

cnf(f_400_5,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_997),U_996))
    | ~ sP85(U_996,U_997,U_998) ),
    inference(clausify,[status(thm)],[f_400_3]) ).

cnf(f_400_6,plain,
    ( U_997 != U_998
    | ~ sP85(U_996,U_997,U_998) ),
    inference(clausify,[status(thm)],[f_400_3]) ).

fof(f_401_1,plain,
    ! [B_3,A_2,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_3),B)))
      | ( A_2 != B_3
        & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_294_insertCI]) ).

fof(f_401_2,plain,
    ! [U_1001,U_1000,U_999] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1000),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1001),U_999)))
      | ( U_1000 != U_1001
        & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1000),U_999)) ) ),
    inference(variable_rename,[status(thm)],[f_401_1]) ).

fof(f_401_3,plain,
    ( ! [U_1000,U_999,U_1001] :
        ( U_1000 != U_1001
        | ~ sP86(U_1000,U_999,U_1001) )
    & ! [U_1000,U_999,U_1001] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1000),U_999))
        | ~ sP86(U_1000,U_999,U_1001) )
    & ! [U_1000,U_999,U_1001] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1000),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1001),U_999)))
        | sP86(U_1000,U_999,U_1001) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP86])],[f_401_2]) ).

cnf(f_401_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1000),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1001),U_999)))
    | sP86(U_1000,U_999,U_1001) ),
    inference(clausify,[status(thm)],[f_401_3]) ).

cnf(f_401_5,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1000),U_999))
    | ~ sP86(U_1000,U_999,U_1001) ),
    inference(clausify,[status(thm)],[f_401_3]) ).

cnf(f_401_6,plain,
    ( U_1000 != U_1001
    | ~ sP86(U_1000,U_999,U_1001) ),
    inference(clausify,[status(thm)],[f_401_3]) ).

fof(f_402_1,plain,
    ! [A_2,B_3,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
      | A_2 = B_3
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),A)))
      | ~ is_a(B_3)
      | ~ is_a(A_2) ),
    inference(fof_nnf,[status(thm)],[fact_295_insertE]) ).

fof(f_402_2,plain,
    ! [U_1004,U_1003,U_1002] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1004),U_1002))
      | U_1004 = U_1003
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1004),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1003),U_1002)))
      | ~ is_a(U_1003)
      | ~ is_a(U_1004) ),
    inference(variable_rename,[status(thm)],[f_402_1]) ).

fof(f_402_3,plain,
    ! [U_1004,U_1003] :
      ( ! [U_1002] :
          ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1004),U_1002))
          | U_1004 = U_1003
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1004),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1003),U_1002))) )
      | ~ is_a(U_1003)
      | ~ is_a(U_1004) ),
    inference(miniscope,[status(thm)],[f_402_2]) ).

fof(f_402_4,plain,
    ! [U_1003,U_1002,U_1004] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1004),U_1002))
      | U_1004 = U_1003
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1004),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1003),U_1002)))
      | ~ is_a(U_1003)
      | ~ is_a(U_1004) ),
    inference(definitional_conversion,[status(esa)],[f_402_3]) ).

cnf(f_402_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1004),U_1002))
    | U_1004 = U_1003
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1004),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1003),U_1002)))
    | ~ is_a(U_1003)
    | ~ is_a(U_1004) ),
    inference(clausify,[status(thm)],[f_402_4]) ).

fof(f_403_1,plain,
    ! [A_2,B_3,A] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),A))
      | A_2 = B_3
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_3),A))) ),
    inference(fof_nnf,[status(thm)],[fact_296_insertE]) ).

fof(f_403_2,plain,
    ! [U_1007,U_1006,U_1005] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1007),U_1005))
      | U_1007 = U_1006
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1007),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1006),U_1005))) ),
    inference(variable_rename,[status(thm)],[f_403_1]) ).

fof(f_403_3,plain,
    ! [U_1006,U_1007,U_1005] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1007),U_1005))
      | U_1007 = U_1006
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1007),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1006),U_1005))) ),
    inference(definitional_conversion,[status(esa)],[f_403_2]) ).

cnf(f_403_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1007),U_1005))
    | U_1007 = U_1006
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1007),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1006),U_1005))) ),
    inference(clausify,[status(thm)],[f_403_3]) ).

fof(f_404_1,plain,
    ! [A_2,B_3,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A))
      | A_2 = B_3
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_3),A))) ),
    inference(fof_nnf,[status(thm)],[fact_297_insertE]) ).

fof(f_404_2,plain,
    ! [U_1010,U_1009,U_1008] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1010),U_1008))
      | U_1010 = U_1009
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1010),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1009),U_1008))) ),
    inference(variable_rename,[status(thm)],[f_404_1]) ).

fof(f_404_3,plain,
    ! [U_1008,U_1009,U_1010] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1010),U_1008))
      | U_1010 = U_1009
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1010),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1009),U_1008))) ),
    inference(definitional_conversion,[status(esa)],[f_404_2]) ).

cnf(f_404_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1010),U_1008))
    | U_1010 = U_1009
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1010),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1009),U_1008))) ),
    inference(clausify,[status(thm)],[f_404_3]) ).

fof(f_405_1,plain,
    ! [A_2,B_3,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A))
      | A_2 = B_3
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_3),A)))
      | ~ is_pname(B_3)
      | ~ is_pname(A_2) ),
    inference(fof_nnf,[status(thm)],[fact_298_insertE]) ).

fof(f_405_2,plain,
    ! [U_1013,U_1012,U_1011] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1013),U_1011))
      | U_1013 = U_1012
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1013),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1012),U_1011)))
      | ~ is_pname(U_1012)
      | ~ is_pname(U_1013) ),
    inference(variable_rename,[status(thm)],[f_405_1]) ).

fof(f_405_3,plain,
    ! [U_1013,U_1012] :
      ( ! [U_1011] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1013),U_1011))
          | U_1013 = U_1012
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1013),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1012),U_1011))) )
      | ~ is_pname(U_1012)
      | ~ is_pname(U_1013) ),
    inference(miniscope,[status(thm)],[f_405_2]) ).

fof(f_405_4,plain,
    ! [U_1011,U_1012,U_1013] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1013),U_1011))
      | U_1013 = U_1012
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1013),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1012),U_1011)))
      | ~ is_pname(U_1012)
      | ~ is_pname(U_1013) ),
    inference(definitional_conversion,[status(esa)],[f_405_3]) ).

cnf(f_405_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1013),U_1011))
    | U_1013 = U_1012
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1013),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1012),U_1011)))
    | ~ is_pname(U_1012)
    | ~ is_pname(U_1013) ),
    inference(clausify,[status(thm)],[f_405_4]) ).

fof(f_406_1,plain,
    ! [I_2,Pa,K] :
      ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,K),I_2)))
      | ? [N_1] :
          ( ~ hBOOL(hAPP_nat_bool(Pa,N_1))
          & hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_1))) )
      | ~ hBOOL(hAPP_nat_bool(Pa,K)) ),
    inference(fof_nnf,[status(thm)],[fact_299_zero__induct__lemma]) ).

fof(f_406_2,plain,
    ! [U_1017,U_1016,U_1015] :
      ( hBOOL(hAPP_nat_bool(U_1016,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_1015),U_1017)))
      | ? [U_1014] :
          ( ~ hBOOL(hAPP_nat_bool(U_1016,U_1014))
          & hBOOL(hAPP_nat_bool(U_1016,hAPP_nat_nat(suc,U_1014))) )
      | ~ hBOOL(hAPP_nat_bool(U_1016,U_1015)) ),
    inference(variable_rename,[status(thm)],[f_406_1]) ).

fof(f_406_3,plain,
    ! [U_1017,U_1016,U_1015] :
      ( hBOOL(hAPP_nat_bool(U_1016,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_1015),U_1017)))
      | ( ~ hBOOL(hAPP_nat_bool(U_1016,sK64(U_1017,U_1016,U_1015)))
        & hBOOL(hAPP_nat_bool(U_1016,hAPP_nat_nat(suc,sK64(U_1017,U_1016,U_1015)))) )
      | ~ hBOOL(hAPP_nat_bool(U_1016,U_1015)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_1014,sK64(U_1017,U_1016,U_1015))],[f_406_2]) ).

fof(f_406_4,plain,
    ( ! [U_1016,U_1017,U_1015] :
        ( ~ hBOOL(hAPP_nat_bool(U_1016,sK64(U_1017,U_1016,U_1015)))
        | ~ sP87(U_1016,U_1017,U_1015) )
    & ! [U_1016,U_1017,U_1015] :
        ( hBOOL(hAPP_nat_bool(U_1016,hAPP_nat_nat(suc,sK64(U_1017,U_1016,U_1015))))
        | ~ sP87(U_1016,U_1017,U_1015) )
    & ! [U_1016,U_1017,U_1015] :
        ( hBOOL(hAPP_nat_bool(U_1016,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_1015),U_1017)))
        | sP87(U_1016,U_1017,U_1015)
        | ~ hBOOL(hAPP_nat_bool(U_1016,U_1015)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP87])],[f_406_3]) ).

cnf(f_406_5,plain,
    ( hBOOL(hAPP_nat_bool(U_1016,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_1015),U_1017)))
    | sP87(U_1016,U_1017,U_1015)
    | ~ hBOOL(hAPP_nat_bool(U_1016,U_1015)) ),
    inference(clausify,[status(thm)],[f_406_4]) ).

cnf(f_406_6,plain,
    ( hBOOL(hAPP_nat_bool(U_1016,hAPP_nat_nat(suc,sK64(U_1017,U_1016,U_1015))))
    | ~ sP87(U_1016,U_1017,U_1015) ),
    inference(clausify,[status(thm)],[f_406_4]) ).

cnf(f_406_7,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_1016,sK64(U_1017,U_1016,U_1015)))
    | ~ sP87(U_1016,U_1017,U_1015) ),
    inference(clausify,[status(thm)],[f_406_4]) ).

fof(f_407_1,plain,
    ! [N,M_4] :
      ( ? [M_2] : M_4 = hAPP_nat_nat(suc,M_2)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N)),M_4)) ),
    inference(fof_nnf,[status(thm)],[fact_300_Suc__le__D]) ).

fof(f_407_2,plain,
    ! [U_1020,U_1019] :
      ( ? [U_1018] : U_1019 = hAPP_nat_nat(suc,U_1018)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_1020)),U_1019)) ),
    inference(variable_rename,[status(thm)],[f_407_1]) ).

fof(f_407_3,plain,
    ! [U_1020,U_1019] :
      ( U_1019 = hAPP_nat_nat(suc,sK65(U_1020,U_1019))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_1020)),U_1019)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_1018,sK65(U_1020,U_1019))],[f_407_2]) ).

fof(f_407_4,plain,
    ! [U_1020,U_1019] :
      ( U_1019 = hAPP_nat_nat(suc,sK65(U_1020,U_1019))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_1020)),U_1019)) ),
    inference(definitional_conversion,[status(esa)],[f_407_3]) ).

cnf(f_407_5,plain,
    ( U_1019 = hAPP_nat_nat(suc,sK65(U_1020,U_1019))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_1020)),U_1019)) ),
    inference(clausify,[status(thm)],[f_407_4]) ).

fof(f_408_1,plain,
    ! [X_1] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),X_1)),
    inference(fof_nnf,[status(thm)],[fact_301_order__refl]) ).

fof(f_408_2,plain,
    ! [U_1021] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1021),U_1021)),
    inference(variable_rename,[status(thm)],[f_408_1]) ).

fof(f_408_3,plain,
    ! [U_1021] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1021),U_1021)),
    inference(definitional_conversion,[status(esa)],[f_408_2]) ).

cnf(f_408_4,plain,
    hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1021),U_1021)),
    inference(clausify,[status(thm)],[f_408_3]) ).

fof(f_409_1,plain,
    ! [X_1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),X_1)),
    inference(fof_nnf,[status(thm)],[fact_302_order__refl]) ).

fof(f_409_2,plain,
    ! [U_1022] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1022),U_1022)),
    inference(variable_rename,[status(thm)],[f_409_1]) ).

fof(f_409_3,plain,
    ! [U_1022] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1022),U_1022)),
    inference(definitional_conversion,[status(esa)],[f_409_2]) ).

cnf(f_409_4,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1022),U_1022)),
    inference(clausify,[status(thm)],[f_409_3]) ).

fof(f_410_1,plain,
    ! [X_11] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_11),X_11)),
    inference(fof_nnf,[status(thm)],[fact_303_order__refl]) ).

fof(f_410_2,plain,
    ! [U_1023] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1023),U_1023)),
    inference(variable_rename,[status(thm)],[f_410_1]) ).

fof(f_410_3,plain,
    ! [U_1023] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1023),U_1023)),
    inference(definitional_conversion,[status(esa)],[f_410_2]) ).

cnf(f_410_4,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1023),U_1023)),
    inference(clausify,[status(thm)],[f_410_3]) ).

fof(f_411_1,plain,
    ! [X_11] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_11),X_11)),
    inference(fof_nnf,[status(thm)],[fact_304_order__refl]) ).

fof(f_411_2,plain,
    ! [U_1024] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1024),U_1024)),
    inference(variable_rename,[status(thm)],[f_411_1]) ).

fof(f_411_3,plain,
    ! [U_1024] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1024),U_1024)),
    inference(definitional_conversion,[status(esa)],[f_411_2]) ).

cnf(f_411_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1024),U_1024)),
    inference(clausify,[status(thm)],[f_411_3]) ).

fof(f_412_1,plain,
    ! [X_1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),X_1)),
    inference(fof_nnf,[status(thm)],[fact_305_order__refl]) ).

fof(f_412_2,plain,
    ! [U_1025] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1025),U_1025)),
    inference(variable_rename,[status(thm)],[f_412_1]) ).

fof(f_412_3,plain,
    ! [U_1025] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1025),U_1025)),
    inference(definitional_conversion,[status(esa)],[f_412_2]) ).

cnf(f_412_4,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1025),U_1025)),
    inference(clausify,[status(thm)],[f_412_3]) ).

fof(f_413_1,plain,
    ! [X_10,Y_9] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_9),X_10))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_10),Y_9)) ),
    inference(fof_nnf,[status(thm)],[fact_306_linorder__linear]) ).

fof(f_413_2,plain,
    ! [U_1027,U_1026] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1026),U_1027))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1027),U_1026)) ),
    inference(variable_rename,[status(thm)],[f_413_1]) ).

fof(f_413_3,plain,
    ! [U_1026,U_1027] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1026),U_1027))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1027),U_1026)) ),
    inference(definitional_conversion,[status(esa)],[f_413_2]) ).

cnf(f_413_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1026),U_1027))
    | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1027),U_1026)) ),
    inference(clausify,[status(thm)],[f_413_3]) ).

fof(f_414_1,plain,
    ! [X_10,Y_9] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_9),X_10))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_10),Y_9)) ),
    inference(fof_nnf,[status(thm)],[fact_307_linorder__linear]) ).

fof(f_414_2,plain,
    ! [U_1029,U_1028] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1028),U_1029))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1029),U_1028)) ),
    inference(variable_rename,[status(thm)],[f_414_1]) ).

fof(f_414_3,plain,
    ! [U_1028,U_1029] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1028),U_1029))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1029),U_1028)) ),
    inference(definitional_conversion,[status(esa)],[f_414_2]) ).

cnf(f_414_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1028),U_1029))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1029),U_1028)) ),
    inference(clausify,[status(thm)],[f_414_3]) ).

fof(f_415_1,plain,
    ! [X_1,Y_1] :
      ( ( X_1 = Y_1
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),X_1))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1)) )
      & ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),X_1))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1)) )
        | X_1 != Y_1 ) ),
    inference(fof_nnf,[status(thm)],[fact_308_order__eq__iff]) ).

fof(f_415_2,plain,
    ! [U_1031,U_1030] :
      ( ( U_1031 = U_1030
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1030),U_1031))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1031),U_1030)) )
      & ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1030),U_1031))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1031),U_1030)) )
        | U_1031 != U_1030 ) ),
    inference(variable_rename,[status(thm)],[f_415_1]) ).

fof(f_415_3,plain,
    ( ! [U_1035,U_1033] :
        ( U_1035 = U_1033
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1033),U_1035))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1035),U_1033)) )
    & ! [U_1034,U_1032] :
        ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1032),U_1034))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1034),U_1032)) )
        | U_1034 != U_1032 ) ),
    inference(miniscope,[status(thm)],[f_415_2]) ).

fof(f_415_4,plain,
    ( ! [U_1034,U_1032] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1032),U_1034))
        | ~ sP88(U_1034,U_1032) )
    & ! [U_1034,U_1032] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1034),U_1032))
        | ~ sP88(U_1034,U_1032) )
    & ! [U_1035,U_1033] :
        ( U_1035 = U_1033
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1033),U_1035))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1035),U_1033)) )
    & ! [U_1034,U_1032] :
        ( sP88(U_1034,U_1032)
        | U_1034 != U_1032 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP88])],[f_415_3]) ).

cnf(f_415_5,plain,
    ( sP88(U_1034,U_1032)
    | U_1034 != U_1032 ),
    inference(clausify,[status(thm)],[f_415_4]) ).

cnf(f_415_6,plain,
    ( U_1035 = U_1033
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1033),U_1035))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1035),U_1033)) ),
    inference(clausify,[status(thm)],[f_415_4]) ).

cnf(f_415_7,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1034),U_1032))
    | ~ sP88(U_1034,U_1032) ),
    inference(clausify,[status(thm)],[f_415_4]) ).

cnf(f_415_8,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1032),U_1034))
    | ~ sP88(U_1034,U_1032) ),
    inference(clausify,[status(thm)],[f_415_4]) ).

fof(f_416_1,plain,
    ! [X_1,Y_1] :
      ( ( X_1 = Y_1
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) )
      & ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) )
        | X_1 != Y_1 ) ),
    inference(fof_nnf,[status(thm)],[fact_309_order__eq__iff]) ).

fof(f_416_2,plain,
    ! [U_1037,U_1036] :
      ( ( U_1037 = U_1036
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1036),U_1037))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1037),U_1036)) )
      & ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1036),U_1037))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1037),U_1036)) )
        | U_1037 != U_1036 ) ),
    inference(variable_rename,[status(thm)],[f_416_1]) ).

fof(f_416_3,plain,
    ( ! [U_1041,U_1039] :
        ( U_1041 = U_1039
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1039),U_1041))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1041),U_1039)) )
    & ! [U_1040,U_1038] :
        ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1038),U_1040))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1040),U_1038)) )
        | U_1040 != U_1038 ) ),
    inference(miniscope,[status(thm)],[f_416_2]) ).

fof(f_416_4,plain,
    ( ! [U_1038,U_1040] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1038),U_1040))
        | ~ sP89(U_1038,U_1040) )
    & ! [U_1038,U_1040] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1040),U_1038))
        | ~ sP89(U_1038,U_1040) )
    & ! [U_1041,U_1039] :
        ( U_1041 = U_1039
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1039),U_1041))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1041),U_1039)) )
    & ! [U_1038,U_1040] :
        ( sP89(U_1038,U_1040)
        | U_1040 != U_1038 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP89])],[f_416_3]) ).

cnf(f_416_5,plain,
    ( sP89(U_1038,U_1040)
    | U_1040 != U_1038 ),
    inference(clausify,[status(thm)],[f_416_4]) ).

cnf(f_416_6,plain,
    ( U_1041 = U_1039
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1039),U_1041))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1041),U_1039)) ),
    inference(clausify,[status(thm)],[f_416_4]) ).

cnf(f_416_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1040),U_1038))
    | ~ sP89(U_1038,U_1040) ),
    inference(clausify,[status(thm)],[f_416_4]) ).

cnf(f_416_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1038),U_1040))
    | ~ sP89(U_1038,U_1040) ),
    inference(clausify,[status(thm)],[f_416_4]) ).

fof(f_417_1,plain,
    ! [X_1,Y_1] :
      ( ( X_1 = Y_1
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_1),X_1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)) )
      & ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_1),X_1))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)) )
        | X_1 != Y_1 ) ),
    inference(fof_nnf,[status(thm)],[fact_310_order__eq__iff]) ).

fof(f_417_2,plain,
    ! [U_1043,U_1042] :
      ( ( U_1043 = U_1042
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1042),U_1043))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1043),U_1042)) )
      & ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1042),U_1043))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1043),U_1042)) )
        | U_1043 != U_1042 ) ),
    inference(variable_rename,[status(thm)],[f_417_1]) ).

fof(f_417_3,plain,
    ( ! [U_1047,U_1045] :
        ( U_1047 = U_1045
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1045),U_1047))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1047),U_1045)) )
    & ! [U_1046,U_1044] :
        ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1044),U_1046))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1046),U_1044)) )
        | U_1046 != U_1044 ) ),
    inference(miniscope,[status(thm)],[f_417_2]) ).

fof(f_417_4,plain,
    ( ! [U_1046,U_1044] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1044),U_1046))
        | ~ sP90(U_1046,U_1044) )
    & ! [U_1046,U_1044] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1046),U_1044))
        | ~ sP90(U_1046,U_1044) )
    & ! [U_1047,U_1045] :
        ( U_1047 = U_1045
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1045),U_1047))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1047),U_1045)) )
    & ! [U_1046,U_1044] :
        ( sP90(U_1046,U_1044)
        | U_1046 != U_1044 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP90])],[f_417_3]) ).

cnf(f_417_5,plain,
    ( sP90(U_1046,U_1044)
    | U_1046 != U_1044 ),
    inference(clausify,[status(thm)],[f_417_4]) ).

cnf(f_417_6,plain,
    ( U_1047 = U_1045
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1045),U_1047))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1047),U_1045)) ),
    inference(clausify,[status(thm)],[f_417_4]) ).

cnf(f_417_7,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1046),U_1044))
    | ~ sP90(U_1046,U_1044) ),
    inference(clausify,[status(thm)],[f_417_4]) ).

cnf(f_417_8,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1044),U_1046))
    | ~ sP90(U_1046,U_1044) ),
    inference(clausify,[status(thm)],[f_417_4]) ).

fof(f_418_1,plain,
    ! [X_1,Y_1] :
      ( ( X_1 = Y_1
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) )
        | X_1 != Y_1 ) ),
    inference(fof_nnf,[status(thm)],[fact_311_order__eq__iff]) ).

fof(f_418_2,plain,
    ! [U_1049,U_1048] :
      ( ( U_1049 = U_1048
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1048),U_1049))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1049),U_1048)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1048),U_1049))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1049),U_1048)) )
        | U_1049 != U_1048 ) ),
    inference(variable_rename,[status(thm)],[f_418_1]) ).

fof(f_418_3,plain,
    ( ! [U_1053,U_1051] :
        ( U_1053 = U_1051
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1051),U_1053))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1053),U_1051)) )
    & ! [U_1052,U_1050] :
        ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1050),U_1052))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1052),U_1050)) )
        | U_1052 != U_1050 ) ),
    inference(miniscope,[status(thm)],[f_418_2]) ).

fof(f_418_4,plain,
    ( ! [U_1052,U_1050] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1050),U_1052))
        | ~ sP91(U_1052,U_1050) )
    & ! [U_1052,U_1050] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1052),U_1050))
        | ~ sP91(U_1052,U_1050) )
    & ! [U_1053,U_1051] :
        ( U_1053 = U_1051
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1051),U_1053))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1053),U_1051)) )
    & ! [U_1052,U_1050] :
        ( sP91(U_1052,U_1050)
        | U_1052 != U_1050 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP91])],[f_418_3]) ).

cnf(f_418_5,plain,
    ( sP91(U_1052,U_1050)
    | U_1052 != U_1050 ),
    inference(clausify,[status(thm)],[f_418_4]) ).

cnf(f_418_6,plain,
    ( U_1053 = U_1051
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1051),U_1053))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1053),U_1051)) ),
    inference(clausify,[status(thm)],[f_418_4]) ).

cnf(f_418_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1052),U_1050))
    | ~ sP91(U_1052,U_1050) ),
    inference(clausify,[status(thm)],[f_418_4]) ).

cnf(f_418_8,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1050),U_1052))
    | ~ sP91(U_1052,U_1050) ),
    inference(clausify,[status(thm)],[f_418_4]) ).

fof(f_419_1,plain,
    ! [X_1,Y_1] :
      ( ( ( X_1 = Y_1
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_1),X_1))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),Y_1)) )
        & ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_1),X_1))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),Y_1)) )
          | X_1 != Y_1 ) )
      | ~ is_fun_a_bool(Y_1)
      | ~ is_fun_a_bool(X_1) ),
    inference(fof_nnf,[status(thm)],[fact_312_order__eq__iff]) ).

fof(f_419_2,plain,
    ! [U_1055,U_1054] :
      ( ( ( U_1055 = U_1054
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1054),U_1055))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1055),U_1054)) )
        & ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1054),U_1055))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1055),U_1054)) )
          | U_1055 != U_1054 ) )
      | ~ is_fun_a_bool(U_1054)
      | ~ is_fun_a_bool(U_1055) ),
    inference(variable_rename,[status(thm)],[f_419_1]) ).

fof(f_419_3,plain,
    ( ! [U_1054,U_1055] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1054),U_1055))
        | ~ sP92(U_1054,U_1055) )
    & ! [U_1054,U_1055] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1055),U_1054))
        | ~ sP92(U_1054,U_1055) )
    & ! [U_1054,U_1055] :
        ( U_1055 = U_1054
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1054),U_1055))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1055),U_1054))
        | ~ sP93(U_1054,U_1055) )
    & ! [U_1054,U_1055] :
        ( sP92(U_1054,U_1055)
        | U_1055 != U_1054
        | ~ sP93(U_1054,U_1055) )
    & ! [U_1054,U_1055] :
        ( sP93(U_1054,U_1055)
        | ~ is_fun_a_bool(U_1054)
        | ~ is_fun_a_bool(U_1055) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP92,sP93])],[f_419_2]) ).

cnf(f_419_4,plain,
    ( sP93(U_1054,U_1055)
    | ~ is_fun_a_bool(U_1054)
    | ~ is_fun_a_bool(U_1055) ),
    inference(clausify,[status(thm)],[f_419_3]) ).

cnf(f_419_5,plain,
    ( sP92(U_1054,U_1055)
    | U_1055 != U_1054
    | ~ sP93(U_1054,U_1055) ),
    inference(clausify,[status(thm)],[f_419_3]) ).

cnf(f_419_6,plain,
    ( U_1055 = U_1054
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1054),U_1055))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1055),U_1054))
    | ~ sP93(U_1054,U_1055) ),
    inference(clausify,[status(thm)],[f_419_3]) ).

cnf(f_419_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1055),U_1054))
    | ~ sP92(U_1054,U_1055) ),
    inference(clausify,[status(thm)],[f_419_3]) ).

cnf(f_419_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1054),U_1055))
    | ~ sP92(U_1054,U_1055) ),
    inference(clausify,[status(thm)],[f_419_3]) ).

fof(f_420_1,plain,
    ! [X_1,Y_1] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1))
      | X_1 != Y_1 ),
    inference(fof_nnf,[status(thm)],[fact_313_order__eq__refl]) ).

fof(f_420_2,plain,
    ! [U_1057,U_1056] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1057),U_1056))
      | U_1057 != U_1056 ),
    inference(variable_rename,[status(thm)],[f_420_1]) ).

fof(f_420_3,plain,
    ! [U_1056,U_1057] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1057),U_1056))
      | U_1057 != U_1056 ),
    inference(definitional_conversion,[status(esa)],[f_420_2]) ).

cnf(f_420_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1057),U_1056))
    | U_1057 != U_1056 ),
    inference(clausify,[status(thm)],[f_420_3]) ).

fof(f_421_1,plain,
    ! [X_1,Y_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
      | X_1 != Y_1 ),
    inference(fof_nnf,[status(thm)],[fact_314_order__eq__refl]) ).

fof(f_421_2,plain,
    ! [U_1059,U_1058] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1059),U_1058))
      | U_1059 != U_1058 ),
    inference(variable_rename,[status(thm)],[f_421_1]) ).

fof(f_421_3,plain,
    ! [U_1059,U_1058] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1059),U_1058))
      | U_1059 != U_1058 ),
    inference(definitional_conversion,[status(esa)],[f_421_2]) ).

cnf(f_421_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1059),U_1058))
    | U_1059 != U_1058 ),
    inference(clausify,[status(thm)],[f_421_3]) ).

fof(f_422_1,plain,
    ! [X_9,Y_8] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_9),Y_8))
      | X_9 != Y_8 ),
    inference(fof_nnf,[status(thm)],[fact_315_order__eq__refl]) ).

fof(f_422_2,plain,
    ! [U_1061,U_1060] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1061),U_1060))
      | U_1061 != U_1060 ),
    inference(variable_rename,[status(thm)],[f_422_1]) ).

fof(f_422_3,plain,
    ! [U_1060,U_1061] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1061),U_1060))
      | U_1061 != U_1060 ),
    inference(definitional_conversion,[status(esa)],[f_422_2]) ).

cnf(f_422_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1061),U_1060))
    | U_1061 != U_1060 ),
    inference(clausify,[status(thm)],[f_422_3]) ).

fof(f_423_1,plain,
    ! [X_9,Y_8] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_9),Y_8))
      | X_9 != Y_8 ),
    inference(fof_nnf,[status(thm)],[fact_316_order__eq__refl]) ).

fof(f_423_2,plain,
    ! [U_1063,U_1062] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1063),U_1062))
      | U_1063 != U_1062 ),
    inference(variable_rename,[status(thm)],[f_423_1]) ).

fof(f_423_3,plain,
    ! [U_1063,U_1062] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1063),U_1062))
      | U_1063 != U_1062 ),
    inference(definitional_conversion,[status(esa)],[f_423_2]) ).

cnf(f_423_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1063),U_1062))
    | U_1063 != U_1062 ),
    inference(clausify,[status(thm)],[f_423_3]) ).

fof(f_424_1,plain,
    ! [X_1,Y_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),Y_1))
      | X_1 != Y_1 ),
    inference(fof_nnf,[status(thm)],[fact_317_order__eq__refl]) ).

fof(f_424_2,plain,
    ! [U_1065,U_1064] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1065),U_1064))
      | U_1065 != U_1064 ),
    inference(variable_rename,[status(thm)],[f_424_1]) ).

fof(f_424_3,plain,
    ! [U_1065,U_1064] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1065),U_1064))
      | U_1065 != U_1064 ),
    inference(definitional_conversion,[status(esa)],[f_424_2]) ).

cnf(f_424_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1065),U_1064))
    | U_1065 != U_1064 ),
    inference(clausify,[status(thm)],[f_424_3]) ).

fof(f_425_1,plain,
    ! [Y_1,X_1] :
      ( ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1))
          | X_1 != Y_1 )
        & ( X_1 = Y_1
          | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1)) ) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),X_1)) ),
    inference(fof_nnf,[status(thm)],[fact_318_order__antisym__conv]) ).

fof(f_425_2,plain,
    ! [U_1067,U_1066] :
      ( ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1066),U_1067))
          | U_1066 != U_1067 )
        & ( U_1066 = U_1067
          | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1066),U_1067)) ) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1067),U_1066)) ),
    inference(variable_rename,[status(thm)],[f_425_1]) ).

fof(f_425_3,plain,
    ( ! [U_1066,U_1067] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1066),U_1067))
        | U_1066 != U_1067
        | ~ sP94(U_1066,U_1067) )
    & ! [U_1066,U_1067] :
        ( U_1066 = U_1067
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1066),U_1067))
        | ~ sP94(U_1066,U_1067) )
    & ! [U_1066,U_1067] :
        ( sP94(U_1066,U_1067)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1067),U_1066)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP94])],[f_425_2]) ).

cnf(f_425_4,plain,
    ( sP94(U_1066,U_1067)
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1067),U_1066)) ),
    inference(clausify,[status(thm)],[f_425_3]) ).

cnf(f_425_5,plain,
    ( U_1066 = U_1067
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1066),U_1067))
    | ~ sP94(U_1066,U_1067) ),
    inference(clausify,[status(thm)],[f_425_3]) ).

cnf(f_425_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1066),U_1067))
    | U_1066 != U_1067
    | ~ sP94(U_1066,U_1067) ),
    inference(clausify,[status(thm)],[f_425_3]) ).

fof(f_426_1,plain,
    ! [Y_1,X_1] :
      ( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
          | X_1 != Y_1 )
        & ( X_1 = Y_1
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) ),
    inference(fof_nnf,[status(thm)],[fact_319_order__antisym__conv]) ).

fof(f_426_2,plain,
    ! [U_1069,U_1068] :
      ( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1068),U_1069))
          | U_1068 != U_1069 )
        & ( U_1068 = U_1069
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1068),U_1069)) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1069),U_1068)) ),
    inference(variable_rename,[status(thm)],[f_426_1]) ).

fof(f_426_3,plain,
    ( ! [U_1069,U_1068] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1068),U_1069))
        | U_1068 != U_1069
        | ~ sP95(U_1069,U_1068) )
    & ! [U_1069,U_1068] :
        ( U_1068 = U_1069
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1068),U_1069))
        | ~ sP95(U_1069,U_1068) )
    & ! [U_1069,U_1068] :
        ( sP95(U_1069,U_1068)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1069),U_1068)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP95])],[f_426_2]) ).

cnf(f_426_4,plain,
    ( sP95(U_1069,U_1068)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1069),U_1068)) ),
    inference(clausify,[status(thm)],[f_426_3]) ).

cnf(f_426_5,plain,
    ( U_1068 = U_1069
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1068),U_1069))
    | ~ sP95(U_1069,U_1068) ),
    inference(clausify,[status(thm)],[f_426_3]) ).

cnf(f_426_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1068),U_1069))
    | U_1068 != U_1069
    | ~ sP95(U_1069,U_1068) ),
    inference(clausify,[status(thm)],[f_426_3]) ).

fof(f_427_1,plain,
    ! [Y_1,X_1] :
      ( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1))
          | X_1 != Y_1 )
        & ( X_1 = Y_1
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_1)) ) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_1),X_1)) ),
    inference(fof_nnf,[status(thm)],[fact_320_order__antisym__conv]) ).

fof(f_427_2,plain,
    ! [U_1071,U_1070] :
      ( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1070),U_1071))
          | U_1070 != U_1071 )
        & ( U_1070 = U_1071
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1070),U_1071)) ) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1071),U_1070)) ),
    inference(variable_rename,[status(thm)],[f_427_1]) ).

fof(f_427_3,plain,
    ( ! [U_1071,U_1070] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1070),U_1071))
        | U_1070 != U_1071
        | ~ sP96(U_1071,U_1070) )
    & ! [U_1071,U_1070] :
        ( U_1070 = U_1071
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1070),U_1071))
        | ~ sP96(U_1071,U_1070) )
    & ! [U_1071,U_1070] :
        ( sP96(U_1071,U_1070)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1071),U_1070)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP96])],[f_427_2]) ).

cnf(f_427_4,plain,
    ( sP96(U_1071,U_1070)
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1071),U_1070)) ),
    inference(clausify,[status(thm)],[f_427_3]) ).

cnf(f_427_5,plain,
    ( U_1070 = U_1071
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1070),U_1071))
    | ~ sP96(U_1071,U_1070) ),
    inference(clausify,[status(thm)],[f_427_3]) ).

cnf(f_427_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1070),U_1071))
    | U_1070 != U_1071
    | ~ sP96(U_1071,U_1070) ),
    inference(clausify,[status(thm)],[f_427_3]) ).

fof(f_428_1,plain,
    ! [Y_1,X_1] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
          | X_1 != Y_1 )
        & ( X_1 = Y_1
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) ),
    inference(fof_nnf,[status(thm)],[fact_321_order__antisym__conv]) ).

fof(f_428_2,plain,
    ! [U_1073,U_1072] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1072),U_1073))
          | U_1072 != U_1073 )
        & ( U_1072 = U_1073
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1072),U_1073)) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1073),U_1072)) ),
    inference(variable_rename,[status(thm)],[f_428_1]) ).

fof(f_428_3,plain,
    ( ! [U_1073,U_1072] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1072),U_1073))
        | U_1072 != U_1073
        | ~ sP97(U_1073,U_1072) )
    & ! [U_1073,U_1072] :
        ( U_1072 = U_1073
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1072),U_1073))
        | ~ sP97(U_1073,U_1072) )
    & ! [U_1073,U_1072] :
        ( sP97(U_1073,U_1072)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1073),U_1072)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP97])],[f_428_2]) ).

cnf(f_428_4,plain,
    ( sP97(U_1073,U_1072)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1073),U_1072)) ),
    inference(clausify,[status(thm)],[f_428_3]) ).

cnf(f_428_5,plain,
    ( U_1072 = U_1073
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1072),U_1073))
    | ~ sP97(U_1073,U_1072) ),
    inference(clausify,[status(thm)],[f_428_3]) ).

cnf(f_428_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1072),U_1073))
    | U_1072 != U_1073
    | ~ sP97(U_1073,U_1072) ),
    inference(clausify,[status(thm)],[f_428_3]) ).

fof(f_429_1,plain,
    ! [Y_1,X_1] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),Y_1))
          | X_1 != Y_1 )
        & ( X_1 = Y_1
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),Y_1)) ) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_1),X_1))
      | ~ is_fun_a_bool(X_1)
      | ~ is_fun_a_bool(Y_1) ),
    inference(fof_nnf,[status(thm)],[fact_322_order__antisym__conv]) ).

fof(f_429_2,plain,
    ! [U_1075,U_1074] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1074),U_1075))
          | U_1074 != U_1075 )
        & ( U_1074 = U_1075
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1074),U_1075)) ) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1075),U_1074))
      | ~ is_fun_a_bool(U_1074)
      | ~ is_fun_a_bool(U_1075) ),
    inference(variable_rename,[status(thm)],[f_429_1]) ).

fof(f_429_3,plain,
    ( ! [U_1075,U_1074] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1074),U_1075))
        | U_1074 != U_1075
        | ~ sP98(U_1075,U_1074) )
    & ! [U_1075,U_1074] :
        ( U_1074 = U_1075
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1074),U_1075))
        | ~ sP98(U_1075,U_1074) )
    & ! [U_1075,U_1074] :
        ( sP98(U_1075,U_1074)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1075),U_1074))
        | ~ is_fun_a_bool(U_1074)
        | ~ is_fun_a_bool(U_1075) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP98])],[f_429_2]) ).

cnf(f_429_4,plain,
    ( sP98(U_1075,U_1074)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1075),U_1074))
    | ~ is_fun_a_bool(U_1074)
    | ~ is_fun_a_bool(U_1075) ),
    inference(clausify,[status(thm)],[f_429_3]) ).

cnf(f_429_5,plain,
    ( U_1074 = U_1075
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1074),U_1075))
    | ~ sP98(U_1075,U_1074) ),
    inference(clausify,[status(thm)],[f_429_3]) ).

cnf(f_429_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1074),U_1075))
    | U_1074 != U_1075
    | ~ sP98(U_1075,U_1074) ),
    inference(clausify,[status(thm)],[f_429_3]) ).

fof(f_430_1,plain,
    ! [C_6,A_2,B_3] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),C_6))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B_3),C_6))
      | A_2 != B_3 ),
    inference(fof_nnf,[status(thm)],[fact_323_ord__eq__le__trans]) ).

fof(f_430_2,plain,
    ! [U_1078,U_1077,U_1076] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1077),U_1078))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1076),U_1078))
      | U_1077 != U_1076 ),
    inference(variable_rename,[status(thm)],[f_430_1]) ).

fof(f_430_3,plain,
    ! [U_1077,U_1076,U_1078] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1077),U_1078))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1076),U_1078))
      | U_1077 != U_1076 ),
    inference(definitional_conversion,[status(esa)],[f_430_2]) ).

cnf(f_430_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1077),U_1078))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1076),U_1078))
    | U_1077 != U_1076 ),
    inference(clausify,[status(thm)],[f_430_3]) ).

fof(f_431_1,plain,
    ! [C_6,A_2,B_3] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),C_6))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_3),C_6))
      | A_2 != B_3 ),
    inference(fof_nnf,[status(thm)],[fact_324_ord__eq__le__trans]) ).

fof(f_431_2,plain,
    ! [U_1081,U_1080,U_1079] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1080),U_1081))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1079),U_1081))
      | U_1080 != U_1079 ),
    inference(variable_rename,[status(thm)],[f_431_1]) ).

fof(f_431_3,plain,
    ! [U_1080,U_1081,U_1079] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1080),U_1081))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1079),U_1081))
      | U_1080 != U_1079 ),
    inference(definitional_conversion,[status(esa)],[f_431_2]) ).

cnf(f_431_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1080),U_1081))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1079),U_1081))
    | U_1080 != U_1079 ),
    inference(clausify,[status(thm)],[f_431_3]) ).

fof(f_432_1,plain,
    ! [C_15,A_21,B_19] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_21),C_15))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_19),C_15))
      | A_21 != B_19 ),
    inference(fof_nnf,[status(thm)],[fact_325_ord__eq__le__trans]) ).

fof(f_432_2,plain,
    ! [U_1084,U_1083,U_1082] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1083),U_1084))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1082),U_1084))
      | U_1083 != U_1082 ),
    inference(variable_rename,[status(thm)],[f_432_1]) ).

fof(f_432_3,plain,
    ! [U_1083,U_1082,U_1084] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1083),U_1084))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1082),U_1084))
      | U_1083 != U_1082 ),
    inference(definitional_conversion,[status(esa)],[f_432_2]) ).

cnf(f_432_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1083),U_1084))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1082),U_1084))
    | U_1083 != U_1082 ),
    inference(clausify,[status(thm)],[f_432_3]) ).

fof(f_433_1,plain,
    ! [C_15,A_21,B_19] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_21),C_15))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_19),C_15))
      | A_21 != B_19 ),
    inference(fof_nnf,[status(thm)],[fact_326_ord__eq__le__trans]) ).

fof(f_433_2,plain,
    ! [U_1087,U_1086,U_1085] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1086),U_1087))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1085),U_1087))
      | U_1086 != U_1085 ),
    inference(variable_rename,[status(thm)],[f_433_1]) ).

fof(f_433_3,plain,
    ! [U_1085,U_1086,U_1087] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1086),U_1087))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1085),U_1087))
      | U_1086 != U_1085 ),
    inference(definitional_conversion,[status(esa)],[f_433_2]) ).

cnf(f_433_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1086),U_1087))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1085),U_1087))
    | U_1086 != U_1085 ),
    inference(clausify,[status(thm)],[f_433_3]) ).

fof(f_434_1,plain,
    ! [C_6,A_2,B_3] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_2),C_6))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_3),C_6))
      | A_2 != B_3 ),
    inference(fof_nnf,[status(thm)],[fact_327_ord__eq__le__trans]) ).

fof(f_434_2,plain,
    ! [U_1090,U_1089,U_1088] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1089),U_1090))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1088),U_1090))
      | U_1089 != U_1088 ),
    inference(variable_rename,[status(thm)],[f_434_1]) ).

fof(f_434_3,plain,
    ! [U_1088,U_1089,U_1090] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1089),U_1090))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1088),U_1090))
      | U_1089 != U_1088 ),
    inference(definitional_conversion,[status(esa)],[f_434_2]) ).

cnf(f_434_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1089),U_1090))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1088),U_1090))
    | U_1089 != U_1088 ),
    inference(clausify,[status(thm)],[f_434_3]) ).

fof(f_435_1,plain,
    ! [C_6,A_2,B_3] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_6),A_2))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_6),B_3))
      | A_2 != B_3 ),
    inference(fof_nnf,[status(thm)],[fact_328_xt1_I3_J]) ).

fof(f_435_2,plain,
    ! [U_1093,U_1092,U_1091] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1093),U_1092))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1093),U_1091))
      | U_1092 != U_1091 ),
    inference(variable_rename,[status(thm)],[f_435_1]) ).

fof(f_435_3,plain,
    ! [U_1091,U_1092,U_1093] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1093),U_1092))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1093),U_1091))
      | U_1092 != U_1091 ),
    inference(definitional_conversion,[status(esa)],[f_435_2]) ).

cnf(f_435_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1093),U_1092))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1093),U_1091))
    | U_1092 != U_1091 ),
    inference(clausify,[status(thm)],[f_435_3]) ).

fof(f_436_1,plain,
    ! [C_6,A_2,B_3] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_6),A_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_6),B_3))
      | A_2 != B_3 ),
    inference(fof_nnf,[status(thm)],[fact_329_xt1_I3_J]) ).

fof(f_436_2,plain,
    ! [U_1096,U_1095,U_1094] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1096),U_1095))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1096),U_1094))
      | U_1095 != U_1094 ),
    inference(variable_rename,[status(thm)],[f_436_1]) ).

fof(f_436_3,plain,
    ! [U_1094,U_1095,U_1096] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1096),U_1095))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1096),U_1094))
      | U_1095 != U_1094 ),
    inference(definitional_conversion,[status(esa)],[f_436_2]) ).

cnf(f_436_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1096),U_1095))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1096),U_1094))
    | U_1095 != U_1094 ),
    inference(clausify,[status(thm)],[f_436_3]) ).

fof(f_437_1,plain,
    ! [C_14,A_20,B_18] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_14),A_20))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_14),B_18))
      | A_20 != B_18 ),
    inference(fof_nnf,[status(thm)],[fact_330_xt1_I3_J]) ).

fof(f_437_2,plain,
    ! [U_1099,U_1098,U_1097] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1099),U_1098))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1099),U_1097))
      | U_1098 != U_1097 ),
    inference(variable_rename,[status(thm)],[f_437_1]) ).

fof(f_437_3,plain,
    ! [U_1097,U_1098,U_1099] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1099),U_1098))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1099),U_1097))
      | U_1098 != U_1097 ),
    inference(definitional_conversion,[status(esa)],[f_437_2]) ).

cnf(f_437_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1099),U_1098))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1099),U_1097))
    | U_1098 != U_1097 ),
    inference(clausify,[status(thm)],[f_437_3]) ).

fof(f_438_1,plain,
    ! [C_14,A_20,B_18] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_14),A_20))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_14),B_18))
      | A_20 != B_18 ),
    inference(fof_nnf,[status(thm)],[fact_331_xt1_I3_J]) ).

fof(f_438_2,plain,
    ! [U_1102,U_1101,U_1100] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1102),U_1101))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1102),U_1100))
      | U_1101 != U_1100 ),
    inference(variable_rename,[status(thm)],[f_438_1]) ).

fof(f_438_3,plain,
    ! [U_1101,U_1100,U_1102] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1102),U_1101))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1102),U_1100))
      | U_1101 != U_1100 ),
    inference(definitional_conversion,[status(esa)],[f_438_2]) ).

cnf(f_438_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1102),U_1101))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1102),U_1100))
    | U_1101 != U_1100 ),
    inference(clausify,[status(thm)],[f_438_3]) ).

fof(f_439_1,plain,
    ! [C_6,A_2,B_3] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_6),A_2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_6),B_3))
      | A_2 != B_3 ),
    inference(fof_nnf,[status(thm)],[fact_332_xt1_I3_J]) ).

fof(f_439_2,plain,
    ! [U_1105,U_1104,U_1103] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1105),U_1104))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1105),U_1103))
      | U_1104 != U_1103 ),
    inference(variable_rename,[status(thm)],[f_439_1]) ).

fof(f_439_3,plain,
    ! [U_1105,U_1103,U_1104] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1105),U_1104))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1105),U_1103))
      | U_1104 != U_1103 ),
    inference(definitional_conversion,[status(esa)],[f_439_2]) ).

cnf(f_439_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1105),U_1104))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1105),U_1103))
    | U_1104 != U_1103 ),
    inference(clausify,[status(thm)],[f_439_3]) ).

fof(f_440_1,plain,
    ! [C_6,A_2,B_3] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),C_6))
      | B_3 != C_6
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),B_3)) ),
    inference(fof_nnf,[status(thm)],[fact_333_ord__le__eq__trans]) ).

fof(f_440_2,plain,
    ! [U_1108,U_1107,U_1106] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1107),U_1108))
      | U_1106 != U_1108
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1107),U_1106)) ),
    inference(variable_rename,[status(thm)],[f_440_1]) ).

fof(f_440_3,plain,
    ! [U_1106,U_1107,U_1108] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1107),U_1108))
      | U_1106 != U_1108
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1107),U_1106)) ),
    inference(definitional_conversion,[status(esa)],[f_440_2]) ).

cnf(f_440_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1107),U_1108))
    | U_1106 != U_1108
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1107),U_1106)) ),
    inference(clausify,[status(thm)],[f_440_3]) ).

fof(f_441_1,plain,
    ! [C_6,A_2,B_3] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),C_6))
      | B_3 != C_6
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),B_3)) ),
    inference(fof_nnf,[status(thm)],[fact_334_ord__le__eq__trans]) ).

fof(f_441_2,plain,
    ! [U_1111,U_1110,U_1109] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1110),U_1111))
      | U_1109 != U_1111
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1110),U_1109)) ),
    inference(variable_rename,[status(thm)],[f_441_1]) ).

fof(f_441_3,plain,
    ! [U_1110,U_1109,U_1111] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1110),U_1111))
      | U_1109 != U_1111
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1110),U_1109)) ),
    inference(definitional_conversion,[status(esa)],[f_441_2]) ).

cnf(f_441_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1110),U_1111))
    | U_1109 != U_1111
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1110),U_1109)) ),
    inference(clausify,[status(thm)],[f_441_3]) ).

fof(f_442_1,plain,
    ! [C_13,A_19,B_17] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_19),C_13))
      | B_17 != C_13
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_19),B_17)) ),
    inference(fof_nnf,[status(thm)],[fact_335_ord__le__eq__trans]) ).

fof(f_442_2,plain,
    ! [U_1114,U_1113,U_1112] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1113),U_1114))
      | U_1112 != U_1114
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1113),U_1112)) ),
    inference(variable_rename,[status(thm)],[f_442_1]) ).

fof(f_442_3,plain,
    ! [U_1112,U_1113,U_1114] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1113),U_1114))
      | U_1112 != U_1114
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1113),U_1112)) ),
    inference(definitional_conversion,[status(esa)],[f_442_2]) ).

cnf(f_442_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1113),U_1114))
    | U_1112 != U_1114
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1113),U_1112)) ),
    inference(clausify,[status(thm)],[f_442_3]) ).

fof(f_443_1,plain,
    ! [C_13,A_19,B_17] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_19),C_13))
      | B_17 != C_13
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_19),B_17)) ),
    inference(fof_nnf,[status(thm)],[fact_336_ord__le__eq__trans]) ).

fof(f_443_2,plain,
    ! [U_1117,U_1116,U_1115] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1116),U_1117))
      | U_1115 != U_1117
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1116),U_1115)) ),
    inference(variable_rename,[status(thm)],[f_443_1]) ).

fof(f_443_3,plain,
    ! [U_1115,U_1116,U_1117] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1116),U_1117))
      | U_1115 != U_1117
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1116),U_1115)) ),
    inference(definitional_conversion,[status(esa)],[f_443_2]) ).

cnf(f_443_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1116),U_1117))
    | U_1115 != U_1117
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1116),U_1115)) ),
    inference(clausify,[status(thm)],[f_443_3]) ).

fof(f_444_1,plain,
    ! [C_6,A_2,B_3] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_2),C_6))
      | B_3 != C_6
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_2),B_3)) ),
    inference(fof_nnf,[status(thm)],[fact_337_ord__le__eq__trans]) ).

fof(f_444_2,plain,
    ! [U_1120,U_1119,U_1118] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1119),U_1120))
      | U_1118 != U_1120
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1119),U_1118)) ),
    inference(variable_rename,[status(thm)],[f_444_1]) ).

fof(f_444_3,plain,
    ! [U_1119,U_1118,U_1120] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1119),U_1120))
      | U_1118 != U_1120
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1119),U_1118)) ),
    inference(definitional_conversion,[status(esa)],[f_444_2]) ).

cnf(f_444_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1119),U_1120))
    | U_1118 != U_1120
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1119),U_1118)) ),
    inference(clausify,[status(thm)],[f_444_3]) ).

fof(f_445_1,plain,
    ! [C_6,B_3,A_2] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_6),A_2))
      | B_3 != C_6
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B_3),A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_338_xt1_I4_J]) ).

fof(f_445_2,plain,
    ! [U_1123,U_1122,U_1121] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1123),U_1121))
      | U_1122 != U_1123
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1122),U_1121)) ),
    inference(variable_rename,[status(thm)],[f_445_1]) ).

fof(f_445_3,plain,
    ! [U_1121,U_1122,U_1123] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1123),U_1121))
      | U_1122 != U_1123
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1122),U_1121)) ),
    inference(definitional_conversion,[status(esa)],[f_445_2]) ).

cnf(f_445_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1123),U_1121))
    | U_1122 != U_1123
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1122),U_1121)) ),
    inference(clausify,[status(thm)],[f_445_3]) ).

fof(f_446_1,plain,
    ! [C_6,B_3,A_2] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_6),A_2))
      | B_3 != C_6
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B_3),A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_339_xt1_I4_J]) ).

fof(f_446_2,plain,
    ! [U_1126,U_1125,U_1124] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1126),U_1124))
      | U_1125 != U_1126
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1125),U_1124)) ),
    inference(variable_rename,[status(thm)],[f_446_1]) ).

fof(f_446_3,plain,
    ! [U_1124,U_1125,U_1126] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1126),U_1124))
      | U_1125 != U_1126
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1125),U_1124)) ),
    inference(definitional_conversion,[status(esa)],[f_446_2]) ).

cnf(f_446_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1126),U_1124))
    | U_1125 != U_1126
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1125),U_1124)) ),
    inference(clausify,[status(thm)],[f_446_3]) ).

fof(f_447_1,plain,
    ! [C_12,B_16,A_18] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_12),A_18))
      | B_16 != C_12
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_16),A_18)) ),
    inference(fof_nnf,[status(thm)],[fact_340_xt1_I4_J]) ).

fof(f_447_2,plain,
    ! [U_1129,U_1128,U_1127] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1129),U_1127))
      | U_1128 != U_1129
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1128),U_1127)) ),
    inference(variable_rename,[status(thm)],[f_447_1]) ).

fof(f_447_3,plain,
    ! [U_1127,U_1128,U_1129] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1129),U_1127))
      | U_1128 != U_1129
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1128),U_1127)) ),
    inference(definitional_conversion,[status(esa)],[f_447_2]) ).

cnf(f_447_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1129),U_1127))
    | U_1128 != U_1129
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1128),U_1127)) ),
    inference(clausify,[status(thm)],[f_447_3]) ).

fof(f_448_1,plain,
    ! [C_12,B_16,A_18] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_12),A_18))
      | B_16 != C_12
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,B_16),A_18)) ),
    inference(fof_nnf,[status(thm)],[fact_341_xt1_I4_J]) ).

fof(f_448_2,plain,
    ! [U_1132,U_1131,U_1130] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1132),U_1130))
      | U_1131 != U_1132
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1131),U_1130)) ),
    inference(variable_rename,[status(thm)],[f_448_1]) ).

fof(f_448_3,plain,
    ! [U_1131,U_1130,U_1132] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1132),U_1130))
      | U_1131 != U_1132
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1131),U_1130)) ),
    inference(definitional_conversion,[status(esa)],[f_448_2]) ).

cnf(f_448_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1132),U_1130))
    | U_1131 != U_1132
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1131),U_1130)) ),
    inference(clausify,[status(thm)],[f_448_3]) ).

fof(f_449_1,plain,
    ! [C_6,B_3,A_2] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_6),A_2))
      | B_3 != C_6
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B_3),A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_342_xt1_I4_J]) ).

fof(f_449_2,plain,
    ! [U_1135,U_1134,U_1133] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1135),U_1133))
      | U_1134 != U_1135
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1134),U_1133)) ),
    inference(variable_rename,[status(thm)],[f_449_1]) ).

fof(f_449_3,plain,
    ! [U_1134,U_1133,U_1135] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1135),U_1133))
      | U_1134 != U_1135
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1134),U_1133)) ),
    inference(definitional_conversion,[status(esa)],[f_449_2]) ).

cnf(f_449_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1135),U_1133))
    | U_1134 != U_1135
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1134),U_1133)) ),
    inference(clausify,[status(thm)],[f_449_3]) ).

fof(f_450_1,plain,
    ! [X_1,Y_1] :
      ( X_1 = Y_1
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),X_1))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1)) ),
    inference(fof_nnf,[status(thm)],[fact_343_order__antisym]) ).

fof(f_450_2,plain,
    ! [U_1137,U_1136] :
      ( U_1137 = U_1136
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1136),U_1137))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1137),U_1136)) ),
    inference(variable_rename,[status(thm)],[f_450_1]) ).

fof(f_450_3,plain,
    ! [U_1137,U_1136] :
      ( U_1137 = U_1136
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1136),U_1137))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1137),U_1136)) ),
    inference(definitional_conversion,[status(esa)],[f_450_2]) ).

cnf(f_450_4,plain,
    ( U_1137 = U_1136
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1136),U_1137))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1137),U_1136)) ),
    inference(clausify,[status(thm)],[f_450_3]) ).

fof(f_451_1,plain,
    ! [X_1,Y_1] :
      ( X_1 = Y_1
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) ),
    inference(fof_nnf,[status(thm)],[fact_344_order__antisym]) ).

fof(f_451_2,plain,
    ! [U_1139,U_1138] :
      ( U_1139 = U_1138
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1138),U_1139))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1139),U_1138)) ),
    inference(variable_rename,[status(thm)],[f_451_1]) ).

fof(f_451_3,plain,
    ! [U_1138,U_1139] :
      ( U_1139 = U_1138
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1138),U_1139))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1139),U_1138)) ),
    inference(definitional_conversion,[status(esa)],[f_451_2]) ).

cnf(f_451_4,plain,
    ( U_1139 = U_1138
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1138),U_1139))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1139),U_1138)) ),
    inference(clausify,[status(thm)],[f_451_3]) ).

fof(f_452_1,plain,
    ! [X_8,Y_7] :
      ( X_8 = Y_7
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_7),X_8))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_8),Y_7)) ),
    inference(fof_nnf,[status(thm)],[fact_345_order__antisym]) ).

fof(f_452_2,plain,
    ! [U_1141,U_1140] :
      ( U_1141 = U_1140
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1140),U_1141))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1141),U_1140)) ),
    inference(variable_rename,[status(thm)],[f_452_1]) ).

fof(f_452_3,plain,
    ! [U_1140,U_1141] :
      ( U_1141 = U_1140
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1140),U_1141))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1141),U_1140)) ),
    inference(definitional_conversion,[status(esa)],[f_452_2]) ).

cnf(f_452_4,plain,
    ( U_1141 = U_1140
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1140),U_1141))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1141),U_1140)) ),
    inference(clausify,[status(thm)],[f_452_3]) ).

fof(f_453_1,plain,
    ! [X_8,Y_7] :
      ( X_8 = Y_7
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_7),X_8))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_8),Y_7)) ),
    inference(fof_nnf,[status(thm)],[fact_346_order__antisym]) ).

fof(f_453_2,plain,
    ! [U_1143,U_1142] :
      ( U_1143 = U_1142
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1142),U_1143))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1143),U_1142)) ),
    inference(variable_rename,[status(thm)],[f_453_1]) ).

fof(f_453_3,plain,
    ! [U_1142,U_1143] :
      ( U_1143 = U_1142
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1142),U_1143))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1143),U_1142)) ),
    inference(definitional_conversion,[status(esa)],[f_453_2]) ).

cnf(f_453_4,plain,
    ( U_1143 = U_1142
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1142),U_1143))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1143),U_1142)) ),
    inference(clausify,[status(thm)],[f_453_3]) ).

fof(f_454_1,plain,
    ! [X_1,Y_1] :
      ( X_1 = Y_1
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_1),X_1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),Y_1))
      | ~ is_fun_a_bool(Y_1)
      | ~ is_fun_a_bool(X_1) ),
    inference(fof_nnf,[status(thm)],[fact_347_order__antisym]) ).

fof(f_454_2,plain,
    ! [U_1145,U_1144] :
      ( U_1145 = U_1144
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1144),U_1145))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1145),U_1144))
      | ~ is_fun_a_bool(U_1144)
      | ~ is_fun_a_bool(U_1145) ),
    inference(variable_rename,[status(thm)],[f_454_1]) ).

fof(f_454_3,plain,
    ! [U_1144,U_1145] :
      ( U_1145 = U_1144
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1144),U_1145))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1145),U_1144))
      | ~ is_fun_a_bool(U_1144)
      | ~ is_fun_a_bool(U_1145) ),
    inference(definitional_conversion,[status(esa)],[f_454_2]) ).

cnf(f_454_4,plain,
    ( U_1145 = U_1144
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1144),U_1145))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1145),U_1144))
    | ~ is_fun_a_bool(U_1144)
    | ~ is_fun_a_bool(U_1145) ),
    inference(clausify,[status(thm)],[f_454_3]) ).

fof(f_455_1,plain,
    ! [Z_2,X_1,Y_1] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Z_2))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),Z_2))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1)) ),
    inference(fof_nnf,[status(thm)],[fact_348_order__trans]) ).

fof(f_455_2,plain,
    ! [U_1148,U_1147,U_1146] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1147),U_1148))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1146),U_1148))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1147),U_1146)) ),
    inference(variable_rename,[status(thm)],[f_455_1]) ).

fof(f_455_3,plain,
    ! [U_1148,U_1146,U_1147] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1147),U_1148))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1146),U_1148))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1147),U_1146)) ),
    inference(definitional_conversion,[status(esa)],[f_455_2]) ).

cnf(f_455_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1147),U_1148))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1146),U_1148))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1147),U_1146)) ),
    inference(clausify,[status(thm)],[f_455_3]) ).

fof(f_456_1,plain,
    ! [Z_2,X_1,Y_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Z_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),Z_2))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1)) ),
    inference(fof_nnf,[status(thm)],[fact_349_order__trans]) ).

fof(f_456_2,plain,
    ! [U_1151,U_1150,U_1149] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1150),U_1151))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1149),U_1151))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1150),U_1149)) ),
    inference(variable_rename,[status(thm)],[f_456_1]) ).

fof(f_456_3,plain,
    ! [U_1150,U_1149,U_1151] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1150),U_1151))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1149),U_1151))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1150),U_1149)) ),
    inference(definitional_conversion,[status(esa)],[f_456_2]) ).

cnf(f_456_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1150),U_1151))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1149),U_1151))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1150),U_1149)) ),
    inference(clausify,[status(thm)],[f_456_3]) ).

fof(f_457_1,plain,
    ! [Z_6,X_7,Y_6] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_7),Z_6))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_6),Z_6))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_7),Y_6)) ),
    inference(fof_nnf,[status(thm)],[fact_350_order__trans]) ).

fof(f_457_2,plain,
    ! [U_1154,U_1153,U_1152] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1153),U_1154))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1152),U_1154))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1153),U_1152)) ),
    inference(variable_rename,[status(thm)],[f_457_1]) ).

fof(f_457_3,plain,
    ! [U_1152,U_1153,U_1154] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1153),U_1154))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1152),U_1154))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1153),U_1152)) ),
    inference(definitional_conversion,[status(esa)],[f_457_2]) ).

cnf(f_457_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1153),U_1154))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1152),U_1154))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1153),U_1152)) ),
    inference(clausify,[status(thm)],[f_457_3]) ).

fof(f_458_1,plain,
    ! [Z_6,X_7,Y_6] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_7),Z_6))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_6),Z_6))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_7),Y_6)) ),
    inference(fof_nnf,[status(thm)],[fact_351_order__trans]) ).

fof(f_458_2,plain,
    ! [U_1157,U_1156,U_1155] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1156),U_1157))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1155),U_1157))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1156),U_1155)) ),
    inference(variable_rename,[status(thm)],[f_458_1]) ).

fof(f_458_3,plain,
    ! [U_1155,U_1156,U_1157] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1156),U_1157))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1155),U_1157))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1156),U_1155)) ),
    inference(definitional_conversion,[status(esa)],[f_458_2]) ).

cnf(f_458_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1156),U_1157))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1155),U_1157))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1156),U_1155)) ),
    inference(clausify,[status(thm)],[f_458_3]) ).

fof(f_459_1,plain,
    ! [Z_2,X_1,Y_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),Z_2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_1),Z_2))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),Y_1)) ),
    inference(fof_nnf,[status(thm)],[fact_352_order__trans]) ).

fof(f_459_2,plain,
    ! [U_1160,U_1159,U_1158] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1159),U_1160))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1158),U_1160))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1159),U_1158)) ),
    inference(variable_rename,[status(thm)],[f_459_1]) ).

fof(f_459_3,plain,
    ! [U_1159,U_1158,U_1160] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1159),U_1160))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1158),U_1160))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1159),U_1158)) ),
    inference(definitional_conversion,[status(esa)],[f_459_2]) ).

cnf(f_459_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1159),U_1160))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1158),U_1160))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1159),U_1158)) ),
    inference(clausify,[status(thm)],[f_459_3]) ).

fof(f_460_1,plain,
    ! [Y_1,X_1] :
      ( X_1 = Y_1
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,X_1),Y_1))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),X_1)) ),
    inference(fof_nnf,[status(thm)],[fact_353_xt1_I5_J]) ).

fof(f_460_2,plain,
    ! [U_1162,U_1161] :
      ( U_1161 = U_1162
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1161),U_1162))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1162),U_1161)) ),
    inference(variable_rename,[status(thm)],[f_460_1]) ).

fof(f_460_3,plain,
    ! [U_1161,U_1162] :
      ( U_1161 = U_1162
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1161),U_1162))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1162),U_1161)) ),
    inference(definitional_conversion,[status(esa)],[f_460_2]) ).

cnf(f_460_4,plain,
    ( U_1161 = U_1162
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1161),U_1162))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1162),U_1161)) ),
    inference(clausify,[status(thm)],[f_460_3]) ).

fof(f_461_1,plain,
    ! [Y_1,X_1] :
      ( X_1 = Y_1
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_1),Y_1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) ),
    inference(fof_nnf,[status(thm)],[fact_354_xt1_I5_J]) ).

fof(f_461_2,plain,
    ! [U_1164,U_1163] :
      ( U_1163 = U_1164
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1163),U_1164))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1164),U_1163)) ),
    inference(variable_rename,[status(thm)],[f_461_1]) ).

fof(f_461_3,plain,
    ! [U_1163,U_1164] :
      ( U_1163 = U_1164
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1163),U_1164))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1164),U_1163)) ),
    inference(definitional_conversion,[status(esa)],[f_461_2]) ).

cnf(f_461_4,plain,
    ( U_1163 = U_1164
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1163),U_1164))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1164),U_1163)) ),
    inference(clausify,[status(thm)],[f_461_3]) ).

fof(f_462_1,plain,
    ! [Y_5,X_6] :
      ( X_6 = Y_5
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_6),Y_5))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_5),X_6)) ),
    inference(fof_nnf,[status(thm)],[fact_355_xt1_I5_J]) ).

fof(f_462_2,plain,
    ! [U_1166,U_1165] :
      ( U_1165 = U_1166
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1165),U_1166))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1166),U_1165)) ),
    inference(variable_rename,[status(thm)],[f_462_1]) ).

fof(f_462_3,plain,
    ! [U_1165,U_1166] :
      ( U_1165 = U_1166
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1165),U_1166))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1166),U_1165)) ),
    inference(definitional_conversion,[status(esa)],[f_462_2]) ).

cnf(f_462_4,plain,
    ( U_1165 = U_1166
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1165),U_1166))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1166),U_1165)) ),
    inference(clausify,[status(thm)],[f_462_3]) ).

fof(f_463_1,plain,
    ! [Y_5,X_6] :
      ( X_6 = Y_5
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_6),Y_5))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_5),X_6)) ),
    inference(fof_nnf,[status(thm)],[fact_356_xt1_I5_J]) ).

fof(f_463_2,plain,
    ! [U_1168,U_1167] :
      ( U_1167 = U_1168
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1167),U_1168))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1168),U_1167)) ),
    inference(variable_rename,[status(thm)],[f_463_1]) ).

fof(f_463_3,plain,
    ! [U_1167,U_1168] :
      ( U_1167 = U_1168
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1167),U_1168))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1168),U_1167)) ),
    inference(definitional_conversion,[status(esa)],[f_463_2]) ).

cnf(f_463_4,plain,
    ( U_1167 = U_1168
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1167),U_1168))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1168),U_1167)) ),
    inference(clausify,[status(thm)],[f_463_3]) ).

fof(f_464_1,plain,
    ! [Y_1,X_1] :
      ( X_1 = Y_1
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_1),Y_1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_1),X_1))
      | ~ is_fun_a_bool(X_1)
      | ~ is_fun_a_bool(Y_1) ),
    inference(fof_nnf,[status(thm)],[fact_357_xt1_I5_J]) ).

fof(f_464_2,plain,
    ! [U_1170,U_1169] :
      ( U_1169 = U_1170
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1169),U_1170))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1170),U_1169))
      | ~ is_fun_a_bool(U_1169)
      | ~ is_fun_a_bool(U_1170) ),
    inference(variable_rename,[status(thm)],[f_464_1]) ).

fof(f_464_3,plain,
    ! [U_1170,U_1169] :
      ( U_1169 = U_1170
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1169),U_1170))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1170),U_1169))
      | ~ is_fun_a_bool(U_1169)
      | ~ is_fun_a_bool(U_1170) ),
    inference(definitional_conversion,[status(esa)],[f_464_2]) ).

cnf(f_464_4,plain,
    ( U_1169 = U_1170
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1169),U_1170))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1170),U_1169))
    | ~ is_fun_a_bool(U_1169)
    | ~ is_fun_a_bool(U_1170) ),
    inference(clausify,[status(thm)],[f_464_3]) ).

fof(f_465_1,plain,
    ! [Z_2,Y_1,X_1] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Z_2),X_1))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Z_2),Y_1))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,Y_1),X_1)) ),
    inference(fof_nnf,[status(thm)],[fact_358_xt1_I6_J]) ).

fof(f_465_2,plain,
    ! [U_1173,U_1172,U_1171] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1173),U_1171))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1173),U_1172))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1172),U_1171)) ),
    inference(variable_rename,[status(thm)],[f_465_1]) ).

fof(f_465_3,plain,
    ! [U_1173,U_1172,U_1171] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1173),U_1171))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1173),U_1172))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1172),U_1171)) ),
    inference(definitional_conversion,[status(esa)],[f_465_2]) ).

cnf(f_465_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1173),U_1171))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1173),U_1172))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1172),U_1171)) ),
    inference(clausify,[status(thm)],[f_465_3]) ).

fof(f_466_1,plain,
    ! [Z_2,Y_1,X_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_2),X_1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Z_2),Y_1))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,Y_1),X_1)) ),
    inference(fof_nnf,[status(thm)],[fact_359_xt1_I6_J]) ).

fof(f_466_2,plain,
    ! [U_1176,U_1175,U_1174] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1176),U_1174))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1176),U_1175))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1175),U_1174)) ),
    inference(variable_rename,[status(thm)],[f_466_1]) ).

fof(f_466_3,plain,
    ! [U_1174,U_1175,U_1176] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1176),U_1174))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1176),U_1175))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1175),U_1174)) ),
    inference(definitional_conversion,[status(esa)],[f_466_2]) ).

cnf(f_466_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1176),U_1174))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1176),U_1175))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1175),U_1174)) ),
    inference(clausify,[status(thm)],[f_466_3]) ).

fof(f_467_1,plain,
    ! [Z_5,Y_4,X_5] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_5),X_5))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_5),Y_4))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_4),X_5)) ),
    inference(fof_nnf,[status(thm)],[fact_360_xt1_I6_J]) ).

fof(f_467_2,plain,
    ! [U_1179,U_1178,U_1177] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1179),U_1177))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1179),U_1178))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1178),U_1177)) ),
    inference(variable_rename,[status(thm)],[f_467_1]) ).

fof(f_467_3,plain,
    ! [U_1177,U_1178,U_1179] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1179),U_1177))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1179),U_1178))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1178),U_1177)) ),
    inference(definitional_conversion,[status(esa)],[f_467_2]) ).

cnf(f_467_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1179),U_1177))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1179),U_1178))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1178),U_1177)) ),
    inference(clausify,[status(thm)],[f_467_3]) ).

fof(f_468_1,plain,
    ! [Z_5,Y_4,X_5] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_5),X_5))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Z_5),Y_4))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_4),X_5)) ),
    inference(fof_nnf,[status(thm)],[fact_361_xt1_I6_J]) ).

fof(f_468_2,plain,
    ! [U_1182,U_1181,U_1180] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1182),U_1180))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1182),U_1181))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1181),U_1180)) ),
    inference(variable_rename,[status(thm)],[f_468_1]) ).

fof(f_468_3,plain,
    ! [U_1180,U_1181,U_1182] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1182),U_1180))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1182),U_1181))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1181),U_1180)) ),
    inference(definitional_conversion,[status(esa)],[f_468_2]) ).

cnf(f_468_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1182),U_1180))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1182),U_1181))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1181),U_1180)) ),
    inference(clausify,[status(thm)],[f_468_3]) ).

fof(f_469_1,plain,
    ! [Z_2,Y_1,X_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Z_2),X_1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Z_2),Y_1))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Y_1),X_1)) ),
    inference(fof_nnf,[status(thm)],[fact_362_xt1_I6_J]) ).

fof(f_469_2,plain,
    ! [U_1185,U_1184,U_1183] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1185),U_1183))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1185),U_1184))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1184),U_1183)) ),
    inference(variable_rename,[status(thm)],[f_469_1]) ).

fof(f_469_3,plain,
    ! [U_1183,U_1184,U_1185] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1185),U_1183))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1185),U_1184))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1184),U_1183)) ),
    inference(definitional_conversion,[status(esa)],[f_469_2]) ).

cnf(f_469_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1185),U_1183))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1185),U_1184))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1184),U_1183)) ),
    inference(clausify,[status(thm)],[f_469_3]) ).

fof(f_470_1,plain,
    ! [X_4,Y_3] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y_3),X_4))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_4),Y_3)) ),
    inference(fof_nnf,[status(thm)],[fact_363_linorder__le__cases]) ).

fof(f_470_2,plain,
    ! [U_1187,U_1186] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1186),U_1187))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1187),U_1186)) ),
    inference(variable_rename,[status(thm)],[f_470_1]) ).

fof(f_470_3,plain,
    ! [U_1186,U_1187] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1186),U_1187))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1187),U_1186)) ),
    inference(definitional_conversion,[status(esa)],[f_470_2]) ).

cnf(f_470_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1186),U_1187))
    | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1187),U_1186)) ),
    inference(clausify,[status(thm)],[f_470_3]) ).

fof(f_471_1,plain,
    ! [X_4,Y_3] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_3),X_4))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_4),Y_3)) ),
    inference(fof_nnf,[status(thm)],[fact_364_linorder__le__cases]) ).

fof(f_471_2,plain,
    ! [U_1189,U_1188] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1188),U_1189))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1189),U_1188)) ),
    inference(variable_rename,[status(thm)],[f_471_1]) ).

fof(f_471_3,plain,
    ! [U_1188,U_1189] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1188),U_1189))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1189),U_1188)) ),
    inference(definitional_conversion,[status(esa)],[f_471_2]) ).

cnf(f_471_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1188),U_1189))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1189),U_1188)) ),
    inference(clausify,[status(thm)],[f_471_3]) ).

fof(f_472_1,plain,
    ! [A_2,B] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),B))),
    inference(fof_nnf,[status(thm)],[fact_365_insertI1]) ).

fof(f_472_2,plain,
    ! [U_1191,U_1190] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1191),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1191),U_1190))),
    inference(variable_rename,[status(thm)],[f_472_1]) ).

fof(f_472_3,plain,
    ! [U_1190,U_1191] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1191),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1191),U_1190))),
    inference(definitional_conversion,[status(esa)],[f_472_2]) ).

cnf(f_472_4,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1191),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1191),U_1190))),
    inference(clausify,[status(thm)],[f_472_3]) ).

fof(f_473_1,plain,
    ! [A_2,B] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),B))),
    inference(fof_nnf,[status(thm)],[fact_366_insertI1]) ).

fof(f_473_2,plain,
    ! [U_1193,U_1192] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1193),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1193),U_1192))),
    inference(variable_rename,[status(thm)],[f_473_1]) ).

fof(f_473_3,plain,
    ! [U_1192,U_1193] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1193),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1193),U_1192))),
    inference(definitional_conversion,[status(esa)],[f_473_2]) ).

cnf(f_473_4,plain,
    hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1193),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1193),U_1192))),
    inference(clausify,[status(thm)],[f_473_3]) ).

fof(f_474_1,plain,
    ! [A_2,B] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B))),
    inference(fof_nnf,[status(thm)],[fact_367_insertI1]) ).

fof(f_474_2,plain,
    ! [U_1195,U_1194] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1195),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1195),U_1194))),
    inference(variable_rename,[status(thm)],[f_474_1]) ).

fof(f_474_3,plain,
    ! [U_1194,U_1195] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1195),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1195),U_1194))),
    inference(definitional_conversion,[status(esa)],[f_474_2]) ).

cnf(f_474_4,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1195),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1195),U_1194))),
    inference(clausify,[status(thm)],[f_474_3]) ).

fof(f_475_1,plain,
    ! [A_2,B] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B))),
    inference(fof_nnf,[status(thm)],[fact_368_insertI1]) ).

fof(f_475_2,plain,
    ! [U_1197,U_1196] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1197),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1197),U_1196))),
    inference(variable_rename,[status(thm)],[f_475_1]) ).

fof(f_475_3,plain,
    ! [U_1196,U_1197] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1197),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1197),U_1196))),
    inference(definitional_conversion,[status(esa)],[f_475_2]) ).

cnf(f_475_4,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1197),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1197),U_1196))),
    inference(clausify,[status(thm)],[f_475_3]) ).

fof(f_476_1,plain,
    ! [A_2,B] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),B) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),B))),
    inference(fof_nnf,[status(thm)],[fact_369_insert__compr]) ).

fof(f_476_2,plain,
    ! [U_1199,U_1198] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1199),U_1198) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_1199)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_1198))),
    inference(variable_rename,[status(thm)],[f_476_1]) ).

fof(f_476_3,plain,
    ! [U_1198,U_1199] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1199),U_1198) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_1199)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_1198))),
    inference(definitional_conversion,[status(esa)],[f_476_2]) ).

cnf(f_476_4,plain,
    hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1199),U_1198) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_1199)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_1198))),
    inference(clausify,[status(thm)],[f_476_3]) ).

fof(f_477_1,plain,
    ! [A_2,B] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),B) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),A_2)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),B))),
    inference(fof_nnf,[status(thm)],[fact_370_insert__compr]) ).

fof(f_477_2,plain,
    ! [U_1201,U_1200] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1201),U_1200) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),U_1201)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_1200))),
    inference(variable_rename,[status(thm)],[f_477_1]) ).

fof(f_477_3,plain,
    ! [U_1200,U_1201] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1201),U_1200) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),U_1201)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_1200))),
    inference(definitional_conversion,[status(esa)],[f_477_2]) ).

cnf(f_477_4,plain,
    hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1201),U_1200) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),U_1201)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_1200))),
    inference(clausify,[status(thm)],[f_477_3]) ).

fof(f_478_1,plain,
    ! [A_2,B] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),B))),
    inference(fof_nnf,[status(thm)],[fact_371_insert__compr]) ).

fof(f_478_2,plain,
    ! [U_1203,U_1202] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1203),U_1202) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_1203)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_1202))),
    inference(variable_rename,[status(thm)],[f_478_1]) ).

fof(f_478_3,plain,
    ! [U_1202,U_1203] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1203),U_1202) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_1203)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_1202))),
    inference(definitional_conversion,[status(esa)],[f_478_2]) ).

cnf(f_478_4,plain,
    hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1203),U_1202) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_1203)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_1202))),
    inference(clausify,[status(thm)],[f_478_3]) ).

fof(f_479_1,plain,
    ! [A_2,B] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),B))),
    inference(fof_nnf,[status(thm)],[fact_372_insert__compr]) ).

fof(f_479_2,plain,
    ! [U_1205,U_1204] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1205),U_1204) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_1205)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_1204))),
    inference(variable_rename,[status(thm)],[f_479_1]) ).

fof(f_479_3,plain,
    ! [U_1204,U_1205] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1205),U_1204) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_1205)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_1204))),
    inference(definitional_conversion,[status(esa)],[f_479_2]) ).

cnf(f_479_4,plain,
    hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1205),U_1204) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_1205)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_1204))),
    inference(clausify,[status(thm)],[f_479_3]) ).

fof(f_480_1,plain,
    ! [A_2,Pa] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),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_2))),Pa)),
    inference(fof_nnf,[status(thm)],[fact_373_insert__Collect]) ).

fof(f_480_2,plain,
    ! [U_1207,U_1206] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1207),collect_a(U_1206)) = 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_1207))),U_1206)),
    inference(variable_rename,[status(thm)],[f_480_1]) ).

fof(f_480_3,plain,
    ! [U_1206,U_1207] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1207),collect_a(U_1206)) = 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_1207))),U_1206)),
    inference(definitional_conversion,[status(esa)],[f_480_2]) ).

cnf(f_480_4,plain,
    hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1207),collect_a(U_1206)) = 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_1207))),U_1206)),
    inference(clausify,[status(thm)],[f_480_3]) ).

fof(f_481_1,plain,
    ! [A_2,Pa] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),collect_int(Pa)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fimplies,cOMBB_bool_bool_int(fNot,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),A_2))),Pa)),
    inference(fof_nnf,[status(thm)],[fact_374_insert__Collect]) ).

fof(f_481_2,plain,
    ! [U_1209,U_1208] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1209),collect_int(U_1208)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fimplies,cOMBB_bool_bool_int(fNot,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),U_1209))),U_1208)),
    inference(variable_rename,[status(thm)],[f_481_1]) ).

fof(f_481_3,plain,
    ! [U_1208,U_1209] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1209),collect_int(U_1208)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fimplies,cOMBB_bool_bool_int(fNot,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),U_1209))),U_1208)),
    inference(definitional_conversion,[status(esa)],[f_481_2]) ).

cnf(f_481_4,plain,
    hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1209),collect_int(U_1208)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fimplies,cOMBB_bool_bool_int(fNot,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),U_1209))),U_1208)),
    inference(clausify,[status(thm)],[f_481_3]) ).

fof(f_482_1,plain,
    ! [A_2,Pa] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),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_2))),Pa)),
    inference(fof_nnf,[status(thm)],[fact_375_insert__Collect]) ).

fof(f_482_2,plain,
    ! [U_1211,U_1210] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1211),collect_nat(U_1210)) = 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_1211))),U_1210)),
    inference(variable_rename,[status(thm)],[f_482_1]) ).

fof(f_482_3,plain,
    ! [U_1210,U_1211] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1211),collect_nat(U_1210)) = 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_1211))),U_1210)),
    inference(definitional_conversion,[status(esa)],[f_482_2]) ).

cnf(f_482_4,plain,
    hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1211),collect_nat(U_1210)) = 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_1211))),U_1210)),
    inference(clausify,[status(thm)],[f_482_3]) ).

fof(f_483_1,plain,
    ! [X_1,A] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
        | ~ hBOOL(hAPP_int_bool(A,X_1)) )
      & ( hBOOL(hAPP_int_bool(A,X_1))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_376_mem__def]) ).

fof(f_483_2,plain,
    ! [U_1213,U_1212] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1213),U_1212))
        | ~ hBOOL(hAPP_int_bool(U_1212,U_1213)) )
      & ( hBOOL(hAPP_int_bool(U_1212,U_1213))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1213),U_1212)) ) ),
    inference(variable_rename,[status(thm)],[f_483_1]) ).

fof(f_483_3,plain,
    ( ! [U_1217,U_1215] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1217),U_1215))
        | ~ hBOOL(hAPP_int_bool(U_1215,U_1217)) )
    & ! [U_1216,U_1214] :
        ( hBOOL(hAPP_int_bool(U_1214,U_1216))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1216),U_1214)) ) ),
    inference(miniscope,[status(thm)],[f_483_2]) ).

fof(f_483_4,plain,
    ( ! [U_1215,U_1217] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1217),U_1215))
        | ~ hBOOL(hAPP_int_bool(U_1215,U_1217)) )
    & ! [U_1216,U_1214] :
        ( hBOOL(hAPP_int_bool(U_1214,U_1216))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1216),U_1214)) ) ),
    inference(definitional_conversion,[status(esa)],[f_483_3]) ).

cnf(f_483_5,plain,
    ( hBOOL(hAPP_int_bool(U_1214,U_1216))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1216),U_1214)) ),
    inference(clausify,[status(thm)],[f_483_4]) ).

cnf(f_483_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1217),U_1215))
    | ~ hBOOL(hAPP_int_bool(U_1215,U_1217)) ),
    inference(clausify,[status(thm)],[f_483_4]) ).

fof(f_484_1,plain,
    ! [X_1,A] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
        | ~ hBOOL(hAPP_nat_bool(A,X_1)) )
      & ( hBOOL(hAPP_nat_bool(A,X_1))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_377_mem__def]) ).

fof(f_484_2,plain,
    ! [U_1219,U_1218] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1219),U_1218))
        | ~ hBOOL(hAPP_nat_bool(U_1218,U_1219)) )
      & ( hBOOL(hAPP_nat_bool(U_1218,U_1219))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1219),U_1218)) ) ),
    inference(variable_rename,[status(thm)],[f_484_1]) ).

fof(f_484_3,plain,
    ( ! [U_1223,U_1221] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1223),U_1221))
        | ~ hBOOL(hAPP_nat_bool(U_1221,U_1223)) )
    & ! [U_1222,U_1220] :
        ( hBOOL(hAPP_nat_bool(U_1220,U_1222))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1222),U_1220)) ) ),
    inference(miniscope,[status(thm)],[f_484_2]) ).

fof(f_484_4,plain,
    ( ! [U_1221,U_1223] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1223),U_1221))
        | ~ hBOOL(hAPP_nat_bool(U_1221,U_1223)) )
    & ! [U_1222,U_1220] :
        ( hBOOL(hAPP_nat_bool(U_1220,U_1222))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1222),U_1220)) ) ),
    inference(definitional_conversion,[status(esa)],[f_484_3]) ).

cnf(f_484_5,plain,
    ( hBOOL(hAPP_nat_bool(U_1220,U_1222))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1222),U_1220)) ),
    inference(clausify,[status(thm)],[f_484_4]) ).

cnf(f_484_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1223),U_1221))
    | ~ hBOOL(hAPP_nat_bool(U_1221,U_1223)) ),
    inference(clausify,[status(thm)],[f_484_4]) ).

fof(f_485_1,plain,
    ! [X_1,A] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
        | ~ hBOOL(hAPP_a_bool(A,X_1)) )
      & ( hBOOL(hAPP_a_bool(A,X_1))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_378_mem__def]) ).

fof(f_485_2,plain,
    ! [U_1225,U_1224] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1225),U_1224))
        | ~ hBOOL(hAPP_a_bool(U_1224,U_1225)) )
      & ( hBOOL(hAPP_a_bool(U_1224,U_1225))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1225),U_1224)) ) ),
    inference(variable_rename,[status(thm)],[f_485_1]) ).

fof(f_485_3,plain,
    ( ! [U_1229,U_1227] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1229),U_1227))
        | ~ hBOOL(hAPP_a_bool(U_1227,U_1229)) )
    & ! [U_1228,U_1226] :
        ( hBOOL(hAPP_a_bool(U_1226,U_1228))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1228),U_1226)) ) ),
    inference(miniscope,[status(thm)],[f_485_2]) ).

fof(f_485_4,plain,
    ( ! [U_1227,U_1229] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1229),U_1227))
        | ~ hBOOL(hAPP_a_bool(U_1227,U_1229)) )
    & ! [U_1228,U_1226] :
        ( hBOOL(hAPP_a_bool(U_1226,U_1228))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1228),U_1226)) ) ),
    inference(definitional_conversion,[status(esa)],[f_485_3]) ).

cnf(f_485_5,plain,
    ( hBOOL(hAPP_a_bool(U_1226,U_1228))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1228),U_1226)) ),
    inference(clausify,[status(thm)],[f_485_4]) ).

cnf(f_485_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1229),U_1227))
    | ~ hBOOL(hAPP_a_bool(U_1227,U_1229)) ),
    inference(clausify,[status(thm)],[f_485_4]) ).

fof(f_486_1,plain,
    ! [X_1,A] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
        | ~ hBOOL(hAPP_pname_bool(A,X_1)) )
      & ( hBOOL(hAPP_pname_bool(A,X_1))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_379_mem__def]) ).

fof(f_486_2,plain,
    ! [U_1231,U_1230] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1231),U_1230))
        | ~ hBOOL(hAPP_pname_bool(U_1230,U_1231)) )
      & ( hBOOL(hAPP_pname_bool(U_1230,U_1231))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1231),U_1230)) ) ),
    inference(variable_rename,[status(thm)],[f_486_1]) ).

fof(f_486_3,plain,
    ( ! [U_1235,U_1233] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1235),U_1233))
        | ~ hBOOL(hAPP_pname_bool(U_1233,U_1235)) )
    & ! [U_1234,U_1232] :
        ( hBOOL(hAPP_pname_bool(U_1232,U_1234))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1234),U_1232)) ) ),
    inference(miniscope,[status(thm)],[f_486_2]) ).

fof(f_486_4,plain,
    ( ! [U_1233,U_1235] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1235),U_1233))
        | ~ hBOOL(hAPP_pname_bool(U_1233,U_1235)) )
    & ! [U_1234,U_1232] :
        ( hBOOL(hAPP_pname_bool(U_1232,U_1234))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1234),U_1232)) ) ),
    inference(definitional_conversion,[status(esa)],[f_486_3]) ).

cnf(f_486_5,plain,
    ( hBOOL(hAPP_pname_bool(U_1232,U_1234))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1234),U_1232)) ),
    inference(clausify,[status(thm)],[f_486_4]) ).

cnf(f_486_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1235),U_1233))
    | ~ hBOOL(hAPP_pname_bool(U_1233,U_1235)) ),
    inference(clausify,[status(thm)],[f_486_4]) ).

fof(f_487_1,plain,
    ! [Pa] : collect_int(Pa) = Pa,
    inference(fof_nnf,[status(thm)],[fact_380_Collect__def]) ).

fof(f_487_2,plain,
    ! [U_1236] : collect_int(U_1236) = U_1236,
    inference(variable_rename,[status(thm)],[f_487_1]) ).

fof(f_487_3,plain,
    ! [U_1236] : collect_int(U_1236) = U_1236,
    inference(definitional_conversion,[status(esa)],[f_487_2]) ).

cnf(f_487_4,plain,
    collect_int(U_1236) = U_1236,
    inference(clausify,[status(thm)],[f_487_3]) ).

fof(f_488_1,plain,
    ! [Pa] : collect_nat(Pa) = Pa,
    inference(fof_nnf,[status(thm)],[fact_381_Collect__def]) ).

fof(f_488_2,plain,
    ! [U_1237] : collect_nat(U_1237) = U_1237,
    inference(variable_rename,[status(thm)],[f_488_1]) ).

fof(f_488_3,plain,
    ! [U_1237] : collect_nat(U_1237) = U_1237,
    inference(definitional_conversion,[status(esa)],[f_488_2]) ).

cnf(f_488_4,plain,
    collect_nat(U_1237) = U_1237,
    inference(clausify,[status(thm)],[f_488_3]) ).

fof(f_489_1,plain,
    ! [X_1,A] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A),
    inference(fof_nnf,[status(thm)],[fact_382_insert__absorb2]) ).

fof(f_489_2,plain,
    ! [U_1239,U_1238] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1239),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1239),U_1238)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1239),U_1238),
    inference(variable_rename,[status(thm)],[f_489_1]) ).

fof(f_489_3,plain,
    ! [U_1238,U_1239] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1239),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1239),U_1238)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1239),U_1238),
    inference(definitional_conversion,[status(esa)],[f_489_2]) ).

cnf(f_489_4,plain,
    hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1239),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1239),U_1238)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1239),U_1238),
    inference(clausify,[status(thm)],[f_489_3]) ).

fof(f_490_1,plain,
    ! [X_1,Y_1,A] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,Y_1),A)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,Y_1),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)),
    inference(fof_nnf,[status(thm)],[fact_383_insert__commute]) ).

fof(f_490_2,plain,
    ! [U_1242,U_1241,U_1240] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1242),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1241),U_1240)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1241),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1242),U_1240)),
    inference(variable_rename,[status(thm)],[f_490_1]) ).

fof(f_490_3,plain,
    ! [U_1240,U_1241,U_1242] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1242),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1241),U_1240)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1241),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1242),U_1240)),
    inference(definitional_conversion,[status(esa)],[f_490_2]) ).

cnf(f_490_4,plain,
    hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1242),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1241),U_1240)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1241),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1242),U_1240)),
    inference(clausify,[status(thm)],[f_490_3]) ).

fof(f_491_1,plain,
    ! [A_2,B_3,A] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),A)))
          | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
            & A_2 != B_3 ) )
        & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
          | A_2 = B_3
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),A))) ) )
      | ~ is_a(B_3)
      | ~ is_a(A_2) ),
    inference(fof_nnf,[status(thm)],[fact_384_insert__iff]) ).

fof(f_491_2,plain,
    ! [U_1245,U_1244,U_1243] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1245),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1244),U_1243)))
          | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1245),U_1243))
            & U_1245 != U_1244 ) )
        & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1245),U_1243))
          | U_1245 = U_1244
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1245),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1244),U_1243))) ) )
      | ~ is_a(U_1244)
      | ~ is_a(U_1245) ),
    inference(variable_rename,[status(thm)],[f_491_1]) ).

fof(f_491_3,plain,
    ! [U_1245,U_1244] :
      ( ( ! [U_1247] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1245),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1244),U_1247)))
            | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1245),U_1247))
              & U_1245 != U_1244 ) )
        & ! [U_1246] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1245),U_1246))
            | U_1245 = U_1244
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1245),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1244),U_1246))) ) )
      | ~ is_a(U_1244)
      | ~ is_a(U_1245) ),
    inference(miniscope,[status(thm)],[f_491_2]) ).

fof(f_491_4,plain,
    ( ! [U_1244,U_1245,U_1247] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1245),U_1247))
        | ~ sP99(U_1244,U_1245,U_1247) )
    & ! [U_1244,U_1245,U_1247] :
        ( U_1245 != U_1244
        | ~ sP99(U_1244,U_1245,U_1247) )
    & ! [U_1244,U_1245,U_1246,U_1247] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1245),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1244),U_1247)))
        | sP99(U_1244,U_1245,U_1247)
        | ~ sP100(U_1244,U_1245,U_1246,U_1247) )
    & ! [U_1244,U_1245,U_1246,U_1247] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1245),U_1246))
        | U_1245 = U_1244
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1245),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1244),U_1246)))
        | ~ sP100(U_1244,U_1245,U_1246,U_1247) )
    & ! [U_1244,U_1245,U_1246,U_1247] :
        ( sP100(U_1244,U_1245,U_1246,U_1247)
        | ~ is_a(U_1244)
        | ~ is_a(U_1245) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP99,sP100])],[f_491_3]) ).

cnf(f_491_5,plain,
    ( sP100(U_1244,U_1245,U_1246,U_1247)
    | ~ is_a(U_1244)
    | ~ is_a(U_1245) ),
    inference(clausify,[status(thm)],[f_491_4]) ).

cnf(f_491_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1245),U_1246))
    | U_1245 = U_1244
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1245),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1244),U_1246)))
    | ~ sP100(U_1244,U_1245,U_1246,U_1247) ),
    inference(clausify,[status(thm)],[f_491_4]) ).

cnf(f_491_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1245),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1244),U_1247)))
    | sP99(U_1244,U_1245,U_1247)
    | ~ sP100(U_1244,U_1245,U_1246,U_1247) ),
    inference(clausify,[status(thm)],[f_491_4]) ).

cnf(f_491_8,plain,
    ( U_1245 != U_1244
    | ~ sP99(U_1244,U_1245,U_1247) ),
    inference(clausify,[status(thm)],[f_491_4]) ).

cnf(f_491_9,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1245),U_1247))
    | ~ sP99(U_1244,U_1245,U_1247) ),
    inference(clausify,[status(thm)],[f_491_4]) ).

fof(f_492_1,plain,
    ! [A_2,B_3,A] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_3),A)))
        | ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),A))
          & A_2 != B_3 ) )
      & ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),A))
        | A_2 = B_3
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_3),A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_385_insert__iff]) ).

fof(f_492_2,plain,
    ! [U_1250,U_1249,U_1248] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1250),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1249),U_1248)))
        | ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1250),U_1248))
          & U_1250 != U_1249 ) )
      & ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1250),U_1248))
        | U_1250 = U_1249
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1250),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1249),U_1248))) ) ),
    inference(variable_rename,[status(thm)],[f_492_1]) ).

fof(f_492_3,plain,
    ( ! [U_1256,U_1254,U_1252] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1256),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1254),U_1252)))
        | ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1256),U_1252))
          & U_1256 != U_1254 ) )
    & ! [U_1255,U_1253,U_1251] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1255),U_1251))
        | U_1255 = U_1253
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1255),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1253),U_1251))) ) ),
    inference(miniscope,[status(thm)],[f_492_2]) ).

fof(f_492_4,plain,
    ( ! [U_1252,U_1254,U_1256] :
        ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1256),U_1252))
        | ~ sP101(U_1252,U_1254,U_1256) )
    & ! [U_1252,U_1254,U_1256] :
        ( U_1256 != U_1254
        | ~ sP101(U_1252,U_1254,U_1256) )
    & ! [U_1252,U_1254,U_1256] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1256),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1254),U_1252)))
        | sP101(U_1252,U_1254,U_1256) )
    & ! [U_1255,U_1253,U_1251] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1255),U_1251))
        | U_1255 = U_1253
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1255),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1253),U_1251))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP101])],[f_492_3]) ).

cnf(f_492_5,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1255),U_1251))
    | U_1255 = U_1253
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1255),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1253),U_1251))) ),
    inference(clausify,[status(thm)],[f_492_4]) ).

cnf(f_492_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1256),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1254),U_1252)))
    | sP101(U_1252,U_1254,U_1256) ),
    inference(clausify,[status(thm)],[f_492_4]) ).

cnf(f_492_7,plain,
    ( U_1256 != U_1254
    | ~ sP101(U_1252,U_1254,U_1256) ),
    inference(clausify,[status(thm)],[f_492_4]) ).

cnf(f_492_8,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1256),U_1252))
    | ~ sP101(U_1252,U_1254,U_1256) ),
    inference(clausify,[status(thm)],[f_492_4]) ).

fof(f_493_1,plain,
    ! [A_2,B_3,A] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_3),A)))
        | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A))
          & A_2 != B_3 ) )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A))
        | A_2 = B_3
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_3),A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_386_insert__iff]) ).

fof(f_493_2,plain,
    ! [U_1259,U_1258,U_1257] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1259),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1258),U_1257)))
        | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1259),U_1257))
          & U_1259 != U_1258 ) )
      & ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1259),U_1257))
        | U_1259 = U_1258
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1259),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1258),U_1257))) ) ),
    inference(variable_rename,[status(thm)],[f_493_1]) ).

fof(f_493_3,plain,
    ( ! [U_1265,U_1263,U_1261] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1265),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1263),U_1261)))
        | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1265),U_1261))
          & U_1265 != U_1263 ) )
    & ! [U_1264,U_1262,U_1260] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1264),U_1260))
        | U_1264 = U_1262
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1264),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1262),U_1260))) ) ),
    inference(miniscope,[status(thm)],[f_493_2]) ).

fof(f_493_4,plain,
    ( ! [U_1265,U_1263,U_1261] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1265),U_1261))
        | ~ sP102(U_1265,U_1263,U_1261) )
    & ! [U_1265,U_1263,U_1261] :
        ( U_1265 != U_1263
        | ~ sP102(U_1265,U_1263,U_1261) )
    & ! [U_1265,U_1263,U_1261] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1265),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1263),U_1261)))
        | sP102(U_1265,U_1263,U_1261) )
    & ! [U_1260,U_1262,U_1264] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1264),U_1260))
        | U_1264 = U_1262
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1264),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1262),U_1260))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP102])],[f_493_3]) ).

cnf(f_493_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1264),U_1260))
    | U_1264 = U_1262
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1264),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1262),U_1260))) ),
    inference(clausify,[status(thm)],[f_493_4]) ).

cnf(f_493_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1265),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1263),U_1261)))
    | sP102(U_1265,U_1263,U_1261) ),
    inference(clausify,[status(thm)],[f_493_4]) ).

cnf(f_493_7,plain,
    ( U_1265 != U_1263
    | ~ sP102(U_1265,U_1263,U_1261) ),
    inference(clausify,[status(thm)],[f_493_4]) ).

cnf(f_493_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1265),U_1261))
    | ~ sP102(U_1265,U_1263,U_1261) ),
    inference(clausify,[status(thm)],[f_493_4]) ).

fof(f_494_1,plain,
    ! [A_2,B_3,A] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_3),A)))
          | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A))
            & A_2 != B_3 ) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A))
          | A_2 = B_3
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_3),A))) ) )
      | ~ is_pname(B_3)
      | ~ is_pname(A_2) ),
    inference(fof_nnf,[status(thm)],[fact_387_insert__iff]) ).

fof(f_494_2,plain,
    ! [U_1268,U_1267,U_1266] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1268),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1267),U_1266)))
          | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1268),U_1266))
            & U_1268 != U_1267 ) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1268),U_1266))
          | U_1268 = U_1267
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1268),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1267),U_1266))) ) )
      | ~ is_pname(U_1267)
      | ~ is_pname(U_1268) ),
    inference(variable_rename,[status(thm)],[f_494_1]) ).

fof(f_494_3,plain,
    ! [U_1268,U_1267] :
      ( ( ! [U_1270] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1268),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1267),U_1270)))
            | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1268),U_1270))
              & U_1268 != U_1267 ) )
        & ! [U_1269] :
            ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1268),U_1269))
            | U_1268 = U_1267
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1268),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1267),U_1269))) ) )
      | ~ is_pname(U_1267)
      | ~ is_pname(U_1268) ),
    inference(miniscope,[status(thm)],[f_494_2]) ).

fof(f_494_4,plain,
    ( ! [U_1267,U_1268,U_1270] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1268),U_1270))
        | ~ sP103(U_1267,U_1268,U_1270) )
    & ! [U_1267,U_1268,U_1270] :
        ( U_1268 != U_1267
        | ~ sP103(U_1267,U_1268,U_1270) )
    & ! [U_1267,U_1268,U_1269,U_1270] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1268),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1267),U_1270)))
        | sP103(U_1267,U_1268,U_1270)
        | ~ sP104(U_1267,U_1268,U_1269,U_1270) )
    & ! [U_1267,U_1268,U_1269,U_1270] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1268),U_1269))
        | U_1268 = U_1267
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1268),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1267),U_1269)))
        | ~ sP104(U_1267,U_1268,U_1269,U_1270) )
    & ! [U_1267,U_1268,U_1269,U_1270] :
        ( sP104(U_1267,U_1268,U_1269,U_1270)
        | ~ is_pname(U_1267)
        | ~ is_pname(U_1268) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP103,sP104])],[f_494_3]) ).

cnf(f_494_5,plain,
    ( sP104(U_1267,U_1268,U_1269,U_1270)
    | ~ is_pname(U_1267)
    | ~ is_pname(U_1268) ),
    inference(clausify,[status(thm)],[f_494_4]) ).

cnf(f_494_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1268),U_1269))
    | U_1268 = U_1267
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1268),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1267),U_1269)))
    | ~ sP104(U_1267,U_1268,U_1269,U_1270) ),
    inference(clausify,[status(thm)],[f_494_4]) ).

cnf(f_494_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1268),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1267),U_1270)))
    | sP103(U_1267,U_1268,U_1270)
    | ~ sP104(U_1267,U_1268,U_1269,U_1270) ),
    inference(clausify,[status(thm)],[f_494_4]) ).

cnf(f_494_8,plain,
    ( U_1268 != U_1267
    | ~ sP103(U_1267,U_1268,U_1270) ),
    inference(clausify,[status(thm)],[f_494_4]) ).

cnf(f_494_9,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1268),U_1270))
    | ~ sP103(U_1267,U_1268,U_1270) ),
    inference(clausify,[status(thm)],[f_494_4]) ).

fof(f_495_1,plain,
    ! [Y_1,A,X_1] :
      ( ( ( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,Y_1),A),X_1))
          | ( ~ hBOOL(hAPP_a_bool(A,X_1))
            & Y_1 != X_1 ) )
        & ( hBOOL(hAPP_a_bool(A,X_1))
          | Y_1 = X_1
          | ~ hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,Y_1),A),X_1)) ) )
      | ~ is_a(X_1)
      | ~ is_a(Y_1) ),
    inference(fof_nnf,[status(thm)],[fact_388_insert__code]) ).

fof(f_495_2,plain,
    ! [U_1273,U_1272,U_1271] :
      ( ( ( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1273),U_1272),U_1271))
          | ( ~ hBOOL(hAPP_a_bool(U_1272,U_1271))
            & U_1273 != U_1271 ) )
        & ( hBOOL(hAPP_a_bool(U_1272,U_1271))
          | U_1273 = U_1271
          | ~ hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1273),U_1272),U_1271)) ) )
      | ~ is_a(U_1271)
      | ~ is_a(U_1273) ),
    inference(variable_rename,[status(thm)],[f_495_1]) ).

fof(f_495_3,plain,
    ( ! [U_1273,U_1272,U_1271] :
        ( ~ hBOOL(hAPP_a_bool(U_1272,U_1271))
        | ~ sP105(U_1273,U_1272,U_1271) )
    & ! [U_1273,U_1272,U_1271] :
        ( U_1273 != U_1271
        | ~ sP105(U_1273,U_1272,U_1271) )
    & ! [U_1273,U_1272,U_1271] :
        ( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1273),U_1272),U_1271))
        | sP105(U_1273,U_1272,U_1271)
        | ~ sP106(U_1273,U_1272,U_1271) )
    & ! [U_1273,U_1272,U_1271] :
        ( hBOOL(hAPP_a_bool(U_1272,U_1271))
        | U_1273 = U_1271
        | ~ hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1273),U_1272),U_1271))
        | ~ sP106(U_1273,U_1272,U_1271) )
    & ! [U_1273,U_1272,U_1271] :
        ( sP106(U_1273,U_1272,U_1271)
        | ~ is_a(U_1271)
        | ~ is_a(U_1273) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP105,sP106])],[f_495_2]) ).

cnf(f_495_4,plain,
    ( sP106(U_1273,U_1272,U_1271)
    | ~ is_a(U_1271)
    | ~ is_a(U_1273) ),
    inference(clausify,[status(thm)],[f_495_3]) ).

cnf(f_495_5,plain,
    ( hBOOL(hAPP_a_bool(U_1272,U_1271))
    | U_1273 = U_1271
    | ~ hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1273),U_1272),U_1271))
    | ~ sP106(U_1273,U_1272,U_1271) ),
    inference(clausify,[status(thm)],[f_495_3]) ).

cnf(f_495_6,plain,
    ( hBOOL(hAPP_a_bool(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1273),U_1272),U_1271))
    | sP105(U_1273,U_1272,U_1271)
    | ~ sP106(U_1273,U_1272,U_1271) ),
    inference(clausify,[status(thm)],[f_495_3]) ).

cnf(f_495_7,plain,
    ( U_1273 != U_1271
    | ~ sP105(U_1273,U_1272,U_1271) ),
    inference(clausify,[status(thm)],[f_495_3]) ).

cnf(f_495_8,plain,
    ( ~ hBOOL(hAPP_a_bool(U_1272,U_1271))
    | ~ sP105(U_1273,U_1272,U_1271) ),
    inference(clausify,[status(thm)],[f_495_3]) ).

fof(f_496_1,plain,
    ! [B,X_1,A] :
      ( ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),B)
          | A != B )
        & ( A = B
          | hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),B) ) )
      | 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_fun_a_bool(A)
      | ~ is_fun_a_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_389_insert__ident]) ).

fof(f_496_2,plain,
    ! [U_1276,U_1275,U_1274] :
      ( ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1275),U_1274) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1275),U_1276)
          | U_1274 != U_1276 )
        & ( U_1274 = U_1276
          | hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1275),U_1274) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1275),U_1276) ) )
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1275),U_1276))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1275),U_1274))
      | ~ is_fun_a_bool(U_1274)
      | ~ is_fun_a_bool(U_1276) ),
    inference(variable_rename,[status(thm)],[f_496_1]) ).

fof(f_496_3,plain,
    ( ! [U_1275,U_1274,U_1276] :
        ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1275),U_1274) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1275),U_1276)
        | U_1274 != U_1276
        | ~ sP107(U_1275,U_1274,U_1276) )
    & ! [U_1275,U_1274,U_1276] :
        ( U_1274 = U_1276
        | hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1275),U_1274) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1275),U_1276)
        | ~ sP107(U_1275,U_1274,U_1276) )
    & ! [U_1275,U_1274,U_1276] :
        ( sP107(U_1275,U_1274,U_1276)
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1275),U_1276))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1275),U_1274))
        | ~ is_fun_a_bool(U_1274)
        | ~ is_fun_a_bool(U_1276) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP107])],[f_496_2]) ).

cnf(f_496_4,plain,
    ( sP107(U_1275,U_1274,U_1276)
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1275),U_1276))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1275),U_1274))
    | ~ is_fun_a_bool(U_1274)
    | ~ is_fun_a_bool(U_1276) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

cnf(f_496_5,plain,
    ( U_1274 = U_1276
    | hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1275),U_1274) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1275),U_1276)
    | ~ sP107(U_1275,U_1274,U_1276) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

cnf(f_496_6,plain,
    ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1275),U_1274) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1275),U_1276)
    | U_1274 != U_1276
    | ~ sP107(U_1275,U_1274,U_1276) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

fof(f_497_1,plain,
    ! [B,X_1,A] :
      ( ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B)
          | A != B )
        & ( A = B
          | hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B) ) )
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B))
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) ),
    inference(fof_nnf,[status(thm)],[fact_390_insert__ident]) ).

fof(f_497_2,plain,
    ! [U_1279,U_1278,U_1277] :
      ( ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1278),U_1277) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1278),U_1279)
          | U_1277 != U_1279 )
        & ( U_1277 = U_1279
          | hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1278),U_1277) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1278),U_1279) ) )
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1278),U_1279))
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1278),U_1277)) ),
    inference(variable_rename,[status(thm)],[f_497_1]) ).

fof(f_497_3,plain,
    ( ! [U_1279,U_1277,U_1278] :
        ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1278),U_1277) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1278),U_1279)
        | U_1277 != U_1279
        | ~ sP108(U_1279,U_1277,U_1278) )
    & ! [U_1279,U_1277,U_1278] :
        ( U_1277 = U_1279
        | hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1278),U_1277) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1278),U_1279)
        | ~ sP108(U_1279,U_1277,U_1278) )
    & ! [U_1279,U_1277,U_1278] :
        ( sP108(U_1279,U_1277,U_1278)
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1278),U_1279))
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1278),U_1277)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP108])],[f_497_2]) ).

cnf(f_497_4,plain,
    ( sP108(U_1279,U_1277,U_1278)
    | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1278),U_1279))
    | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1278),U_1277)) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

cnf(f_497_5,plain,
    ( U_1277 = U_1279
    | hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1278),U_1277) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1278),U_1279)
    | ~ sP108(U_1279,U_1277,U_1278) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

cnf(f_497_6,plain,
    ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1278),U_1277) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1278),U_1279)
    | U_1277 != U_1279
    | ~ sP108(U_1279,U_1277,U_1278) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

fof(f_498_1,plain,
    ! [B,X_1,A] :
      ( ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B)
          | A != B )
        & ( A = B
          | hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B) ) )
      | 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_391_insert__ident]) ).

fof(f_498_2,plain,
    ! [U_1282,U_1281,U_1280] :
      ( ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1281),U_1280) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1281),U_1282)
          | U_1280 != U_1282 )
        & ( U_1280 = U_1282
          | hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1281),U_1280) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1281),U_1282) ) )
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1281),U_1282))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1281),U_1280)) ),
    inference(variable_rename,[status(thm)],[f_498_1]) ).

fof(f_498_3,plain,
    ( ! [U_1282,U_1280,U_1281] :
        ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1281),U_1280) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1281),U_1282)
        | U_1280 != U_1282
        | ~ sP109(U_1282,U_1280,U_1281) )
    & ! [U_1282,U_1280,U_1281] :
        ( U_1280 = U_1282
        | hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1281),U_1280) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1281),U_1282)
        | ~ sP109(U_1282,U_1280,U_1281) )
    & ! [U_1282,U_1280,U_1281] :
        ( sP109(U_1282,U_1280,U_1281)
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1281),U_1282))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1281),U_1280)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP109])],[f_498_2]) ).

cnf(f_498_4,plain,
    ( sP109(U_1282,U_1280,U_1281)
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1281),U_1282))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1281),U_1280)) ),
    inference(clausify,[status(thm)],[f_498_3]) ).

cnf(f_498_5,plain,
    ( U_1280 = U_1282
    | hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1281),U_1280) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1281),U_1282)
    | ~ sP109(U_1282,U_1280,U_1281) ),
    inference(clausify,[status(thm)],[f_498_3]) ).

cnf(f_498_6,plain,
    ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1281),U_1280) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1281),U_1282)
    | U_1280 != U_1282
    | ~ sP109(U_1282,U_1280,U_1281) ),
    inference(clausify,[status(thm)],[f_498_3]) ).

fof(f_499_1,plain,
    ! [B,X_1,A] :
      ( ( ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B)
          | A != B )
        & ( A = B
          | hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A) != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B) ) )
      | 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_fun_pname_bool(A)
      | ~ is_fun_pname_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_392_insert__ident]) ).

fof(f_499_2,plain,
    ! [U_1285,U_1284,U_1283] :
      ( ( ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1284),U_1283) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1284),U_1285)
          | U_1283 != U_1285 )
        & ( U_1283 = U_1285
          | hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1284),U_1283) != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1284),U_1285) ) )
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1284),U_1285))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1284),U_1283))
      | ~ is_fun_pname_bool(U_1283)
      | ~ is_fun_pname_bool(U_1285) ),
    inference(variable_rename,[status(thm)],[f_499_1]) ).

fof(f_499_3,plain,
    ( ! [U_1285,U_1283,U_1284] :
        ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1284),U_1283) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1284),U_1285)
        | U_1283 != U_1285
        | ~ sP110(U_1285,U_1283,U_1284) )
    & ! [U_1285,U_1283,U_1284] :
        ( U_1283 = U_1285
        | hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1284),U_1283) != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1284),U_1285)
        | ~ sP110(U_1285,U_1283,U_1284) )
    & ! [U_1285,U_1283,U_1284] :
        ( sP110(U_1285,U_1283,U_1284)
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1284),U_1285))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1284),U_1283))
        | ~ is_fun_pname_bool(U_1283)
        | ~ is_fun_pname_bool(U_1285) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP110])],[f_499_2]) ).

cnf(f_499_4,plain,
    ( sP110(U_1285,U_1283,U_1284)
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1284),U_1285))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1284),U_1283))
    | ~ is_fun_pname_bool(U_1283)
    | ~ is_fun_pname_bool(U_1285) ),
    inference(clausify,[status(thm)],[f_499_3]) ).

cnf(f_499_5,plain,
    ( U_1283 = U_1285
    | hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1284),U_1283) != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1284),U_1285)
    | ~ sP110(U_1285,U_1283,U_1284) ),
    inference(clausify,[status(thm)],[f_499_3]) ).

cnf(f_499_6,plain,
    ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1284),U_1283) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1284),U_1285)
    | U_1283 != U_1285
    | ~ sP110(U_1285,U_1283,U_1284) ),
    inference(clausify,[status(thm)],[f_499_3]) ).

fof(f_500_1,plain,
    ! [B_3,A_2,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),B)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),B)) ),
    inference(fof_nnf,[status(thm)],[fact_393_insertI2]) ).

fof(f_500_2,plain,
    ! [U_1288,U_1287,U_1286] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1287),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1288),U_1286)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1287),U_1286)) ),
    inference(variable_rename,[status(thm)],[f_500_1]) ).

fof(f_500_3,plain,
    ! [U_1288,U_1287,U_1286] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1287),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1288),U_1286)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1287),U_1286)) ),
    inference(definitional_conversion,[status(esa)],[f_500_2]) ).

cnf(f_500_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1287),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1288),U_1286)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1287),U_1286)) ),
    inference(clausify,[status(thm)],[f_500_3]) ).

fof(f_501_1,plain,
    ! [B_3,A_2,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_3),B)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),B)) ),
    inference(fof_nnf,[status(thm)],[fact_394_insertI2]) ).

fof(f_501_2,plain,
    ! [U_1291,U_1290,U_1289] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1290),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1291),U_1289)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1290),U_1289)) ),
    inference(variable_rename,[status(thm)],[f_501_1]) ).

fof(f_501_3,plain,
    ! [U_1291,U_1290,U_1289] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1290),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1291),U_1289)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1290),U_1289)) ),
    inference(definitional_conversion,[status(esa)],[f_501_2]) ).

cnf(f_501_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1290),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1291),U_1289)))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1290),U_1289)) ),
    inference(clausify,[status(thm)],[f_501_3]) ).

fof(f_502_1,plain,
    ! [B_3,A_2,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_3),B)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),B)) ),
    inference(fof_nnf,[status(thm)],[fact_395_insertI2]) ).

fof(f_502_2,plain,
    ! [U_1294,U_1293,U_1292] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1293),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1294),U_1292)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1293),U_1292)) ),
    inference(variable_rename,[status(thm)],[f_502_1]) ).

fof(f_502_3,plain,
    ! [U_1292,U_1293,U_1294] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1293),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1294),U_1292)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1293),U_1292)) ),
    inference(definitional_conversion,[status(esa)],[f_502_2]) ).

cnf(f_502_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1293),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1294),U_1292)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1293),U_1292)) ),
    inference(clausify,[status(thm)],[f_502_3]) ).

fof(f_503_1,plain,
    ! [B_3,A_2,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,B_3),B)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),B)) ),
    inference(fof_nnf,[status(thm)],[fact_396_insertI2]) ).

fof(f_503_2,plain,
    ! [U_1297,U_1296,U_1295] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1296),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1297),U_1295)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1296),U_1295)) ),
    inference(variable_rename,[status(thm)],[f_503_1]) ).

fof(f_503_3,plain,
    ! [U_1295,U_1296,U_1297] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1296),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1297),U_1295)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1296),U_1295)) ),
    inference(definitional_conversion,[status(esa)],[f_503_2]) ).

cnf(f_503_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1296),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1297),U_1295)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1296),U_1295)) ),
    inference(clausify,[status(thm)],[f_503_3]) ).

fof(f_504_1,plain,
    ! [A_2,A] :
      ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),A) = A
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
      | ~ is_fun_a_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_397_insert__absorb]) ).

fof(f_504_2,plain,
    ! [U_1299,U_1298] :
      ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1299),U_1298) = U_1298
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1299),U_1298))
      | ~ is_fun_a_bool(U_1298) ),
    inference(variable_rename,[status(thm)],[f_504_1]) ).

fof(f_504_3,plain,
    ! [U_1298,U_1299] :
      ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1299),U_1298) = U_1298
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1299),U_1298))
      | ~ is_fun_a_bool(U_1298) ),
    inference(definitional_conversion,[status(esa)],[f_504_2]) ).

cnf(f_504_4,plain,
    ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1299),U_1298) = U_1298
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1299),U_1298))
    | ~ is_fun_a_bool(U_1298) ),
    inference(clausify,[status(thm)],[f_504_3]) ).

fof(f_505_1,plain,
    ! [A_2,A] :
      ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),A) = A
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_398_insert__absorb]) ).

fof(f_505_2,plain,
    ! [U_1301,U_1300] :
      ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1301),U_1300) = U_1300
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1301),U_1300)) ),
    inference(variable_rename,[status(thm)],[f_505_1]) ).

fof(f_505_3,plain,
    ! [U_1301,U_1300] :
      ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1301),U_1300) = U_1300
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1301),U_1300)) ),
    inference(definitional_conversion,[status(esa)],[f_505_2]) ).

cnf(f_505_4,plain,
    ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1301),U_1300) = U_1300
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1301),U_1300)) ),
    inference(clausify,[status(thm)],[f_505_3]) ).

fof(f_506_1,plain,
    ! [A_2,A] :
      ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A) = A
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_399_insert__absorb]) ).

fof(f_506_2,plain,
    ! [U_1303,U_1302] :
      ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1303),U_1302) = U_1302
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1303),U_1302)) ),
    inference(variable_rename,[status(thm)],[f_506_1]) ).

fof(f_506_3,plain,
    ! [U_1302,U_1303] :
      ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1303),U_1302) = U_1302
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1303),U_1302)) ),
    inference(definitional_conversion,[status(esa)],[f_506_2]) ).

cnf(f_506_4,plain,
    ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1303),U_1302) = U_1302
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1303),U_1302)) ),
    inference(clausify,[status(thm)],[f_506_3]) ).

fof(f_507_1,plain,
    ! [A_2,A] :
      ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),A) = A
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A))
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_400_insert__absorb]) ).

fof(f_507_2,plain,
    ! [U_1305,U_1304] :
      ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1305),U_1304) = U_1304
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1305),U_1304))
      | ~ is_fun_pname_bool(U_1304) ),
    inference(variable_rename,[status(thm)],[f_507_1]) ).

fof(f_507_3,plain,
    ! [U_1304,U_1305] :
      ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1305),U_1304) = U_1304
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1305),U_1304))
      | ~ is_fun_pname_bool(U_1304) ),
    inference(definitional_conversion,[status(esa)],[f_507_2]) ).

cnf(f_507_4,plain,
    ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1305),U_1304) = U_1304
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1305),U_1304))
    | ~ is_fun_pname_bool(U_1304) ),
    inference(clausify,[status(thm)],[f_507_3]) ).

fof(f_508_1,plain,
    ! [A] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),A)),
    inference(fof_nnf,[status(thm)],[fact_401_subset__refl]) ).

fof(f_508_2,plain,
    ! [U_1306] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1306),U_1306)),
    inference(variable_rename,[status(thm)],[f_508_1]) ).

fof(f_508_3,plain,
    ! [U_1306] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1306),U_1306)),
    inference(definitional_conversion,[status(esa)],[f_508_2]) ).

cnf(f_508_4,plain,
    hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1306),U_1306)),
    inference(clausify,[status(thm)],[f_508_3]) ).

fof(f_509_1,plain,
    ! [A] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),A)),
    inference(fof_nnf,[status(thm)],[fact_402_subset__refl]) ).

fof(f_509_2,plain,
    ! [U_1307] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1307),U_1307)),
    inference(variable_rename,[status(thm)],[f_509_1]) ).

fof(f_509_3,plain,
    ! [U_1307] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1307),U_1307)),
    inference(definitional_conversion,[status(esa)],[f_509_2]) ).

cnf(f_509_4,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1307),U_1307)),
    inference(clausify,[status(thm)],[f_509_3]) ).

fof(f_510_1,plain,
    ! [A] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),A)),
    inference(fof_nnf,[status(thm)],[fact_403_subset__refl]) ).

fof(f_510_2,plain,
    ! [U_1308] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1308),U_1308)),
    inference(variable_rename,[status(thm)],[f_510_1]) ).

fof(f_510_3,plain,
    ! [U_1308] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1308),U_1308)),
    inference(definitional_conversion,[status(esa)],[f_510_2]) ).

cnf(f_510_4,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1308),U_1308)),
    inference(clausify,[status(thm)],[f_510_3]) ).

fof(f_511_1,plain,
    ! [A,B] :
      ( ( A = B
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) )
      & ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) )
        | A != B ) ),
    inference(fof_nnf,[status(thm)],[fact_404_set__eq__subset]) ).

fof(f_511_2,plain,
    ! [U_1310,U_1309] :
      ( ( U_1310 = U_1309
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1309),U_1310))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1310),U_1309)) )
      & ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1309),U_1310))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1310),U_1309)) )
        | U_1310 != U_1309 ) ),
    inference(variable_rename,[status(thm)],[f_511_1]) ).

fof(f_511_3,plain,
    ( ! [U_1314,U_1312] :
        ( U_1314 = U_1312
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1312),U_1314))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1314),U_1312)) )
    & ! [U_1313,U_1311] :
        ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1311),U_1313))
          & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1313),U_1311)) )
        | U_1313 != U_1311 ) ),
    inference(miniscope,[status(thm)],[f_511_2]) ).

fof(f_511_4,plain,
    ( ! [U_1313,U_1311] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1311),U_1313))
        | ~ sP111(U_1313,U_1311) )
    & ! [U_1313,U_1311] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1313),U_1311))
        | ~ sP111(U_1313,U_1311) )
    & ! [U_1314,U_1312] :
        ( U_1314 = U_1312
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1312),U_1314))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1314),U_1312)) )
    & ! [U_1313,U_1311] :
        ( sP111(U_1313,U_1311)
        | U_1313 != U_1311 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP111])],[f_511_3]) ).

cnf(f_511_5,plain,
    ( sP111(U_1313,U_1311)
    | U_1313 != U_1311 ),
    inference(clausify,[status(thm)],[f_511_4]) ).

cnf(f_511_6,plain,
    ( U_1314 = U_1312
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1312),U_1314))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1314),U_1312)) ),
    inference(clausify,[status(thm)],[f_511_4]) ).

cnf(f_511_7,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1313),U_1311))
    | ~ sP111(U_1313,U_1311) ),
    inference(clausify,[status(thm)],[f_511_4]) ).

cnf(f_511_8,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1311),U_1313))
    | ~ sP111(U_1313,U_1311) ),
    inference(clausify,[status(thm)],[f_511_4]) ).

fof(f_512_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_405_set__eq__subset]) ).

fof(f_512_2,plain,
    ! [U_1316,U_1315] :
      ( ( U_1316 = U_1315
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1315),U_1316))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1316),U_1315)) )
      & ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1315),U_1316))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1316),U_1315)) )
        | U_1316 != U_1315 ) ),
    inference(variable_rename,[status(thm)],[f_512_1]) ).

fof(f_512_3,plain,
    ( ! [U_1320,U_1318] :
        ( U_1320 = U_1318
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1318),U_1320))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1320),U_1318)) )
    & ! [U_1319,U_1317] :
        ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1317),U_1319))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1319),U_1317)) )
        | U_1319 != U_1317 ) ),
    inference(miniscope,[status(thm)],[f_512_2]) ).

fof(f_512_4,plain,
    ( ! [U_1319,U_1317] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1317),U_1319))
        | ~ sP112(U_1319,U_1317) )
    & ! [U_1319,U_1317] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1319),U_1317))
        | ~ sP112(U_1319,U_1317) )
    & ! [U_1320,U_1318] :
        ( U_1320 = U_1318
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1318),U_1320))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1320),U_1318)) )
    & ! [U_1319,U_1317] :
        ( sP112(U_1319,U_1317)
        | U_1319 != U_1317 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP112])],[f_512_3]) ).

cnf(f_512_5,plain,
    ( sP112(U_1319,U_1317)
    | U_1319 != U_1317 ),
    inference(clausify,[status(thm)],[f_512_4]) ).

cnf(f_512_6,plain,
    ( U_1320 = U_1318
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1318),U_1320))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1320),U_1318)) ),
    inference(clausify,[status(thm)],[f_512_4]) ).

cnf(f_512_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1319),U_1317))
    | ~ sP112(U_1319,U_1317) ),
    inference(clausify,[status(thm)],[f_512_4]) ).

cnf(f_512_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1317),U_1319))
    | ~ sP112(U_1319,U_1317) ),
    inference(clausify,[status(thm)],[f_512_4]) ).

fof(f_513_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_406_set__eq__subset]) ).

fof(f_513_2,plain,
    ! [U_1322,U_1321] :
      ( ( ( U_1322 = U_1321
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1321),U_1322))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1322),U_1321)) )
        & ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1321),U_1322))
            & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1322),U_1321)) )
          | U_1322 != U_1321 ) )
      | ~ is_fun_a_bool(U_1321)
      | ~ is_fun_a_bool(U_1322) ),
    inference(variable_rename,[status(thm)],[f_513_1]) ).

fof(f_513_3,plain,
    ( ! [U_1321,U_1322] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1321),U_1322))
        | ~ sP113(U_1321,U_1322) )
    & ! [U_1321,U_1322] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1322),U_1321))
        | ~ sP113(U_1321,U_1322) )
    & ! [U_1321,U_1322] :
        ( U_1322 = U_1321
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1321),U_1322))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1322),U_1321))
        | ~ sP114(U_1321,U_1322) )
    & ! [U_1321,U_1322] :
        ( sP113(U_1321,U_1322)
        | U_1322 != U_1321
        | ~ sP114(U_1321,U_1322) )
    & ! [U_1321,U_1322] :
        ( sP114(U_1321,U_1322)
        | ~ is_fun_a_bool(U_1321)
        | ~ is_fun_a_bool(U_1322) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP113,sP114])],[f_513_2]) ).

cnf(f_513_4,plain,
    ( sP114(U_1321,U_1322)
    | ~ is_fun_a_bool(U_1321)
    | ~ is_fun_a_bool(U_1322) ),
    inference(clausify,[status(thm)],[f_513_3]) ).

cnf(f_513_5,plain,
    ( sP113(U_1321,U_1322)
    | U_1322 != U_1321
    | ~ sP114(U_1321,U_1322) ),
    inference(clausify,[status(thm)],[f_513_3]) ).

cnf(f_513_6,plain,
    ( U_1322 = U_1321
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1321),U_1322))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1322),U_1321))
    | ~ sP114(U_1321,U_1322) ),
    inference(clausify,[status(thm)],[f_513_3]) ).

cnf(f_513_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1322),U_1321))
    | ~ sP113(U_1321,U_1322) ),
    inference(clausify,[status(thm)],[f_513_3]) ).

cnf(f_513_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1321),U_1322))
    | ~ sP113(U_1321,U_1322) ),
    inference(clausify,[status(thm)],[f_513_3]) ).

fof(f_514_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_407_equalityD1]) ).

fof(f_514_2,plain,
    ! [U_1324,U_1323] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1324),U_1323))
      | U_1324 != U_1323 ),
    inference(variable_rename,[status(thm)],[f_514_1]) ).

fof(f_514_3,plain,
    ! [U_1323,U_1324] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1324),U_1323))
      | U_1324 != U_1323 ),
    inference(definitional_conversion,[status(esa)],[f_514_2]) ).

cnf(f_514_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1324),U_1323))
    | U_1324 != U_1323 ),
    inference(clausify,[status(thm)],[f_514_3]) ).

fof(f_515_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_408_equalityD1]) ).

fof(f_515_2,plain,
    ! [U_1326,U_1325] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1326),U_1325))
      | U_1326 != U_1325 ),
    inference(variable_rename,[status(thm)],[f_515_1]) ).

fof(f_515_3,plain,
    ! [U_1325,U_1326] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1326),U_1325))
      | U_1326 != U_1325 ),
    inference(definitional_conversion,[status(esa)],[f_515_2]) ).

cnf(f_515_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1326),U_1325))
    | U_1326 != U_1325 ),
    inference(clausify,[status(thm)],[f_515_3]) ).

fof(f_516_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_409_equalityD1]) ).

fof(f_516_2,plain,
    ! [U_1328,U_1327] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1328),U_1327))
      | U_1328 != U_1327 ),
    inference(variable_rename,[status(thm)],[f_516_1]) ).

fof(f_516_3,plain,
    ! [U_1327,U_1328] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1328),U_1327))
      | U_1328 != U_1327 ),
    inference(definitional_conversion,[status(esa)],[f_516_2]) ).

cnf(f_516_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1328),U_1327))
    | U_1328 != U_1327 ),
    inference(clausify,[status(thm)],[f_516_3]) ).

fof(f_517_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A))
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_410_equalityD2]) ).

fof(f_517_2,plain,
    ! [U_1330,U_1329] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1329),U_1330))
      | U_1330 != U_1329 ),
    inference(variable_rename,[status(thm)],[f_517_1]) ).

fof(f_517_3,plain,
    ! [U_1330,U_1329] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1329),U_1330))
      | U_1330 != U_1329 ),
    inference(definitional_conversion,[status(esa)],[f_517_2]) ).

cnf(f_517_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1329),U_1330))
    | U_1330 != U_1329 ),
    inference(clausify,[status(thm)],[f_517_3]) ).

fof(f_518_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_411_equalityD2]) ).

fof(f_518_2,plain,
    ! [U_1332,U_1331] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1331),U_1332))
      | U_1332 != U_1331 ),
    inference(variable_rename,[status(thm)],[f_518_1]) ).

fof(f_518_3,plain,
    ! [U_1331,U_1332] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1331),U_1332))
      | U_1332 != U_1331 ),
    inference(definitional_conversion,[status(esa)],[f_518_2]) ).

cnf(f_518_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1331),U_1332))
    | U_1332 != U_1331 ),
    inference(clausify,[status(thm)],[f_518_3]) ).

fof(f_519_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_412_equalityD2]) ).

fof(f_519_2,plain,
    ! [U_1334,U_1333] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1333),U_1334))
      | U_1334 != U_1333 ),
    inference(variable_rename,[status(thm)],[f_519_1]) ).

fof(f_519_3,plain,
    ! [U_1333,U_1334] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1333),U_1334))
      | U_1334 != U_1333 ),
    inference(definitional_conversion,[status(esa)],[f_519_2]) ).

cnf(f_519_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1333),U_1334))
    | U_1334 != U_1333 ),
    inference(clausify,[status(thm)],[f_519_3]) ).

fof(f_520_1,plain,
    ! [X_1,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_413_in__mono]) ).

fof(f_520_2,plain,
    ! [U_1337,U_1336,U_1335] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1337),U_1335))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1337),U_1336))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1336),U_1335)) ),
    inference(variable_rename,[status(thm)],[f_520_1]) ).

fof(f_520_3,plain,
    ! [U_1335,U_1336,U_1337] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1337),U_1335))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1337),U_1336))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1336),U_1335)) ),
    inference(definitional_conversion,[status(esa)],[f_520_2]) ).

cnf(f_520_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1337),U_1335))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1337),U_1336))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1336),U_1335)) ),
    inference(clausify,[status(thm)],[f_520_3]) ).

fof(f_521_1,plain,
    ! [X_1,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_414_in__mono]) ).

fof(f_521_2,plain,
    ! [U_1340,U_1339,U_1338] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1340),U_1338))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1340),U_1339))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1339),U_1338)) ),
    inference(variable_rename,[status(thm)],[f_521_1]) ).

fof(f_521_3,plain,
    ! [U_1338,U_1339,U_1340] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1340),U_1338))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1340),U_1339))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1339),U_1338)) ),
    inference(definitional_conversion,[status(esa)],[f_521_2]) ).

cnf(f_521_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1340),U_1338))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1340),U_1339))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1339),U_1338)) ),
    inference(clausify,[status(thm)],[f_521_3]) ).

fof(f_522_1,plain,
    ! [X_1,A,B] :
      ( 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))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_415_in__mono]) ).

fof(f_522_2,plain,
    ! [U_1343,U_1342,U_1341] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1343),U_1341))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1343),U_1342))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1342),U_1341)) ),
    inference(variable_rename,[status(thm)],[f_522_1]) ).

fof(f_522_3,plain,
    ! [U_1341,U_1342,U_1343] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1343),U_1341))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1343),U_1342))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1342),U_1341)) ),
    inference(definitional_conversion,[status(esa)],[f_522_2]) ).

cnf(f_522_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1343),U_1341))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1343),U_1342))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1342),U_1341)) ),
    inference(clausify,[status(thm)],[f_522_3]) ).

fof(f_523_1,plain,
    ! [X_1,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_416_in__mono]) ).

fof(f_523_2,plain,
    ! [U_1346,U_1345,U_1344] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1346),U_1344))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1346),U_1345))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1345),U_1344)) ),
    inference(variable_rename,[status(thm)],[f_523_1]) ).

fof(f_523_3,plain,
    ! [U_1345,U_1344,U_1346] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1346),U_1344))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1346),U_1345))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1345),U_1344)) ),
    inference(definitional_conversion,[status(esa)],[f_523_2]) ).

cnf(f_523_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1346),U_1344))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1346),U_1345))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1345),U_1344)) ),
    inference(clausify,[status(thm)],[f_523_3]) ).

fof(f_524_1,plain,
    ! [B,X_1,A] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) ),
    inference(fof_nnf,[status(thm)],[fact_417_set__rev__mp]) ).

fof(f_524_2,plain,
    ! [U_1349,U_1348,U_1347] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1348),U_1349))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1347),U_1349))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1348),U_1347)) ),
    inference(variable_rename,[status(thm)],[f_524_1]) ).

fof(f_524_3,plain,
    ! [U_1347,U_1348,U_1349] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1348),U_1349))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1347),U_1349))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1348),U_1347)) ),
    inference(definitional_conversion,[status(esa)],[f_524_2]) ).

cnf(f_524_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1348),U_1349))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1347),U_1349))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1348),U_1347)) ),
    inference(clausify,[status(thm)],[f_524_3]) ).

fof(f_525_1,plain,
    ! [B,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))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) ),
    inference(fof_nnf,[status(thm)],[fact_418_set__rev__mp]) ).

fof(f_525_2,plain,
    ! [U_1352,U_1351,U_1350] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1351),U_1352))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1350),U_1352))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1351),U_1350)) ),
    inference(variable_rename,[status(thm)],[f_525_1]) ).

fof(f_525_3,plain,
    ! [U_1350,U_1351,U_1352] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1351),U_1352))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1350),U_1352))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1351),U_1350)) ),
    inference(definitional_conversion,[status(esa)],[f_525_2]) ).

cnf(f_525_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1351),U_1352))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1350),U_1352))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1351),U_1350)) ),
    inference(clausify,[status(thm)],[f_525_3]) ).

fof(f_526_1,plain,
    ! [B,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))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) ),
    inference(fof_nnf,[status(thm)],[fact_419_set__rev__mp]) ).

fof(f_526_2,plain,
    ! [U_1355,U_1354,U_1353] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1354),U_1355))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1353),U_1355))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1354),U_1353)) ),
    inference(variable_rename,[status(thm)],[f_526_1]) ).

fof(f_526_3,plain,
    ! [U_1353,U_1354,U_1355] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1354),U_1355))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1353),U_1355))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1354),U_1353)) ),
    inference(definitional_conversion,[status(esa)],[f_526_2]) ).

cnf(f_526_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1354),U_1355))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1353),U_1355))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1354),U_1353)) ),
    inference(clausify,[status(thm)],[f_526_3]) ).

fof(f_527_1,plain,
    ! [B,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))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) ),
    inference(fof_nnf,[status(thm)],[fact_420_set__rev__mp]) ).

fof(f_527_2,plain,
    ! [U_1358,U_1357,U_1356] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1357),U_1358))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1356),U_1358))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1357),U_1356)) ),
    inference(variable_rename,[status(thm)],[f_527_1]) ).

fof(f_527_3,plain,
    ! [U_1357,U_1356,U_1358] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1357),U_1358))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1356),U_1358))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1357),U_1356)) ),
    inference(definitional_conversion,[status(esa)],[f_527_2]) ).

cnf(f_527_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1357),U_1358))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1356),U_1358))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1357),U_1356)) ),
    inference(clausify,[status(thm)],[f_527_3]) ).

fof(f_528_1,plain,
    ! [X_1,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_421_set__mp]) ).

fof(f_528_2,plain,
    ! [U_1361,U_1360,U_1359] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1361),U_1359))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1361),U_1360))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1360),U_1359)) ),
    inference(variable_rename,[status(thm)],[f_528_1]) ).

fof(f_528_3,plain,
    ! [U_1360,U_1359,U_1361] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1361),U_1359))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1361),U_1360))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1360),U_1359)) ),
    inference(definitional_conversion,[status(esa)],[f_528_2]) ).

cnf(f_528_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1361),U_1359))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1361),U_1360))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1360),U_1359)) ),
    inference(clausify,[status(thm)],[f_528_3]) ).

fof(f_529_1,plain,
    ! [X_1,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_422_set__mp]) ).

fof(f_529_2,plain,
    ! [U_1364,U_1363,U_1362] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1364),U_1362))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1364),U_1363))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1363),U_1362)) ),
    inference(variable_rename,[status(thm)],[f_529_1]) ).

fof(f_529_3,plain,
    ! [U_1362,U_1363,U_1364] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1364),U_1362))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1364),U_1363))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1363),U_1362)) ),
    inference(definitional_conversion,[status(esa)],[f_529_2]) ).

cnf(f_529_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1364),U_1362))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1364),U_1363))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1363),U_1362)) ),
    inference(clausify,[status(thm)],[f_529_3]) ).

fof(f_530_1,plain,
    ! [X_1,A,B] :
      ( 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))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_423_set__mp]) ).

fof(f_530_2,plain,
    ! [U_1367,U_1366,U_1365] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1367),U_1365))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1367),U_1366))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1366),U_1365)) ),
    inference(variable_rename,[status(thm)],[f_530_1]) ).

fof(f_530_3,plain,
    ! [U_1365,U_1366,U_1367] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1367),U_1365))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1367),U_1366))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1366),U_1365)) ),
    inference(definitional_conversion,[status(esa)],[f_530_2]) ).

cnf(f_530_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1367),U_1365))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1367),U_1366))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1366),U_1365)) ),
    inference(clausify,[status(thm)],[f_530_3]) ).

fof(f_531_1,plain,
    ! [X_1,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_424_set__mp]) ).

fof(f_531_2,plain,
    ! [U_1370,U_1369,U_1368] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1370),U_1368))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1370),U_1369))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1369),U_1368)) ),
    inference(variable_rename,[status(thm)],[f_531_1]) ).

fof(f_531_3,plain,
    ! [U_1368,U_1369,U_1370] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1370),U_1368))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1370),U_1369))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1369),U_1368)) ),
    inference(definitional_conversion,[status(esa)],[f_531_2]) ).

cnf(f_531_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1370),U_1368))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1370),U_1369))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1369),U_1368)) ),
    inference(clausify,[status(thm)],[f_531_3]) ).

fof(f_532_1,plain,
    ! [C_11,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),C_11))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),C_11))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_425_subset__trans]) ).

fof(f_532_2,plain,
    ! [U_1373,U_1372,U_1371] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1372),U_1373))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1371),U_1373))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1372),U_1371)) ),
    inference(variable_rename,[status(thm)],[f_532_1]) ).

fof(f_532_3,plain,
    ! [U_1371,U_1372,U_1373] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1372),U_1373))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1371),U_1373))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1372),U_1371)) ),
    inference(definitional_conversion,[status(esa)],[f_532_2]) ).

cnf(f_532_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1372),U_1373))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1371),U_1373))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1372),U_1371)) ),
    inference(clausify,[status(thm)],[f_532_3]) ).

fof(f_533_1,plain,
    ! [C_11,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),C_11))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),C_11))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_426_subset__trans]) ).

fof(f_533_2,plain,
    ! [U_1376,U_1375,U_1374] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1375),U_1376))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1374),U_1376))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1375),U_1374)) ),
    inference(variable_rename,[status(thm)],[f_533_1]) ).

fof(f_533_3,plain,
    ! [U_1374,U_1375,U_1376] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1375),U_1376))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1374),U_1376))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1375),U_1374)) ),
    inference(definitional_conversion,[status(esa)],[f_533_2]) ).

cnf(f_533_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1375),U_1376))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1374),U_1376))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1375),U_1374)) ),
    inference(clausify,[status(thm)],[f_533_3]) ).

fof(f_534_1,plain,
    ! [C_11,A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),C_11))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),C_11))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_427_subset__trans]) ).

fof(f_534_2,plain,
    ! [U_1379,U_1378,U_1377] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1378),U_1379))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1377),U_1379))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1378),U_1377)) ),
    inference(variable_rename,[status(thm)],[f_534_1]) ).

fof(f_534_3,plain,
    ! [U_1377,U_1378,U_1379] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1378),U_1379))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1377),U_1379))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1378),U_1377)) ),
    inference(definitional_conversion,[status(esa)],[f_534_2]) ).

cnf(f_534_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1378),U_1379))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1377),U_1379))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1378),U_1377)) ),
    inference(clausify,[status(thm)],[f_534_3]) ).

fof(f_535_1,plain,
    ! [A,B] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A))
        & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) )
      | A != B ),
    inference(fof_nnf,[status(thm)],[fact_428_equalityE]) ).

fof(f_535_2,plain,
    ! [U_1381,U_1380] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1380),U_1381))
        & hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1381),U_1380)) )
      | U_1381 != U_1380 ),
    inference(variable_rename,[status(thm)],[f_535_1]) ).

fof(f_535_3,plain,
    ( ! [U_1380,U_1381] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1380),U_1381))
        | ~ sP115(U_1380,U_1381) )
    & ! [U_1380,U_1381] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1381),U_1380))
        | ~ sP115(U_1380,U_1381) )
    & ! [U_1380,U_1381] :
        ( sP115(U_1380,U_1381)
        | U_1381 != U_1380 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP115])],[f_535_2]) ).

cnf(f_535_4,plain,
    ( sP115(U_1380,U_1381)
    | U_1381 != U_1380 ),
    inference(clausify,[status(thm)],[f_535_3]) ).

cnf(f_535_5,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1381),U_1380))
    | ~ sP115(U_1380,U_1381) ),
    inference(clausify,[status(thm)],[f_535_3]) ).

cnf(f_535_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1380),U_1381))
    | ~ sP115(U_1380,U_1381) ),
    inference(clausify,[status(thm)],[f_535_3]) ).

fof(f_536_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_429_equalityE]) ).

fof(f_536_2,plain,
    ! [U_1383,U_1382] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1382),U_1383))
        & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1383),U_1382)) )
      | U_1383 != U_1382 ),
    inference(variable_rename,[status(thm)],[f_536_1]) ).

fof(f_536_3,plain,
    ( ! [U_1382,U_1383] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1382),U_1383))
        | ~ sP116(U_1382,U_1383) )
    & ! [U_1382,U_1383] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1383),U_1382))
        | ~ sP116(U_1382,U_1383) )
    & ! [U_1382,U_1383] :
        ( sP116(U_1382,U_1383)
        | U_1383 != U_1382 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP116])],[f_536_2]) ).

cnf(f_536_4,plain,
    ( sP116(U_1382,U_1383)
    | U_1383 != U_1382 ),
    inference(clausify,[status(thm)],[f_536_3]) ).

cnf(f_536_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1383),U_1382))
    | ~ sP116(U_1382,U_1383) ),
    inference(clausify,[status(thm)],[f_536_3]) ).

cnf(f_536_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1382),U_1383))
    | ~ sP116(U_1382,U_1383) ),
    inference(clausify,[status(thm)],[f_536_3]) ).

fof(f_537_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_430_equalityE]) ).

fof(f_537_2,plain,
    ! [U_1385,U_1384] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1384),U_1385))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1385),U_1384)) )
      | U_1385 != U_1384 ),
    inference(variable_rename,[status(thm)],[f_537_1]) ).

fof(f_537_3,plain,
    ( ! [U_1384,U_1385] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1384),U_1385))
        | ~ sP117(U_1384,U_1385) )
    & ! [U_1384,U_1385] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1385),U_1384))
        | ~ sP117(U_1384,U_1385) )
    & ! [U_1384,U_1385] :
        ( sP117(U_1384,U_1385)
        | U_1385 != U_1384 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP117])],[f_537_2]) ).

cnf(f_537_4,plain,
    ( sP117(U_1384,U_1385)
    | U_1385 != U_1384 ),
    inference(clausify,[status(thm)],[f_537_3]) ).

cnf(f_537_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1385),U_1384))
    | ~ sP117(U_1384,U_1385) ),
    inference(clausify,[status(thm)],[f_537_3]) ).

cnf(f_537_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1384),U_1385))
    | ~ sP117(U_1384,U_1385) ),
    inference(clausify,[status(thm)],[f_537_3]) ).

fof(f_538_1,plain,
    ! [Z_2,F,A] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Z_2),image_nat_int(F,A)))
        | ! [X_2] :
            ( Z_2 != hAPP_nat_int(F,X_2)
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) )
      & ( ? [X_2] :
            ( Z_2 = hAPP_nat_int(F,X_2)
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,Z_2),image_nat_int(F,A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_431_image__iff]) ).

fof(f_538_2,plain,
    ! [U_1390,U_1389,U_1388] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1390),image_nat_int(U_1389,U_1388)))
        | ! [U_1387] :
            ( U_1390 != hAPP_nat_int(U_1389,U_1387)
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1387),U_1388)) ) )
      & ( ? [U_1386] :
            ( U_1390 = hAPP_nat_int(U_1389,U_1386)
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1386),U_1388)) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1390),image_nat_int(U_1389,U_1388))) ) ),
    inference(variable_rename,[status(thm)],[f_538_1]) ).

fof(f_538_3,plain,
    ( ! [U_1396,U_1394,U_1392] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1396),image_nat_int(U_1394,U_1392)))
        | ! [U_1387] :
            ( U_1396 != hAPP_nat_int(U_1394,U_1387)
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1387),U_1392)) ) )
    & ! [U_1395,U_1393,U_1391] :
        ( ? [U_1386] :
            ( U_1395 = hAPP_nat_int(U_1393,U_1386)
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1386),U_1391)) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1395),image_nat_int(U_1393,U_1391))) ) ),
    inference(miniscope,[status(thm)],[f_538_2]) ).

fof(f_538_4,plain,
    ( ! [U_1396,U_1394,U_1392] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1396),image_nat_int(U_1394,U_1392)))
        | ! [U_1387] :
            ( U_1396 != hAPP_nat_int(U_1394,U_1387)
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1387),U_1392)) ) )
    & ! [U_1395,U_1393,U_1391] :
        ( ( U_1395 = hAPP_nat_int(U_1393,sK66(U_1395,U_1393,U_1391))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK66(U_1395,U_1393,U_1391)),U_1391)) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1395),image_nat_int(U_1393,U_1391))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_1386,sK66(U_1395,U_1393,U_1391))],[f_538_3]) ).

fof(f_538_5,plain,
    ( ! [U_1393,U_1391,U_1395] :
        ( U_1395 = hAPP_nat_int(U_1393,sK66(U_1395,U_1393,U_1391))
        | ~ sP118(U_1393,U_1391,U_1395) )
    & ! [U_1393,U_1391,U_1395] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK66(U_1395,U_1393,U_1391)),U_1391))
        | ~ sP118(U_1393,U_1391,U_1395) )
    & ! [U_1387,U_1394,U_1392,U_1396] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1396),image_nat_int(U_1394,U_1392)))
        | U_1396 != hAPP_nat_int(U_1394,U_1387)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1387),U_1392)) )
    & ! [U_1393,U_1391,U_1395] :
        ( sP118(U_1393,U_1391,U_1395)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1395),image_nat_int(U_1393,U_1391))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP118])],[f_538_4]) ).

cnf(f_538_6,plain,
    ( sP118(U_1393,U_1391,U_1395)
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1395),image_nat_int(U_1393,U_1391))) ),
    inference(clausify,[status(thm)],[f_538_5]) ).

cnf(f_538_7,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1396),image_nat_int(U_1394,U_1392)))
    | U_1396 != hAPP_nat_int(U_1394,U_1387)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1387),U_1392)) ),
    inference(clausify,[status(thm)],[f_538_5]) ).

cnf(f_538_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK66(U_1395,U_1393,U_1391)),U_1391))
    | ~ sP118(U_1393,U_1391,U_1395) ),
    inference(clausify,[status(thm)],[f_538_5]) ).

cnf(f_538_9,plain,
    ( U_1395 = hAPP_nat_int(U_1393,sK66(U_1395,U_1393,U_1391))
    | ~ sP118(U_1393,U_1391,U_1395) ),
    inference(clausify,[status(thm)],[f_538_5]) ).

fof(f_539_1,plain,
    ! [Z_2,F,A] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,Z_2),image_pname_a(F,A)))
          | ! [X_2] :
              ( Z_2 != hAPP_pname_a(F,X_2)
              | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
              | ~ is_pname(X_2) ) )
        & ( ? [X_2] :
              ( Z_2 = hAPP_pname_a(F,X_2)
              & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
              & is_pname(X_2) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,Z_2),image_pname_a(F,A))) ) )
      | ~ is_a(Z_2) ),
    inference(fof_nnf,[status(thm)],[fact_432_image__iff]) ).

fof(f_539_2,plain,
    ! [U_1401,U_1400,U_1399] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1401),image_pname_a(U_1400,U_1399)))
          | ! [U_1398] :
              ( U_1401 != hAPP_pname_a(U_1400,U_1398)
              | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1398),U_1399))
              | ~ is_pname(U_1398) ) )
        & ( ? [U_1397] :
              ( U_1401 = hAPP_pname_a(U_1400,U_1397)
              & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1397),U_1399))
              & is_pname(U_1397) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1401),image_pname_a(U_1400,U_1399))) ) )
      | ~ is_a(U_1401) ),
    inference(variable_rename,[status(thm)],[f_539_1]) ).

fof(f_539_3,plain,
    ! [U_1401] :
      ( ( ! [U_1405,U_1403] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1401),image_pname_a(U_1405,U_1403)))
            | ! [U_1398] :
                ( U_1401 != hAPP_pname_a(U_1405,U_1398)
                | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1398),U_1403))
                | ~ is_pname(U_1398) ) )
        & ! [U_1404,U_1402] :
            ( ? [U_1397] :
                ( U_1401 = hAPP_pname_a(U_1404,U_1397)
                & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1397),U_1402))
                & is_pname(U_1397) )
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1401),image_pname_a(U_1404,U_1402))) ) )
      | ~ is_a(U_1401) ),
    inference(miniscope,[status(thm)],[f_539_2]) ).

fof(f_539_4,plain,
    ! [U_1401] :
      ( ( ! [U_1405,U_1403] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1401),image_pname_a(U_1405,U_1403)))
            | ! [U_1398] :
                ( U_1401 != hAPP_pname_a(U_1405,U_1398)
                | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1398),U_1403))
                | ~ is_pname(U_1398) ) )
        & ! [U_1404,U_1402] :
            ( ( U_1401 = hAPP_pname_a(U_1404,sK67(U_1401,U_1404,U_1402))
              & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK67(U_1401,U_1404,U_1402)),U_1402))
              & is_pname(sK67(U_1401,U_1404,U_1402)) )
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1401),image_pname_a(U_1404,U_1402))) ) )
      | ~ is_a(U_1401) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_1397,sK67(U_1401,U_1404,U_1402))],[f_539_3]) ).

fof(f_539_5,plain,
    ( ! [U_1402,U_1401,U_1404] :
        ( U_1401 = hAPP_pname_a(U_1404,sK67(U_1401,U_1404,U_1402))
        | ~ sP119(U_1402,U_1401,U_1404) )
    & ! [U_1402,U_1401,U_1404] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK67(U_1401,U_1404,U_1402)),U_1402))
        | ~ sP119(U_1402,U_1401,U_1404) )
    & ! [U_1402,U_1401,U_1404] :
        ( is_pname(sK67(U_1401,U_1404,U_1402))
        | ~ sP119(U_1402,U_1401,U_1404) )
    & ! [U_1398,U_1402,U_1401,U_1405,U_1404,U_1403] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1401),image_pname_a(U_1405,U_1403)))
        | U_1401 != hAPP_pname_a(U_1405,U_1398)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1398),U_1403))
        | ~ is_pname(U_1398)
        | ~ sP120(U_1398,U_1402,U_1401,U_1405,U_1404,U_1403) )
    & ! [U_1398,U_1402,U_1401,U_1405,U_1404,U_1403] :
        ( sP119(U_1402,U_1401,U_1404)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1401),image_pname_a(U_1404,U_1402)))
        | ~ sP120(U_1398,U_1402,U_1401,U_1405,U_1404,U_1403) )
    & ! [U_1398,U_1402,U_1401,U_1405,U_1404,U_1403] :
        ( sP120(U_1398,U_1402,U_1401,U_1405,U_1404,U_1403)
        | ~ is_a(U_1401) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP119,sP120])],[f_539_4]) ).

cnf(f_539_6,plain,
    ( sP120(U_1398,U_1402,U_1401,U_1405,U_1404,U_1403)
    | ~ is_a(U_1401) ),
    inference(clausify,[status(thm)],[f_539_5]) ).

cnf(f_539_7,plain,
    ( sP119(U_1402,U_1401,U_1404)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1401),image_pname_a(U_1404,U_1402)))
    | ~ sP120(U_1398,U_1402,U_1401,U_1405,U_1404,U_1403) ),
    inference(clausify,[status(thm)],[f_539_5]) ).

cnf(f_539_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1401),image_pname_a(U_1405,U_1403)))
    | U_1401 != hAPP_pname_a(U_1405,U_1398)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1398),U_1403))
    | ~ is_pname(U_1398)
    | ~ sP120(U_1398,U_1402,U_1401,U_1405,U_1404,U_1403) ),
    inference(clausify,[status(thm)],[f_539_5]) ).

cnf(f_539_9,plain,
    ( is_pname(sK67(U_1401,U_1404,U_1402))
    | ~ sP119(U_1402,U_1401,U_1404) ),
    inference(clausify,[status(thm)],[f_539_5]) ).

cnf(f_539_10,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK67(U_1401,U_1404,U_1402)),U_1402))
    | ~ sP119(U_1402,U_1401,U_1404) ),
    inference(clausify,[status(thm)],[f_539_5]) ).

cnf(f_539_11,plain,
    ( U_1401 = hAPP_pname_a(U_1404,sK67(U_1401,U_1404,U_1402))
    | ~ sP119(U_1402,U_1401,U_1404) ),
    inference(clausify,[status(thm)],[f_539_5]) ).

fof(f_540_1,plain,
    ! [F,X_1,A] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(F,X_1)),image_nat_int(F,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) ),
    inference(fof_nnf,[status(thm)],[fact_433_imageI]) ).

fof(f_540_2,plain,
    ! [U_1408,U_1407,U_1406] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(U_1408,U_1407)),image_nat_int(U_1408,U_1406)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1407),U_1406)) ),
    inference(variable_rename,[status(thm)],[f_540_1]) ).

fof(f_540_3,plain,
    ! [U_1407,U_1408,U_1406] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(U_1408,U_1407)),image_nat_int(U_1408,U_1406)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1407),U_1406)) ),
    inference(definitional_conversion,[status(esa)],[f_540_2]) ).

cnf(f_540_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(U_1408,U_1407)),image_nat_int(U_1408,U_1406)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1407),U_1406)) ),
    inference(clausify,[status(thm)],[f_540_3]) ).

fof(f_541_1,plain,
    ! [F,X_1,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(F,X_1)),image_pname_a(F,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) ),
    inference(fof_nnf,[status(thm)],[fact_434_imageI]) ).

fof(f_541_2,plain,
    ! [U_1411,U_1410,U_1409] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(U_1411,U_1410)),image_pname_a(U_1411,U_1409)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1410),U_1409)) ),
    inference(variable_rename,[status(thm)],[f_541_1]) ).

fof(f_541_3,plain,
    ! [U_1409,U_1411,U_1410] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(U_1411,U_1410)),image_pname_a(U_1411,U_1409)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1410),U_1409)) ),
    inference(definitional_conversion,[status(esa)],[f_541_2]) ).

cnf(f_541_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(U_1411,U_1410)),image_pname_a(U_1411,U_1409)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1410),U_1409)) ),
    inference(clausify,[status(thm)],[f_541_3]) ).

fof(f_542_1,plain,
    ! [B_3,F,X_1,A] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_3),image_nat_int(F,A)))
      | B_3 != hAPP_nat_int(F,X_1)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) ),
    inference(fof_nnf,[status(thm)],[fact_435_rev__image__eqI]) ).

fof(f_542_2,plain,
    ! [U_1415,U_1414,U_1413,U_1412] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1415),image_nat_int(U_1414,U_1412)))
      | U_1415 != hAPP_nat_int(U_1414,U_1413)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1413),U_1412)) ),
    inference(variable_rename,[status(thm)],[f_542_1]) ).

fof(f_542_3,plain,
    ! [U_1412,U_1413,U_1414,U_1415] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1415),image_nat_int(U_1414,U_1412)))
      | U_1415 != hAPP_nat_int(U_1414,U_1413)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1413),U_1412)) ),
    inference(definitional_conversion,[status(esa)],[f_542_2]) ).

cnf(f_542_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1415),image_nat_int(U_1414,U_1412)))
    | U_1415 != hAPP_nat_int(U_1414,U_1413)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1413),U_1412)) ),
    inference(clausify,[status(thm)],[f_542_3]) ).

fof(f_543_1,plain,
    ! [B_3,F,X_1,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
      | B_3 != hAPP_pname_a(F,X_1)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) ),
    inference(fof_nnf,[status(thm)],[fact_436_rev__image__eqI]) ).

fof(f_543_2,plain,
    ! [U_1419,U_1418,U_1417,U_1416] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1419),image_pname_a(U_1418,U_1416)))
      | U_1419 != hAPP_pname_a(U_1418,U_1417)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1417),U_1416)) ),
    inference(variable_rename,[status(thm)],[f_543_1]) ).

fof(f_543_3,plain,
    ! [U_1417,U_1416,U_1418,U_1419] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1419),image_pname_a(U_1418,U_1416)))
      | U_1419 != hAPP_pname_a(U_1418,U_1417)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1417),U_1416)) ),
    inference(definitional_conversion,[status(esa)],[f_543_2]) ).

cnf(f_543_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1419),image_pname_a(U_1418,U_1416)))
    | U_1419 != hAPP_pname_a(U_1418,U_1417)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1417),U_1416)) ),
    inference(clausify,[status(thm)],[f_543_3]) ).

fof(f_544_1,plain,
    ! [X_2,Xa] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_2),Xa) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X_2)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),Xa))),
    inference(fof_nnf,[status(thm)],[fact_437_insert__compr__raw]) ).

fof(f_544_2,plain,
    ! [U_1421,U_1420] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1421),U_1420) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_1421)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_1420))),
    inference(variable_rename,[status(thm)],[f_544_1]) ).

fof(f_544_3,plain,
    ! [U_1421,U_1420] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1421),U_1420) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_1421)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_1420))),
    inference(definitional_conversion,[status(esa)],[f_544_2]) ).

cnf(f_544_4,plain,
    hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1421),U_1420) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_1421)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_1420))),
    inference(clausify,[status(thm)],[f_544_3]) ).

fof(f_545_1,plain,
    ! [X_2,Xa] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),Xa) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),X_2)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),Xa))),
    inference(fof_nnf,[status(thm)],[fact_438_insert__compr__raw]) ).

fof(f_545_2,plain,
    ! [U_1423,U_1422] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1423),U_1422) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),U_1423)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_1422))),
    inference(variable_rename,[status(thm)],[f_545_1]) ).

fof(f_545_3,plain,
    ! [U_1422,U_1423] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1423),U_1422) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),U_1423)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_1422))),
    inference(definitional_conversion,[status(esa)],[f_545_2]) ).

cnf(f_545_4,plain,
    hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1423),U_1422) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fdisj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),U_1423)),hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_1422))),
    inference(clausify,[status(thm)],[f_545_3]) ).

fof(f_546_1,plain,
    ! [X_2,Xa] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),Xa) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X_2)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),Xa))),
    inference(fof_nnf,[status(thm)],[fact_439_insert__compr__raw]) ).

fof(f_546_2,plain,
    ! [U_1425,U_1424] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1425),U_1424) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_1425)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_1424))),
    inference(variable_rename,[status(thm)],[f_546_1]) ).

fof(f_546_3,plain,
    ! [U_1425,U_1424] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1425),U_1424) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_1425)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_1424))),
    inference(definitional_conversion,[status(esa)],[f_546_2]) ).

cnf(f_546_4,plain,
    hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1425),U_1424) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_1425)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_1424))),
    inference(clausify,[status(thm)],[f_546_3]) ).

fof(f_547_1,plain,
    ! [X_2,Xa] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),Xa) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X_2)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),Xa))),
    inference(fof_nnf,[status(thm)],[fact_440_insert__compr__raw]) ).

fof(f_547_2,plain,
    ! [U_1427,U_1426] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1427),U_1426) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_1427)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_1426))),
    inference(variable_rename,[status(thm)],[f_547_1]) ).

fof(f_547_3,plain,
    ! [U_1426,U_1427] : hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1427),U_1426) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_1427)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_1426))),
    inference(definitional_conversion,[status(esa)],[f_547_2]) ).

cnf(f_547_4,plain,
    hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1427),U_1426) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),U_1427)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_1426))),
    inference(clausify,[status(thm)],[f_547_3]) ).

fof(f_548_1,plain,
    ! [F,G_1] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F),G_1))
        | ? [X_2] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(F,X_2)),hAPP_int_bool(G_1,X_2))) )
      & ( ! [X_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(F,X_2)),hAPP_int_bool(G_1,X_2)))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F),G_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_441_le__fun__def]) ).

fof(f_548_2,plain,
    ! [U_1431,U_1430] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1431),U_1430))
        | ? [U_1429] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(U_1431,U_1429)),hAPP_int_bool(U_1430,U_1429))) )
      & ( ! [U_1428] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(U_1431,U_1428)),hAPP_int_bool(U_1430,U_1428)))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1431),U_1430)) ) ),
    inference(variable_rename,[status(thm)],[f_548_1]) ).

fof(f_548_3,plain,
    ( ! [U_1435,U_1433] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1435),U_1433))
        | ? [U_1429] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(U_1435,U_1429)),hAPP_int_bool(U_1433,U_1429))) )
    & ! [U_1434,U_1432] :
        ( ! [U_1428] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(U_1434,U_1428)),hAPP_int_bool(U_1432,U_1428)))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1434),U_1432)) ) ),
    inference(miniscope,[status(thm)],[f_548_2]) ).

fof(f_548_4,plain,
    ( ! [U_1435,U_1433] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1435),U_1433))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(U_1435,sK68(U_1435,U_1433))),hAPP_int_bool(U_1433,sK68(U_1435,U_1433)))) )
    & ! [U_1434,U_1432] :
        ( ! [U_1428] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(U_1434,U_1428)),hAPP_int_bool(U_1432,U_1428)))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1434),U_1432)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_1429,sK68(U_1435,U_1433))],[f_548_3]) ).

fof(f_548_5,plain,
    ( ! [U_1433,U_1435] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1435),U_1433))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(U_1435,sK68(U_1435,U_1433))),hAPP_int_bool(U_1433,sK68(U_1435,U_1433)))) )
    & ! [U_1434,U_1428,U_1432] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(U_1434,U_1428)),hAPP_int_bool(U_1432,U_1428)))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1434),U_1432)) ) ),
    inference(definitional_conversion,[status(esa)],[f_548_4]) ).

cnf(f_548_6,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(U_1434,U_1428)),hAPP_int_bool(U_1432,U_1428)))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1434),U_1432)) ),
    inference(clausify,[status(thm)],[f_548_5]) ).

cnf(f_548_7,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1435),U_1433))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(U_1435,sK68(U_1435,U_1433))),hAPP_int_bool(U_1433,sK68(U_1435,U_1433)))) ),
    inference(clausify,[status(thm)],[f_548_5]) ).

fof(f_549_1,plain,
    ! [F,G_1] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G_1))
        | ? [X_2] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G_1,X_2))) )
      & ( ! [X_2] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G_1,X_2)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_442_le__fun__def]) ).

fof(f_549_2,plain,
    ! [U_1439,U_1438] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1439),U_1438))
        | ? [U_1437] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1439,U_1437)),hAPP_nat_bool(U_1438,U_1437))) )
      & ( ! [U_1436] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1439,U_1436)),hAPP_nat_bool(U_1438,U_1436)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1439),U_1438)) ) ),
    inference(variable_rename,[status(thm)],[f_549_1]) ).

fof(f_549_3,plain,
    ( ! [U_1443,U_1441] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1443),U_1441))
        | ? [U_1437] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1443,U_1437)),hAPP_nat_bool(U_1441,U_1437))) )
    & ! [U_1442,U_1440] :
        ( ! [U_1436] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1442,U_1436)),hAPP_nat_bool(U_1440,U_1436)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1442),U_1440)) ) ),
    inference(miniscope,[status(thm)],[f_549_2]) ).

fof(f_549_4,plain,
    ( ! [U_1443,U_1441] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1443),U_1441))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1443,sK69(U_1443,U_1441))),hAPP_nat_bool(U_1441,sK69(U_1443,U_1441)))) )
    & ! [U_1442,U_1440] :
        ( ! [U_1436] : hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1442,U_1436)),hAPP_nat_bool(U_1440,U_1436)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1442),U_1440)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_1437,sK69(U_1443,U_1441))],[f_549_3]) ).

fof(f_549_5,plain,
    ( ! [U_1441,U_1443] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1443),U_1441))
        | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1443,sK69(U_1443,U_1441))),hAPP_nat_bool(U_1441,sK69(U_1443,U_1441)))) )
    & ! [U_1436,U_1442,U_1440] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1442,U_1436)),hAPP_nat_bool(U_1440,U_1436)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1442),U_1440)) ) ),
    inference(definitional_conversion,[status(esa)],[f_549_4]) ).

cnf(f_549_6,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1442,U_1436)),hAPP_nat_bool(U_1440,U_1436)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1442),U_1440)) ),
    inference(clausify,[status(thm)],[f_549_5]) ).

cnf(f_549_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1443),U_1441))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1443,sK69(U_1443,U_1441))),hAPP_nat_bool(U_1441,sK69(U_1443,U_1441)))) ),
    inference(clausify,[status(thm)],[f_549_5]) ).

fof(f_550_1,plain,
    ! [F,G_1] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F),G_1))
        | ? [X_2] :
            ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(F,X_2)),hAPP_a_bool(G_1,X_2)))
            & is_a(X_2) ) )
      & ( ! [X_2] :
            ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(F,X_2)),hAPP_a_bool(G_1,X_2)))
            | ~ is_a(X_2) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F),G_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_443_le__fun__def]) ).

fof(f_550_2,plain,
    ! [U_1447,U_1446] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1447),U_1446))
        | ? [U_1445] :
            ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1447,U_1445)),hAPP_a_bool(U_1446,U_1445)))
            & is_a(U_1445) ) )
      & ( ! [U_1444] :
            ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1447,U_1444)),hAPP_a_bool(U_1446,U_1444)))
            | ~ is_a(U_1444) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1447),U_1446)) ) ),
    inference(variable_rename,[status(thm)],[f_550_1]) ).

fof(f_550_3,plain,
    ( ! [U_1451,U_1449] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1451),U_1449))
        | ? [U_1445] :
            ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1451,U_1445)),hAPP_a_bool(U_1449,U_1445)))
            & is_a(U_1445) ) )
    & ! [U_1450,U_1448] :
        ( ! [U_1444] :
            ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1450,U_1444)),hAPP_a_bool(U_1448,U_1444)))
            | ~ is_a(U_1444) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1450),U_1448)) ) ),
    inference(miniscope,[status(thm)],[f_550_2]) ).

fof(f_550_4,plain,
    ( ! [U_1451,U_1449] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1451),U_1449))
        | ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1451,sK70(U_1451,U_1449))),hAPP_a_bool(U_1449,sK70(U_1451,U_1449))))
          & is_a(sK70(U_1451,U_1449)) ) )
    & ! [U_1450,U_1448] :
        ( ! [U_1444] :
            ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1450,U_1444)),hAPP_a_bool(U_1448,U_1444)))
            | ~ is_a(U_1444) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1450),U_1448)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_1445,sK70(U_1451,U_1449))],[f_550_3]) ).

fof(f_550_5,plain,
    ( ! [U_1449,U_1451] :
        ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1451,sK70(U_1451,U_1449))),hAPP_a_bool(U_1449,sK70(U_1451,U_1449))))
        | ~ sP121(U_1449,U_1451) )
    & ! [U_1449,U_1451] :
        ( is_a(sK70(U_1451,U_1449))
        | ~ sP121(U_1449,U_1451) )
    & ! [U_1449,U_1451] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1451),U_1449))
        | sP121(U_1449,U_1451) )
    & ! [U_1444,U_1448,U_1450] :
        ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1450,U_1444)),hAPP_a_bool(U_1448,U_1444)))
        | ~ is_a(U_1444)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1450),U_1448)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP121])],[f_550_4]) ).

cnf(f_550_6,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1450,U_1444)),hAPP_a_bool(U_1448,U_1444)))
    | ~ is_a(U_1444)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1450),U_1448)) ),
    inference(clausify,[status(thm)],[f_550_5]) ).

cnf(f_550_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1451),U_1449))
    | sP121(U_1449,U_1451) ),
    inference(clausify,[status(thm)],[f_550_5]) ).

cnf(f_550_8,plain,
    ( is_a(sK70(U_1451,U_1449))
    | ~ sP121(U_1449,U_1451) ),
    inference(clausify,[status(thm)],[f_550_5]) ).

cnf(f_550_9,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1451,sK70(U_1451,U_1449))),hAPP_a_bool(U_1449,sK70(U_1451,U_1449))))
    | ~ sP121(U_1449,U_1451) ),
    inference(clausify,[status(thm)],[f_550_5]) ).

fof(f_551_1,plain,
    ! [X_1,F,G_1] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(F,X_1)),hAPP_int_bool(G_1,X_1)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F),G_1)) ),
    inference(fof_nnf,[status(thm)],[fact_444_le__funD]) ).

fof(f_551_2,plain,
    ! [U_1454,U_1453,U_1452] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(U_1453,U_1454)),hAPP_int_bool(U_1452,U_1454)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1453),U_1452)) ),
    inference(variable_rename,[status(thm)],[f_551_1]) ).

fof(f_551_3,plain,
    ! [U_1453,U_1454,U_1452] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(U_1453,U_1454)),hAPP_int_bool(U_1452,U_1454)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1453),U_1452)) ),
    inference(definitional_conversion,[status(esa)],[f_551_2]) ).

cnf(f_551_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(U_1453,U_1454)),hAPP_int_bool(U_1452,U_1454)))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1453),U_1452)) ),
    inference(clausify,[status(thm)],[f_551_3]) ).

fof(f_552_1,plain,
    ! [X_1,F,G_1] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G_1,X_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G_1)) ),
    inference(fof_nnf,[status(thm)],[fact_445_le__funD]) ).

fof(f_552_2,plain,
    ! [U_1457,U_1456,U_1455] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1456,U_1457)),hAPP_nat_bool(U_1455,U_1457)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1456),U_1455)) ),
    inference(variable_rename,[status(thm)],[f_552_1]) ).

fof(f_552_3,plain,
    ! [U_1455,U_1457,U_1456] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1456,U_1457)),hAPP_nat_bool(U_1455,U_1457)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1456),U_1455)) ),
    inference(definitional_conversion,[status(esa)],[f_552_2]) ).

cnf(f_552_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1456,U_1457)),hAPP_nat_bool(U_1455,U_1457)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1456),U_1455)) ),
    inference(clausify,[status(thm)],[f_552_3]) ).

fof(f_553_1,plain,
    ! [X_1,F,G_1] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(F,X_1)),hAPP_a_bool(G_1,X_1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F),G_1)) ),
    inference(fof_nnf,[status(thm)],[fact_446_le__funD]) ).

fof(f_553_2,plain,
    ! [U_1460,U_1459,U_1458] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1459,U_1460)),hAPP_a_bool(U_1458,U_1460)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1459),U_1458)) ),
    inference(variable_rename,[status(thm)],[f_553_1]) ).

fof(f_553_3,plain,
    ! [U_1458,U_1459,U_1460] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1459,U_1460)),hAPP_a_bool(U_1458,U_1460)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1459),U_1458)) ),
    inference(definitional_conversion,[status(esa)],[f_553_2]) ).

cnf(f_553_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1459,U_1460)),hAPP_a_bool(U_1458,U_1460)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1459),U_1458)) ),
    inference(clausify,[status(thm)],[f_553_3]) ).

fof(f_554_1,plain,
    ! [X_1,F,G_1] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(F,X_1)),hAPP_int_bool(G_1,X_1)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F),G_1)) ),
    inference(fof_nnf,[status(thm)],[fact_447_le__funE]) ).

fof(f_554_2,plain,
    ! [U_1463,U_1462,U_1461] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(U_1462,U_1463)),hAPP_int_bool(U_1461,U_1463)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1462),U_1461)) ),
    inference(variable_rename,[status(thm)],[f_554_1]) ).

fof(f_554_3,plain,
    ! [U_1461,U_1462,U_1463] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(U_1462,U_1463)),hAPP_int_bool(U_1461,U_1463)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1462),U_1461)) ),
    inference(definitional_conversion,[status(esa)],[f_554_2]) ).

cnf(f_554_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(U_1462,U_1463)),hAPP_int_bool(U_1461,U_1463)))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1462),U_1461)) ),
    inference(clausify,[status(thm)],[f_554_3]) ).

fof(f_555_1,plain,
    ! [X_1,F,G_1] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_1)),hAPP_nat_bool(G_1,X_1)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G_1)) ),
    inference(fof_nnf,[status(thm)],[fact_448_le__funE]) ).

fof(f_555_2,plain,
    ! [U_1466,U_1465,U_1464] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1465,U_1466)),hAPP_nat_bool(U_1464,U_1466)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1465),U_1464)) ),
    inference(variable_rename,[status(thm)],[f_555_1]) ).

fof(f_555_3,plain,
    ! [U_1464,U_1465,U_1466] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1465,U_1466)),hAPP_nat_bool(U_1464,U_1466)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1465),U_1464)) ),
    inference(definitional_conversion,[status(esa)],[f_555_2]) ).

cnf(f_555_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1465,U_1466)),hAPP_nat_bool(U_1464,U_1466)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1465),U_1464)) ),
    inference(clausify,[status(thm)],[f_555_3]) ).

fof(f_556_1,plain,
    ! [X_1,F,G_1] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(F,X_1)),hAPP_a_bool(G_1,X_1)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F),G_1)) ),
    inference(fof_nnf,[status(thm)],[fact_449_le__funE]) ).

fof(f_556_2,plain,
    ! [U_1469,U_1468,U_1467] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1468,U_1469)),hAPP_a_bool(U_1467,U_1469)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1468),U_1467)) ),
    inference(variable_rename,[status(thm)],[f_556_1]) ).

fof(f_556_3,plain,
    ! [U_1467,U_1468,U_1469] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1468,U_1469)),hAPP_a_bool(U_1467,U_1469)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1468),U_1467)) ),
    inference(definitional_conversion,[status(esa)],[f_556_2]) ).

cnf(f_556_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1468,U_1469)),hAPP_a_bool(U_1467,U_1469)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1468),U_1467)) ),
    inference(clausify,[status(thm)],[f_556_3]) ).

fof(f_557_1,plain,
    ! [B,A_2] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),B))),
    inference(fof_nnf,[status(thm)],[fact_450_subset__insertI]) ).

fof(f_557_2,plain,
    ! [U_1471,U_1470] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1471),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1470),U_1471))),
    inference(variable_rename,[status(thm)],[f_557_1]) ).

fof(f_557_3,plain,
    ! [U_1470,U_1471] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1471),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1470),U_1471))),
    inference(definitional_conversion,[status(esa)],[f_557_2]) ).

cnf(f_557_4,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1471),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1470),U_1471))),
    inference(clausify,[status(thm)],[f_557_3]) ).

fof(f_558_1,plain,
    ! [B,A_2] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),B))),
    inference(fof_nnf,[status(thm)],[fact_451_subset__insertI]) ).

fof(f_558_2,plain,
    ! [U_1473,U_1472] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1473),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1472),U_1473))),
    inference(variable_rename,[status(thm)],[f_558_1]) ).

fof(f_558_3,plain,
    ! [U_1472,U_1473] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1473),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1472),U_1473))),
    inference(definitional_conversion,[status(esa)],[f_558_2]) ).

cnf(f_558_4,plain,
    hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1473),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1472),U_1473))),
    inference(clausify,[status(thm)],[f_558_3]) ).

fof(f_559_1,plain,
    ! [B,A_2] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B))),
    inference(fof_nnf,[status(thm)],[fact_452_subset__insertI]) ).

fof(f_559_2,plain,
    ! [U_1475,U_1474] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1475),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1474),U_1475))),
    inference(variable_rename,[status(thm)],[f_559_1]) ).

fof(f_559_3,plain,
    ! [U_1474,U_1475] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1475),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1474),U_1475))),
    inference(definitional_conversion,[status(esa)],[f_559_2]) ).

cnf(f_559_4,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1475),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1474),U_1475))),
    inference(clausify,[status(thm)],[f_559_3]) ).

fof(f_560_1,plain,
    ! [X_1,A,B] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_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,X_1),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_1),B)) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_453_insert__subset]) ).

fof(f_560_2,plain,
    ! [U_1478,U_1477,U_1476] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1478),U_1477)),U_1476))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1477),U_1476))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1478),U_1476)) )
      & ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1477),U_1476))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1478),U_1476)) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1478),U_1477)),U_1476)) ) ),
    inference(variable_rename,[status(thm)],[f_560_1]) ).

fof(f_560_3,plain,
    ( ! [U_1484,U_1482,U_1480] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1484),U_1482)),U_1480))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1482),U_1480))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1484),U_1480)) )
    & ! [U_1483,U_1481,U_1479] :
        ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1481),U_1479))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1483),U_1479)) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1483),U_1481)),U_1479)) ) ),
    inference(miniscope,[status(thm)],[f_560_2]) ).

fof(f_560_4,plain,
    ( ! [U_1481,U_1479,U_1483] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1481),U_1479))
        | ~ sP122(U_1481,U_1479,U_1483) )
    & ! [U_1481,U_1479,U_1483] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1483),U_1479))
        | ~ sP122(U_1481,U_1479,U_1483) )
    & ! [U_1482,U_1480,U_1484] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1484),U_1482)),U_1480))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1482),U_1480))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1484),U_1480)) )
    & ! [U_1481,U_1479,U_1483] :
        ( sP122(U_1481,U_1479,U_1483)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1483),U_1481)),U_1479)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP122])],[f_560_3]) ).

cnf(f_560_5,plain,
    ( sP122(U_1481,U_1479,U_1483)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1483),U_1481)),U_1479)) ),
    inference(clausify,[status(thm)],[f_560_4]) ).

cnf(f_560_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1484),U_1482)),U_1480))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1482),U_1480))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1484),U_1480)) ),
    inference(clausify,[status(thm)],[f_560_4]) ).

cnf(f_560_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1483),U_1479))
    | ~ sP122(U_1481,U_1479,U_1483) ),
    inference(clausify,[status(thm)],[f_560_4]) ).

cnf(f_560_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1481),U_1479))
    | ~ sP122(U_1481,U_1479,U_1483) ),
    inference(clausify,[status(thm)],[f_560_4]) ).

fof(f_561_1,plain,
    ! [X_1,A,B] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)),B))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B)) )
      & ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B)) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_454_insert__subset]) ).

fof(f_561_2,plain,
    ! [U_1487,U_1486,U_1485] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1487),U_1486)),U_1485))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1486),U_1485))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1487),U_1485)) )
      & ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1486),U_1485))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1487),U_1485)) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1487),U_1486)),U_1485)) ) ),
    inference(variable_rename,[status(thm)],[f_561_1]) ).

fof(f_561_3,plain,
    ( ! [U_1493,U_1491,U_1489] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1493),U_1491)),U_1489))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1491),U_1489))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1493),U_1489)) )
    & ! [U_1492,U_1490,U_1488] :
        ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1490),U_1488))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1492),U_1488)) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1492),U_1490)),U_1488)) ) ),
    inference(miniscope,[status(thm)],[f_561_2]) ).

fof(f_561_4,plain,
    ( ! [U_1488,U_1490,U_1492] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1490),U_1488))
        | ~ sP123(U_1488,U_1490,U_1492) )
    & ! [U_1488,U_1490,U_1492] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1492),U_1488))
        | ~ sP123(U_1488,U_1490,U_1492) )
    & ! [U_1491,U_1489,U_1493] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1493),U_1491)),U_1489))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1491),U_1489))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1493),U_1489)) )
    & ! [U_1488,U_1490,U_1492] :
        ( sP123(U_1488,U_1490,U_1492)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1492),U_1490)),U_1488)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP123])],[f_561_3]) ).

cnf(f_561_5,plain,
    ( sP123(U_1488,U_1490,U_1492)
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1492),U_1490)),U_1488)) ),
    inference(clausify,[status(thm)],[f_561_4]) ).

cnf(f_561_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1493),U_1491)),U_1489))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1491),U_1489))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1493),U_1489)) ),
    inference(clausify,[status(thm)],[f_561_4]) ).

cnf(f_561_7,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1492),U_1488))
    | ~ sP123(U_1488,U_1490,U_1492) ),
    inference(clausify,[status(thm)],[f_561_4]) ).

cnf(f_561_8,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1490),U_1488))
    | ~ sP123(U_1488,U_1490,U_1492) ),
    inference(clausify,[status(thm)],[f_561_4]) ).

fof(f_562_1,plain,
    ! [X_1,A,B] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),B))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) )
      & ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_455_insert__subset]) ).

fof(f_562_2,plain,
    ! [U_1496,U_1495,U_1494] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1496),U_1495)),U_1494))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1495),U_1494))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1496),U_1494)) )
      & ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1495),U_1494))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1496),U_1494)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1496),U_1495)),U_1494)) ) ),
    inference(variable_rename,[status(thm)],[f_562_1]) ).

fof(f_562_3,plain,
    ( ! [U_1502,U_1500,U_1498] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1502),U_1500)),U_1498))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1500),U_1498))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1502),U_1498)) )
    & ! [U_1501,U_1499,U_1497] :
        ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1499),U_1497))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1501),U_1497)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1501),U_1499)),U_1497)) ) ),
    inference(miniscope,[status(thm)],[f_562_2]) ).

fof(f_562_4,plain,
    ( ! [U_1497,U_1499,U_1501] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1499),U_1497))
        | ~ sP124(U_1497,U_1499,U_1501) )
    & ! [U_1497,U_1499,U_1501] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1501),U_1497))
        | ~ sP124(U_1497,U_1499,U_1501) )
    & ! [U_1500,U_1498,U_1502] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1502),U_1500)),U_1498))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1500),U_1498))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1502),U_1498)) )
    & ! [U_1497,U_1499,U_1501] :
        ( sP124(U_1497,U_1499,U_1501)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1501),U_1499)),U_1497)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP124])],[f_562_3]) ).

cnf(f_562_5,plain,
    ( sP124(U_1497,U_1499,U_1501)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1501),U_1499)),U_1497)) ),
    inference(clausify,[status(thm)],[f_562_4]) ).

cnf(f_562_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1502),U_1500)),U_1498))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1500),U_1498))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1502),U_1498)) ),
    inference(clausify,[status(thm)],[f_562_4]) ).

cnf(f_562_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1501),U_1497))
    | ~ sP124(U_1497,U_1499,U_1501) ),
    inference(clausify,[status(thm)],[f_562_4]) ).

cnf(f_562_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1499),U_1497))
    | ~ sP124(U_1497,U_1499,U_1501) ),
    inference(clausify,[status(thm)],[f_562_4]) ).

fof(f_563_1,plain,
    ! [X_1,A,B] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) )
      & ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_456_insert__subset]) ).

fof(f_563_2,plain,
    ! [U_1505,U_1504,U_1503] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1505),U_1504)),U_1503))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1504),U_1503))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1505),U_1503)) )
      & ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1504),U_1503))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1505),U_1503)) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1505),U_1504)),U_1503)) ) ),
    inference(variable_rename,[status(thm)],[f_563_1]) ).

fof(f_563_3,plain,
    ( ! [U_1511,U_1509,U_1507] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1511),U_1509)),U_1507))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1509),U_1507))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1511),U_1507)) )
    & ! [U_1510,U_1508,U_1506] :
        ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1508),U_1506))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1510),U_1506)) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1510),U_1508)),U_1506)) ) ),
    inference(miniscope,[status(thm)],[f_563_2]) ).

fof(f_563_4,plain,
    ( ! [U_1508,U_1506,U_1510] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1508),U_1506))
        | ~ sP125(U_1508,U_1506,U_1510) )
    & ! [U_1508,U_1506,U_1510] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1510),U_1506))
        | ~ sP125(U_1508,U_1506,U_1510) )
    & ! [U_1509,U_1507,U_1511] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1511),U_1509)),U_1507))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1509),U_1507))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1511),U_1507)) )
    & ! [U_1508,U_1506,U_1510] :
        ( sP125(U_1508,U_1506,U_1510)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1510),U_1508)),U_1506)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP125])],[f_563_3]) ).

cnf(f_563_5,plain,
    ( sP125(U_1508,U_1506,U_1510)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1510),U_1508)),U_1506)) ),
    inference(clausify,[status(thm)],[f_563_4]) ).

cnf(f_563_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1511),U_1509)),U_1507))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1509),U_1507))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1511),U_1507)) ),
    inference(clausify,[status(thm)],[f_563_4]) ).

cnf(f_563_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1510),U_1506))
    | ~ sP125(U_1508,U_1506,U_1510) ),
    inference(clausify,[status(thm)],[f_563_4]) ).

cnf(f_563_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1508),U_1506))
    | ~ sP125(U_1508,U_1506,U_1510) ),
    inference(clausify,[status(thm)],[f_563_4]) ).

fof(f_564_1,plain,
    ! [B,X_1,A] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),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),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),B))) ) )
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) ),
    inference(fof_nnf,[status(thm)],[fact_457_subset__insert]) ).

fof(f_564_2,plain,
    ! [U_1514,U_1513,U_1512] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1512),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1513),U_1514)))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1512),U_1514)) )
        & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1512),U_1514))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1512),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1513),U_1514))) ) )
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1513),U_1512)) ),
    inference(variable_rename,[status(thm)],[f_564_1]) ).

fof(f_564_3,plain,
    ( ! [U_1513,U_1514,U_1512] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1512),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1513),U_1514)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1512),U_1514))
        | ~ sP126(U_1513,U_1514,U_1512) )
    & ! [U_1513,U_1514,U_1512] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1512),U_1514))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1512),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1513),U_1514)))
        | ~ sP126(U_1513,U_1514,U_1512) )
    & ! [U_1513,U_1514,U_1512] :
        ( sP126(U_1513,U_1514,U_1512)
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1513),U_1512)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP126])],[f_564_2]) ).

cnf(f_564_4,plain,
    ( sP126(U_1513,U_1514,U_1512)
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1513),U_1512)) ),
    inference(clausify,[status(thm)],[f_564_3]) ).

cnf(f_564_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1512),U_1514))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1512),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1513),U_1514)))
    | ~ sP126(U_1513,U_1514,U_1512) ),
    inference(clausify,[status(thm)],[f_564_3]) ).

cnf(f_564_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1512),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1513),U_1514)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1512),U_1514))
    | ~ sP126(U_1513,U_1514,U_1512) ),
    inference(clausify,[status(thm)],[f_564_3]) ).

fof(f_565_1,plain,
    ! [B,X_1,A] :
      ( ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B)))
          | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) )
        & ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
          | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B))) ) )
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) ),
    inference(fof_nnf,[status(thm)],[fact_458_subset__insert]) ).

fof(f_565_2,plain,
    ! [U_1517,U_1516,U_1515] :
      ( ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1515),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1516),U_1517)))
          | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1515),U_1517)) )
        & ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1515),U_1517))
          | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1515),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1516),U_1517))) ) )
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1516),U_1515)) ),
    inference(variable_rename,[status(thm)],[f_565_1]) ).

fof(f_565_3,plain,
    ( ! [U_1517,U_1516,U_1515] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1515),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1516),U_1517)))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1515),U_1517))
        | ~ sP127(U_1517,U_1516,U_1515) )
    & ! [U_1517,U_1516,U_1515] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1515),U_1517))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1515),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1516),U_1517)))
        | ~ sP127(U_1517,U_1516,U_1515) )
    & ! [U_1517,U_1516,U_1515] :
        ( sP127(U_1517,U_1516,U_1515)
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1516),U_1515)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP127])],[f_565_2]) ).

cnf(f_565_4,plain,
    ( sP127(U_1517,U_1516,U_1515)
    | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1516),U_1515)) ),
    inference(clausify,[status(thm)],[f_565_3]) ).

cnf(f_565_5,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1515),U_1517))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1515),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1516),U_1517)))
    | ~ sP127(U_1517,U_1516,U_1515) ),
    inference(clausify,[status(thm)],[f_565_3]) ).

cnf(f_565_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1515),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1516),U_1517)))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1515),U_1517))
    | ~ sP127(U_1517,U_1516,U_1515) ),
    inference(clausify,[status(thm)],[f_565_3]) ).

fof(f_566_1,plain,
    ! [B,X_1,A] :
      ( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),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),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B))) ) )
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) ),
    inference(fof_nnf,[status(thm)],[fact_459_subset__insert]) ).

fof(f_566_2,plain,
    ! [U_1520,U_1519,U_1518] :
      ( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1518),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1519),U_1520)))
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1518),U_1520)) )
        & ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1518),U_1520))
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1518),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1519),U_1520))) ) )
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1519),U_1518)) ),
    inference(variable_rename,[status(thm)],[f_566_1]) ).

fof(f_566_3,plain,
    ( ! [U_1520,U_1518,U_1519] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1518),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1519),U_1520)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1518),U_1520))
        | ~ sP128(U_1520,U_1518,U_1519) )
    & ! [U_1520,U_1518,U_1519] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1518),U_1520))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1518),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1519),U_1520)))
        | ~ sP128(U_1520,U_1518,U_1519) )
    & ! [U_1520,U_1518,U_1519] :
        ( sP128(U_1520,U_1518,U_1519)
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1519),U_1518)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP128])],[f_566_2]) ).

cnf(f_566_4,plain,
    ( sP128(U_1520,U_1518,U_1519)
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1519),U_1518)) ),
    inference(clausify,[status(thm)],[f_566_3]) ).

cnf(f_566_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1518),U_1520))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1518),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1519),U_1520)))
    | ~ sP128(U_1520,U_1518,U_1519) ),
    inference(clausify,[status(thm)],[f_566_3]) ).

cnf(f_566_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1518),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1519),U_1520)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1518),U_1520))
    | ~ sP128(U_1520,U_1518,U_1519) ),
    inference(clausify,[status(thm)],[f_566_3]) ).

fof(f_567_1,plain,
    ! [B,X_1,A] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),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),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B))) ) )
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) ),
    inference(fof_nnf,[status(thm)],[fact_460_subset__insert]) ).

fof(f_567_2,plain,
    ! [U_1523,U_1522,U_1521] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1521),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1522),U_1523)))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1521),U_1523)) )
        & ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1521),U_1523))
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1521),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1522),U_1523))) ) )
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1522),U_1521)) ),
    inference(variable_rename,[status(thm)],[f_567_1]) ).

fof(f_567_3,plain,
    ( ! [U_1523,U_1522,U_1521] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1521),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1522),U_1523)))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1521),U_1523))
        | ~ sP129(U_1523,U_1522,U_1521) )
    & ! [U_1523,U_1522,U_1521] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1521),U_1523))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1521),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1522),U_1523)))
        | ~ sP129(U_1523,U_1522,U_1521) )
    & ! [U_1523,U_1522,U_1521] :
        ( sP129(U_1523,U_1522,U_1521)
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1522),U_1521)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP129])],[f_567_2]) ).

cnf(f_567_4,plain,
    ( sP129(U_1523,U_1522,U_1521)
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1522),U_1521)) ),
    inference(clausify,[status(thm)],[f_567_3]) ).

cnf(f_567_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1521),U_1523))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1521),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1522),U_1523)))
    | ~ sP129(U_1523,U_1522,U_1521) ),
    inference(clausify,[status(thm)],[f_567_3]) ).

cnf(f_567_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1521),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1522),U_1523)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1521),U_1523))
    | ~ sP129(U_1523,U_1522,U_1521) ),
    inference(clausify,[status(thm)],[f_567_3]) ).

fof(f_568_1,plain,
    ! [B_3,A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),B)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_461_subset__insertI2]) ).

fof(f_568_2,plain,
    ! [U_1526,U_1525,U_1524] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1525),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1526),U_1524)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1525),U_1524)) ),
    inference(variable_rename,[status(thm)],[f_568_1]) ).

fof(f_568_3,plain,
    ! [U_1525,U_1524,U_1526] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1525),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1526),U_1524)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1525),U_1524)) ),
    inference(definitional_conversion,[status(esa)],[f_568_2]) ).

cnf(f_568_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1525),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1526),U_1524)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1525),U_1524)) ),
    inference(clausify,[status(thm)],[f_568_3]) ).

fof(f_569_1,plain,
    ! [B_3,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_3),B)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_462_subset__insertI2]) ).

fof(f_569_2,plain,
    ! [U_1529,U_1528,U_1527] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1528),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1529),U_1527)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1528),U_1527)) ),
    inference(variable_rename,[status(thm)],[f_569_1]) ).

fof(f_569_3,plain,
    ! [U_1527,U_1528,U_1529] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1528),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1529),U_1527)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1528),U_1527)) ),
    inference(definitional_conversion,[status(esa)],[f_569_2]) ).

cnf(f_569_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1528),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1529),U_1527)))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1528),U_1527)) ),
    inference(clausify,[status(thm)],[f_569_3]) ).

fof(f_570_1,plain,
    ! [B_3,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_3),B)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_463_subset__insertI2]) ).

fof(f_570_2,plain,
    ! [U_1532,U_1531,U_1530] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1531),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1532),U_1530)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1531),U_1530)) ),
    inference(variable_rename,[status(thm)],[f_570_1]) ).

fof(f_570_3,plain,
    ! [U_1530,U_1531,U_1532] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1531),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1532),U_1530)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1531),U_1530)) ),
    inference(definitional_conversion,[status(esa)],[f_570_2]) ).

cnf(f_570_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1531),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1532),U_1530)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1531),U_1530)) ),
    inference(clausify,[status(thm)],[f_570_3]) ).

fof(f_571_1,plain,
    ! [A_2,C_11,D_4] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),C_11)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),D_4)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C_11),D_4)) ),
    inference(fof_nnf,[status(thm)],[fact_464_insert__mono]) ).

fof(f_571_2,plain,
    ! [U_1535,U_1534,U_1533] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1535),U_1534)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1535),U_1533)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1534),U_1533)) ),
    inference(variable_rename,[status(thm)],[f_571_1]) ).

fof(f_571_3,plain,
    ! [U_1533,U_1534,U_1535] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1535),U_1534)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1535),U_1533)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1534),U_1533)) ),
    inference(definitional_conversion,[status(esa)],[f_571_2]) ).

cnf(f_571_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1535),U_1534)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1535),U_1533)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1534),U_1533)) ),
    inference(clausify,[status(thm)],[f_571_3]) ).

fof(f_572_1,plain,
    ! [A_2,C_11,D_4] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),C_11)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),D_4)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,C_11),D_4)) ),
    inference(fof_nnf,[status(thm)],[fact_465_insert__mono]) ).

fof(f_572_2,plain,
    ! [U_1538,U_1537,U_1536] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1538),U_1537)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1538),U_1536)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1537),U_1536)) ),
    inference(variable_rename,[status(thm)],[f_572_1]) ).

fof(f_572_3,plain,
    ! [U_1536,U_1537,U_1538] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1538),U_1537)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1538),U_1536)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1537),U_1536)) ),
    inference(definitional_conversion,[status(esa)],[f_572_2]) ).

cnf(f_572_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1538),U_1537)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1538),U_1536)))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1537),U_1536)) ),
    inference(clausify,[status(thm)],[f_572_3]) ).

fof(f_573_1,plain,
    ! [A_2,C_11,D_4] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),C_11)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),D_4)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C_11),D_4)) ),
    inference(fof_nnf,[status(thm)],[fact_466_insert__mono]) ).

fof(f_573_2,plain,
    ! [U_1541,U_1540,U_1539] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1541),U_1540)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1541),U_1539)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1540),U_1539)) ),
    inference(variable_rename,[status(thm)],[f_573_1]) ).

fof(f_573_3,plain,
    ! [U_1539,U_1540,U_1541] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1541),U_1540)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1541),U_1539)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1540),U_1539)) ),
    inference(definitional_conversion,[status(esa)],[f_573_2]) ).

cnf(f_573_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1541),U_1540)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1541),U_1539)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1540),U_1539)) ),
    inference(clausify,[status(thm)],[f_573_3]) ).

fof(f_574_1,plain,
    ! [F,A_2,B] : image_nat_int(F,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(F,A_2)),image_nat_int(F,B)),
    inference(fof_nnf,[status(thm)],[fact_467_image__insert]) ).

fof(f_574_2,plain,
    ! [U_1544,U_1543,U_1542] : image_nat_int(U_1544,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1543),U_1542)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(U_1544,U_1543)),image_nat_int(U_1544,U_1542)),
    inference(variable_rename,[status(thm)],[f_574_1]) ).

fof(f_574_3,plain,
    ! [U_1542,U_1543,U_1544] : image_nat_int(U_1544,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1543),U_1542)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(U_1544,U_1543)),image_nat_int(U_1544,U_1542)),
    inference(definitional_conversion,[status(esa)],[f_574_2]) ).

cnf(f_574_4,plain,
    image_nat_int(U_1544,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1543),U_1542)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(U_1544,U_1543)),image_nat_int(U_1544,U_1542)),
    inference(clausify,[status(thm)],[f_574_3]) ).

fof(f_575_1,plain,
    ! [F,A_2,B] : image_pname_a(F,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(F,A_2)),image_pname_a(F,B)),
    inference(fof_nnf,[status(thm)],[fact_468_image__insert]) ).

fof(f_575_2,plain,
    ! [U_1547,U_1546,U_1545] : image_pname_a(U_1547,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1546),U_1545)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(U_1547,U_1546)),image_pname_a(U_1547,U_1545)),
    inference(variable_rename,[status(thm)],[f_575_1]) ).

fof(f_575_3,plain,
    ! [U_1545,U_1546,U_1547] : image_pname_a(U_1547,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1546),U_1545)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(U_1547,U_1546)),image_pname_a(U_1547,U_1545)),
    inference(definitional_conversion,[status(esa)],[f_575_2]) ).

cnf(f_575_4,plain,
    image_pname_a(U_1547,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1546),U_1545)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(U_1547,U_1546)),image_pname_a(U_1547,U_1545)),
    inference(clausify,[status(thm)],[f_575_3]) ).

fof(f_576_1,plain,
    ! [F,X_1,A] :
      ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(F,X_1)),image_nat_int(F,A)) = image_nat_int(F,A)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) ),
    inference(fof_nnf,[status(thm)],[fact_469_insert__image]) ).

fof(f_576_2,plain,
    ! [U_1550,U_1549,U_1548] :
      ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(U_1550,U_1549)),image_nat_int(U_1550,U_1548)) = image_nat_int(U_1550,U_1548)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1549),U_1548)) ),
    inference(variable_rename,[status(thm)],[f_576_1]) ).

fof(f_576_3,plain,
    ! [U_1548,U_1549,U_1550] :
      ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(U_1550,U_1549)),image_nat_int(U_1550,U_1548)) = image_nat_int(U_1550,U_1548)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1549),U_1548)) ),
    inference(definitional_conversion,[status(esa)],[f_576_2]) ).

cnf(f_576_4,plain,
    ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,hAPP_nat_int(U_1550,U_1549)),image_nat_int(U_1550,U_1548)) = image_nat_int(U_1550,U_1548)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1549),U_1548)) ),
    inference(clausify,[status(thm)],[f_576_3]) ).

fof(f_577_1,plain,
    ! [F,X_1,A] :
      ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(F,X_1)),image_pname_a(F,A)) = image_pname_a(F,A)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) ),
    inference(fof_nnf,[status(thm)],[fact_470_insert__image]) ).

fof(f_577_2,plain,
    ! [U_1553,U_1552,U_1551] :
      ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(U_1553,U_1552)),image_pname_a(U_1553,U_1551)) = image_pname_a(U_1553,U_1551)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1552),U_1551)) ),
    inference(variable_rename,[status(thm)],[f_577_1]) ).

fof(f_577_3,plain,
    ! [U_1551,U_1552,U_1553] :
      ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(U_1553,U_1552)),image_pname_a(U_1553,U_1551)) = image_pname_a(U_1553,U_1551)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1552),U_1551)) ),
    inference(definitional_conversion,[status(esa)],[f_577_2]) ).

cnf(f_577_4,plain,
    ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(U_1553,U_1552)),image_pname_a(U_1553,U_1551)) = image_pname_a(U_1553,U_1551)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1552),U_1551)) ),
    inference(clausify,[status(thm)],[f_577_3]) ).

fof(f_578_1,plain,
    ! [B,F,A] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_nat_int(F,A)))
        | ! [AA] :
            ( B != image_nat_int(F,AA)
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,AA),A)) ) )
      & ( ? [AA] :
            ( B = image_nat_int(F,AA)
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,AA),A)) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),image_nat_int(F,A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_471_subset__image__iff]) ).

fof(f_578_2,plain,
    ! [U_1558,U_1557,U_1556] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1558),image_nat_int(U_1557,U_1556)))
        | ! [U_1555] :
            ( U_1558 != image_nat_int(U_1557,U_1555)
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1555),U_1556)) ) )
      & ( ? [U_1554] :
            ( U_1558 = image_nat_int(U_1557,U_1554)
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1554),U_1556)) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1558),image_nat_int(U_1557,U_1556))) ) ),
    inference(variable_rename,[status(thm)],[f_578_1]) ).

fof(f_578_3,plain,
    ( ! [U_1564,U_1562,U_1560] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1564),image_nat_int(U_1562,U_1560)))
        | ! [U_1555] :
            ( U_1564 != image_nat_int(U_1562,U_1555)
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1555),U_1560)) ) )
    & ! [U_1563,U_1561,U_1559] :
        ( ? [U_1554] :
            ( U_1563 = image_nat_int(U_1561,U_1554)
            & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1554),U_1559)) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1563),image_nat_int(U_1561,U_1559))) ) ),
    inference(miniscope,[status(thm)],[f_578_2]) ).

fof(f_578_4,plain,
    ( ! [U_1564,U_1562,U_1560] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1564),image_nat_int(U_1562,U_1560)))
        | ! [U_1555] :
            ( U_1564 != image_nat_int(U_1562,U_1555)
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1555),U_1560)) ) )
    & ! [U_1563,U_1561,U_1559] :
        ( ( U_1563 = image_nat_int(U_1561,sK71(U_1563,U_1561,U_1559))
          & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK71(U_1563,U_1561,U_1559)),U_1559)) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1563),image_nat_int(U_1561,U_1559))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_1554,sK71(U_1563,U_1561,U_1559))],[f_578_3]) ).

fof(f_578_5,plain,
    ( ! [U_1563,U_1561,U_1559] :
        ( U_1563 = image_nat_int(U_1561,sK71(U_1563,U_1561,U_1559))
        | ~ sP130(U_1563,U_1561,U_1559) )
    & ! [U_1563,U_1561,U_1559] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK71(U_1563,U_1561,U_1559)),U_1559))
        | ~ sP130(U_1563,U_1561,U_1559) )
    & ! [U_1555,U_1562,U_1560,U_1564] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1564),image_nat_int(U_1562,U_1560)))
        | U_1564 != image_nat_int(U_1562,U_1555)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1555),U_1560)) )
    & ! [U_1563,U_1561,U_1559] :
        ( sP130(U_1563,U_1561,U_1559)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1563),image_nat_int(U_1561,U_1559))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP130])],[f_578_4]) ).

cnf(f_578_6,plain,
    ( sP130(U_1563,U_1561,U_1559)
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1563),image_nat_int(U_1561,U_1559))) ),
    inference(clausify,[status(thm)],[f_578_5]) ).

cnf(f_578_7,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1564),image_nat_int(U_1562,U_1560)))
    | U_1564 != image_nat_int(U_1562,U_1555)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1555),U_1560)) ),
    inference(clausify,[status(thm)],[f_578_5]) ).

cnf(f_578_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,sK71(U_1563,U_1561,U_1559)),U_1559))
    | ~ sP130(U_1563,U_1561,U_1559) ),
    inference(clausify,[status(thm)],[f_578_5]) ).

cnf(f_578_9,plain,
    ( U_1563 = image_nat_int(U_1561,sK71(U_1563,U_1561,U_1559))
    | ~ sP130(U_1563,U_1561,U_1559) ),
    inference(clausify,[status(thm)],[f_578_5]) ).

fof(f_579_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_472_subset__image__iff]) ).

fof(f_579_2,plain,
    ! [U_1569,U_1568,U_1567] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1569),image_pname_a(U_1568,U_1567)))
          | ! [U_1566] :
              ( U_1569 != image_pname_a(U_1568,U_1566)
              | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1566),U_1567))
              | ~ is_fun_pname_bool(U_1566) ) )
        & ( ? [U_1565] :
              ( U_1569 = image_pname_a(U_1568,U_1565)
              & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1565),U_1567))
              & is_fun_pname_bool(U_1565) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1569),image_pname_a(U_1568,U_1567))) ) )
      | ~ is_fun_a_bool(U_1569) ),
    inference(variable_rename,[status(thm)],[f_579_1]) ).

fof(f_579_3,plain,
    ! [U_1569] :
      ( ( ! [U_1573,U_1571] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1569),image_pname_a(U_1573,U_1571)))
            | ! [U_1566] :
                ( U_1569 != image_pname_a(U_1573,U_1566)
                | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1566),U_1571))
                | ~ is_fun_pname_bool(U_1566) ) )
        & ! [U_1572,U_1570] :
            ( ? [U_1565] :
                ( U_1569 = image_pname_a(U_1572,U_1565)
                & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1565),U_1570))
                & is_fun_pname_bool(U_1565) )
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1569),image_pname_a(U_1572,U_1570))) ) )
      | ~ is_fun_a_bool(U_1569) ),
    inference(miniscope,[status(thm)],[f_579_2]) ).

fof(f_579_4,plain,
    ! [U_1569] :
      ( ( ! [U_1573,U_1571] :
            ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1569),image_pname_a(U_1573,U_1571)))
            | ! [U_1566] :
                ( U_1569 != image_pname_a(U_1573,U_1566)
                | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1566),U_1571))
                | ~ is_fun_pname_bool(U_1566) ) )
        & ! [U_1572,U_1570] :
            ( ( U_1569 = image_pname_a(U_1572,sK72(U_1569,U_1572,U_1570))
              & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK72(U_1569,U_1572,U_1570)),U_1570))
              & is_fun_pname_bool(sK72(U_1569,U_1572,U_1570)) )
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1569),image_pname_a(U_1572,U_1570))) ) )
      | ~ is_fun_a_bool(U_1569) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_1565,sK72(U_1569,U_1572,U_1570))],[f_579_3]) ).

fof(f_579_5,plain,
    ( ! [U_1569,U_1570,U_1572] :
        ( U_1569 = image_pname_a(U_1572,sK72(U_1569,U_1572,U_1570))
        | ~ sP131(U_1569,U_1570,U_1572) )
    & ! [U_1569,U_1570,U_1572] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK72(U_1569,U_1572,U_1570)),U_1570))
        | ~ sP131(U_1569,U_1570,U_1572) )
    & ! [U_1569,U_1570,U_1572] :
        ( is_fun_pname_bool(sK72(U_1569,U_1572,U_1570))
        | ~ sP131(U_1569,U_1570,U_1572) )
    & ! [U_1569,U_1570,U_1566,U_1573,U_1572,U_1571] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1569),image_pname_a(U_1573,U_1571)))
        | U_1569 != image_pname_a(U_1573,U_1566)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1566),U_1571))
        | ~ is_fun_pname_bool(U_1566)
        | ~ sP132(U_1569,U_1570,U_1566,U_1573,U_1572,U_1571) )
    & ! [U_1569,U_1570,U_1566,U_1573,U_1572,U_1571] :
        ( sP131(U_1569,U_1570,U_1572)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1569),image_pname_a(U_1572,U_1570)))
        | ~ sP132(U_1569,U_1570,U_1566,U_1573,U_1572,U_1571) )
    & ! [U_1569,U_1570,U_1566,U_1573,U_1572,U_1571] :
        ( sP132(U_1569,U_1570,U_1566,U_1573,U_1572,U_1571)
        | ~ is_fun_a_bool(U_1569) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP131,sP132])],[f_579_4]) ).

cnf(f_579_6,plain,
    ( sP132(U_1569,U_1570,U_1566,U_1573,U_1572,U_1571)
    | ~ is_fun_a_bool(U_1569) ),
    inference(clausify,[status(thm)],[f_579_5]) ).

cnf(f_579_7,plain,
    ( sP131(U_1569,U_1570,U_1572)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1569),image_pname_a(U_1572,U_1570)))
    | ~ sP132(U_1569,U_1570,U_1566,U_1573,U_1572,U_1571) ),
    inference(clausify,[status(thm)],[f_579_5]) ).

cnf(f_579_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1569),image_pname_a(U_1573,U_1571)))
    | U_1569 != image_pname_a(U_1573,U_1566)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1566),U_1571))
    | ~ is_fun_pname_bool(U_1566)
    | ~ sP132(U_1569,U_1570,U_1566,U_1573,U_1572,U_1571) ),
    inference(clausify,[status(thm)],[f_579_5]) ).

cnf(f_579_9,plain,
    ( is_fun_pname_bool(sK72(U_1569,U_1572,U_1570))
    | ~ sP131(U_1569,U_1570,U_1572) ),
    inference(clausify,[status(thm)],[f_579_5]) ).

cnf(f_579_10,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,sK72(U_1569,U_1572,U_1570)),U_1570))
    | ~ sP131(U_1569,U_1570,U_1572) ),
    inference(clausify,[status(thm)],[f_579_5]) ).

cnf(f_579_11,plain,
    ( U_1569 = image_pname_a(U_1572,sK72(U_1569,U_1572,U_1570))
    | ~ sP131(U_1569,U_1570,U_1572) ),
    inference(clausify,[status(thm)],[f_579_5]) ).

fof(f_580_1,plain,
    ! [F,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(F,A)),image_nat_int(F,B)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_473_image__mono]) ).

fof(f_580_2,plain,
    ! [U_1576,U_1575,U_1574] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(U_1576,U_1575)),image_nat_int(U_1576,U_1574)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1575),U_1574)) ),
    inference(variable_rename,[status(thm)],[f_580_1]) ).

fof(f_580_3,plain,
    ! [U_1576,U_1575,U_1574] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(U_1576,U_1575)),image_nat_int(U_1576,U_1574)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1575),U_1574)) ),
    inference(definitional_conversion,[status(esa)],[f_580_2]) ).

cnf(f_580_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(U_1576,U_1575)),image_nat_int(U_1576,U_1574)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1575),U_1574)) ),
    inference(clausify,[status(thm)],[f_580_3]) ).

fof(f_581_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_474_image__mono]) ).

fof(f_581_2,plain,
    ! [U_1579,U_1578,U_1577] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(U_1579,U_1578)),image_pname_a(U_1579,U_1577)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1578),U_1577)) ),
    inference(variable_rename,[status(thm)],[f_581_1]) ).

fof(f_581_3,plain,
    ! [U_1578,U_1579,U_1577] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(U_1579,U_1578)),image_pname_a(U_1579,U_1577)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1578),U_1577)) ),
    inference(definitional_conversion,[status(esa)],[f_581_2]) ).

cnf(f_581_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(U_1579,U_1578)),image_pname_a(U_1579,U_1577)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1578),U_1577)) ),
    inference(clausify,[status(thm)],[f_581_3]) ).

fof(f_582_1,plain,
    ! [B_3,F,A] :
      ( ? [X_2] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
          & B_3 = hAPP_nat_int(F,X_2) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_3),image_nat_int(F,A))) ),
    inference(fof_nnf,[status(thm)],[fact_475_imageE]) ).

fof(f_582_2,plain,
    ! [U_1583,U_1582,U_1581] :
      ( ? [U_1580] :
          ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1580),U_1581))
          & U_1583 = hAPP_nat_int(U_1582,U_1580) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1583),image_nat_int(U_1582,U_1581))) ),
    inference(variable_rename,[status(thm)],[f_582_1]) ).

fof(f_582_3,plain,
    ! [U_1583,U_1582,U_1581] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK73(U_1583,U_1582,U_1581)),U_1581))
        & U_1583 = hAPP_nat_int(U_1582,sK73(U_1583,U_1582,U_1581)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1583),image_nat_int(U_1582,U_1581))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_1580,sK73(U_1583,U_1582,U_1581))],[f_582_2]) ).

fof(f_582_4,plain,
    ( ! [U_1581,U_1582,U_1583] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK73(U_1583,U_1582,U_1581)),U_1581))
        | ~ sP133(U_1581,U_1582,U_1583) )
    & ! [U_1581,U_1582,U_1583] :
        ( U_1583 = hAPP_nat_int(U_1582,sK73(U_1583,U_1582,U_1581))
        | ~ sP133(U_1581,U_1582,U_1583) )
    & ! [U_1581,U_1582,U_1583] :
        ( sP133(U_1581,U_1582,U_1583)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1583),image_nat_int(U_1582,U_1581))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP133])],[f_582_3]) ).

cnf(f_582_5,plain,
    ( sP133(U_1581,U_1582,U_1583)
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1583),image_nat_int(U_1582,U_1581))) ),
    inference(clausify,[status(thm)],[f_582_4]) ).

cnf(f_582_6,plain,
    ( U_1583 = hAPP_nat_int(U_1582,sK73(U_1583,U_1582,U_1581))
    | ~ sP133(U_1581,U_1582,U_1583) ),
    inference(clausify,[status(thm)],[f_582_4]) ).

cnf(f_582_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK73(U_1583,U_1582,U_1581)),U_1581))
    | ~ sP133(U_1581,U_1582,U_1583) ),
    inference(clausify,[status(thm)],[f_582_4]) ).

fof(f_583_1,plain,
    ! [B_3,F,A] :
      ( ? [X_2] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
          & B_3 = hAPP_pname_a(F,X_2)
          & is_pname(X_2) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),image_pname_a(F,A)))
      | ~ is_a(B_3) ),
    inference(fof_nnf,[status(thm)],[fact_476_imageE]) ).

fof(f_583_2,plain,
    ! [U_1587,U_1586,U_1585] :
      ( ? [U_1584] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1584),U_1585))
          & U_1587 = hAPP_pname_a(U_1586,U_1584)
          & is_pname(U_1584) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1587),image_pname_a(U_1586,U_1585)))
      | ~ is_a(U_1587) ),
    inference(variable_rename,[status(thm)],[f_583_1]) ).

fof(f_583_3,plain,
    ! [U_1587] :
      ( ! [U_1586,U_1585] :
          ( ? [U_1584] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1584),U_1585))
              & U_1587 = hAPP_pname_a(U_1586,U_1584)
              & is_pname(U_1584) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1587),image_pname_a(U_1586,U_1585))) )
      | ~ is_a(U_1587) ),
    inference(miniscope,[status(thm)],[f_583_2]) ).

fof(f_583_4,plain,
    ! [U_1587] :
      ( ! [U_1586,U_1585] :
          ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK74(U_1587,U_1586,U_1585)),U_1585))
            & U_1587 = hAPP_pname_a(U_1586,sK74(U_1587,U_1586,U_1585))
            & is_pname(sK74(U_1587,U_1586,U_1585)) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1587),image_pname_a(U_1586,U_1585))) )
      | ~ is_a(U_1587) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_1584,sK74(U_1587,U_1586,U_1585))],[f_583_3]) ).

fof(f_583_5,plain,
    ( ! [U_1585,U_1586,U_1587] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK74(U_1587,U_1586,U_1585)),U_1585))
        | ~ sP134(U_1585,U_1586,U_1587) )
    & ! [U_1585,U_1586,U_1587] :
        ( U_1587 = hAPP_pname_a(U_1586,sK74(U_1587,U_1586,U_1585))
        | ~ sP134(U_1585,U_1586,U_1587) )
    & ! [U_1585,U_1586,U_1587] :
        ( is_pname(sK74(U_1587,U_1586,U_1585))
        | ~ sP134(U_1585,U_1586,U_1587) )
    & ! [U_1585,U_1586,U_1587] :
        ( sP134(U_1585,U_1586,U_1587)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1587),image_pname_a(U_1586,U_1585)))
        | ~ is_a(U_1587) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP134])],[f_583_4]) ).

cnf(f_583_6,plain,
    ( sP134(U_1585,U_1586,U_1587)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1587),image_pname_a(U_1586,U_1585)))
    | ~ is_a(U_1587) ),
    inference(clausify,[status(thm)],[f_583_5]) ).

cnf(f_583_7,plain,
    ( is_pname(sK74(U_1587,U_1586,U_1585))
    | ~ sP134(U_1585,U_1586,U_1587) ),
    inference(clausify,[status(thm)],[f_583_5]) ).

cnf(f_583_8,plain,
    ( U_1587 = hAPP_pname_a(U_1586,sK74(U_1587,U_1586,U_1585))
    | ~ sP134(U_1585,U_1586,U_1587) ),
    inference(clausify,[status(thm)],[f_583_5]) ).

cnf(f_583_9,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK74(U_1587,U_1586,U_1585)),U_1585))
    | ~ sP134(U_1585,U_1586,U_1587) ),
    inference(clausify,[status(thm)],[f_583_5]) ).

fof(f_584_1,plain,
    ! [B,A] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
      | ? [X_2] :
          ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),B))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_477_subsetI]) ).

fof(f_584_2,plain,
    ! [U_1590,U_1589] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1589),U_1590))
      | ? [U_1588] :
          ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1588),U_1590))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1588),U_1589)) ) ),
    inference(variable_rename,[status(thm)],[f_584_1]) ).

fof(f_584_3,plain,
    ! [U_1590,U_1589] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1589),U_1590))
      | ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK75(U_1590,U_1589)),U_1590))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK75(U_1590,U_1589)),U_1589)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_1588,sK75(U_1590,U_1589))],[f_584_2]) ).

fof(f_584_4,plain,
    ( ! [U_1590,U_1589] :
        ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK75(U_1590,U_1589)),U_1590))
        | ~ sP135(U_1590,U_1589) )
    & ! [U_1590,U_1589] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK75(U_1590,U_1589)),U_1589))
        | ~ sP135(U_1590,U_1589) )
    & ! [U_1590,U_1589] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1589),U_1590))
        | sP135(U_1590,U_1589) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP135])],[f_584_3]) ).

cnf(f_584_5,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1589),U_1590))
    | sP135(U_1590,U_1589) ),
    inference(clausify,[status(thm)],[f_584_4]) ).

cnf(f_584_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK75(U_1590,U_1589)),U_1589))
    | ~ sP135(U_1590,U_1589) ),
    inference(clausify,[status(thm)],[f_584_4]) ).

cnf(f_584_7,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK75(U_1590,U_1589)),U_1590))
    | ~ sP135(U_1590,U_1589) ),
    inference(clausify,[status(thm)],[f_584_4]) ).

fof(f_585_1,plain,
    ! [B,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
      | ? [X_2] :
          ( ~ 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_478_subsetI]) ).

fof(f_585_2,plain,
    ! [U_1593,U_1592] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1592),U_1593))
      | ? [U_1591] :
          ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1591),U_1593))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1591),U_1592)) ) ),
    inference(variable_rename,[status(thm)],[f_585_1]) ).

fof(f_585_3,plain,
    ! [U_1593,U_1592] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1592),U_1593))
      | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK76(U_1593,U_1592)),U_1593))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK76(U_1593,U_1592)),U_1592)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_1591,sK76(U_1593,U_1592))],[f_585_2]) ).

fof(f_585_4,plain,
    ( ! [U_1592,U_1593] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK76(U_1593,U_1592)),U_1593))
        | ~ sP136(U_1592,U_1593) )
    & ! [U_1592,U_1593] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK76(U_1593,U_1592)),U_1592))
        | ~ sP136(U_1592,U_1593) )
    & ! [U_1592,U_1593] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1592),U_1593))
        | sP136(U_1592,U_1593) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP136])],[f_585_3]) ).

cnf(f_585_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1592),U_1593))
    | sP136(U_1592,U_1593) ),
    inference(clausify,[status(thm)],[f_585_4]) ).

cnf(f_585_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK76(U_1593,U_1592)),U_1592))
    | ~ sP136(U_1592,U_1593) ),
    inference(clausify,[status(thm)],[f_585_4]) ).

cnf(f_585_7,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK76(U_1593,U_1592)),U_1593))
    | ~ sP136(U_1592,U_1593) ),
    inference(clausify,[status(thm)],[f_585_4]) ).

fof(f_586_1,plain,
    ! [B,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
      | ? [X_2] :
          ( ~ 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_a(X_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_479_subsetI]) ).

fof(f_586_2,plain,
    ! [U_1596,U_1595] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1595),U_1596))
      | ? [U_1594] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1594),U_1596))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1594),U_1595))
          & is_a(U_1594) ) ),
    inference(variable_rename,[status(thm)],[f_586_1]) ).

fof(f_586_3,plain,
    ! [U_1596,U_1595] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1595),U_1596))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK77(U_1596,U_1595)),U_1596))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK77(U_1596,U_1595)),U_1595))
        & is_a(sK77(U_1596,U_1595)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_1594,sK77(U_1596,U_1595))],[f_586_2]) ).

fof(f_586_4,plain,
    ( ! [U_1595,U_1596] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK77(U_1596,U_1595)),U_1596))
        | ~ sP137(U_1595,U_1596) )
    & ! [U_1595,U_1596] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK77(U_1596,U_1595)),U_1595))
        | ~ sP137(U_1595,U_1596) )
    & ! [U_1595,U_1596] :
        ( is_a(sK77(U_1596,U_1595))
        | ~ sP137(U_1595,U_1596) )
    & ! [U_1595,U_1596] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1595),U_1596))
        | sP137(U_1595,U_1596) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP137])],[f_586_3]) ).

cnf(f_586_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1595),U_1596))
    | sP137(U_1595,U_1596) ),
    inference(clausify,[status(thm)],[f_586_4]) ).

cnf(f_586_6,plain,
    ( is_a(sK77(U_1596,U_1595))
    | ~ sP137(U_1595,U_1596) ),
    inference(clausify,[status(thm)],[f_586_4]) ).

cnf(f_586_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK77(U_1596,U_1595)),U_1595))
    | ~ sP137(U_1595,U_1596) ),
    inference(clausify,[status(thm)],[f_586_4]) ).

cnf(f_586_8,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK77(U_1596,U_1595)),U_1596))
    | ~ sP137(U_1595,U_1596) ),
    inference(clausify,[status(thm)],[f_586_4]) ).

fof(f_587_1,plain,
    ! [B,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
      | ? [X_2] :
          ( ~ 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_pname(X_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_480_subsetI]) ).

fof(f_587_2,plain,
    ! [U_1599,U_1598] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1598),U_1599))
      | ? [U_1597] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1597),U_1599))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1597),U_1598))
          & is_pname(U_1597) ) ),
    inference(variable_rename,[status(thm)],[f_587_1]) ).

fof(f_587_3,plain,
    ! [U_1599,U_1598] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1598),U_1599))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK78(U_1599,U_1598)),U_1599))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK78(U_1599,U_1598)),U_1598))
        & is_pname(sK78(U_1599,U_1598)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_1597,sK78(U_1599,U_1598))],[f_587_2]) ).

fof(f_587_4,plain,
    ( ! [U_1598,U_1599] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK78(U_1599,U_1598)),U_1599))
        | ~ sP138(U_1598,U_1599) )
    & ! [U_1598,U_1599] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK78(U_1599,U_1598)),U_1598))
        | ~ sP138(U_1598,U_1599) )
    & ! [U_1598,U_1599] :
        ( is_pname(sK78(U_1599,U_1598))
        | ~ sP138(U_1598,U_1599) )
    & ! [U_1598,U_1599] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1598),U_1599))
        | sP138(U_1598,U_1599) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP138])],[f_587_3]) ).

cnf(f_587_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1598),U_1599))
    | sP138(U_1598,U_1599) ),
    inference(clausify,[status(thm)],[f_587_4]) ).

cnf(f_587_6,plain,
    ( is_pname(sK78(U_1599,U_1598))
    | ~ sP138(U_1598,U_1599) ),
    inference(clausify,[status(thm)],[f_587_4]) ).

cnf(f_587_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK78(U_1599,U_1598)),U_1598))
    | ~ sP138(U_1598,U_1599) ),
    inference(clausify,[status(thm)],[f_587_4]) ).

cnf(f_587_8,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK78(U_1599,U_1598)),U_1599))
    | ~ sP138(U_1598,U_1599) ),
    inference(clausify,[status(thm)],[f_587_4]) ).

fof(f_588_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(F,A)),B))
      | ? [X_2] :
          ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(F,X_2)),B))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_481_image__subsetI]) ).

fof(f_588_2,plain,
    ! [U_1603,U_1602,U_1601] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(U_1603,U_1601)),U_1602))
      | ? [U_1600] :
          ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(U_1603,U_1600)),U_1602))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1600),U_1601)) ) ),
    inference(variable_rename,[status(thm)],[f_588_1]) ).

fof(f_588_3,plain,
    ! [U_1603,U_1602,U_1601] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(U_1603,U_1601)),U_1602))
      | ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(U_1603,sK79(U_1603,U_1602,U_1601))),U_1602))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK79(U_1603,U_1602,U_1601)),U_1601)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_1600,sK79(U_1603,U_1602,U_1601))],[f_588_2]) ).

fof(f_588_4,plain,
    ( ! [U_1601,U_1602,U_1603] :
        ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(U_1603,sK79(U_1603,U_1602,U_1601))),U_1602))
        | ~ sP139(U_1601,U_1602,U_1603) )
    & ! [U_1601,U_1602,U_1603] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK79(U_1603,U_1602,U_1601)),U_1601))
        | ~ sP139(U_1601,U_1602,U_1603) )
    & ! [U_1601,U_1602,U_1603] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(U_1603,U_1601)),U_1602))
        | sP139(U_1601,U_1602,U_1603) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP139])],[f_588_3]) ).

cnf(f_588_5,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(U_1603,U_1601)),U_1602))
    | sP139(U_1601,U_1602,U_1603) ),
    inference(clausify,[status(thm)],[f_588_4]) ).

cnf(f_588_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK79(U_1603,U_1602,U_1601)),U_1601))
    | ~ sP139(U_1601,U_1602,U_1603) ),
    inference(clausify,[status(thm)],[f_588_4]) ).

cnf(f_588_7,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(U_1603,sK79(U_1603,U_1602,U_1601))),U_1602))
    | ~ sP139(U_1601,U_1602,U_1603) ),
    inference(clausify,[status(thm)],[f_588_4]) ).

fof(f_589_1,plain,
    ! [F,B,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(F,A)),B))
      | ? [X_2] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(F,X_2)),B))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
          & is_pname(X_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_482_image__subsetI]) ).

fof(f_589_2,plain,
    ! [U_1607,U_1606,U_1605] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(U_1607,U_1605)),U_1606))
      | ? [U_1604] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(U_1607,U_1604)),U_1606))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1604),U_1605))
          & is_pname(U_1604) ) ),
    inference(variable_rename,[status(thm)],[f_589_1]) ).

fof(f_589_3,plain,
    ! [U_1607,U_1606,U_1605] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(U_1607,U_1605)),U_1606))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(U_1607,sK80(U_1607,U_1606,U_1605))),U_1606))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK80(U_1607,U_1606,U_1605)),U_1605))
        & is_pname(sK80(U_1607,U_1606,U_1605)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_1604,sK80(U_1607,U_1606,U_1605))],[f_589_2]) ).

fof(f_589_4,plain,
    ( ! [U_1605,U_1606,U_1607] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(U_1607,sK80(U_1607,U_1606,U_1605))),U_1606))
        | ~ sP140(U_1605,U_1606,U_1607) )
    & ! [U_1605,U_1606,U_1607] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK80(U_1607,U_1606,U_1605)),U_1605))
        | ~ sP140(U_1605,U_1606,U_1607) )
    & ! [U_1605,U_1606,U_1607] :
        ( is_pname(sK80(U_1607,U_1606,U_1605))
        | ~ sP140(U_1605,U_1606,U_1607) )
    & ! [U_1605,U_1606,U_1607] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(U_1607,U_1605)),U_1606))
        | sP140(U_1605,U_1606,U_1607) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP140])],[f_589_3]) ).

cnf(f_589_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(U_1607,U_1605)),U_1606))
    | sP140(U_1605,U_1606,U_1607) ),
    inference(clausify,[status(thm)],[f_589_4]) ).

cnf(f_589_6,plain,
    ( is_pname(sK80(U_1607,U_1606,U_1605))
    | ~ sP140(U_1605,U_1606,U_1607) ),
    inference(clausify,[status(thm)],[f_589_4]) ).

cnf(f_589_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK80(U_1607,U_1606,U_1605)),U_1605))
    | ~ sP140(U_1605,U_1606,U_1607) ),
    inference(clausify,[status(thm)],[f_589_4]) ).

cnf(f_589_8,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(U_1607,sK80(U_1607,U_1606,U_1605))),U_1606))
    | ~ sP140(U_1605,U_1606,U_1607) ),
    inference(clausify,[status(thm)],[f_589_4]) ).

fof(f_590_1,plain,
    ! [F,G_1] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F),G_1))
      | ? [X_2] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(F,X_2)),hAPP_int_bool(G_1,X_2))) ),
    inference(fof_nnf,[status(thm)],[fact_483_le__funI]) ).

fof(f_590_2,plain,
    ! [U_1610,U_1609] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1610),U_1609))
      | ? [U_1608] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(U_1610,U_1608)),hAPP_int_bool(U_1609,U_1608))) ),
    inference(variable_rename,[status(thm)],[f_590_1]) ).

fof(f_590_3,plain,
    ! [U_1610,U_1609] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1610),U_1609))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(U_1610,sK81(U_1610,U_1609))),hAPP_int_bool(U_1609,sK81(U_1610,U_1609)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_1608,sK81(U_1610,U_1609))],[f_590_2]) ).

fof(f_590_4,plain,
    ! [U_1610,U_1609] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1610),U_1609))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(U_1610,sK81(U_1610,U_1609))),hAPP_int_bool(U_1609,sK81(U_1610,U_1609)))) ),
    inference(definitional_conversion,[status(esa)],[f_590_3]) ).

cnf(f_590_5,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1610),U_1609))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_int_bool(U_1610,sK81(U_1610,U_1609))),hAPP_int_bool(U_1609,sK81(U_1610,U_1609)))) ),
    inference(clausify,[status(thm)],[f_590_4]) ).

fof(f_591_1,plain,
    ! [F,G_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F),G_1))
      | ? [X_2] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(F,X_2)),hAPP_nat_bool(G_1,X_2))) ),
    inference(fof_nnf,[status(thm)],[fact_484_le__funI]) ).

fof(f_591_2,plain,
    ! [U_1613,U_1612] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1613),U_1612))
      | ? [U_1611] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1613,U_1611)),hAPP_nat_bool(U_1612,U_1611))) ),
    inference(variable_rename,[status(thm)],[f_591_1]) ).

fof(f_591_3,plain,
    ! [U_1613,U_1612] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1613),U_1612))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1613,sK82(U_1613,U_1612))),hAPP_nat_bool(U_1612,sK82(U_1613,U_1612)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_1611,sK82(U_1613,U_1612))],[f_591_2]) ).

fof(f_591_4,plain,
    ! [U_1612,U_1613] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1613),U_1612))
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1613,sK82(U_1613,U_1612))),hAPP_nat_bool(U_1612,sK82(U_1613,U_1612)))) ),
    inference(definitional_conversion,[status(esa)],[f_591_3]) ).

cnf(f_591_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1613),U_1612))
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_nat_bool(U_1613,sK82(U_1613,U_1612))),hAPP_nat_bool(U_1612,sK82(U_1613,U_1612)))) ),
    inference(clausify,[status(thm)],[f_591_4]) ).

fof(f_592_1,plain,
    ! [F,G_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F),G_1))
      | ? [X_2] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(F,X_2)),hAPP_a_bool(G_1,X_2)))
          & is_a(X_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_485_le__funI]) ).

fof(f_592_2,plain,
    ! [U_1616,U_1615] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1616),U_1615))
      | ? [U_1614] :
          ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1616,U_1614)),hAPP_a_bool(U_1615,U_1614)))
          & is_a(U_1614) ) ),
    inference(variable_rename,[status(thm)],[f_592_1]) ).

fof(f_592_3,plain,
    ! [U_1616,U_1615] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1616),U_1615))
      | ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1616,sK83(U_1616,U_1615))),hAPP_a_bool(U_1615,sK83(U_1616,U_1615))))
        & is_a(sK83(U_1616,U_1615)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_1614,sK83(U_1616,U_1615))],[f_592_2]) ).

fof(f_592_4,plain,
    ( ! [U_1615,U_1616] :
        ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1616,sK83(U_1616,U_1615))),hAPP_a_bool(U_1615,sK83(U_1616,U_1615))))
        | ~ sP141(U_1615,U_1616) )
    & ! [U_1615,U_1616] :
        ( is_a(sK83(U_1616,U_1615))
        | ~ sP141(U_1615,U_1616) )
    & ! [U_1615,U_1616] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1616),U_1615))
        | sP141(U_1615,U_1616) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP141])],[f_592_3]) ).

cnf(f_592_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1616),U_1615))
    | sP141(U_1615,U_1616) ),
    inference(clausify,[status(thm)],[f_592_4]) ).

cnf(f_592_6,plain,
    ( is_a(sK83(U_1616,U_1615))
    | ~ sP141(U_1615,U_1616) ),
    inference(clausify,[status(thm)],[f_592_4]) ).

cnf(f_592_7,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(ord_less_eq_bool,hAPP_a_bool(U_1616,sK83(U_1616,U_1615))),hAPP_a_bool(U_1615,sK83(U_1616,U_1615))))
    | ~ sP141(U_1615,U_1616) ),
    inference(clausify,[status(thm)],[f_592_4]) ).

fof(f_593_1,plain,
    ! [N_2] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2))
        | ! [M_2] :
          ? [X_2] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),M_2))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),N_2)) ) )
      & ( ? [M_2] :
          ! [X_2] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_2),M_2))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),N_2)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_486_finite__nat__set__iff__bounded__le]) ).

fof(f_593_2,plain,
    ! [U_1621] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1621))
        | ! [U_1620] :
          ? [U_1619] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1619),U_1620))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1619),U_1621)) ) )
      & ( ? [U_1618] :
          ! [U_1617] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1617),U_1618))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1617),U_1621)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1621)) ) ),
    inference(variable_rename,[status(thm)],[f_593_1]) ).

fof(f_593_3,plain,
    ( ! [U_1623] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1623))
        | ! [U_1620] :
          ? [U_1619] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1619),U_1620))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1619),U_1623)) ) )
    & ! [U_1622] :
        ( ? [U_1618] :
          ! [U_1617] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1617),U_1618))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1617),U_1622)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1622)) ) ),
    inference(miniscope,[status(thm)],[f_593_2]) ).

fof(f_593_4,plain,
    ( ! [U_1623] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1623))
        | ! [U_1620] :
          ? [U_1619] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1619),U_1620))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1619),U_1623)) ) )
    & ! [U_1622] :
        ( ! [U_1617] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1617),sK84(U_1622)))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1617),U_1622)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1622)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_1618,sK84(U_1622))],[f_593_3]) ).

fof(f_593_5,plain,
    ( ! [U_1623] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1623))
        | ! [U_1620] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK85(U_1623,U_1620)),U_1620))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK85(U_1623,U_1620)),U_1623)) ) )
    & ! [U_1622] :
        ( ! [U_1617] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1617),sK84(U_1622)))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1617),U_1622)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1622)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_1619,sK85(U_1623,U_1620))],[f_593_4]) ).

fof(f_593_6,plain,
    ( ! [U_1620,U_1623] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK85(U_1623,U_1620)),U_1620))
        | ~ sP142(U_1620,U_1623) )
    & ! [U_1620,U_1623] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK85(U_1623,U_1620)),U_1623))
        | ~ sP142(U_1620,U_1623) )
    & ! [U_1620,U_1623] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1623))
        | sP142(U_1620,U_1623) )
    & ! [U_1617,U_1622] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1617),sK84(U_1622)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1617),U_1622))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1622)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP142])],[f_593_5]) ).

cnf(f_593_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_1617),sK84(U_1622)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1617),U_1622))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1622)) ),
    inference(clausify,[status(thm)],[f_593_6]) ).

cnf(f_593_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1623))
    | sP142(U_1620,U_1623) ),
    inference(clausify,[status(thm)],[f_593_6]) ).

cnf(f_593_9,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK85(U_1623,U_1620)),U_1623))
    | ~ sP142(U_1620,U_1623) ),
    inference(clausify,[status(thm)],[f_593_6]) ).

cnf(f_593_10,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK85(U_1623,U_1620)),U_1620))
    | ~ sP142(U_1620,U_1623) ),
    inference(clausify,[status(thm)],[f_593_6]) ).

fof(f_594_1,plain,
    ! [G,C_6] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(G),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(C_6)),bot_bot_fun_a_bool)))
      | ? [X_2] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(p(G),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,X_2)),bot_bot_fun_a_bool)))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),u))
          & is_pname(X_2) )
      | ~ hBOOL(wt(C_6)) ),
    inference(fof_nnf,[status(thm)],[fact_487_assms_I3_J]) ).

fof(f_594_2,plain,
    ! [U_1626,U_1625] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(U_1626),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(U_1625)),bot_bot_fun_a_bool)))
      | ? [U_1624] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(p(U_1626),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,U_1624)),bot_bot_fun_a_bool)))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1624),u))
          & is_pname(U_1624) )
      | ~ hBOOL(wt(U_1625)) ),
    inference(variable_rename,[status(thm)],[f_594_1]) ).

fof(f_594_3,plain,
    ! [U_1626,U_1625] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(U_1626),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(U_1625)),bot_bot_fun_a_bool)))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(p(U_1626),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,sK86(U_1626,U_1625))),bot_bot_fun_a_bool)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK86(U_1626,U_1625)),u))
        & is_pname(sK86(U_1626,U_1625)) )
      | ~ hBOOL(wt(U_1625)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_1624,sK86(U_1626,U_1625))],[f_594_2]) ).

fof(f_594_4,plain,
    ( ! [U_1625,U_1626] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(p(U_1626),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,sK86(U_1626,U_1625))),bot_bot_fun_a_bool)))
        | ~ sP143(U_1625,U_1626) )
    & ! [U_1625,U_1626] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK86(U_1626,U_1625)),u))
        | ~ sP143(U_1625,U_1626) )
    & ! [U_1625,U_1626] :
        ( is_pname(sK86(U_1626,U_1625))
        | ~ sP143(U_1625,U_1626) )
    & ! [U_1625,U_1626] :
        ( hBOOL(hAPP_fun_a_bool_bool(p(U_1626),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(U_1625)),bot_bot_fun_a_bool)))
        | sP143(U_1625,U_1626)
        | ~ hBOOL(wt(U_1625)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP143])],[f_594_3]) ).

cnf(f_594_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(p(U_1626),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(U_1625)),bot_bot_fun_a_bool)))
    | sP143(U_1625,U_1626)
    | ~ hBOOL(wt(U_1625)) ),
    inference(clausify,[status(thm)],[f_594_4]) ).

cnf(f_594_6,plain,
    ( is_pname(sK86(U_1626,U_1625))
    | ~ sP143(U_1625,U_1626) ),
    inference(clausify,[status(thm)],[f_594_4]) ).

cnf(f_594_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK86(U_1626,U_1625)),u))
    | ~ sP143(U_1625,U_1626) ),
    inference(clausify,[status(thm)],[f_594_4]) ).

cnf(f_594_8,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(p(U_1626),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,sK86(U_1626,U_1625))),bot_bot_fun_a_bool)))
    | ~ sP143(U_1625,U_1626) ),
    inference(clausify,[status(thm)],[f_594_4]) ).

fof(f_595_1,plain,
    ! [A_2,B_3,C_6,D_1] :
      ( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),B_3))
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_6),D_1)) )
        & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_6),D_1))
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),B_3)) ) )
      | hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_2),B_3) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,C_6),D_1) ),
    inference(fof_nnf,[status(thm)],[fact_488_diff__eq__diff__less__eq]) ).

fof(f_595_2,plain,
    ! [U_1630,U_1629,U_1628,U_1627] :
      ( ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1630),U_1629))
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1628),U_1627)) )
        & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1628),U_1627))
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1630),U_1629)) ) )
      | hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_1630),U_1629) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_1628),U_1627) ),
    inference(variable_rename,[status(thm)],[f_595_1]) ).

fof(f_595_3,plain,
    ( ! [U_1628,U_1627,U_1629,U_1630] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1630),U_1629))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1628),U_1627))
        | ~ sP144(U_1628,U_1627,U_1629,U_1630) )
    & ! [U_1628,U_1627,U_1629,U_1630] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1628),U_1627))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1630),U_1629))
        | ~ sP144(U_1628,U_1627,U_1629,U_1630) )
    & ! [U_1628,U_1627,U_1629,U_1630] :
        ( sP144(U_1628,U_1627,U_1629,U_1630)
        | hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_1630),U_1629) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_1628),U_1627) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP144])],[f_595_2]) ).

cnf(f_595_4,plain,
    ( sP144(U_1628,U_1627,U_1629,U_1630)
    | hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_1630),U_1629) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_1628),U_1627) ),
    inference(clausify,[status(thm)],[f_595_3]) ).

cnf(f_595_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1628),U_1627))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1630),U_1629))
    | ~ sP144(U_1628,U_1627,U_1629,U_1630) ),
    inference(clausify,[status(thm)],[f_595_3]) ).

cnf(f_595_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1630),U_1629))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_1628),U_1627))
    | ~ sP144(U_1628,U_1627,U_1629,U_1630) ),
    inference(clausify,[status(thm)],[f_595_3]) ).

fof(f_596_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),Na))
        | ~ hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,M)),Na)) )
      & ( hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,M)),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_489_less__eq__nat_Osimps_I2_J]) ).

fof(f_596_2,plain,
    ! [U_1632,U_1631] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_1632)),U_1631))
        | ~ hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,U_1632)),U_1631)) )
      & ( hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,U_1632)),U_1631))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_1632)),U_1631)) ) ),
    inference(variable_rename,[status(thm)],[f_596_1]) ).

fof(f_596_3,plain,
    ( ! [U_1636,U_1634] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_1636)),U_1634))
        | ~ hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,U_1636)),U_1634)) )
    & ! [U_1635,U_1633] :
        ( hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,U_1635)),U_1633))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_1635)),U_1633)) ) ),
    inference(miniscope,[status(thm)],[f_596_2]) ).

fof(f_596_4,plain,
    ( ! [U_1634,U_1636] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_1636)),U_1634))
        | ~ hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,U_1636)),U_1634)) )
    & ! [U_1635,U_1633] :
        ( hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,U_1635)),U_1633))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_1635)),U_1633)) ) ),
    inference(definitional_conversion,[status(esa)],[f_596_3]) ).

cnf(f_596_5,plain,
    ( hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,U_1635)),U_1633))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_1635)),U_1633)) ),
    inference(clausify,[status(thm)],[f_596_4]) ).

cnf(f_596_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_1636)),U_1634))
    | ~ hBOOL(hAPP_nat_bool(nat_case_bool(fFalse,hAPP_n1699378549t_bool(ord_less_eq_nat,U_1636)),U_1634)) ),
    inference(clausify,[status(thm)],[f_596_4]) ).

fof(f_597_1,plain,
    ! [A_2] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),bot_bot_fun_int_bool)),
    inference(fof_nnf,[status(thm)],[fact_490_emptyE]) ).

fof(f_597_2,plain,
    ! [U_1637] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1637),bot_bot_fun_int_bool)),
    inference(variable_rename,[status(thm)],[f_597_1]) ).

fof(f_597_3,plain,
    ! [U_1637] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1637),bot_bot_fun_int_bool)),
    inference(definitional_conversion,[status(esa)],[f_597_2]) ).

cnf(f_597_4,plain,
    ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1637),bot_bot_fun_int_bool)),
    inference(clausify,[status(thm)],[f_597_3]) ).

fof(f_598_1,plain,
    ! [A_2] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),bot_bot_fun_nat_bool)),
    inference(fof_nnf,[status(thm)],[fact_491_emptyE]) ).

fof(f_598_2,plain,
    ! [U_1638] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1638),bot_bot_fun_nat_bool)),
    inference(variable_rename,[status(thm)],[f_598_1]) ).

fof(f_598_3,plain,
    ! [U_1638] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1638),bot_bot_fun_nat_bool)),
    inference(definitional_conversion,[status(esa)],[f_598_2]) ).

cnf(f_598_4,plain,
    ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1638),bot_bot_fun_nat_bool)),
    inference(clausify,[status(thm)],[f_598_3]) ).

fof(f_599_1,plain,
    ! [A_2] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),bot_bot_fun_a_bool)),
    inference(fof_nnf,[status(thm)],[fact_492_emptyE]) ).

fof(f_599_2,plain,
    ! [U_1639] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1639),bot_bot_fun_a_bool)),
    inference(variable_rename,[status(thm)],[f_599_1]) ).

fof(f_599_3,plain,
    ! [U_1639] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1639),bot_bot_fun_a_bool)),
    inference(definitional_conversion,[status(esa)],[f_599_2]) ).

cnf(f_599_4,plain,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1639),bot_bot_fun_a_bool)),
    inference(clausify,[status(thm)],[f_599_3]) ).

fof(f_600_1,plain,
    ! [A_2] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),bot_bo844097828e_bool)),
    inference(fof_nnf,[status(thm)],[fact_493_emptyE]) ).

fof(f_600_2,plain,
    ! [U_1640] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1640),bot_bo844097828e_bool)),
    inference(variable_rename,[status(thm)],[f_600_1]) ).

fof(f_600_3,plain,
    ! [U_1640] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1640),bot_bo844097828e_bool)),
    inference(definitional_conversion,[status(esa)],[f_600_2]) ).

cnf(f_600_4,plain,
    ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1640),bot_bo844097828e_bool)),
    inference(clausify,[status(thm)],[f_600_3]) ).

fof(f_601_1,plain,
    ! [B,A] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_494_finite__Diff]) ).

fof(f_601_2,plain,
    ! [U_1642,U_1641] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1641),U_1642)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_1641)) ),
    inference(variable_rename,[status(thm)],[f_601_1]) ).

fof(f_601_3,plain,
    ! [U_1641,U_1642] :
      ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1641),U_1642)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_1641)) ),
    inference(definitional_conversion,[status(esa)],[f_601_2]) ).

cnf(f_601_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1641),U_1642)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_1641)) ),
    inference(clausify,[status(thm)],[f_601_3]) ).

fof(f_602_1,plain,
    ! [B,A] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_495_finite__Diff]) ).

fof(f_602_2,plain,
    ! [U_1644,U_1643] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1643),U_1644)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1643)) ),
    inference(variable_rename,[status(thm)],[f_602_1]) ).

fof(f_602_3,plain,
    ! [U_1643,U_1644] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1643),U_1644)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1643)) ),
    inference(definitional_conversion,[status(esa)],[f_602_2]) ).

cnf(f_602_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1643),U_1644)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1643)) ),
    inference(clausify,[status(thm)],[f_602_3]) ).

fof(f_603_1,plain,
    ! [B,A] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_496_finite__Diff]) ).

fof(f_603_2,plain,
    ! [U_1646,U_1645] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1645),U_1646)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1645)) ),
    inference(variable_rename,[status(thm)],[f_603_1]) ).

fof(f_603_3,plain,
    ! [U_1645,U_1646] :
      ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1645),U_1646)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1645)) ),
    inference(definitional_conversion,[status(esa)],[f_603_2]) ).

cnf(f_603_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1645),U_1646)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1645)) ),
    inference(clausify,[status(thm)],[f_603_3]) ).

fof(f_604_1,plain,
    hBOOL(hAPP_f448129468l_bool(finite_finite_int,bot_bot_fun_int_bool)),
    inference(fof_nnf,[status(thm)],[fact_497_finite_OemptyI]) ).

fof(f_604_2,plain,
    hBOOL(hAPP_f448129468l_bool(finite_finite_int,bot_bot_fun_int_bool)),
    inference(definitional_conversion,[status(esa)],[f_604_1]) ).

cnf(f_604_3,plain,
    hBOOL(hAPP_f448129468l_bool(finite_finite_int,bot_bot_fun_int_bool)),
    inference(clausify,[status(thm)],[f_604_2]) ).

fof(f_605_1,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)),
    inference(fof_nnf,[status(thm)],[fact_498_finite_OemptyI]) ).

fof(f_605_2,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)),
    inference(definitional_conversion,[status(esa)],[f_605_1]) ).

cnf(f_605_3,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,bot_bot_fun_nat_bool)),
    inference(clausify,[status(thm)],[f_605_2]) ).

fof(f_606_1,plain,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)),
    inference(fof_nnf,[status(thm)],[fact_499_finite_OemptyI]) ).

fof(f_606_2,plain,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)),
    inference(definitional_conversion,[status(esa)],[f_606_1]) ).

cnf(f_606_3,plain,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,bot_bo844097828e_bool)),
    inference(clausify,[status(thm)],[f_606_2]) ).

fof(f_607_1,plain,
    hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,bot_bot_fun_a_bool)),
    inference(fof_nnf,[status(thm)],[fact_500_finite_OemptyI]) ).

fof(f_607_2,plain,
    hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,bot_bot_fun_a_bool)),
    inference(definitional_conversion,[status(esa)],[f_607_1]) ).

cnf(f_607_3,plain,
    hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,bot_bot_fun_a_bool)),
    inference(clausify,[status(thm)],[f_607_2]) ).

fof(f_608_1,plain,
    ! [A] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),A)),
    inference(fof_nnf,[status(thm)],[fact_501_empty__subsetI]) ).

fof(f_608_2,plain,
    ! [U_1647] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),U_1647)),
    inference(variable_rename,[status(thm)],[f_608_1]) ).

fof(f_608_3,plain,
    ! [U_1647] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),U_1647)),
    inference(definitional_conversion,[status(esa)],[f_608_2]) ).

cnf(f_608_4,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),U_1647)),
    inference(clausify,[status(thm)],[f_608_3]) ).

fof(f_609_1,plain,
    ! [A] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),A)),
    inference(fof_nnf,[status(thm)],[fact_502_empty__subsetI]) ).

fof(f_609_2,plain,
    ! [U_1648] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),U_1648)),
    inference(variable_rename,[status(thm)],[f_609_1]) ).

fof(f_609_3,plain,
    ! [U_1648] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),U_1648)),
    inference(definitional_conversion,[status(esa)],[f_609_2]) ).

cnf(f_609_4,plain,
    hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),U_1648)),
    inference(clausify,[status(thm)],[f_609_3]) ).

fof(f_610_1,plain,
    ! [A] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),A)),
    inference(fof_nnf,[status(thm)],[fact_503_empty__subsetI]) ).

fof(f_610_2,plain,
    ! [U_1649] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),U_1649)),
    inference(variable_rename,[status(thm)],[f_610_1]) ).

fof(f_610_3,plain,
    ! [U_1649] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),U_1649)),
    inference(definitional_conversion,[status(esa)],[f_610_2]) ).

cnf(f_610_4,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),U_1649)),
    inference(clausify,[status(thm)],[f_610_3]) ).

fof(f_611_1,plain,
    ! [A_2,A] :
      ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),A))
      | A != bot_bot_fun_int_bool ),
    inference(fof_nnf,[status(thm)],[fact_504_equals0D]) ).

fof(f_611_2,plain,
    ! [U_1651,U_1650] :
      ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1651),U_1650))
      | U_1650 != bot_bot_fun_int_bool ),
    inference(variable_rename,[status(thm)],[f_611_1]) ).

fof(f_611_3,plain,
    ! [U_1650,U_1651] :
      ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1651),U_1650))
      | U_1650 != bot_bot_fun_int_bool ),
    inference(definitional_conversion,[status(esa)],[f_611_2]) ).

cnf(f_611_4,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1651),U_1650))
    | U_1650 != bot_bot_fun_int_bool ),
    inference(clausify,[status(thm)],[f_611_3]) ).

fof(f_612_1,plain,
    ! [A_2,A] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A))
      | A != bot_bot_fun_nat_bool ),
    inference(fof_nnf,[status(thm)],[fact_505_equals0D]) ).

fof(f_612_2,plain,
    ! [U_1653,U_1652] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1653),U_1652))
      | U_1652 != bot_bot_fun_nat_bool ),
    inference(variable_rename,[status(thm)],[f_612_1]) ).

fof(f_612_3,plain,
    ! [U_1652,U_1653] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1653),U_1652))
      | U_1652 != bot_bot_fun_nat_bool ),
    inference(definitional_conversion,[status(esa)],[f_612_2]) ).

cnf(f_612_4,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1653),U_1652))
    | U_1652 != bot_bot_fun_nat_bool ),
    inference(clausify,[status(thm)],[f_612_3]) ).

fof(f_613_1,plain,
    ! [A_2,A] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
      | A != bot_bot_fun_a_bool ),
    inference(fof_nnf,[status(thm)],[fact_506_equals0D]) ).

fof(f_613_2,plain,
    ! [U_1655,U_1654] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1655),U_1654))
      | U_1654 != bot_bot_fun_a_bool ),
    inference(variable_rename,[status(thm)],[f_613_1]) ).

fof(f_613_3,plain,
    ! [U_1654,U_1655] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1655),U_1654))
      | U_1654 != bot_bot_fun_a_bool ),
    inference(definitional_conversion,[status(esa)],[f_613_2]) ).

cnf(f_613_4,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1655),U_1654))
    | U_1654 != bot_bot_fun_a_bool ),
    inference(clausify,[status(thm)],[f_613_3]) ).

fof(f_614_1,plain,
    ! [A_2,A] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A))
      | A != bot_bo844097828e_bool ),
    inference(fof_nnf,[status(thm)],[fact_507_equals0D]) ).

fof(f_614_2,plain,
    ! [U_1657,U_1656] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1657),U_1656))
      | U_1656 != bot_bo844097828e_bool ),
    inference(variable_rename,[status(thm)],[f_614_1]) ).

fof(f_614_3,plain,
    ! [U_1656,U_1657] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1657),U_1656))
      | U_1656 != bot_bo844097828e_bool ),
    inference(definitional_conversion,[status(esa)],[f_614_2]) ).

cnf(f_614_4,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1657),U_1656))
    | U_1656 != bot_bo844097828e_bool ),
    inference(clausify,[status(thm)],[f_614_3]) ).

fof(f_615_1,plain,
    ! [Pa] :
      ( ( collect_int(Pa) = bot_bot_fun_int_bool
        | ? [X_2] : hBOOL(hAPP_int_bool(Pa,X_2)) )
      & ( ! [X_2] : ~ hBOOL(hAPP_int_bool(Pa,X_2))
        | collect_int(Pa) != bot_bot_fun_int_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_508_Collect__empty__eq]) ).

fof(f_615_2,plain,
    ! [U_1660] :
      ( ( collect_int(U_1660) = bot_bot_fun_int_bool
        | ? [U_1659] : hBOOL(hAPP_int_bool(U_1660,U_1659)) )
      & ( ! [U_1658] : ~ hBOOL(hAPP_int_bool(U_1660,U_1658))
        | collect_int(U_1660) != bot_bot_fun_int_bool ) ),
    inference(variable_rename,[status(thm)],[f_615_1]) ).

fof(f_615_3,plain,
    ( ! [U_1662] :
        ( collect_int(U_1662) = bot_bot_fun_int_bool
        | ? [U_1659] : hBOOL(hAPP_int_bool(U_1662,U_1659)) )
    & ! [U_1661] :
        ( ! [U_1658] : ~ hBOOL(hAPP_int_bool(U_1661,U_1658))
        | collect_int(U_1661) != bot_bot_fun_int_bool ) ),
    inference(miniscope,[status(thm)],[f_615_2]) ).

fof(f_615_4,plain,
    ( ! [U_1662] :
        ( collect_int(U_1662) = bot_bot_fun_int_bool
        | hBOOL(hAPP_int_bool(U_1662,sK87(U_1662))) )
    & ! [U_1661] :
        ( ! [U_1658] : ~ hBOOL(hAPP_int_bool(U_1661,U_1658))
        | collect_int(U_1661) != bot_bot_fun_int_bool ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_1659,sK87(U_1662))],[f_615_3]) ).

fof(f_615_5,plain,
    ( ! [U_1662] :
        ( collect_int(U_1662) = bot_bot_fun_int_bool
        | hBOOL(hAPP_int_bool(U_1662,sK87(U_1662))) )
    & ! [U_1658,U_1661] :
        ( ~ hBOOL(hAPP_int_bool(U_1661,U_1658))
        | collect_int(U_1661) != bot_bot_fun_int_bool ) ),
    inference(definitional_conversion,[status(esa)],[f_615_4]) ).

cnf(f_615_6,plain,
    ( ~ hBOOL(hAPP_int_bool(U_1661,U_1658))
    | collect_int(U_1661) != bot_bot_fun_int_bool ),
    inference(clausify,[status(thm)],[f_615_5]) ).

cnf(f_615_7,plain,
    ( collect_int(U_1662) = bot_bot_fun_int_bool
    | hBOOL(hAPP_int_bool(U_1662,sK87(U_1662))) ),
    inference(clausify,[status(thm)],[f_615_5]) ).

fof(f_616_1,plain,
    ! [Pa] :
      ( ( collect_nat(Pa) = bot_bot_fun_nat_bool
        | ? [X_2] : hBOOL(hAPP_nat_bool(Pa,X_2)) )
      & ( ! [X_2] : ~ hBOOL(hAPP_nat_bool(Pa,X_2))
        | collect_nat(Pa) != bot_bot_fun_nat_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_509_Collect__empty__eq]) ).

fof(f_616_2,plain,
    ! [U_1665] :
      ( ( collect_nat(U_1665) = bot_bot_fun_nat_bool
        | ? [U_1664] : hBOOL(hAPP_nat_bool(U_1665,U_1664)) )
      & ( ! [U_1663] : ~ hBOOL(hAPP_nat_bool(U_1665,U_1663))
        | collect_nat(U_1665) != bot_bot_fun_nat_bool ) ),
    inference(variable_rename,[status(thm)],[f_616_1]) ).

fof(f_616_3,plain,
    ( ! [U_1667] :
        ( collect_nat(U_1667) = bot_bot_fun_nat_bool
        | ? [U_1664] : hBOOL(hAPP_nat_bool(U_1667,U_1664)) )
    & ! [U_1666] :
        ( ! [U_1663] : ~ hBOOL(hAPP_nat_bool(U_1666,U_1663))
        | collect_nat(U_1666) != bot_bot_fun_nat_bool ) ),
    inference(miniscope,[status(thm)],[f_616_2]) ).

fof(f_616_4,plain,
    ( ! [U_1667] :
        ( collect_nat(U_1667) = bot_bot_fun_nat_bool
        | hBOOL(hAPP_nat_bool(U_1667,sK88(U_1667))) )
    & ! [U_1666] :
        ( ! [U_1663] : ~ hBOOL(hAPP_nat_bool(U_1666,U_1663))
        | collect_nat(U_1666) != bot_bot_fun_nat_bool ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_1664,sK88(U_1667))],[f_616_3]) ).

fof(f_616_5,plain,
    ( ! [U_1667] :
        ( collect_nat(U_1667) = bot_bot_fun_nat_bool
        | hBOOL(hAPP_nat_bool(U_1667,sK88(U_1667))) )
    & ! [U_1663,U_1666] :
        ( ~ hBOOL(hAPP_nat_bool(U_1666,U_1663))
        | collect_nat(U_1666) != bot_bot_fun_nat_bool ) ),
    inference(definitional_conversion,[status(esa)],[f_616_4]) ).

cnf(f_616_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_1666,U_1663))
    | collect_nat(U_1666) != bot_bot_fun_nat_bool ),
    inference(clausify,[status(thm)],[f_616_5]) ).

cnf(f_616_7,plain,
    ( collect_nat(U_1667) = bot_bot_fun_nat_bool
    | hBOOL(hAPP_nat_bool(U_1667,sK88(U_1667))) ),
    inference(clausify,[status(thm)],[f_616_5]) ).

fof(f_617_1,plain,
    ! [Pa] :
      ( ( collect_a(Pa) = bot_bot_fun_a_bool
        | ? [X_2] :
            ( hBOOL(hAPP_a_bool(Pa,X_2))
            & is_a(X_2) ) )
      & ( ! [X_2] :
            ( ~ hBOOL(hAPP_a_bool(Pa,X_2))
            | ~ is_a(X_2) )
        | collect_a(Pa) != bot_bot_fun_a_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_510_Collect__empty__eq]) ).

fof(f_617_2,plain,
    ! [U_1670] :
      ( ( collect_a(U_1670) = bot_bot_fun_a_bool
        | ? [U_1669] :
            ( hBOOL(hAPP_a_bool(U_1670,U_1669))
            & is_a(U_1669) ) )
      & ( ! [U_1668] :
            ( ~ hBOOL(hAPP_a_bool(U_1670,U_1668))
            | ~ is_a(U_1668) )
        | collect_a(U_1670) != bot_bot_fun_a_bool ) ),
    inference(variable_rename,[status(thm)],[f_617_1]) ).

fof(f_617_3,plain,
    ( ! [U_1672] :
        ( collect_a(U_1672) = bot_bot_fun_a_bool
        | ? [U_1669] :
            ( hBOOL(hAPP_a_bool(U_1672,U_1669))
            & is_a(U_1669) ) )
    & ! [U_1671] :
        ( ! [U_1668] :
            ( ~ hBOOL(hAPP_a_bool(U_1671,U_1668))
            | ~ is_a(U_1668) )
        | collect_a(U_1671) != bot_bot_fun_a_bool ) ),
    inference(miniscope,[status(thm)],[f_617_2]) ).

fof(f_617_4,plain,
    ( ! [U_1672] :
        ( collect_a(U_1672) = bot_bot_fun_a_bool
        | ( hBOOL(hAPP_a_bool(U_1672,sK89(U_1672)))
          & is_a(sK89(U_1672)) ) )
    & ! [U_1671] :
        ( ! [U_1668] :
            ( ~ hBOOL(hAPP_a_bool(U_1671,U_1668))
            | ~ is_a(U_1668) )
        | collect_a(U_1671) != bot_bot_fun_a_bool ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_1669,sK89(U_1672))],[f_617_3]) ).

fof(f_617_5,plain,
    ( ! [U_1672] :
        ( hBOOL(hAPP_a_bool(U_1672,sK89(U_1672)))
        | ~ sP145(U_1672) )
    & ! [U_1672] :
        ( is_a(sK89(U_1672))
        | ~ sP145(U_1672) )
    & ! [U_1672] :
        ( collect_a(U_1672) = bot_bot_fun_a_bool
        | sP145(U_1672) )
    & ! [U_1668,U_1671] :
        ( ~ hBOOL(hAPP_a_bool(U_1671,U_1668))
        | ~ is_a(U_1668)
        | collect_a(U_1671) != bot_bot_fun_a_bool ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP145])],[f_617_4]) ).

cnf(f_617_6,plain,
    ( ~ hBOOL(hAPP_a_bool(U_1671,U_1668))
    | ~ is_a(U_1668)
    | collect_a(U_1671) != bot_bot_fun_a_bool ),
    inference(clausify,[status(thm)],[f_617_5]) ).

cnf(f_617_7,plain,
    ( collect_a(U_1672) = bot_bot_fun_a_bool
    | sP145(U_1672) ),
    inference(clausify,[status(thm)],[f_617_5]) ).

cnf(f_617_8,plain,
    ( is_a(sK89(U_1672))
    | ~ sP145(U_1672) ),
    inference(clausify,[status(thm)],[f_617_5]) ).

cnf(f_617_9,plain,
    ( hBOOL(hAPP_a_bool(U_1672,sK89(U_1672)))
    | ~ sP145(U_1672) ),
    inference(clausify,[status(thm)],[f_617_5]) ).

fof(f_618_1,plain,
    ! [A] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),A) = bot_bot_fun_nat_bool,
    inference(fof_nnf,[status(thm)],[fact_511_Diff__cancel]) ).

fof(f_618_2,plain,
    ! [U_1673] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1673),U_1673) = bot_bot_fun_nat_bool,
    inference(variable_rename,[status(thm)],[f_618_1]) ).

fof(f_618_3,plain,
    ! [U_1673] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1673),U_1673) = bot_bot_fun_nat_bool,
    inference(definitional_conversion,[status(esa)],[f_618_2]) ).

cnf(f_618_4,plain,
    hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1673),U_1673) = bot_bot_fun_nat_bool,
    inference(clausify,[status(thm)],[f_618_3]) ).

fof(f_619_1,plain,
    ! [A] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),A) = bot_bot_fun_int_bool,
    inference(fof_nnf,[status(thm)],[fact_512_Diff__cancel]) ).

fof(f_619_2,plain,
    ! [U_1674] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1674),U_1674) = bot_bot_fun_int_bool,
    inference(variable_rename,[status(thm)],[f_619_1]) ).

fof(f_619_3,plain,
    ! [U_1674] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1674),U_1674) = bot_bot_fun_int_bool,
    inference(definitional_conversion,[status(esa)],[f_619_2]) ).

cnf(f_619_4,plain,
    hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1674),U_1674) = bot_bot_fun_int_bool,
    inference(clausify,[status(thm)],[f_619_3]) ).

fof(f_620_1,plain,
    ! [A] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),A) = bot_bot_fun_a_bool,
    inference(fof_nnf,[status(thm)],[fact_513_Diff__cancel]) ).

fof(f_620_2,plain,
    ! [U_1675] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1675),U_1675) = bot_bot_fun_a_bool,
    inference(variable_rename,[status(thm)],[f_620_1]) ).

fof(f_620_3,plain,
    ! [U_1675] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1675),U_1675) = bot_bot_fun_a_bool,
    inference(definitional_conversion,[status(esa)],[f_620_2]) ).

cnf(f_620_4,plain,
    hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1675),U_1675) = bot_bot_fun_a_bool,
    inference(clausify,[status(thm)],[f_620_3]) ).

fof(f_621_1,plain,
    ! [A] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),bot_bot_fun_nat_bool) = A,
    inference(fof_nnf,[status(thm)],[fact_514_Diff__empty]) ).

fof(f_621_2,plain,
    ! [U_1676] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1676),bot_bot_fun_nat_bool) = U_1676,
    inference(variable_rename,[status(thm)],[f_621_1]) ).

fof(f_621_3,plain,
    ! [U_1676] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1676),bot_bot_fun_nat_bool) = U_1676,
    inference(definitional_conversion,[status(esa)],[f_621_2]) ).

cnf(f_621_4,plain,
    hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1676),bot_bot_fun_nat_bool) = U_1676,
    inference(clausify,[status(thm)],[f_621_3]) ).

fof(f_622_1,plain,
    ! [A] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),bot_bot_fun_int_bool) = A,
    inference(fof_nnf,[status(thm)],[fact_515_Diff__empty]) ).

fof(f_622_2,plain,
    ! [U_1677] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1677),bot_bot_fun_int_bool) = U_1677,
    inference(variable_rename,[status(thm)],[f_622_1]) ).

fof(f_622_3,plain,
    ! [U_1677] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1677),bot_bot_fun_int_bool) = U_1677,
    inference(definitional_conversion,[status(esa)],[f_622_2]) ).

cnf(f_622_4,plain,
    hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1677),bot_bot_fun_int_bool) = U_1677,
    inference(clausify,[status(thm)],[f_622_3]) ).

fof(f_623_1,plain,
    ! [A] :
      ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),bot_bot_fun_a_bool) = A
      | ~ is_fun_a_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_516_Diff__empty]) ).

fof(f_623_2,plain,
    ! [U_1678] :
      ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1678),bot_bot_fun_a_bool) = U_1678
      | ~ is_fun_a_bool(U_1678) ),
    inference(variable_rename,[status(thm)],[f_623_1]) ).

fof(f_623_3,plain,
    ! [U_1678] :
      ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1678),bot_bot_fun_a_bool) = U_1678
      | ~ is_fun_a_bool(U_1678) ),
    inference(definitional_conversion,[status(esa)],[f_623_2]) ).

cnf(f_623_4,plain,
    ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1678),bot_bot_fun_a_bool) = U_1678
    | ~ is_fun_a_bool(U_1678) ),
    inference(clausify,[status(thm)],[f_623_3]) ).

fof(f_624_1,plain,
    ! [C_6] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),bot_bot_fun_int_bool)),
    inference(fof_nnf,[status(thm)],[fact_517_empty__iff]) ).

fof(f_624_2,plain,
    ! [U_1679] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1679),bot_bot_fun_int_bool)),
    inference(variable_rename,[status(thm)],[f_624_1]) ).

fof(f_624_3,plain,
    ! [U_1679] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1679),bot_bot_fun_int_bool)),
    inference(definitional_conversion,[status(esa)],[f_624_2]) ).

cnf(f_624_4,plain,
    ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1679),bot_bot_fun_int_bool)),
    inference(clausify,[status(thm)],[f_624_3]) ).

fof(f_625_1,plain,
    ! [C_6] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),bot_bot_fun_nat_bool)),
    inference(fof_nnf,[status(thm)],[fact_518_empty__iff]) ).

fof(f_625_2,plain,
    ! [U_1680] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1680),bot_bot_fun_nat_bool)),
    inference(variable_rename,[status(thm)],[f_625_1]) ).

fof(f_625_3,plain,
    ! [U_1680] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1680),bot_bot_fun_nat_bool)),
    inference(definitional_conversion,[status(esa)],[f_625_2]) ).

cnf(f_625_4,plain,
    ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1680),bot_bot_fun_nat_bool)),
    inference(clausify,[status(thm)],[f_625_3]) ).

fof(f_626_1,plain,
    ! [C_6] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),bot_bot_fun_a_bool)),
    inference(fof_nnf,[status(thm)],[fact_519_empty__iff]) ).

fof(f_626_2,plain,
    ! [U_1681] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1681),bot_bot_fun_a_bool)),
    inference(variable_rename,[status(thm)],[f_626_1]) ).

fof(f_626_3,plain,
    ! [U_1681] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1681),bot_bot_fun_a_bool)),
    inference(definitional_conversion,[status(esa)],[f_626_2]) ).

cnf(f_626_4,plain,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1681),bot_bot_fun_a_bool)),
    inference(clausify,[status(thm)],[f_626_3]) ).

fof(f_627_1,plain,
    ! [C_6] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),bot_bo844097828e_bool)),
    inference(fof_nnf,[status(thm)],[fact_520_empty__iff]) ).

fof(f_627_2,plain,
    ! [U_1682] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1682),bot_bo844097828e_bool)),
    inference(variable_rename,[status(thm)],[f_627_1]) ).

fof(f_627_3,plain,
    ! [U_1682] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1682),bot_bo844097828e_bool)),
    inference(definitional_conversion,[status(esa)],[f_627_2]) ).

cnf(f_627_4,plain,
    ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1682),bot_bo844097828e_bool)),
    inference(clausify,[status(thm)],[f_627_3]) ).

fof(f_628_1,plain,
    ! [Pa] :
      ( ( bot_bot_fun_int_bool = collect_int(Pa)
        | ? [X_2] : hBOOL(hAPP_int_bool(Pa,X_2)) )
      & ( ! [X_2] : ~ hBOOL(hAPP_int_bool(Pa,X_2))
        | bot_bot_fun_int_bool != collect_int(Pa) ) ),
    inference(fof_nnf,[status(thm)],[fact_521_empty__Collect__eq]) ).

fof(f_628_2,plain,
    ! [U_1685] :
      ( ( bot_bot_fun_int_bool = collect_int(U_1685)
        | ? [U_1684] : hBOOL(hAPP_int_bool(U_1685,U_1684)) )
      & ( ! [U_1683] : ~ hBOOL(hAPP_int_bool(U_1685,U_1683))
        | bot_bot_fun_int_bool != collect_int(U_1685) ) ),
    inference(variable_rename,[status(thm)],[f_628_1]) ).

fof(f_628_3,plain,
    ( ! [U_1687] :
        ( bot_bot_fun_int_bool = collect_int(U_1687)
        | ? [U_1684] : hBOOL(hAPP_int_bool(U_1687,U_1684)) )
    & ! [U_1686] :
        ( ! [U_1683] : ~ hBOOL(hAPP_int_bool(U_1686,U_1683))
        | bot_bot_fun_int_bool != collect_int(U_1686) ) ),
    inference(miniscope,[status(thm)],[f_628_2]) ).

fof(f_628_4,plain,
    ( ! [U_1687] :
        ( bot_bot_fun_int_bool = collect_int(U_1687)
        | hBOOL(hAPP_int_bool(U_1687,sK90(U_1687))) )
    & ! [U_1686] :
        ( ! [U_1683] : ~ hBOOL(hAPP_int_bool(U_1686,U_1683))
        | bot_bot_fun_int_bool != collect_int(U_1686) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_1684,sK90(U_1687))],[f_628_3]) ).

fof(f_628_5,plain,
    ( ! [U_1687] :
        ( bot_bot_fun_int_bool = collect_int(U_1687)
        | hBOOL(hAPP_int_bool(U_1687,sK90(U_1687))) )
    & ! [U_1683,U_1686] :
        ( ~ hBOOL(hAPP_int_bool(U_1686,U_1683))
        | bot_bot_fun_int_bool != collect_int(U_1686) ) ),
    inference(definitional_conversion,[status(esa)],[f_628_4]) ).

cnf(f_628_6,plain,
    ( ~ hBOOL(hAPP_int_bool(U_1686,U_1683))
    | bot_bot_fun_int_bool != collect_int(U_1686) ),
    inference(clausify,[status(thm)],[f_628_5]) ).

cnf(f_628_7,plain,
    ( bot_bot_fun_int_bool = collect_int(U_1687)
    | hBOOL(hAPP_int_bool(U_1687,sK90(U_1687))) ),
    inference(clausify,[status(thm)],[f_628_5]) ).

fof(f_629_1,plain,
    ! [Pa] :
      ( ( bot_bot_fun_nat_bool = collect_nat(Pa)
        | ? [X_2] : hBOOL(hAPP_nat_bool(Pa,X_2)) )
      & ( ! [X_2] : ~ hBOOL(hAPP_nat_bool(Pa,X_2))
        | bot_bot_fun_nat_bool != collect_nat(Pa) ) ),
    inference(fof_nnf,[status(thm)],[fact_522_empty__Collect__eq]) ).

fof(f_629_2,plain,
    ! [U_1690] :
      ( ( bot_bot_fun_nat_bool = collect_nat(U_1690)
        | ? [U_1689] : hBOOL(hAPP_nat_bool(U_1690,U_1689)) )
      & ( ! [U_1688] : ~ hBOOL(hAPP_nat_bool(U_1690,U_1688))
        | bot_bot_fun_nat_bool != collect_nat(U_1690) ) ),
    inference(variable_rename,[status(thm)],[f_629_1]) ).

fof(f_629_3,plain,
    ( ! [U_1692] :
        ( bot_bot_fun_nat_bool = collect_nat(U_1692)
        | ? [U_1689] : hBOOL(hAPP_nat_bool(U_1692,U_1689)) )
    & ! [U_1691] :
        ( ! [U_1688] : ~ hBOOL(hAPP_nat_bool(U_1691,U_1688))
        | bot_bot_fun_nat_bool != collect_nat(U_1691) ) ),
    inference(miniscope,[status(thm)],[f_629_2]) ).

fof(f_629_4,plain,
    ( ! [U_1692] :
        ( bot_bot_fun_nat_bool = collect_nat(U_1692)
        | hBOOL(hAPP_nat_bool(U_1692,sK91(U_1692))) )
    & ! [U_1691] :
        ( ! [U_1688] : ~ hBOOL(hAPP_nat_bool(U_1691,U_1688))
        | bot_bot_fun_nat_bool != collect_nat(U_1691) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_1689,sK91(U_1692))],[f_629_3]) ).

fof(f_629_5,plain,
    ( ! [U_1692] :
        ( bot_bot_fun_nat_bool = collect_nat(U_1692)
        | hBOOL(hAPP_nat_bool(U_1692,sK91(U_1692))) )
    & ! [U_1688,U_1691] :
        ( ~ hBOOL(hAPP_nat_bool(U_1691,U_1688))
        | bot_bot_fun_nat_bool != collect_nat(U_1691) ) ),
    inference(definitional_conversion,[status(esa)],[f_629_4]) ).

cnf(f_629_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_1691,U_1688))
    | bot_bot_fun_nat_bool != collect_nat(U_1691) ),
    inference(clausify,[status(thm)],[f_629_5]) ).

cnf(f_629_7,plain,
    ( bot_bot_fun_nat_bool = collect_nat(U_1692)
    | hBOOL(hAPP_nat_bool(U_1692,sK91(U_1692))) ),
    inference(clausify,[status(thm)],[f_629_5]) ).

fof(f_630_1,plain,
    ! [Pa] :
      ( ( bot_bot_fun_a_bool = collect_a(Pa)
        | ? [X_2] :
            ( hBOOL(hAPP_a_bool(Pa,X_2))
            & is_a(X_2) ) )
      & ( ! [X_2] :
            ( ~ hBOOL(hAPP_a_bool(Pa,X_2))
            | ~ is_a(X_2) )
        | bot_bot_fun_a_bool != collect_a(Pa) ) ),
    inference(fof_nnf,[status(thm)],[fact_523_empty__Collect__eq]) ).

fof(f_630_2,plain,
    ! [U_1695] :
      ( ( bot_bot_fun_a_bool = collect_a(U_1695)
        | ? [U_1694] :
            ( hBOOL(hAPP_a_bool(U_1695,U_1694))
            & is_a(U_1694) ) )
      & ( ! [U_1693] :
            ( ~ hBOOL(hAPP_a_bool(U_1695,U_1693))
            | ~ is_a(U_1693) )
        | bot_bot_fun_a_bool != collect_a(U_1695) ) ),
    inference(variable_rename,[status(thm)],[f_630_1]) ).

fof(f_630_3,plain,
    ( ! [U_1697] :
        ( bot_bot_fun_a_bool = collect_a(U_1697)
        | ? [U_1694] :
            ( hBOOL(hAPP_a_bool(U_1697,U_1694))
            & is_a(U_1694) ) )
    & ! [U_1696] :
        ( ! [U_1693] :
            ( ~ hBOOL(hAPP_a_bool(U_1696,U_1693))
            | ~ is_a(U_1693) )
        | bot_bot_fun_a_bool != collect_a(U_1696) ) ),
    inference(miniscope,[status(thm)],[f_630_2]) ).

fof(f_630_4,plain,
    ( ! [U_1697] :
        ( bot_bot_fun_a_bool = collect_a(U_1697)
        | ( hBOOL(hAPP_a_bool(U_1697,sK92(U_1697)))
          & is_a(sK92(U_1697)) ) )
    & ! [U_1696] :
        ( ! [U_1693] :
            ( ~ hBOOL(hAPP_a_bool(U_1696,U_1693))
            | ~ is_a(U_1693) )
        | bot_bot_fun_a_bool != collect_a(U_1696) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_1694,sK92(U_1697))],[f_630_3]) ).

fof(f_630_5,plain,
    ( ! [U_1697] :
        ( hBOOL(hAPP_a_bool(U_1697,sK92(U_1697)))
        | ~ sP146(U_1697) )
    & ! [U_1697] :
        ( is_a(sK92(U_1697))
        | ~ sP146(U_1697) )
    & ! [U_1697] :
        ( bot_bot_fun_a_bool = collect_a(U_1697)
        | sP146(U_1697) )
    & ! [U_1693,U_1696] :
        ( ~ hBOOL(hAPP_a_bool(U_1696,U_1693))
        | ~ is_a(U_1693)
        | bot_bot_fun_a_bool != collect_a(U_1696) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP146])],[f_630_4]) ).

cnf(f_630_6,plain,
    ( ~ hBOOL(hAPP_a_bool(U_1696,U_1693))
    | ~ is_a(U_1693)
    | bot_bot_fun_a_bool != collect_a(U_1696) ),
    inference(clausify,[status(thm)],[f_630_5]) ).

cnf(f_630_7,plain,
    ( bot_bot_fun_a_bool = collect_a(U_1697)
    | sP146(U_1697) ),
    inference(clausify,[status(thm)],[f_630_5]) ).

cnf(f_630_8,plain,
    ( is_a(sK92(U_1697))
    | ~ sP146(U_1697) ),
    inference(clausify,[status(thm)],[f_630_5]) ).

cnf(f_630_9,plain,
    ( hBOOL(hAPP_a_bool(U_1697,sK92(U_1697)))
    | ~ sP146(U_1697) ),
    inference(clausify,[status(thm)],[f_630_5]) ).

fof(f_631_1,plain,
    ! [A] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,bot_bot_fun_nat_bool),A) = bot_bot_fun_nat_bool,
    inference(fof_nnf,[status(thm)],[fact_524_empty__Diff]) ).

fof(f_631_2,plain,
    ! [U_1698] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,bot_bot_fun_nat_bool),U_1698) = bot_bot_fun_nat_bool,
    inference(variable_rename,[status(thm)],[f_631_1]) ).

fof(f_631_3,plain,
    ! [U_1698] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,bot_bot_fun_nat_bool),U_1698) = bot_bot_fun_nat_bool,
    inference(definitional_conversion,[status(esa)],[f_631_2]) ).

cnf(f_631_4,plain,
    hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,bot_bot_fun_nat_bool),U_1698) = bot_bot_fun_nat_bool,
    inference(clausify,[status(thm)],[f_631_3]) ).

fof(f_632_1,plain,
    ! [A] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,bot_bot_fun_int_bool),A) = bot_bot_fun_int_bool,
    inference(fof_nnf,[status(thm)],[fact_525_empty__Diff]) ).

fof(f_632_2,plain,
    ! [U_1699] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,bot_bot_fun_int_bool),U_1699) = bot_bot_fun_int_bool,
    inference(variable_rename,[status(thm)],[f_632_1]) ).

fof(f_632_3,plain,
    ! [U_1699] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,bot_bot_fun_int_bool),U_1699) = bot_bot_fun_int_bool,
    inference(definitional_conversion,[status(esa)],[f_632_2]) ).

cnf(f_632_4,plain,
    hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,bot_bot_fun_int_bool),U_1699) = bot_bot_fun_int_bool,
    inference(clausify,[status(thm)],[f_632_3]) ).

fof(f_633_1,plain,
    ! [A] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,bot_bot_fun_a_bool),A) = bot_bot_fun_a_bool,
    inference(fof_nnf,[status(thm)],[fact_526_empty__Diff]) ).

fof(f_633_2,plain,
    ! [U_1700] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,bot_bot_fun_a_bool),U_1700) = bot_bot_fun_a_bool,
    inference(variable_rename,[status(thm)],[f_633_1]) ).

fof(f_633_3,plain,
    ! [U_1700] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,bot_bot_fun_a_bool),U_1700) = bot_bot_fun_a_bool,
    inference(definitional_conversion,[status(esa)],[f_633_2]) ).

cnf(f_633_4,plain,
    hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,bot_bot_fun_a_bool),U_1700) = bot_bot_fun_a_bool,
    inference(clausify,[status(thm)],[f_633_3]) ).

fof(f_634_1,plain,
    ! [A] :
      ( ( ? [X_2] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A))
        | A = bot_bot_fun_int_bool )
      & ( A != bot_bot_fun_int_bool
        | ! [X_2] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_527_ex__in__conv]) ).

fof(f_634_2,plain,
    ! [U_1703] :
      ( ( ? [U_1702] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1702),U_1703))
        | U_1703 = bot_bot_fun_int_bool )
      & ( U_1703 != bot_bot_fun_int_bool
        | ! [U_1701] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1701),U_1703)) ) ),
    inference(variable_rename,[status(thm)],[f_634_1]) ).

fof(f_634_3,plain,
    ( ! [U_1705] :
        ( ? [U_1702] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1702),U_1705))
        | U_1705 = bot_bot_fun_int_bool )
    & ! [U_1704] :
        ( U_1704 != bot_bot_fun_int_bool
        | ! [U_1701] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1701),U_1704)) ) ),
    inference(miniscope,[status(thm)],[f_634_2]) ).

fof(f_634_4,plain,
    ( ! [U_1705] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK93(U_1705)),U_1705))
        | U_1705 = bot_bot_fun_int_bool )
    & ! [U_1704] :
        ( U_1704 != bot_bot_fun_int_bool
        | ! [U_1701] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1701),U_1704)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_1702,sK93(U_1705))],[f_634_3]) ).

fof(f_634_5,plain,
    ( ! [U_1705] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK93(U_1705)),U_1705))
        | U_1705 = bot_bot_fun_int_bool )
    & ! [U_1701,U_1704] :
        ( U_1704 != bot_bot_fun_int_bool
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1701),U_1704)) ) ),
    inference(definitional_conversion,[status(esa)],[f_634_4]) ).

cnf(f_634_6,plain,
    ( U_1704 != bot_bot_fun_int_bool
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1701),U_1704)) ),
    inference(clausify,[status(thm)],[f_634_5]) ).

cnf(f_634_7,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK93(U_1705)),U_1705))
    | U_1705 = bot_bot_fun_int_bool ),
    inference(clausify,[status(thm)],[f_634_5]) ).

fof(f_635_1,plain,
    ! [A] :
      ( ( ? [X_2] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
        | A = bot_bot_fun_nat_bool )
      & ( A != bot_bot_fun_nat_bool
        | ! [X_2] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_528_ex__in__conv]) ).

fof(f_635_2,plain,
    ! [U_1708] :
      ( ( ? [U_1707] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1707),U_1708))
        | U_1708 = bot_bot_fun_nat_bool )
      & ( U_1708 != bot_bot_fun_nat_bool
        | ! [U_1706] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1706),U_1708)) ) ),
    inference(variable_rename,[status(thm)],[f_635_1]) ).

fof(f_635_3,plain,
    ( ! [U_1710] :
        ( ? [U_1707] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1707),U_1710))
        | U_1710 = bot_bot_fun_nat_bool )
    & ! [U_1709] :
        ( U_1709 != bot_bot_fun_nat_bool
        | ! [U_1706] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1706),U_1709)) ) ),
    inference(miniscope,[status(thm)],[f_635_2]) ).

fof(f_635_4,plain,
    ( ! [U_1710] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK94(U_1710)),U_1710))
        | U_1710 = bot_bot_fun_nat_bool )
    & ! [U_1709] :
        ( U_1709 != bot_bot_fun_nat_bool
        | ! [U_1706] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1706),U_1709)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_1707,sK94(U_1710))],[f_635_3]) ).

fof(f_635_5,plain,
    ( ! [U_1710] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK94(U_1710)),U_1710))
        | U_1710 = bot_bot_fun_nat_bool )
    & ! [U_1709,U_1706] :
        ( U_1709 != bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1706),U_1709)) ) ),
    inference(definitional_conversion,[status(esa)],[f_635_4]) ).

cnf(f_635_6,plain,
    ( U_1709 != bot_bot_fun_nat_bool
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1706),U_1709)) ),
    inference(clausify,[status(thm)],[f_635_5]) ).

cnf(f_635_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK94(U_1710)),U_1710))
    | U_1710 = bot_bot_fun_nat_bool ),
    inference(clausify,[status(thm)],[f_635_5]) ).

fof(f_636_1,plain,
    ! [A] :
      ( ( ( ? [X_2] :
              ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
              & is_a(X_2) )
          | A = bot_bot_fun_a_bool )
        & ( A != bot_bot_fun_a_bool
          | ! [X_2] :
              ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
              | ~ is_a(X_2) ) ) )
      | ~ is_fun_a_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_529_ex__in__conv]) ).

fof(f_636_2,plain,
    ! [U_1713] :
      ( ( ( ? [U_1712] :
              ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1712),U_1713))
              & is_a(U_1712) )
          | U_1713 = bot_bot_fun_a_bool )
        & ( U_1713 != bot_bot_fun_a_bool
          | ! [U_1711] :
              ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1711),U_1713))
              | ~ is_a(U_1711) ) ) )
      | ~ is_fun_a_bool(U_1713) ),
    inference(variable_rename,[status(thm)],[f_636_1]) ).

fof(f_636_3,plain,
    ! [U_1713] :
      ( ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK95(U_1713)),U_1713))
            & is_a(sK95(U_1713)) )
          | U_1713 = bot_bot_fun_a_bool )
        & ( U_1713 != bot_bot_fun_a_bool
          | ! [U_1711] :
              ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1711),U_1713))
              | ~ is_a(U_1711) ) ) )
      | ~ is_fun_a_bool(U_1713) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_1712,sK95(U_1713))],[f_636_2]) ).

fof(f_636_4,plain,
    ( ! [U_1713] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK95(U_1713)),U_1713))
        | ~ sP147(U_1713) )
    & ! [U_1713] :
        ( is_a(sK95(U_1713))
        | ~ sP147(U_1713) )
    & ! [U_1711,U_1713] :
        ( sP147(U_1713)
        | U_1713 = bot_bot_fun_a_bool
        | ~ sP148(U_1711,U_1713) )
    & ! [U_1711,U_1713] :
        ( U_1713 != bot_bot_fun_a_bool
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1711),U_1713))
        | ~ is_a(U_1711)
        | ~ sP148(U_1711,U_1713) )
    & ! [U_1711,U_1713] :
        ( sP148(U_1711,U_1713)
        | ~ is_fun_a_bool(U_1713) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP147,sP148])],[f_636_3]) ).

cnf(f_636_5,plain,
    ( sP148(U_1711,U_1713)
    | ~ is_fun_a_bool(U_1713) ),
    inference(clausify,[status(thm)],[f_636_4]) ).

cnf(f_636_6,plain,
    ( U_1713 != bot_bot_fun_a_bool
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1711),U_1713))
    | ~ is_a(U_1711)
    | ~ sP148(U_1711,U_1713) ),
    inference(clausify,[status(thm)],[f_636_4]) ).

cnf(f_636_7,plain,
    ( sP147(U_1713)
    | U_1713 = bot_bot_fun_a_bool
    | ~ sP148(U_1711,U_1713) ),
    inference(clausify,[status(thm)],[f_636_4]) ).

cnf(f_636_8,plain,
    ( is_a(sK95(U_1713))
    | ~ sP147(U_1713) ),
    inference(clausify,[status(thm)],[f_636_4]) ).

cnf(f_636_9,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK95(U_1713)),U_1713))
    | ~ sP147(U_1713) ),
    inference(clausify,[status(thm)],[f_636_4]) ).

fof(f_637_1,plain,
    ! [A] :
      ( ( ( ? [X_2] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
              & is_pname(X_2) )
          | A = bot_bo844097828e_bool )
        & ( A != bot_bo844097828e_bool
          | ! [X_2] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
              | ~ is_pname(X_2) ) ) )
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_530_ex__in__conv]) ).

fof(f_637_2,plain,
    ! [U_1716] :
      ( ( ( ? [U_1715] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1715),U_1716))
              & is_pname(U_1715) )
          | U_1716 = bot_bo844097828e_bool )
        & ( U_1716 != bot_bo844097828e_bool
          | ! [U_1714] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1714),U_1716))
              | ~ is_pname(U_1714) ) ) )
      | ~ is_fun_pname_bool(U_1716) ),
    inference(variable_rename,[status(thm)],[f_637_1]) ).

fof(f_637_3,plain,
    ! [U_1716] :
      ( ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK96(U_1716)),U_1716))
            & is_pname(sK96(U_1716)) )
          | U_1716 = bot_bo844097828e_bool )
        & ( U_1716 != bot_bo844097828e_bool
          | ! [U_1714] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1714),U_1716))
              | ~ is_pname(U_1714) ) ) )
      | ~ is_fun_pname_bool(U_1716) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_1715,sK96(U_1716))],[f_637_2]) ).

fof(f_637_4,plain,
    ( ! [U_1716] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK96(U_1716)),U_1716))
        | ~ sP149(U_1716) )
    & ! [U_1716] :
        ( is_pname(sK96(U_1716))
        | ~ sP149(U_1716) )
    & ! [U_1716,U_1714] :
        ( sP149(U_1716)
        | U_1716 = bot_bo844097828e_bool
        | ~ sP150(U_1716,U_1714) )
    & ! [U_1716,U_1714] :
        ( U_1716 != bot_bo844097828e_bool
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1714),U_1716))
        | ~ is_pname(U_1714)
        | ~ sP150(U_1716,U_1714) )
    & ! [U_1716,U_1714] :
        ( sP150(U_1716,U_1714)
        | ~ is_fun_pname_bool(U_1716) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP149,sP150])],[f_637_3]) ).

cnf(f_637_5,plain,
    ( sP150(U_1716,U_1714)
    | ~ is_fun_pname_bool(U_1716) ),
    inference(clausify,[status(thm)],[f_637_4]) ).

cnf(f_637_6,plain,
    ( U_1716 != bot_bo844097828e_bool
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1714),U_1716))
    | ~ is_pname(U_1714)
    | ~ sP150(U_1716,U_1714) ),
    inference(clausify,[status(thm)],[f_637_4]) ).

cnf(f_637_7,plain,
    ( sP149(U_1716)
    | U_1716 = bot_bo844097828e_bool
    | ~ sP150(U_1716,U_1714) ),
    inference(clausify,[status(thm)],[f_637_4]) ).

cnf(f_637_8,plain,
    ( is_pname(sK96(U_1716))
    | ~ sP149(U_1716) ),
    inference(clausify,[status(thm)],[f_637_4]) ).

cnf(f_637_9,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK96(U_1716)),U_1716))
    | ~ sP149(U_1716) ),
    inference(clausify,[status(thm)],[f_637_4]) ).

fof(f_638_1,plain,
    ! [A] :
      ( ( ! [X_2] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A))
        | A != bot_bot_fun_int_bool )
      & ( A = bot_bot_fun_int_bool
        | ? [X_2] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_531_all__not__in__conv]) ).

fof(f_638_2,plain,
    ! [U_1719] :
      ( ( ! [U_1718] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1718),U_1719))
        | U_1719 != bot_bot_fun_int_bool )
      & ( U_1719 = bot_bot_fun_int_bool
        | ? [U_1717] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1717),U_1719)) ) ),
    inference(variable_rename,[status(thm)],[f_638_1]) ).

fof(f_638_3,plain,
    ( ! [U_1721] :
        ( ! [U_1718] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1718),U_1721))
        | U_1721 != bot_bot_fun_int_bool )
    & ! [U_1720] :
        ( U_1720 = bot_bot_fun_int_bool
        | ? [U_1717] : hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1717),U_1720)) ) ),
    inference(miniscope,[status(thm)],[f_638_2]) ).

fof(f_638_4,plain,
    ( ! [U_1721] :
        ( ! [U_1718] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1718),U_1721))
        | U_1721 != bot_bot_fun_int_bool )
    & ! [U_1720] :
        ( U_1720 = bot_bot_fun_int_bool
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK97(U_1720)),U_1720)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_1717,sK97(U_1720))],[f_638_3]) ).

fof(f_638_5,plain,
    ( ! [U_1718,U_1721] :
        ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1718),U_1721))
        | U_1721 != bot_bot_fun_int_bool )
    & ! [U_1720] :
        ( U_1720 = bot_bot_fun_int_bool
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK97(U_1720)),U_1720)) ) ),
    inference(definitional_conversion,[status(esa)],[f_638_4]) ).

cnf(f_638_6,plain,
    ( U_1720 = bot_bot_fun_int_bool
    | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK97(U_1720)),U_1720)) ),
    inference(clausify,[status(thm)],[f_638_5]) ).

cnf(f_638_7,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1718),U_1721))
    | U_1721 != bot_bot_fun_int_bool ),
    inference(clausify,[status(thm)],[f_638_5]) ).

fof(f_639_1,plain,
    ! [A] :
      ( ( ! [X_2] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
        | A != bot_bot_fun_nat_bool )
      & ( A = bot_bot_fun_nat_bool
        | ? [X_2] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_532_all__not__in__conv]) ).

fof(f_639_2,plain,
    ! [U_1724] :
      ( ( ! [U_1723] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1723),U_1724))
        | U_1724 != bot_bot_fun_nat_bool )
      & ( U_1724 = bot_bot_fun_nat_bool
        | ? [U_1722] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1722),U_1724)) ) ),
    inference(variable_rename,[status(thm)],[f_639_1]) ).

fof(f_639_3,plain,
    ( ! [U_1726] :
        ( ! [U_1723] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1723),U_1726))
        | U_1726 != bot_bot_fun_nat_bool )
    & ! [U_1725] :
        ( U_1725 = bot_bot_fun_nat_bool
        | ? [U_1722] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1722),U_1725)) ) ),
    inference(miniscope,[status(thm)],[f_639_2]) ).

fof(f_639_4,plain,
    ( ! [U_1726] :
        ( ! [U_1723] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1723),U_1726))
        | U_1726 != bot_bot_fun_nat_bool )
    & ! [U_1725] :
        ( U_1725 = bot_bot_fun_nat_bool
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK98(U_1725)),U_1725)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_1722,sK98(U_1725))],[f_639_3]) ).

fof(f_639_5,plain,
    ( ! [U_1723,U_1726] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1723),U_1726))
        | U_1726 != bot_bot_fun_nat_bool )
    & ! [U_1725] :
        ( U_1725 = bot_bot_fun_nat_bool
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK98(U_1725)),U_1725)) ) ),
    inference(definitional_conversion,[status(esa)],[f_639_4]) ).

cnf(f_639_6,plain,
    ( U_1725 = bot_bot_fun_nat_bool
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK98(U_1725)),U_1725)) ),
    inference(clausify,[status(thm)],[f_639_5]) ).

cnf(f_639_7,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1723),U_1726))
    | U_1726 != bot_bot_fun_nat_bool ),
    inference(clausify,[status(thm)],[f_639_5]) ).

fof(f_640_1,plain,
    ! [A] :
      ( ( ( ! [X_2] :
              ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
              | ~ is_a(X_2) )
          | A != bot_bot_fun_a_bool )
        & ( A = bot_bot_fun_a_bool
          | ? [X_2] :
              ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
              & is_a(X_2) ) ) )
      | ~ is_fun_a_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_533_all__not__in__conv]) ).

fof(f_640_2,plain,
    ! [U_1729] :
      ( ( ( ! [U_1728] :
              ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1728),U_1729))
              | ~ is_a(U_1728) )
          | U_1729 != bot_bot_fun_a_bool )
        & ( U_1729 = bot_bot_fun_a_bool
          | ? [U_1727] :
              ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1727),U_1729))
              & is_a(U_1727) ) ) )
      | ~ is_fun_a_bool(U_1729) ),
    inference(variable_rename,[status(thm)],[f_640_1]) ).

fof(f_640_3,plain,
    ! [U_1729] :
      ( ( ( ! [U_1728] :
              ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1728),U_1729))
              | ~ is_a(U_1728) )
          | U_1729 != bot_bot_fun_a_bool )
        & ( U_1729 = bot_bot_fun_a_bool
          | ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK99(U_1729)),U_1729))
            & is_a(sK99(U_1729)) ) ) )
      | ~ is_fun_a_bool(U_1729) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_1727,sK99(U_1729))],[f_640_2]) ).

fof(f_640_4,plain,
    ( ! [U_1729] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK99(U_1729)),U_1729))
        | ~ sP151(U_1729) )
    & ! [U_1729] :
        ( is_a(sK99(U_1729))
        | ~ sP151(U_1729) )
    & ! [U_1728,U_1729] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1728),U_1729))
        | ~ is_a(U_1728)
        | U_1729 != bot_bot_fun_a_bool
        | ~ sP152(U_1728,U_1729) )
    & ! [U_1728,U_1729] :
        ( U_1729 = bot_bot_fun_a_bool
        | sP151(U_1729)
        | ~ sP152(U_1728,U_1729) )
    & ! [U_1728,U_1729] :
        ( sP152(U_1728,U_1729)
        | ~ is_fun_a_bool(U_1729) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP151,sP152])],[f_640_3]) ).

cnf(f_640_5,plain,
    ( sP152(U_1728,U_1729)
    | ~ is_fun_a_bool(U_1729) ),
    inference(clausify,[status(thm)],[f_640_4]) ).

cnf(f_640_6,plain,
    ( U_1729 = bot_bot_fun_a_bool
    | sP151(U_1729)
    | ~ sP152(U_1728,U_1729) ),
    inference(clausify,[status(thm)],[f_640_4]) ).

cnf(f_640_7,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1728),U_1729))
    | ~ is_a(U_1728)
    | U_1729 != bot_bot_fun_a_bool
    | ~ sP152(U_1728,U_1729) ),
    inference(clausify,[status(thm)],[f_640_4]) ).

cnf(f_640_8,plain,
    ( is_a(sK99(U_1729))
    | ~ sP151(U_1729) ),
    inference(clausify,[status(thm)],[f_640_4]) ).

cnf(f_640_9,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK99(U_1729)),U_1729))
    | ~ sP151(U_1729) ),
    inference(clausify,[status(thm)],[f_640_4]) ).

fof(f_641_1,plain,
    ! [A] :
      ( ( ( ! [X_2] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
              | ~ is_pname(X_2) )
          | A != bot_bo844097828e_bool )
        & ( A = bot_bo844097828e_bool
          | ? [X_2] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
              & is_pname(X_2) ) ) )
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_534_all__not__in__conv]) ).

fof(f_641_2,plain,
    ! [U_1732] :
      ( ( ( ! [U_1731] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1731),U_1732))
              | ~ is_pname(U_1731) )
          | U_1732 != bot_bo844097828e_bool )
        & ( U_1732 = bot_bo844097828e_bool
          | ? [U_1730] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1730),U_1732))
              & is_pname(U_1730) ) ) )
      | ~ is_fun_pname_bool(U_1732) ),
    inference(variable_rename,[status(thm)],[f_641_1]) ).

fof(f_641_3,plain,
    ! [U_1732] :
      ( ( ( ! [U_1731] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1731),U_1732))
              | ~ is_pname(U_1731) )
          | U_1732 != bot_bo844097828e_bool )
        & ( U_1732 = bot_bo844097828e_bool
          | ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK100(U_1732)),U_1732))
            & is_pname(sK100(U_1732)) ) ) )
      | ~ is_fun_pname_bool(U_1732) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_1730,sK100(U_1732))],[f_641_2]) ).

fof(f_641_4,plain,
    ( ! [U_1732] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK100(U_1732)),U_1732))
        | ~ sP153(U_1732) )
    & ! [U_1732] :
        ( is_pname(sK100(U_1732))
        | ~ sP153(U_1732) )
    & ! [U_1731,U_1732] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1731),U_1732))
        | ~ is_pname(U_1731)
        | U_1732 != bot_bo844097828e_bool
        | ~ sP154(U_1731,U_1732) )
    & ! [U_1731,U_1732] :
        ( U_1732 = bot_bo844097828e_bool
        | sP153(U_1732)
        | ~ sP154(U_1731,U_1732) )
    & ! [U_1731,U_1732] :
        ( sP154(U_1731,U_1732)
        | ~ is_fun_pname_bool(U_1732) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP153,sP154])],[f_641_3]) ).

cnf(f_641_5,plain,
    ( sP154(U_1731,U_1732)
    | ~ is_fun_pname_bool(U_1732) ),
    inference(clausify,[status(thm)],[f_641_4]) ).

cnf(f_641_6,plain,
    ( U_1732 = bot_bo844097828e_bool
    | sP153(U_1732)
    | ~ sP154(U_1731,U_1732) ),
    inference(clausify,[status(thm)],[f_641_4]) ).

cnf(f_641_7,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1731),U_1732))
    | ~ is_pname(U_1731)
    | U_1732 != bot_bo844097828e_bool
    | ~ sP154(U_1731,U_1732) ),
    inference(clausify,[status(thm)],[f_641_4]) ).

cnf(f_641_8,plain,
    ( is_pname(sK100(U_1732))
    | ~ sP153(U_1732) ),
    inference(clausify,[status(thm)],[f_641_4]) ).

cnf(f_641_9,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK100(U_1732)),U_1732))
    | ~ sP153(U_1732) ),
    inference(clausify,[status(thm)],[f_641_4]) ).

fof(f_642_1,plain,
    ! [X_1] :
      ( ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_1))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_535_bot__apply]) ).

fof(f_642_2,plain,
    ! [U_1733] :
      ( ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1733))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1733)) ) ),
    inference(variable_rename,[status(thm)],[f_642_1]) ).

fof(f_642_3,plain,
    ( ( ! [U_1735] : hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1735))
      | ~ hBOOL(bot_bot_bool) )
    & ( ! [U_1734] : ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1734))
      | hBOOL(bot_bot_bool) ) ),
    inference(miniscope,[status(thm)],[f_642_2]) ).

fof(f_642_4,plain,
    ( ! [U_1735] :
        ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1735))
        | ~ hBOOL(bot_bot_bool) )
    & ! [U_1734] :
        ( ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1734))
        | hBOOL(bot_bot_bool) ) ),
    inference(definitional_conversion,[status(esa)],[f_642_3]) ).

cnf(f_642_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1734))
    | hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_642_4]) ).

cnf(f_642_6,plain,
    ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1735))
    | ~ hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_642_4]) ).

fof(f_643_1,plain,
    ! [X_1] :
      ( ( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X_1))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_536_bot__apply]) ).

fof(f_643_2,plain,
    ! [U_1736] :
      ( ( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,U_1736))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,U_1736)) ) ),
    inference(variable_rename,[status(thm)],[f_643_1]) ).

fof(f_643_3,plain,
    ( ( ! [U_1738] : hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,U_1738))
      | ~ hBOOL(bot_bot_bool) )
    & ( ! [U_1737] : ~ hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,U_1737))
      | hBOOL(bot_bot_bool) ) ),
    inference(miniscope,[status(thm)],[f_643_2]) ).

fof(f_643_4,plain,
    ( ! [U_1738] :
        ( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,U_1738))
        | ~ hBOOL(bot_bot_bool) )
    & ! [U_1737] :
        ( ~ hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,U_1737))
        | hBOOL(bot_bot_bool) ) ),
    inference(definitional_conversion,[status(esa)],[f_643_3]) ).

cnf(f_643_5,plain,
    ( ~ hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,U_1737))
    | hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_643_4]) ).

cnf(f_643_6,plain,
    ( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,U_1738))
    | ~ hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_643_4]) ).

fof(f_644_1,plain,
    ! [X_1] :
      ( ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X_1))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_537_bot__apply]) ).

fof(f_644_2,plain,
    ! [U_1739] :
      ( ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1739))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1739)) ) ),
    inference(variable_rename,[status(thm)],[f_644_1]) ).

fof(f_644_3,plain,
    ( ( ! [U_1741] : hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1741))
      | ~ hBOOL(bot_bot_bool) )
    & ( ! [U_1740] : ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1740))
      | hBOOL(bot_bot_bool) ) ),
    inference(miniscope,[status(thm)],[f_644_2]) ).

fof(f_644_4,plain,
    ( ! [U_1741] :
        ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1741))
        | ~ hBOOL(bot_bot_bool) )
    & ! [U_1740] :
        ( ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1740))
        | hBOOL(bot_bot_bool) ) ),
    inference(definitional_conversion,[status(esa)],[f_644_3]) ).

cnf(f_644_5,plain,
    ( ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1740))
    | hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_644_4]) ).

cnf(f_644_6,plain,
    ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1741))
    | ~ hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_644_4]) ).

fof(f_645_1,plain,
    bot_bot_fun_int_bool = collect_int(cOMBK_bool_int(fFalse)),
    inference(fof_nnf,[status(thm)],[fact_538_empty__def]) ).

fof(f_645_2,plain,
    bot_bot_fun_int_bool = collect_int(cOMBK_bool_int(fFalse)),
    inference(definitional_conversion,[status(esa)],[f_645_1]) ).

cnf(f_645_3,plain,
    bot_bot_fun_int_bool = collect_int(cOMBK_bool_int(fFalse)),
    inference(clausify,[status(thm)],[f_645_2]) ).

fof(f_646_1,plain,
    bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse)),
    inference(fof_nnf,[status(thm)],[fact_539_empty__def]) ).

fof(f_646_2,plain,
    bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse)),
    inference(definitional_conversion,[status(esa)],[f_646_1]) ).

cnf(f_646_3,plain,
    bot_bot_fun_nat_bool = collect_nat(cOMBK_bool_nat(fFalse)),
    inference(clausify,[status(thm)],[f_646_2]) ).

fof(f_647_1,plain,
    bot_bot_fun_a_bool = collect_a(cOMBK_bool_a(fFalse)),
    inference(fof_nnf,[status(thm)],[fact_540_empty__def]) ).

fof(f_647_2,plain,
    bot_bot_fun_a_bool = collect_a(cOMBK_bool_a(fFalse)),
    inference(definitional_conversion,[status(esa)],[f_647_1]) ).

cnf(f_647_3,plain,
    bot_bot_fun_a_bool = collect_a(cOMBK_bool_a(fFalse)),
    inference(clausify,[status(thm)],[f_647_2]) ).

fof(f_648_1,plain,
    ! [X_2] :
      ( ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_2))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_541_bot__fun__def]) ).

fof(f_648_2,plain,
    ! [U_1742] :
      ( ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1742))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1742)) ) ),
    inference(variable_rename,[status(thm)],[f_648_1]) ).

fof(f_648_3,plain,
    ( ( ! [U_1744] : hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1744))
      | ~ hBOOL(bot_bot_bool) )
    & ( ! [U_1743] : ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1743))
      | hBOOL(bot_bot_bool) ) ),
    inference(miniscope,[status(thm)],[f_648_2]) ).

fof(f_648_4,plain,
    ( ! [U_1744] :
        ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1744))
        | ~ hBOOL(bot_bot_bool) )
    & ! [U_1743] :
        ( ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1743))
        | hBOOL(bot_bot_bool) ) ),
    inference(definitional_conversion,[status(esa)],[f_648_3]) ).

cnf(f_648_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1743))
    | hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_648_4]) ).

cnf(f_648_6,plain,
    ( hBOOL(hAPP_nat_bool(bot_bot_fun_nat_bool,U_1744))
    | ~ hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_648_4]) ).

fof(f_649_1,plain,
    ! [X_2] :
      ( ( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X_2))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_542_bot__fun__def]) ).

fof(f_649_2,plain,
    ! [U_1745] :
      ( ( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,U_1745))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,U_1745)) ) ),
    inference(variable_rename,[status(thm)],[f_649_1]) ).

fof(f_649_3,plain,
    ( ( ! [U_1747] : hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,U_1747))
      | ~ hBOOL(bot_bot_bool) )
    & ( ! [U_1746] : ~ hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,U_1746))
      | hBOOL(bot_bot_bool) ) ),
    inference(miniscope,[status(thm)],[f_649_2]) ).

fof(f_649_4,plain,
    ( ! [U_1747] :
        ( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,U_1747))
        | ~ hBOOL(bot_bot_bool) )
    & ! [U_1746] :
        ( ~ hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,U_1746))
        | hBOOL(bot_bot_bool) ) ),
    inference(definitional_conversion,[status(esa)],[f_649_3]) ).

cnf(f_649_5,plain,
    ( ~ hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,U_1746))
    | hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_649_4]) ).

cnf(f_649_6,plain,
    ( hBOOL(hAPP_int_bool(bot_bot_fun_int_bool,U_1747))
    | ~ hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_649_4]) ).

fof(f_650_1,plain,
    ! [X_2] :
      ( ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X_2))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_543_bot__fun__def]) ).

fof(f_650_2,plain,
    ! [U_1748] :
      ( ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1748))
        | ~ hBOOL(bot_bot_bool) )
      & ( hBOOL(bot_bot_bool)
        | ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1748)) ) ),
    inference(variable_rename,[status(thm)],[f_650_1]) ).

fof(f_650_3,plain,
    ( ( ! [U_1750] : hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1750))
      | ~ hBOOL(bot_bot_bool) )
    & ( ! [U_1749] : ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1749))
      | hBOOL(bot_bot_bool) ) ),
    inference(miniscope,[status(thm)],[f_650_2]) ).

fof(f_650_4,plain,
    ( ! [U_1750] :
        ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1750))
        | ~ hBOOL(bot_bot_bool) )
    & ! [U_1749] :
        ( ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1749))
        | hBOOL(bot_bot_bool) ) ),
    inference(definitional_conversion,[status(esa)],[f_650_3]) ).

cnf(f_650_5,plain,
    ( ~ hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1749))
    | hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_650_4]) ).

cnf(f_650_6,plain,
    ( hBOOL(hAPP_a_bool(bot_bot_fun_a_bool,U_1750))
    | ~ hBOOL(bot_bot_bool) ),
    inference(clausify,[status(thm)],[f_650_4]) ).

fof(f_651_1,plain,
    ! [A_2,A] :
      ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool))) = A
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
      | ~ is_fun_a_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_544_insert__Diff]) ).

fof(f_651_2,plain,
    ! [U_1752,U_1751] :
      ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1752),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1751),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1752),bot_bot_fun_a_bool))) = U_1751
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1752),U_1751))
      | ~ is_fun_a_bool(U_1751) ),
    inference(variable_rename,[status(thm)],[f_651_1]) ).

fof(f_651_3,plain,
    ! [U_1752,U_1751] :
      ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1752),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1751),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1752),bot_bot_fun_a_bool))) = U_1751
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1752),U_1751))
      | ~ is_fun_a_bool(U_1751) ),
    inference(definitional_conversion,[status(esa)],[f_651_2]) ).

cnf(f_651_4,plain,
    ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1752),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1751),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1752),bot_bot_fun_a_bool))) = U_1751
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1752),U_1751))
    | ~ is_fun_a_bool(U_1751) ),
    inference(clausify,[status(thm)],[f_651_3]) ).

fof(f_652_1,plain,
    ! [A_2,A] :
      ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool))) = A
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_545_insert__Diff]) ).

fof(f_652_2,plain,
    ! [U_1754,U_1753] :
      ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1754),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1753),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1754),bot_bot_fun_int_bool))) = U_1753
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1754),U_1753)) ),
    inference(variable_rename,[status(thm)],[f_652_1]) ).

fof(f_652_3,plain,
    ! [U_1753,U_1754] :
      ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1754),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1753),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1754),bot_bot_fun_int_bool))) = U_1753
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1754),U_1753)) ),
    inference(definitional_conversion,[status(esa)],[f_652_2]) ).

cnf(f_652_4,plain,
    ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1754),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1753),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1754),bot_bot_fun_int_bool))) = U_1753
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1754),U_1753)) ),
    inference(clausify,[status(thm)],[f_652_3]) ).

fof(f_653_1,plain,
    ! [A_2,A] :
      ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool))) = A
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A)) ),
    inference(fof_nnf,[status(thm)],[fact_546_insert__Diff]) ).

fof(f_653_2,plain,
    ! [U_1756,U_1755] :
      ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1756),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1755),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1756),bot_bot_fun_nat_bool))) = U_1755
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1756),U_1755)) ),
    inference(variable_rename,[status(thm)],[f_653_1]) ).

fof(f_653_3,plain,
    ! [U_1755,U_1756] :
      ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1756),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1755),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1756),bot_bot_fun_nat_bool))) = U_1755
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1756),U_1755)) ),
    inference(definitional_conversion,[status(esa)],[f_653_2]) ).

cnf(f_653_4,plain,
    ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1756),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1755),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1756),bot_bot_fun_nat_bool))) = U_1755
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1756),U_1755)) ),
    inference(clausify,[status(thm)],[f_653_3]) ).

fof(f_654_1,plain,
    ! [A_2,A] :
      ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool))) = A
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A))
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_547_insert__Diff]) ).

fof(f_654_2,plain,
    ! [U_1758,U_1757] :
      ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1758),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1757),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1758),bot_bo844097828e_bool))) = U_1757
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1758),U_1757))
      | ~ is_fun_pname_bool(U_1757) ),
    inference(variable_rename,[status(thm)],[f_654_1]) ).

fof(f_654_3,plain,
    ! [U_1757,U_1758] :
      ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1758),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1757),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1758),bot_bo844097828e_bool))) = U_1757
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1758),U_1757))
      | ~ is_fun_pname_bool(U_1757) ),
    inference(definitional_conversion,[status(esa)],[f_654_2]) ).

cnf(f_654_4,plain,
    ( hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1758),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1757),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1758),bot_bo844097828e_bool))) = U_1757
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1758),U_1757))
    | ~ is_fun_pname_bool(U_1757) ),
    inference(clausify,[status(thm)],[f_654_3]) ).

fof(f_655_1,plain,
    ! [X_1,A] :
      ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)) = A
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
      | ~ is_fun_a_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_548_Diff__insert__absorb]) ).

fof(f_655_2,plain,
    ! [U_1760,U_1759] :
      ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1760),U_1759)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1760),bot_bot_fun_a_bool)) = U_1759
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1760),U_1759))
      | ~ is_fun_a_bool(U_1759) ),
    inference(variable_rename,[status(thm)],[f_655_1]) ).

fof(f_655_3,plain,
    ! [U_1759,U_1760] :
      ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1760),U_1759)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1760),bot_bot_fun_a_bool)) = U_1759
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1760),U_1759))
      | ~ is_fun_a_bool(U_1759) ),
    inference(definitional_conversion,[status(esa)],[f_655_2]) ).

cnf(f_655_4,plain,
    ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1760),U_1759)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1760),bot_bot_fun_a_bool)) = U_1759
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1760),U_1759))
    | ~ is_fun_a_bool(U_1759) ),
    inference(clausify,[status(thm)],[f_655_3]) ).

fof(f_656_1,plain,
    ! [X_1,A] :
      ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = A
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) ),
    inference(fof_nnf,[status(thm)],[fact_549_Diff__insert__absorb]) ).

fof(f_656_2,plain,
    ! [U_1762,U_1761] :
      ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1762),U_1761)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1762),bot_bot_fun_int_bool)) = U_1761
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1762),U_1761)) ),
    inference(variable_rename,[status(thm)],[f_656_1]) ).

fof(f_656_3,plain,
    ! [U_1761,U_1762] :
      ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1762),U_1761)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1762),bot_bot_fun_int_bool)) = U_1761
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1762),U_1761)) ),
    inference(definitional_conversion,[status(esa)],[f_656_2]) ).

cnf(f_656_4,plain,
    ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1762),U_1761)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1762),bot_bot_fun_int_bool)) = U_1761
    | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1762),U_1761)) ),
    inference(clausify,[status(thm)],[f_656_3]) ).

fof(f_657_1,plain,
    ! [X_1,A] :
      ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = A
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) ),
    inference(fof_nnf,[status(thm)],[fact_550_Diff__insert__absorb]) ).

fof(f_657_2,plain,
    ! [U_1764,U_1763] :
      ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1764),U_1763)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1764),bot_bot_fun_nat_bool)) = U_1763
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1764),U_1763)) ),
    inference(variable_rename,[status(thm)],[f_657_1]) ).

fof(f_657_3,plain,
    ! [U_1763,U_1764] :
      ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1764),U_1763)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1764),bot_bot_fun_nat_bool)) = U_1763
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1764),U_1763)) ),
    inference(definitional_conversion,[status(esa)],[f_657_2]) ).

cnf(f_657_4,plain,
    ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1764),U_1763)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1764),bot_bot_fun_nat_bool)) = U_1763
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1764),U_1763)) ),
    inference(clausify,[status(thm)],[f_657_3]) ).

fof(f_658_1,plain,
    ! [X_1,A] :
      ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = A
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_551_Diff__insert__absorb]) ).

fof(f_658_2,plain,
    ! [U_1766,U_1765] :
      ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1766),U_1765)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1766),bot_bo844097828e_bool)) = U_1765
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1766),U_1765))
      | ~ is_fun_pname_bool(U_1765) ),
    inference(variable_rename,[status(thm)],[f_658_1]) ).

fof(f_658_3,plain,
    ! [U_1765,U_1766] :
      ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1766),U_1765)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1766),bot_bo844097828e_bool)) = U_1765
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1766),U_1765))
      | ~ is_fun_pname_bool(U_1765) ),
    inference(definitional_conversion,[status(esa)],[f_658_2]) ).

cnf(f_658_4,plain,
    ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1766),U_1765)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1766),bot_bo844097828e_bool)) = U_1765
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1766),U_1765))
    | ~ is_fun_pname_bool(U_1765) ),
    inference(clausify,[status(thm)],[f_658_3]) ).

fof(f_659_1,plain,
    ! [A_2,A] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool))) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),A),
    inference(fof_nnf,[status(thm)],[fact_552_insert__Diff__single]) ).

fof(f_659_2,plain,
    ! [U_1768,U_1767] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1768),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1767),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1768),bot_bot_fun_a_bool))) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1768),U_1767),
    inference(variable_rename,[status(thm)],[f_659_1]) ).

fof(f_659_3,plain,
    ! [U_1767,U_1768] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1768),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1767),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1768),bot_bot_fun_a_bool))) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1768),U_1767),
    inference(definitional_conversion,[status(esa)],[f_659_2]) ).

cnf(f_659_4,plain,
    hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1768),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1767),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1768),bot_bot_fun_a_bool))) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1768),U_1767),
    inference(clausify,[status(thm)],[f_659_3]) ).

fof(f_660_1,plain,
    ! [A_2,A] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool))) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A),
    inference(fof_nnf,[status(thm)],[fact_553_insert__Diff__single]) ).

fof(f_660_2,plain,
    ! [U_1770,U_1769] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1770),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1769),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1770),bot_bot_fun_nat_bool))) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1770),U_1769),
    inference(variable_rename,[status(thm)],[f_660_1]) ).

fof(f_660_3,plain,
    ! [U_1769,U_1770] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1770),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1769),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1770),bot_bot_fun_nat_bool))) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1770),U_1769),
    inference(definitional_conversion,[status(esa)],[f_660_2]) ).

cnf(f_660_4,plain,
    hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1770),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1769),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1770),bot_bot_fun_nat_bool))) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1770),U_1769),
    inference(clausify,[status(thm)],[f_660_3]) ).

fof(f_661_1,plain,
    ! [A_2,A] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool))) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),A),
    inference(fof_nnf,[status(thm)],[fact_554_insert__Diff__single]) ).

fof(f_661_2,plain,
    ! [U_1772,U_1771] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1772),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1771),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1772),bot_bot_fun_int_bool))) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1772),U_1771),
    inference(variable_rename,[status(thm)],[f_661_1]) ).

fof(f_661_3,plain,
    ! [U_1771,U_1772] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1772),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1771),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1772),bot_bot_fun_int_bool))) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1772),U_1771),
    inference(definitional_conversion,[status(esa)],[f_661_2]) ).

cnf(f_661_4,plain,
    hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1772),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1771),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1772),bot_bot_fun_int_bool))) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1772),U_1771),
    inference(clausify,[status(thm)],[f_661_3]) ).

fof(f_662_1,plain,
    ! [A,A_2,B] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),B)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool))),B),
    inference(fof_nnf,[status(thm)],[fact_555_Diff__insert2]) ).

fof(f_662_2,plain,
    ! [U_1775,U_1774,U_1773] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1775),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1774),U_1773)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1775),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1774),bot_bot_fun_a_bool))),U_1773),
    inference(variable_rename,[status(thm)],[f_662_1]) ).

fof(f_662_3,plain,
    ! [U_1773,U_1774,U_1775] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1775),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1774),U_1773)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1775),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1774),bot_bot_fun_a_bool))),U_1773),
    inference(definitional_conversion,[status(esa)],[f_662_2]) ).

cnf(f_662_4,plain,
    hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1775),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1774),U_1773)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1775),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1774),bot_bot_fun_a_bool))),U_1773),
    inference(clausify,[status(thm)],[f_662_3]) ).

fof(f_663_1,plain,
    ! [A,A_2,B] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool))),B),
    inference(fof_nnf,[status(thm)],[fact_556_Diff__insert2]) ).

fof(f_663_2,plain,
    ! [U_1778,U_1777,U_1776] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1778),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1777),U_1776)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1778),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1777),bot_bot_fun_nat_bool))),U_1776),
    inference(variable_rename,[status(thm)],[f_663_1]) ).

fof(f_663_3,plain,
    ! [U_1776,U_1777,U_1778] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1778),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1777),U_1776)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1778),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1777),bot_bot_fun_nat_bool))),U_1776),
    inference(definitional_conversion,[status(esa)],[f_663_2]) ).

cnf(f_663_4,plain,
    hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1778),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1777),U_1776)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1778),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1777),bot_bot_fun_nat_bool))),U_1776),
    inference(clausify,[status(thm)],[f_663_3]) ).

fof(f_664_1,plain,
    ! [A,A_2,B] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),B)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool))),B),
    inference(fof_nnf,[status(thm)],[fact_557_Diff__insert2]) ).

fof(f_664_2,plain,
    ! [U_1781,U_1780,U_1779] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1781),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1780),U_1779)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1781),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1780),bot_bot_fun_int_bool))),U_1779),
    inference(variable_rename,[status(thm)],[f_664_1]) ).

fof(f_664_3,plain,
    ! [U_1779,U_1780,U_1781] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1781),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1780),U_1779)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1781),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1780),bot_bot_fun_int_bool))),U_1779),
    inference(definitional_conversion,[status(esa)],[f_664_2]) ).

cnf(f_664_4,plain,
    hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1781),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1780),U_1779)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1781),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1780),bot_bot_fun_int_bool))),U_1779),
    inference(clausify,[status(thm)],[f_664_3]) ).

fof(f_665_1,plain,
    ! [A,A_2,B] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),B)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool)),
    inference(fof_nnf,[status(thm)],[fact_558_Diff__insert]) ).

fof(f_665_2,plain,
    ! [U_1784,U_1783,U_1782] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1784),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1783),U_1782)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1784),U_1782)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1783),bot_bot_fun_a_bool)),
    inference(variable_rename,[status(thm)],[f_665_1]) ).

fof(f_665_3,plain,
    ! [U_1782,U_1783,U_1784] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1784),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1783),U_1782)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1784),U_1782)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1783),bot_bot_fun_a_bool)),
    inference(definitional_conversion,[status(esa)],[f_665_2]) ).

cnf(f_665_4,plain,
    hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1784),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1783),U_1782)) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1784),U_1782)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1783),bot_bot_fun_a_bool)),
    inference(clausify,[status(thm)],[f_665_3]) ).

fof(f_666_1,plain,
    ! [A,A_2,B] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool)),
    inference(fof_nnf,[status(thm)],[fact_559_Diff__insert]) ).

fof(f_666_2,plain,
    ! [U_1787,U_1786,U_1785] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1787),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1786),U_1785)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1787),U_1785)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1786),bot_bot_fun_nat_bool)),
    inference(variable_rename,[status(thm)],[f_666_1]) ).

fof(f_666_3,plain,
    ! [U_1785,U_1786,U_1787] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1787),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1786),U_1785)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1787),U_1785)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1786),bot_bot_fun_nat_bool)),
    inference(definitional_conversion,[status(esa)],[f_666_2]) ).

cnf(f_666_4,plain,
    hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1787),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1786),U_1785)) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1787),U_1785)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1786),bot_bot_fun_nat_bool)),
    inference(clausify,[status(thm)],[f_666_3]) ).

fof(f_667_1,plain,
    ! [A,A_2,B] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),B)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool)),
    inference(fof_nnf,[status(thm)],[fact_560_Diff__insert]) ).

fof(f_667_2,plain,
    ! [U_1790,U_1789,U_1788] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1790),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1789),U_1788)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1790),U_1788)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1789),bot_bot_fun_int_bool)),
    inference(variable_rename,[status(thm)],[f_667_1]) ).

fof(f_667_3,plain,
    ! [U_1788,U_1789,U_1790] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1790),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1789),U_1788)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1790),U_1788)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1789),bot_bot_fun_int_bool)),
    inference(definitional_conversion,[status(esa)],[f_667_2]) ).

cnf(f_667_4,plain,
    hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1790),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1789),U_1788)) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1790),U_1788)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1789),bot_bot_fun_int_bool)),
    inference(clausify,[status(thm)],[f_667_3]) ).

fof(f_668_1,plain,
    ! [A,X_1,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),B)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))),B)) ),
    inference(fof_nnf,[status(thm)],[fact_561_diff__single__insert]) ).

fof(f_668_2,plain,
    ! [U_1793,U_1792,U_1791] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1793),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1792),U_1791)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1792),U_1793))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1793),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1792),bot_bot_fun_a_bool))),U_1791)) ),
    inference(variable_rename,[status(thm)],[f_668_1]) ).

fof(f_668_3,plain,
    ! [U_1791,U_1792,U_1793] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1793),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1792),U_1791)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1792),U_1793))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1793),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1792),bot_bot_fun_a_bool))),U_1791)) ),
    inference(definitional_conversion,[status(esa)],[f_668_2]) ).

cnf(f_668_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1793),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1792),U_1791)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1792),U_1793))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1793),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1792),bot_bot_fun_a_bool))),U_1791)) ),
    inference(clausify,[status(thm)],[f_668_3]) ).

fof(f_669_1,plain,
    ! [A,X_1,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))),B)) ),
    inference(fof_nnf,[status(thm)],[fact_562_diff__single__insert]) ).

fof(f_669_2,plain,
    ! [U_1796,U_1795,U_1794] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1796),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1795),U_1794)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1795),U_1796))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1796),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1795),bot_bot_fun_int_bool))),U_1794)) ),
    inference(variable_rename,[status(thm)],[f_669_1]) ).

fof(f_669_3,plain,
    ! [U_1794,U_1795,U_1796] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1796),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1795),U_1794)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1795),U_1796))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1796),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1795),bot_bot_fun_int_bool))),U_1794)) ),
    inference(definitional_conversion,[status(esa)],[f_669_2]) ).

cnf(f_669_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1796),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1795),U_1794)))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1795),U_1796))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1796),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1795),bot_bot_fun_int_bool))),U_1794)) ),
    inference(clausify,[status(thm)],[f_669_3]) ).

fof(f_670_1,plain,
    ! [A,X_1,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))),B)) ),
    inference(fof_nnf,[status(thm)],[fact_563_diff__single__insert]) ).

fof(f_670_2,plain,
    ! [U_1799,U_1798,U_1797] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1799),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1798),U_1797)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1798),U_1799))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1799),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1798),bot_bot_fun_nat_bool))),U_1797)) ),
    inference(variable_rename,[status(thm)],[f_670_1]) ).

fof(f_670_3,plain,
    ! [U_1797,U_1798,U_1799] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1799),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1798),U_1797)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1798),U_1799))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1799),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1798),bot_bot_fun_nat_bool))),U_1797)) ),
    inference(definitional_conversion,[status(esa)],[f_670_2]) ).

cnf(f_670_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1799),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1798),U_1797)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1798),U_1799))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1799),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1798),bot_bot_fun_nat_bool))),U_1797)) ),
    inference(clausify,[status(thm)],[f_670_3]) ).

fof(f_671_1,plain,
    ! [A,X_1,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))),B)) ),
    inference(fof_nnf,[status(thm)],[fact_564_diff__single__insert]) ).

fof(f_671_2,plain,
    ! [U_1802,U_1801,U_1800] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1802),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1801),U_1800)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1801),U_1802))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1802),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1801),bot_bo844097828e_bool))),U_1800)) ),
    inference(variable_rename,[status(thm)],[f_671_1]) ).

fof(f_671_3,plain,
    ! [U_1800,U_1801,U_1802] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1802),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1801),U_1800)))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1801),U_1802))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1802),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1801),bot_bo844097828e_bool))),U_1800)) ),
    inference(definitional_conversion,[status(esa)],[f_671_2]) ).

cnf(f_671_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1802),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1801),U_1800)))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1801),U_1802))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1802),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1801),bot_bo844097828e_bool))),U_1800)) ),
    inference(clausify,[status(thm)],[f_671_3]) ).

fof(f_672_1,plain,
    ! [A,X_1,B] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),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_1),A)) )
        | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))),B))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),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_1),A)) )
          & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))),B))
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) ) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),B))) ) ),
    inference(fof_nnf,[status(thm)],[fact_565_subset__insert__iff]) ).

fof(f_672_2,plain,
    ! [U_1805,U_1804,U_1803] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1805),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1804),U_1803)))
        | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1805),U_1803))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1804),U_1805)) )
        | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1805),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1804),bot_bot_fun_a_bool))),U_1803))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1804),U_1805)) ) )
      & ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1805),U_1803))
            | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1804),U_1805)) )
          & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1805),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1804),bot_bot_fun_a_bool))),U_1803))
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1804),U_1805)) ) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1805),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1804),U_1803))) ) ),
    inference(variable_rename,[status(thm)],[f_672_1]) ).

fof(f_672_3,plain,
    ( ! [U_1811,U_1809,U_1807] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1811),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1809),U_1807)))
        | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1811),U_1807))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1809),U_1811)) )
        | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1811),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1809),bot_bot_fun_a_bool))),U_1807))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1809),U_1811)) ) )
    & ! [U_1810,U_1808,U_1806] :
        ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1810),U_1806))
            | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1808),U_1810)) )
          & ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1810),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1808),bot_bot_fun_a_bool))),U_1806))
            | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1808),U_1810)) ) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1810),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1808),U_1806))) ) ),
    inference(miniscope,[status(thm)],[f_672_2]) ).

fof(f_672_4,plain,
    ( ! [U_1809,U_1807,U_1811] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1811),U_1807))
        | ~ sP157(U_1809,U_1807,U_1811) )
    & ! [U_1809,U_1807,U_1811] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1809),U_1811))
        | ~ sP157(U_1809,U_1807,U_1811) )
    & ! [U_1809,U_1807,U_1811] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1811),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1809),bot_bot_fun_a_bool))),U_1807))
        | ~ sP156(U_1809,U_1807,U_1811) )
    & ! [U_1809,U_1807,U_1811] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1809),U_1811))
        | ~ sP156(U_1809,U_1807,U_1811) )
    & ! [U_1806,U_1808,U_1810] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1810),U_1806))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1808),U_1810))
        | ~ sP155(U_1806,U_1808,U_1810) )
    & ! [U_1806,U_1808,U_1810] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1810),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1808),bot_bot_fun_a_bool))),U_1806))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1808),U_1810))
        | ~ sP155(U_1806,U_1808,U_1810) )
    & ! [U_1809,U_1807,U_1811] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1811),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1809),U_1807)))
        | sP157(U_1809,U_1807,U_1811)
        | sP156(U_1809,U_1807,U_1811) )
    & ! [U_1806,U_1808,U_1810] :
        ( sP155(U_1806,U_1808,U_1810)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1810),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1808),U_1806))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP155,sP156,sP157])],[f_672_3]) ).

cnf(f_672_5,plain,
    ( sP155(U_1806,U_1808,U_1810)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1810),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1808),U_1806))) ),
    inference(clausify,[status(thm)],[f_672_4]) ).

cnf(f_672_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1811),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1809),U_1807)))
    | sP157(U_1809,U_1807,U_1811)
    | sP156(U_1809,U_1807,U_1811) ),
    inference(clausify,[status(thm)],[f_672_4]) ).

cnf(f_672_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1810),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1808),bot_bot_fun_a_bool))),U_1806))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1808),U_1810))
    | ~ sP155(U_1806,U_1808,U_1810) ),
    inference(clausify,[status(thm)],[f_672_4]) ).

cnf(f_672_8,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1810),U_1806))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1808),U_1810))
    | ~ sP155(U_1806,U_1808,U_1810) ),
    inference(clausify,[status(thm)],[f_672_4]) ).

cnf(f_672_9,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1809),U_1811))
    | ~ sP156(U_1809,U_1807,U_1811) ),
    inference(clausify,[status(thm)],[f_672_4]) ).

cnf(f_672_10,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1811),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1809),bot_bot_fun_a_bool))),U_1807))
    | ~ sP156(U_1809,U_1807,U_1811) ),
    inference(clausify,[status(thm)],[f_672_4]) ).

cnf(f_672_11,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1809),U_1811))
    | ~ sP157(U_1809,U_1807,U_1811) ),
    inference(clausify,[status(thm)],[f_672_4]) ).

cnf(f_672_12,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1811),U_1807))
    | ~ sP157(U_1809,U_1807,U_1811) ),
    inference(clausify,[status(thm)],[f_672_4]) ).

fof(f_673_1,plain,
    ! [A,X_1,B] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B)))
        | ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) )
        | ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))),B))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) ) )
      & ( ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B))
            | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) )
          & ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))),B))
            | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) ) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),B))) ) ),
    inference(fof_nnf,[status(thm)],[fact_566_subset__insert__iff]) ).

fof(f_673_2,plain,
    ! [U_1814,U_1813,U_1812] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1814),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1813),U_1812)))
        | ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1814),U_1812))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1813),U_1814)) )
        | ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1814),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1813),bot_bot_fun_int_bool))),U_1812))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1813),U_1814)) ) )
      & ( ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1814),U_1812))
            | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1813),U_1814)) )
          & ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1814),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1813),bot_bot_fun_int_bool))),U_1812))
            | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1813),U_1814)) ) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1814),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1813),U_1812))) ) ),
    inference(variable_rename,[status(thm)],[f_673_1]) ).

fof(f_673_3,plain,
    ( ! [U_1820,U_1818,U_1816] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1820),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1818),U_1816)))
        | ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1820),U_1816))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1818),U_1820)) )
        | ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1820),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1818),bot_bot_fun_int_bool))),U_1816))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1818),U_1820)) ) )
    & ! [U_1819,U_1817,U_1815] :
        ( ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1819),U_1815))
            | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1817),U_1819)) )
          & ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1819),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1817),bot_bot_fun_int_bool))),U_1815))
            | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1817),U_1819)) ) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1819),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1817),U_1815))) ) ),
    inference(miniscope,[status(thm)],[f_673_2]) ).

fof(f_673_4,plain,
    ( ! [U_1818,U_1816,U_1820] :
        ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1820),U_1816))
        | ~ sP160(U_1818,U_1816,U_1820) )
    & ! [U_1818,U_1816,U_1820] :
        ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1818),U_1820))
        | ~ sP160(U_1818,U_1816,U_1820) )
    & ! [U_1818,U_1816,U_1820] :
        ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1820),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1818),bot_bot_fun_int_bool))),U_1816))
        | ~ sP159(U_1818,U_1816,U_1820) )
    & ! [U_1818,U_1816,U_1820] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1818),U_1820))
        | ~ sP159(U_1818,U_1816,U_1820) )
    & ! [U_1817,U_1815,U_1819] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1819),U_1815))
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1817),U_1819))
        | ~ sP158(U_1817,U_1815,U_1819) )
    & ! [U_1817,U_1815,U_1819] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1819),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1817),bot_bot_fun_int_bool))),U_1815))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1817),U_1819))
        | ~ sP158(U_1817,U_1815,U_1819) )
    & ! [U_1818,U_1816,U_1820] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1820),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1818),U_1816)))
        | sP160(U_1818,U_1816,U_1820)
        | sP159(U_1818,U_1816,U_1820) )
    & ! [U_1817,U_1815,U_1819] :
        ( sP158(U_1817,U_1815,U_1819)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1819),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1817),U_1815))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP158,sP159,sP160])],[f_673_3]) ).

cnf(f_673_5,plain,
    ( sP158(U_1817,U_1815,U_1819)
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1819),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1817),U_1815))) ),
    inference(clausify,[status(thm)],[f_673_4]) ).

cnf(f_673_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1820),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1818),U_1816)))
    | sP160(U_1818,U_1816,U_1820)
    | sP159(U_1818,U_1816,U_1820) ),
    inference(clausify,[status(thm)],[f_673_4]) ).

cnf(f_673_7,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1819),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1817),bot_bot_fun_int_bool))),U_1815))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1817),U_1819))
    | ~ sP158(U_1817,U_1815,U_1819) ),
    inference(clausify,[status(thm)],[f_673_4]) ).

cnf(f_673_8,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1819),U_1815))
    | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1817),U_1819))
    | ~ sP158(U_1817,U_1815,U_1819) ),
    inference(clausify,[status(thm)],[f_673_4]) ).

cnf(f_673_9,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1818),U_1820))
    | ~ sP159(U_1818,U_1816,U_1820) ),
    inference(clausify,[status(thm)],[f_673_4]) ).

cnf(f_673_10,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1820),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1818),bot_bot_fun_int_bool))),U_1816))
    | ~ sP159(U_1818,U_1816,U_1820) ),
    inference(clausify,[status(thm)],[f_673_4]) ).

cnf(f_673_11,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1818),U_1820))
    | ~ sP160(U_1818,U_1816,U_1820) ),
    inference(clausify,[status(thm)],[f_673_4]) ).

cnf(f_673_12,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1820),U_1816))
    | ~ sP160(U_1818,U_1816,U_1820) ),
    inference(clausify,[status(thm)],[f_673_4]) ).

fof(f_674_1,plain,
    ! [A,X_1,B] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B)))
        | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) )
        | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))),B))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) ) )
      & ( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
            | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) )
          & ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))),B))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) ) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),B))) ) ),
    inference(fof_nnf,[status(thm)],[fact_567_subset__insert__iff]) ).

fof(f_674_2,plain,
    ! [U_1823,U_1822,U_1821] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1823),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1822),U_1821)))
        | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1823),U_1821))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1822),U_1823)) )
        | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1823),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1822),bot_bot_fun_nat_bool))),U_1821))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1822),U_1823)) ) )
      & ( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1823),U_1821))
            | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1822),U_1823)) )
          & ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1823),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1822),bot_bot_fun_nat_bool))),U_1821))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1822),U_1823)) ) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1823),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1822),U_1821))) ) ),
    inference(variable_rename,[status(thm)],[f_674_1]) ).

fof(f_674_3,plain,
    ( ! [U_1829,U_1827,U_1825] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1829),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1827),U_1825)))
        | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1829),U_1825))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1827),U_1829)) )
        | ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1829),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1827),bot_bot_fun_nat_bool))),U_1825))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1827),U_1829)) ) )
    & ! [U_1828,U_1826,U_1824] :
        ( ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1828),U_1824))
            | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1826),U_1828)) )
          & ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1828),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1826),bot_bot_fun_nat_bool))),U_1824))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1826),U_1828)) ) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1828),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1826),U_1824))) ) ),
    inference(miniscope,[status(thm)],[f_674_2]) ).

fof(f_674_4,plain,
    ( ! [U_1825,U_1827,U_1829] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1829),U_1825))
        | ~ sP163(U_1825,U_1827,U_1829) )
    & ! [U_1825,U_1827,U_1829] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1827),U_1829))
        | ~ sP163(U_1825,U_1827,U_1829) )
    & ! [U_1825,U_1827,U_1829] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1829),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1827),bot_bot_fun_nat_bool))),U_1825))
        | ~ sP162(U_1825,U_1827,U_1829) )
    & ! [U_1825,U_1827,U_1829] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1827),U_1829))
        | ~ sP162(U_1825,U_1827,U_1829) )
    & ! [U_1826,U_1824,U_1828] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1828),U_1824))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1826),U_1828))
        | ~ sP161(U_1826,U_1824,U_1828) )
    & ! [U_1826,U_1824,U_1828] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1828),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1826),bot_bot_fun_nat_bool))),U_1824))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1826),U_1828))
        | ~ sP161(U_1826,U_1824,U_1828) )
    & ! [U_1825,U_1827,U_1829] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1829),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1827),U_1825)))
        | sP163(U_1825,U_1827,U_1829)
        | sP162(U_1825,U_1827,U_1829) )
    & ! [U_1826,U_1824,U_1828] :
        ( sP161(U_1826,U_1824,U_1828)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1828),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1826),U_1824))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP161,sP162,sP163])],[f_674_3]) ).

cnf(f_674_5,plain,
    ( sP161(U_1826,U_1824,U_1828)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1828),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1826),U_1824))) ),
    inference(clausify,[status(thm)],[f_674_4]) ).

cnf(f_674_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1829),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1827),U_1825)))
    | sP163(U_1825,U_1827,U_1829)
    | sP162(U_1825,U_1827,U_1829) ),
    inference(clausify,[status(thm)],[f_674_4]) ).

cnf(f_674_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1828),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1826),bot_bot_fun_nat_bool))),U_1824))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1826),U_1828))
    | ~ sP161(U_1826,U_1824,U_1828) ),
    inference(clausify,[status(thm)],[f_674_4]) ).

cnf(f_674_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1828),U_1824))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1826),U_1828))
    | ~ sP161(U_1826,U_1824,U_1828) ),
    inference(clausify,[status(thm)],[f_674_4]) ).

cnf(f_674_9,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1827),U_1829))
    | ~ sP162(U_1825,U_1827,U_1829) ),
    inference(clausify,[status(thm)],[f_674_4]) ).

cnf(f_674_10,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1829),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1827),bot_bot_fun_nat_bool))),U_1825))
    | ~ sP162(U_1825,U_1827,U_1829) ),
    inference(clausify,[status(thm)],[f_674_4]) ).

cnf(f_674_11,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1827),U_1829))
    | ~ sP163(U_1825,U_1827,U_1829) ),
    inference(clausify,[status(thm)],[f_674_4]) ).

cnf(f_674_12,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1829),U_1825))
    | ~ sP163(U_1825,U_1827,U_1829) ),
    inference(clausify,[status(thm)],[f_674_4]) ).

fof(f_675_1,plain,
    ! [A,X_1,B] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B)))
        | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) )
        | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))),B))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) ) )
      & ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
            | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) )
          & ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))),B))
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) ) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),B))) ) ),
    inference(fof_nnf,[status(thm)],[fact_568_subset__insert__iff]) ).

fof(f_675_2,plain,
    ! [U_1832,U_1831,U_1830] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1832),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1831),U_1830)))
        | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1832),U_1830))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1831),U_1832)) )
        | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1832),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1831),bot_bo844097828e_bool))),U_1830))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1831),U_1832)) ) )
      & ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1832),U_1830))
            | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1831),U_1832)) )
          & ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1832),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1831),bot_bo844097828e_bool))),U_1830))
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1831),U_1832)) ) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1832),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1831),U_1830))) ) ),
    inference(variable_rename,[status(thm)],[f_675_1]) ).

fof(f_675_3,plain,
    ( ! [U_1838,U_1836,U_1834] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1838),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1836),U_1834)))
        | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1838),U_1834))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1836),U_1838)) )
        | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1838),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1836),bot_bo844097828e_bool))),U_1834))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1836),U_1838)) ) )
    & ! [U_1837,U_1835,U_1833] :
        ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1837),U_1833))
            | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1835),U_1837)) )
          & ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1837),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1835),bot_bo844097828e_bool))),U_1833))
            | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1835),U_1837)) ) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1837),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1835),U_1833))) ) ),
    inference(miniscope,[status(thm)],[f_675_2]) ).

fof(f_675_4,plain,
    ( ! [U_1834,U_1836,U_1838] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1838),U_1834))
        | ~ sP166(U_1834,U_1836,U_1838) )
    & ! [U_1834,U_1836,U_1838] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1836),U_1838))
        | ~ sP166(U_1834,U_1836,U_1838) )
    & ! [U_1834,U_1836,U_1838] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1838),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1836),bot_bo844097828e_bool))),U_1834))
        | ~ sP165(U_1834,U_1836,U_1838) )
    & ! [U_1834,U_1836,U_1838] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1836),U_1838))
        | ~ sP165(U_1834,U_1836,U_1838) )
    & ! [U_1835,U_1833,U_1837] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1837),U_1833))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1835),U_1837))
        | ~ sP164(U_1835,U_1833,U_1837) )
    & ! [U_1835,U_1833,U_1837] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1837),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1835),bot_bo844097828e_bool))),U_1833))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1835),U_1837))
        | ~ sP164(U_1835,U_1833,U_1837) )
    & ! [U_1834,U_1836,U_1838] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1838),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1836),U_1834)))
        | sP166(U_1834,U_1836,U_1838)
        | sP165(U_1834,U_1836,U_1838) )
    & ! [U_1835,U_1833,U_1837] :
        ( sP164(U_1835,U_1833,U_1837)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1837),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1835),U_1833))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP164,sP165,sP166])],[f_675_3]) ).

cnf(f_675_5,plain,
    ( sP164(U_1835,U_1833,U_1837)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1837),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1835),U_1833))) ),
    inference(clausify,[status(thm)],[f_675_4]) ).

cnf(f_675_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1838),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1836),U_1834)))
    | sP166(U_1834,U_1836,U_1838)
    | sP165(U_1834,U_1836,U_1838) ),
    inference(clausify,[status(thm)],[f_675_4]) ).

cnf(f_675_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1837),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1835),bot_bo844097828e_bool))),U_1833))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1835),U_1837))
    | ~ sP164(U_1835,U_1833,U_1837) ),
    inference(clausify,[status(thm)],[f_675_4]) ).

cnf(f_675_8,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1837),U_1833))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1835),U_1837))
    | ~ sP164(U_1835,U_1833,U_1837) ),
    inference(clausify,[status(thm)],[f_675_4]) ).

cnf(f_675_9,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1836),U_1838))
    | ~ sP165(U_1834,U_1836,U_1838) ),
    inference(clausify,[status(thm)],[f_675_4]) ).

cnf(f_675_10,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1838),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1836),bot_bo844097828e_bool))),U_1834))
    | ~ sP165(U_1834,U_1836,U_1838) ),
    inference(clausify,[status(thm)],[f_675_4]) ).

cnf(f_675_11,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1836),U_1838))
    | ~ sP166(U_1834,U_1836,U_1838) ),
    inference(clausify,[status(thm)],[f_675_4]) ).

cnf(f_675_12,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_1838),U_1834))
    | ~ sP166(U_1834,U_1836,U_1838) ),
    inference(clausify,[status(thm)],[f_675_4]) ).

fof(f_676_1,plain,
    ! [A,B] :
      ( ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)))
          | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) )
        & ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
          | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))) ) )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) ),
    inference(fof_nnf,[status(thm)],[fact_569_finite__Diff2]) ).

fof(f_676_2,plain,
    ! [U_1840,U_1839] :
      ( ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1840),U_1839)))
          | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_1840)) )
        & ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_1840))
          | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1840),U_1839))) ) )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_1839)) ),
    inference(variable_rename,[status(thm)],[f_676_1]) ).

fof(f_676_3,plain,
    ( ! [U_1839,U_1840] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1840),U_1839)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_1840))
        | ~ sP167(U_1839,U_1840) )
    & ! [U_1839,U_1840] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_1840))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1840),U_1839)))
        | ~ sP167(U_1839,U_1840) )
    & ! [U_1839,U_1840] :
        ( sP167(U_1839,U_1840)
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_1839)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP167])],[f_676_2]) ).

cnf(f_676_4,plain,
    ( sP167(U_1839,U_1840)
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_1839)) ),
    inference(clausify,[status(thm)],[f_676_3]) ).

cnf(f_676_5,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_1840))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1840),U_1839)))
    | ~ sP167(U_1839,U_1840) ),
    inference(clausify,[status(thm)],[f_676_3]) ).

cnf(f_676_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1840),U_1839)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_1840))
    | ~ sP167(U_1839,U_1840) ),
    inference(clausify,[status(thm)],[f_676_3]) ).

fof(f_677_1,plain,
    ! [A,B] :
      ( ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)))
          | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) )
        & ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
          | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) ),
    inference(fof_nnf,[status(thm)],[fact_570_finite__Diff2]) ).

fof(f_677_2,plain,
    ! [U_1842,U_1841] :
      ( ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1842),U_1841)))
          | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1842)) )
        & ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1842))
          | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1842),U_1841))) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1841)) ),
    inference(variable_rename,[status(thm)],[f_677_1]) ).

fof(f_677_3,plain,
    ( ! [U_1841,U_1842] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1842),U_1841)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1842))
        | ~ sP168(U_1841,U_1842) )
    & ! [U_1841,U_1842] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1842))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1842),U_1841)))
        | ~ sP168(U_1841,U_1842) )
    & ! [U_1841,U_1842] :
        ( sP168(U_1841,U_1842)
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1841)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP168])],[f_677_2]) ).

cnf(f_677_4,plain,
    ( sP168(U_1841,U_1842)
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1841)) ),
    inference(clausify,[status(thm)],[f_677_3]) ).

cnf(f_677_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1842))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1842),U_1841)))
    | ~ sP168(U_1841,U_1842) ),
    inference(clausify,[status(thm)],[f_677_3]) ).

cnf(f_677_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1842),U_1841)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_1842))
    | ~ sP168(U_1841,U_1842) ),
    inference(clausify,[status(thm)],[f_677_3]) ).

fof(f_678_1,plain,
    ! [A,B] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))
          | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) )
        & ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
          | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) ) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ),
    inference(fof_nnf,[status(thm)],[fact_571_finite__Diff2]) ).

fof(f_678_2,plain,
    ! [U_1844,U_1843] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1844),U_1843)))
          | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1844)) )
        & ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1844))
          | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1844),U_1843))) ) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1843)) ),
    inference(variable_rename,[status(thm)],[f_678_1]) ).

fof(f_678_3,plain,
    ( ! [U_1844,U_1843] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1844),U_1843)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1844))
        | ~ sP169(U_1844,U_1843) )
    & ! [U_1844,U_1843] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1844))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1844),U_1843)))
        | ~ sP169(U_1844,U_1843) )
    & ! [U_1844,U_1843] :
        ( sP169(U_1844,U_1843)
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1843)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP169])],[f_678_2]) ).

cnf(f_678_4,plain,
    ( sP169(U_1844,U_1843)
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1843)) ),
    inference(clausify,[status(thm)],[f_678_3]) ).

cnf(f_678_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1844))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1844),U_1843)))
    | ~ sP169(U_1844,U_1843) ),
    inference(clausify,[status(thm)],[f_678_3]) ).

cnf(f_678_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1844),U_1843)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_1844))
    | ~ sP169(U_1844,U_1843) ),
    inference(clausify,[status(thm)],[f_678_3]) ).

fof(f_679_1,plain,
    ! [A,X_1,B] :
      ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)),B) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_572_insert__Diff1]) ).

fof(f_679_2,plain,
    ! [U_1847,U_1846,U_1845] :
      ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1846),U_1847)),U_1845) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1847),U_1845)
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1846),U_1845)) ),
    inference(variable_rename,[status(thm)],[f_679_1]) ).

fof(f_679_3,plain,
    ! [U_1847,U_1846,U_1845] :
      ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1846),U_1847)),U_1845) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1847),U_1845)
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1846),U_1845)) ),
    inference(definitional_conversion,[status(esa)],[f_679_2]) ).

cnf(f_679_4,plain,
    ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1846),U_1847)),U_1845) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1847),U_1845)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1846),U_1845)) ),
    inference(clausify,[status(thm)],[f_679_3]) ).

fof(f_680_1,plain,
    ! [A,X_1,B] :
      ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)),B) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_573_insert__Diff1]) ).

fof(f_680_2,plain,
    ! [U_1850,U_1849,U_1848] :
      ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1849),U_1850)),U_1848) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1850),U_1848)
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1849),U_1848)) ),
    inference(variable_rename,[status(thm)],[f_680_1]) ).

fof(f_680_3,plain,
    ! [U_1848,U_1849,U_1850] :
      ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1849),U_1850)),U_1848) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1850),U_1848)
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1849),U_1848)) ),
    inference(definitional_conversion,[status(esa)],[f_680_2]) ).

cnf(f_680_4,plain,
    ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1849),U_1850)),U_1848) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1850),U_1848)
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1849),U_1848)) ),
    inference(clausify,[status(thm)],[f_680_3]) ).

fof(f_681_1,plain,
    ! [A,X_1,B] :
      ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),B) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_574_insert__Diff1]) ).

fof(f_681_2,plain,
    ! [U_1853,U_1852,U_1851] :
      ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1852),U_1853)),U_1851) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1853),U_1851)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1852),U_1851)) ),
    inference(variable_rename,[status(thm)],[f_681_1]) ).

fof(f_681_3,plain,
    ! [U_1851,U_1852,U_1853] :
      ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1852),U_1853)),U_1851) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1853),U_1851)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1852),U_1851)) ),
    inference(definitional_conversion,[status(esa)],[f_681_2]) ).

cnf(f_681_4,plain,
    ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1852),U_1853)),U_1851) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1853),U_1851)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1852),U_1851)) ),
    inference(clausify,[status(thm)],[f_681_3]) ).

fof(f_682_1,plain,
    ! [A,X_1,B] :
      ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) ),
    inference(fof_nnf,[status(thm)],[fact_575_insert__Diff1]) ).

fof(f_682_2,plain,
    ! [U_1856,U_1855,U_1854] :
      ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1855),U_1856)),U_1854) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1856),U_1854)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1855),U_1854)) ),
    inference(variable_rename,[status(thm)],[f_682_1]) ).

fof(f_682_3,plain,
    ! [U_1854,U_1855,U_1856] :
      ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1855),U_1856)),U_1854) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1856),U_1854)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1855),U_1854)) ),
    inference(definitional_conversion,[status(esa)],[f_682_2]) ).

cnf(f_682_4,plain,
    ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1855),U_1856)),U_1854) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1856),U_1854)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1855),U_1854)) ),
    inference(clausify,[status(thm)],[f_682_3]) ).

fof(f_683_1,plain,
    ! [A,X_1,B] :
      ( ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)),B) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B)) )
      & ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)),B) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_576_insert__Diff__if]) ).

fof(f_683_2,plain,
    ! [U_1859,U_1858,U_1857] :
      ( ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1858),U_1859)),U_1857) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1858),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1859),U_1857))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1858),U_1857)) )
      & ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1858),U_1859)),U_1857) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1859),U_1857)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1858),U_1857)) ) ),
    inference(variable_rename,[status(thm)],[f_683_1]) ).

fof(f_683_3,plain,
    ( ! [U_1865,U_1863,U_1861] :
        ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1863),U_1865)),U_1861) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1863),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1865),U_1861))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1863),U_1861)) )
    & ! [U_1864,U_1862,U_1860] :
        ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1862),U_1864)),U_1860) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1864),U_1860)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1862),U_1860)) ) ),
    inference(miniscope,[status(thm)],[f_683_2]) ).

fof(f_683_4,plain,
    ( ! [U_1863,U_1861,U_1865] :
        ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1863),U_1865)),U_1861) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1863),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1865),U_1861))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1863),U_1861)) )
    & ! [U_1862,U_1864,U_1860] :
        ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1862),U_1864)),U_1860) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1864),U_1860)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1862),U_1860)) ) ),
    inference(definitional_conversion,[status(esa)],[f_683_3]) ).

cnf(f_683_5,plain,
    ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1862),U_1864)),U_1860) = hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1864),U_1860)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1862),U_1860)) ),
    inference(clausify,[status(thm)],[f_683_4]) ).

cnf(f_683_6,plain,
    ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1863),U_1865)),U_1861) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1863),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1865),U_1861))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1863),U_1861)) ),
    inference(clausify,[status(thm)],[f_683_4]) ).

fof(f_684_1,plain,
    ! [A,X_1,B] :
      ( ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)),B) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B)) )
      & ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)),B) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_577_insert__Diff__if]) ).

fof(f_684_2,plain,
    ! [U_1868,U_1867,U_1866] :
      ( ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1867),U_1868)),U_1866) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1867),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1868),U_1866))
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1867),U_1866)) )
      & ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1867),U_1868)),U_1866) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1868),U_1866)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1867),U_1866)) ) ),
    inference(variable_rename,[status(thm)],[f_684_1]) ).

fof(f_684_3,plain,
    ( ! [U_1874,U_1872,U_1870] :
        ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1872),U_1874)),U_1870) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1872),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1874),U_1870))
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1872),U_1870)) )
    & ! [U_1873,U_1871,U_1869] :
        ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1871),U_1873)),U_1869) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1873),U_1869)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1871),U_1869)) ) ),
    inference(miniscope,[status(thm)],[f_684_2]) ).

fof(f_684_4,plain,
    ( ! [U_1870,U_1872,U_1874] :
        ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1872),U_1874)),U_1870) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1872),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1874),U_1870))
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1872),U_1870)) )
    & ! [U_1871,U_1869,U_1873] :
        ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1871),U_1873)),U_1869) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1873),U_1869)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1871),U_1869)) ) ),
    inference(definitional_conversion,[status(esa)],[f_684_3]) ).

cnf(f_684_5,plain,
    ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1871),U_1873)),U_1869) = hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1873),U_1869)
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1871),U_1869)) ),
    inference(clausify,[status(thm)],[f_684_4]) ).

cnf(f_684_6,plain,
    ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1872),U_1874)),U_1870) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1872),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1874),U_1870))
    | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1872),U_1870)) ),
    inference(clausify,[status(thm)],[f_684_4]) ).

fof(f_685_1,plain,
    ! [A,X_1,B] :
      ( ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),B) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) )
      & ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)),B) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_578_insert__Diff__if]) ).

fof(f_685_2,plain,
    ! [U_1877,U_1876,U_1875] :
      ( ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1876),U_1877)),U_1875) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1876),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1877),U_1875))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1876),U_1875)) )
      & ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1876),U_1877)),U_1875) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1877),U_1875)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1876),U_1875)) ) ),
    inference(variable_rename,[status(thm)],[f_685_1]) ).

fof(f_685_3,plain,
    ( ! [U_1883,U_1881,U_1879] :
        ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1881),U_1883)),U_1879) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1881),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1883),U_1879))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1881),U_1879)) )
    & ! [U_1882,U_1880,U_1878] :
        ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1880),U_1882)),U_1878) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1882),U_1878)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1880),U_1878)) ) ),
    inference(miniscope,[status(thm)],[f_685_2]) ).

fof(f_685_4,plain,
    ( ! [U_1879,U_1881,U_1883] :
        ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1881),U_1883)),U_1879) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1881),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1883),U_1879))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1881),U_1879)) )
    & ! [U_1882,U_1880,U_1878] :
        ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1880),U_1882)),U_1878) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1882),U_1878)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1880),U_1878)) ) ),
    inference(definitional_conversion,[status(esa)],[f_685_3]) ).

cnf(f_685_5,plain,
    ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1880),U_1882)),U_1878) = hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1882),U_1878)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1880),U_1878)) ),
    inference(clausify,[status(thm)],[f_685_4]) ).

cnf(f_685_6,plain,
    ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1881),U_1883)),U_1879) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1881),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1883),U_1879))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1881),U_1879)) ),
    inference(clausify,[status(thm)],[f_685_4]) ).

fof(f_686_1,plain,
    ! [A,X_1,B] :
      ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) )
      & ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)),B) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_579_insert__Diff__if]) ).

fof(f_686_2,plain,
    ! [U_1886,U_1885,U_1884] :
      ( ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1885),U_1886)),U_1884) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1885),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1886),U_1884))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1885),U_1884)) )
      & ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1885),U_1886)),U_1884) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1886),U_1884)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1885),U_1884)) ) ),
    inference(variable_rename,[status(thm)],[f_686_1]) ).

fof(f_686_3,plain,
    ( ! [U_1892,U_1890,U_1888] :
        ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1890),U_1892)),U_1888) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1890),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1892),U_1888))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1890),U_1888)) )
    & ! [U_1891,U_1889,U_1887] :
        ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1889),U_1891)),U_1887) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1891),U_1887)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1889),U_1887)) ) ),
    inference(miniscope,[status(thm)],[f_686_2]) ).

fof(f_686_4,plain,
    ( ! [U_1888,U_1890,U_1892] :
        ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1890),U_1892)),U_1888) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1890),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1892),U_1888))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1890),U_1888)) )
    & ! [U_1889,U_1887,U_1891] :
        ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1889),U_1891)),U_1887) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1891),U_1887)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1889),U_1887)) ) ),
    inference(definitional_conversion,[status(esa)],[f_686_3]) ).

cnf(f_686_5,plain,
    ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1889),U_1891)),U_1887) = hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1891),U_1887)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1889),U_1887)) ),
    inference(clausify,[status(thm)],[f_686_4]) ).

cnf(f_686_6,plain,
    ( hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1890),U_1892)),U_1888) = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1890),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_1892),U_1888))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1890),U_1888)) ),
    inference(clausify,[status(thm)],[f_686_4]) ).

fof(f_687_1,plain,
    ! [C_11,A,B] :
      ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,B),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,C_11),A)) = A
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),C_11))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_580_double__diff]) ).

fof(f_687_2,plain,
    ! [U_1895,U_1894,U_1893] :
      ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1893),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1895),U_1894)) = U_1894
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1893),U_1895))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1894),U_1893)) ),
    inference(variable_rename,[status(thm)],[f_687_1]) ).

fof(f_687_3,plain,
    ! [U_1893,U_1894,U_1895] :
      ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1893),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1895),U_1894)) = U_1894
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1893),U_1895))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1894),U_1893)) ),
    inference(definitional_conversion,[status(esa)],[f_687_2]) ).

cnf(f_687_4,plain,
    ( hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1893),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1895),U_1894)) = U_1894
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1893),U_1895))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1894),U_1893)) ),
    inference(clausify,[status(thm)],[f_687_3]) ).

fof(f_688_1,plain,
    ! [C_11,A,B] :
      ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,B),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,C_11),A)) = A
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),C_11))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ),
    inference(fof_nnf,[status(thm)],[fact_581_double__diff]) ).

fof(f_688_2,plain,
    ! [U_1898,U_1897,U_1896] :
      ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1896),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1898),U_1897)) = U_1897
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1896),U_1898))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1897),U_1896)) ),
    inference(variable_rename,[status(thm)],[f_688_1]) ).

fof(f_688_3,plain,
    ! [U_1897,U_1898,U_1896] :
      ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1896),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1898),U_1897)) = U_1897
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1896),U_1898))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1897),U_1896)) ),
    inference(definitional_conversion,[status(esa)],[f_688_2]) ).

cnf(f_688_4,plain,
    ( hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1896),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1898),U_1897)) = U_1897
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1896),U_1898))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1897),U_1896)) ),
    inference(clausify,[status(thm)],[f_688_3]) ).

fof(f_689_1,plain,
    ! [C_11,A,B] :
      ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,B),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,C_11),A)) = A
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),C_11))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
      | ~ is_fun_a_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_582_double__diff]) ).

fof(f_689_2,plain,
    ! [U_1901,U_1900,U_1899] :
      ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1899),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1901),U_1900)) = U_1900
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1899),U_1901))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1900),U_1899))
      | ~ is_fun_a_bool(U_1900) ),
    inference(variable_rename,[status(thm)],[f_689_1]) ).

fof(f_689_3,plain,
    ! [U_1901,U_1900] :
      ( ! [U_1899] :
          ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1899),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1901),U_1900)) = U_1900
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1899),U_1901))
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1900),U_1899)) )
      | ~ is_fun_a_bool(U_1900) ),
    inference(miniscope,[status(thm)],[f_689_2]) ).

fof(f_689_4,plain,
    ! [U_1899,U_1900,U_1901] :
      ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1899),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1901),U_1900)) = U_1900
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1899),U_1901))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1900),U_1899))
      | ~ is_fun_a_bool(U_1900) ),
    inference(definitional_conversion,[status(esa)],[f_689_3]) ).

cnf(f_689_5,plain,
    ( hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1899),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1901),U_1900)) = U_1900
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1899),U_1901))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1900),U_1899))
    | ~ is_fun_a_bool(U_1900) ),
    inference(clausify,[status(thm)],[f_689_4]) ).

fof(f_690_1,plain,
    ! [D_4,B,A,C_11] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,C_11),D_4)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,D_4),B))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),C_11)) ),
    inference(fof_nnf,[status(thm)],[fact_583_Diff__mono]) ).

fof(f_690_2,plain,
    ! [U_1905,U_1904,U_1903,U_1902] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1903),U_1904)),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1902),U_1905)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1905),U_1904))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1903),U_1902)) ),
    inference(variable_rename,[status(thm)],[f_690_1]) ).

fof(f_690_3,plain,
    ! [U_1902,U_1903,U_1904,U_1905] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1903),U_1904)),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1902),U_1905)))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1905),U_1904))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1903),U_1902)) ),
    inference(definitional_conversion,[status(esa)],[f_690_2]) ).

cnf(f_690_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1903),U_1904)),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1902),U_1905)))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1905),U_1904))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1903),U_1902)) ),
    inference(clausify,[status(thm)],[f_690_3]) ).

fof(f_691_1,plain,
    ! [D_4,B,A,C_11] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,C_11),D_4)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,D_4),B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),C_11)) ),
    inference(fof_nnf,[status(thm)],[fact_584_Diff__mono]) ).

fof(f_691_2,plain,
    ! [U_1909,U_1908,U_1907,U_1906] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1907),U_1908)),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1906),U_1909)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1909),U_1908))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1907),U_1906)) ),
    inference(variable_rename,[status(thm)],[f_691_1]) ).

fof(f_691_3,plain,
    ! [U_1906,U_1907,U_1908,U_1909] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1907),U_1908)),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1906),U_1909)))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1909),U_1908))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1907),U_1906)) ),
    inference(definitional_conversion,[status(esa)],[f_691_2]) ).

cnf(f_691_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1907),U_1908)),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1906),U_1909)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1909),U_1908))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1907),U_1906)) ),
    inference(clausify,[status(thm)],[f_691_3]) ).

fof(f_692_1,plain,
    ! [D_4,B,A,C_11] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,C_11),D_4)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,D_4),B))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),C_11)) ),
    inference(fof_nnf,[status(thm)],[fact_585_Diff__mono]) ).

fof(f_692_2,plain,
    ! [U_1913,U_1912,U_1911,U_1910] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1911),U_1912)),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1910),U_1913)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1913),U_1912))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1911),U_1910)) ),
    inference(variable_rename,[status(thm)],[f_692_1]) ).

fof(f_692_3,plain,
    ! [U_1910,U_1912,U_1913,U_1911] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1911),U_1912)),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1910),U_1913)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1913),U_1912))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1911),U_1910)) ),
    inference(definitional_conversion,[status(esa)],[f_692_2]) ).

cnf(f_692_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1911),U_1912)),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1910),U_1913)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1913),U_1912))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1911),U_1910)) ),
    inference(clausify,[status(thm)],[f_692_3]) ).

fof(f_693_1,plain,
    ! [A,B] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)),A)),
    inference(fof_nnf,[status(thm)],[fact_586_Diff__subset]) ).

fof(f_693_2,plain,
    ! [U_1915,U_1914] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1915),U_1914)),U_1915)),
    inference(variable_rename,[status(thm)],[f_693_1]) ).

fof(f_693_3,plain,
    ! [U_1915,U_1914] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1915),U_1914)),U_1915)),
    inference(definitional_conversion,[status(esa)],[f_693_2]) ).

cnf(f_693_4,plain,
    hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_1915),U_1914)),U_1915)),
    inference(clausify,[status(thm)],[f_693_3]) ).

fof(f_694_1,plain,
    ! [A,B] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)),A)),
    inference(fof_nnf,[status(thm)],[fact_587_Diff__subset]) ).

fof(f_694_2,plain,
    ! [U_1917,U_1916] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1917),U_1916)),U_1917)),
    inference(variable_rename,[status(thm)],[f_694_1]) ).

fof(f_694_3,plain,
    ! [U_1916,U_1917] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1917),U_1916)),U_1917)),
    inference(definitional_conversion,[status(esa)],[f_694_2]) ).

cnf(f_694_4,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_1917),U_1916)),U_1917)),
    inference(clausify,[status(thm)],[f_694_3]) ).

fof(f_695_1,plain,
    ! [A,B] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)),A)),
    inference(fof_nnf,[status(thm)],[fact_588_Diff__subset]) ).

fof(f_695_2,plain,
    ! [U_1919,U_1918] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1919),U_1918)),U_1919)),
    inference(variable_rename,[status(thm)],[f_695_1]) ).

fof(f_695_3,plain,
    ! [U_1918,U_1919] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1919),U_1918)),U_1919)),
    inference(definitional_conversion,[status(esa)],[f_695_2]) ).

cnf(f_695_4,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_1919),U_1918)),U_1919)),
    inference(clausify,[status(thm)],[f_695_3]) ).

fof(f_696_1,plain,
    ! [A_2,B_3] :
      ( A_2 = B_3
      | hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),bot_bot_fun_a_bool)
      | ~ is_a(B_3)
      | ~ is_a(A_2) ),
    inference(fof_nnf,[status(thm)],[fact_589_singleton__inject]) ).

fof(f_696_2,plain,
    ! [U_1921,U_1920] :
      ( U_1921 = U_1920
      | hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1921),bot_bot_fun_a_bool) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1920),bot_bot_fun_a_bool)
      | ~ is_a(U_1920)
      | ~ is_a(U_1921) ),
    inference(variable_rename,[status(thm)],[f_696_1]) ).

fof(f_696_3,plain,
    ! [U_1920,U_1921] :
      ( U_1921 = U_1920
      | hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1921),bot_bot_fun_a_bool) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1920),bot_bot_fun_a_bool)
      | ~ is_a(U_1920)
      | ~ is_a(U_1921) ),
    inference(definitional_conversion,[status(esa)],[f_696_2]) ).

cnf(f_696_4,plain,
    ( U_1921 = U_1920
    | hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1921),bot_bot_fun_a_bool) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1920),bot_bot_fun_a_bool)
    | ~ is_a(U_1920)
    | ~ is_a(U_1921) ),
    inference(clausify,[status(thm)],[f_696_3]) ).

fof(f_697_1,plain,
    ! [A_2,B_3] :
      ( A_2 = B_3
      | hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_3),bot_bot_fun_nat_bool) ),
    inference(fof_nnf,[status(thm)],[fact_590_singleton__inject]) ).

fof(f_697_2,plain,
    ! [U_1923,U_1922] :
      ( U_1923 = U_1922
      | hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1923),bot_bot_fun_nat_bool) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1922),bot_bot_fun_nat_bool) ),
    inference(variable_rename,[status(thm)],[f_697_1]) ).

fof(f_697_3,plain,
    ! [U_1922,U_1923] :
      ( U_1923 = U_1922
      | hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1923),bot_bot_fun_nat_bool) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1922),bot_bot_fun_nat_bool) ),
    inference(definitional_conversion,[status(esa)],[f_697_2]) ).

cnf(f_697_4,plain,
    ( U_1923 = U_1922
    | hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1923),bot_bot_fun_nat_bool) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1922),bot_bot_fun_nat_bool) ),
    inference(clausify,[status(thm)],[f_697_3]) ).

fof(f_698_1,plain,
    ! [A_2,B_3] :
      ( A_2 = B_3
      | hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_3),bot_bot_fun_int_bool) ),
    inference(fof_nnf,[status(thm)],[fact_591_singleton__inject]) ).

fof(f_698_2,plain,
    ! [U_1925,U_1924] :
      ( U_1925 = U_1924
      | hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1925),bot_bot_fun_int_bool) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1924),bot_bot_fun_int_bool) ),
    inference(variable_rename,[status(thm)],[f_698_1]) ).

fof(f_698_3,plain,
    ! [U_1924,U_1925] :
      ( U_1925 = U_1924
      | hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1925),bot_bot_fun_int_bool) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1924),bot_bot_fun_int_bool) ),
    inference(definitional_conversion,[status(esa)],[f_698_2]) ).

cnf(f_698_4,plain,
    ( U_1925 = U_1924
    | hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1925),bot_bot_fun_int_bool) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1924),bot_bot_fun_int_bool) ),
    inference(clausify,[status(thm)],[f_698_3]) ).

fof(f_699_1,plain,
    ! [B_3,A_2] :
      ( B_3 = A_2
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool)))
      | ~ is_a(A_2)
      | ~ is_a(B_3) ),
    inference(fof_nnf,[status(thm)],[fact_592_singletonE]) ).

fof(f_699_2,plain,
    ! [U_1927,U_1926] :
      ( U_1927 = U_1926
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1927),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1926),bot_bot_fun_a_bool)))
      | ~ is_a(U_1926)
      | ~ is_a(U_1927) ),
    inference(variable_rename,[status(thm)],[f_699_1]) ).

fof(f_699_3,plain,
    ! [U_1926,U_1927] :
      ( U_1927 = U_1926
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1927),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1926),bot_bot_fun_a_bool)))
      | ~ is_a(U_1926)
      | ~ is_a(U_1927) ),
    inference(definitional_conversion,[status(esa)],[f_699_2]) ).

cnf(f_699_4,plain,
    ( U_1927 = U_1926
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1927),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1926),bot_bot_fun_a_bool)))
    | ~ is_a(U_1926)
    | ~ is_a(U_1927) ),
    inference(clausify,[status(thm)],[f_699_3]) ).

fof(f_700_1,plain,
    ! [B_3,A_2] :
      ( B_3 = A_2
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_3),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool))) ),
    inference(fof_nnf,[status(thm)],[fact_593_singletonE]) ).

fof(f_700_2,plain,
    ! [U_1929,U_1928] :
      ( U_1929 = U_1928
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1929),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1928),bot_bot_fun_int_bool))) ),
    inference(variable_rename,[status(thm)],[f_700_1]) ).

fof(f_700_3,plain,
    ! [U_1929,U_1928] :
      ( U_1929 = U_1928
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1929),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1928),bot_bot_fun_int_bool))) ),
    inference(definitional_conversion,[status(esa)],[f_700_2]) ).

cnf(f_700_4,plain,
    ( U_1929 = U_1928
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1929),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1928),bot_bot_fun_int_bool))) ),
    inference(clausify,[status(thm)],[f_700_3]) ).

fof(f_701_1,plain,
    ! [B_3,A_2] :
      ( B_3 = A_2
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_3),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool))) ),
    inference(fof_nnf,[status(thm)],[fact_594_singletonE]) ).

fof(f_701_2,plain,
    ! [U_1931,U_1930] :
      ( U_1931 = U_1930
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1931),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1930),bot_bot_fun_nat_bool))) ),
    inference(variable_rename,[status(thm)],[f_701_1]) ).

fof(f_701_3,plain,
    ! [U_1930,U_1931] :
      ( U_1931 = U_1930
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1931),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1930),bot_bot_fun_nat_bool))) ),
    inference(definitional_conversion,[status(esa)],[f_701_2]) ).

cnf(f_701_4,plain,
    ( U_1931 = U_1930
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1931),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1930),bot_bot_fun_nat_bool))) ),
    inference(clausify,[status(thm)],[f_701_3]) ).

fof(f_702_1,plain,
    ! [B_3,A_2] :
      ( B_3 = A_2
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_3),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool)))
      | ~ is_pname(A_2)
      | ~ is_pname(B_3) ),
    inference(fof_nnf,[status(thm)],[fact_595_singletonE]) ).

fof(f_702_2,plain,
    ! [U_1933,U_1932] :
      ( U_1933 = U_1932
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1933),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1932),bot_bo844097828e_bool)))
      | ~ is_pname(U_1932)
      | ~ is_pname(U_1933) ),
    inference(variable_rename,[status(thm)],[f_702_1]) ).

fof(f_702_3,plain,
    ! [U_1932,U_1933] :
      ( U_1933 = U_1932
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1933),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1932),bot_bo844097828e_bool)))
      | ~ is_pname(U_1932)
      | ~ is_pname(U_1933) ),
    inference(definitional_conversion,[status(esa)],[f_702_2]) ).

cnf(f_702_4,plain,
    ( U_1933 = U_1932
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1933),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1932),bot_bo844097828e_bool)))
    | ~ is_pname(U_1932)
    | ~ is_pname(U_1933) ),
    inference(clausify,[status(thm)],[f_702_3]) ).

fof(f_703_1,plain,
    ! [A_2,B_3,C_6,D_1] :
      ( ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),bot_bot_fun_a_bool)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,C_6),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,D_1),bot_bot_fun_a_bool))
          | ( ( B_3 != C_6
              | A_2 != D_1 )
            & ( B_3 != D_1
              | A_2 != C_6 ) ) )
        & ( ( B_3 = C_6
            & A_2 = D_1 )
          | ( B_3 = D_1
            & A_2 = C_6 )
          | hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,B_3),bot_bot_fun_a_bool)) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,C_6),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,D_1),bot_bot_fun_a_bool)) ) )
      | ~ is_a(D_1)
      | ~ is_a(C_6)
      | ~ is_a(B_3)
      | ~ is_a(A_2) ),
    inference(fof_nnf,[status(thm)],[fact_596_doubleton__eq__iff]) ).

fof(f_703_2,plain,
    ! [U_1937,U_1936,U_1935,U_1934] :
      ( ( ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1937),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1936),bot_bot_fun_a_bool)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1935),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1934),bot_bot_fun_a_bool))
          | ( ( U_1936 != U_1935
              | U_1937 != U_1934 )
            & ( U_1936 != U_1934
              | U_1937 != U_1935 ) ) )
        & ( ( U_1936 = U_1935
            & U_1937 = U_1934 )
          | ( U_1936 = U_1934
            & U_1937 = U_1935 )
          | hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1937),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1936),bot_bot_fun_a_bool)) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1935),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1934),bot_bot_fun_a_bool)) ) )
      | ~ is_a(U_1934)
      | ~ is_a(U_1935)
      | ~ is_a(U_1936)
      | ~ is_a(U_1937) ),
    inference(variable_rename,[status(thm)],[f_703_1]) ).

fof(f_703_3,plain,
    ( ! [U_1934,U_1935,U_1936,U_1937] :
        ( U_1936 != U_1935
        | U_1937 != U_1934
        | ~ sP172(U_1934,U_1935,U_1936,U_1937) )
    & ! [U_1934,U_1935,U_1936,U_1937] :
        ( U_1936 != U_1934
        | U_1937 != U_1935
        | ~ sP172(U_1934,U_1935,U_1936,U_1937) )
    & ! [U_1934,U_1935,U_1936,U_1937] :
        ( U_1936 = U_1935
        | ~ sP171(U_1934,U_1935,U_1936,U_1937) )
    & ! [U_1934,U_1935,U_1936,U_1937] :
        ( U_1937 = U_1934
        | ~ sP171(U_1934,U_1935,U_1936,U_1937) )
    & ! [U_1934,U_1935,U_1936,U_1937] :
        ( U_1936 = U_1934
        | ~ sP170(U_1934,U_1935,U_1936,U_1937) )
    & ! [U_1934,U_1935,U_1936,U_1937] :
        ( U_1937 = U_1935
        | ~ sP170(U_1934,U_1935,U_1936,U_1937) )
    & ! [U_1934,U_1935,U_1936,U_1937] :
        ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1937),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1936),bot_bot_fun_a_bool)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1935),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1934),bot_bot_fun_a_bool))
        | sP172(U_1934,U_1935,U_1936,U_1937)
        | ~ sP173(U_1934,U_1935,U_1936,U_1937) )
    & ! [U_1934,U_1935,U_1936,U_1937] :
        ( sP171(U_1934,U_1935,U_1936,U_1937)
        | sP170(U_1934,U_1935,U_1936,U_1937)
        | hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1937),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1936),bot_bot_fun_a_bool)) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1935),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1934),bot_bot_fun_a_bool))
        | ~ sP173(U_1934,U_1935,U_1936,U_1937) )
    & ! [U_1934,U_1935,U_1936,U_1937] :
        ( sP173(U_1934,U_1935,U_1936,U_1937)
        | ~ is_a(U_1934)
        | ~ is_a(U_1935)
        | ~ is_a(U_1936)
        | ~ is_a(U_1937) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP170,sP171,sP172,sP173])],[f_703_2]) ).

cnf(f_703_4,plain,
    ( sP173(U_1934,U_1935,U_1936,U_1937)
    | ~ is_a(U_1934)
    | ~ is_a(U_1935)
    | ~ is_a(U_1936)
    | ~ is_a(U_1937) ),
    inference(clausify,[status(thm)],[f_703_3]) ).

cnf(f_703_5,plain,
    ( sP171(U_1934,U_1935,U_1936,U_1937)
    | sP170(U_1934,U_1935,U_1936,U_1937)
    | hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1937),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1936),bot_bot_fun_a_bool)) != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1935),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1934),bot_bot_fun_a_bool))
    | ~ sP173(U_1934,U_1935,U_1936,U_1937) ),
    inference(clausify,[status(thm)],[f_703_3]) ).

cnf(f_703_6,plain,
    ( hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1937),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1936),bot_bot_fun_a_bool)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1935),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1934),bot_bot_fun_a_bool))
    | sP172(U_1934,U_1935,U_1936,U_1937)
    | ~ sP173(U_1934,U_1935,U_1936,U_1937) ),
    inference(clausify,[status(thm)],[f_703_3]) ).

cnf(f_703_7,plain,
    ( U_1937 = U_1935
    | ~ sP170(U_1934,U_1935,U_1936,U_1937) ),
    inference(clausify,[status(thm)],[f_703_3]) ).

cnf(f_703_8,plain,
    ( U_1936 = U_1934
    | ~ sP170(U_1934,U_1935,U_1936,U_1937) ),
    inference(clausify,[status(thm)],[f_703_3]) ).

cnf(f_703_9,plain,
    ( U_1937 = U_1934
    | ~ sP171(U_1934,U_1935,U_1936,U_1937) ),
    inference(clausify,[status(thm)],[f_703_3]) ).

cnf(f_703_10,plain,
    ( U_1936 = U_1935
    | ~ sP171(U_1934,U_1935,U_1936,U_1937) ),
    inference(clausify,[status(thm)],[f_703_3]) ).

cnf(f_703_11,plain,
    ( U_1936 != U_1934
    | U_1937 != U_1935
    | ~ sP172(U_1934,U_1935,U_1936,U_1937) ),
    inference(clausify,[status(thm)],[f_703_3]) ).

cnf(f_703_12,plain,
    ( U_1936 != U_1935
    | U_1937 != U_1934
    | ~ sP172(U_1934,U_1935,U_1936,U_1937) ),
    inference(clausify,[status(thm)],[f_703_3]) ).

fof(f_704_1,plain,
    ! [A_2,B_3,C_6,D_1] :
      ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_3),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,C_6),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,D_1),bot_bot_fun_nat_bool))
        | ( ( B_3 != C_6
            | A_2 != D_1 )
          & ( B_3 != D_1
            | A_2 != C_6 ) ) )
      & ( ( B_3 = C_6
          & A_2 = D_1 )
        | ( B_3 = D_1
          & A_2 = C_6 )
        | hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,B_3),bot_bot_fun_nat_bool)) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,C_6),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,D_1),bot_bot_fun_nat_bool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_597_doubleton__eq__iff]) ).

fof(f_704_2,plain,
    ! [U_1941,U_1940,U_1939,U_1938] :
      ( ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1941),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1940),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1939),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1938),bot_bot_fun_nat_bool))
        | ( ( U_1940 != U_1939
            | U_1941 != U_1938 )
          & ( U_1940 != U_1938
            | U_1941 != U_1939 ) ) )
      & ( ( U_1940 = U_1939
          & U_1941 = U_1938 )
        | ( U_1940 = U_1938
          & U_1941 = U_1939 )
        | hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1941),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1940),bot_bot_fun_nat_bool)) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1939),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1938),bot_bot_fun_nat_bool)) ) ),
    inference(variable_rename,[status(thm)],[f_704_1]) ).

fof(f_704_3,plain,
    ( ! [U_1949,U_1947,U_1945,U_1943] :
        ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1949),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1947),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1945),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1943),bot_bot_fun_nat_bool))
        | ( ( U_1947 != U_1945
            | U_1949 != U_1943 )
          & ( U_1947 != U_1943
            | U_1949 != U_1945 ) ) )
    & ! [U_1948,U_1946,U_1944,U_1942] :
        ( ( U_1946 = U_1944
          & U_1948 = U_1942 )
        | ( U_1946 = U_1942
          & U_1948 = U_1944 )
        | hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1948),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1946),bot_bot_fun_nat_bool)) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1944),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1942),bot_bot_fun_nat_bool)) ) ),
    inference(miniscope,[status(thm)],[f_704_2]) ).

fof(f_704_4,plain,
    ( ! [U_1949,U_1947,U_1943,U_1945] :
        ( U_1947 != U_1945
        | U_1949 != U_1943
        | ~ sP176(U_1949,U_1947,U_1943,U_1945) )
    & ! [U_1949,U_1947,U_1943,U_1945] :
        ( U_1947 != U_1943
        | U_1949 != U_1945
        | ~ sP176(U_1949,U_1947,U_1943,U_1945) )
    & ! [U_1942,U_1948,U_1946,U_1944] :
        ( U_1946 = U_1944
        | ~ sP175(U_1942,U_1948,U_1946,U_1944) )
    & ! [U_1942,U_1948,U_1946,U_1944] :
        ( U_1948 = U_1942
        | ~ sP175(U_1942,U_1948,U_1946,U_1944) )
    & ! [U_1942,U_1948,U_1946,U_1944] :
        ( U_1946 = U_1942
        | ~ sP174(U_1942,U_1948,U_1946,U_1944) )
    & ! [U_1942,U_1948,U_1946,U_1944] :
        ( U_1948 = U_1944
        | ~ sP174(U_1942,U_1948,U_1946,U_1944) )
    & ! [U_1949,U_1947,U_1943,U_1945] :
        ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1949),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1947),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1945),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1943),bot_bot_fun_nat_bool))
        | sP176(U_1949,U_1947,U_1943,U_1945) )
    & ! [U_1942,U_1948,U_1946,U_1944] :
        ( sP175(U_1942,U_1948,U_1946,U_1944)
        | sP174(U_1942,U_1948,U_1946,U_1944)
        | hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1948),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1946),bot_bot_fun_nat_bool)) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1944),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1942),bot_bot_fun_nat_bool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP174,sP175,sP176])],[f_704_3]) ).

cnf(f_704_5,plain,
    ( sP175(U_1942,U_1948,U_1946,U_1944)
    | sP174(U_1942,U_1948,U_1946,U_1944)
    | hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1948),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1946),bot_bot_fun_nat_bool)) != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1944),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1942),bot_bot_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_704_4]) ).

cnf(f_704_6,plain,
    ( hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1949),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1947),bot_bot_fun_nat_bool)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1945),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1943),bot_bot_fun_nat_bool))
    | sP176(U_1949,U_1947,U_1943,U_1945) ),
    inference(clausify,[status(thm)],[f_704_4]) ).

cnf(f_704_7,plain,
    ( U_1948 = U_1944
    | ~ sP174(U_1942,U_1948,U_1946,U_1944) ),
    inference(clausify,[status(thm)],[f_704_4]) ).

cnf(f_704_8,plain,
    ( U_1946 = U_1942
    | ~ sP174(U_1942,U_1948,U_1946,U_1944) ),
    inference(clausify,[status(thm)],[f_704_4]) ).

cnf(f_704_9,plain,
    ( U_1948 = U_1942
    | ~ sP175(U_1942,U_1948,U_1946,U_1944) ),
    inference(clausify,[status(thm)],[f_704_4]) ).

cnf(f_704_10,plain,
    ( U_1946 = U_1944
    | ~ sP175(U_1942,U_1948,U_1946,U_1944) ),
    inference(clausify,[status(thm)],[f_704_4]) ).

cnf(f_704_11,plain,
    ( U_1947 != U_1943
    | U_1949 != U_1945
    | ~ sP176(U_1949,U_1947,U_1943,U_1945) ),
    inference(clausify,[status(thm)],[f_704_4]) ).

cnf(f_704_12,plain,
    ( U_1947 != U_1945
    | U_1949 != U_1943
    | ~ sP176(U_1949,U_1947,U_1943,U_1945) ),
    inference(clausify,[status(thm)],[f_704_4]) ).

fof(f_705_1,plain,
    ! [A_2,B_3,C_6,D_1] :
      ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_3),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,C_6),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,D_1),bot_bot_fun_int_bool))
        | ( ( B_3 != C_6
            | A_2 != D_1 )
          & ( B_3 != D_1
            | A_2 != C_6 ) ) )
      & ( ( B_3 = C_6
          & A_2 = D_1 )
        | ( B_3 = D_1
          & A_2 = C_6 )
        | hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,B_3),bot_bot_fun_int_bool)) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,C_6),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,D_1),bot_bot_fun_int_bool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_598_doubleton__eq__iff]) ).

fof(f_705_2,plain,
    ! [U_1953,U_1952,U_1951,U_1950] :
      ( ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1953),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1952),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1951),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1950),bot_bot_fun_int_bool))
        | ( ( U_1952 != U_1951
            | U_1953 != U_1950 )
          & ( U_1952 != U_1950
            | U_1953 != U_1951 ) ) )
      & ( ( U_1952 = U_1951
          & U_1953 = U_1950 )
        | ( U_1952 = U_1950
          & U_1953 = U_1951 )
        | hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1953),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1952),bot_bot_fun_int_bool)) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1951),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1950),bot_bot_fun_int_bool)) ) ),
    inference(variable_rename,[status(thm)],[f_705_1]) ).

fof(f_705_3,plain,
    ( ! [U_1961,U_1959,U_1957,U_1955] :
        ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1961),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1959),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1957),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1955),bot_bot_fun_int_bool))
        | ( ( U_1959 != U_1957
            | U_1961 != U_1955 )
          & ( U_1959 != U_1955
            | U_1961 != U_1957 ) ) )
    & ! [U_1960,U_1958,U_1956,U_1954] :
        ( ( U_1958 = U_1956
          & U_1960 = U_1954 )
        | ( U_1958 = U_1954
          & U_1960 = U_1956 )
        | hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1960),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1958),bot_bot_fun_int_bool)) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1956),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1954),bot_bot_fun_int_bool)) ) ),
    inference(miniscope,[status(thm)],[f_705_2]) ).

fof(f_705_4,plain,
    ( ! [U_1961,U_1959,U_1955,U_1957] :
        ( U_1959 != U_1957
        | U_1961 != U_1955
        | ~ sP179(U_1961,U_1959,U_1955,U_1957) )
    & ! [U_1961,U_1959,U_1955,U_1957] :
        ( U_1959 != U_1955
        | U_1961 != U_1957
        | ~ sP179(U_1961,U_1959,U_1955,U_1957) )
    & ! [U_1958,U_1956,U_1960,U_1954] :
        ( U_1958 = U_1956
        | ~ sP178(U_1958,U_1956,U_1960,U_1954) )
    & ! [U_1958,U_1956,U_1960,U_1954] :
        ( U_1960 = U_1954
        | ~ sP178(U_1958,U_1956,U_1960,U_1954) )
    & ! [U_1958,U_1956,U_1960,U_1954] :
        ( U_1958 = U_1954
        | ~ sP177(U_1958,U_1956,U_1960,U_1954) )
    & ! [U_1958,U_1956,U_1960,U_1954] :
        ( U_1960 = U_1956
        | ~ sP177(U_1958,U_1956,U_1960,U_1954) )
    & ! [U_1961,U_1959,U_1955,U_1957] :
        ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1961),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1959),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1957),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1955),bot_bot_fun_int_bool))
        | sP179(U_1961,U_1959,U_1955,U_1957) )
    & ! [U_1958,U_1956,U_1960,U_1954] :
        ( sP178(U_1958,U_1956,U_1960,U_1954)
        | sP177(U_1958,U_1956,U_1960,U_1954)
        | hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1960),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1958),bot_bot_fun_int_bool)) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1956),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1954),bot_bot_fun_int_bool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP177,sP178,sP179])],[f_705_3]) ).

cnf(f_705_5,plain,
    ( sP178(U_1958,U_1956,U_1960,U_1954)
    | sP177(U_1958,U_1956,U_1960,U_1954)
    | hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1960),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1958),bot_bot_fun_int_bool)) != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1956),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1954),bot_bot_fun_int_bool)) ),
    inference(clausify,[status(thm)],[f_705_4]) ).

cnf(f_705_6,plain,
    ( hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1961),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1959),bot_bot_fun_int_bool)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1957),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1955),bot_bot_fun_int_bool))
    | sP179(U_1961,U_1959,U_1955,U_1957) ),
    inference(clausify,[status(thm)],[f_705_4]) ).

cnf(f_705_7,plain,
    ( U_1960 = U_1956
    | ~ sP177(U_1958,U_1956,U_1960,U_1954) ),
    inference(clausify,[status(thm)],[f_705_4]) ).

cnf(f_705_8,plain,
    ( U_1958 = U_1954
    | ~ sP177(U_1958,U_1956,U_1960,U_1954) ),
    inference(clausify,[status(thm)],[f_705_4]) ).

cnf(f_705_9,plain,
    ( U_1960 = U_1954
    | ~ sP178(U_1958,U_1956,U_1960,U_1954) ),
    inference(clausify,[status(thm)],[f_705_4]) ).

cnf(f_705_10,plain,
    ( U_1958 = U_1956
    | ~ sP178(U_1958,U_1956,U_1960,U_1954) ),
    inference(clausify,[status(thm)],[f_705_4]) ).

cnf(f_705_11,plain,
    ( U_1959 != U_1955
    | U_1961 != U_1957
    | ~ sP179(U_1961,U_1959,U_1955,U_1957) ),
    inference(clausify,[status(thm)],[f_705_4]) ).

cnf(f_705_12,plain,
    ( U_1959 != U_1957
    | U_1961 != U_1955
    | ~ sP179(U_1961,U_1959,U_1955,U_1957) ),
    inference(clausify,[status(thm)],[f_705_4]) ).

fof(f_706_1,plain,
    ! [B_3,A_2] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool)))
          | B_3 != A_2 )
        & ( B_3 = A_2
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_3),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool))) ) )
      | ~ is_a(A_2)
      | ~ is_a(B_3) ),
    inference(fof_nnf,[status(thm)],[fact_599_singleton__iff]) ).

fof(f_706_2,plain,
    ! [U_1963,U_1962] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1963),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1962),bot_bot_fun_a_bool)))
          | U_1963 != U_1962 )
        & ( U_1963 = U_1962
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1963),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1962),bot_bot_fun_a_bool))) ) )
      | ~ is_a(U_1962)
      | ~ is_a(U_1963) ),
    inference(variable_rename,[status(thm)],[f_706_1]) ).

fof(f_706_3,plain,
    ( ! [U_1963,U_1962] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1963),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1962),bot_bot_fun_a_bool)))
        | U_1963 != U_1962
        | ~ sP180(U_1963,U_1962) )
    & ! [U_1963,U_1962] :
        ( U_1963 = U_1962
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1963),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1962),bot_bot_fun_a_bool)))
        | ~ sP180(U_1963,U_1962) )
    & ! [U_1963,U_1962] :
        ( sP180(U_1963,U_1962)
        | ~ is_a(U_1962)
        | ~ is_a(U_1963) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP180])],[f_706_2]) ).

cnf(f_706_4,plain,
    ( sP180(U_1963,U_1962)
    | ~ is_a(U_1962)
    | ~ is_a(U_1963) ),
    inference(clausify,[status(thm)],[f_706_3]) ).

cnf(f_706_5,plain,
    ( U_1963 = U_1962
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1963),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1962),bot_bot_fun_a_bool)))
    | ~ sP180(U_1963,U_1962) ),
    inference(clausify,[status(thm)],[f_706_3]) ).

cnf(f_706_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_1963),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1962),bot_bot_fun_a_bool)))
    | U_1963 != U_1962
    | ~ sP180(U_1963,U_1962) ),
    inference(clausify,[status(thm)],[f_706_3]) ).

fof(f_707_1,plain,
    ! [B_3,A_2] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_3),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool)))
        | B_3 != A_2 )
      & ( B_3 = A_2
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,B_3),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool))) ) ),
    inference(fof_nnf,[status(thm)],[fact_600_singleton__iff]) ).

fof(f_707_2,plain,
    ! [U_1965,U_1964] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1965),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1964),bot_bot_fun_int_bool)))
        | U_1965 != U_1964 )
      & ( U_1965 = U_1964
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1965),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1964),bot_bot_fun_int_bool))) ) ),
    inference(variable_rename,[status(thm)],[f_707_1]) ).

fof(f_707_3,plain,
    ( ! [U_1969,U_1967] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1969),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1967),bot_bot_fun_int_bool)))
        | U_1969 != U_1967 )
    & ! [U_1968,U_1966] :
        ( U_1968 = U_1966
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1968),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1966),bot_bot_fun_int_bool))) ) ),
    inference(miniscope,[status(thm)],[f_707_2]) ).

fof(f_707_4,plain,
    ( ! [U_1967,U_1969] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1969),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1967),bot_bot_fun_int_bool)))
        | U_1969 != U_1967 )
    & ! [U_1966,U_1968] :
        ( U_1968 = U_1966
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1968),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1966),bot_bot_fun_int_bool))) ) ),
    inference(definitional_conversion,[status(esa)],[f_707_3]) ).

cnf(f_707_5,plain,
    ( U_1968 = U_1966
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1968),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1966),bot_bot_fun_int_bool))) ),
    inference(clausify,[status(thm)],[f_707_4]) ).

cnf(f_707_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_1969),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1967),bot_bot_fun_int_bool)))
    | U_1969 != U_1967 ),
    inference(clausify,[status(thm)],[f_707_4]) ).

fof(f_708_1,plain,
    ! [B_3,A_2] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_3),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool)))
        | B_3 != A_2 )
      & ( B_3 = A_2
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,B_3),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool))) ) ),
    inference(fof_nnf,[status(thm)],[fact_601_singleton__iff]) ).

fof(f_708_2,plain,
    ! [U_1971,U_1970] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1971),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1970),bot_bot_fun_nat_bool)))
        | U_1971 != U_1970 )
      & ( U_1971 = U_1970
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1971),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1970),bot_bot_fun_nat_bool))) ) ),
    inference(variable_rename,[status(thm)],[f_708_1]) ).

fof(f_708_3,plain,
    ( ! [U_1975,U_1973] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1975),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1973),bot_bot_fun_nat_bool)))
        | U_1975 != U_1973 )
    & ! [U_1974,U_1972] :
        ( U_1974 = U_1972
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1974),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1972),bot_bot_fun_nat_bool))) ) ),
    inference(miniscope,[status(thm)],[f_708_2]) ).

fof(f_708_4,plain,
    ( ! [U_1975,U_1973] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1975),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1973),bot_bot_fun_nat_bool)))
        | U_1975 != U_1973 )
    & ! [U_1974,U_1972] :
        ( U_1974 = U_1972
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1974),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1972),bot_bot_fun_nat_bool))) ) ),
    inference(definitional_conversion,[status(esa)],[f_708_3]) ).

cnf(f_708_5,plain,
    ( U_1974 = U_1972
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1974),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1972),bot_bot_fun_nat_bool))) ),
    inference(clausify,[status(thm)],[f_708_4]) ).

cnf(f_708_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_1975),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1973),bot_bot_fun_nat_bool)))
    | U_1975 != U_1973 ),
    inference(clausify,[status(thm)],[f_708_4]) ).

fof(f_709_1,plain,
    ! [B_3,A_2] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_3),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool)))
          | B_3 != A_2 )
        & ( B_3 = A_2
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,B_3),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),bot_bo844097828e_bool))) ) )
      | ~ is_pname(A_2)
      | ~ is_pname(B_3) ),
    inference(fof_nnf,[status(thm)],[fact_602_singleton__iff]) ).

fof(f_709_2,plain,
    ! [U_1977,U_1976] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1977),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1976),bot_bo844097828e_bool)))
          | U_1977 != U_1976 )
        & ( U_1977 = U_1976
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1977),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1976),bot_bo844097828e_bool))) ) )
      | ~ is_pname(U_1976)
      | ~ is_pname(U_1977) ),
    inference(variable_rename,[status(thm)],[f_709_1]) ).

fof(f_709_3,plain,
    ( ! [U_1976,U_1977] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1977),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1976),bot_bo844097828e_bool)))
        | U_1977 != U_1976
        | ~ sP181(U_1976,U_1977) )
    & ! [U_1976,U_1977] :
        ( U_1977 = U_1976
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1977),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1976),bot_bo844097828e_bool)))
        | ~ sP181(U_1976,U_1977) )
    & ! [U_1976,U_1977] :
        ( sP181(U_1976,U_1977)
        | ~ is_pname(U_1976)
        | ~ is_pname(U_1977) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP181])],[f_709_2]) ).

cnf(f_709_4,plain,
    ( sP181(U_1976,U_1977)
    | ~ is_pname(U_1976)
    | ~ is_pname(U_1977) ),
    inference(clausify,[status(thm)],[f_709_3]) ).

cnf(f_709_5,plain,
    ( U_1977 = U_1976
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1977),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1976),bot_bo844097828e_bool)))
    | ~ sP181(U_1976,U_1977) ),
    inference(clausify,[status(thm)],[f_709_3]) ).

cnf(f_709_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_1977),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_1976),bot_bo844097828e_bool)))
    | U_1977 != U_1976
    | ~ sP181(U_1976,U_1977) ),
    inference(clausify,[status(thm)],[f_709_3]) ).

fof(f_710_1,plain,
    ! [A_2,A] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),A) != bot_bot_fun_a_bool,
    inference(fof_nnf,[status(thm)],[fact_603_insert__not__empty]) ).

fof(f_710_2,plain,
    ! [U_1979,U_1978] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1979),U_1978) != bot_bot_fun_a_bool,
    inference(variable_rename,[status(thm)],[f_710_1]) ).

fof(f_710_3,plain,
    ! [U_1978,U_1979] : hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1979),U_1978) != bot_bot_fun_a_bool,
    inference(definitional_conversion,[status(esa)],[f_710_2]) ).

cnf(f_710_4,plain,
    hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1979),U_1978) != bot_bot_fun_a_bool,
    inference(clausify,[status(thm)],[f_710_3]) ).

fof(f_711_1,plain,
    ! [A_2,A] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A) != bot_bot_fun_nat_bool,
    inference(fof_nnf,[status(thm)],[fact_604_insert__not__empty]) ).

fof(f_711_2,plain,
    ! [U_1981,U_1980] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1981),U_1980) != bot_bot_fun_nat_bool,
    inference(variable_rename,[status(thm)],[f_711_1]) ).

fof(f_711_3,plain,
    ! [U_1980,U_1981] : hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1981),U_1980) != bot_bot_fun_nat_bool,
    inference(definitional_conversion,[status(esa)],[f_711_2]) ).

cnf(f_711_4,plain,
    hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1981),U_1980) != bot_bot_fun_nat_bool,
    inference(clausify,[status(thm)],[f_711_3]) ).

fof(f_712_1,plain,
    ! [A_2,A] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),A) != bot_bot_fun_int_bool,
    inference(fof_nnf,[status(thm)],[fact_605_insert__not__empty]) ).

fof(f_712_2,plain,
    ! [U_1983,U_1982] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1983),U_1982) != bot_bot_fun_int_bool,
    inference(variable_rename,[status(thm)],[f_712_1]) ).

fof(f_712_3,plain,
    ! [U_1982,U_1983] : hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1983),U_1982) != bot_bot_fun_int_bool,
    inference(definitional_conversion,[status(esa)],[f_712_2]) ).

cnf(f_712_4,plain,
    hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1983),U_1982) != bot_bot_fun_int_bool,
    inference(clausify,[status(thm)],[f_712_3]) ).

fof(f_713_1,plain,
    ! [A_2,A] : bot_bot_fun_a_bool != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),A),
    inference(fof_nnf,[status(thm)],[fact_606_empty__not__insert]) ).

fof(f_713_2,plain,
    ! [U_1985,U_1984] : bot_bot_fun_a_bool != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1985),U_1984),
    inference(variable_rename,[status(thm)],[f_713_1]) ).

fof(f_713_3,plain,
    ! [U_1984,U_1985] : bot_bot_fun_a_bool != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1985),U_1984),
    inference(definitional_conversion,[status(esa)],[f_713_2]) ).

cnf(f_713_4,plain,
    bot_bot_fun_a_bool != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_1985),U_1984),
    inference(clausify,[status(thm)],[f_713_3]) ).

fof(f_714_1,plain,
    ! [A_2,A] : bot_bot_fun_nat_bool != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),A),
    inference(fof_nnf,[status(thm)],[fact_607_empty__not__insert]) ).

fof(f_714_2,plain,
    ! [U_1987,U_1986] : bot_bot_fun_nat_bool != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1987),U_1986),
    inference(variable_rename,[status(thm)],[f_714_1]) ).

fof(f_714_3,plain,
    ! [U_1987,U_1986] : bot_bot_fun_nat_bool != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1987),U_1986),
    inference(definitional_conversion,[status(esa)],[f_714_2]) ).

cnf(f_714_4,plain,
    bot_bot_fun_nat_bool != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_1987),U_1986),
    inference(clausify,[status(thm)],[f_714_3]) ).

fof(f_715_1,plain,
    ! [A_2,A] : bot_bot_fun_int_bool != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),A),
    inference(fof_nnf,[status(thm)],[fact_608_empty__not__insert]) ).

fof(f_715_2,plain,
    ! [U_1989,U_1988] : bot_bot_fun_int_bool != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1989),U_1988),
    inference(variable_rename,[status(thm)],[f_715_1]) ).

fof(f_715_3,plain,
    ! [U_1989,U_1988] : bot_bot_fun_int_bool != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1989),U_1988),
    inference(definitional_conversion,[status(esa)],[f_715_2]) ).

cnf(f_715_4,plain,
    bot_bot_fun_int_bool != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_1989),U_1988),
    inference(clausify,[status(thm)],[f_715_3]) ).

fof(f_716_1,plain,
    ! [A] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),bot_bot_fun_nat_bool))
        | A != bot_bot_fun_nat_bool )
      & ( A = bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),bot_bot_fun_nat_bool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_609_subset__empty]) ).

fof(f_716_2,plain,
    ! [U_1990] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1990),bot_bot_fun_nat_bool))
        | U_1990 != bot_bot_fun_nat_bool )
      & ( U_1990 = bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1990),bot_bot_fun_nat_bool)) ) ),
    inference(variable_rename,[status(thm)],[f_716_1]) ).

fof(f_716_3,plain,
    ( ! [U_1992] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1992),bot_bot_fun_nat_bool))
        | U_1992 != bot_bot_fun_nat_bool )
    & ! [U_1991] :
        ( U_1991 = bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1991),bot_bot_fun_nat_bool)) ) ),
    inference(miniscope,[status(thm)],[f_716_2]) ).

fof(f_716_4,plain,
    ( ! [U_1992] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1992),bot_bot_fun_nat_bool))
        | U_1992 != bot_bot_fun_nat_bool )
    & ! [U_1991] :
        ( U_1991 = bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1991),bot_bot_fun_nat_bool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_716_3]) ).

cnf(f_716_5,plain,
    ( U_1991 = bot_bot_fun_nat_bool
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1991),bot_bot_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_716_4]) ).

cnf(f_716_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_1992),bot_bot_fun_nat_bool))
    | U_1992 != bot_bot_fun_nat_bool ),
    inference(clausify,[status(thm)],[f_716_4]) ).

fof(f_717_1,plain,
    ! [A] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),bot_bot_fun_int_bool))
        | A != bot_bot_fun_int_bool )
      & ( A = bot_bot_fun_int_bool
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),bot_bot_fun_int_bool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_610_subset__empty]) ).

fof(f_717_2,plain,
    ! [U_1993] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1993),bot_bot_fun_int_bool))
        | U_1993 != bot_bot_fun_int_bool )
      & ( U_1993 = bot_bot_fun_int_bool
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1993),bot_bot_fun_int_bool)) ) ),
    inference(variable_rename,[status(thm)],[f_717_1]) ).

fof(f_717_3,plain,
    ( ! [U_1995] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1995),bot_bot_fun_int_bool))
        | U_1995 != bot_bot_fun_int_bool )
    & ! [U_1994] :
        ( U_1994 = bot_bot_fun_int_bool
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1994),bot_bot_fun_int_bool)) ) ),
    inference(miniscope,[status(thm)],[f_717_2]) ).

fof(f_717_4,plain,
    ( ! [U_1995] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1995),bot_bot_fun_int_bool))
        | U_1995 != bot_bot_fun_int_bool )
    & ! [U_1994] :
        ( U_1994 = bot_bot_fun_int_bool
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1994),bot_bot_fun_int_bool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_717_3]) ).

cnf(f_717_5,plain,
    ( U_1994 = bot_bot_fun_int_bool
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1994),bot_bot_fun_int_bool)) ),
    inference(clausify,[status(thm)],[f_717_4]) ).

cnf(f_717_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_1995),bot_bot_fun_int_bool))
    | U_1995 != bot_bot_fun_int_bool ),
    inference(clausify,[status(thm)],[f_717_4]) ).

fof(f_718_1,plain,
    ! [A] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),bot_bot_fun_a_bool))
          | A != bot_bot_fun_a_bool )
        & ( A = bot_bot_fun_a_bool
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),bot_bot_fun_a_bool)) ) )
      | ~ is_fun_a_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_611_subset__empty]) ).

fof(f_718_2,plain,
    ! [U_1996] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1996),bot_bot_fun_a_bool))
          | U_1996 != bot_bot_fun_a_bool )
        & ( U_1996 = bot_bot_fun_a_bool
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1996),bot_bot_fun_a_bool)) ) )
      | ~ is_fun_a_bool(U_1996) ),
    inference(variable_rename,[status(thm)],[f_718_1]) ).

fof(f_718_3,plain,
    ( ! [U_1996] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1996),bot_bot_fun_a_bool))
        | U_1996 != bot_bot_fun_a_bool
        | ~ sP182(U_1996) )
    & ! [U_1996] :
        ( U_1996 = bot_bot_fun_a_bool
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1996),bot_bot_fun_a_bool))
        | ~ sP182(U_1996) )
    & ! [U_1996] :
        ( sP182(U_1996)
        | ~ is_fun_a_bool(U_1996) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP182])],[f_718_2]) ).

cnf(f_718_4,plain,
    ( sP182(U_1996)
    | ~ is_fun_a_bool(U_1996) ),
    inference(clausify,[status(thm)],[f_718_3]) ).

cnf(f_718_5,plain,
    ( U_1996 = bot_bot_fun_a_bool
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1996),bot_bot_fun_a_bool))
    | ~ sP182(U_1996) ),
    inference(clausify,[status(thm)],[f_718_3]) ).

cnf(f_718_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_1996),bot_bot_fun_a_bool))
    | U_1996 != bot_bot_fun_a_bool
    | ~ sP182(U_1996) ),
    inference(clausify,[status(thm)],[f_718_3]) ).

fof(f_719_1,plain,
    ! [F,A] :
      ( ( image_nat_int(F,A) = bot_bot_fun_int_bool
        | A != bot_bot_fun_nat_bool )
      & ( A = bot_bot_fun_nat_bool
        | image_nat_int(F,A) != bot_bot_fun_int_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_612_image__is__empty]) ).

fof(f_719_2,plain,
    ! [U_1998,U_1997] :
      ( ( image_nat_int(U_1998,U_1997) = bot_bot_fun_int_bool
        | U_1997 != bot_bot_fun_nat_bool )
      & ( U_1997 = bot_bot_fun_nat_bool
        | image_nat_int(U_1998,U_1997) != bot_bot_fun_int_bool ) ),
    inference(variable_rename,[status(thm)],[f_719_1]) ).

fof(f_719_3,plain,
    ( ! [U_2002,U_2000] :
        ( image_nat_int(U_2002,U_2000) = bot_bot_fun_int_bool
        | U_2000 != bot_bot_fun_nat_bool )
    & ! [U_2001,U_1999] :
        ( U_1999 = bot_bot_fun_nat_bool
        | image_nat_int(U_2001,U_1999) != bot_bot_fun_int_bool ) ),
    inference(miniscope,[status(thm)],[f_719_2]) ).

fof(f_719_4,plain,
    ( ! [U_2000,U_2002] :
        ( image_nat_int(U_2002,U_2000) = bot_bot_fun_int_bool
        | U_2000 != bot_bot_fun_nat_bool )
    & ! [U_1999,U_2001] :
        ( U_1999 = bot_bot_fun_nat_bool
        | image_nat_int(U_2001,U_1999) != bot_bot_fun_int_bool ) ),
    inference(definitional_conversion,[status(esa)],[f_719_3]) ).

cnf(f_719_5,plain,
    ( U_1999 = bot_bot_fun_nat_bool
    | image_nat_int(U_2001,U_1999) != bot_bot_fun_int_bool ),
    inference(clausify,[status(thm)],[f_719_4]) ).

cnf(f_719_6,plain,
    ( image_nat_int(U_2002,U_2000) = bot_bot_fun_int_bool
    | U_2000 != bot_bot_fun_nat_bool ),
    inference(clausify,[status(thm)],[f_719_4]) ).

fof(f_720_1,plain,
    ! [F,A] :
      ( ( ( image_pname_a(F,A) = bot_bot_fun_a_bool
          | A != bot_bo844097828e_bool )
        & ( A = bot_bo844097828e_bool
          | image_pname_a(F,A) != bot_bot_fun_a_bool ) )
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_613_image__is__empty]) ).

fof(f_720_2,plain,
    ! [U_2004,U_2003] :
      ( ( ( image_pname_a(U_2004,U_2003) = bot_bot_fun_a_bool
          | U_2003 != bot_bo844097828e_bool )
        & ( U_2003 = bot_bo844097828e_bool
          | image_pname_a(U_2004,U_2003) != bot_bot_fun_a_bool ) )
      | ~ is_fun_pname_bool(U_2003) ),
    inference(variable_rename,[status(thm)],[f_720_1]) ).

fof(f_720_3,plain,
    ( ! [U_2004,U_2003] :
        ( image_pname_a(U_2004,U_2003) = bot_bot_fun_a_bool
        | U_2003 != bot_bo844097828e_bool
        | ~ sP183(U_2004,U_2003) )
    & ! [U_2004,U_2003] :
        ( U_2003 = bot_bo844097828e_bool
        | image_pname_a(U_2004,U_2003) != bot_bot_fun_a_bool
        | ~ sP183(U_2004,U_2003) )
    & ! [U_2004,U_2003] :
        ( sP183(U_2004,U_2003)
        | ~ is_fun_pname_bool(U_2003) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP183])],[f_720_2]) ).

cnf(f_720_4,plain,
    ( sP183(U_2004,U_2003)
    | ~ is_fun_pname_bool(U_2003) ),
    inference(clausify,[status(thm)],[f_720_3]) ).

cnf(f_720_5,plain,
    ( U_2003 = bot_bo844097828e_bool
    | image_pname_a(U_2004,U_2003) != bot_bot_fun_a_bool
    | ~ sP183(U_2004,U_2003) ),
    inference(clausify,[status(thm)],[f_720_3]) ).

cnf(f_720_6,plain,
    ( image_pname_a(U_2004,U_2003) = bot_bot_fun_a_bool
    | U_2003 != bot_bo844097828e_bool
    | ~ sP183(U_2004,U_2003) ),
    inference(clausify,[status(thm)],[f_720_3]) ).

fof(f_721_1,plain,
    ! [F] : image_nat_int(F,bot_bot_fun_nat_bool) = bot_bot_fun_int_bool,
    inference(fof_nnf,[status(thm)],[fact_614_image__empty]) ).

fof(f_721_2,plain,
    ! [U_2005] : image_nat_int(U_2005,bot_bot_fun_nat_bool) = bot_bot_fun_int_bool,
    inference(variable_rename,[status(thm)],[f_721_1]) ).

fof(f_721_3,plain,
    ! [U_2005] : image_nat_int(U_2005,bot_bot_fun_nat_bool) = bot_bot_fun_int_bool,
    inference(definitional_conversion,[status(esa)],[f_721_2]) ).

cnf(f_721_4,plain,
    image_nat_int(U_2005,bot_bot_fun_nat_bool) = bot_bot_fun_int_bool,
    inference(clausify,[status(thm)],[f_721_3]) ).

fof(f_722_1,plain,
    ! [F] : image_pname_a(F,bot_bo844097828e_bool) = bot_bot_fun_a_bool,
    inference(fof_nnf,[status(thm)],[fact_615_image__empty]) ).

fof(f_722_2,plain,
    ! [U_2006] : image_pname_a(U_2006,bot_bo844097828e_bool) = bot_bot_fun_a_bool,
    inference(variable_rename,[status(thm)],[f_722_1]) ).

fof(f_722_3,plain,
    ! [U_2006] : image_pname_a(U_2006,bot_bo844097828e_bool) = bot_bot_fun_a_bool,
    inference(definitional_conversion,[status(esa)],[f_722_2]) ).

cnf(f_722_4,plain,
    image_pname_a(U_2006,bot_bo844097828e_bool) = bot_bot_fun_a_bool,
    inference(clausify,[status(thm)],[f_722_3]) ).

fof(f_723_1,plain,
    ! [F,A] :
      ( ( bot_bot_fun_int_bool = image_nat_int(F,A)
        | A != bot_bot_fun_nat_bool )
      & ( A = bot_bot_fun_nat_bool
        | bot_bot_fun_int_bool != image_nat_int(F,A) ) ),
    inference(fof_nnf,[status(thm)],[fact_616_empty__is__image]) ).

fof(f_723_2,plain,
    ! [U_2008,U_2007] :
      ( ( bot_bot_fun_int_bool = image_nat_int(U_2008,U_2007)
        | U_2007 != bot_bot_fun_nat_bool )
      & ( U_2007 = bot_bot_fun_nat_bool
        | bot_bot_fun_int_bool != image_nat_int(U_2008,U_2007) ) ),
    inference(variable_rename,[status(thm)],[f_723_1]) ).

fof(f_723_3,plain,
    ( ! [U_2012,U_2010] :
        ( bot_bot_fun_int_bool = image_nat_int(U_2012,U_2010)
        | U_2010 != bot_bot_fun_nat_bool )
    & ! [U_2011,U_2009] :
        ( U_2009 = bot_bot_fun_nat_bool
        | bot_bot_fun_int_bool != image_nat_int(U_2011,U_2009) ) ),
    inference(miniscope,[status(thm)],[f_723_2]) ).

fof(f_723_4,plain,
    ( ! [U_2012,U_2010] :
        ( bot_bot_fun_int_bool = image_nat_int(U_2012,U_2010)
        | U_2010 != bot_bot_fun_nat_bool )
    & ! [U_2011,U_2009] :
        ( U_2009 = bot_bot_fun_nat_bool
        | bot_bot_fun_int_bool != image_nat_int(U_2011,U_2009) ) ),
    inference(definitional_conversion,[status(esa)],[f_723_3]) ).

cnf(f_723_5,plain,
    ( U_2009 = bot_bot_fun_nat_bool
    | bot_bot_fun_int_bool != image_nat_int(U_2011,U_2009) ),
    inference(clausify,[status(thm)],[f_723_4]) ).

cnf(f_723_6,plain,
    ( bot_bot_fun_int_bool = image_nat_int(U_2012,U_2010)
    | U_2010 != bot_bot_fun_nat_bool ),
    inference(clausify,[status(thm)],[f_723_4]) ).

fof(f_724_1,plain,
    ! [F,A] :
      ( ( ( bot_bot_fun_a_bool = image_pname_a(F,A)
          | A != bot_bo844097828e_bool )
        & ( A = bot_bo844097828e_bool
          | bot_bot_fun_a_bool != image_pname_a(F,A) ) )
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_617_empty__is__image]) ).

fof(f_724_2,plain,
    ! [U_2014,U_2013] :
      ( ( ( bot_bot_fun_a_bool = image_pname_a(U_2014,U_2013)
          | U_2013 != bot_bo844097828e_bool )
        & ( U_2013 = bot_bo844097828e_bool
          | bot_bot_fun_a_bool != image_pname_a(U_2014,U_2013) ) )
      | ~ is_fun_pname_bool(U_2013) ),
    inference(variable_rename,[status(thm)],[f_724_1]) ).

fof(f_724_3,plain,
    ( ! [U_2014,U_2013] :
        ( bot_bot_fun_a_bool = image_pname_a(U_2014,U_2013)
        | U_2013 != bot_bo844097828e_bool
        | ~ sP184(U_2014,U_2013) )
    & ! [U_2014,U_2013] :
        ( U_2013 = bot_bo844097828e_bool
        | bot_bot_fun_a_bool != image_pname_a(U_2014,U_2013)
        | ~ sP184(U_2014,U_2013) )
    & ! [U_2014,U_2013] :
        ( sP184(U_2014,U_2013)
        | ~ is_fun_pname_bool(U_2013) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP184])],[f_724_2]) ).

cnf(f_724_4,plain,
    ( sP184(U_2014,U_2013)
    | ~ is_fun_pname_bool(U_2013) ),
    inference(clausify,[status(thm)],[f_724_3]) ).

cnf(f_724_5,plain,
    ( U_2013 = bot_bo844097828e_bool
    | bot_bot_fun_a_bool != image_pname_a(U_2014,U_2013)
    | ~ sP184(U_2014,U_2013) ),
    inference(clausify,[status(thm)],[f_724_3]) ).

cnf(f_724_6,plain,
    ( bot_bot_fun_a_bool = image_pname_a(U_2014,U_2013)
    | U_2013 != bot_bo844097828e_bool
    | ~ sP184(U_2014,U_2013) ),
    inference(clausify,[status(thm)],[f_724_3]) ).

fof(f_725_1,plain,
    ! [A_2] :
      ( A_2 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),bot_bot_fun_nat_bool)) ),
    inference(fof_nnf,[status(thm)],[fact_618_le__bot]) ).

fof(f_725_2,plain,
    ! [U_2015] :
      ( U_2015 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2015),bot_bot_fun_nat_bool)) ),
    inference(variable_rename,[status(thm)],[f_725_1]) ).

fof(f_725_3,plain,
    ! [U_2015] :
      ( U_2015 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2015),bot_bot_fun_nat_bool)) ),
    inference(definitional_conversion,[status(esa)],[f_725_2]) ).

cnf(f_725_4,plain,
    ( U_2015 = bot_bot_fun_nat_bool
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2015),bot_bot_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_725_3]) ).

fof(f_726_1,plain,
    ! [A_2] :
      ( A_2 = bot_bot_fun_int_bool
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),bot_bot_fun_int_bool)) ),
    inference(fof_nnf,[status(thm)],[fact_619_le__bot]) ).

fof(f_726_2,plain,
    ! [U_2016] :
      ( U_2016 = bot_bot_fun_int_bool
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2016),bot_bot_fun_int_bool)) ),
    inference(variable_rename,[status(thm)],[f_726_1]) ).

fof(f_726_3,plain,
    ! [U_2016] :
      ( U_2016 = bot_bot_fun_int_bool
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2016),bot_bot_fun_int_bool)) ),
    inference(definitional_conversion,[status(esa)],[f_726_2]) ).

cnf(f_726_4,plain,
    ( U_2016 = bot_bot_fun_int_bool
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2016),bot_bot_fun_int_bool)) ),
    inference(clausify,[status(thm)],[f_726_3]) ).

fof(f_727_1,plain,
    ! [A_17] :
      ( A_17 = bot_bot_nat
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_17),bot_bot_nat)) ),
    inference(fof_nnf,[status(thm)],[fact_620_le__bot]) ).

fof(f_727_2,plain,
    ! [U_2017] :
      ( U_2017 = bot_bot_nat
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2017),bot_bot_nat)) ),
    inference(variable_rename,[status(thm)],[f_727_1]) ).

fof(f_727_3,plain,
    ! [U_2017] :
      ( U_2017 = bot_bot_nat
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2017),bot_bot_nat)) ),
    inference(definitional_conversion,[status(esa)],[f_727_2]) ).

cnf(f_727_4,plain,
    ( U_2017 = bot_bot_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2017),bot_bot_nat)) ),
    inference(clausify,[status(thm)],[f_727_3]) ).

fof(f_728_1,plain,
    ! [A_2] :
      ( A_2 = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_2),bot_bot_fun_a_bool))
      | ~ is_fun_a_bool(A_2) ),
    inference(fof_nnf,[status(thm)],[fact_621_le__bot]) ).

fof(f_728_2,plain,
    ! [U_2018] :
      ( U_2018 = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2018),bot_bot_fun_a_bool))
      | ~ is_fun_a_bool(U_2018) ),
    inference(variable_rename,[status(thm)],[f_728_1]) ).

fof(f_728_3,plain,
    ! [U_2018] :
      ( U_2018 = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2018),bot_bot_fun_a_bool))
      | ~ is_fun_a_bool(U_2018) ),
    inference(definitional_conversion,[status(esa)],[f_728_2]) ).

cnf(f_728_4,plain,
    ( U_2018 = bot_bot_fun_a_bool
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2018),bot_bot_fun_a_bool))
    | ~ is_fun_a_bool(U_2018) ),
    inference(clausify,[status(thm)],[f_728_3]) ).

fof(f_729_1,plain,
    ! [A_2] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),bot_bot_fun_nat_bool))
        | A_2 != bot_bot_fun_nat_bool )
      & ( A_2 = bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A_2),bot_bot_fun_nat_bool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_622_bot__unique]) ).

fof(f_729_2,plain,
    ! [U_2019] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2019),bot_bot_fun_nat_bool))
        | U_2019 != bot_bot_fun_nat_bool )
      & ( U_2019 = bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2019),bot_bot_fun_nat_bool)) ) ),
    inference(variable_rename,[status(thm)],[f_729_1]) ).

fof(f_729_3,plain,
    ( ! [U_2021] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2021),bot_bot_fun_nat_bool))
        | U_2021 != bot_bot_fun_nat_bool )
    & ! [U_2020] :
        ( U_2020 = bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2020),bot_bot_fun_nat_bool)) ) ),
    inference(miniscope,[status(thm)],[f_729_2]) ).

fof(f_729_4,plain,
    ( ! [U_2021] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2021),bot_bot_fun_nat_bool))
        | U_2021 != bot_bot_fun_nat_bool )
    & ! [U_2020] :
        ( U_2020 = bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2020),bot_bot_fun_nat_bool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_729_3]) ).

cnf(f_729_5,plain,
    ( U_2020 = bot_bot_fun_nat_bool
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2020),bot_bot_fun_nat_bool)) ),
    inference(clausify,[status(thm)],[f_729_4]) ).

cnf(f_729_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2021),bot_bot_fun_nat_bool))
    | U_2021 != bot_bot_fun_nat_bool ),
    inference(clausify,[status(thm)],[f_729_4]) ).

fof(f_730_1,plain,
    ! [A_2] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),bot_bot_fun_int_bool))
        | A_2 != bot_bot_fun_int_bool )
      & ( A_2 = bot_bot_fun_int_bool
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A_2),bot_bot_fun_int_bool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_623_bot__unique]) ).

fof(f_730_2,plain,
    ! [U_2022] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2022),bot_bot_fun_int_bool))
        | U_2022 != bot_bot_fun_int_bool )
      & ( U_2022 = bot_bot_fun_int_bool
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2022),bot_bot_fun_int_bool)) ) ),
    inference(variable_rename,[status(thm)],[f_730_1]) ).

fof(f_730_3,plain,
    ( ! [U_2024] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2024),bot_bot_fun_int_bool))
        | U_2024 != bot_bot_fun_int_bool )
    & ! [U_2023] :
        ( U_2023 = bot_bot_fun_int_bool
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2023),bot_bot_fun_int_bool)) ) ),
    inference(miniscope,[status(thm)],[f_730_2]) ).

fof(f_730_4,plain,
    ( ! [U_2024] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2024),bot_bot_fun_int_bool))
        | U_2024 != bot_bot_fun_int_bool )
    & ! [U_2023] :
        ( U_2023 = bot_bot_fun_int_bool
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2023),bot_bot_fun_int_bool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_730_3]) ).

cnf(f_730_5,plain,
    ( U_2023 = bot_bot_fun_int_bool
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2023),bot_bot_fun_int_bool)) ),
    inference(clausify,[status(thm)],[f_730_4]) ).

cnf(f_730_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2024),bot_bot_fun_int_bool))
    | U_2024 != bot_bot_fun_int_bool ),
    inference(clausify,[status(thm)],[f_730_4]) ).

fof(f_731_1,plain,
    ! [A_2] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_2),bot_bot_nat))
        | A_2 != bot_bot_nat )
      & ( A_2 = bot_bot_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_2),bot_bot_nat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_624_bot__unique]) ).

fof(f_731_2,plain,
    ! [U_2025] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2025),bot_bot_nat))
        | U_2025 != bot_bot_nat )
      & ( U_2025 = bot_bot_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2025),bot_bot_nat)) ) ),
    inference(variable_rename,[status(thm)],[f_731_1]) ).

fof(f_731_3,plain,
    ( ! [U_2027] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2027),bot_bot_nat))
        | U_2027 != bot_bot_nat )
    & ! [U_2026] :
        ( U_2026 = bot_bot_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2026),bot_bot_nat)) ) ),
    inference(miniscope,[status(thm)],[f_731_2]) ).

fof(f_731_4,plain,
    ( ! [U_2027] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2027),bot_bot_nat))
        | U_2027 != bot_bot_nat )
    & ! [U_2026] :
        ( U_2026 = bot_bot_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2026),bot_bot_nat)) ) ),
    inference(definitional_conversion,[status(esa)],[f_731_3]) ).

cnf(f_731_5,plain,
    ( U_2026 = bot_bot_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2026),bot_bot_nat)) ),
    inference(clausify,[status(thm)],[f_731_4]) ).

cnf(f_731_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2027),bot_bot_nat))
    | U_2027 != bot_bot_nat ),
    inference(clausify,[status(thm)],[f_731_4]) ).

fof(f_732_1,plain,
    ! [A_2] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_2),bot_bot_fun_a_bool))
          | A_2 != bot_bot_fun_a_bool )
        & ( A_2 = bot_bot_fun_a_bool
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A_2),bot_bot_fun_a_bool)) ) )
      | ~ is_fun_a_bool(A_2) ),
    inference(fof_nnf,[status(thm)],[fact_625_bot__unique]) ).

fof(f_732_2,plain,
    ! [U_2028] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2028),bot_bot_fun_a_bool))
          | U_2028 != bot_bot_fun_a_bool )
        & ( U_2028 = bot_bot_fun_a_bool
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2028),bot_bot_fun_a_bool)) ) )
      | ~ is_fun_a_bool(U_2028) ),
    inference(variable_rename,[status(thm)],[f_732_1]) ).

fof(f_732_3,plain,
    ( ! [U_2028] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2028),bot_bot_fun_a_bool))
        | U_2028 != bot_bot_fun_a_bool
        | ~ sP185(U_2028) )
    & ! [U_2028] :
        ( U_2028 = bot_bot_fun_a_bool
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2028),bot_bot_fun_a_bool))
        | ~ sP185(U_2028) )
    & ! [U_2028] :
        ( sP185(U_2028)
        | ~ is_fun_a_bool(U_2028) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP185])],[f_732_2]) ).

cnf(f_732_4,plain,
    ( sP185(U_2028)
    | ~ is_fun_a_bool(U_2028) ),
    inference(clausify,[status(thm)],[f_732_3]) ).

cnf(f_732_5,plain,
    ( U_2028 = bot_bot_fun_a_bool
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2028),bot_bot_fun_a_bool))
    | ~ sP185(U_2028) ),
    inference(clausify,[status(thm)],[f_732_3]) ).

cnf(f_732_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2028),bot_bot_fun_a_bool))
    | U_2028 != bot_bot_fun_a_bool
    | ~ sP185(U_2028) ),
    inference(clausify,[status(thm)],[f_732_3]) ).

fof(f_733_1,plain,
    ! [A_2] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),A_2)),
    inference(fof_nnf,[status(thm)],[fact_626_bot__least]) ).

fof(f_733_2,plain,
    ! [U_2029] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),U_2029)),
    inference(variable_rename,[status(thm)],[f_733_1]) ).

fof(f_733_3,plain,
    ! [U_2029] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),U_2029)),
    inference(definitional_conversion,[status(esa)],[f_733_2]) ).

cnf(f_733_4,plain,
    hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,bot_bot_fun_nat_bool),U_2029)),
    inference(clausify,[status(thm)],[f_733_3]) ).

fof(f_734_1,plain,
    ! [A_2] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),A_2)),
    inference(fof_nnf,[status(thm)],[fact_627_bot__least]) ).

fof(f_734_2,plain,
    ! [U_2030] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),U_2030)),
    inference(variable_rename,[status(thm)],[f_734_1]) ).

fof(f_734_3,plain,
    ! [U_2030] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),U_2030)),
    inference(definitional_conversion,[status(esa)],[f_734_2]) ).

cnf(f_734_4,plain,
    hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,bot_bot_fun_int_bool),U_2030)),
    inference(clausify,[status(thm)],[f_734_3]) ).

fof(f_735_1,plain,
    ! [A_16] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),A_16)),
    inference(fof_nnf,[status(thm)],[fact_628_bot__least]) ).

fof(f_735_2,plain,
    ! [U_2031] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),U_2031)),
    inference(variable_rename,[status(thm)],[f_735_1]) ).

fof(f_735_3,plain,
    ! [U_2031] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),U_2031)),
    inference(definitional_conversion,[status(esa)],[f_735_2]) ).

cnf(f_735_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,bot_bot_nat),U_2031)),
    inference(clausify,[status(thm)],[f_735_3]) ).

fof(f_736_1,plain,
    ! [A_2] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),A_2)),
    inference(fof_nnf,[status(thm)],[fact_629_bot__least]) ).

fof(f_736_2,plain,
    ! [U_2032] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),U_2032)),
    inference(variable_rename,[status(thm)],[f_736_1]) ).

fof(f_736_3,plain,
    ! [U_2032] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),U_2032)),
    inference(definitional_conversion,[status(esa)],[f_736_2]) ).

cnf(f_736_4,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,bot_bot_fun_a_bool),U_2032)),
    inference(clausify,[status(thm)],[f_736_3]) ).

fof(f_737_1,plain,
    ! [Pa,A_2] :
      ( ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_2)),Pa)) = bot_bot_fun_a_bool
        | hBOOL(hAPP_a_bool(Pa,A_2)) )
      & ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_2)),Pa)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool)
        | ~ hBOOL(hAPP_a_bool(Pa,A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_630_Collect__conv__if]) ).

fof(f_737_2,plain,
    ! [U_2034,U_2033] :
      ( ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_2033)),U_2034)) = bot_bot_fun_a_bool
        | hBOOL(hAPP_a_bool(U_2034,U_2033)) )
      & ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_2033)),U_2034)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2033),bot_bot_fun_a_bool)
        | ~ hBOOL(hAPP_a_bool(U_2034,U_2033)) ) ),
    inference(variable_rename,[status(thm)],[f_737_1]) ).

fof(f_737_3,plain,
    ( ! [U_2038,U_2036] :
        ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_2036)),U_2038)) = bot_bot_fun_a_bool
        | hBOOL(hAPP_a_bool(U_2038,U_2036)) )
    & ! [U_2037,U_2035] :
        ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_2035)),U_2037)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2035),bot_bot_fun_a_bool)
        | ~ hBOOL(hAPP_a_bool(U_2037,U_2035)) ) ),
    inference(miniscope,[status(thm)],[f_737_2]) ).

fof(f_737_4,plain,
    ( ! [U_2036,U_2038] :
        ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_2036)),U_2038)) = bot_bot_fun_a_bool
        | hBOOL(hAPP_a_bool(U_2038,U_2036)) )
    & ! [U_2037,U_2035] :
        ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_2035)),U_2037)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2035),bot_bot_fun_a_bool)
        | ~ hBOOL(hAPP_a_bool(U_2037,U_2035)) ) ),
    inference(definitional_conversion,[status(esa)],[f_737_3]) ).

cnf(f_737_5,plain,
    ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_2035)),U_2037)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2035),bot_bot_fun_a_bool)
    | ~ hBOOL(hAPP_a_bool(U_2037,U_2035)) ),
    inference(clausify,[status(thm)],[f_737_4]) ).

cnf(f_737_6,plain,
    ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_2036)),U_2038)) = bot_bot_fun_a_bool
    | hBOOL(hAPP_a_bool(U_2038,U_2036)) ),
    inference(clausify,[status(thm)],[f_737_4]) ).

fof(f_738_1,plain,
    ! [Pa,A_2] :
      ( ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),A_2)),Pa)) = bot_bot_fun_int_bool
        | hBOOL(hAPP_int_bool(Pa,A_2)) )
      & ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),A_2)),Pa)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool)
        | ~ hBOOL(hAPP_int_bool(Pa,A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_631_Collect__conv__if]) ).

fof(f_738_2,plain,
    ! [U_2040,U_2039] :
      ( ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),U_2039)),U_2040)) = bot_bot_fun_int_bool
        | hBOOL(hAPP_int_bool(U_2040,U_2039)) )
      & ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),U_2039)),U_2040)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2039),bot_bot_fun_int_bool)
        | ~ hBOOL(hAPP_int_bool(U_2040,U_2039)) ) ),
    inference(variable_rename,[status(thm)],[f_738_1]) ).

fof(f_738_3,plain,
    ( ! [U_2044,U_2042] :
        ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),U_2042)),U_2044)) = bot_bot_fun_int_bool
        | hBOOL(hAPP_int_bool(U_2044,U_2042)) )
    & ! [U_2043,U_2041] :
        ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),U_2041)),U_2043)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2041),bot_bot_fun_int_bool)
        | ~ hBOOL(hAPP_int_bool(U_2043,U_2041)) ) ),
    inference(miniscope,[status(thm)],[f_738_2]) ).

fof(f_738_4,plain,
    ( ! [U_2042,U_2044] :
        ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),U_2042)),U_2044)) = bot_bot_fun_int_bool
        | hBOOL(hAPP_int_bool(U_2044,U_2042)) )
    & ! [U_2043,U_2041] :
        ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),U_2041)),U_2043)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2041),bot_bot_fun_int_bool)
        | ~ hBOOL(hAPP_int_bool(U_2043,U_2041)) ) ),
    inference(definitional_conversion,[status(esa)],[f_738_3]) ).

cnf(f_738_5,plain,
    ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),U_2041)),U_2043)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2041),bot_bot_fun_int_bool)
    | ~ hBOOL(hAPP_int_bool(U_2043,U_2041)) ),
    inference(clausify,[status(thm)],[f_738_4]) ).

cnf(f_738_6,plain,
    ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),U_2042)),U_2044)) = bot_bot_fun_int_bool
    | hBOOL(hAPP_int_bool(U_2044,U_2042)) ),
    inference(clausify,[status(thm)],[f_738_4]) ).

fof(f_739_1,plain,
    ! [Pa,A_2] :
      ( ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_2)),Pa)) = bot_bot_fun_nat_bool
        | hBOOL(hAPP_nat_bool(Pa,A_2)) )
      & ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_2)),Pa)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool)
        | ~ hBOOL(hAPP_nat_bool(Pa,A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_632_Collect__conv__if]) ).

fof(f_739_2,plain,
    ! [U_2046,U_2045] :
      ( ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_2045)),U_2046)) = bot_bot_fun_nat_bool
        | hBOOL(hAPP_nat_bool(U_2046,U_2045)) )
      & ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_2045)),U_2046)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2045),bot_bot_fun_nat_bool)
        | ~ hBOOL(hAPP_nat_bool(U_2046,U_2045)) ) ),
    inference(variable_rename,[status(thm)],[f_739_1]) ).

fof(f_739_3,plain,
    ( ! [U_2050,U_2048] :
        ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_2048)),U_2050)) = bot_bot_fun_nat_bool
        | hBOOL(hAPP_nat_bool(U_2050,U_2048)) )
    & ! [U_2049,U_2047] :
        ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_2047)),U_2049)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2047),bot_bot_fun_nat_bool)
        | ~ hBOOL(hAPP_nat_bool(U_2049,U_2047)) ) ),
    inference(miniscope,[status(thm)],[f_739_2]) ).

fof(f_739_4,plain,
    ( ! [U_2048,U_2050] :
        ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_2048)),U_2050)) = bot_bot_fun_nat_bool
        | hBOOL(hAPP_nat_bool(U_2050,U_2048)) )
    & ! [U_2049,U_2047] :
        ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_2047)),U_2049)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2047),bot_bot_fun_nat_bool)
        | ~ hBOOL(hAPP_nat_bool(U_2049,U_2047)) ) ),
    inference(definitional_conversion,[status(esa)],[f_739_3]) ).

cnf(f_739_5,plain,
    ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_2047)),U_2049)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2047),bot_bot_fun_nat_bool)
    | ~ hBOOL(hAPP_nat_bool(U_2049,U_2047)) ),
    inference(clausify,[status(thm)],[f_739_4]) ).

cnf(f_739_6,plain,
    ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_2048)),U_2050)) = bot_bot_fun_nat_bool
    | hBOOL(hAPP_nat_bool(U_2050,U_2048)) ),
    inference(clausify,[status(thm)],[f_739_4]) ).

fof(f_740_1,plain,
    ! [Pa,A_2] :
      ( ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,A_2)),Pa)) = bot_bot_fun_a_bool
        | hBOOL(hAPP_a_bool(Pa,A_2)) )
      & ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,A_2)),Pa)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool)
        | ~ hBOOL(hAPP_a_bool(Pa,A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_633_Collect__conv__if2]) ).

fof(f_740_2,plain,
    ! [U_2052,U_2051] :
      ( ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,U_2051)),U_2052)) = bot_bot_fun_a_bool
        | hBOOL(hAPP_a_bool(U_2052,U_2051)) )
      & ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,U_2051)),U_2052)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2051),bot_bot_fun_a_bool)
        | ~ hBOOL(hAPP_a_bool(U_2052,U_2051)) ) ),
    inference(variable_rename,[status(thm)],[f_740_1]) ).

fof(f_740_3,plain,
    ( ! [U_2056,U_2054] :
        ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,U_2054)),U_2056)) = bot_bot_fun_a_bool
        | hBOOL(hAPP_a_bool(U_2056,U_2054)) )
    & ! [U_2055,U_2053] :
        ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,U_2053)),U_2055)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2053),bot_bot_fun_a_bool)
        | ~ hBOOL(hAPP_a_bool(U_2055,U_2053)) ) ),
    inference(miniscope,[status(thm)],[f_740_2]) ).

fof(f_740_4,plain,
    ( ! [U_2054,U_2056] :
        ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,U_2054)),U_2056)) = bot_bot_fun_a_bool
        | hBOOL(hAPP_a_bool(U_2056,U_2054)) )
    & ! [U_2055,U_2053] :
        ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,U_2053)),U_2055)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2053),bot_bot_fun_a_bool)
        | ~ hBOOL(hAPP_a_bool(U_2055,U_2053)) ) ),
    inference(definitional_conversion,[status(esa)],[f_740_3]) ).

cnf(f_740_5,plain,
    ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,U_2053)),U_2055)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2053),bot_bot_fun_a_bool)
    | ~ hBOOL(hAPP_a_bool(U_2055,U_2053)) ),
    inference(clausify,[status(thm)],[f_740_4]) ).

cnf(f_740_6,plain,
    ( collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_a_fun_a_bool(fequal_a,U_2054)),U_2056)) = bot_bot_fun_a_bool
    | hBOOL(hAPP_a_bool(U_2056,U_2054)) ),
    inference(clausify,[status(thm)],[f_740_4]) ).

fof(f_741_1,plain,
    ! [Pa,A_2] :
      ( ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,A_2)),Pa)) = bot_bot_fun_int_bool
        | hBOOL(hAPP_int_bool(Pa,A_2)) )
      & ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,A_2)),Pa)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool)
        | ~ hBOOL(hAPP_int_bool(Pa,A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_634_Collect__conv__if2]) ).

fof(f_741_2,plain,
    ! [U_2058,U_2057] :
      ( ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,U_2057)),U_2058)) = bot_bot_fun_int_bool
        | hBOOL(hAPP_int_bool(U_2058,U_2057)) )
      & ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,U_2057)),U_2058)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2057),bot_bot_fun_int_bool)
        | ~ hBOOL(hAPP_int_bool(U_2058,U_2057)) ) ),
    inference(variable_rename,[status(thm)],[f_741_1]) ).

fof(f_741_3,plain,
    ( ! [U_2062,U_2060] :
        ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,U_2060)),U_2062)) = bot_bot_fun_int_bool
        | hBOOL(hAPP_int_bool(U_2062,U_2060)) )
    & ! [U_2061,U_2059] :
        ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,U_2059)),U_2061)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2059),bot_bot_fun_int_bool)
        | ~ hBOOL(hAPP_int_bool(U_2061,U_2059)) ) ),
    inference(miniscope,[status(thm)],[f_741_2]) ).

fof(f_741_4,plain,
    ( ! [U_2060,U_2062] :
        ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,U_2060)),U_2062)) = bot_bot_fun_int_bool
        | hBOOL(hAPP_int_bool(U_2062,U_2060)) )
    & ! [U_2061,U_2059] :
        ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,U_2059)),U_2061)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2059),bot_bot_fun_int_bool)
        | ~ hBOOL(hAPP_int_bool(U_2061,U_2059)) ) ),
    inference(definitional_conversion,[status(esa)],[f_741_3]) ).

cnf(f_741_5,plain,
    ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,U_2059)),U_2061)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2059),bot_bot_fun_int_bool)
    | ~ hBOOL(hAPP_int_bool(U_2061,U_2059)) ),
    inference(clausify,[status(thm)],[f_741_4]) ).

cnf(f_741_6,plain,
    ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(fequal_int,U_2060)),U_2062)) = bot_bot_fun_int_bool
    | hBOOL(hAPP_int_bool(U_2062,U_2060)) ),
    inference(clausify,[status(thm)],[f_741_4]) ).

fof(f_742_1,plain,
    ! [Pa,A_2] :
      ( ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,A_2)),Pa)) = bot_bot_fun_nat_bool
        | hBOOL(hAPP_nat_bool(Pa,A_2)) )
      & ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,A_2)),Pa)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool)
        | ~ hBOOL(hAPP_nat_bool(Pa,A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_635_Collect__conv__if2]) ).

fof(f_742_2,plain,
    ! [U_2064,U_2063] :
      ( ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,U_2063)),U_2064)) = bot_bot_fun_nat_bool
        | hBOOL(hAPP_nat_bool(U_2064,U_2063)) )
      & ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,U_2063)),U_2064)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2063),bot_bot_fun_nat_bool)
        | ~ hBOOL(hAPP_nat_bool(U_2064,U_2063)) ) ),
    inference(variable_rename,[status(thm)],[f_742_1]) ).

fof(f_742_3,plain,
    ( ! [U_2068,U_2066] :
        ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,U_2066)),U_2068)) = bot_bot_fun_nat_bool
        | hBOOL(hAPP_nat_bool(U_2068,U_2066)) )
    & ! [U_2067,U_2065] :
        ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,U_2065)),U_2067)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2065),bot_bot_fun_nat_bool)
        | ~ hBOOL(hAPP_nat_bool(U_2067,U_2065)) ) ),
    inference(miniscope,[status(thm)],[f_742_2]) ).

fof(f_742_4,plain,
    ( ! [U_2066,U_2068] :
        ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,U_2066)),U_2068)) = bot_bot_fun_nat_bool
        | hBOOL(hAPP_nat_bool(U_2068,U_2066)) )
    & ! [U_2067,U_2065] :
        ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,U_2065)),U_2067)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2065),bot_bot_fun_nat_bool)
        | ~ hBOOL(hAPP_nat_bool(U_2067,U_2065)) ) ),
    inference(definitional_conversion,[status(esa)],[f_742_3]) ).

cnf(f_742_5,plain,
    ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,U_2065)),U_2067)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2065),bot_bot_fun_nat_bool)
    | ~ hBOOL(hAPP_nat_bool(U_2067,U_2065)) ),
    inference(clausify,[status(thm)],[f_742_4]) ).

cnf(f_742_6,plain,
    ( collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_n1699378549t_bool(fequal_nat,U_2066)),U_2068)) = bot_bot_fun_nat_bool
    | hBOOL(hAPP_nat_bool(U_2068,U_2066)) ),
    inference(clausify,[status(thm)],[f_742_4]) ).

fof(f_743_1,plain,
    ! [A_2] : collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_2)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool),
    inference(fof_nnf,[status(thm)],[fact_636_singleton__conv]) ).

fof(f_743_2,plain,
    ! [U_2069] : collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_2069)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2069),bot_bot_fun_a_bool),
    inference(variable_rename,[status(thm)],[f_743_1]) ).

fof(f_743_3,plain,
    ! [U_2069] : collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_2069)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2069),bot_bot_fun_a_bool),
    inference(definitional_conversion,[status(esa)],[f_743_2]) ).

cnf(f_743_4,plain,
    collect_a(hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),U_2069)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2069),bot_bot_fun_a_bool),
    inference(clausify,[status(thm)],[f_743_3]) ).

fof(f_744_1,plain,
    ! [A_2] : collect_int(hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),A_2)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool),
    inference(fof_nnf,[status(thm)],[fact_637_singleton__conv]) ).

fof(f_744_2,plain,
    ! [U_2070] : collect_int(hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),U_2070)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2070),bot_bot_fun_int_bool),
    inference(variable_rename,[status(thm)],[f_744_1]) ).

fof(f_744_3,plain,
    ! [U_2070] : collect_int(hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),U_2070)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2070),bot_bot_fun_int_bool),
    inference(definitional_conversion,[status(esa)],[f_744_2]) ).

cnf(f_744_4,plain,
    collect_int(hAPP_i1948725293t_bool(cOMBC_int_int_bool(fequal_int),U_2070)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2070),bot_bot_fun_int_bool),
    inference(clausify,[status(thm)],[f_744_3]) ).

fof(f_745_1,plain,
    ! [A_2] : collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_2)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool),
    inference(fof_nnf,[status(thm)],[fact_638_singleton__conv]) ).

fof(f_745_2,plain,
    ! [U_2071] : collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_2071)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2071),bot_bot_fun_nat_bool),
    inference(variable_rename,[status(thm)],[f_745_1]) ).

fof(f_745_3,plain,
    ! [U_2071] : collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_2071)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2071),bot_bot_fun_nat_bool),
    inference(definitional_conversion,[status(esa)],[f_745_2]) ).

cnf(f_745_4,plain,
    collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),U_2071)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2071),bot_bot_fun_nat_bool),
    inference(clausify,[status(thm)],[f_745_3]) ).

fof(f_746_1,plain,
    ! [A_2] : collect_a(hAPP_a_fun_a_bool(fequal_a,A_2)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),bot_bot_fun_a_bool),
    inference(fof_nnf,[status(thm)],[fact_639_singleton__conv2]) ).

fof(f_746_2,plain,
    ! [U_2072] : collect_a(hAPP_a_fun_a_bool(fequal_a,U_2072)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2072),bot_bot_fun_a_bool),
    inference(variable_rename,[status(thm)],[f_746_1]) ).

fof(f_746_3,plain,
    ! [U_2072] : collect_a(hAPP_a_fun_a_bool(fequal_a,U_2072)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2072),bot_bot_fun_a_bool),
    inference(definitional_conversion,[status(esa)],[f_746_2]) ).

cnf(f_746_4,plain,
    collect_a(hAPP_a_fun_a_bool(fequal_a,U_2072)) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2072),bot_bot_fun_a_bool),
    inference(clausify,[status(thm)],[f_746_3]) ).

fof(f_747_1,plain,
    ! [A_2] : collect_int(hAPP_i1948725293t_bool(fequal_int,A_2)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),bot_bot_fun_int_bool),
    inference(fof_nnf,[status(thm)],[fact_640_singleton__conv2]) ).

fof(f_747_2,plain,
    ! [U_2073] : collect_int(hAPP_i1948725293t_bool(fequal_int,U_2073)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2073),bot_bot_fun_int_bool),
    inference(variable_rename,[status(thm)],[f_747_1]) ).

fof(f_747_3,plain,
    ! [U_2073] : collect_int(hAPP_i1948725293t_bool(fequal_int,U_2073)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2073),bot_bot_fun_int_bool),
    inference(definitional_conversion,[status(esa)],[f_747_2]) ).

cnf(f_747_4,plain,
    collect_int(hAPP_i1948725293t_bool(fequal_int,U_2073)) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2073),bot_bot_fun_int_bool),
    inference(clausify,[status(thm)],[f_747_3]) ).

fof(f_748_1,plain,
    ! [A_2] : collect_nat(hAPP_n1699378549t_bool(fequal_nat,A_2)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),bot_bot_fun_nat_bool),
    inference(fof_nnf,[status(thm)],[fact_641_singleton__conv2]) ).

fof(f_748_2,plain,
    ! [U_2074] : collect_nat(hAPP_n1699378549t_bool(fequal_nat,U_2074)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2074),bot_bot_fun_nat_bool),
    inference(variable_rename,[status(thm)],[f_748_1]) ).

fof(f_748_3,plain,
    ! [U_2074] : collect_nat(hAPP_n1699378549t_bool(fequal_nat,U_2074)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2074),bot_bot_fun_nat_bool),
    inference(definitional_conversion,[status(esa)],[f_748_2]) ).

cnf(f_748_4,plain,
    collect_nat(hAPP_n1699378549t_bool(fequal_nat,U_2074)) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2074),bot_bot_fun_nat_bool),
    inference(clausify,[status(thm)],[f_748_3]) ).

fof(f_749_1,plain,
    ! [X_1,A] :
      ( hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)))) = hAPP_fun_a_bool_nat(finite_card_a,A)
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_642_card__Suc__Diff1]) ).

fof(f_749_2,plain,
    ! [U_2076,U_2075] :
      ( hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2075),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2076),bot_bot_fun_a_bool)))) = hAPP_fun_a_bool_nat(finite_card_a,U_2075)
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2076),U_2075))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2075)) ),
    inference(variable_rename,[status(thm)],[f_749_1]) ).

fof(f_749_3,plain,
    ! [U_2075,U_2076] :
      ( hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2075),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2076),bot_bot_fun_a_bool)))) = hAPP_fun_a_bool_nat(finite_card_a,U_2075)
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2076),U_2075))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2075)) ),
    inference(definitional_conversion,[status(esa)],[f_749_2]) ).

cnf(f_749_4,plain,
    ( hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2075),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2076),bot_bot_fun_a_bool)))) = hAPP_fun_a_bool_nat(finite_card_a,U_2075)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2076),U_2075))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2075)) ),
    inference(clausify,[status(thm)],[f_749_3]) ).

fof(f_750_1,plain,
    ! [X_1,A] :
      ( hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))) = hAPP_f957591787ol_nat(finite_card_int,A)
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_643_card__Suc__Diff1]) ).

fof(f_750_2,plain,
    ! [U_2078,U_2077] :
      ( hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2077),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2078),bot_bot_fun_int_bool)))) = hAPP_f957591787ol_nat(finite_card_int,U_2077)
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2078),U_2077))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2077)) ),
    inference(variable_rename,[status(thm)],[f_750_1]) ).

fof(f_750_3,plain,
    ! [U_2077,U_2078] :
      ( hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2077),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2078),bot_bot_fun_int_bool)))) = hAPP_f957591787ol_nat(finite_card_int,U_2077)
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2078),U_2077))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2077)) ),
    inference(definitional_conversion,[status(esa)],[f_750_2]) ).

cnf(f_750_4,plain,
    ( hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2077),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2078),bot_bot_fun_int_bool)))) = hAPP_f957591787ol_nat(finite_card_int,U_2077)
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2078),U_2077))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2077)) ),
    inference(clausify,[status(thm)],[f_750_3]) ).

fof(f_751_1,plain,
    ! [X_1,A] :
      ( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))) = hAPP_f22106695ol_nat(finite_card_nat,A)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_644_card__Suc__Diff1]) ).

fof(f_751_2,plain,
    ! [U_2080,U_2079] :
      ( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2079),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2080),bot_bot_fun_nat_bool)))) = hAPP_f22106695ol_nat(finite_card_nat,U_2079)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2080),U_2079))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2079)) ),
    inference(variable_rename,[status(thm)],[f_751_1]) ).

fof(f_751_3,plain,
    ! [U_2079,U_2080] :
      ( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2079),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2080),bot_bot_fun_nat_bool)))) = hAPP_f22106695ol_nat(finite_card_nat,U_2079)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2080),U_2079))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2079)) ),
    inference(definitional_conversion,[status(esa)],[f_751_2]) ).

cnf(f_751_4,plain,
    ( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2079),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2080),bot_bot_fun_nat_bool)))) = hAPP_f22106695ol_nat(finite_card_nat,U_2079)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2080),U_2079))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2079)) ),
    inference(clausify,[status(thm)],[f_751_3]) ).

fof(f_752_1,plain,
    ! [X_1,A] :
      ( hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))) = hAPP_f921600141ol_nat(finite_card_pname,A)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_645_card__Suc__Diff1]) ).

fof(f_752_2,plain,
    ! [U_2082,U_2081] :
      ( hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2081),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2082),bot_bo844097828e_bool)))) = hAPP_f921600141ol_nat(finite_card_pname,U_2081)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2082),U_2081))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2081)) ),
    inference(variable_rename,[status(thm)],[f_752_1]) ).

fof(f_752_3,plain,
    ! [U_2081,U_2082] :
      ( hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2081),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2082),bot_bo844097828e_bool)))) = hAPP_f921600141ol_nat(finite_card_pname,U_2081)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2082),U_2081))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2081)) ),
    inference(definitional_conversion,[status(esa)],[f_752_2]) ).

cnf(f_752_4,plain,
    ( hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2081),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2082),bot_bo844097828e_bool)))) = hAPP_f921600141ol_nat(finite_card_pname,U_2081)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2082),U_2081))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2081)) ),
    inference(clausify,[status(thm)],[f_752_3]) ).

fof(f_753_1,plain,
    ! [X_1,A] :
      ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_646_card__insert]) ).

fof(f_753_2,plain,
    ! [U_2084,U_2083] :
      ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2084),U_2083)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2083),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2084),bot_bot_fun_a_bool))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2083)) ),
    inference(variable_rename,[status(thm)],[f_753_1]) ).

fof(f_753_3,plain,
    ! [U_2083,U_2084] :
      ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2084),U_2083)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2083),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2084),bot_bot_fun_a_bool))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2083)) ),
    inference(definitional_conversion,[status(esa)],[f_753_2]) ).

cnf(f_753_4,plain,
    ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2084),U_2083)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2083),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2084),bot_bot_fun_a_bool))))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2083)) ),
    inference(clausify,[status(thm)],[f_753_3]) ).

fof(f_754_1,plain,
    ! [X_1,A] :
      ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_647_card__insert]) ).

fof(f_754_2,plain,
    ! [U_2086,U_2085] :
      ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2086),U_2085)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2085),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2086),bot_bot_fun_int_bool))))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2085)) ),
    inference(variable_rename,[status(thm)],[f_754_1]) ).

fof(f_754_3,plain,
    ! [U_2085,U_2086] :
      ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2086),U_2085)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2085),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2086),bot_bot_fun_int_bool))))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2085)) ),
    inference(definitional_conversion,[status(esa)],[f_754_2]) ).

cnf(f_754_4,plain,
    ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2086),U_2085)) = hAPP_nat_nat(suc,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2085),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2086),bot_bot_fun_int_bool))))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2085)) ),
    inference(clausify,[status(thm)],[f_754_3]) ).

fof(f_755_1,plain,
    ! [X_1,A] :
      ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_648_card__insert]) ).

fof(f_755_2,plain,
    ! [U_2088,U_2087] :
      ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2088),U_2087)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2087),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2088),bot_bot_fun_nat_bool))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2087)) ),
    inference(variable_rename,[status(thm)],[f_755_1]) ).

fof(f_755_3,plain,
    ! [U_2087,U_2088] :
      ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2088),U_2087)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2087),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2088),bot_bot_fun_nat_bool))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2087)) ),
    inference(definitional_conversion,[status(esa)],[f_755_2]) ).

cnf(f_755_4,plain,
    ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2088),U_2087)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2087),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2088),bot_bot_fun_nat_bool))))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2087)) ),
    inference(clausify,[status(thm)],[f_755_3]) ).

fof(f_756_1,plain,
    ! [X_1,A] :
      ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_649_card__insert]) ).

fof(f_756_2,plain,
    ! [U_2090,U_2089] :
      ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2090),U_2089)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2089),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2090),bot_bo844097828e_bool))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2089)) ),
    inference(variable_rename,[status(thm)],[f_756_1]) ).

fof(f_756_3,plain,
    ! [U_2089,U_2090] :
      ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2090),U_2089)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2089),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2090),bot_bo844097828e_bool))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2089)) ),
    inference(definitional_conversion,[status(esa)],[f_756_2]) ).

cnf(f_756_4,plain,
    ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2090),U_2089)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2089),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2090),bot_bo844097828e_bool))))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2089)) ),
    inference(clausify,[status(thm)],[f_756_3]) ).

fof(f_757_1,plain,
    ! [X_1,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)))),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_650_card__Diff1__le]) ).

fof(f_757_2,plain,
    ! [U_2092,U_2091] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2091),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2092),bot_bot_fun_a_bool)))),hAPP_fun_a_bool_nat(finite_card_a,U_2091)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2091)) ),
    inference(variable_rename,[status(thm)],[f_757_1]) ).

fof(f_757_3,plain,
    ! [U_2091,U_2092] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2091),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2092),bot_bot_fun_a_bool)))),hAPP_fun_a_bool_nat(finite_card_a,U_2091)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2091)) ),
    inference(definitional_conversion,[status(esa)],[f_757_2]) ).

cnf(f_757_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2091),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2092),bot_bot_fun_a_bool)))),hAPP_fun_a_bool_nat(finite_card_a,U_2091)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2091)) ),
    inference(clausify,[status(thm)],[f_757_3]) ).

fof(f_758_1,plain,
    ! [X_1,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)))),hAPP_f957591787ol_nat(finite_card_int,A)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_651_card__Diff1__le]) ).

fof(f_758_2,plain,
    ! [U_2094,U_2093] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2093),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2094),bot_bot_fun_int_bool)))),hAPP_f957591787ol_nat(finite_card_int,U_2093)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2093)) ),
    inference(variable_rename,[status(thm)],[f_758_1]) ).

fof(f_758_3,plain,
    ! [U_2093,U_2094] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2093),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2094),bot_bot_fun_int_bool)))),hAPP_f957591787ol_nat(finite_card_int,U_2093)))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2093)) ),
    inference(definitional_conversion,[status(esa)],[f_758_2]) ).

cnf(f_758_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2093),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2094),bot_bot_fun_int_bool)))),hAPP_f957591787ol_nat(finite_card_int,U_2093)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2093)) ),
    inference(clausify,[status(thm)],[f_758_3]) ).

fof(f_759_1,plain,
    ! [X_1,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)))),hAPP_f22106695ol_nat(finite_card_nat,A)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_652_card__Diff1__le]) ).

fof(f_759_2,plain,
    ! [U_2096,U_2095] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2095),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2096),bot_bot_fun_nat_bool)))),hAPP_f22106695ol_nat(finite_card_nat,U_2095)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2095)) ),
    inference(variable_rename,[status(thm)],[f_759_1]) ).

fof(f_759_3,plain,
    ! [U_2095,U_2096] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2095),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2096),bot_bot_fun_nat_bool)))),hAPP_f22106695ol_nat(finite_card_nat,U_2095)))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2095)) ),
    inference(definitional_conversion,[status(esa)],[f_759_2]) ).

cnf(f_759_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2095),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2096),bot_bot_fun_nat_bool)))),hAPP_f22106695ol_nat(finite_card_nat,U_2095)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2095)) ),
    inference(clausify,[status(thm)],[f_759_3]) ).

fof(f_760_1,plain,
    ! [X_1,A] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)))),hAPP_f921600141ol_nat(finite_card_pname,A)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_653_card__Diff1__le]) ).

fof(f_760_2,plain,
    ! [U_2098,U_2097] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2097),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2098),bot_bo844097828e_bool)))),hAPP_f921600141ol_nat(finite_card_pname,U_2097)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2097)) ),
    inference(variable_rename,[status(thm)],[f_760_1]) ).

fof(f_760_3,plain,
    ! [U_2097,U_2098] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2097),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2098),bot_bo844097828e_bool)))),hAPP_f921600141ol_nat(finite_card_pname,U_2097)))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2097)) ),
    inference(definitional_conversion,[status(esa)],[f_760_2]) ).

cnf(f_760_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2097),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2098),bot_bo844097828e_bool)))),hAPP_f921600141ol_nat(finite_card_pname,U_2097)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2097)) ),
    inference(clausify,[status(thm)],[f_760_3]) ).

fof(f_761_1,plain,
    ! [A,A_2,B] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),B))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B))) )
      & ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),B)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_654_finite__Diff__insert]) ).

fof(f_761_2,plain,
    ! [U_2101,U_2100,U_2099] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2101),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2100),U_2099))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2101),U_2099))) )
      & ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2101),U_2099)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2101),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2100),U_2099)))) ) ),
    inference(variable_rename,[status(thm)],[f_761_1]) ).

fof(f_761_3,plain,
    ( ! [U_2107,U_2105,U_2103] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2107),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2105),U_2103))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2107),U_2103))) )
    & ! [U_2106,U_2104,U_2102] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2106),U_2102)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2106),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2104),U_2102)))) ) ),
    inference(miniscope,[status(thm)],[f_761_2]) ).

fof(f_761_4,plain,
    ( ! [U_2103,U_2105,U_2107] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2107),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2105),U_2103))))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2107),U_2103))) )
    & ! [U_2104,U_2102,U_2106] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2106),U_2102)))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2106),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2104),U_2102)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_761_3]) ).

cnf(f_761_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2106),U_2102)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2106),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2104),U_2102)))) ),
    inference(clausify,[status(thm)],[f_761_4]) ).

cnf(f_761_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2107),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2105),U_2103))))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2107),U_2103))) ),
    inference(clausify,[status(thm)],[f_761_4]) ).

fof(f_762_1,plain,
    ! [A,A_2,B] :
      ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),B))))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))) )
      & ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),B)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_655_finite__Diff__insert]) ).

fof(f_762_2,plain,
    ! [U_2110,U_2109,U_2108] :
      ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2110),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2109),U_2108))))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2110),U_2108))) )
      & ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2110),U_2108)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2110),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2109),U_2108)))) ) ),
    inference(variable_rename,[status(thm)],[f_762_1]) ).

fof(f_762_3,plain,
    ( ! [U_2116,U_2114,U_2112] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2116),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2114),U_2112))))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2116),U_2112))) )
    & ! [U_2115,U_2113,U_2111] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2115),U_2111)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2115),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2113),U_2111)))) ) ),
    inference(miniscope,[status(thm)],[f_762_2]) ).

fof(f_762_4,plain,
    ( ! [U_2112,U_2114,U_2116] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2116),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2114),U_2112))))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2116),U_2112))) )
    & ! [U_2113,U_2111,U_2115] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2115),U_2111)))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2115),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2113),U_2111)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_762_3]) ).

cnf(f_762_5,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2115),U_2111)))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2115),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2113),U_2111)))) ),
    inference(clausify,[status(thm)],[f_762_4]) ).

cnf(f_762_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2116),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2114),U_2112))))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2116),U_2112))) ),
    inference(clausify,[status(thm)],[f_762_4]) ).

fof(f_763_1,plain,
    ! [A,A_2,B] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B))))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) )
      & ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_656_finite__Diff__insert]) ).

fof(f_763_2,plain,
    ! [U_2119,U_2118,U_2117] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2119),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2118),U_2117))))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2119),U_2117))) )
      & ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2119),U_2117)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2119),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2118),U_2117)))) ) ),
    inference(variable_rename,[status(thm)],[f_763_1]) ).

fof(f_763_3,plain,
    ( ! [U_2125,U_2123,U_2121] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2125),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2123),U_2121))))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2125),U_2121))) )
    & ! [U_2124,U_2122,U_2120] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2124),U_2120)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2124),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2122),U_2120)))) ) ),
    inference(miniscope,[status(thm)],[f_763_2]) ).

fof(f_763_4,plain,
    ( ! [U_2121,U_2123,U_2125] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2125),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2123),U_2121))))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2125),U_2121))) )
    & ! [U_2124,U_2122,U_2120] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2124),U_2120)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2124),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2122),U_2120)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_763_3]) ).

cnf(f_763_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2124),U_2120)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2124),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2122),U_2120)))) ),
    inference(clausify,[status(thm)],[f_763_4]) ).

cnf(f_763_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2125),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2123),U_2121))))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2125),U_2121))) ),
    inference(clausify,[status(thm)],[f_763_4]) ).

fof(f_764_1,plain,
    ! [A,A_2,B] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) )
      & ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_657_finite__Diff__insert]) ).

fof(f_764_2,plain,
    ! [U_2128,U_2127,U_2126] :
      ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2128),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2127),U_2126))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2128),U_2126))) )
      & ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2128),U_2126)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2128),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2127),U_2126)))) ) ),
    inference(variable_rename,[status(thm)],[f_764_1]) ).

fof(f_764_3,plain,
    ( ! [U_2134,U_2132,U_2130] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2134),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2132),U_2130))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2134),U_2130))) )
    & ! [U_2133,U_2131,U_2129] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2133),U_2129)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2133),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2131),U_2129)))) ) ),
    inference(miniscope,[status(thm)],[f_764_2]) ).

fof(f_764_4,plain,
    ( ! [U_2130,U_2132,U_2134] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2134),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2132),U_2130))))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2134),U_2130))) )
    & ! [U_2131,U_2129,U_2133] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2133),U_2129)))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2133),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2131),U_2129)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_764_3]) ).

cnf(f_764_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2133),U_2129)))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2133),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2131),U_2129)))) ),
    inference(clausify,[status(thm)],[f_764_4]) ).

cnf(f_764_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2134),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2132),U_2130))))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2134),U_2130))) ),
    inference(clausify,[status(thm)],[f_764_4]) ).

fof(f_765_1,plain,
    ! [F,A,B] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,image_nat_int(F,A)),image_nat_int(F,B))),image_nat_int(F,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)))),
    inference(fof_nnf,[status(thm)],[fact_658_image__diff__subset]) ).

fof(f_765_2,plain,
    ! [U_2137,U_2136,U_2135] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,image_nat_int(U_2137,U_2136)),image_nat_int(U_2137,U_2135))),image_nat_int(U_2137,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2136),U_2135)))),
    inference(variable_rename,[status(thm)],[f_765_1]) ).

fof(f_765_3,plain,
    ! [U_2135,U_2136,U_2137] : hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,image_nat_int(U_2137,U_2136)),image_nat_int(U_2137,U_2135))),image_nat_int(U_2137,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2136),U_2135)))),
    inference(definitional_conversion,[status(esa)],[f_765_2]) ).

cnf(f_765_4,plain,
    hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,image_nat_int(U_2137,U_2136)),image_nat_int(U_2137,U_2135))),image_nat_int(U_2137,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2136),U_2135)))),
    inference(clausify,[status(thm)],[f_765_3]) ).

fof(f_766_1,plain,
    ! [F,A,B] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,image_pname_a(F,A)),image_pname_a(F,B))),image_pname_a(F,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))),
    inference(fof_nnf,[status(thm)],[fact_659_image__diff__subset]) ).

fof(f_766_2,plain,
    ! [U_2140,U_2139,U_2138] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,image_pname_a(U_2140,U_2139)),image_pname_a(U_2140,U_2138))),image_pname_a(U_2140,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2139),U_2138)))),
    inference(variable_rename,[status(thm)],[f_766_1]) ).

fof(f_766_3,plain,
    ! [U_2138,U_2139,U_2140] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,image_pname_a(U_2140,U_2139)),image_pname_a(U_2140,U_2138))),image_pname_a(U_2140,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2139),U_2138)))),
    inference(definitional_conversion,[status(esa)],[f_766_2]) ).

cnf(f_766_4,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,image_pname_a(U_2140,U_2139)),image_pname_a(U_2140,U_2138))),image_pname_a(U_2140,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2139),U_2138)))),
    inference(clausify,[status(thm)],[f_766_3]) ).

fof(f_767_1,plain,
    ! [A,X_1] :
      ( A = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)
      | A = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)))
      | ~ is_fun_a_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_660_subset__singletonD]) ).

fof(f_767_2,plain,
    ! [U_2142,U_2141] :
      ( U_2142 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2141),bot_bot_fun_a_bool)
      | U_2142 = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2142),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2141),bot_bot_fun_a_bool)))
      | ~ is_fun_a_bool(U_2142) ),
    inference(variable_rename,[status(thm)],[f_767_1]) ).

fof(f_767_3,plain,
    ! [U_2142] :
      ( ! [U_2141] :
          ( U_2142 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2141),bot_bot_fun_a_bool)
          | U_2142 = bot_bot_fun_a_bool
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2142),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2141),bot_bot_fun_a_bool))) )
      | ~ is_fun_a_bool(U_2142) ),
    inference(miniscope,[status(thm)],[f_767_2]) ).

fof(f_767_4,plain,
    ! [U_2141,U_2142] :
      ( U_2142 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2141),bot_bot_fun_a_bool)
      | U_2142 = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2142),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2141),bot_bot_fun_a_bool)))
      | ~ is_fun_a_bool(U_2142) ),
    inference(definitional_conversion,[status(esa)],[f_767_3]) ).

cnf(f_767_5,plain,
    ( U_2142 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2141),bot_bot_fun_a_bool)
    | U_2142 = bot_bot_fun_a_bool
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2142),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2141),bot_bot_fun_a_bool)))
    | ~ is_fun_a_bool(U_2142) ),
    inference(clausify,[status(thm)],[f_767_4]) ).

fof(f_768_1,plain,
    ! [A,X_1] :
      ( A = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)
      | A = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) ),
    inference(fof_nnf,[status(thm)],[fact_661_subset__singletonD]) ).

fof(f_768_2,plain,
    ! [U_2144,U_2143] :
      ( U_2144 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2143),bot_bot_fun_nat_bool)
      | U_2144 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2144),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2143),bot_bot_fun_nat_bool))) ),
    inference(variable_rename,[status(thm)],[f_768_1]) ).

fof(f_768_3,plain,
    ! [U_2143,U_2144] :
      ( U_2144 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2143),bot_bot_fun_nat_bool)
      | U_2144 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2144),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2143),bot_bot_fun_nat_bool))) ),
    inference(definitional_conversion,[status(esa)],[f_768_2]) ).

cnf(f_768_4,plain,
    ( U_2144 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2143),bot_bot_fun_nat_bool)
    | U_2144 = bot_bot_fun_nat_bool
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2144),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2143),bot_bot_fun_nat_bool))) ),
    inference(clausify,[status(thm)],[f_768_3]) ).

fof(f_769_1,plain,
    ! [A,X_1] :
      ( A = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)
      | A = bot_bot_fun_int_bool
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))) ),
    inference(fof_nnf,[status(thm)],[fact_662_subset__singletonD]) ).

fof(f_769_2,plain,
    ! [U_2146,U_2145] :
      ( U_2146 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2145),bot_bot_fun_int_bool)
      | U_2146 = bot_bot_fun_int_bool
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2146),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2145),bot_bot_fun_int_bool))) ),
    inference(variable_rename,[status(thm)],[f_769_1]) ).

fof(f_769_3,plain,
    ! [U_2146,U_2145] :
      ( U_2146 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2145),bot_bot_fun_int_bool)
      | U_2146 = bot_bot_fun_int_bool
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2146),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2145),bot_bot_fun_int_bool))) ),
    inference(definitional_conversion,[status(esa)],[f_769_2]) ).

cnf(f_769_4,plain,
    ( U_2146 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2145),bot_bot_fun_int_bool)
    | U_2146 = bot_bot_fun_int_bool
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2146),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2145),bot_bot_fun_int_bool))) ),
    inference(clausify,[status(thm)],[f_769_3]) ).

fof(f_770_1,plain,
    ! [F1,F2,Nat_3] : hAPP_nat_nat(nat_case_nat(F1,F2),hAPP_nat_nat(suc,Nat_3)) = hAPP_nat_nat(F2,Nat_3),
    inference(fof_nnf,[status(thm)],[fact_663_nat__case__Suc]) ).

fof(f_770_2,plain,
    ! [U_2149,U_2148,U_2147] : hAPP_nat_nat(nat_case_nat(U_2149,U_2148),hAPP_nat_nat(suc,U_2147)) = hAPP_nat_nat(U_2148,U_2147),
    inference(variable_rename,[status(thm)],[f_770_1]) ).

fof(f_770_3,plain,
    ! [U_2147,U_2148,U_2149] : hAPP_nat_nat(nat_case_nat(U_2149,U_2148),hAPP_nat_nat(suc,U_2147)) = hAPP_nat_nat(U_2148,U_2147),
    inference(definitional_conversion,[status(esa)],[f_770_2]) ).

cnf(f_770_4,plain,
    hAPP_nat_nat(nat_case_nat(U_2149,U_2148),hAPP_nat_nat(suc,U_2147)) = hAPP_nat_nat(U_2148,U_2147),
    inference(clausify,[status(thm)],[f_770_3]) ).

fof(f_771_1,plain,
    ! [F1,F2,Nat_3] :
      ( ( hBOOL(hAPP_nat_bool(nat_case_bool(F1,F2),hAPP_nat_nat(suc,Nat_3)))
        | ~ hBOOL(hAPP_nat_bool(F2,Nat_3)) )
      & ( hBOOL(hAPP_nat_bool(F2,Nat_3))
        | ~ hBOOL(hAPP_nat_bool(nat_case_bool(F1,F2),hAPP_nat_nat(suc,Nat_3))) ) ),
    inference(fof_nnf,[status(thm)],[fact_664_nat__case__Suc]) ).

fof(f_771_2,plain,
    ! [U_2152,U_2151,U_2150] :
      ( ( hBOOL(hAPP_nat_bool(nat_case_bool(U_2152,U_2151),hAPP_nat_nat(suc,U_2150)))
        | ~ hBOOL(hAPP_nat_bool(U_2151,U_2150)) )
      & ( hBOOL(hAPP_nat_bool(U_2151,U_2150))
        | ~ hBOOL(hAPP_nat_bool(nat_case_bool(U_2152,U_2151),hAPP_nat_nat(suc,U_2150))) ) ),
    inference(variable_rename,[status(thm)],[f_771_1]) ).

fof(f_771_3,plain,
    ( ! [U_2158,U_2156,U_2154] :
        ( hBOOL(hAPP_nat_bool(nat_case_bool(U_2158,U_2156),hAPP_nat_nat(suc,U_2154)))
        | ~ hBOOL(hAPP_nat_bool(U_2156,U_2154)) )
    & ! [U_2157,U_2155,U_2153] :
        ( hBOOL(hAPP_nat_bool(U_2155,U_2153))
        | ~ hBOOL(hAPP_nat_bool(nat_case_bool(U_2157,U_2155),hAPP_nat_nat(suc,U_2153))) ) ),
    inference(miniscope,[status(thm)],[f_771_2]) ).

fof(f_771_4,plain,
    ( ! [U_2154,U_2156,U_2158] :
        ( hBOOL(hAPP_nat_bool(nat_case_bool(U_2158,U_2156),hAPP_nat_nat(suc,U_2154)))
        | ~ hBOOL(hAPP_nat_bool(U_2156,U_2154)) )
    & ! [U_2157,U_2155,U_2153] :
        ( hBOOL(hAPP_nat_bool(U_2155,U_2153))
        | ~ hBOOL(hAPP_nat_bool(nat_case_bool(U_2157,U_2155),hAPP_nat_nat(suc,U_2153))) ) ),
    inference(definitional_conversion,[status(esa)],[f_771_3]) ).

cnf(f_771_5,plain,
    ( hBOOL(hAPP_nat_bool(U_2155,U_2153))
    | ~ hBOOL(hAPP_nat_bool(nat_case_bool(U_2157,U_2155),hAPP_nat_nat(suc,U_2153))) ),
    inference(clausify,[status(thm)],[f_771_4]) ).

cnf(f_771_6,plain,
    ( hBOOL(hAPP_nat_bool(nat_case_bool(U_2158,U_2156),hAPP_nat_nat(suc,U_2154)))
    | ~ hBOOL(hAPP_nat_bool(U_2156,U_2154)) ),
    inference(clausify,[status(thm)],[f_771_4]) ).

fof(f_772_1,plain,
    ! [C_6,X_1,A] :
      ( image_nat_int(cOMBK_int_nat(C_6),A) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,C_6),bot_bot_fun_int_bool)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) ),
    inference(fof_nnf,[status(thm)],[fact_665_image__constant]) ).

fof(f_772_2,plain,
    ! [U_2161,U_2160,U_2159] :
      ( image_nat_int(cOMBK_int_nat(U_2161),U_2159) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2161),bot_bot_fun_int_bool)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2160),U_2159)) ),
    inference(variable_rename,[status(thm)],[f_772_1]) ).

fof(f_772_3,plain,
    ! [U_2159,U_2160,U_2161] :
      ( image_nat_int(cOMBK_int_nat(U_2161),U_2159) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2161),bot_bot_fun_int_bool)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2160),U_2159)) ),
    inference(definitional_conversion,[status(esa)],[f_772_2]) ).

cnf(f_772_4,plain,
    ( image_nat_int(cOMBK_int_nat(U_2161),U_2159) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2161),bot_bot_fun_int_bool)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2160),U_2159)) ),
    inference(clausify,[status(thm)],[f_772_3]) ).

fof(f_773_1,plain,
    ! [C_6,X_1,A] :
      ( image_pname_a(cOMBK_a_pname(C_6),A) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,C_6),bot_bot_fun_a_bool)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) ),
    inference(fof_nnf,[status(thm)],[fact_666_image__constant]) ).

fof(f_773_2,plain,
    ! [U_2164,U_2163,U_2162] :
      ( image_pname_a(cOMBK_a_pname(U_2164),U_2162) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2164),bot_bot_fun_a_bool)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2163),U_2162)) ),
    inference(variable_rename,[status(thm)],[f_773_1]) ).

fof(f_773_3,plain,
    ! [U_2162,U_2163,U_2164] :
      ( image_pname_a(cOMBK_a_pname(U_2164),U_2162) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2164),bot_bot_fun_a_bool)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2163),U_2162)) ),
    inference(definitional_conversion,[status(esa)],[f_773_2]) ).

cnf(f_773_4,plain,
    ( image_pname_a(cOMBK_a_pname(U_2164),U_2162) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2164),bot_bot_fun_a_bool)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2163),U_2162)) ),
    inference(clausify,[status(thm)],[f_773_3]) ).

fof(f_774_1,plain,
    ! [C_6,A] :
      ( ( image_nat_int(cOMBK_int_nat(C_6),A) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,C_6),bot_bot_fun_int_bool)
        | A = bot_bot_fun_nat_bool )
      & ( image_nat_int(cOMBK_int_nat(C_6),A) = bot_bot_fun_int_bool
        | A != bot_bot_fun_nat_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_667_image__constant__conv]) ).

fof(f_774_2,plain,
    ! [U_2166,U_2165] :
      ( ( image_nat_int(cOMBK_int_nat(U_2166),U_2165) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2166),bot_bot_fun_int_bool)
        | U_2165 = bot_bot_fun_nat_bool )
      & ( image_nat_int(cOMBK_int_nat(U_2166),U_2165) = bot_bot_fun_int_bool
        | U_2165 != bot_bot_fun_nat_bool ) ),
    inference(variable_rename,[status(thm)],[f_774_1]) ).

fof(f_774_3,plain,
    ( ! [U_2170,U_2168] :
        ( image_nat_int(cOMBK_int_nat(U_2170),U_2168) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2170),bot_bot_fun_int_bool)
        | U_2168 = bot_bot_fun_nat_bool )
    & ! [U_2169,U_2167] :
        ( image_nat_int(cOMBK_int_nat(U_2169),U_2167) = bot_bot_fun_int_bool
        | U_2167 != bot_bot_fun_nat_bool ) ),
    inference(miniscope,[status(thm)],[f_774_2]) ).

fof(f_774_4,plain,
    ( ! [U_2168,U_2170] :
        ( image_nat_int(cOMBK_int_nat(U_2170),U_2168) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2170),bot_bot_fun_int_bool)
        | U_2168 = bot_bot_fun_nat_bool )
    & ! [U_2169,U_2167] :
        ( image_nat_int(cOMBK_int_nat(U_2169),U_2167) = bot_bot_fun_int_bool
        | U_2167 != bot_bot_fun_nat_bool ) ),
    inference(definitional_conversion,[status(esa)],[f_774_3]) ).

cnf(f_774_5,plain,
    ( image_nat_int(cOMBK_int_nat(U_2169),U_2167) = bot_bot_fun_int_bool
    | U_2167 != bot_bot_fun_nat_bool ),
    inference(clausify,[status(thm)],[f_774_4]) ).

cnf(f_774_6,plain,
    ( image_nat_int(cOMBK_int_nat(U_2170),U_2168) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2170),bot_bot_fun_int_bool)
    | U_2168 = bot_bot_fun_nat_bool ),
    inference(clausify,[status(thm)],[f_774_4]) ).

fof(f_775_1,plain,
    ! [C_6,A] :
      ( ( ( image_pname_a(cOMBK_a_pname(C_6),A) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,C_6),bot_bot_fun_a_bool)
          | A = bot_bo844097828e_bool )
        & ( image_pname_a(cOMBK_a_pname(C_6),A) = bot_bot_fun_a_bool
          | A != bot_bo844097828e_bool ) )
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_668_image__constant__conv]) ).

fof(f_775_2,plain,
    ! [U_2172,U_2171] :
      ( ( ( image_pname_a(cOMBK_a_pname(U_2172),U_2171) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2172),bot_bot_fun_a_bool)
          | U_2171 = bot_bo844097828e_bool )
        & ( image_pname_a(cOMBK_a_pname(U_2172),U_2171) = bot_bot_fun_a_bool
          | U_2171 != bot_bo844097828e_bool ) )
      | ~ is_fun_pname_bool(U_2171) ),
    inference(variable_rename,[status(thm)],[f_775_1]) ).

fof(f_775_3,plain,
    ( ! [U_2171,U_2172] :
        ( image_pname_a(cOMBK_a_pname(U_2172),U_2171) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2172),bot_bot_fun_a_bool)
        | U_2171 = bot_bo844097828e_bool
        | ~ sP186(U_2171,U_2172) )
    & ! [U_2171,U_2172] :
        ( image_pname_a(cOMBK_a_pname(U_2172),U_2171) = bot_bot_fun_a_bool
        | U_2171 != bot_bo844097828e_bool
        | ~ sP186(U_2171,U_2172) )
    & ! [U_2171,U_2172] :
        ( sP186(U_2171,U_2172)
        | ~ is_fun_pname_bool(U_2171) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP186])],[f_775_2]) ).

cnf(f_775_4,plain,
    ( sP186(U_2171,U_2172)
    | ~ is_fun_pname_bool(U_2171) ),
    inference(clausify,[status(thm)],[f_775_3]) ).

cnf(f_775_5,plain,
    ( image_pname_a(cOMBK_a_pname(U_2172),U_2171) = bot_bot_fun_a_bool
    | U_2171 != bot_bo844097828e_bool
    | ~ sP186(U_2171,U_2172) ),
    inference(clausify,[status(thm)],[f_775_3]) ).

cnf(f_775_6,plain,
    ( image_pname_a(cOMBK_a_pname(U_2172),U_2171) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2172),bot_bot_fun_a_bool)
    | U_2171 = bot_bo844097828e_bool
    | ~ sP186(U_2171,U_2172) ),
    inference(clausify,[status(thm)],[f_775_3]) ).

fof(f_776_1,plain,
    ! [A_2,B_3,C_6,D_1] :
      ( ( ( A_2 = B_3
          | C_6 != D_1 )
        & ( C_6 = D_1
          | A_2 != B_3 ) )
      | hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_2),B_3) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,C_6),D_1) ),
    inference(fof_nnf,[status(thm)],[fact_669_diff__eq__diff__eq]) ).

fof(f_776_2,plain,
    ! [U_2176,U_2175,U_2174,U_2173] :
      ( ( ( U_2176 = U_2175
          | U_2174 != U_2173 )
        & ( U_2174 = U_2173
          | U_2176 != U_2175 ) )
      | hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_2176),U_2175) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_2174),U_2173) ),
    inference(variable_rename,[status(thm)],[f_776_1]) ).

fof(f_776_3,plain,
    ( ! [U_2176,U_2175,U_2174,U_2173] :
        ( U_2176 = U_2175
        | U_2174 != U_2173
        | ~ sP187(U_2176,U_2175,U_2174,U_2173) )
    & ! [U_2176,U_2175,U_2174,U_2173] :
        ( U_2174 = U_2173
        | U_2176 != U_2175
        | ~ sP187(U_2176,U_2175,U_2174,U_2173) )
    & ! [U_2176,U_2175,U_2174,U_2173] :
        ( sP187(U_2176,U_2175,U_2174,U_2173)
        | hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_2176),U_2175) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_2174),U_2173) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP187])],[f_776_2]) ).

cnf(f_776_4,plain,
    ( sP187(U_2176,U_2175,U_2174,U_2173)
    | hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_2176),U_2175) != hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_2174),U_2173) ),
    inference(clausify,[status(thm)],[f_776_3]) ).

cnf(f_776_5,plain,
    ( U_2174 = U_2173
    | U_2176 != U_2175
    | ~ sP187(U_2176,U_2175,U_2174,U_2173) ),
    inference(clausify,[status(thm)],[f_776_3]) ).

cnf(f_776_6,plain,
    ( U_2176 = U_2175
    | U_2174 != U_2173
    | ~ sP187(U_2176,U_2175,U_2174,U_2173) ),
    inference(clausify,[status(thm)],[f_776_3]) ).

fof(f_777_1,plain,
    ! [A,B] :
      ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,A)),hAPP_f957591787ol_nat(finite_card_int,B))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) ),
    inference(fof_nnf,[status(thm)],[fact_670_card__Diff__subset]) ).

fof(f_777_2,plain,
    ! [U_2178,U_2177] :
      ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2178),U_2177)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,U_2178)),hAPP_f957591787ol_nat(finite_card_int,U_2177))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2177),U_2178))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2177)) ),
    inference(variable_rename,[status(thm)],[f_777_1]) ).

fof(f_777_3,plain,
    ! [U_2178,U_2177] :
      ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2178),U_2177)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,U_2178)),hAPP_f957591787ol_nat(finite_card_int,U_2177))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2177),U_2178))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2177)) ),
    inference(definitional_conversion,[status(esa)],[f_777_2]) ).

cnf(f_777_4,plain,
    ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2178),U_2177)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,U_2178)),hAPP_f957591787ol_nat(finite_card_int,U_2177))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2177),U_2178))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2177)) ),
    inference(clausify,[status(thm)],[f_777_3]) ).

fof(f_778_1,plain,
    ! [A,B] :
      ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_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,B),A))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) ),
    inference(fof_nnf,[status(thm)],[fact_671_card__Diff__subset]) ).

fof(f_778_2,plain,
    ! [U_2180,U_2179] :
      ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2180),U_2179)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,U_2180)),hAPP_f22106695ol_nat(finite_card_nat,U_2179))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2179),U_2180))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2179)) ),
    inference(variable_rename,[status(thm)],[f_778_1]) ).

fof(f_778_3,plain,
    ! [U_2179,U_2180] :
      ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2180),U_2179)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,U_2180)),hAPP_f22106695ol_nat(finite_card_nat,U_2179))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2179),U_2180))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2179)) ),
    inference(definitional_conversion,[status(esa)],[f_778_2]) ).

cnf(f_778_4,plain,
    ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2180),U_2179)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,U_2180)),hAPP_f22106695ol_nat(finite_card_nat,U_2179))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2179),U_2180))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2179)) ),
    inference(clausify,[status(thm)],[f_778_3]) ).

fof(f_779_1,plain,
    ! [A,B] :
      ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_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,B),A))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) ),
    inference(fof_nnf,[status(thm)],[fact_672_card__Diff__subset]) ).

fof(f_779_2,plain,
    ! [U_2182,U_2181] :
      ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2182),U_2181)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,U_2182)),hAPP_fun_a_bool_nat(finite_card_a,U_2181))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2181),U_2182))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2181)) ),
    inference(variable_rename,[status(thm)],[f_779_1]) ).

fof(f_779_3,plain,
    ! [U_2181,U_2182] :
      ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2182),U_2181)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,U_2182)),hAPP_fun_a_bool_nat(finite_card_a,U_2181))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2181),U_2182))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2181)) ),
    inference(definitional_conversion,[status(esa)],[f_779_2]) ).

cnf(f_779_4,plain,
    ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2182),U_2181)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,U_2182)),hAPP_fun_a_bool_nat(finite_card_a,U_2181))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2181),U_2182))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2181)) ),
    inference(clausify,[status(thm)],[f_779_3]) ).

fof(f_780_1,plain,
    ! [A,B] :
      ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_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,B),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ),
    inference(fof_nnf,[status(thm)],[fact_673_card__Diff__subset]) ).

fof(f_780_2,plain,
    ! [U_2184,U_2183] :
      ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2184),U_2183)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,U_2184)),hAPP_f921600141ol_nat(finite_card_pname,U_2183))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_2183),U_2184))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2183)) ),
    inference(variable_rename,[status(thm)],[f_780_1]) ).

fof(f_780_3,plain,
    ! [U_2183,U_2184] :
      ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2184),U_2183)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,U_2184)),hAPP_f921600141ol_nat(finite_card_pname,U_2183))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_2183),U_2184))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2183)) ),
    inference(definitional_conversion,[status(esa)],[f_780_2]) ).

cnf(f_780_4,plain,
    ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2184),U_2183)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,U_2184)),hAPP_f921600141ol_nat(finite_card_pname,U_2183))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_2183),U_2184))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2183)) ),
    inference(clausify,[status(thm)],[f_780_3]) ).

fof(f_781_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,A)),hAPP_f957591787ol_nat(finite_card_int,B))),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,B)) ),
    inference(fof_nnf,[status(thm)],[fact_674_diff__card__le__card__Diff]) ).

fof(f_781_2,plain,
    ! [U_2186,U_2185] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,U_2186)),hAPP_f957591787ol_nat(finite_card_int,U_2185))),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2186),U_2185))))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2185)) ),
    inference(variable_rename,[status(thm)],[f_781_1]) ).

fof(f_781_3,plain,
    ! [U_2185,U_2186] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,U_2186)),hAPP_f957591787ol_nat(finite_card_int,U_2185))),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2186),U_2185))))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2185)) ),
    inference(definitional_conversion,[status(esa)],[f_781_2]) ).

cnf(f_781_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,U_2186)),hAPP_f957591787ol_nat(finite_card_int,U_2185))),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2186),U_2185))))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2185)) ),
    inference(clausify,[status(thm)],[f_781_3]) ).

fof(f_782_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,A)),hAPP_f22106695ol_nat(finite_card_nat,B))),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B)) ),
    inference(fof_nnf,[status(thm)],[fact_675_diff__card__le__card__Diff]) ).

fof(f_782_2,plain,
    ! [U_2188,U_2187] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,U_2188)),hAPP_f22106695ol_nat(finite_card_nat,U_2187))),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2188),U_2187))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2187)) ),
    inference(variable_rename,[status(thm)],[f_782_1]) ).

fof(f_782_3,plain,
    ! [U_2187,U_2188] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,U_2188)),hAPP_f22106695ol_nat(finite_card_nat,U_2187))),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2188),U_2187))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2187)) ),
    inference(definitional_conversion,[status(esa)],[f_782_2]) ).

cnf(f_782_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,U_2188)),hAPP_f22106695ol_nat(finite_card_nat,U_2187))),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2188),U_2187))))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2187)) ),
    inference(clausify,[status(thm)],[f_782_3]) ).

fof(f_783_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,A)),hAPP_fun_a_bool_nat(finite_card_a,B))),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) ),
    inference(fof_nnf,[status(thm)],[fact_676_diff__card__le__card__Diff]) ).

fof(f_783_2,plain,
    ! [U_2190,U_2189] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,U_2190)),hAPP_fun_a_bool_nat(finite_card_a,U_2189))),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2190),U_2189))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2189)) ),
    inference(variable_rename,[status(thm)],[f_783_1]) ).

fof(f_783_3,plain,
    ! [U_2189,U_2190] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,U_2190)),hAPP_fun_a_bool_nat(finite_card_a,U_2189))),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2190),U_2189))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2189)) ),
    inference(definitional_conversion,[status(esa)],[f_783_2]) ).

cnf(f_783_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,U_2190)),hAPP_fun_a_bool_nat(finite_card_a,U_2189))),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2190),U_2189))))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2189)) ),
    inference(clausify,[status(thm)],[f_783_3]) ).

fof(f_784_1,plain,
    ! [A,B] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,A)),hAPP_f921600141ol_nat(finite_card_pname,B))),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B)) ),
    inference(fof_nnf,[status(thm)],[fact_677_diff__card__le__card__Diff]) ).

fof(f_784_2,plain,
    ! [U_2192,U_2191] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,U_2192)),hAPP_f921600141ol_nat(finite_card_pname,U_2191))),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2192),U_2191))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2191)) ),
    inference(variable_rename,[status(thm)],[f_784_1]) ).

fof(f_784_3,plain,
    ! [U_2191,U_2192] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,U_2192)),hAPP_f921600141ol_nat(finite_card_pname,U_2191))),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2192),U_2191))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2191)) ),
    inference(definitional_conversion,[status(esa)],[f_784_2]) ).

cnf(f_784_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,U_2192)),hAPP_f921600141ol_nat(finite_card_pname,U_2191))),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2192),U_2191))))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2191)) ),
    inference(clausify,[status(thm)],[f_784_3]) ).

fof(f_785_1,plain,
    ! [Pa,A,F_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(Pa,F_1))
      | ? [A_14,F_2] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(Pa,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_14),F_2)))
          & hBOOL(hAPP_fun_a_bool_bool(Pa,F_2))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_14),F_2))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_14),A))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_2))
          & is_fun_a_bool(F_2)
          & is_a(A_14) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(Pa,bot_bot_fun_a_bool))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,F_1),A))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_678_finite__subset__induct]) ).

fof(f_785_2,plain,
    ! [U_2197,U_2196,U_2195] :
      ( hBOOL(hAPP_fun_a_bool_bool(U_2197,U_2195))
      | ? [U_2194,U_2193] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2197,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2194),U_2193)))
          & hBOOL(hAPP_fun_a_bool_bool(U_2197,U_2193))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2194),U_2193))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2194),U_2196))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2193))
          & is_fun_a_bool(U_2193)
          & is_a(U_2194) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(U_2197,bot_bot_fun_a_bool))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2195),U_2196))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2195)) ),
    inference(variable_rename,[status(thm)],[f_785_1]) ).

fof(f_785_3,plain,
    ! [U_2197,U_2196,U_2195] :
      ( hBOOL(hAPP_fun_a_bool_bool(U_2197,U_2195))
      | ? [U_2193] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2197,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK101(U_2197,U_2196,U_2195)),U_2193)))
          & hBOOL(hAPP_fun_a_bool_bool(U_2197,U_2193))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK101(U_2197,U_2196,U_2195)),U_2193))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK101(U_2197,U_2196,U_2195)),U_2196))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2193))
          & is_fun_a_bool(U_2193)
          & is_a(sK101(U_2197,U_2196,U_2195)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(U_2197,bot_bot_fun_a_bool))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2195),U_2196))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2195)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_2194,sK101(U_2197,U_2196,U_2195))],[f_785_2]) ).

fof(f_785_4,plain,
    ! [U_2197,U_2196,U_2195] :
      ( hBOOL(hAPP_fun_a_bool_bool(U_2197,U_2195))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2197,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK101(U_2197,U_2196,U_2195)),sK102(U_2197,U_2196,U_2195))))
        & hBOOL(hAPP_fun_a_bool_bool(U_2197,sK102(U_2197,U_2196,U_2195)))
        & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK101(U_2197,U_2196,U_2195)),sK102(U_2197,U_2196,U_2195)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK101(U_2197,U_2196,U_2195)),U_2196))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK102(U_2197,U_2196,U_2195)))
        & is_fun_a_bool(sK102(U_2197,U_2196,U_2195))
        & is_a(sK101(U_2197,U_2196,U_2195)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(U_2197,bot_bot_fun_a_bool))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2195),U_2196))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2195)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_2193,sK102(U_2197,U_2196,U_2195))],[f_785_3]) ).

fof(f_785_5,plain,
    ( ! [U_2197,U_2195,U_2196] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2197,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK101(U_2197,U_2196,U_2195)),sK102(U_2197,U_2196,U_2195))))
        | ~ sP188(U_2197,U_2195,U_2196) )
    & ! [U_2197,U_2195,U_2196] :
        ( hBOOL(hAPP_fun_a_bool_bool(U_2197,sK102(U_2197,U_2196,U_2195)))
        | ~ sP188(U_2197,U_2195,U_2196) )
    & ! [U_2197,U_2195,U_2196] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK101(U_2197,U_2196,U_2195)),sK102(U_2197,U_2196,U_2195)))
        | ~ sP188(U_2197,U_2195,U_2196) )
    & ! [U_2197,U_2195,U_2196] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK101(U_2197,U_2196,U_2195)),U_2196))
        | ~ sP188(U_2197,U_2195,U_2196) )
    & ! [U_2197,U_2195,U_2196] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK102(U_2197,U_2196,U_2195)))
        | ~ sP188(U_2197,U_2195,U_2196) )
    & ! [U_2197,U_2195,U_2196] :
        ( is_fun_a_bool(sK102(U_2197,U_2196,U_2195))
        | ~ sP188(U_2197,U_2195,U_2196) )
    & ! [U_2197,U_2195,U_2196] :
        ( is_a(sK101(U_2197,U_2196,U_2195))
        | ~ sP188(U_2197,U_2195,U_2196) )
    & ! [U_2197,U_2195,U_2196] :
        ( hBOOL(hAPP_fun_a_bool_bool(U_2197,U_2195))
        | sP188(U_2197,U_2195,U_2196)
        | ~ hBOOL(hAPP_fun_a_bool_bool(U_2197,bot_bot_fun_a_bool))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2195),U_2196))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2195)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP188])],[f_785_4]) ).

cnf(f_785_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(U_2197,U_2195))
    | sP188(U_2197,U_2195,U_2196)
    | ~ hBOOL(hAPP_fun_a_bool_bool(U_2197,bot_bot_fun_a_bool))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2195),U_2196))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2195)) ),
    inference(clausify,[status(thm)],[f_785_5]) ).

cnf(f_785_7,plain,
    ( is_a(sK101(U_2197,U_2196,U_2195))
    | ~ sP188(U_2197,U_2195,U_2196) ),
    inference(clausify,[status(thm)],[f_785_5]) ).

cnf(f_785_8,plain,
    ( is_fun_a_bool(sK102(U_2197,U_2196,U_2195))
    | ~ sP188(U_2197,U_2195,U_2196) ),
    inference(clausify,[status(thm)],[f_785_5]) ).

cnf(f_785_9,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK102(U_2197,U_2196,U_2195)))
    | ~ sP188(U_2197,U_2195,U_2196) ),
    inference(clausify,[status(thm)],[f_785_5]) ).

cnf(f_785_10,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK101(U_2197,U_2196,U_2195)),U_2196))
    | ~ sP188(U_2197,U_2195,U_2196) ),
    inference(clausify,[status(thm)],[f_785_5]) ).

cnf(f_785_11,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK101(U_2197,U_2196,U_2195)),sK102(U_2197,U_2196,U_2195)))
    | ~ sP188(U_2197,U_2195,U_2196) ),
    inference(clausify,[status(thm)],[f_785_5]) ).

cnf(f_785_12,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(U_2197,sK102(U_2197,U_2196,U_2195)))
    | ~ sP188(U_2197,U_2195,U_2196) ),
    inference(clausify,[status(thm)],[f_785_5]) ).

cnf(f_785_13,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2197,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK101(U_2197,U_2196,U_2195)),sK102(U_2197,U_2196,U_2195))))
    | ~ sP188(U_2197,U_2195,U_2196) ),
    inference(clausify,[status(thm)],[f_785_5]) ).

fof(f_786_1,plain,
    ! [Pa,A,F_1] :
      ( hBOOL(hAPP_f448129468l_bool(Pa,F_1))
      | ? [A_14,F_2] :
          ( ~ hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_14),F_2)))
          & hBOOL(hAPP_f448129468l_bool(Pa,F_2))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_14),F_2))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_14),A))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_2)) )
      | ~ hBOOL(hAPP_f448129468l_bool(Pa,bot_bot_fun_int_bool))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,F_1),A))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_679_finite__subset__induct]) ).

fof(f_786_2,plain,
    ! [U_2202,U_2201,U_2200] :
      ( hBOOL(hAPP_f448129468l_bool(U_2202,U_2200))
      | ? [U_2199,U_2198] :
          ( ~ hBOOL(hAPP_f448129468l_bool(U_2202,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2199),U_2198)))
          & hBOOL(hAPP_f448129468l_bool(U_2202,U_2198))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2199),U_2198))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2199),U_2201))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2198)) )
      | ~ hBOOL(hAPP_f448129468l_bool(U_2202,bot_bot_fun_int_bool))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2200),U_2201))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2200)) ),
    inference(variable_rename,[status(thm)],[f_786_1]) ).

fof(f_786_3,plain,
    ! [U_2202,U_2201,U_2200] :
      ( hBOOL(hAPP_f448129468l_bool(U_2202,U_2200))
      | ? [U_2198] :
          ( ~ hBOOL(hAPP_f448129468l_bool(U_2202,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK103(U_2202,U_2201,U_2200)),U_2198)))
          & hBOOL(hAPP_f448129468l_bool(U_2202,U_2198))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK103(U_2202,U_2201,U_2200)),U_2198))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK103(U_2202,U_2201,U_2200)),U_2201))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2198)) )
      | ~ hBOOL(hAPP_f448129468l_bool(U_2202,bot_bot_fun_int_bool))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2200),U_2201))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2200)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_2199,sK103(U_2202,U_2201,U_2200))],[f_786_2]) ).

fof(f_786_4,plain,
    ! [U_2202,U_2201,U_2200] :
      ( hBOOL(hAPP_f448129468l_bool(U_2202,U_2200))
      | ( ~ hBOOL(hAPP_f448129468l_bool(U_2202,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK103(U_2202,U_2201,U_2200)),sK104(U_2202,U_2201,U_2200))))
        & hBOOL(hAPP_f448129468l_bool(U_2202,sK104(U_2202,U_2201,U_2200)))
        & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK103(U_2202,U_2201,U_2200)),sK104(U_2202,U_2201,U_2200)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK103(U_2202,U_2201,U_2200)),U_2201))
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK104(U_2202,U_2201,U_2200))) )
      | ~ hBOOL(hAPP_f448129468l_bool(U_2202,bot_bot_fun_int_bool))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2200),U_2201))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2200)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_2198,sK104(U_2202,U_2201,U_2200))],[f_786_3]) ).

fof(f_786_5,plain,
    ( ! [U_2202,U_2201,U_2200] :
        ( ~ hBOOL(hAPP_f448129468l_bool(U_2202,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK103(U_2202,U_2201,U_2200)),sK104(U_2202,U_2201,U_2200))))
        | ~ sP189(U_2202,U_2201,U_2200) )
    & ! [U_2202,U_2201,U_2200] :
        ( hBOOL(hAPP_f448129468l_bool(U_2202,sK104(U_2202,U_2201,U_2200)))
        | ~ sP189(U_2202,U_2201,U_2200) )
    & ! [U_2202,U_2201,U_2200] :
        ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK103(U_2202,U_2201,U_2200)),sK104(U_2202,U_2201,U_2200)))
        | ~ sP189(U_2202,U_2201,U_2200) )
    & ! [U_2202,U_2201,U_2200] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK103(U_2202,U_2201,U_2200)),U_2201))
        | ~ sP189(U_2202,U_2201,U_2200) )
    & ! [U_2202,U_2201,U_2200] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK104(U_2202,U_2201,U_2200)))
        | ~ sP189(U_2202,U_2201,U_2200) )
    & ! [U_2202,U_2201,U_2200] :
        ( hBOOL(hAPP_f448129468l_bool(U_2202,U_2200))
        | sP189(U_2202,U_2201,U_2200)
        | ~ hBOOL(hAPP_f448129468l_bool(U_2202,bot_bot_fun_int_bool))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2200),U_2201))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2200)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP189])],[f_786_4]) ).

cnf(f_786_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(U_2202,U_2200))
    | sP189(U_2202,U_2201,U_2200)
    | ~ hBOOL(hAPP_f448129468l_bool(U_2202,bot_bot_fun_int_bool))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2200),U_2201))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2200)) ),
    inference(clausify,[status(thm)],[f_786_5]) ).

cnf(f_786_7,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK104(U_2202,U_2201,U_2200)))
    | ~ sP189(U_2202,U_2201,U_2200) ),
    inference(clausify,[status(thm)],[f_786_5]) ).

cnf(f_786_8,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK103(U_2202,U_2201,U_2200)),U_2201))
    | ~ sP189(U_2202,U_2201,U_2200) ),
    inference(clausify,[status(thm)],[f_786_5]) ).

cnf(f_786_9,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK103(U_2202,U_2201,U_2200)),sK104(U_2202,U_2201,U_2200)))
    | ~ sP189(U_2202,U_2201,U_2200) ),
    inference(clausify,[status(thm)],[f_786_5]) ).

cnf(f_786_10,plain,
    ( hBOOL(hAPP_f448129468l_bool(U_2202,sK104(U_2202,U_2201,U_2200)))
    | ~ sP189(U_2202,U_2201,U_2200) ),
    inference(clausify,[status(thm)],[f_786_5]) ).

cnf(f_786_11,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(U_2202,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK103(U_2202,U_2201,U_2200)),sK104(U_2202,U_2201,U_2200))))
    | ~ sP189(U_2202,U_2201,U_2200) ),
    inference(clausify,[status(thm)],[f_786_5]) ).

fof(f_787_1,plain,
    ! [Pa,A,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(Pa,F_1))
      | ? [A_14,F_2] :
          ( ~ hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_14),F_2)))
          & hBOOL(hAPP_f54304608l_bool(Pa,F_2))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_14),F_2))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_14),A))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2)) )
      | ~ hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,F_1),A))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_680_finite__subset__induct]) ).

fof(f_787_2,plain,
    ! [U_2207,U_2206,U_2205] :
      ( hBOOL(hAPP_f54304608l_bool(U_2207,U_2205))
      | ? [U_2204,U_2203] :
          ( ~ hBOOL(hAPP_f54304608l_bool(U_2207,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2204),U_2203)))
          & hBOOL(hAPP_f54304608l_bool(U_2207,U_2203))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2204),U_2203))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2204),U_2206))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2203)) )
      | ~ hBOOL(hAPP_f54304608l_bool(U_2207,bot_bot_fun_nat_bool))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2205),U_2206))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2205)) ),
    inference(variable_rename,[status(thm)],[f_787_1]) ).

fof(f_787_3,plain,
    ! [U_2207,U_2206,U_2205] :
      ( hBOOL(hAPP_f54304608l_bool(U_2207,U_2205))
      | ? [U_2203] :
          ( ~ hBOOL(hAPP_f54304608l_bool(U_2207,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK105(U_2207,U_2206,U_2205)),U_2203)))
          & hBOOL(hAPP_f54304608l_bool(U_2207,U_2203))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK105(U_2207,U_2206,U_2205)),U_2203))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK105(U_2207,U_2206,U_2205)),U_2206))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2203)) )
      | ~ hBOOL(hAPP_f54304608l_bool(U_2207,bot_bot_fun_nat_bool))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2205),U_2206))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2205)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_2204,sK105(U_2207,U_2206,U_2205))],[f_787_2]) ).

fof(f_787_4,plain,
    ! [U_2207,U_2206,U_2205] :
      ( hBOOL(hAPP_f54304608l_bool(U_2207,U_2205))
      | ( ~ hBOOL(hAPP_f54304608l_bool(U_2207,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK105(U_2207,U_2206,U_2205)),sK106(U_2207,U_2206,U_2205))))
        & hBOOL(hAPP_f54304608l_bool(U_2207,sK106(U_2207,U_2206,U_2205)))
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK105(U_2207,U_2206,U_2205)),sK106(U_2207,U_2206,U_2205)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK105(U_2207,U_2206,U_2205)),U_2206))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK106(U_2207,U_2206,U_2205))) )
      | ~ hBOOL(hAPP_f54304608l_bool(U_2207,bot_bot_fun_nat_bool))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2205),U_2206))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2205)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_2203,sK106(U_2207,U_2206,U_2205))],[f_787_3]) ).

fof(f_787_5,plain,
    ( ! [U_2205,U_2207,U_2206] :
        ( ~ hBOOL(hAPP_f54304608l_bool(U_2207,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK105(U_2207,U_2206,U_2205)),sK106(U_2207,U_2206,U_2205))))
        | ~ sP190(U_2205,U_2207,U_2206) )
    & ! [U_2205,U_2207,U_2206] :
        ( hBOOL(hAPP_f54304608l_bool(U_2207,sK106(U_2207,U_2206,U_2205)))
        | ~ sP190(U_2205,U_2207,U_2206) )
    & ! [U_2205,U_2207,U_2206] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK105(U_2207,U_2206,U_2205)),sK106(U_2207,U_2206,U_2205)))
        | ~ sP190(U_2205,U_2207,U_2206) )
    & ! [U_2205,U_2207,U_2206] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK105(U_2207,U_2206,U_2205)),U_2206))
        | ~ sP190(U_2205,U_2207,U_2206) )
    & ! [U_2205,U_2207,U_2206] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK106(U_2207,U_2206,U_2205)))
        | ~ sP190(U_2205,U_2207,U_2206) )
    & ! [U_2205,U_2207,U_2206] :
        ( hBOOL(hAPP_f54304608l_bool(U_2207,U_2205))
        | sP190(U_2205,U_2207,U_2206)
        | ~ hBOOL(hAPP_f54304608l_bool(U_2207,bot_bot_fun_nat_bool))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2205),U_2206))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2205)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP190])],[f_787_4]) ).

cnf(f_787_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(U_2207,U_2205))
    | sP190(U_2205,U_2207,U_2206)
    | ~ hBOOL(hAPP_f54304608l_bool(U_2207,bot_bot_fun_nat_bool))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2205),U_2206))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2205)) ),
    inference(clausify,[status(thm)],[f_787_5]) ).

cnf(f_787_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK106(U_2207,U_2206,U_2205)))
    | ~ sP190(U_2205,U_2207,U_2206) ),
    inference(clausify,[status(thm)],[f_787_5]) ).

cnf(f_787_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK105(U_2207,U_2206,U_2205)),U_2206))
    | ~ sP190(U_2205,U_2207,U_2206) ),
    inference(clausify,[status(thm)],[f_787_5]) ).

cnf(f_787_9,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK105(U_2207,U_2206,U_2205)),sK106(U_2207,U_2206,U_2205)))
    | ~ sP190(U_2205,U_2207,U_2206) ),
    inference(clausify,[status(thm)],[f_787_5]) ).

cnf(f_787_10,plain,
    ( hBOOL(hAPP_f54304608l_bool(U_2207,sK106(U_2207,U_2206,U_2205)))
    | ~ sP190(U_2205,U_2207,U_2206) ),
    inference(clausify,[status(thm)],[f_787_5]) ).

cnf(f_787_11,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(U_2207,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK105(U_2207,U_2206,U_2205)),sK106(U_2207,U_2206,U_2205))))
    | ~ sP190(U_2205,U_2207,U_2206) ),
    inference(clausify,[status(thm)],[f_787_5]) ).

fof(f_788_1,plain,
    ! [Pa,A,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(Pa,F_1))
      | ? [A_14,F_2] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(Pa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_14),F_2)))
          & hBOOL(hAPP_f1664156314l_bool(Pa,F_2))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_14),F_2))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_14),A))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_2))
          & is_fun_pname_bool(F_2)
          & is_pname(A_14) )
      | ~ hBOOL(hAPP_f1664156314l_bool(Pa,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,F_1),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_681_finite__subset__induct]) ).

fof(f_788_2,plain,
    ! [U_2212,U_2211,U_2210] :
      ( hBOOL(hAPP_f1664156314l_bool(U_2212,U_2210))
      | ? [U_2209,U_2208] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(U_2212,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2209),U_2208)))
          & hBOOL(hAPP_f1664156314l_bool(U_2212,U_2208))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2209),U_2208))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2209),U_2211))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2208))
          & is_fun_pname_bool(U_2208)
          & is_pname(U_2209) )
      | ~ hBOOL(hAPP_f1664156314l_bool(U_2212,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_2210),U_2211))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2210)) ),
    inference(variable_rename,[status(thm)],[f_788_1]) ).

fof(f_788_3,plain,
    ! [U_2212,U_2211,U_2210] :
      ( hBOOL(hAPP_f1664156314l_bool(U_2212,U_2210))
      | ? [U_2208] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(U_2212,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK107(U_2212,U_2211,U_2210)),U_2208)))
          & hBOOL(hAPP_f1664156314l_bool(U_2212,U_2208))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK107(U_2212,U_2211,U_2210)),U_2208))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK107(U_2212,U_2211,U_2210)),U_2211))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2208))
          & is_fun_pname_bool(U_2208)
          & is_pname(sK107(U_2212,U_2211,U_2210)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(U_2212,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_2210),U_2211))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2210)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_2209,sK107(U_2212,U_2211,U_2210))],[f_788_2]) ).

fof(f_788_4,plain,
    ! [U_2212,U_2211,U_2210] :
      ( hBOOL(hAPP_f1664156314l_bool(U_2212,U_2210))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(U_2212,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK107(U_2212,U_2211,U_2210)),sK108(U_2212,U_2211,U_2210))))
        & hBOOL(hAPP_f1664156314l_bool(U_2212,sK108(U_2212,U_2211,U_2210)))
        & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK107(U_2212,U_2211,U_2210)),sK108(U_2212,U_2211,U_2210)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK107(U_2212,U_2211,U_2210)),U_2211))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK108(U_2212,U_2211,U_2210)))
        & is_fun_pname_bool(sK108(U_2212,U_2211,U_2210))
        & is_pname(sK107(U_2212,U_2211,U_2210)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(U_2212,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_2210),U_2211))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2210)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_2208,sK108(U_2212,U_2211,U_2210))],[f_788_3]) ).

fof(f_788_5,plain,
    ( ! [U_2210,U_2211,U_2212] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(U_2212,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK107(U_2212,U_2211,U_2210)),sK108(U_2212,U_2211,U_2210))))
        | ~ sP191(U_2210,U_2211,U_2212) )
    & ! [U_2210,U_2211,U_2212] :
        ( hBOOL(hAPP_f1664156314l_bool(U_2212,sK108(U_2212,U_2211,U_2210)))
        | ~ sP191(U_2210,U_2211,U_2212) )
    & ! [U_2210,U_2211,U_2212] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK107(U_2212,U_2211,U_2210)),sK108(U_2212,U_2211,U_2210)))
        | ~ sP191(U_2210,U_2211,U_2212) )
    & ! [U_2210,U_2211,U_2212] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK107(U_2212,U_2211,U_2210)),U_2211))
        | ~ sP191(U_2210,U_2211,U_2212) )
    & ! [U_2210,U_2211,U_2212] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK108(U_2212,U_2211,U_2210)))
        | ~ sP191(U_2210,U_2211,U_2212) )
    & ! [U_2210,U_2211,U_2212] :
        ( is_fun_pname_bool(sK108(U_2212,U_2211,U_2210))
        | ~ sP191(U_2210,U_2211,U_2212) )
    & ! [U_2210,U_2211,U_2212] :
        ( is_pname(sK107(U_2212,U_2211,U_2210))
        | ~ sP191(U_2210,U_2211,U_2212) )
    & ! [U_2210,U_2211,U_2212] :
        ( hBOOL(hAPP_f1664156314l_bool(U_2212,U_2210))
        | sP191(U_2210,U_2211,U_2212)
        | ~ hBOOL(hAPP_f1664156314l_bool(U_2212,bot_bo844097828e_bool))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_2210),U_2211))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2210)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP191])],[f_788_4]) ).

cnf(f_788_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(U_2212,U_2210))
    | sP191(U_2210,U_2211,U_2212)
    | ~ hBOOL(hAPP_f1664156314l_bool(U_2212,bot_bo844097828e_bool))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_2210),U_2211))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2210)) ),
    inference(clausify,[status(thm)],[f_788_5]) ).

cnf(f_788_7,plain,
    ( is_pname(sK107(U_2212,U_2211,U_2210))
    | ~ sP191(U_2210,U_2211,U_2212) ),
    inference(clausify,[status(thm)],[f_788_5]) ).

cnf(f_788_8,plain,
    ( is_fun_pname_bool(sK108(U_2212,U_2211,U_2210))
    | ~ sP191(U_2210,U_2211,U_2212) ),
    inference(clausify,[status(thm)],[f_788_5]) ).

cnf(f_788_9,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK108(U_2212,U_2211,U_2210)))
    | ~ sP191(U_2210,U_2211,U_2212) ),
    inference(clausify,[status(thm)],[f_788_5]) ).

cnf(f_788_10,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK107(U_2212,U_2211,U_2210)),U_2211))
    | ~ sP191(U_2210,U_2211,U_2212) ),
    inference(clausify,[status(thm)],[f_788_5]) ).

cnf(f_788_11,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK107(U_2212,U_2211,U_2210)),sK108(U_2212,U_2211,U_2210)))
    | ~ sP191(U_2210,U_2211,U_2212) ),
    inference(clausify,[status(thm)],[f_788_5]) ).

cnf(f_788_12,plain,
    ( hBOOL(hAPP_f1664156314l_bool(U_2212,sK108(U_2212,U_2211,U_2210)))
    | ~ sP191(U_2210,U_2211,U_2212) ),
    inference(clausify,[status(thm)],[f_788_5]) ).

cnf(f_788_13,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(U_2212,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK107(U_2212,U_2211,U_2210)),sK108(U_2212,U_2211,U_2210))))
    | ~ sP191(U_2210,U_2211,U_2212) ),
    inference(clausify,[status(thm)],[f_788_5]) ).

fof(f_789_1,plain,
    ! [Pn,G] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(G),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,Pn)),bot_bot_fun_a_bool)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(p(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,Pn)),G)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(the_com(body(Pn)))),bot_bot_fun_a_bool))) ),
    inference(fof_nnf,[status(thm)],[fact_682_assms_I2_J]) ).

fof(f_789_2,plain,
    ! [U_2214,U_2213] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(U_2213),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,U_2214)),bot_bot_fun_a_bool)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(p(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,U_2214)),U_2213)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(the_com(body(U_2214)))),bot_bot_fun_a_bool))) ),
    inference(variable_rename,[status(thm)],[f_789_1]) ).

fof(f_789_3,plain,
    ! [U_2214,U_2213] :
      ( hBOOL(hAPP_fun_a_bool_bool(p(U_2213),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,U_2214)),bot_bot_fun_a_bool)))
      | ~ hBOOL(hAPP_fun_a_bool_bool(p(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,U_2214)),U_2213)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(the_com(body(U_2214)))),bot_bot_fun_a_bool))) ),
    inference(definitional_conversion,[status(esa)],[f_789_2]) ).

cnf(f_789_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(p(U_2213),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,U_2214)),bot_bot_fun_a_bool)))
    | ~ hBOOL(hAPP_fun_a_bool_bool(p(hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,U_2214)),U_2213)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,mgt(the_com(body(U_2214)))),bot_bot_fun_a_bool))) ),
    inference(clausify,[status(thm)],[f_789_3]) ).

fof(f_790_1,plain,
    ! [Pa,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(Pa,bot_bot_fun_a_bool))
      | ? [A_14,A_15] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(Pa,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A_15),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_14),bot_bot_fun_a_bool))))
          & hBOOL(hAPP_fun_a_bool_bool(Pa,A_15))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_14),A_15))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_15))
          & is_fun_a_bool(A_15)
          & is_a(A_14) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(Pa,A))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_683_finite__empty__induct]) ).

fof(f_790_2,plain,
    ! [U_2218,U_2217] :
      ( hBOOL(hAPP_fun_a_bool_bool(U_2218,bot_bot_fun_a_bool))
      | ? [U_2216,U_2215] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2218,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2215),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2216),bot_bot_fun_a_bool))))
          & hBOOL(hAPP_fun_a_bool_bool(U_2218,U_2215))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2216),U_2215))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2215))
          & is_fun_a_bool(U_2215)
          & is_a(U_2216) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(U_2218,U_2217))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2217)) ),
    inference(variable_rename,[status(thm)],[f_790_1]) ).

fof(f_790_3,plain,
    ! [U_2218,U_2217] :
      ( hBOOL(hAPP_fun_a_bool_bool(U_2218,bot_bot_fun_a_bool))
      | ? [U_2215] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2218,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2215),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK109(U_2218,U_2217)),bot_bot_fun_a_bool))))
          & hBOOL(hAPP_fun_a_bool_bool(U_2218,U_2215))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK109(U_2218,U_2217)),U_2215))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2215))
          & is_fun_a_bool(U_2215)
          & is_a(sK109(U_2218,U_2217)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(U_2218,U_2217))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2217)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_2216,sK109(U_2218,U_2217))],[f_790_2]) ).

fof(f_790_4,plain,
    ! [U_2218,U_2217] :
      ( hBOOL(hAPP_fun_a_bool_bool(U_2218,bot_bot_fun_a_bool))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2218,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,sK110(U_2218,U_2217)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK109(U_2218,U_2217)),bot_bot_fun_a_bool))))
        & hBOOL(hAPP_fun_a_bool_bool(U_2218,sK110(U_2218,U_2217)))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK109(U_2218,U_2217)),sK110(U_2218,U_2217)))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK110(U_2218,U_2217)))
        & is_fun_a_bool(sK110(U_2218,U_2217))
        & is_a(sK109(U_2218,U_2217)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(U_2218,U_2217))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2217)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_2215,sK110(U_2218,U_2217))],[f_790_3]) ).

fof(f_790_5,plain,
    ( ! [U_2217,U_2218] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2218,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,sK110(U_2218,U_2217)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK109(U_2218,U_2217)),bot_bot_fun_a_bool))))
        | ~ sP192(U_2217,U_2218) )
    & ! [U_2217,U_2218] :
        ( hBOOL(hAPP_fun_a_bool_bool(U_2218,sK110(U_2218,U_2217)))
        | ~ sP192(U_2217,U_2218) )
    & ! [U_2217,U_2218] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK109(U_2218,U_2217)),sK110(U_2218,U_2217)))
        | ~ sP192(U_2217,U_2218) )
    & ! [U_2217,U_2218] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK110(U_2218,U_2217)))
        | ~ sP192(U_2217,U_2218) )
    & ! [U_2217,U_2218] :
        ( is_fun_a_bool(sK110(U_2218,U_2217))
        | ~ sP192(U_2217,U_2218) )
    & ! [U_2217,U_2218] :
        ( is_a(sK109(U_2218,U_2217))
        | ~ sP192(U_2217,U_2218) )
    & ! [U_2217,U_2218] :
        ( hBOOL(hAPP_fun_a_bool_bool(U_2218,bot_bot_fun_a_bool))
        | sP192(U_2217,U_2218)
        | ~ hBOOL(hAPP_fun_a_bool_bool(U_2218,U_2217))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2217)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP192])],[f_790_4]) ).

cnf(f_790_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(U_2218,bot_bot_fun_a_bool))
    | sP192(U_2217,U_2218)
    | ~ hBOOL(hAPP_fun_a_bool_bool(U_2218,U_2217))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2217)) ),
    inference(clausify,[status(thm)],[f_790_5]) ).

cnf(f_790_7,plain,
    ( is_a(sK109(U_2218,U_2217))
    | ~ sP192(U_2217,U_2218) ),
    inference(clausify,[status(thm)],[f_790_5]) ).

cnf(f_790_8,plain,
    ( is_fun_a_bool(sK110(U_2218,U_2217))
    | ~ sP192(U_2217,U_2218) ),
    inference(clausify,[status(thm)],[f_790_5]) ).

cnf(f_790_9,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK110(U_2218,U_2217)))
    | ~ sP192(U_2217,U_2218) ),
    inference(clausify,[status(thm)],[f_790_5]) ).

cnf(f_790_10,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK109(U_2218,U_2217)),sK110(U_2218,U_2217)))
    | ~ sP192(U_2217,U_2218) ),
    inference(clausify,[status(thm)],[f_790_5]) ).

cnf(f_790_11,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(U_2218,sK110(U_2218,U_2217)))
    | ~ sP192(U_2217,U_2218) ),
    inference(clausify,[status(thm)],[f_790_5]) ).

cnf(f_790_12,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2218,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,sK110(U_2218,U_2217)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK109(U_2218,U_2217)),bot_bot_fun_a_bool))))
    | ~ sP192(U_2217,U_2218) ),
    inference(clausify,[status(thm)],[f_790_5]) ).

fof(f_791_1,plain,
    ! [Pa,A] :
      ( hBOOL(hAPP_f448129468l_bool(Pa,bot_bot_fun_int_bool))
      | ? [A_14,A_15] :
          ( ~ hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A_15),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_14),bot_bot_fun_int_bool))))
          & hBOOL(hAPP_f448129468l_bool(Pa,A_15))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_14),A_15))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_15)) )
      | ~ hBOOL(hAPP_f448129468l_bool(Pa,A))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_684_finite__empty__induct]) ).

fof(f_791_2,plain,
    ! [U_2222,U_2221] :
      ( hBOOL(hAPP_f448129468l_bool(U_2222,bot_bot_fun_int_bool))
      | ? [U_2220,U_2219] :
          ( ~ hBOOL(hAPP_f448129468l_bool(U_2222,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2219),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2220),bot_bot_fun_int_bool))))
          & hBOOL(hAPP_f448129468l_bool(U_2222,U_2219))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2220),U_2219))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2219)) )
      | ~ hBOOL(hAPP_f448129468l_bool(U_2222,U_2221))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2221)) ),
    inference(variable_rename,[status(thm)],[f_791_1]) ).

fof(f_791_3,plain,
    ! [U_2222,U_2221] :
      ( hBOOL(hAPP_f448129468l_bool(U_2222,bot_bot_fun_int_bool))
      | ? [U_2219] :
          ( ~ hBOOL(hAPP_f448129468l_bool(U_2222,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2219),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK111(U_2222,U_2221)),bot_bot_fun_int_bool))))
          & hBOOL(hAPP_f448129468l_bool(U_2222,U_2219))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK111(U_2222,U_2221)),U_2219))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2219)) )
      | ~ hBOOL(hAPP_f448129468l_bool(U_2222,U_2221))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2221)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_2220,sK111(U_2222,U_2221))],[f_791_2]) ).

fof(f_791_4,plain,
    ! [U_2222,U_2221] :
      ( hBOOL(hAPP_f448129468l_bool(U_2222,bot_bot_fun_int_bool))
      | ( ~ hBOOL(hAPP_f448129468l_bool(U_2222,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,sK112(U_2222,U_2221)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK111(U_2222,U_2221)),bot_bot_fun_int_bool))))
        & hBOOL(hAPP_f448129468l_bool(U_2222,sK112(U_2222,U_2221)))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK111(U_2222,U_2221)),sK112(U_2222,U_2221)))
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK112(U_2222,U_2221))) )
      | ~ hBOOL(hAPP_f448129468l_bool(U_2222,U_2221))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2221)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_2219,sK112(U_2222,U_2221))],[f_791_3]) ).

fof(f_791_5,plain,
    ( ! [U_2222,U_2221] :
        ( ~ hBOOL(hAPP_f448129468l_bool(U_2222,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,sK112(U_2222,U_2221)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK111(U_2222,U_2221)),bot_bot_fun_int_bool))))
        | ~ sP193(U_2222,U_2221) )
    & ! [U_2222,U_2221] :
        ( hBOOL(hAPP_f448129468l_bool(U_2222,sK112(U_2222,U_2221)))
        | ~ sP193(U_2222,U_2221) )
    & ! [U_2222,U_2221] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK111(U_2222,U_2221)),sK112(U_2222,U_2221)))
        | ~ sP193(U_2222,U_2221) )
    & ! [U_2222,U_2221] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK112(U_2222,U_2221)))
        | ~ sP193(U_2222,U_2221) )
    & ! [U_2222,U_2221] :
        ( hBOOL(hAPP_f448129468l_bool(U_2222,bot_bot_fun_int_bool))
        | sP193(U_2222,U_2221)
        | ~ hBOOL(hAPP_f448129468l_bool(U_2222,U_2221))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2221)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP193])],[f_791_4]) ).

cnf(f_791_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(U_2222,bot_bot_fun_int_bool))
    | sP193(U_2222,U_2221)
    | ~ hBOOL(hAPP_f448129468l_bool(U_2222,U_2221))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2221)) ),
    inference(clausify,[status(thm)],[f_791_5]) ).

cnf(f_791_7,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK112(U_2222,U_2221)))
    | ~ sP193(U_2222,U_2221) ),
    inference(clausify,[status(thm)],[f_791_5]) ).

cnf(f_791_8,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK111(U_2222,U_2221)),sK112(U_2222,U_2221)))
    | ~ sP193(U_2222,U_2221) ),
    inference(clausify,[status(thm)],[f_791_5]) ).

cnf(f_791_9,plain,
    ( hBOOL(hAPP_f448129468l_bool(U_2222,sK112(U_2222,U_2221)))
    | ~ sP193(U_2222,U_2221) ),
    inference(clausify,[status(thm)],[f_791_5]) ).

cnf(f_791_10,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(U_2222,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,sK112(U_2222,U_2221)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK111(U_2222,U_2221)),bot_bot_fun_int_bool))))
    | ~ sP193(U_2222,U_2221) ),
    inference(clausify,[status(thm)],[f_791_5]) ).

fof(f_792_1,plain,
    ! [Pa,A] :
      ( hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool))
      | ? [A_14,A_15] :
          ( ~ hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A_15),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_14),bot_bot_fun_nat_bool))))
          & hBOOL(hAPP_f54304608l_bool(Pa,A_15))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_14),A_15))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_15)) )
      | ~ hBOOL(hAPP_f54304608l_bool(Pa,A))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_685_finite__empty__induct]) ).

fof(f_792_2,plain,
    ! [U_2226,U_2225] :
      ( hBOOL(hAPP_f54304608l_bool(U_2226,bot_bot_fun_nat_bool))
      | ? [U_2224,U_2223] :
          ( ~ hBOOL(hAPP_f54304608l_bool(U_2226,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2223),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2224),bot_bot_fun_nat_bool))))
          & hBOOL(hAPP_f54304608l_bool(U_2226,U_2223))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2224),U_2223))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2223)) )
      | ~ hBOOL(hAPP_f54304608l_bool(U_2226,U_2225))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2225)) ),
    inference(variable_rename,[status(thm)],[f_792_1]) ).

fof(f_792_3,plain,
    ! [U_2226,U_2225] :
      ( hBOOL(hAPP_f54304608l_bool(U_2226,bot_bot_fun_nat_bool))
      | ? [U_2223] :
          ( ~ hBOOL(hAPP_f54304608l_bool(U_2226,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2223),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK113(U_2226,U_2225)),bot_bot_fun_nat_bool))))
          & hBOOL(hAPP_f54304608l_bool(U_2226,U_2223))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK113(U_2226,U_2225)),U_2223))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2223)) )
      | ~ hBOOL(hAPP_f54304608l_bool(U_2226,U_2225))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2225)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_2224,sK113(U_2226,U_2225))],[f_792_2]) ).

fof(f_792_4,plain,
    ! [U_2226,U_2225] :
      ( hBOOL(hAPP_f54304608l_bool(U_2226,bot_bot_fun_nat_bool))
      | ( ~ hBOOL(hAPP_f54304608l_bool(U_2226,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,sK114(U_2226,U_2225)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK113(U_2226,U_2225)),bot_bot_fun_nat_bool))))
        & hBOOL(hAPP_f54304608l_bool(U_2226,sK114(U_2226,U_2225)))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK113(U_2226,U_2225)),sK114(U_2226,U_2225)))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK114(U_2226,U_2225))) )
      | ~ hBOOL(hAPP_f54304608l_bool(U_2226,U_2225))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2225)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_2223,sK114(U_2226,U_2225))],[f_792_3]) ).

fof(f_792_5,plain,
    ( ! [U_2225,U_2226] :
        ( ~ hBOOL(hAPP_f54304608l_bool(U_2226,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,sK114(U_2226,U_2225)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK113(U_2226,U_2225)),bot_bot_fun_nat_bool))))
        | ~ sP194(U_2225,U_2226) )
    & ! [U_2225,U_2226] :
        ( hBOOL(hAPP_f54304608l_bool(U_2226,sK114(U_2226,U_2225)))
        | ~ sP194(U_2225,U_2226) )
    & ! [U_2225,U_2226] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK113(U_2226,U_2225)),sK114(U_2226,U_2225)))
        | ~ sP194(U_2225,U_2226) )
    & ! [U_2225,U_2226] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK114(U_2226,U_2225)))
        | ~ sP194(U_2225,U_2226) )
    & ! [U_2225,U_2226] :
        ( hBOOL(hAPP_f54304608l_bool(U_2226,bot_bot_fun_nat_bool))
        | sP194(U_2225,U_2226)
        | ~ hBOOL(hAPP_f54304608l_bool(U_2226,U_2225))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2225)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP194])],[f_792_4]) ).

cnf(f_792_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(U_2226,bot_bot_fun_nat_bool))
    | sP194(U_2225,U_2226)
    | ~ hBOOL(hAPP_f54304608l_bool(U_2226,U_2225))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2225)) ),
    inference(clausify,[status(thm)],[f_792_5]) ).

cnf(f_792_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK114(U_2226,U_2225)))
    | ~ sP194(U_2225,U_2226) ),
    inference(clausify,[status(thm)],[f_792_5]) ).

cnf(f_792_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK113(U_2226,U_2225)),sK114(U_2226,U_2225)))
    | ~ sP194(U_2225,U_2226) ),
    inference(clausify,[status(thm)],[f_792_5]) ).

cnf(f_792_9,plain,
    ( hBOOL(hAPP_f54304608l_bool(U_2226,sK114(U_2226,U_2225)))
    | ~ sP194(U_2225,U_2226) ),
    inference(clausify,[status(thm)],[f_792_5]) ).

cnf(f_792_10,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(U_2226,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,sK114(U_2226,U_2225)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK113(U_2226,U_2225)),bot_bot_fun_nat_bool))))
    | ~ sP194(U_2225,U_2226) ),
    inference(clausify,[status(thm)],[f_792_5]) ).

fof(f_793_1,plain,
    ! [Pa,A] :
      ( hBOOL(hAPP_f1664156314l_bool(Pa,bot_bo844097828e_bool))
      | ? [A_14,A_15] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(Pa,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A_15),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_14),bot_bo844097828e_bool))))
          & hBOOL(hAPP_f1664156314l_bool(Pa,A_15))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_14),A_15))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_15))
          & is_fun_pname_bool(A_15)
          & is_pname(A_14) )
      | ~ hBOOL(hAPP_f1664156314l_bool(Pa,A))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_686_finite__empty__induct]) ).

fof(f_793_2,plain,
    ! [U_2230,U_2229] :
      ( hBOOL(hAPP_f1664156314l_bool(U_2230,bot_bo844097828e_bool))
      | ? [U_2228,U_2227] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(U_2230,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2227),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2228),bot_bo844097828e_bool))))
          & hBOOL(hAPP_f1664156314l_bool(U_2230,U_2227))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2228),U_2227))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2227))
          & is_fun_pname_bool(U_2227)
          & is_pname(U_2228) )
      | ~ hBOOL(hAPP_f1664156314l_bool(U_2230,U_2229))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2229)) ),
    inference(variable_rename,[status(thm)],[f_793_1]) ).

fof(f_793_3,plain,
    ! [U_2230,U_2229] :
      ( hBOOL(hAPP_f1664156314l_bool(U_2230,bot_bo844097828e_bool))
      | ? [U_2227] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(U_2230,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2227),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK115(U_2230,U_2229)),bot_bo844097828e_bool))))
          & hBOOL(hAPP_f1664156314l_bool(U_2230,U_2227))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK115(U_2230,U_2229)),U_2227))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2227))
          & is_fun_pname_bool(U_2227)
          & is_pname(sK115(U_2230,U_2229)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(U_2230,U_2229))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2229)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_2228,sK115(U_2230,U_2229))],[f_793_2]) ).

fof(f_793_4,plain,
    ! [U_2230,U_2229] :
      ( hBOOL(hAPP_f1664156314l_bool(U_2230,bot_bo844097828e_bool))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(U_2230,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,sK116(U_2230,U_2229)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK115(U_2230,U_2229)),bot_bo844097828e_bool))))
        & hBOOL(hAPP_f1664156314l_bool(U_2230,sK116(U_2230,U_2229)))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK115(U_2230,U_2229)),sK116(U_2230,U_2229)))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK116(U_2230,U_2229)))
        & is_fun_pname_bool(sK116(U_2230,U_2229))
        & is_pname(sK115(U_2230,U_2229)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(U_2230,U_2229))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2229)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_2227,sK116(U_2230,U_2229))],[f_793_3]) ).

fof(f_793_5,plain,
    ( ! [U_2230,U_2229] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(U_2230,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,sK116(U_2230,U_2229)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK115(U_2230,U_2229)),bot_bo844097828e_bool))))
        | ~ sP195(U_2230,U_2229) )
    & ! [U_2230,U_2229] :
        ( hBOOL(hAPP_f1664156314l_bool(U_2230,sK116(U_2230,U_2229)))
        | ~ sP195(U_2230,U_2229) )
    & ! [U_2230,U_2229] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK115(U_2230,U_2229)),sK116(U_2230,U_2229)))
        | ~ sP195(U_2230,U_2229) )
    & ! [U_2230,U_2229] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK116(U_2230,U_2229)))
        | ~ sP195(U_2230,U_2229) )
    & ! [U_2230,U_2229] :
        ( is_fun_pname_bool(sK116(U_2230,U_2229))
        | ~ sP195(U_2230,U_2229) )
    & ! [U_2230,U_2229] :
        ( is_pname(sK115(U_2230,U_2229))
        | ~ sP195(U_2230,U_2229) )
    & ! [U_2230,U_2229] :
        ( hBOOL(hAPP_f1664156314l_bool(U_2230,bot_bo844097828e_bool))
        | sP195(U_2230,U_2229)
        | ~ hBOOL(hAPP_f1664156314l_bool(U_2230,U_2229))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2229)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP195])],[f_793_4]) ).

cnf(f_793_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(U_2230,bot_bo844097828e_bool))
    | sP195(U_2230,U_2229)
    | ~ hBOOL(hAPP_f1664156314l_bool(U_2230,U_2229))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2229)) ),
    inference(clausify,[status(thm)],[f_793_5]) ).

cnf(f_793_7,plain,
    ( is_pname(sK115(U_2230,U_2229))
    | ~ sP195(U_2230,U_2229) ),
    inference(clausify,[status(thm)],[f_793_5]) ).

cnf(f_793_8,plain,
    ( is_fun_pname_bool(sK116(U_2230,U_2229))
    | ~ sP195(U_2230,U_2229) ),
    inference(clausify,[status(thm)],[f_793_5]) ).

cnf(f_793_9,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK116(U_2230,U_2229)))
    | ~ sP195(U_2230,U_2229) ),
    inference(clausify,[status(thm)],[f_793_5]) ).

cnf(f_793_10,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK115(U_2230,U_2229)),sK116(U_2230,U_2229)))
    | ~ sP195(U_2230,U_2229) ),
    inference(clausify,[status(thm)],[f_793_5]) ).

cnf(f_793_11,plain,
    ( hBOOL(hAPP_f1664156314l_bool(U_2230,sK116(U_2230,U_2229)))
    | ~ sP195(U_2230,U_2229) ),
    inference(clausify,[status(thm)],[f_793_5]) ).

cnf(f_793_12,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(U_2230,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,sK116(U_2230,U_2229)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK115(U_2230,U_2229)),bot_bo844097828e_bool))))
    | ~ sP195(U_2230,U_2229) ),
    inference(clausify,[status(thm)],[f_793_5]) ).

fof(f_794_1,plain,
    ! [Pa,F_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(Pa,F_1))
      | ? [X_2,F_2] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(Pa,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_2),F_2)))
          & hBOOL(hAPP_fun_a_bool_bool(Pa,F_2))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),F_2))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_2))
          & is_fun_a_bool(F_2)
          & is_a(X_2) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(Pa,bot_bot_fun_a_bool))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_687_finite__induct]) ).

fof(f_794_2,plain,
    ! [U_2234,U_2233] :
      ( hBOOL(hAPP_fun_a_bool_bool(U_2234,U_2233))
      | ? [U_2232,U_2231] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2234,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2232),U_2231)))
          & hBOOL(hAPP_fun_a_bool_bool(U_2234,U_2231))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2232),U_2231))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2231))
          & is_fun_a_bool(U_2231)
          & is_a(U_2232) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(U_2234,bot_bot_fun_a_bool))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2233)) ),
    inference(variable_rename,[status(thm)],[f_794_1]) ).

fof(f_794_3,plain,
    ! [U_2234,U_2233] :
      ( hBOOL(hAPP_fun_a_bool_bool(U_2234,U_2233))
      | ? [U_2231] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2234,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK117(U_2234,U_2233)),U_2231)))
          & hBOOL(hAPP_fun_a_bool_bool(U_2234,U_2231))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK117(U_2234,U_2233)),U_2231))
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2231))
          & is_fun_a_bool(U_2231)
          & is_a(sK117(U_2234,U_2233)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(U_2234,bot_bot_fun_a_bool))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2233)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_2232,sK117(U_2234,U_2233))],[f_794_2]) ).

fof(f_794_4,plain,
    ! [U_2234,U_2233] :
      ( hBOOL(hAPP_fun_a_bool_bool(U_2234,U_2233))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2234,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK117(U_2234,U_2233)),sK118(U_2234,U_2233))))
        & hBOOL(hAPP_fun_a_bool_bool(U_2234,sK118(U_2234,U_2233)))
        & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK117(U_2234,U_2233)),sK118(U_2234,U_2233)))
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK118(U_2234,U_2233)))
        & is_fun_a_bool(sK118(U_2234,U_2233))
        & is_a(sK117(U_2234,U_2233)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(U_2234,bot_bot_fun_a_bool))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2233)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_2231,sK118(U_2234,U_2233))],[f_794_3]) ).

fof(f_794_5,plain,
    ( ! [U_2233,U_2234] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2234,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK117(U_2234,U_2233)),sK118(U_2234,U_2233))))
        | ~ sP196(U_2233,U_2234) )
    & ! [U_2233,U_2234] :
        ( hBOOL(hAPP_fun_a_bool_bool(U_2234,sK118(U_2234,U_2233)))
        | ~ sP196(U_2233,U_2234) )
    & ! [U_2233,U_2234] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK117(U_2234,U_2233)),sK118(U_2234,U_2233)))
        | ~ sP196(U_2233,U_2234) )
    & ! [U_2233,U_2234] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK118(U_2234,U_2233)))
        | ~ sP196(U_2233,U_2234) )
    & ! [U_2233,U_2234] :
        ( is_fun_a_bool(sK118(U_2234,U_2233))
        | ~ sP196(U_2233,U_2234) )
    & ! [U_2233,U_2234] :
        ( is_a(sK117(U_2234,U_2233))
        | ~ sP196(U_2233,U_2234) )
    & ! [U_2233,U_2234] :
        ( hBOOL(hAPP_fun_a_bool_bool(U_2234,U_2233))
        | sP196(U_2233,U_2234)
        | ~ hBOOL(hAPP_fun_a_bool_bool(U_2234,bot_bot_fun_a_bool))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2233)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP196])],[f_794_4]) ).

cnf(f_794_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(U_2234,U_2233))
    | sP196(U_2233,U_2234)
    | ~ hBOOL(hAPP_fun_a_bool_bool(U_2234,bot_bot_fun_a_bool))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2233)) ),
    inference(clausify,[status(thm)],[f_794_5]) ).

cnf(f_794_7,plain,
    ( is_a(sK117(U_2234,U_2233))
    | ~ sP196(U_2233,U_2234) ),
    inference(clausify,[status(thm)],[f_794_5]) ).

cnf(f_794_8,plain,
    ( is_fun_a_bool(sK118(U_2234,U_2233))
    | ~ sP196(U_2233,U_2234) ),
    inference(clausify,[status(thm)],[f_794_5]) ).

cnf(f_794_9,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK118(U_2234,U_2233)))
    | ~ sP196(U_2233,U_2234) ),
    inference(clausify,[status(thm)],[f_794_5]) ).

cnf(f_794_10,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK117(U_2234,U_2233)),sK118(U_2234,U_2233)))
    | ~ sP196(U_2233,U_2234) ),
    inference(clausify,[status(thm)],[f_794_5]) ).

cnf(f_794_11,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(U_2234,sK118(U_2234,U_2233)))
    | ~ sP196(U_2233,U_2234) ),
    inference(clausify,[status(thm)],[f_794_5]) ).

cnf(f_794_12,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2234,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK117(U_2234,U_2233)),sK118(U_2234,U_2233))))
    | ~ sP196(U_2233,U_2234) ),
    inference(clausify,[status(thm)],[f_794_5]) ).

fof(f_795_1,plain,
    ! [Pa,F_1] :
      ( hBOOL(hAPP_f448129468l_bool(Pa,F_1))
      | ? [X_2,F_2] :
          ( ~ hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),F_2)))
          & hBOOL(hAPP_f448129468l_bool(Pa,F_2))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),F_2))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_2)) )
      | ~ hBOOL(hAPP_f448129468l_bool(Pa,bot_bot_fun_int_bool))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_688_finite__induct]) ).

fof(f_795_2,plain,
    ! [U_2238,U_2237] :
      ( hBOOL(hAPP_f448129468l_bool(U_2238,U_2237))
      | ? [U_2236,U_2235] :
          ( ~ hBOOL(hAPP_f448129468l_bool(U_2238,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2236),U_2235)))
          & hBOOL(hAPP_f448129468l_bool(U_2238,U_2235))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2236),U_2235))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2235)) )
      | ~ hBOOL(hAPP_f448129468l_bool(U_2238,bot_bot_fun_int_bool))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2237)) ),
    inference(variable_rename,[status(thm)],[f_795_1]) ).

fof(f_795_3,plain,
    ! [U_2238,U_2237] :
      ( hBOOL(hAPP_f448129468l_bool(U_2238,U_2237))
      | ? [U_2235] :
          ( ~ hBOOL(hAPP_f448129468l_bool(U_2238,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK119(U_2238,U_2237)),U_2235)))
          & hBOOL(hAPP_f448129468l_bool(U_2238,U_2235))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK119(U_2238,U_2237)),U_2235))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2235)) )
      | ~ hBOOL(hAPP_f448129468l_bool(U_2238,bot_bot_fun_int_bool))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2237)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_2236,sK119(U_2238,U_2237))],[f_795_2]) ).

fof(f_795_4,plain,
    ! [U_2238,U_2237] :
      ( hBOOL(hAPP_f448129468l_bool(U_2238,U_2237))
      | ( ~ hBOOL(hAPP_f448129468l_bool(U_2238,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK119(U_2238,U_2237)),sK120(U_2238,U_2237))))
        & hBOOL(hAPP_f448129468l_bool(U_2238,sK120(U_2238,U_2237)))
        & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK119(U_2238,U_2237)),sK120(U_2238,U_2237)))
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK120(U_2238,U_2237))) )
      | ~ hBOOL(hAPP_f448129468l_bool(U_2238,bot_bot_fun_int_bool))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2237)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_2235,sK120(U_2238,U_2237))],[f_795_3]) ).

fof(f_795_5,plain,
    ( ! [U_2238,U_2237] :
        ( ~ hBOOL(hAPP_f448129468l_bool(U_2238,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK119(U_2238,U_2237)),sK120(U_2238,U_2237))))
        | ~ sP197(U_2238,U_2237) )
    & ! [U_2238,U_2237] :
        ( hBOOL(hAPP_f448129468l_bool(U_2238,sK120(U_2238,U_2237)))
        | ~ sP197(U_2238,U_2237) )
    & ! [U_2238,U_2237] :
        ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK119(U_2238,U_2237)),sK120(U_2238,U_2237)))
        | ~ sP197(U_2238,U_2237) )
    & ! [U_2238,U_2237] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK120(U_2238,U_2237)))
        | ~ sP197(U_2238,U_2237) )
    & ! [U_2238,U_2237] :
        ( hBOOL(hAPP_f448129468l_bool(U_2238,U_2237))
        | sP197(U_2238,U_2237)
        | ~ hBOOL(hAPP_f448129468l_bool(U_2238,bot_bot_fun_int_bool))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2237)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP197])],[f_795_4]) ).

cnf(f_795_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(U_2238,U_2237))
    | sP197(U_2238,U_2237)
    | ~ hBOOL(hAPP_f448129468l_bool(U_2238,bot_bot_fun_int_bool))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2237)) ),
    inference(clausify,[status(thm)],[f_795_5]) ).

cnf(f_795_7,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK120(U_2238,U_2237)))
    | ~ sP197(U_2238,U_2237) ),
    inference(clausify,[status(thm)],[f_795_5]) ).

cnf(f_795_8,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK119(U_2238,U_2237)),sK120(U_2238,U_2237)))
    | ~ sP197(U_2238,U_2237) ),
    inference(clausify,[status(thm)],[f_795_5]) ).

cnf(f_795_9,plain,
    ( hBOOL(hAPP_f448129468l_bool(U_2238,sK120(U_2238,U_2237)))
    | ~ sP197(U_2238,U_2237) ),
    inference(clausify,[status(thm)],[f_795_5]) ).

cnf(f_795_10,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(U_2238,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK119(U_2238,U_2237)),sK120(U_2238,U_2237))))
    | ~ sP197(U_2238,U_2237) ),
    inference(clausify,[status(thm)],[f_795_5]) ).

fof(f_796_1,plain,
    ! [Pa,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(Pa,F_1))
      | ? [X_2,F_2] :
          ( ~ hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),F_2)))
          & hBOOL(hAPP_f54304608l_bool(Pa,F_2))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),F_2))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2)) )
      | ~ hBOOL(hAPP_f54304608l_bool(Pa,bot_bot_fun_nat_bool))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_689_finite__induct]) ).

fof(f_796_2,plain,
    ! [U_2242,U_2241] :
      ( hBOOL(hAPP_f54304608l_bool(U_2242,U_2241))
      | ? [U_2240,U_2239] :
          ( ~ hBOOL(hAPP_f54304608l_bool(U_2242,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2240),U_2239)))
          & hBOOL(hAPP_f54304608l_bool(U_2242,U_2239))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2240),U_2239))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2239)) )
      | ~ hBOOL(hAPP_f54304608l_bool(U_2242,bot_bot_fun_nat_bool))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2241)) ),
    inference(variable_rename,[status(thm)],[f_796_1]) ).

fof(f_796_3,plain,
    ! [U_2242,U_2241] :
      ( hBOOL(hAPP_f54304608l_bool(U_2242,U_2241))
      | ? [U_2239] :
          ( ~ hBOOL(hAPP_f54304608l_bool(U_2242,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK121(U_2242,U_2241)),U_2239)))
          & hBOOL(hAPP_f54304608l_bool(U_2242,U_2239))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK121(U_2242,U_2241)),U_2239))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2239)) )
      | ~ hBOOL(hAPP_f54304608l_bool(U_2242,bot_bot_fun_nat_bool))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2241)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_2240,sK121(U_2242,U_2241))],[f_796_2]) ).

fof(f_796_4,plain,
    ! [U_2242,U_2241] :
      ( hBOOL(hAPP_f54304608l_bool(U_2242,U_2241))
      | ( ~ hBOOL(hAPP_f54304608l_bool(U_2242,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK121(U_2242,U_2241)),sK122(U_2242,U_2241))))
        & hBOOL(hAPP_f54304608l_bool(U_2242,sK122(U_2242,U_2241)))
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK121(U_2242,U_2241)),sK122(U_2242,U_2241)))
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK122(U_2242,U_2241))) )
      | ~ hBOOL(hAPP_f54304608l_bool(U_2242,bot_bot_fun_nat_bool))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2241)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_2239,sK122(U_2242,U_2241))],[f_796_3]) ).

fof(f_796_5,plain,
    ( ! [U_2242,U_2241] :
        ( ~ hBOOL(hAPP_f54304608l_bool(U_2242,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK121(U_2242,U_2241)),sK122(U_2242,U_2241))))
        | ~ sP198(U_2242,U_2241) )
    & ! [U_2242,U_2241] :
        ( hBOOL(hAPP_f54304608l_bool(U_2242,sK122(U_2242,U_2241)))
        | ~ sP198(U_2242,U_2241) )
    & ! [U_2242,U_2241] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK121(U_2242,U_2241)),sK122(U_2242,U_2241)))
        | ~ sP198(U_2242,U_2241) )
    & ! [U_2242,U_2241] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK122(U_2242,U_2241)))
        | ~ sP198(U_2242,U_2241) )
    & ! [U_2242,U_2241] :
        ( hBOOL(hAPP_f54304608l_bool(U_2242,U_2241))
        | sP198(U_2242,U_2241)
        | ~ hBOOL(hAPP_f54304608l_bool(U_2242,bot_bot_fun_nat_bool))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2241)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP198])],[f_796_4]) ).

cnf(f_796_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(U_2242,U_2241))
    | sP198(U_2242,U_2241)
    | ~ hBOOL(hAPP_f54304608l_bool(U_2242,bot_bot_fun_nat_bool))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2241)) ),
    inference(clausify,[status(thm)],[f_796_5]) ).

cnf(f_796_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK122(U_2242,U_2241)))
    | ~ sP198(U_2242,U_2241) ),
    inference(clausify,[status(thm)],[f_796_5]) ).

cnf(f_796_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK121(U_2242,U_2241)),sK122(U_2242,U_2241)))
    | ~ sP198(U_2242,U_2241) ),
    inference(clausify,[status(thm)],[f_796_5]) ).

cnf(f_796_9,plain,
    ( hBOOL(hAPP_f54304608l_bool(U_2242,sK122(U_2242,U_2241)))
    | ~ sP198(U_2242,U_2241) ),
    inference(clausify,[status(thm)],[f_796_5]) ).

cnf(f_796_10,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(U_2242,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK121(U_2242,U_2241)),sK122(U_2242,U_2241))))
    | ~ sP198(U_2242,U_2241) ),
    inference(clausify,[status(thm)],[f_796_5]) ).

fof(f_797_1,plain,
    ! [Pa,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(Pa,F_1))
      | ? [X_2,F_2] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(Pa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),F_2)))
          & hBOOL(hAPP_f1664156314l_bool(Pa,F_2))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),F_2))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_2))
          & is_fun_pname_bool(F_2)
          & is_pname(X_2) )
      | ~ hBOOL(hAPP_f1664156314l_bool(Pa,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_690_finite__induct]) ).

fof(f_797_2,plain,
    ! [U_2246,U_2245] :
      ( hBOOL(hAPP_f1664156314l_bool(U_2246,U_2245))
      | ? [U_2244,U_2243] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(U_2246,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2244),U_2243)))
          & hBOOL(hAPP_f1664156314l_bool(U_2246,U_2243))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2244),U_2243))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2243))
          & is_fun_pname_bool(U_2243)
          & is_pname(U_2244) )
      | ~ hBOOL(hAPP_f1664156314l_bool(U_2246,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2245)) ),
    inference(variable_rename,[status(thm)],[f_797_1]) ).

fof(f_797_3,plain,
    ! [U_2246,U_2245] :
      ( hBOOL(hAPP_f1664156314l_bool(U_2246,U_2245))
      | ? [U_2243] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(U_2246,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK123(U_2246,U_2245)),U_2243)))
          & hBOOL(hAPP_f1664156314l_bool(U_2246,U_2243))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK123(U_2246,U_2245)),U_2243))
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2243))
          & is_fun_pname_bool(U_2243)
          & is_pname(sK123(U_2246,U_2245)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(U_2246,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2245)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_2244,sK123(U_2246,U_2245))],[f_797_2]) ).

fof(f_797_4,plain,
    ! [U_2246,U_2245] :
      ( hBOOL(hAPP_f1664156314l_bool(U_2246,U_2245))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(U_2246,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK123(U_2246,U_2245)),sK124(U_2246,U_2245))))
        & hBOOL(hAPP_f1664156314l_bool(U_2246,sK124(U_2246,U_2245)))
        & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK123(U_2246,U_2245)),sK124(U_2246,U_2245)))
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK124(U_2246,U_2245)))
        & is_fun_pname_bool(sK124(U_2246,U_2245))
        & is_pname(sK123(U_2246,U_2245)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(U_2246,bot_bo844097828e_bool))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2245)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_2243,sK124(U_2246,U_2245))],[f_797_3]) ).

fof(f_797_5,plain,
    ( ! [U_2246,U_2245] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(U_2246,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK123(U_2246,U_2245)),sK124(U_2246,U_2245))))
        | ~ sP199(U_2246,U_2245) )
    & ! [U_2246,U_2245] :
        ( hBOOL(hAPP_f1664156314l_bool(U_2246,sK124(U_2246,U_2245)))
        | ~ sP199(U_2246,U_2245) )
    & ! [U_2246,U_2245] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK123(U_2246,U_2245)),sK124(U_2246,U_2245)))
        | ~ sP199(U_2246,U_2245) )
    & ! [U_2246,U_2245] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK124(U_2246,U_2245)))
        | ~ sP199(U_2246,U_2245) )
    & ! [U_2246,U_2245] :
        ( is_fun_pname_bool(sK124(U_2246,U_2245))
        | ~ sP199(U_2246,U_2245) )
    & ! [U_2246,U_2245] :
        ( is_pname(sK123(U_2246,U_2245))
        | ~ sP199(U_2246,U_2245) )
    & ! [U_2246,U_2245] :
        ( hBOOL(hAPP_f1664156314l_bool(U_2246,U_2245))
        | sP199(U_2246,U_2245)
        | ~ hBOOL(hAPP_f1664156314l_bool(U_2246,bot_bo844097828e_bool))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2245)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP199])],[f_797_4]) ).

cnf(f_797_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(U_2246,U_2245))
    | sP199(U_2246,U_2245)
    | ~ hBOOL(hAPP_f1664156314l_bool(U_2246,bot_bo844097828e_bool))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2245)) ),
    inference(clausify,[status(thm)],[f_797_5]) ).

cnf(f_797_7,plain,
    ( is_pname(sK123(U_2246,U_2245))
    | ~ sP199(U_2246,U_2245) ),
    inference(clausify,[status(thm)],[f_797_5]) ).

cnf(f_797_8,plain,
    ( is_fun_pname_bool(sK124(U_2246,U_2245))
    | ~ sP199(U_2246,U_2245) ),
    inference(clausify,[status(thm)],[f_797_5]) ).

cnf(f_797_9,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK124(U_2246,U_2245)))
    | ~ sP199(U_2246,U_2245) ),
    inference(clausify,[status(thm)],[f_797_5]) ).

cnf(f_797_10,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK123(U_2246,U_2245)),sK124(U_2246,U_2245)))
    | ~ sP199(U_2246,U_2245) ),
    inference(clausify,[status(thm)],[f_797_5]) ).

cnf(f_797_11,plain,
    ( hBOOL(hAPP_f1664156314l_bool(U_2246,sK124(U_2246,U_2245)))
    | ~ sP199(U_2246,U_2245) ),
    inference(clausify,[status(thm)],[f_797_5]) ).

cnf(f_797_12,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(U_2246,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK123(U_2246,U_2245)),sK124(U_2246,U_2245))))
    | ~ sP199(U_2246,U_2245) ),
    inference(clausify,[status(thm)],[f_797_5]) ).

fof(f_798_1,plain,
    ! [A_2] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_2))
          | ( ! [A_15,A_14] :
                ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_15))
                | A_2 != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_14),A_15)
                | ~ is_a(A_14)
                | ~ is_fun_a_bool(A_15) )
            & A_2 != bot_bot_fun_a_bool ) )
        & ( ? [A_15,A_14] :
              ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_15))
              & A_2 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_14),A_15)
              & is_a(A_14)
              & is_fun_a_bool(A_15) )
          | A_2 = bot_bot_fun_a_bool
          | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A_2)) ) )
      | ~ is_fun_a_bool(A_2) ),
    inference(fof_nnf,[status(thm)],[fact_691_finite_Osimps]) ).

fof(f_798_2,plain,
    ! [U_2251] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2251))
          | ( ! [U_2250,U_2249] :
                ( ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2250))
                | U_2251 != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2249),U_2250)
                | ~ is_a(U_2249)
                | ~ is_fun_a_bool(U_2250) )
            & U_2251 != bot_bot_fun_a_bool ) )
        & ( ? [U_2248,U_2247] :
              ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2248))
              & U_2251 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2247),U_2248)
              & is_a(U_2247)
              & is_fun_a_bool(U_2248) )
          | U_2251 = bot_bot_fun_a_bool
          | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2251)) ) )
      | ~ is_fun_a_bool(U_2251) ),
    inference(variable_rename,[status(thm)],[f_798_1]) ).

fof(f_798_3,plain,
    ! [U_2251] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2251))
          | ( ! [U_2250] :
                ( ! [U_2249] :
                    ( U_2251 != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2249),U_2250)
                    | ~ is_a(U_2249) )
                | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2250))
                | ~ is_fun_a_bool(U_2250) )
            & U_2251 != bot_bot_fun_a_bool ) )
        & ( ? [U_2248] :
              ( ? [U_2247] :
                  ( U_2251 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2247),U_2248)
                  & is_a(U_2247) )
              & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2248))
              & is_fun_a_bool(U_2248) )
          | U_2251 = bot_bot_fun_a_bool
          | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2251)) ) )
      | ~ is_fun_a_bool(U_2251) ),
    inference(miniscope,[status(thm)],[f_798_2]) ).

fof(f_798_4,plain,
    ! [U_2251] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2251))
          | ( ! [U_2250] :
                ( ! [U_2249] :
                    ( U_2251 != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2249),U_2250)
                    | ~ is_a(U_2249) )
                | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2250))
                | ~ is_fun_a_bool(U_2250) )
            & U_2251 != bot_bot_fun_a_bool ) )
        & ( ( ? [U_2247] :
                ( U_2251 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2247),sK125(U_2251))
                & is_a(U_2247) )
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK125(U_2251)))
            & is_fun_a_bool(sK125(U_2251)) )
          | U_2251 = bot_bot_fun_a_bool
          | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2251)) ) )
      | ~ is_fun_a_bool(U_2251) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_2248,sK125(U_2251))],[f_798_3]) ).

fof(f_798_5,plain,
    ! [U_2251] :
      ( ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2251))
          | ( ! [U_2250] :
                ( ! [U_2249] :
                    ( U_2251 != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2249),U_2250)
                    | ~ is_a(U_2249) )
                | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2250))
                | ~ is_fun_a_bool(U_2250) )
            & U_2251 != bot_bot_fun_a_bool ) )
        & ( ( U_2251 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK126(U_2251)),sK125(U_2251))
            & is_a(sK126(U_2251))
            & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK125(U_2251)))
            & is_fun_a_bool(sK125(U_2251)) )
          | U_2251 = bot_bot_fun_a_bool
          | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2251)) ) )
      | ~ is_fun_a_bool(U_2251) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_2247,sK126(U_2251))],[f_798_4]) ).

fof(f_798_6,plain,
    ( ! [U_2249,U_2251,U_2250] :
        ( U_2251 != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2249),U_2250)
        | ~ is_a(U_2249)
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2250))
        | ~ is_fun_a_bool(U_2250)
        | ~ sP201(U_2249,U_2251,U_2250) )
    & ! [U_2249,U_2251,U_2250] :
        ( U_2251 != bot_bot_fun_a_bool
        | ~ sP201(U_2249,U_2251,U_2250) )
    & ! [U_2251] :
        ( U_2251 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK126(U_2251)),sK125(U_2251))
        | ~ sP200(U_2251) )
    & ! [U_2251] :
        ( is_a(sK126(U_2251))
        | ~ sP200(U_2251) )
    & ! [U_2251] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK125(U_2251)))
        | ~ sP200(U_2251) )
    & ! [U_2251] :
        ( is_fun_a_bool(sK125(U_2251))
        | ~ sP200(U_2251) )
    & ! [U_2249,U_2251,U_2250] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2251))
        | sP201(U_2249,U_2251,U_2250)
        | ~ sP202(U_2249,U_2251,U_2250) )
    & ! [U_2249,U_2251,U_2250] :
        ( sP200(U_2251)
        | U_2251 = bot_bot_fun_a_bool
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2251))
        | ~ sP202(U_2249,U_2251,U_2250) )
    & ! [U_2249,U_2251,U_2250] :
        ( sP202(U_2249,U_2251,U_2250)
        | ~ is_fun_a_bool(U_2251) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP200,sP201,sP202])],[f_798_5]) ).

cnf(f_798_7,plain,
    ( sP202(U_2249,U_2251,U_2250)
    | ~ is_fun_a_bool(U_2251) ),
    inference(clausify,[status(thm)],[f_798_6]) ).

cnf(f_798_8,plain,
    ( sP200(U_2251)
    | U_2251 = bot_bot_fun_a_bool
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2251))
    | ~ sP202(U_2249,U_2251,U_2250) ),
    inference(clausify,[status(thm)],[f_798_6]) ).

cnf(f_798_9,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2251))
    | sP201(U_2249,U_2251,U_2250)
    | ~ sP202(U_2249,U_2251,U_2250) ),
    inference(clausify,[status(thm)],[f_798_6]) ).

cnf(f_798_10,plain,
    ( is_fun_a_bool(sK125(U_2251))
    | ~ sP200(U_2251) ),
    inference(clausify,[status(thm)],[f_798_6]) ).

cnf(f_798_11,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK125(U_2251)))
    | ~ sP200(U_2251) ),
    inference(clausify,[status(thm)],[f_798_6]) ).

cnf(f_798_12,plain,
    ( is_a(sK126(U_2251))
    | ~ sP200(U_2251) ),
    inference(clausify,[status(thm)],[f_798_6]) ).

cnf(f_798_13,plain,
    ( U_2251 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK126(U_2251)),sK125(U_2251))
    | ~ sP200(U_2251) ),
    inference(clausify,[status(thm)],[f_798_6]) ).

cnf(f_798_14,plain,
    ( U_2251 != bot_bot_fun_a_bool
    | ~ sP201(U_2249,U_2251,U_2250) ),
    inference(clausify,[status(thm)],[f_798_6]) ).

cnf(f_798_15,plain,
    ( U_2251 != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2249),U_2250)
    | ~ is_a(U_2249)
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2250))
    | ~ is_fun_a_bool(U_2250)
    | ~ sP201(U_2249,U_2251,U_2250) ),
    inference(clausify,[status(thm)],[f_798_6]) ).

fof(f_799_1,plain,
    ! [A_2] :
      ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2))
        | ( ! [A_15,A_14] :
              ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_15))
              | A_2 != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_14),A_15) )
          & A_2 != bot_bot_fun_int_bool ) )
      & ( ? [A_15,A_14] :
            ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_15))
            & A_2 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_14),A_15) )
        | A_2 = bot_bot_fun_int_bool
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_692_finite_Osimps]) ).

fof(f_799_2,plain,
    ! [U_2256] :
      ( ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2256))
        | ( ! [U_2255,U_2254] :
              ( ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2255))
              | U_2256 != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2254),U_2255) )
          & U_2256 != bot_bot_fun_int_bool ) )
      & ( ? [U_2253,U_2252] :
            ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2253))
            & U_2256 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2252),U_2253) )
        | U_2256 = bot_bot_fun_int_bool
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2256)) ) ),
    inference(variable_rename,[status(thm)],[f_799_1]) ).

fof(f_799_3,plain,
    ( ! [U_2258] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2258))
        | ( ! [U_2255] :
              ( ! [U_2254] : U_2258 != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2254),U_2255)
              | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2255)) )
          & U_2258 != bot_bot_fun_int_bool ) )
    & ! [U_2257] :
        ( ? [U_2253] :
            ( ? [U_2252] : U_2257 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2252),U_2253)
            & hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2253)) )
        | U_2257 = bot_bot_fun_int_bool
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2257)) ) ),
    inference(miniscope,[status(thm)],[f_799_2]) ).

fof(f_799_4,plain,
    ( ! [U_2258] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2258))
        | ( ! [U_2255] :
              ( ! [U_2254] : U_2258 != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2254),U_2255)
              | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2255)) )
          & U_2258 != bot_bot_fun_int_bool ) )
    & ! [U_2257] :
        ( ( ? [U_2252] : U_2257 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2252),sK127(U_2257))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK127(U_2257))) )
        | U_2257 = bot_bot_fun_int_bool
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2257)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_2253,sK127(U_2257))],[f_799_3]) ).

fof(f_799_5,plain,
    ( ! [U_2258] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2258))
        | ( ! [U_2255] :
              ( ! [U_2254] : U_2258 != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2254),U_2255)
              | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2255)) )
          & U_2258 != bot_bot_fun_int_bool ) )
    & ! [U_2257] :
        ( ( U_2257 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK128(U_2257)),sK127(U_2257))
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK127(U_2257))) )
        | U_2257 = bot_bot_fun_int_bool
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2257)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_2252,sK128(U_2257))],[f_799_4]) ).

fof(f_799_6,plain,
    ( ! [U_2255,U_2258,U_2254] :
        ( U_2258 != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2254),U_2255)
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2255))
        | ~ sP204(U_2255,U_2258,U_2254) )
    & ! [U_2255,U_2258,U_2254] :
        ( U_2258 != bot_bot_fun_int_bool
        | ~ sP204(U_2255,U_2258,U_2254) )
    & ! [U_2257] :
        ( U_2257 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK128(U_2257)),sK127(U_2257))
        | ~ sP203(U_2257) )
    & ! [U_2257] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK127(U_2257)))
        | ~ sP203(U_2257) )
    & ! [U_2255,U_2258,U_2254] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2258))
        | sP204(U_2255,U_2258,U_2254) )
    & ! [U_2257] :
        ( sP203(U_2257)
        | U_2257 = bot_bot_fun_int_bool
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2257)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP203,sP204])],[f_799_5]) ).

cnf(f_799_7,plain,
    ( sP203(U_2257)
    | U_2257 = bot_bot_fun_int_bool
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2257)) ),
    inference(clausify,[status(thm)],[f_799_6]) ).

cnf(f_799_8,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2258))
    | sP204(U_2255,U_2258,U_2254) ),
    inference(clausify,[status(thm)],[f_799_6]) ).

cnf(f_799_9,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK127(U_2257)))
    | ~ sP203(U_2257) ),
    inference(clausify,[status(thm)],[f_799_6]) ).

cnf(f_799_10,plain,
    ( U_2257 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK128(U_2257)),sK127(U_2257))
    | ~ sP203(U_2257) ),
    inference(clausify,[status(thm)],[f_799_6]) ).

cnf(f_799_11,plain,
    ( U_2258 != bot_bot_fun_int_bool
    | ~ sP204(U_2255,U_2258,U_2254) ),
    inference(clausify,[status(thm)],[f_799_6]) ).

cnf(f_799_12,plain,
    ( U_2258 != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2254),U_2255)
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2255))
    | ~ sP204(U_2255,U_2258,U_2254) ),
    inference(clausify,[status(thm)],[f_799_6]) ).

fof(f_800_1,plain,
    ! [A_2] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2))
        | ( ! [A_15,A_14] :
              ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_15))
              | A_2 != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_14),A_15) )
          & A_2 != bot_bot_fun_nat_bool ) )
      & ( ? [A_15,A_14] :
            ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_15))
            & A_2 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_14),A_15) )
        | A_2 = bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_693_finite_Osimps]) ).

fof(f_800_2,plain,
    ! [U_2263] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2263))
        | ( ! [U_2262,U_2261] :
              ( ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2262))
              | U_2263 != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2261),U_2262) )
          & U_2263 != bot_bot_fun_nat_bool ) )
      & ( ? [U_2260,U_2259] :
            ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2260))
            & U_2263 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2259),U_2260) )
        | U_2263 = bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2263)) ) ),
    inference(variable_rename,[status(thm)],[f_800_1]) ).

fof(f_800_3,plain,
    ( ! [U_2265] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2265))
        | ( ! [U_2262] :
              ( ! [U_2261] : U_2265 != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2261),U_2262)
              | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2262)) )
          & U_2265 != bot_bot_fun_nat_bool ) )
    & ! [U_2264] :
        ( ? [U_2260] :
            ( ? [U_2259] : U_2264 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2259),U_2260)
            & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2260)) )
        | U_2264 = bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2264)) ) ),
    inference(miniscope,[status(thm)],[f_800_2]) ).

fof(f_800_4,plain,
    ( ! [U_2265] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2265))
        | ( ! [U_2262] :
              ( ! [U_2261] : U_2265 != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2261),U_2262)
              | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2262)) )
          & U_2265 != bot_bot_fun_nat_bool ) )
    & ! [U_2264] :
        ( ( ? [U_2259] : U_2264 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2259),sK129(U_2264))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK129(U_2264))) )
        | U_2264 = bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2264)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(U_2260,sK129(U_2264))],[f_800_3]) ).

fof(f_800_5,plain,
    ( ! [U_2265] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2265))
        | ( ! [U_2262] :
              ( ! [U_2261] : U_2265 != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2261),U_2262)
              | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2262)) )
          & U_2265 != bot_bot_fun_nat_bool ) )
    & ! [U_2264] :
        ( ( U_2264 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK130(U_2264)),sK129(U_2264))
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK129(U_2264))) )
        | U_2264 = bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2264)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(U_2259,sK130(U_2264))],[f_800_4]) ).

fof(f_800_6,plain,
    ( ! [U_2262,U_2265,U_2261] :
        ( U_2265 != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2261),U_2262)
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2262))
        | ~ sP206(U_2262,U_2265,U_2261) )
    & ! [U_2262,U_2265,U_2261] :
        ( U_2265 != bot_bot_fun_nat_bool
        | ~ sP206(U_2262,U_2265,U_2261) )
    & ! [U_2264] :
        ( U_2264 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK130(U_2264)),sK129(U_2264))
        | ~ sP205(U_2264) )
    & ! [U_2264] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK129(U_2264)))
        | ~ sP205(U_2264) )
    & ! [U_2262,U_2265,U_2261] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2265))
        | sP206(U_2262,U_2265,U_2261) )
    & ! [U_2264] :
        ( sP205(U_2264)
        | U_2264 = bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2264)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP205,sP206])],[f_800_5]) ).

cnf(f_800_7,plain,
    ( sP205(U_2264)
    | U_2264 = bot_bot_fun_nat_bool
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2264)) ),
    inference(clausify,[status(thm)],[f_800_6]) ).

cnf(f_800_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2265))
    | sP206(U_2262,U_2265,U_2261) ),
    inference(clausify,[status(thm)],[f_800_6]) ).

cnf(f_800_9,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK129(U_2264)))
    | ~ sP205(U_2264) ),
    inference(clausify,[status(thm)],[f_800_6]) ).

cnf(f_800_10,plain,
    ( U_2264 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK130(U_2264)),sK129(U_2264))
    | ~ sP205(U_2264) ),
    inference(clausify,[status(thm)],[f_800_6]) ).

cnf(f_800_11,plain,
    ( U_2265 != bot_bot_fun_nat_bool
    | ~ sP206(U_2262,U_2265,U_2261) ),
    inference(clausify,[status(thm)],[f_800_6]) ).

cnf(f_800_12,plain,
    ( U_2265 != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2261),U_2262)
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2262))
    | ~ sP206(U_2262,U_2265,U_2261) ),
    inference(clausify,[status(thm)],[f_800_6]) ).

fof(f_801_1,plain,
    ! [A_2] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_2))
          | ( ! [A_15,A_14] :
                ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_15))
                | A_2 != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_14),A_15)
                | ~ is_pname(A_14)
                | ~ is_fun_pname_bool(A_15) )
            & A_2 != bot_bo844097828e_bool ) )
        & ( ? [A_15,A_14] :
              ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_15))
              & A_2 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_14),A_15)
              & is_pname(A_14)
              & is_fun_pname_bool(A_15) )
          | A_2 = bot_bo844097828e_bool
          | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A_2)) ) )
      | ~ is_fun_pname_bool(A_2) ),
    inference(fof_nnf,[status(thm)],[fact_694_finite_Osimps]) ).

fof(f_801_2,plain,
    ! [U_2270] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2270))
          | ( ! [U_2269,U_2268] :
                ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2269))
                | U_2270 != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2268),U_2269)
                | ~ is_pname(U_2268)
                | ~ is_fun_pname_bool(U_2269) )
            & U_2270 != bot_bo844097828e_bool ) )
        & ( ? [U_2267,U_2266] :
              ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2267))
              & U_2270 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2266),U_2267)
              & is_pname(U_2266)
              & is_fun_pname_bool(U_2267) )
          | U_2270 = bot_bo844097828e_bool
          | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2270)) ) )
      | ~ is_fun_pname_bool(U_2270) ),
    inference(variable_rename,[status(thm)],[f_801_1]) ).

fof(f_801_3,plain,
    ! [U_2270] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2270))
          | ( ! [U_2269] :
                ( ! [U_2268] :
                    ( U_2270 != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2268),U_2269)
                    | ~ is_pname(U_2268) )
                | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2269))
                | ~ is_fun_pname_bool(U_2269) )
            & U_2270 != bot_bo844097828e_bool ) )
        & ( ? [U_2267] :
              ( ? [U_2266] :
                  ( U_2270 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2266),U_2267)
                  & is_pname(U_2266) )
              & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2267))
              & is_fun_pname_bool(U_2267) )
          | U_2270 = bot_bo844097828e_bool
          | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2270)) ) )
      | ~ is_fun_pname_bool(U_2270) ),
    inference(miniscope,[status(thm)],[f_801_2]) ).

fof(f_801_4,plain,
    ! [U_2270] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2270))
          | ( ! [U_2269] :
                ( ! [U_2268] :
                    ( U_2270 != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2268),U_2269)
                    | ~ is_pname(U_2268) )
                | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2269))
                | ~ is_fun_pname_bool(U_2269) )
            & U_2270 != bot_bo844097828e_bool ) )
        & ( ( ? [U_2266] :
                ( U_2270 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2266),sK131(U_2270))
                & is_pname(U_2266) )
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK131(U_2270)))
            & is_fun_pname_bool(sK131(U_2270)) )
          | U_2270 = bot_bo844097828e_bool
          | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2270)) ) )
      | ~ is_fun_pname_bool(U_2270) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(U_2267,sK131(U_2270))],[f_801_3]) ).

fof(f_801_5,plain,
    ! [U_2270] :
      ( ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2270))
          | ( ! [U_2269] :
                ( ! [U_2268] :
                    ( U_2270 != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2268),U_2269)
                    | ~ is_pname(U_2268) )
                | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2269))
                | ~ is_fun_pname_bool(U_2269) )
            & U_2270 != bot_bo844097828e_bool ) )
        & ( ( U_2270 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK132(U_2270)),sK131(U_2270))
            & is_pname(sK132(U_2270))
            & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK131(U_2270)))
            & is_fun_pname_bool(sK131(U_2270)) )
          | U_2270 = bot_bo844097828e_bool
          | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2270)) ) )
      | ~ is_fun_pname_bool(U_2270) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(U_2266,sK132(U_2270))],[f_801_4]) ).

fof(f_801_6,plain,
    ( ! [U_2270,U_2269,U_2268] :
        ( U_2270 != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2268),U_2269)
        | ~ is_pname(U_2268)
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2269))
        | ~ is_fun_pname_bool(U_2269)
        | ~ sP208(U_2270,U_2269,U_2268) )
    & ! [U_2270,U_2269,U_2268] :
        ( U_2270 != bot_bo844097828e_bool
        | ~ sP208(U_2270,U_2269,U_2268) )
    & ! [U_2270] :
        ( U_2270 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK132(U_2270)),sK131(U_2270))
        | ~ sP207(U_2270) )
    & ! [U_2270] :
        ( is_pname(sK132(U_2270))
        | ~ sP207(U_2270) )
    & ! [U_2270] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK131(U_2270)))
        | ~ sP207(U_2270) )
    & ! [U_2270] :
        ( is_fun_pname_bool(sK131(U_2270))
        | ~ sP207(U_2270) )
    & ! [U_2270,U_2269,U_2268] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2270))
        | sP208(U_2270,U_2269,U_2268)
        | ~ sP209(U_2270,U_2269,U_2268) )
    & ! [U_2270,U_2269,U_2268] :
        ( sP207(U_2270)
        | U_2270 = bot_bo844097828e_bool
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2270))
        | ~ sP209(U_2270,U_2269,U_2268) )
    & ! [U_2270,U_2269,U_2268] :
        ( sP209(U_2270,U_2269,U_2268)
        | ~ is_fun_pname_bool(U_2270) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP207,sP208,sP209])],[f_801_5]) ).

cnf(f_801_7,plain,
    ( sP209(U_2270,U_2269,U_2268)
    | ~ is_fun_pname_bool(U_2270) ),
    inference(clausify,[status(thm)],[f_801_6]) ).

cnf(f_801_8,plain,
    ( sP207(U_2270)
    | U_2270 = bot_bo844097828e_bool
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2270))
    | ~ sP209(U_2270,U_2269,U_2268) ),
    inference(clausify,[status(thm)],[f_801_6]) ).

cnf(f_801_9,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2270))
    | sP208(U_2270,U_2269,U_2268)
    | ~ sP209(U_2270,U_2269,U_2268) ),
    inference(clausify,[status(thm)],[f_801_6]) ).

cnf(f_801_10,plain,
    ( is_fun_pname_bool(sK131(U_2270))
    | ~ sP207(U_2270) ),
    inference(clausify,[status(thm)],[f_801_6]) ).

cnf(f_801_11,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK131(U_2270)))
    | ~ sP207(U_2270) ),
    inference(clausify,[status(thm)],[f_801_6]) ).

cnf(f_801_12,plain,
    ( is_pname(sK132(U_2270))
    | ~ sP207(U_2270) ),
    inference(clausify,[status(thm)],[f_801_6]) ).

cnf(f_801_13,plain,
    ( U_2270 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK132(U_2270)),sK131(U_2270))
    | ~ sP207(U_2270) ),
    inference(clausify,[status(thm)],[f_801_6]) ).

cnf(f_801_14,plain,
    ( U_2270 != bot_bo844097828e_bool
    | ~ sP208(U_2270,U_2269,U_2268) ),
    inference(clausify,[status(thm)],[f_801_6]) ).

cnf(f_801_15,plain,
    ( U_2270 != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2268),U_2269)
    | ~ is_pname(U_2268)
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2269))
    | ~ is_fun_pname_bool(U_2269)
    | ~ sP208(U_2270,U_2269,U_2268) ),
    inference(clausify,[status(thm)],[f_801_6]) ).

fof(f_802_1,plain,
    ! [U,F] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,F)),U))))
      | ? [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(F,N_1))) ),
    inference(fof_nnf,[status(thm)],[fact_695_finite__less__ub]) ).

fof(f_802_2,plain,
    ! [U_2273,U_2272] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,U_2272)),U_2273))))
      | ? [U_2271] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2271),hAPP_nat_nat(U_2272,U_2271))) ),
    inference(variable_rename,[status(thm)],[f_802_1]) ).

fof(f_802_3,plain,
    ! [U_2273,U_2272] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,U_2272)),U_2273))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK133(U_2273,U_2272)),hAPP_nat_nat(U_2272,sK133(U_2273,U_2272)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(U_2271,sK133(U_2273,U_2272))],[f_802_2]) ).

fof(f_802_4,plain,
    ! [U_2273,U_2272] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,U_2272)),U_2273))))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK133(U_2273,U_2272)),hAPP_nat_nat(U_2272,sK133(U_2273,U_2272)))) ),
    inference(definitional_conversion,[status(esa)],[f_802_3]) ).

cnf(f_802_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(cOMBB_800536526ol_nat(ord_less_eq_nat,U_2272)),U_2273))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK133(U_2273,U_2272)),hAPP_nat_nat(U_2272,sK133(U_2273,U_2272)))) ),
    inference(clausify,[status(thm)],[f_802_4]) ).

fof(f_803_1,plain,
    ! [X_1] :
      ( hAPP_fun_a_bool_a(the_elem_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)) = X_1
      | ~ is_a(X_1) ),
    inference(fof_nnf,[status(thm)],[fact_696_the__elem__eq]) ).

fof(f_803_2,plain,
    ! [U_2274] :
      ( hAPP_fun_a_bool_a(the_elem_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2274),bot_bot_fun_a_bool)) = U_2274
      | ~ is_a(U_2274) ),
    inference(variable_rename,[status(thm)],[f_803_1]) ).

fof(f_803_3,plain,
    ! [U_2274] :
      ( hAPP_fun_a_bool_a(the_elem_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2274),bot_bot_fun_a_bool)) = U_2274
      | ~ is_a(U_2274) ),
    inference(definitional_conversion,[status(esa)],[f_803_2]) ).

cnf(f_803_4,plain,
    ( hAPP_fun_a_bool_a(the_elem_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2274),bot_bot_fun_a_bool)) = U_2274
    | ~ is_a(U_2274) ),
    inference(clausify,[status(thm)],[f_803_3]) ).

fof(f_804_1,plain,
    ! [X_1] : hAPP_f22106695ol_nat(the_elem_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = X_1,
    inference(fof_nnf,[status(thm)],[fact_697_the__elem__eq]) ).

fof(f_804_2,plain,
    ! [U_2275] : hAPP_f22106695ol_nat(the_elem_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2275),bot_bot_fun_nat_bool)) = U_2275,
    inference(variable_rename,[status(thm)],[f_804_1]) ).

fof(f_804_3,plain,
    ! [U_2275] : hAPP_f22106695ol_nat(the_elem_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2275),bot_bot_fun_nat_bool)) = U_2275,
    inference(definitional_conversion,[status(esa)],[f_804_2]) ).

cnf(f_804_4,plain,
    hAPP_f22106695ol_nat(the_elem_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2275),bot_bot_fun_nat_bool)) = U_2275,
    inference(clausify,[status(thm)],[f_804_3]) ).

fof(f_805_1,plain,
    ! [X_1] : hAPP_f1594865479ol_int(the_elem_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = X_1,
    inference(fof_nnf,[status(thm)],[fact_698_the__elem__eq]) ).

fof(f_805_2,plain,
    ! [U_2276] : hAPP_f1594865479ol_int(the_elem_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2276),bot_bot_fun_int_bool)) = U_2276,
    inference(variable_rename,[status(thm)],[f_805_1]) ).

fof(f_805_3,plain,
    ! [U_2276] : hAPP_f1594865479ol_int(the_elem_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2276),bot_bot_fun_int_bool)) = U_2276,
    inference(definitional_conversion,[status(esa)],[f_805_2]) ).

cnf(f_805_4,plain,
    hAPP_f1594865479ol_int(the_elem_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2276),bot_bot_fun_int_bool)) = U_2276,
    inference(clausify,[status(thm)],[f_805_3]) ).

fof(f_806_1,plain,
    ! [A] :
      ( ( ( A != bot_bot_fun_a_bool
          | ! [X_2,B_15] :
              ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B_15))
              | A != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_2),B_15)
              | ~ is_fun_a_bool(B_15)
              | ~ is_a(X_2) ) )
        & ( ? [X_2,B_15] :
              ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B_15))
              & A = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_2),B_15)
              & is_fun_a_bool(B_15)
              & is_a(X_2) )
          | A = bot_bot_fun_a_bool ) )
      | ~ is_fun_a_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_699_nonempty__iff]) ).

fof(f_806_2,plain,
    ! [U_2281] :
      ( ( ( U_2281 != bot_bot_fun_a_bool
          | ! [U_2280,U_2279] :
              ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2280),U_2279))
              | U_2281 != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2280),U_2279)
              | ~ is_fun_a_bool(U_2279)
              | ~ is_a(U_2280) ) )
        & ( ? [U_2278,U_2277] :
              ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2278),U_2277))
              & U_2281 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2278),U_2277)
              & is_fun_a_bool(U_2277)
              & is_a(U_2278) )
          | U_2281 = bot_bot_fun_a_bool ) )
      | ~ is_fun_a_bool(U_2281) ),
    inference(variable_rename,[status(thm)],[f_806_1]) ).

fof(f_806_3,plain,
    ! [U_2281] :
      ( ( ( U_2281 != bot_bot_fun_a_bool
          | ! [U_2280] :
              ( ! [U_2279] :
                  ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2280),U_2279))
                  | U_2281 != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2280),U_2279)
                  | ~ is_fun_a_bool(U_2279) )
              | ~ is_a(U_2280) ) )
        & ( ? [U_2278] :
              ( ? [U_2277] :
                  ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2278),U_2277))
                  & U_2281 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2278),U_2277)
                  & is_fun_a_bool(U_2277) )
              & is_a(U_2278) )
          | U_2281 = bot_bot_fun_a_bool ) )
      | ~ is_fun_a_bool(U_2281) ),
    inference(miniscope,[status(thm)],[f_806_2]) ).

fof(f_806_4,plain,
    ! [U_2281] :
      ( ( ( U_2281 != bot_bot_fun_a_bool
          | ! [U_2280] :
              ( ! [U_2279] :
                  ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2280),U_2279))
                  | U_2281 != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2280),U_2279)
                  | ~ is_fun_a_bool(U_2279) )
              | ~ is_a(U_2280) ) )
        & ( ( ? [U_2277] :
                ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK134(U_2281)),U_2277))
                & U_2281 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK134(U_2281)),U_2277)
                & is_fun_a_bool(U_2277) )
            & is_a(sK134(U_2281)) )
          | U_2281 = bot_bot_fun_a_bool ) )
      | ~ is_fun_a_bool(U_2281) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(U_2278,sK134(U_2281))],[f_806_3]) ).

fof(f_806_5,plain,
    ! [U_2281] :
      ( ( ( U_2281 != bot_bot_fun_a_bool
          | ! [U_2280] :
              ( ! [U_2279] :
                  ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2280),U_2279))
                  | U_2281 != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2280),U_2279)
                  | ~ is_fun_a_bool(U_2279) )
              | ~ is_a(U_2280) ) )
        & ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK134(U_2281)),sK135(U_2281)))
            & U_2281 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK134(U_2281)),sK135(U_2281))
            & is_fun_a_bool(sK135(U_2281))
            & is_a(sK134(U_2281)) )
          | U_2281 = bot_bot_fun_a_bool ) )
      | ~ is_fun_a_bool(U_2281) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(U_2277,sK135(U_2281))],[f_806_4]) ).

fof(f_806_6,plain,
    ( ! [U_2281] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK134(U_2281)),sK135(U_2281)))
        | ~ sP210(U_2281) )
    & ! [U_2281] :
        ( U_2281 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK134(U_2281)),sK135(U_2281))
        | ~ sP210(U_2281) )
    & ! [U_2281] :
        ( is_fun_a_bool(sK135(U_2281))
        | ~ sP210(U_2281) )
    & ! [U_2281] :
        ( is_a(sK134(U_2281))
        | ~ sP210(U_2281) )
    & ! [U_2279,U_2280,U_2281] :
        ( U_2281 != bot_bot_fun_a_bool
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2280),U_2279))
        | U_2281 != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2280),U_2279)
        | ~ is_fun_a_bool(U_2279)
        | ~ is_a(U_2280)
        | ~ sP211(U_2279,U_2280,U_2281) )
    & ! [U_2279,U_2280,U_2281] :
        ( sP210(U_2281)
        | U_2281 = bot_bot_fun_a_bool
        | ~ sP211(U_2279,U_2280,U_2281) )
    & ! [U_2279,U_2280,U_2281] :
        ( sP211(U_2279,U_2280,U_2281)
        | ~ is_fun_a_bool(U_2281) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP210,sP211])],[f_806_5]) ).

cnf(f_806_7,plain,
    ( sP211(U_2279,U_2280,U_2281)
    | ~ is_fun_a_bool(U_2281) ),
    inference(clausify,[status(thm)],[f_806_6]) ).

cnf(f_806_8,plain,
    ( sP210(U_2281)
    | U_2281 = bot_bot_fun_a_bool
    | ~ sP211(U_2279,U_2280,U_2281) ),
    inference(clausify,[status(thm)],[f_806_6]) ).

cnf(f_806_9,plain,
    ( U_2281 != bot_bot_fun_a_bool
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2280),U_2279))
    | U_2281 != hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2280),U_2279)
    | ~ is_fun_a_bool(U_2279)
    | ~ is_a(U_2280)
    | ~ sP211(U_2279,U_2280,U_2281) ),
    inference(clausify,[status(thm)],[f_806_6]) ).

cnf(f_806_10,plain,
    ( is_a(sK134(U_2281))
    | ~ sP210(U_2281) ),
    inference(clausify,[status(thm)],[f_806_6]) ).

cnf(f_806_11,plain,
    ( is_fun_a_bool(sK135(U_2281))
    | ~ sP210(U_2281) ),
    inference(clausify,[status(thm)],[f_806_6]) ).

cnf(f_806_12,plain,
    ( U_2281 = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK134(U_2281)),sK135(U_2281))
    | ~ sP210(U_2281) ),
    inference(clausify,[status(thm)],[f_806_6]) ).

cnf(f_806_13,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK134(U_2281)),sK135(U_2281)))
    | ~ sP210(U_2281) ),
    inference(clausify,[status(thm)],[f_806_6]) ).

fof(f_807_1,plain,
    ! [A] :
      ( ( A != bot_bot_fun_int_bool
        | ! [X_2,B_15] :
            ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),B_15))
            | A != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),B_15) ) )
      & ( ? [X_2,B_15] :
            ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),B_15))
            & A = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),B_15) )
        | A = bot_bot_fun_int_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_700_nonempty__iff]) ).

fof(f_807_2,plain,
    ! [U_2286] :
      ( ( U_2286 != bot_bot_fun_int_bool
        | ! [U_2285,U_2284] :
            ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2285),U_2284))
            | U_2286 != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2285),U_2284) ) )
      & ( ? [U_2283,U_2282] :
            ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2283),U_2282))
            & U_2286 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2283),U_2282) )
        | U_2286 = bot_bot_fun_int_bool ) ),
    inference(variable_rename,[status(thm)],[f_807_1]) ).

fof(f_807_3,plain,
    ( ! [U_2288] :
        ( U_2288 != bot_bot_fun_int_bool
        | ! [U_2285,U_2284] :
            ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2285),U_2284))
            | U_2288 != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2285),U_2284) ) )
    & ! [U_2287] :
        ( ? [U_2283,U_2282] :
            ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2283),U_2282))
            & U_2287 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2283),U_2282) )
        | U_2287 = bot_bot_fun_int_bool ) ),
    inference(miniscope,[status(thm)],[f_807_2]) ).

fof(f_807_4,plain,
    ( ! [U_2288] :
        ( U_2288 != bot_bot_fun_int_bool
        | ! [U_2285,U_2284] :
            ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2285),U_2284))
            | U_2288 != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2285),U_2284) ) )
    & ! [U_2287] :
        ( ? [U_2282] :
            ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK136(U_2287)),U_2282))
            & U_2287 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK136(U_2287)),U_2282) )
        | U_2287 = bot_bot_fun_int_bool ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK136]),skolemize(U_2283,sK136(U_2287))],[f_807_3]) ).

fof(f_807_5,plain,
    ( ! [U_2288] :
        ( U_2288 != bot_bot_fun_int_bool
        | ! [U_2285,U_2284] :
            ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2285),U_2284))
            | U_2288 != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2285),U_2284) ) )
    & ! [U_2287] :
        ( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK136(U_2287)),sK137(U_2287)))
          & U_2287 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK136(U_2287)),sK137(U_2287)) )
        | U_2287 = bot_bot_fun_int_bool ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK137]),skolemize(U_2282,sK137(U_2287))],[f_807_4]) ).

fof(f_807_6,plain,
    ( ! [U_2287] :
        ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK136(U_2287)),sK137(U_2287)))
        | ~ sP212(U_2287) )
    & ! [U_2287] :
        ( U_2287 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK136(U_2287)),sK137(U_2287))
        | ~ sP212(U_2287) )
    & ! [U_2285,U_2284,U_2288] :
        ( U_2288 != bot_bot_fun_int_bool
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2285),U_2284))
        | U_2288 != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2285),U_2284) )
    & ! [U_2287] :
        ( sP212(U_2287)
        | U_2287 = bot_bot_fun_int_bool ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP212])],[f_807_5]) ).

cnf(f_807_7,plain,
    ( sP212(U_2287)
    | U_2287 = bot_bot_fun_int_bool ),
    inference(clausify,[status(thm)],[f_807_6]) ).

cnf(f_807_8,plain,
    ( U_2288 != bot_bot_fun_int_bool
    | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2285),U_2284))
    | U_2288 != hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2285),U_2284) ),
    inference(clausify,[status(thm)],[f_807_6]) ).

cnf(f_807_9,plain,
    ( U_2287 = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK136(U_2287)),sK137(U_2287))
    | ~ sP212(U_2287) ),
    inference(clausify,[status(thm)],[f_807_6]) ).

cnf(f_807_10,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK136(U_2287)),sK137(U_2287)))
    | ~ sP212(U_2287) ),
    inference(clausify,[status(thm)],[f_807_6]) ).

fof(f_808_1,plain,
    ! [A] :
      ( ( A != bot_bot_fun_nat_bool
        | ! [X_2,B_15] :
            ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_15))
            | A != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),B_15) ) )
      & ( ? [X_2,B_15] :
            ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B_15))
            & A = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),B_15) )
        | A = bot_bot_fun_nat_bool ) ),
    inference(fof_nnf,[status(thm)],[fact_701_nonempty__iff]) ).

fof(f_808_2,plain,
    ! [U_2293] :
      ( ( U_2293 != bot_bot_fun_nat_bool
        | ! [U_2292,U_2291] :
            ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2292),U_2291))
            | U_2293 != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2292),U_2291) ) )
      & ( ? [U_2290,U_2289] :
            ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2290),U_2289))
            & U_2293 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2290),U_2289) )
        | U_2293 = bot_bot_fun_nat_bool ) ),
    inference(variable_rename,[status(thm)],[f_808_1]) ).

fof(f_808_3,plain,
    ( ! [U_2295] :
        ( U_2295 != bot_bot_fun_nat_bool
        | ! [U_2292,U_2291] :
            ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2292),U_2291))
            | U_2295 != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2292),U_2291) ) )
    & ! [U_2294] :
        ( ? [U_2290,U_2289] :
            ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2290),U_2289))
            & U_2294 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2290),U_2289) )
        | U_2294 = bot_bot_fun_nat_bool ) ),
    inference(miniscope,[status(thm)],[f_808_2]) ).

fof(f_808_4,plain,
    ( ! [U_2295] :
        ( U_2295 != bot_bot_fun_nat_bool
        | ! [U_2292,U_2291] :
            ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2292),U_2291))
            | U_2295 != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2292),U_2291) ) )
    & ! [U_2294] :
        ( ? [U_2289] :
            ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK138(U_2294)),U_2289))
            & U_2294 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK138(U_2294)),U_2289) )
        | U_2294 = bot_bot_fun_nat_bool ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK138]),skolemize(U_2290,sK138(U_2294))],[f_808_3]) ).

fof(f_808_5,plain,
    ( ! [U_2295] :
        ( U_2295 != bot_bot_fun_nat_bool
        | ! [U_2292,U_2291] :
            ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2292),U_2291))
            | U_2295 != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2292),U_2291) ) )
    & ! [U_2294] :
        ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK138(U_2294)),sK139(U_2294)))
          & U_2294 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK138(U_2294)),sK139(U_2294)) )
        | U_2294 = bot_bot_fun_nat_bool ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(U_2289,sK139(U_2294))],[f_808_4]) ).

fof(f_808_6,plain,
    ( ! [U_2294] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK138(U_2294)),sK139(U_2294)))
        | ~ sP213(U_2294) )
    & ! [U_2294] :
        ( U_2294 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK138(U_2294)),sK139(U_2294))
        | ~ sP213(U_2294) )
    & ! [U_2292,U_2291,U_2295] :
        ( U_2295 != bot_bot_fun_nat_bool
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2292),U_2291))
        | U_2295 != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2292),U_2291) )
    & ! [U_2294] :
        ( sP213(U_2294)
        | U_2294 = bot_bot_fun_nat_bool ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP213])],[f_808_5]) ).

cnf(f_808_7,plain,
    ( sP213(U_2294)
    | U_2294 = bot_bot_fun_nat_bool ),
    inference(clausify,[status(thm)],[f_808_6]) ).

cnf(f_808_8,plain,
    ( U_2295 != bot_bot_fun_nat_bool
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2292),U_2291))
    | U_2295 != hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2292),U_2291) ),
    inference(clausify,[status(thm)],[f_808_6]) ).

cnf(f_808_9,plain,
    ( U_2294 = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK138(U_2294)),sK139(U_2294))
    | ~ sP213(U_2294) ),
    inference(clausify,[status(thm)],[f_808_6]) ).

cnf(f_808_10,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK138(U_2294)),sK139(U_2294)))
    | ~ sP213(U_2294) ),
    inference(clausify,[status(thm)],[f_808_6]) ).

fof(f_809_1,plain,
    ! [A] :
      ( ( ( A != bot_bo844097828e_bool
          | ! [X_2,B_15] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B_15))
              | A != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),B_15)
              | ~ is_fun_pname_bool(B_15)
              | ~ is_pname(X_2) ) )
        & ( ? [X_2,B_15] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B_15))
              & A = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),B_15)
              & is_fun_pname_bool(B_15)
              & is_pname(X_2) )
          | A = bot_bo844097828e_bool ) )
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_702_nonempty__iff]) ).

fof(f_809_2,plain,
    ! [U_2300] :
      ( ( ( U_2300 != bot_bo844097828e_bool
          | ! [U_2299,U_2298] :
              ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2299),U_2298))
              | U_2300 != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2299),U_2298)
              | ~ is_fun_pname_bool(U_2298)
              | ~ is_pname(U_2299) ) )
        & ( ? [U_2297,U_2296] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2297),U_2296))
              & U_2300 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2297),U_2296)
              & is_fun_pname_bool(U_2296)
              & is_pname(U_2297) )
          | U_2300 = bot_bo844097828e_bool ) )
      | ~ is_fun_pname_bool(U_2300) ),
    inference(variable_rename,[status(thm)],[f_809_1]) ).

fof(f_809_3,plain,
    ! [U_2300] :
      ( ( ( U_2300 != bot_bo844097828e_bool
          | ! [U_2299] :
              ( ! [U_2298] :
                  ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2299),U_2298))
                  | U_2300 != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2299),U_2298)
                  | ~ is_fun_pname_bool(U_2298) )
              | ~ is_pname(U_2299) ) )
        & ( ? [U_2297] :
              ( ? [U_2296] :
                  ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2297),U_2296))
                  & U_2300 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2297),U_2296)
                  & is_fun_pname_bool(U_2296) )
              & is_pname(U_2297) )
          | U_2300 = bot_bo844097828e_bool ) )
      | ~ is_fun_pname_bool(U_2300) ),
    inference(miniscope,[status(thm)],[f_809_2]) ).

fof(f_809_4,plain,
    ! [U_2300] :
      ( ( ( U_2300 != bot_bo844097828e_bool
          | ! [U_2299] :
              ( ! [U_2298] :
                  ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2299),U_2298))
                  | U_2300 != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2299),U_2298)
                  | ~ is_fun_pname_bool(U_2298) )
              | ~ is_pname(U_2299) ) )
        & ( ( ? [U_2296] :
                ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK140(U_2300)),U_2296))
                & U_2300 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK140(U_2300)),U_2296)
                & is_fun_pname_bool(U_2296) )
            & is_pname(sK140(U_2300)) )
          | U_2300 = bot_bo844097828e_bool ) )
      | ~ is_fun_pname_bool(U_2300) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(U_2297,sK140(U_2300))],[f_809_3]) ).

fof(f_809_5,plain,
    ! [U_2300] :
      ( ( ( U_2300 != bot_bo844097828e_bool
          | ! [U_2299] :
              ( ! [U_2298] :
                  ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2299),U_2298))
                  | U_2300 != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2299),U_2298)
                  | ~ is_fun_pname_bool(U_2298) )
              | ~ is_pname(U_2299) ) )
        & ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK140(U_2300)),sK141(U_2300)))
            & U_2300 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK140(U_2300)),sK141(U_2300))
            & is_fun_pname_bool(sK141(U_2300))
            & is_pname(sK140(U_2300)) )
          | U_2300 = bot_bo844097828e_bool ) )
      | ~ is_fun_pname_bool(U_2300) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(U_2296,sK141(U_2300))],[f_809_4]) ).

fof(f_809_6,plain,
    ( ! [U_2300] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK140(U_2300)),sK141(U_2300)))
        | ~ sP214(U_2300) )
    & ! [U_2300] :
        ( U_2300 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK140(U_2300)),sK141(U_2300))
        | ~ sP214(U_2300) )
    & ! [U_2300] :
        ( is_fun_pname_bool(sK141(U_2300))
        | ~ sP214(U_2300) )
    & ! [U_2300] :
        ( is_pname(sK140(U_2300))
        | ~ sP214(U_2300) )
    & ! [U_2300,U_2298,U_2299] :
        ( U_2300 != bot_bo844097828e_bool
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2299),U_2298))
        | U_2300 != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2299),U_2298)
        | ~ is_fun_pname_bool(U_2298)
        | ~ is_pname(U_2299)
        | ~ sP215(U_2300,U_2298,U_2299) )
    & ! [U_2300,U_2298,U_2299] :
        ( sP214(U_2300)
        | U_2300 = bot_bo844097828e_bool
        | ~ sP215(U_2300,U_2298,U_2299) )
    & ! [U_2300,U_2298,U_2299] :
        ( sP215(U_2300,U_2298,U_2299)
        | ~ is_fun_pname_bool(U_2300) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP214,sP215])],[f_809_5]) ).

cnf(f_809_7,plain,
    ( sP215(U_2300,U_2298,U_2299)
    | ~ is_fun_pname_bool(U_2300) ),
    inference(clausify,[status(thm)],[f_809_6]) ).

cnf(f_809_8,plain,
    ( sP214(U_2300)
    | U_2300 = bot_bo844097828e_bool
    | ~ sP215(U_2300,U_2298,U_2299) ),
    inference(clausify,[status(thm)],[f_809_6]) ).

cnf(f_809_9,plain,
    ( U_2300 != bot_bo844097828e_bool
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2299),U_2298))
    | U_2300 != hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2299),U_2298)
    | ~ is_fun_pname_bool(U_2298)
    | ~ is_pname(U_2299)
    | ~ sP215(U_2300,U_2298,U_2299) ),
    inference(clausify,[status(thm)],[f_809_6]) ).

cnf(f_809_10,plain,
    ( is_pname(sK140(U_2300))
    | ~ sP214(U_2300) ),
    inference(clausify,[status(thm)],[f_809_6]) ).

cnf(f_809_11,plain,
    ( is_fun_pname_bool(sK141(U_2300))
    | ~ sP214(U_2300) ),
    inference(clausify,[status(thm)],[f_809_6]) ).

cnf(f_809_12,plain,
    ( U_2300 = hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK140(U_2300)),sK141(U_2300))
    | ~ sP214(U_2300) ),
    inference(clausify,[status(thm)],[f_809_6]) ).

cnf(f_809_13,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK140(U_2300)),sK141(U_2300)))
    | ~ sP214(U_2300) ),
    inference(clausify,[status(thm)],[f_809_6]) ).

fof(f_810_1,plain,
    ! [Pn] :
      ( hBOOL(wt(the_com(body(Pn))))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,Pn),u)) ),
    inference(fof_nnf,[status(thm)],[fact_703_assms_I4_J]) ).

fof(f_810_2,plain,
    ! [U_2301] :
      ( hBOOL(wt(the_com(body(U_2301))))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2301),u)) ),
    inference(variable_rename,[status(thm)],[f_810_1]) ).

fof(f_810_3,plain,
    ! [U_2301] :
      ( hBOOL(wt(the_com(body(U_2301))))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2301),u)) ),
    inference(definitional_conversion,[status(esa)],[f_810_2]) ).

cnf(f_810_4,plain,
    ( hBOOL(wt(the_com(body(U_2301))))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2301),u)) ),
    inference(clausify,[status(thm)],[f_810_3]) ).

fof(f_811_1,plain,
    ! [C_6,A,B] :
      ( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),B))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),A)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))) ),
    inference(fof_nnf,[status(thm)],[fact_704_DiffE]) ).

fof(f_811_2,plain,
    ! [U_2304,U_2303,U_2302] :
      ( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2304),U_2302))
        & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2304),U_2303)) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2304),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2303),U_2302))) ),
    inference(variable_rename,[status(thm)],[f_811_1]) ).

fof(f_811_3,plain,
    ( ! [U_2303,U_2304,U_2302] :
        ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2304),U_2302))
        | ~ sP216(U_2303,U_2304,U_2302) )
    & ! [U_2303,U_2304,U_2302] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2304),U_2303))
        | ~ sP216(U_2303,U_2304,U_2302) )
    & ! [U_2303,U_2304,U_2302] :
        ( sP216(U_2303,U_2304,U_2302)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2304),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2303),U_2302))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP216])],[f_811_2]) ).

cnf(f_811_4,plain,
    ( sP216(U_2303,U_2304,U_2302)
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2304),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2303),U_2302))) ),
    inference(clausify,[status(thm)],[f_811_3]) ).

cnf(f_811_5,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2304),U_2303))
    | ~ sP216(U_2303,U_2304,U_2302) ),
    inference(clausify,[status(thm)],[f_811_3]) ).

cnf(f_811_6,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2304),U_2302))
    | ~ sP216(U_2303,U_2304,U_2302) ),
    inference(clausify,[status(thm)],[f_811_3]) ).

fof(f_812_1,plain,
    ! [C_6,A,B] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),B))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),A)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) ),
    inference(fof_nnf,[status(thm)],[fact_705_DiffE]) ).

fof(f_812_2,plain,
    ! [U_2307,U_2306,U_2305] :
      ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2307),U_2305))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2307),U_2306)) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2307),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2306),U_2305))) ),
    inference(variable_rename,[status(thm)],[f_812_1]) ).

fof(f_812_3,plain,
    ( ! [U_2307,U_2305,U_2306] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2307),U_2305))
        | ~ sP217(U_2307,U_2305,U_2306) )
    & ! [U_2307,U_2305,U_2306] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2307),U_2306))
        | ~ sP217(U_2307,U_2305,U_2306) )
    & ! [U_2307,U_2305,U_2306] :
        ( sP217(U_2307,U_2305,U_2306)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2307),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2306),U_2305))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP217])],[f_812_2]) ).

cnf(f_812_4,plain,
    ( sP217(U_2307,U_2305,U_2306)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2307),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2306),U_2305))) ),
    inference(clausify,[status(thm)],[f_812_3]) ).

cnf(f_812_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2307),U_2306))
    | ~ sP217(U_2307,U_2305,U_2306) ),
    inference(clausify,[status(thm)],[f_812_3]) ).

cnf(f_812_6,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2307),U_2305))
    | ~ sP217(U_2307,U_2305,U_2306) ),
    inference(clausify,[status(thm)],[f_812_3]) ).

fof(f_813_1,plain,
    ! [C_6,A,B] :
      ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),B))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),A)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B))) ),
    inference(fof_nnf,[status(thm)],[fact_706_DiffE]) ).

fof(f_813_2,plain,
    ! [U_2310,U_2309,U_2308] :
      ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2310),U_2308))
        & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2310),U_2309)) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2310),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2309),U_2308))) ),
    inference(variable_rename,[status(thm)],[f_813_1]) ).

fof(f_813_3,plain,
    ( ! [U_2308,U_2310,U_2309] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2310),U_2308))
        | ~ sP218(U_2308,U_2310,U_2309) )
    & ! [U_2308,U_2310,U_2309] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2310),U_2309))
        | ~ sP218(U_2308,U_2310,U_2309) )
    & ! [U_2308,U_2310,U_2309] :
        ( sP218(U_2308,U_2310,U_2309)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2310),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2309),U_2308))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP218])],[f_813_2]) ).

cnf(f_813_4,plain,
    ( sP218(U_2308,U_2310,U_2309)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2310),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2309),U_2308))) ),
    inference(clausify,[status(thm)],[f_813_3]) ).

cnf(f_813_5,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2310),U_2309))
    | ~ sP218(U_2308,U_2310,U_2309) ),
    inference(clausify,[status(thm)],[f_813_3]) ).

cnf(f_813_6,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2310),U_2308))
    | ~ sP218(U_2308,U_2310,U_2309) ),
    inference(clausify,[status(thm)],[f_813_3]) ).

fof(f_814_1,plain,
    ! [C_6,A,B] :
      ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),B))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),A)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) ),
    inference(fof_nnf,[status(thm)],[fact_707_DiffE]) ).

fof(f_814_2,plain,
    ! [U_2313,U_2312,U_2311] :
      ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2313),U_2311))
        & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2313),U_2312)) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2313),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2312),U_2311))) ),
    inference(variable_rename,[status(thm)],[f_814_1]) ).

fof(f_814_3,plain,
    ( ! [U_2311,U_2312,U_2313] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2313),U_2311))
        | ~ sP219(U_2311,U_2312,U_2313) )
    & ! [U_2311,U_2312,U_2313] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2313),U_2312))
        | ~ sP219(U_2311,U_2312,U_2313) )
    & ! [U_2311,U_2312,U_2313] :
        ( sP219(U_2311,U_2312,U_2313)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2313),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2312),U_2311))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP219])],[f_814_2]) ).

cnf(f_814_4,plain,
    ( sP219(U_2311,U_2312,U_2313)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2313),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2312),U_2311))) ),
    inference(clausify,[status(thm)],[f_814_3]) ).

cnf(f_814_5,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2313),U_2312))
    | ~ sP219(U_2311,U_2312,U_2313) ),
    inference(clausify,[status(thm)],[f_814_3]) ).

cnf(f_814_6,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2313),U_2311))
    | ~ sP219(U_2311,U_2312,U_2313) ),
    inference(clausify,[status(thm)],[f_814_3]) ).

fof(f_815_1,plain,
    ! [B,C_6,A] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)))
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),B))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),A)) ),
    inference(fof_nnf,[status(thm)],[fact_708_DiffI]) ).

fof(f_815_2,plain,
    ! [U_2316,U_2315,U_2314] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2315),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2314),U_2316)))
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2315),U_2316))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2315),U_2314)) ),
    inference(variable_rename,[status(thm)],[f_815_1]) ).

fof(f_815_3,plain,
    ! [U_2314,U_2315,U_2316] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2315),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2314),U_2316)))
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2315),U_2316))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2315),U_2314)) ),
    inference(definitional_conversion,[status(esa)],[f_815_2]) ).

cnf(f_815_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2315),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2314),U_2316)))
    | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2315),U_2316))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2315),U_2314)) ),
    inference(clausify,[status(thm)],[f_815_3]) ).

fof(f_816_1,plain,
    ! [B,C_6,A] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),A)) ),
    inference(fof_nnf,[status(thm)],[fact_709_DiffI]) ).

fof(f_816_2,plain,
    ! [U_2319,U_2318,U_2317] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2318),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2317),U_2319)))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2318),U_2319))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2318),U_2317)) ),
    inference(variable_rename,[status(thm)],[f_816_1]) ).

fof(f_816_3,plain,
    ! [U_2317,U_2318,U_2319] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2318),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2317),U_2319)))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2318),U_2319))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2318),U_2317)) ),
    inference(definitional_conversion,[status(esa)],[f_816_2]) ).

cnf(f_816_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2318),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2317),U_2319)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2318),U_2319))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2318),U_2317)) ),
    inference(clausify,[status(thm)],[f_816_3]) ).

fof(f_817_1,plain,
    ! [B,C_6,A] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),B))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),A)) ),
    inference(fof_nnf,[status(thm)],[fact_710_DiffI]) ).

fof(f_817_2,plain,
    ! [U_2322,U_2321,U_2320] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2321),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2320),U_2322)))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2321),U_2322))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2321),U_2320)) ),
    inference(variable_rename,[status(thm)],[f_817_1]) ).

fof(f_817_3,plain,
    ! [U_2320,U_2321,U_2322] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2321),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2320),U_2322)))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2321),U_2322))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2321),U_2320)) ),
    inference(definitional_conversion,[status(esa)],[f_817_2]) ).

cnf(f_817_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2321),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2320),U_2322)))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2321),U_2322))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2321),U_2320)) ),
    inference(clausify,[status(thm)],[f_817_3]) ).

fof(f_818_1,plain,
    ! [B,C_6,A] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),A)) ),
    inference(fof_nnf,[status(thm)],[fact_711_DiffI]) ).

fof(f_818_2,plain,
    ! [U_2325,U_2324,U_2323] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2324),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2323),U_2325)))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2324),U_2325))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2324),U_2323)) ),
    inference(variable_rename,[status(thm)],[f_818_1]) ).

fof(f_818_3,plain,
    ! [U_2323,U_2324,U_2325] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2324),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2323),U_2325)))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2324),U_2325))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2324),U_2323)) ),
    inference(definitional_conversion,[status(esa)],[f_818_2]) ).

cnf(f_818_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2324),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2323),U_2325)))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2324),U_2325))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2324),U_2323)) ),
    inference(clausify,[status(thm)],[f_818_3]) ).

fof(f_819_1,plain,
    ! [C_6,A,B] :
      ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),B))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))) ),
    inference(fof_nnf,[status(thm)],[fact_712_DiffD2]) ).

fof(f_819_2,plain,
    ! [U_2328,U_2327,U_2326] :
      ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2328),U_2326))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2328),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2327),U_2326))) ),
    inference(variable_rename,[status(thm)],[f_819_1]) ).

fof(f_819_3,plain,
    ! [U_2327,U_2326,U_2328] :
      ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2328),U_2326))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2328),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2327),U_2326))) ),
    inference(definitional_conversion,[status(esa)],[f_819_2]) ).

cnf(f_819_4,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2328),U_2326))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2328),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2327),U_2326))) ),
    inference(clausify,[status(thm)],[f_819_3]) ).

fof(f_820_1,plain,
    ! [C_6,A,B] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) ),
    inference(fof_nnf,[status(thm)],[fact_713_DiffD2]) ).

fof(f_820_2,plain,
    ! [U_2331,U_2330,U_2329] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2331),U_2329))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2331),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2330),U_2329))) ),
    inference(variable_rename,[status(thm)],[f_820_1]) ).

fof(f_820_3,plain,
    ! [U_2329,U_2330,U_2331] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2331),U_2329))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2331),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2330),U_2329))) ),
    inference(definitional_conversion,[status(esa)],[f_820_2]) ).

cnf(f_820_4,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2331),U_2329))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2331),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2330),U_2329))) ),
    inference(clausify,[status(thm)],[f_820_3]) ).

fof(f_821_1,plain,
    ! [C_6,A,B] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),B))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B))) ),
    inference(fof_nnf,[status(thm)],[fact_714_DiffD2]) ).

fof(f_821_2,plain,
    ! [U_2334,U_2333,U_2332] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2334),U_2332))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2334),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2333),U_2332))) ),
    inference(variable_rename,[status(thm)],[f_821_1]) ).

fof(f_821_3,plain,
    ! [U_2332,U_2333,U_2334] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2334),U_2332))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2334),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2333),U_2332))) ),
    inference(definitional_conversion,[status(esa)],[f_821_2]) ).

cnf(f_821_4,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2334),U_2332))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2334),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2333),U_2332))) ),
    inference(clausify,[status(thm)],[f_821_3]) ).

fof(f_822_1,plain,
    ! [C_6,A,B] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) ),
    inference(fof_nnf,[status(thm)],[fact_715_DiffD2]) ).

fof(f_822_2,plain,
    ! [U_2337,U_2336,U_2335] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2337),U_2335))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2337),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2336),U_2335))) ),
    inference(variable_rename,[status(thm)],[f_822_1]) ).

fof(f_822_3,plain,
    ! [U_2335,U_2336,U_2337] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2337),U_2335))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2337),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2336),U_2335))) ),
    inference(definitional_conversion,[status(esa)],[f_822_2]) ).

cnf(f_822_4,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2337),U_2335))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2337),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2336),U_2335))) ),
    inference(clausify,[status(thm)],[f_822_3]) ).

fof(f_823_1,plain,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),A))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))) ),
    inference(fof_nnf,[status(thm)],[fact_716_DiffD1]) ).

fof(f_823_2,plain,
    ! [U_2340,U_2339,U_2338] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2340),U_2339))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2340),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2339),U_2338))) ),
    inference(variable_rename,[status(thm)],[f_823_1]) ).

fof(f_823_3,plain,
    ! [U_2340,U_2339] :
      ( ! [U_2338] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2340),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2339),U_2338)))
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2340),U_2339)) ),
    inference(miniscope,[status(thm)],[f_823_2]) ).

fof(f_823_4,plain,
    ! [U_2339,U_2338,U_2340] :
      ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2340),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2339),U_2338)))
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2340),U_2339)) ),
    inference(definitional_conversion,[status(esa)],[f_823_3]) ).

cnf(f_823_5,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2340),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2339),U_2338)))
    | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2340),U_2339)) ),
    inference(clausify,[status(thm)],[f_823_4]) ).

fof(f_824_1,plain,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),A))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) ),
    inference(fof_nnf,[status(thm)],[fact_717_DiffD1]) ).

fof(f_824_2,plain,
    ! [U_2343,U_2342,U_2341] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2343),U_2342))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2343),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2342),U_2341))) ),
    inference(variable_rename,[status(thm)],[f_824_1]) ).

fof(f_824_3,plain,
    ! [U_2343,U_2342] :
      ( ! [U_2341] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2343),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2342),U_2341)))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2343),U_2342)) ),
    inference(miniscope,[status(thm)],[f_824_2]) ).

fof(f_824_4,plain,
    ! [U_2341,U_2342,U_2343] :
      ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2343),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2342),U_2341)))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2343),U_2342)) ),
    inference(definitional_conversion,[status(esa)],[f_824_3]) ).

cnf(f_824_5,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2343),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2342),U_2341)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2343),U_2342)) ),
    inference(clausify,[status(thm)],[f_824_4]) ).

fof(f_825_1,plain,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),A))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B))) ),
    inference(fof_nnf,[status(thm)],[fact_718_DiffD1]) ).

fof(f_825_2,plain,
    ! [U_2346,U_2345,U_2344] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2346),U_2345))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2346),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2345),U_2344))) ),
    inference(variable_rename,[status(thm)],[f_825_1]) ).

fof(f_825_3,plain,
    ! [U_2346,U_2345] :
      ( ! [U_2344] : ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2346),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2345),U_2344)))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2346),U_2345)) ),
    inference(miniscope,[status(thm)],[f_825_2]) ).

fof(f_825_4,plain,
    ! [U_2344,U_2345,U_2346] :
      ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2346),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2345),U_2344)))
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2346),U_2345)) ),
    inference(definitional_conversion,[status(esa)],[f_825_3]) ).

cnf(f_825_5,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2346),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2345),U_2344)))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2346),U_2345)) ),
    inference(clausify,[status(thm)],[f_825_4]) ).

fof(f_826_1,plain,
    ! [C_6,A,B] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) ),
    inference(fof_nnf,[status(thm)],[fact_719_DiffD1]) ).

fof(f_826_2,plain,
    ! [U_2349,U_2348,U_2347] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2349),U_2348))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2349),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2348),U_2347))) ),
    inference(variable_rename,[status(thm)],[f_826_1]) ).

fof(f_826_3,plain,
    ! [U_2349,U_2348] :
      ( ! [U_2347] : ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2349),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2348),U_2347)))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2349),U_2348)) ),
    inference(miniscope,[status(thm)],[f_826_2]) ).

fof(f_826_4,plain,
    ! [U_2347,U_2348,U_2349] :
      ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2349),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2348),U_2347)))
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2349),U_2348)) ),
    inference(definitional_conversion,[status(esa)],[f_826_3]) ).

cnf(f_826_5,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2349),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2348),U_2347)))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2349),U_2348)) ),
    inference(clausify,[status(thm)],[f_826_4]) ).

fof(f_827_1,plain,
    ! [C_6,A,B] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B)))
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),B))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),A)) )
      & ( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),B))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),A)) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,C_6),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))) ) ),
    inference(fof_nnf,[status(thm)],[fact_720_Diff__iff]) ).

fof(f_827_2,plain,
    ! [U_2352,U_2351,U_2350] :
      ( ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2352),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2351),U_2350)))
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2352),U_2350))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2352),U_2351)) )
      & ( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2352),U_2350))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2352),U_2351)) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2352),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2351),U_2350))) ) ),
    inference(variable_rename,[status(thm)],[f_827_1]) ).

fof(f_827_3,plain,
    ( ! [U_2358,U_2356,U_2354] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2358),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2356),U_2354)))
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2358),U_2354))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2358),U_2356)) )
    & ! [U_2357,U_2355,U_2353] :
        ( ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2357),U_2353))
          & hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2357),U_2355)) )
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2357),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2355),U_2353))) ) ),
    inference(miniscope,[status(thm)],[f_827_2]) ).

fof(f_827_4,plain,
    ( ! [U_2355,U_2353,U_2357] :
        ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2357),U_2353))
        | ~ sP220(U_2355,U_2353,U_2357) )
    & ! [U_2355,U_2353,U_2357] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2357),U_2355))
        | ~ sP220(U_2355,U_2353,U_2357) )
    & ! [U_2356,U_2354,U_2358] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2358),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2356),U_2354)))
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2358),U_2354))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2358),U_2356)) )
    & ! [U_2355,U_2353,U_2357] :
        ( sP220(U_2355,U_2353,U_2357)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2357),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2355),U_2353))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP220])],[f_827_3]) ).

cnf(f_827_5,plain,
    ( sP220(U_2355,U_2353,U_2357)
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2357),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2355),U_2353))) ),
    inference(clausify,[status(thm)],[f_827_4]) ).

cnf(f_827_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2358),hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2356),U_2354)))
    | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2358),U_2354))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2358),U_2356)) ),
    inference(clausify,[status(thm)],[f_827_4]) ).

cnf(f_827_7,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2357),U_2355))
    | ~ sP220(U_2355,U_2353,U_2357) ),
    inference(clausify,[status(thm)],[f_827_4]) ).

cnf(f_827_8,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2357),U_2353))
    | ~ sP220(U_2355,U_2353,U_2357) ),
    inference(clausify,[status(thm)],[f_827_4]) ).

fof(f_828_1,plain,
    ! [C_6,A,B] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),B))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),A)) )
      & ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),B))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),A)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_6),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))) ) ),
    inference(fof_nnf,[status(thm)],[fact_721_Diff__iff]) ).

fof(f_828_2,plain,
    ! [U_2361,U_2360,U_2359] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2361),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2360),U_2359)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2361),U_2359))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2361),U_2360)) )
      & ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2361),U_2359))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2361),U_2360)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2361),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2360),U_2359))) ) ),
    inference(variable_rename,[status(thm)],[f_828_1]) ).

fof(f_828_3,plain,
    ( ! [U_2367,U_2365,U_2363] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2367),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2365),U_2363)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2367),U_2363))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2367),U_2365)) )
    & ! [U_2366,U_2364,U_2362] :
        ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2366),U_2362))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2366),U_2364)) )
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2366),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2364),U_2362))) ) ),
    inference(miniscope,[status(thm)],[f_828_2]) ).

fof(f_828_4,plain,
    ( ! [U_2364,U_2362,U_2366] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2366),U_2362))
        | ~ sP221(U_2364,U_2362,U_2366) )
    & ! [U_2364,U_2362,U_2366] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2366),U_2364))
        | ~ sP221(U_2364,U_2362,U_2366) )
    & ! [U_2365,U_2363,U_2367] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2367),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2365),U_2363)))
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2367),U_2363))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2367),U_2365)) )
    & ! [U_2364,U_2362,U_2366] :
        ( sP221(U_2364,U_2362,U_2366)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2366),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2364),U_2362))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP221])],[f_828_3]) ).

cnf(f_828_5,plain,
    ( sP221(U_2364,U_2362,U_2366)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2366),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2364),U_2362))) ),
    inference(clausify,[status(thm)],[f_828_4]) ).

cnf(f_828_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2367),hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2365),U_2363)))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2367),U_2363))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2367),U_2365)) ),
    inference(clausify,[status(thm)],[f_828_4]) ).

cnf(f_828_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2366),U_2364))
    | ~ sP221(U_2364,U_2362,U_2366) ),
    inference(clausify,[status(thm)],[f_828_4]) ).

cnf(f_828_8,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2366),U_2362))
    | ~ sP221(U_2364,U_2362,U_2366) ),
    inference(clausify,[status(thm)],[f_828_4]) ).

fof(f_829_1,plain,
    ! [C_6,A,B] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B)))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),B))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),A)) )
      & ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),B))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),A)) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_6),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B))) ) ),
    inference(fof_nnf,[status(thm)],[fact_722_Diff__iff]) ).

fof(f_829_2,plain,
    ! [U_2370,U_2369,U_2368] :
      ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2370),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2369),U_2368)))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2370),U_2368))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2370),U_2369)) )
      & ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2370),U_2368))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2370),U_2369)) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2370),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2369),U_2368))) ) ),
    inference(variable_rename,[status(thm)],[f_829_1]) ).

fof(f_829_3,plain,
    ( ! [U_2376,U_2374,U_2372] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2376),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2374),U_2372)))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2376),U_2372))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2376),U_2374)) )
    & ! [U_2375,U_2373,U_2371] :
        ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2375),U_2371))
          & hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2375),U_2373)) )
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2375),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2373),U_2371))) ) ),
    inference(miniscope,[status(thm)],[f_829_2]) ).

fof(f_829_4,plain,
    ( ! [U_2373,U_2371,U_2375] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2375),U_2371))
        | ~ sP222(U_2373,U_2371,U_2375) )
    & ! [U_2373,U_2371,U_2375] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2375),U_2373))
        | ~ sP222(U_2373,U_2371,U_2375) )
    & ! [U_2374,U_2372,U_2376] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2376),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2374),U_2372)))
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2376),U_2372))
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2376),U_2374)) )
    & ! [U_2373,U_2371,U_2375] :
        ( sP222(U_2373,U_2371,U_2375)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2375),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2373),U_2371))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP222])],[f_829_3]) ).

cnf(f_829_5,plain,
    ( sP222(U_2373,U_2371,U_2375)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2375),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2373),U_2371))) ),
    inference(clausify,[status(thm)],[f_829_4]) ).

cnf(f_829_6,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2376),hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2374),U_2372)))
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2376),U_2372))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2376),U_2374)) ),
    inference(clausify,[status(thm)],[f_829_4]) ).

cnf(f_829_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2375),U_2373))
    | ~ sP222(U_2373,U_2371,U_2375) ),
    inference(clausify,[status(thm)],[f_829_4]) ).

cnf(f_829_8,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2375),U_2371))
    | ~ sP222(U_2373,U_2371,U_2375) ),
    inference(clausify,[status(thm)],[f_829_4]) ).

fof(f_830_1,plain,
    ! [C_6,A,B] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B)))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),B))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),A)) )
      & ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),B))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),A)) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_6),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))) ) ),
    inference(fof_nnf,[status(thm)],[fact_723_Diff__iff]) ).

fof(f_830_2,plain,
    ! [U_2379,U_2378,U_2377] :
      ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2379),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2378),U_2377)))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2379),U_2377))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2379),U_2378)) )
      & ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2379),U_2377))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2379),U_2378)) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2379),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2378),U_2377))) ) ),
    inference(variable_rename,[status(thm)],[f_830_1]) ).

fof(f_830_3,plain,
    ( ! [U_2385,U_2383,U_2381] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2385),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2383),U_2381)))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2385),U_2381))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2385),U_2383)) )
    & ! [U_2384,U_2382,U_2380] :
        ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2384),U_2380))
          & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2384),U_2382)) )
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2384),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2382),U_2380))) ) ),
    inference(miniscope,[status(thm)],[f_830_2]) ).

fof(f_830_4,plain,
    ( ! [U_2382,U_2380,U_2384] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2384),U_2380))
        | ~ sP223(U_2382,U_2380,U_2384) )
    & ! [U_2382,U_2380,U_2384] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2384),U_2382))
        | ~ sP223(U_2382,U_2380,U_2384) )
    & ! [U_2383,U_2381,U_2385] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2385),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2383),U_2381)))
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2385),U_2381))
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2385),U_2383)) )
    & ! [U_2382,U_2380,U_2384] :
        ( sP223(U_2382,U_2380,U_2384)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2384),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2382),U_2380))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP223])],[f_830_3]) ).

cnf(f_830_5,plain,
    ( sP223(U_2382,U_2380,U_2384)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2384),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2382),U_2380))) ),
    inference(clausify,[status(thm)],[f_830_4]) ).

cnf(f_830_6,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2385),hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2383),U_2381)))
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2385),U_2381))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2385),U_2383)) ),
    inference(clausify,[status(thm)],[f_830_4]) ).

cnf(f_830_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2384),U_2382))
    | ~ sP223(U_2382,U_2380,U_2384) ),
    inference(clausify,[status(thm)],[f_830_4]) ).

cnf(f_830_8,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2384),U_2380))
    | ~ sP223(U_2382,U_2380,U_2384) ),
    inference(clausify,[status(thm)],[f_830_4]) ).

fof(f_831_1,plain,
    ! [A,B] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),A)),cOMBB_bool_bool_int(fNot,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),B)))),
    inference(fof_nnf,[status(thm)],[fact_724_set__diff__eq]) ).

fof(f_831_2,plain,
    ! [U_2387,U_2386] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2387),U_2386) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_2387)),cOMBB_bool_bool_int(fNot,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_2386)))),
    inference(variable_rename,[status(thm)],[f_831_1]) ).

fof(f_831_3,plain,
    ! [U_2386,U_2387] : hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2387),U_2386) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_2387)),cOMBB_bool_bool_int(fNot,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_2386)))),
    inference(definitional_conversion,[status(esa)],[f_831_2]) ).

cnf(f_831_4,plain,
    hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2387),U_2386) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_2387)),cOMBB_bool_bool_int(fNot,hAPP_f1805168059t_bool(cOMBC_94739984l_bool(member_int),U_2386)))),
    inference(clausify,[status(thm)],[f_831_3]) ).

fof(f_832_1,plain,
    ! [A,B] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),A)),cOMBB_bool_bool_nat(fNot,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),B)))),
    inference(fof_nnf,[status(thm)],[fact_725_set__diff__eq]) ).

fof(f_832_2,plain,
    ! [U_2389,U_2388] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2389),U_2388) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_2389)),cOMBB_bool_bool_nat(fNot,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_2388)))),
    inference(variable_rename,[status(thm)],[f_832_1]) ).

fof(f_832_3,plain,
    ! [U_2388,U_2389] : hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2389),U_2388) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_2389)),cOMBB_bool_bool_nat(fNot,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_2388)))),
    inference(definitional_conversion,[status(esa)],[f_832_2]) ).

cnf(f_832_4,plain,
    hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2389),U_2388) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_2389)),cOMBB_bool_bool_nat(fNot,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_2388)))),
    inference(clausify,[status(thm)],[f_832_3]) ).

fof(f_833_1,plain,
    ! [A,B] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),A)),cOMBB_bool_bool_a(fNot,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),B)))),
    inference(fof_nnf,[status(thm)],[fact_726_set__diff__eq]) ).

fof(f_833_2,plain,
    ! [U_2391,U_2390] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2391),U_2390) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_2391)),cOMBB_bool_bool_a(fNot,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_2390)))),
    inference(variable_rename,[status(thm)],[f_833_1]) ).

fof(f_833_3,plain,
    ! [U_2390,U_2391] : hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2391),U_2390) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_2391)),cOMBB_bool_bool_a(fNot,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_2390)))),
    inference(definitional_conversion,[status(esa)],[f_833_2]) ).

cnf(f_833_4,plain,
    hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2391),U_2390) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_2391)),cOMBB_bool_bool_a(fNot,hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),U_2390)))),
    inference(clausify,[status(thm)],[f_833_3]) ).

fof(f_834_1,plain,
    ! [A,B] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A)),cOMBB_647938656_pname(fNot,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),B)))),
    inference(fof_nnf,[status(thm)],[fact_727_set__diff__eq]) ).

fof(f_834_2,plain,
    ! [U_2393,U_2392] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2393),U_2392) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_2393)),cOMBB_647938656_pname(fNot,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_2392)))),
    inference(variable_rename,[status(thm)],[f_834_1]) ).

fof(f_834_3,plain,
    ! [U_2392,U_2393] : hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2393),U_2392) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_2393)),cOMBB_647938656_pname(fNot,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_2392)))),
    inference(definitional_conversion,[status(esa)],[f_834_2]) ).

cnf(f_834_4,plain,
    hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2393),U_2392) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_2393)),cOMBB_647938656_pname(fNot,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),U_2392)))),
    inference(clausify,[status(thm)],[f_834_3]) ).

fof(f_835_1,plain,
    ! [X_1,A,F,F_1] :
      ( ( ( hAPP_fun_a_bool_a(F_1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_a_a(hAPP_a_fun_a_a(F,X_1),hAPP_fun_a_bool_a(F_1,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))))
          | hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)) = bot_bot_fun_a_bool )
        & ( hAPP_fun_a_bool_a(F_1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = X_1
          | hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)) != bot_bot_fun_a_bool ) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
      | ~ hBOOL(finite_folding_one_a(F,F_1))
      | ~ is_a(X_1) ),
    inference(fof_nnf,[status(thm)],[fact_728_folding__one_Oinsert__remove]) ).

fof(f_835_2,plain,
    ! [U_2397,U_2396,U_2395,U_2394] :
      ( ( ( hAPP_fun_a_bool_a(U_2394,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2397),U_2396)) = hAPP_a_a(hAPP_a_fun_a_a(U_2395,U_2397),hAPP_fun_a_bool_a(U_2394,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2396),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2397),bot_bot_fun_a_bool))))
          | hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2396),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2397),bot_bot_fun_a_bool)) = bot_bot_fun_a_bool )
        & ( hAPP_fun_a_bool_a(U_2394,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2397),U_2396)) = U_2397
          | hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2396),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2397),bot_bot_fun_a_bool)) != bot_bot_fun_a_bool ) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2396))
      | ~ hBOOL(finite_folding_one_a(U_2395,U_2394))
      | ~ is_a(U_2397) ),
    inference(variable_rename,[status(thm)],[f_835_1]) ).

fof(f_835_3,plain,
    ! [U_2397] :
      ( ! [U_2396,U_2395,U_2394] :
          ( ( ( hAPP_fun_a_bool_a(U_2394,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2397),U_2396)) = hAPP_a_a(hAPP_a_fun_a_a(U_2395,U_2397),hAPP_fun_a_bool_a(U_2394,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2396),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2397),bot_bot_fun_a_bool))))
              | hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2396),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2397),bot_bot_fun_a_bool)) = bot_bot_fun_a_bool )
            & ( hAPP_fun_a_bool_a(U_2394,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2397),U_2396)) = U_2397
              | hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2396),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2397),bot_bot_fun_a_bool)) != bot_bot_fun_a_bool ) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2396))
          | ~ hBOOL(finite_folding_one_a(U_2395,U_2394)) )
      | ~ is_a(U_2397) ),
    inference(miniscope,[status(thm)],[f_835_2]) ).

fof(f_835_4,plain,
    ( ! [U_2396,U_2395,U_2394,U_2397] :
        ( hAPP_fun_a_bool_a(U_2394,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2397),U_2396)) = hAPP_a_a(hAPP_a_fun_a_a(U_2395,U_2397),hAPP_fun_a_bool_a(U_2394,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2396),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2397),bot_bot_fun_a_bool))))
        | hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2396),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2397),bot_bot_fun_a_bool)) = bot_bot_fun_a_bool
        | ~ sP224(U_2396,U_2395,U_2394,U_2397) )
    & ! [U_2396,U_2395,U_2394,U_2397] :
        ( hAPP_fun_a_bool_a(U_2394,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2397),U_2396)) = U_2397
        | hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2396),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2397),bot_bot_fun_a_bool)) != bot_bot_fun_a_bool
        | ~ sP224(U_2396,U_2395,U_2394,U_2397) )
    & ! [U_2396,U_2395,U_2394,U_2397] :
        ( sP224(U_2396,U_2395,U_2394,U_2397)
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2396))
        | ~ hBOOL(finite_folding_one_a(U_2395,U_2394))
        | ~ is_a(U_2397) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP224])],[f_835_3]) ).

cnf(f_835_5,plain,
    ( sP224(U_2396,U_2395,U_2394,U_2397)
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2396))
    | ~ hBOOL(finite_folding_one_a(U_2395,U_2394))
    | ~ is_a(U_2397) ),
    inference(clausify,[status(thm)],[f_835_4]) ).

cnf(f_835_6,plain,
    ( hAPP_fun_a_bool_a(U_2394,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2397),U_2396)) = U_2397
    | hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2396),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2397),bot_bot_fun_a_bool)) != bot_bot_fun_a_bool
    | ~ sP224(U_2396,U_2395,U_2394,U_2397) ),
    inference(clausify,[status(thm)],[f_835_4]) ).

cnf(f_835_7,plain,
    ( hAPP_fun_a_bool_a(U_2394,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2397),U_2396)) = hAPP_a_a(hAPP_a_fun_a_a(U_2395,U_2397),hAPP_fun_a_bool_a(U_2394,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2396),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2397),bot_bot_fun_a_bool))))
    | hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2396),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2397),bot_bot_fun_a_bool)) = bot_bot_fun_a_bool
    | ~ sP224(U_2396,U_2395,U_2394,U_2397) ),
    inference(clausify,[status(thm)],[f_835_4]) ).

fof(f_836_1,plain,
    ! [X_1,A,F,F_1] :
      ( ( ( hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))))
          | hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = bot_bot_fun_int_bool )
        & ( hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = X_1
          | hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) != bot_bot_fun_int_bool ) )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
      | ~ hBOOL(finite1626084323ne_int(F,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_729_folding__one_Oinsert__remove]) ).

fof(f_836_2,plain,
    ! [U_2401,U_2400,U_2399,U_2398] :
      ( ( ( hAPP_f1594865479ol_int(U_2398,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2401),U_2400)) = hAPP_int_int(hAPP_int_fun_int_int(U_2399,U_2401),hAPP_f1594865479ol_int(U_2398,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2400),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2401),bot_bot_fun_int_bool))))
          | hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2400),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2401),bot_bot_fun_int_bool)) = bot_bot_fun_int_bool )
        & ( hAPP_f1594865479ol_int(U_2398,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2401),U_2400)) = U_2401
          | hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2400),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2401),bot_bot_fun_int_bool)) != bot_bot_fun_int_bool ) )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2400))
      | ~ hBOOL(finite1626084323ne_int(U_2399,U_2398)) ),
    inference(variable_rename,[status(thm)],[f_836_1]) ).

fof(f_836_3,plain,
    ( ! [U_2401,U_2400,U_2399,U_2398] :
        ( hAPP_f1594865479ol_int(U_2398,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2401),U_2400)) = hAPP_int_int(hAPP_int_fun_int_int(U_2399,U_2401),hAPP_f1594865479ol_int(U_2398,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2400),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2401),bot_bot_fun_int_bool))))
        | hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2400),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2401),bot_bot_fun_int_bool)) = bot_bot_fun_int_bool
        | ~ sP225(U_2401,U_2400,U_2399,U_2398) )
    & ! [U_2401,U_2400,U_2399,U_2398] :
        ( hAPP_f1594865479ol_int(U_2398,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2401),U_2400)) = U_2401
        | hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2400),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2401),bot_bot_fun_int_bool)) != bot_bot_fun_int_bool
        | ~ sP225(U_2401,U_2400,U_2399,U_2398) )
    & ! [U_2401,U_2400,U_2399,U_2398] :
        ( sP225(U_2401,U_2400,U_2399,U_2398)
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2400))
        | ~ hBOOL(finite1626084323ne_int(U_2399,U_2398)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP225])],[f_836_2]) ).

cnf(f_836_4,plain,
    ( sP225(U_2401,U_2400,U_2399,U_2398)
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2400))
    | ~ hBOOL(finite1626084323ne_int(U_2399,U_2398)) ),
    inference(clausify,[status(thm)],[f_836_3]) ).

cnf(f_836_5,plain,
    ( hAPP_f1594865479ol_int(U_2398,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2401),U_2400)) = U_2401
    | hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2400),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2401),bot_bot_fun_int_bool)) != bot_bot_fun_int_bool
    | ~ sP225(U_2401,U_2400,U_2399,U_2398) ),
    inference(clausify,[status(thm)],[f_836_3]) ).

cnf(f_836_6,plain,
    ( hAPP_f1594865479ol_int(U_2398,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2401),U_2400)) = hAPP_int_int(hAPP_int_fun_int_int(U_2399,U_2401),hAPP_f1594865479ol_int(U_2398,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2400),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2401),bot_bot_fun_int_bool))))
    | hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2400),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2401),bot_bot_fun_int_bool)) = bot_bot_fun_int_bool
    | ~ sP225(U_2401,U_2400,U_2399,U_2398) ),
    inference(clausify,[status(thm)],[f_836_3]) ).

fof(f_837_1,plain,
    ! [X_1,A,F,F_1] :
      ( ( ( hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))))
          | hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool )
        & ( hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = X_1
          | hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool ) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
      | ~ hBOOL(finite988810631ne_nat(F,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_730_folding__one_Oinsert__remove]) ).

fof(f_837_2,plain,
    ! [U_2405,U_2404,U_2403,U_2402] :
      ( ( ( hAPP_f22106695ol_nat(U_2402,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2405),U_2404)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_2403,U_2405),hAPP_f22106695ol_nat(U_2402,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2404),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2405),bot_bot_fun_nat_bool))))
          | hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2404),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2405),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool )
        & ( hAPP_f22106695ol_nat(U_2402,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2405),U_2404)) = U_2405
          | hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2404),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2405),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool ) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2404))
      | ~ hBOOL(finite988810631ne_nat(U_2403,U_2402)) ),
    inference(variable_rename,[status(thm)],[f_837_1]) ).

fof(f_837_3,plain,
    ( ! [U_2403,U_2402,U_2404,U_2405] :
        ( hAPP_f22106695ol_nat(U_2402,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2405),U_2404)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_2403,U_2405),hAPP_f22106695ol_nat(U_2402,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2404),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2405),bot_bot_fun_nat_bool))))
        | hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2404),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2405),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool
        | ~ sP226(U_2403,U_2402,U_2404,U_2405) )
    & ! [U_2403,U_2402,U_2404,U_2405] :
        ( hAPP_f22106695ol_nat(U_2402,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2405),U_2404)) = U_2405
        | hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2404),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2405),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool
        | ~ sP226(U_2403,U_2402,U_2404,U_2405) )
    & ! [U_2403,U_2402,U_2404,U_2405] :
        ( sP226(U_2403,U_2402,U_2404,U_2405)
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2404))
        | ~ hBOOL(finite988810631ne_nat(U_2403,U_2402)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP226])],[f_837_2]) ).

cnf(f_837_4,plain,
    ( sP226(U_2403,U_2402,U_2404,U_2405)
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2404))
    | ~ hBOOL(finite988810631ne_nat(U_2403,U_2402)) ),
    inference(clausify,[status(thm)],[f_837_3]) ).

cnf(f_837_5,plain,
    ( hAPP_f22106695ol_nat(U_2402,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2405),U_2404)) = U_2405
    | hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2404),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2405),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool
    | ~ sP226(U_2403,U_2402,U_2404,U_2405) ),
    inference(clausify,[status(thm)],[f_837_3]) ).

cnf(f_837_6,plain,
    ( hAPP_f22106695ol_nat(U_2402,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2405),U_2404)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_2403,U_2405),hAPP_f22106695ol_nat(U_2402,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2404),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2405),bot_bot_fun_nat_bool))))
    | hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2404),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2405),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool
    | ~ sP226(U_2403,U_2402,U_2404,U_2405) ),
    inference(clausify,[status(thm)],[f_837_3]) ).

fof(f_838_1,plain,
    ! [X_1,A,F,F_1] :
      ( ( ( hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))))
          | hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = bot_bo844097828e_bool )
        & ( hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = X_1
          | hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) != bot_bo844097828e_bool ) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
      | ~ hBOOL(finite1282449217_pname(F,F_1))
      | ~ is_pname(X_1) ),
    inference(fof_nnf,[status(thm)],[fact_731_folding__one_Oinsert__remove]) ).

fof(f_838_2,plain,
    ! [U_2409,U_2408,U_2407,U_2406] :
      ( ( ( hAPP_f1297739591_pname(U_2406,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2409),U_2408)) = hAPP_pname_pname(hAPP_p1170154830_pname(U_2407,U_2409),hAPP_f1297739591_pname(U_2406,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2408),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2409),bot_bo844097828e_bool))))
          | hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2408),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2409),bot_bo844097828e_bool)) = bot_bo844097828e_bool )
        & ( hAPP_f1297739591_pname(U_2406,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2409),U_2408)) = U_2409
          | hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2408),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2409),bot_bo844097828e_bool)) != bot_bo844097828e_bool ) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2408))
      | ~ hBOOL(finite1282449217_pname(U_2407,U_2406))
      | ~ is_pname(U_2409) ),
    inference(variable_rename,[status(thm)],[f_838_1]) ).

fof(f_838_3,plain,
    ! [U_2409] :
      ( ! [U_2408,U_2407,U_2406] :
          ( ( ( hAPP_f1297739591_pname(U_2406,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2409),U_2408)) = hAPP_pname_pname(hAPP_p1170154830_pname(U_2407,U_2409),hAPP_f1297739591_pname(U_2406,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2408),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2409),bot_bo844097828e_bool))))
              | hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2408),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2409),bot_bo844097828e_bool)) = bot_bo844097828e_bool )
            & ( hAPP_f1297739591_pname(U_2406,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2409),U_2408)) = U_2409
              | hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2408),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2409),bot_bo844097828e_bool)) != bot_bo844097828e_bool ) )
          | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2408))
          | ~ hBOOL(finite1282449217_pname(U_2407,U_2406)) )
      | ~ is_pname(U_2409) ),
    inference(miniscope,[status(thm)],[f_838_2]) ).

fof(f_838_4,plain,
    ( ! [U_2409,U_2407,U_2408,U_2406] :
        ( hAPP_f1297739591_pname(U_2406,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2409),U_2408)) = hAPP_pname_pname(hAPP_p1170154830_pname(U_2407,U_2409),hAPP_f1297739591_pname(U_2406,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2408),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2409),bot_bo844097828e_bool))))
        | hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2408),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2409),bot_bo844097828e_bool)) = bot_bo844097828e_bool
        | ~ sP227(U_2409,U_2407,U_2408,U_2406) )
    & ! [U_2409,U_2407,U_2408,U_2406] :
        ( hAPP_f1297739591_pname(U_2406,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2409),U_2408)) = U_2409
        | hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2408),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2409),bot_bo844097828e_bool)) != bot_bo844097828e_bool
        | ~ sP227(U_2409,U_2407,U_2408,U_2406) )
    & ! [U_2409,U_2407,U_2408,U_2406] :
        ( sP227(U_2409,U_2407,U_2408,U_2406)
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2408))
        | ~ hBOOL(finite1282449217_pname(U_2407,U_2406))
        | ~ is_pname(U_2409) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP227])],[f_838_3]) ).

cnf(f_838_5,plain,
    ( sP227(U_2409,U_2407,U_2408,U_2406)
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2408))
    | ~ hBOOL(finite1282449217_pname(U_2407,U_2406))
    | ~ is_pname(U_2409) ),
    inference(clausify,[status(thm)],[f_838_4]) ).

cnf(f_838_6,plain,
    ( hAPP_f1297739591_pname(U_2406,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2409),U_2408)) = U_2409
    | hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2408),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2409),bot_bo844097828e_bool)) != bot_bo844097828e_bool
    | ~ sP227(U_2409,U_2407,U_2408,U_2406) ),
    inference(clausify,[status(thm)],[f_838_4]) ).

cnf(f_838_7,plain,
    ( hAPP_f1297739591_pname(U_2406,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2409),U_2408)) = hAPP_pname_pname(hAPP_p1170154830_pname(U_2407,U_2409),hAPP_f1297739591_pname(U_2406,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2408),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2409),bot_bo844097828e_bool))))
    | hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2408),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2409),bot_bo844097828e_bool)) = bot_bo844097828e_bool
    | ~ sP227(U_2409,U_2407,U_2408,U_2406) ),
    inference(clausify,[status(thm)],[f_838_4]) ).

fof(f_839_1,plain,
    ! [X_1,A,F,F_1] :
      ( ( ( hAPP_fun_a_bool_a(F_1,A) = hAPP_a_a(hAPP_a_fun_a_a(F,X_1),hAPP_fun_a_bool_a(F_1,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))))
          | hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)) = bot_bot_fun_a_bool )
        & ( hAPP_fun_a_bool_a(F_1,A) = X_1
          | hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)) != bot_bot_fun_a_bool ) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
      | ~ hBOOL(finite_folding_one_a(F,F_1))
      | ~ is_a(X_1) ),
    inference(fof_nnf,[status(thm)],[fact_732_folding__one_Oremove]) ).

fof(f_839_2,plain,
    ! [U_2413,U_2412,U_2411,U_2410] :
      ( ( ( hAPP_fun_a_bool_a(U_2410,U_2412) = hAPP_a_a(hAPP_a_fun_a_a(U_2411,U_2413),hAPP_fun_a_bool_a(U_2410,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2412),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2413),bot_bot_fun_a_bool))))
          | hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2412),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2413),bot_bot_fun_a_bool)) = bot_bot_fun_a_bool )
        & ( hAPP_fun_a_bool_a(U_2410,U_2412) = U_2413
          | hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2412),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2413),bot_bot_fun_a_bool)) != bot_bot_fun_a_bool ) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2413),U_2412))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2412))
      | ~ hBOOL(finite_folding_one_a(U_2411,U_2410))
      | ~ is_a(U_2413) ),
    inference(variable_rename,[status(thm)],[f_839_1]) ).

fof(f_839_3,plain,
    ! [U_2413] :
      ( ! [U_2412,U_2411,U_2410] :
          ( ( ( hAPP_fun_a_bool_a(U_2410,U_2412) = hAPP_a_a(hAPP_a_fun_a_a(U_2411,U_2413),hAPP_fun_a_bool_a(U_2410,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2412),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2413),bot_bot_fun_a_bool))))
              | hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2412),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2413),bot_bot_fun_a_bool)) = bot_bot_fun_a_bool )
            & ( hAPP_fun_a_bool_a(U_2410,U_2412) = U_2413
              | hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2412),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2413),bot_bot_fun_a_bool)) != bot_bot_fun_a_bool ) )
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2413),U_2412))
          | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2412))
          | ~ hBOOL(finite_folding_one_a(U_2411,U_2410)) )
      | ~ is_a(U_2413) ),
    inference(miniscope,[status(thm)],[f_839_2]) ).

fof(f_839_4,plain,
    ( ! [U_2411,U_2413,U_2410,U_2412] :
        ( hAPP_fun_a_bool_a(U_2410,U_2412) = hAPP_a_a(hAPP_a_fun_a_a(U_2411,U_2413),hAPP_fun_a_bool_a(U_2410,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2412),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2413),bot_bot_fun_a_bool))))
        | hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2412),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2413),bot_bot_fun_a_bool)) = bot_bot_fun_a_bool
        | ~ sP228(U_2411,U_2413,U_2410,U_2412) )
    & ! [U_2411,U_2413,U_2410,U_2412] :
        ( hAPP_fun_a_bool_a(U_2410,U_2412) = U_2413
        | hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2412),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2413),bot_bot_fun_a_bool)) != bot_bot_fun_a_bool
        | ~ sP228(U_2411,U_2413,U_2410,U_2412) )
    & ! [U_2411,U_2413,U_2410,U_2412] :
        ( sP228(U_2411,U_2413,U_2410,U_2412)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2413),U_2412))
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2412))
        | ~ hBOOL(finite_folding_one_a(U_2411,U_2410))
        | ~ is_a(U_2413) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP228])],[f_839_3]) ).

cnf(f_839_5,plain,
    ( sP228(U_2411,U_2413,U_2410,U_2412)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2413),U_2412))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2412))
    | ~ hBOOL(finite_folding_one_a(U_2411,U_2410))
    | ~ is_a(U_2413) ),
    inference(clausify,[status(thm)],[f_839_4]) ).

cnf(f_839_6,plain,
    ( hAPP_fun_a_bool_a(U_2410,U_2412) = U_2413
    | hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2412),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2413),bot_bot_fun_a_bool)) != bot_bot_fun_a_bool
    | ~ sP228(U_2411,U_2413,U_2410,U_2412) ),
    inference(clausify,[status(thm)],[f_839_4]) ).

cnf(f_839_7,plain,
    ( hAPP_fun_a_bool_a(U_2410,U_2412) = hAPP_a_a(hAPP_a_fun_a_a(U_2411,U_2413),hAPP_fun_a_bool_a(U_2410,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2412),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2413),bot_bot_fun_a_bool))))
    | hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2412),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2413),bot_bot_fun_a_bool)) = bot_bot_fun_a_bool
    | ~ sP228(U_2411,U_2413,U_2410,U_2412) ),
    inference(clausify,[status(thm)],[f_839_4]) ).

fof(f_840_1,plain,
    ! [X_1,A,F,F_1] :
      ( ( ( hAPP_f1594865479ol_int(F_1,A) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))))
          | hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = bot_bot_fun_int_bool )
        & ( hAPP_f1594865479ol_int(F_1,A) = X_1
          | hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) != bot_bot_fun_int_bool ) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
      | ~ hBOOL(finite1626084323ne_int(F,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_733_folding__one_Oremove]) ).

fof(f_840_2,plain,
    ! [U_2417,U_2416,U_2415,U_2414] :
      ( ( ( hAPP_f1594865479ol_int(U_2414,U_2416) = hAPP_int_int(hAPP_int_fun_int_int(U_2415,U_2417),hAPP_f1594865479ol_int(U_2414,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2416),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2417),bot_bot_fun_int_bool))))
          | hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2416),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2417),bot_bot_fun_int_bool)) = bot_bot_fun_int_bool )
        & ( hAPP_f1594865479ol_int(U_2414,U_2416) = U_2417
          | hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2416),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2417),bot_bot_fun_int_bool)) != bot_bot_fun_int_bool ) )
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2417),U_2416))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2416))
      | ~ hBOOL(finite1626084323ne_int(U_2415,U_2414)) ),
    inference(variable_rename,[status(thm)],[f_840_1]) ).

fof(f_840_3,plain,
    ( ! [U_2416,U_2417,U_2415,U_2414] :
        ( hAPP_f1594865479ol_int(U_2414,U_2416) = hAPP_int_int(hAPP_int_fun_int_int(U_2415,U_2417),hAPP_f1594865479ol_int(U_2414,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2416),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2417),bot_bot_fun_int_bool))))
        | hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2416),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2417),bot_bot_fun_int_bool)) = bot_bot_fun_int_bool
        | ~ sP229(U_2416,U_2417,U_2415,U_2414) )
    & ! [U_2416,U_2417,U_2415,U_2414] :
        ( hAPP_f1594865479ol_int(U_2414,U_2416) = U_2417
        | hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2416),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2417),bot_bot_fun_int_bool)) != bot_bot_fun_int_bool
        | ~ sP229(U_2416,U_2417,U_2415,U_2414) )
    & ! [U_2416,U_2417,U_2415,U_2414] :
        ( sP229(U_2416,U_2417,U_2415,U_2414)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2417),U_2416))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2416))
        | ~ hBOOL(finite1626084323ne_int(U_2415,U_2414)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP229])],[f_840_2]) ).

cnf(f_840_4,plain,
    ( sP229(U_2416,U_2417,U_2415,U_2414)
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2417),U_2416))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2416))
    | ~ hBOOL(finite1626084323ne_int(U_2415,U_2414)) ),
    inference(clausify,[status(thm)],[f_840_3]) ).

cnf(f_840_5,plain,
    ( hAPP_f1594865479ol_int(U_2414,U_2416) = U_2417
    | hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2416),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2417),bot_bot_fun_int_bool)) != bot_bot_fun_int_bool
    | ~ sP229(U_2416,U_2417,U_2415,U_2414) ),
    inference(clausify,[status(thm)],[f_840_3]) ).

cnf(f_840_6,plain,
    ( hAPP_f1594865479ol_int(U_2414,U_2416) = hAPP_int_int(hAPP_int_fun_int_int(U_2415,U_2417),hAPP_f1594865479ol_int(U_2414,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2416),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2417),bot_bot_fun_int_bool))))
    | hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2416),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2417),bot_bot_fun_int_bool)) = bot_bot_fun_int_bool
    | ~ sP229(U_2416,U_2417,U_2415,U_2414) ),
    inference(clausify,[status(thm)],[f_840_3]) ).

fof(f_841_1,plain,
    ! [X_1,A,F,F_1] :
      ( ( ( hAPP_f22106695ol_nat(F_1,A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))))
          | hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool )
        & ( hAPP_f22106695ol_nat(F_1,A) = X_1
          | hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool ) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
      | ~ hBOOL(finite988810631ne_nat(F,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_734_folding__one_Oremove]) ).

fof(f_841_2,plain,
    ! [U_2421,U_2420,U_2419,U_2418] :
      ( ( ( hAPP_f22106695ol_nat(U_2418,U_2420) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_2419,U_2421),hAPP_f22106695ol_nat(U_2418,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2420),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2421),bot_bot_fun_nat_bool))))
          | hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2420),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2421),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool )
        & ( hAPP_f22106695ol_nat(U_2418,U_2420) = U_2421
          | hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2420),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2421),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool ) )
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2421),U_2420))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2420))
      | ~ hBOOL(finite988810631ne_nat(U_2419,U_2418)) ),
    inference(variable_rename,[status(thm)],[f_841_1]) ).

fof(f_841_3,plain,
    ( ! [U_2420,U_2421,U_2419,U_2418] :
        ( hAPP_f22106695ol_nat(U_2418,U_2420) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_2419,U_2421),hAPP_f22106695ol_nat(U_2418,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2420),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2421),bot_bot_fun_nat_bool))))
        | hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2420),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2421),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool
        | ~ sP230(U_2420,U_2421,U_2419,U_2418) )
    & ! [U_2420,U_2421,U_2419,U_2418] :
        ( hAPP_f22106695ol_nat(U_2418,U_2420) = U_2421
        | hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2420),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2421),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool
        | ~ sP230(U_2420,U_2421,U_2419,U_2418) )
    & ! [U_2420,U_2421,U_2419,U_2418] :
        ( sP230(U_2420,U_2421,U_2419,U_2418)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2421),U_2420))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2420))
        | ~ hBOOL(finite988810631ne_nat(U_2419,U_2418)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP230])],[f_841_2]) ).

cnf(f_841_4,plain,
    ( sP230(U_2420,U_2421,U_2419,U_2418)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2421),U_2420))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2420))
    | ~ hBOOL(finite988810631ne_nat(U_2419,U_2418)) ),
    inference(clausify,[status(thm)],[f_841_3]) ).

cnf(f_841_5,plain,
    ( hAPP_f22106695ol_nat(U_2418,U_2420) = U_2421
    | hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2420),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2421),bot_bot_fun_nat_bool)) != bot_bot_fun_nat_bool
    | ~ sP230(U_2420,U_2421,U_2419,U_2418) ),
    inference(clausify,[status(thm)],[f_841_3]) ).

cnf(f_841_6,plain,
    ( hAPP_f22106695ol_nat(U_2418,U_2420) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_2419,U_2421),hAPP_f22106695ol_nat(U_2418,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2420),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2421),bot_bot_fun_nat_bool))))
    | hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2420),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2421),bot_bot_fun_nat_bool)) = bot_bot_fun_nat_bool
    | ~ sP230(U_2420,U_2421,U_2419,U_2418) ),
    inference(clausify,[status(thm)],[f_841_3]) ).

fof(f_842_1,plain,
    ! [X_1,A,F,F_1] :
      ( ( ( hAPP_f1297739591_pname(F_1,A) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))))
          | hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) = bot_bo844097828e_bool )
        & ( hAPP_f1297739591_pname(F_1,A) = X_1
          | hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool)) != bot_bo844097828e_bool ) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
      | ~ hBOOL(finite1282449217_pname(F,F_1))
      | ~ is_pname(X_1) ),
    inference(fof_nnf,[status(thm)],[fact_735_folding__one_Oremove]) ).

fof(f_842_2,plain,
    ! [U_2425,U_2424,U_2423,U_2422] :
      ( ( ( hAPP_f1297739591_pname(U_2422,U_2424) = hAPP_pname_pname(hAPP_p1170154830_pname(U_2423,U_2425),hAPP_f1297739591_pname(U_2422,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2424),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2425),bot_bo844097828e_bool))))
          | hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2424),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2425),bot_bo844097828e_bool)) = bot_bo844097828e_bool )
        & ( hAPP_f1297739591_pname(U_2422,U_2424) = U_2425
          | hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2424),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2425),bot_bo844097828e_bool)) != bot_bo844097828e_bool ) )
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2425),U_2424))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2424))
      | ~ hBOOL(finite1282449217_pname(U_2423,U_2422))
      | ~ is_pname(U_2425) ),
    inference(variable_rename,[status(thm)],[f_842_1]) ).

fof(f_842_3,plain,
    ! [U_2425] :
      ( ! [U_2424,U_2423,U_2422] :
          ( ( ( hAPP_f1297739591_pname(U_2422,U_2424) = hAPP_pname_pname(hAPP_p1170154830_pname(U_2423,U_2425),hAPP_f1297739591_pname(U_2422,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2424),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2425),bot_bo844097828e_bool))))
              | hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2424),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2425),bot_bo844097828e_bool)) = bot_bo844097828e_bool )
            & ( hAPP_f1297739591_pname(U_2422,U_2424) = U_2425
              | hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2424),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2425),bot_bo844097828e_bool)) != bot_bo844097828e_bool ) )
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2425),U_2424))
          | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2424))
          | ~ hBOOL(finite1282449217_pname(U_2423,U_2422)) )
      | ~ is_pname(U_2425) ),
    inference(miniscope,[status(thm)],[f_842_2]) ).

fof(f_842_4,plain,
    ( ! [U_2423,U_2424,U_2422,U_2425] :
        ( hAPP_f1297739591_pname(U_2422,U_2424) = hAPP_pname_pname(hAPP_p1170154830_pname(U_2423,U_2425),hAPP_f1297739591_pname(U_2422,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2424),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2425),bot_bo844097828e_bool))))
        | hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2424),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2425),bot_bo844097828e_bool)) = bot_bo844097828e_bool
        | ~ sP231(U_2423,U_2424,U_2422,U_2425) )
    & ! [U_2423,U_2424,U_2422,U_2425] :
        ( hAPP_f1297739591_pname(U_2422,U_2424) = U_2425
        | hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2424),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2425),bot_bo844097828e_bool)) != bot_bo844097828e_bool
        | ~ sP231(U_2423,U_2424,U_2422,U_2425) )
    & ! [U_2423,U_2424,U_2422,U_2425] :
        ( sP231(U_2423,U_2424,U_2422,U_2425)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2425),U_2424))
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2424))
        | ~ hBOOL(finite1282449217_pname(U_2423,U_2422))
        | ~ is_pname(U_2425) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP231])],[f_842_3]) ).

cnf(f_842_5,plain,
    ( sP231(U_2423,U_2424,U_2422,U_2425)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2425),U_2424))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2424))
    | ~ hBOOL(finite1282449217_pname(U_2423,U_2422))
    | ~ is_pname(U_2425) ),
    inference(clausify,[status(thm)],[f_842_4]) ).

cnf(f_842_6,plain,
    ( hAPP_f1297739591_pname(U_2422,U_2424) = U_2425
    | hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2424),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2425),bot_bo844097828e_bool)) != bot_bo844097828e_bool
    | ~ sP231(U_2423,U_2424,U_2422,U_2425) ),
    inference(clausify,[status(thm)],[f_842_4]) ).

cnf(f_842_7,plain,
    ( hAPP_f1297739591_pname(U_2422,U_2424) = hAPP_pname_pname(hAPP_p1170154830_pname(U_2423,U_2425),hAPP_f1297739591_pname(U_2422,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2424),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2425),bot_bo844097828e_bool))))
    | hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2424),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2425),bot_bo844097828e_bool)) = bot_bo844097828e_bool
    | ~ sP231(U_2423,U_2424,U_2422,U_2425) ),
    inference(clausify,[status(thm)],[f_842_4]) ).

fof(f_843_1,plain,
    ! [X_1,A] :
      ( ( ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))) = hAPP_fun_a_bool_nat(finite_card_a,A)
          | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) )
        & ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,A)),one_one_nat)
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A)) ) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_736_card__Diff__singleton__if]) ).

fof(f_843_2,plain,
    ! [U_2427,U_2426] :
      ( ( ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2426),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2427),bot_bot_fun_a_bool))) = hAPP_fun_a_bool_nat(finite_card_a,U_2426)
          | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2427),U_2426)) )
        & ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2426),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2427),bot_bot_fun_a_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,U_2426)),one_one_nat)
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2427),U_2426)) ) )
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2426)) ),
    inference(variable_rename,[status(thm)],[f_843_1]) ).

fof(f_843_3,plain,
    ( ! [U_2427,U_2426] :
        ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2426),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2427),bot_bot_fun_a_bool))) = hAPP_fun_a_bool_nat(finite_card_a,U_2426)
        | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2427),U_2426))
        | ~ sP232(U_2427,U_2426) )
    & ! [U_2427,U_2426] :
        ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2426),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2427),bot_bot_fun_a_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,U_2426)),one_one_nat)
        | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2427),U_2426))
        | ~ sP232(U_2427,U_2426) )
    & ! [U_2427,U_2426] :
        ( sP232(U_2427,U_2426)
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2426)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP232])],[f_843_2]) ).

cnf(f_843_4,plain,
    ( sP232(U_2427,U_2426)
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2426)) ),
    inference(clausify,[status(thm)],[f_843_3]) ).

cnf(f_843_5,plain,
    ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2426),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2427),bot_bot_fun_a_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,U_2426)),one_one_nat)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2427),U_2426))
    | ~ sP232(U_2427,U_2426) ),
    inference(clausify,[status(thm)],[f_843_3]) ).

cnf(f_843_6,plain,
    ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2426),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2427),bot_bot_fun_a_bool))) = hAPP_fun_a_bool_nat(finite_card_a,U_2426)
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2427),U_2426))
    | ~ sP232(U_2427,U_2426) ),
    inference(clausify,[status(thm)],[f_843_3]) ).

fof(f_844_1,plain,
    ! [X_1,A] :
      ( ( ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))) = hAPP_f957591787ol_nat(finite_card_int,A)
          | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) )
        & ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,A)),one_one_nat)
          | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A)) ) )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_737_card__Diff__singleton__if]) ).

fof(f_844_2,plain,
    ! [U_2429,U_2428] :
      ( ( ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2428),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2429),bot_bot_fun_int_bool))) = hAPP_f957591787ol_nat(finite_card_int,U_2428)
          | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2429),U_2428)) )
        & ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2428),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2429),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,U_2428)),one_one_nat)
          | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2429),U_2428)) ) )
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2428)) ),
    inference(variable_rename,[status(thm)],[f_844_1]) ).

fof(f_844_3,plain,
    ( ! [U_2428,U_2429] :
        ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2428),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2429),bot_bot_fun_int_bool))) = hAPP_f957591787ol_nat(finite_card_int,U_2428)
        | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2429),U_2428))
        | ~ sP233(U_2428,U_2429) )
    & ! [U_2428,U_2429] :
        ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2428),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2429),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,U_2428)),one_one_nat)
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2429),U_2428))
        | ~ sP233(U_2428,U_2429) )
    & ! [U_2428,U_2429] :
        ( sP233(U_2428,U_2429)
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2428)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP233])],[f_844_2]) ).

cnf(f_844_4,plain,
    ( sP233(U_2428,U_2429)
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2428)) ),
    inference(clausify,[status(thm)],[f_844_3]) ).

cnf(f_844_5,plain,
    ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2428),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2429),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,U_2428)),one_one_nat)
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2429),U_2428))
    | ~ sP233(U_2428,U_2429) ),
    inference(clausify,[status(thm)],[f_844_3]) ).

cnf(f_844_6,plain,
    ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2428),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2429),bot_bot_fun_int_bool))) = hAPP_f957591787ol_nat(finite_card_int,U_2428)
    | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2429),U_2428))
    | ~ sP233(U_2428,U_2429) ),
    inference(clausify,[status(thm)],[f_844_3]) ).

fof(f_845_1,plain,
    ! [X_1,A] :
      ( ( ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) = hAPP_f22106695ol_nat(finite_card_nat,A)
          | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) )
        & ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,A)),one_one_nat)
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_738_card__Diff__singleton__if]) ).

fof(f_845_2,plain,
    ! [U_2431,U_2430] :
      ( ( ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2430),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2431),bot_bot_fun_nat_bool))) = hAPP_f22106695ol_nat(finite_card_nat,U_2430)
          | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2431),U_2430)) )
        & ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2430),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2431),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,U_2430)),one_one_nat)
          | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2431),U_2430)) ) )
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2430)) ),
    inference(variable_rename,[status(thm)],[f_845_1]) ).

fof(f_845_3,plain,
    ( ! [U_2431,U_2430] :
        ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2430),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2431),bot_bot_fun_nat_bool))) = hAPP_f22106695ol_nat(finite_card_nat,U_2430)
        | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2431),U_2430))
        | ~ sP234(U_2431,U_2430) )
    & ! [U_2431,U_2430] :
        ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2430),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2431),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,U_2430)),one_one_nat)
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2431),U_2430))
        | ~ sP234(U_2431,U_2430) )
    & ! [U_2431,U_2430] :
        ( sP234(U_2431,U_2430)
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2430)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP234])],[f_845_2]) ).

cnf(f_845_4,plain,
    ( sP234(U_2431,U_2430)
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2430)) ),
    inference(clausify,[status(thm)],[f_845_3]) ).

cnf(f_845_5,plain,
    ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2430),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2431),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,U_2430)),one_one_nat)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2431),U_2430))
    | ~ sP234(U_2431,U_2430) ),
    inference(clausify,[status(thm)],[f_845_3]) ).

cnf(f_845_6,plain,
    ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2430),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2431),bot_bot_fun_nat_bool))) = hAPP_f22106695ol_nat(finite_card_nat,U_2430)
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2431),U_2430))
    | ~ sP234(U_2431,U_2430) ),
    inference(clausify,[status(thm)],[f_845_3]) ).

fof(f_846_1,plain,
    ! [X_1,A] :
      ( ( ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))) = hAPP_f921600141ol_nat(finite_card_pname,A)
          | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) )
        & ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,A)),one_one_nat)
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) ) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_739_card__Diff__singleton__if]) ).

fof(f_846_2,plain,
    ! [U_2433,U_2432] :
      ( ( ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2432),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2433),bot_bo844097828e_bool))) = hAPP_f921600141ol_nat(finite_card_pname,U_2432)
          | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2433),U_2432)) )
        & ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2432),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2433),bot_bo844097828e_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,U_2432)),one_one_nat)
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2433),U_2432)) ) )
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2432)) ),
    inference(variable_rename,[status(thm)],[f_846_1]) ).

fof(f_846_3,plain,
    ( ! [U_2433,U_2432] :
        ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2432),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2433),bot_bo844097828e_bool))) = hAPP_f921600141ol_nat(finite_card_pname,U_2432)
        | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2433),U_2432))
        | ~ sP235(U_2433,U_2432) )
    & ! [U_2433,U_2432] :
        ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2432),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2433),bot_bo844097828e_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,U_2432)),one_one_nat)
        | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2433),U_2432))
        | ~ sP235(U_2433,U_2432) )
    & ! [U_2433,U_2432] :
        ( sP235(U_2433,U_2432)
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2432)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP235])],[f_846_2]) ).

cnf(f_846_4,plain,
    ( sP235(U_2433,U_2432)
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2432)) ),
    inference(clausify,[status(thm)],[f_846_3]) ).

cnf(f_846_5,plain,
    ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2432),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2433),bot_bo844097828e_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,U_2432)),one_one_nat)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2433),U_2432))
    | ~ sP235(U_2433,U_2432) ),
    inference(clausify,[status(thm)],[f_846_3]) ).

cnf(f_846_6,plain,
    ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2432),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2433),bot_bo844097828e_bool))) = hAPP_f921600141ol_nat(finite_card_pname,U_2432)
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2433),U_2432))
    | ~ sP235(U_2433,U_2432) ),
    inference(clausify,[status(thm)],[f_846_3]) ).

fof(f_847_1,plain,
    ! [X_1,A] :
      ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,A)),one_one_nat)
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_740_card__Diff__singleton]) ).

fof(f_847_2,plain,
    ! [U_2435,U_2434] :
      ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2434),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2435),bot_bot_fun_a_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,U_2434)),one_one_nat)
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2435),U_2434))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2434)) ),
    inference(variable_rename,[status(thm)],[f_847_1]) ).

fof(f_847_3,plain,
    ! [U_2435,U_2434] :
      ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2434),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2435),bot_bot_fun_a_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,U_2434)),one_one_nat)
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2435),U_2434))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2434)) ),
    inference(definitional_conversion,[status(esa)],[f_847_2]) ).

cnf(f_847_4,plain,
    ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2434),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2435),bot_bot_fun_a_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,U_2434)),one_one_nat)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2435),U_2434))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2434)) ),
    inference(clausify,[status(thm)],[f_847_3]) ).

fof(f_848_1,plain,
    ! [X_1,A] :
      ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,A)),one_one_nat)
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_741_card__Diff__singleton]) ).

fof(f_848_2,plain,
    ! [U_2437,U_2436] :
      ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2436),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2437),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,U_2436)),one_one_nat)
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2437),U_2436))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2436)) ),
    inference(variable_rename,[status(thm)],[f_848_1]) ).

fof(f_848_3,plain,
    ! [U_2436,U_2437] :
      ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2436),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2437),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,U_2436)),one_one_nat)
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2437),U_2436))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2436)) ),
    inference(definitional_conversion,[status(esa)],[f_848_2]) ).

cnf(f_848_4,plain,
    ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2436),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2437),bot_bot_fun_int_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,U_2436)),one_one_nat)
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2437),U_2436))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2436)) ),
    inference(clausify,[status(thm)],[f_848_3]) ).

fof(f_849_1,plain,
    ! [X_1,A] :
      ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,A)),one_one_nat)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_742_card__Diff__singleton]) ).

fof(f_849_2,plain,
    ! [U_2439,U_2438] :
      ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2438),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2439),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,U_2438)),one_one_nat)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2439),U_2438))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2438)) ),
    inference(variable_rename,[status(thm)],[f_849_1]) ).

fof(f_849_3,plain,
    ! [U_2438,U_2439] :
      ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2438),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2439),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,U_2438)),one_one_nat)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2439),U_2438))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2438)) ),
    inference(definitional_conversion,[status(esa)],[f_849_2]) ).

cnf(f_849_4,plain,
    ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2438),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2439),bot_bot_fun_nat_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,U_2438)),one_one_nat)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2439),U_2438))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2438)) ),
    inference(clausify,[status(thm)],[f_849_3]) ).

fof(f_850_1,plain,
    ! [X_1,A] :
      ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,A)),one_one_nat)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_743_card__Diff__singleton]) ).

fof(f_850_2,plain,
    ! [U_2441,U_2440] :
      ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2440),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2441),bot_bo844097828e_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,U_2440)),one_one_nat)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2441),U_2440))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2440)) ),
    inference(variable_rename,[status(thm)],[f_850_1]) ).

fof(f_850_3,plain,
    ! [U_2440,U_2441] :
      ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2440),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2441),bot_bo844097828e_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,U_2440)),one_one_nat)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2441),U_2440))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2440)) ),
    inference(definitional_conversion,[status(esa)],[f_850_2]) ).

cnf(f_850_4,plain,
    ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2440),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2441),bot_bo844097828e_bool))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,U_2440)),one_one_nat)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2441),U_2440))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2440)) ),
    inference(clausify,[status(thm)],[f_850_3]) ).

fof(f_851_1,plain,
    ! [X_1] :
      ( ( one_one_int = X_1
        | X_1 != one_one_int )
      & ( X_1 = one_one_int
        | one_one_int != X_1 ) ),
    inference(fof_nnf,[status(thm)],[fact_744_one__reorient]) ).

fof(f_851_2,plain,
    ! [U_2442] :
      ( ( one_one_int = U_2442
        | U_2442 != one_one_int )
      & ( U_2442 = one_one_int
        | one_one_int != U_2442 ) ),
    inference(variable_rename,[status(thm)],[f_851_1]) ).

fof(f_851_3,plain,
    ( ! [U_2444] :
        ( one_one_int = U_2444
        | U_2444 != one_one_int )
    & ! [U_2443] :
        ( U_2443 = one_one_int
        | one_one_int != U_2443 ) ),
    inference(miniscope,[status(thm)],[f_851_2]) ).

fof(f_851_4,plain,
    ( ! [U_2444] :
        ( one_one_int = U_2444
        | U_2444 != one_one_int )
    & ! [U_2443] :
        ( U_2443 = one_one_int
        | one_one_int != U_2443 ) ),
    inference(definitional_conversion,[status(esa)],[f_851_3]) ).

cnf(f_851_5,plain,
    ( U_2443 = one_one_int
    | one_one_int != U_2443 ),
    inference(clausify,[status(thm)],[f_851_4]) ).

cnf(f_851_6,plain,
    ( one_one_int = U_2444
    | U_2444 != one_one_int ),
    inference(clausify,[status(thm)],[f_851_4]) ).

fof(f_852_1,plain,
    ! [X_1] :
      ( ( one_one_nat = X_1
        | X_1 != one_one_nat )
      & ( X_1 = one_one_nat
        | one_one_nat != X_1 ) ),
    inference(fof_nnf,[status(thm)],[fact_745_one__reorient]) ).

fof(f_852_2,plain,
    ! [U_2445] :
      ( ( one_one_nat = U_2445
        | U_2445 != one_one_nat )
      & ( U_2445 = one_one_nat
        | one_one_nat != U_2445 ) ),
    inference(variable_rename,[status(thm)],[f_852_1]) ).

fof(f_852_3,plain,
    ( ! [U_2447] :
        ( one_one_nat = U_2447
        | U_2447 != one_one_nat )
    & ! [U_2446] :
        ( U_2446 = one_one_nat
        | one_one_nat != U_2446 ) ),
    inference(miniscope,[status(thm)],[f_852_2]) ).

fof(f_852_4,plain,
    ( ! [U_2447] :
        ( one_one_nat = U_2447
        | U_2447 != one_one_nat )
    & ! [U_2446] :
        ( U_2446 = one_one_nat
        | one_one_nat != U_2446 ) ),
    inference(definitional_conversion,[status(esa)],[f_852_3]) ).

cnf(f_852_5,plain,
    ( U_2446 = one_one_nat
    | one_one_nat != U_2446 ),
    inference(clausify,[status(thm)],[f_852_4]) ).

cnf(f_852_6,plain,
    ( one_one_nat = U_2447
    | U_2447 != one_one_nat ),
    inference(clausify,[status(thm)],[f_852_4]) ).

fof(f_853_1,plain,
    ! [N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,N)),one_one_nat) = N,
    inference(fof_nnf,[status(thm)],[fact_746_diff__Suc__1]) ).

fof(f_853_2,plain,
    ! [U_2448] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,U_2448)),one_one_nat) = U_2448,
    inference(variable_rename,[status(thm)],[f_853_1]) ).

fof(f_853_3,plain,
    ! [U_2448] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,U_2448)),one_one_nat) = U_2448,
    inference(definitional_conversion,[status(esa)],[f_853_2]) ).

cnf(f_853_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,U_2448)),one_one_nat) = U_2448,
    inference(clausify,[status(thm)],[f_853_3]) ).

fof(f_854_1,plain,
    ! [M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),one_one_nat)),N),
    inference(fof_nnf,[status(thm)],[fact_747_diff__Suc__eq__diff__pred]) ).

fof(f_854_2,plain,
    ! [U_2450,U_2449] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2450),hAPP_nat_nat(suc,U_2449)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2450),one_one_nat)),U_2449),
    inference(variable_rename,[status(thm)],[f_854_1]) ).

fof(f_854_3,plain,
    ! [U_2449,U_2450] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2450),hAPP_nat_nat(suc,U_2449)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2450),one_one_nat)),U_2449),
    inference(definitional_conversion,[status(esa)],[f_854_2]) ).

cnf(f_854_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2450),hAPP_nat_nat(suc,U_2449)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2450),one_one_nat)),U_2449),
    inference(clausify,[status(thm)],[f_854_3]) ).

fof(f_855_1,plain,
    ! [X_1,F,F_1] :
      ( hAPP_fun_a_bool_a(F_1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool)) = X_1
      | ~ hBOOL(finite_folding_one_a(F,F_1))
      | ~ is_a(X_1) ),
    inference(fof_nnf,[status(thm)],[fact_748_folding__one_Osingleton]) ).

fof(f_855_2,plain,
    ! [U_2453,U_2452,U_2451] :
      ( hAPP_fun_a_bool_a(U_2451,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2453),bot_bot_fun_a_bool)) = U_2453
      | ~ hBOOL(finite_folding_one_a(U_2452,U_2451))
      | ~ is_a(U_2453) ),
    inference(variable_rename,[status(thm)],[f_855_1]) ).

fof(f_855_3,plain,
    ! [U_2453] :
      ( ! [U_2452,U_2451] :
          ( hAPP_fun_a_bool_a(U_2451,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2453),bot_bot_fun_a_bool)) = U_2453
          | ~ hBOOL(finite_folding_one_a(U_2452,U_2451)) )
      | ~ is_a(U_2453) ),
    inference(miniscope,[status(thm)],[f_855_2]) ).

fof(f_855_4,plain,
    ! [U_2451,U_2452,U_2453] :
      ( hAPP_fun_a_bool_a(U_2451,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2453),bot_bot_fun_a_bool)) = U_2453
      | ~ hBOOL(finite_folding_one_a(U_2452,U_2451))
      | ~ is_a(U_2453) ),
    inference(definitional_conversion,[status(esa)],[f_855_3]) ).

cnf(f_855_5,plain,
    ( hAPP_fun_a_bool_a(U_2451,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2453),bot_bot_fun_a_bool)) = U_2453
    | ~ hBOOL(finite_folding_one_a(U_2452,U_2451))
    | ~ is_a(U_2453) ),
    inference(clausify,[status(thm)],[f_855_4]) ).

fof(f_856_1,plain,
    ! [X_1,F,F_1] :
      ( hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool)) = X_1
      | ~ hBOOL(finite988810631ne_nat(F,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_749_folding__one_Osingleton]) ).

fof(f_856_2,plain,
    ! [U_2456,U_2455,U_2454] :
      ( hAPP_f22106695ol_nat(U_2454,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2456),bot_bot_fun_nat_bool)) = U_2456
      | ~ hBOOL(finite988810631ne_nat(U_2455,U_2454)) ),
    inference(variable_rename,[status(thm)],[f_856_1]) ).

fof(f_856_3,plain,
    ! [U_2455,U_2454,U_2456] :
      ( hAPP_f22106695ol_nat(U_2454,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2456),bot_bot_fun_nat_bool)) = U_2456
      | ~ hBOOL(finite988810631ne_nat(U_2455,U_2454)) ),
    inference(definitional_conversion,[status(esa)],[f_856_2]) ).

cnf(f_856_4,plain,
    ( hAPP_f22106695ol_nat(U_2454,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2456),bot_bot_fun_nat_bool)) = U_2456
    | ~ hBOOL(finite988810631ne_nat(U_2455,U_2454)) ),
    inference(clausify,[status(thm)],[f_856_3]) ).

fof(f_857_1,plain,
    ! [X_1,F,F_1] :
      ( hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool)) = X_1
      | ~ hBOOL(finite1626084323ne_int(F,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_750_folding__one_Osingleton]) ).

fof(f_857_2,plain,
    ! [U_2459,U_2458,U_2457] :
      ( hAPP_f1594865479ol_int(U_2457,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2459),bot_bot_fun_int_bool)) = U_2459
      | ~ hBOOL(finite1626084323ne_int(U_2458,U_2457)) ),
    inference(variable_rename,[status(thm)],[f_857_1]) ).

fof(f_857_3,plain,
    ! [U_2457,U_2458,U_2459] :
      ( hAPP_f1594865479ol_int(U_2457,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2459),bot_bot_fun_int_bool)) = U_2459
      | ~ hBOOL(finite1626084323ne_int(U_2458,U_2457)) ),
    inference(definitional_conversion,[status(esa)],[f_857_2]) ).

cnf(f_857_4,plain,
    ( hAPP_f1594865479ol_int(U_2457,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2459),bot_bot_fun_int_bool)) = U_2459
    | ~ hBOOL(finite1626084323ne_int(U_2458,U_2457)) ),
    inference(clausify,[status(thm)],[f_857_3]) ).

fof(f_858_1,plain,
    ! [B,A_2,A] :
      ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,A_2),B))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),B))),one_one_nat)
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),B))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_2),A))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_751_card__Diff__insert]) ).

fof(f_858_2,plain,
    ! [U_2462,U_2461,U_2460] :
      ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2460),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2461),U_2462))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2460),U_2462))),one_one_nat)
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2461),U_2462))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2461),U_2460))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2460)) ),
    inference(variable_rename,[status(thm)],[f_858_1]) ).

fof(f_858_3,plain,
    ! [U_2460,U_2461,U_2462] :
      ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2460),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2461),U_2462))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2460),U_2462))),one_one_nat)
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2461),U_2462))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2461),U_2460))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2460)) ),
    inference(definitional_conversion,[status(esa)],[f_858_2]) ).

cnf(f_858_4,plain,
    ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2460),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2461),U_2462))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2460),U_2462))),one_one_nat)
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2461),U_2462))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2461),U_2460))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2460)) ),
    inference(clausify,[status(thm)],[f_858_3]) ).

fof(f_859_1,plain,
    ! [B,A_2,A] :
      ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,A_2),B))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),B))),one_one_nat)
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),B))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,A_2),A))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_752_card__Diff__insert]) ).

fof(f_859_2,plain,
    ! [U_2465,U_2464,U_2463] :
      ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2463),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2464),U_2465))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2463),U_2465))),one_one_nat)
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2464),U_2465))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2464),U_2463))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2463)) ),
    inference(variable_rename,[status(thm)],[f_859_1]) ).

fof(f_859_3,plain,
    ! [U_2464,U_2463,U_2465] :
      ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2463),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2464),U_2465))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2463),U_2465))),one_one_nat)
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2464),U_2465))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2464),U_2463))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2463)) ),
    inference(definitional_conversion,[status(esa)],[f_859_2]) ).

cnf(f_859_4,plain,
    ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2463),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2464),U_2465))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2463),U_2465))),one_one_nat)
    | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2464),U_2465))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2464),U_2463))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2463)) ),
    inference(clausify,[status(thm)],[f_859_3]) ).

fof(f_860_1,plain,
    ! [B,A_2,A] :
      ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,A_2),B))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),B))),one_one_nat)
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),B))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_2),A))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_753_card__Diff__insert]) ).

fof(f_860_2,plain,
    ! [U_2468,U_2467,U_2466] :
      ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2466),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2467),U_2468))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2466),U_2468))),one_one_nat)
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2467),U_2468))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2467),U_2466))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2466)) ),
    inference(variable_rename,[status(thm)],[f_860_1]) ).

fof(f_860_3,plain,
    ! [U_2466,U_2467,U_2468] :
      ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2466),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2467),U_2468))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2466),U_2468))),one_one_nat)
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2467),U_2468))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2467),U_2466))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2466)) ),
    inference(definitional_conversion,[status(esa)],[f_860_2]) ).

cnf(f_860_4,plain,
    ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2466),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2467),U_2468))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2466),U_2468))),one_one_nat)
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2467),U_2468))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2467),U_2466))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2466)) ),
    inference(clausify,[status(thm)],[f_860_3]) ).

fof(f_861_1,plain,
    ! [B,A_2,A] :
      ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,A_2),B))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),B))),one_one_nat)
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),B))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_2),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_754_card__Diff__insert]) ).

fof(f_861_2,plain,
    ! [U_2471,U_2470,U_2469] :
      ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2469),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2470),U_2471))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2469),U_2471))),one_one_nat)
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2470),U_2471))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2470),U_2469))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2469)) ),
    inference(variable_rename,[status(thm)],[f_861_1]) ).

fof(f_861_3,plain,
    ! [U_2469,U_2470,U_2471] :
      ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2469),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2470),U_2471))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2469),U_2471))),one_one_nat)
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2470),U_2471))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2470),U_2469))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2469)) ),
    inference(definitional_conversion,[status(esa)],[f_861_2]) ).

cnf(f_861_4,plain,
    ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2469),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2470),U_2471))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2469),U_2471))),one_one_nat)
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2470),U_2471))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2470),U_2469))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2469)) ),
    inference(clausify,[status(thm)],[f_861_3]) ).

fof(f_862_1,plain,
    ! [X_1,A,F,F_1] :
      ( hAPP_fun_a_bool_a(F_1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_a_a(hAPP_a_fun_a_a(F,X_1),hAPP_fun_a_bool_a(F_1,A))
      | A = bot_bot_fun_a_bool
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
      | ~ hBOOL(finite_folding_one_a(F,F_1))
      | ~ is_fun_a_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_755_folding__one_Oinsert]) ).

fof(f_862_2,plain,
    ! [U_2475,U_2474,U_2473,U_2472] :
      ( hAPP_fun_a_bool_a(U_2472,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2475),U_2474)) = hAPP_a_a(hAPP_a_fun_a_a(U_2473,U_2475),hAPP_fun_a_bool_a(U_2472,U_2474))
      | U_2474 = bot_bot_fun_a_bool
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2475),U_2474))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2474))
      | ~ hBOOL(finite_folding_one_a(U_2473,U_2472))
      | ~ is_fun_a_bool(U_2474) ),
    inference(variable_rename,[status(thm)],[f_862_1]) ).

fof(f_862_3,plain,
    ! [U_2475,U_2474] :
      ( ! [U_2473,U_2472] :
          ( hAPP_fun_a_bool_a(U_2472,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2475),U_2474)) = hAPP_a_a(hAPP_a_fun_a_a(U_2473,U_2475),hAPP_fun_a_bool_a(U_2472,U_2474))
          | U_2474 = bot_bot_fun_a_bool
          | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2475),U_2474))
          | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2474))
          | ~ hBOOL(finite_folding_one_a(U_2473,U_2472)) )
      | ~ is_fun_a_bool(U_2474) ),
    inference(miniscope,[status(thm)],[f_862_2]) ).

fof(f_862_4,plain,
    ! [U_2472,U_2473,U_2474,U_2475] :
      ( hAPP_fun_a_bool_a(U_2472,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2475),U_2474)) = hAPP_a_a(hAPP_a_fun_a_a(U_2473,U_2475),hAPP_fun_a_bool_a(U_2472,U_2474))
      | U_2474 = bot_bot_fun_a_bool
      | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2475),U_2474))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2474))
      | ~ hBOOL(finite_folding_one_a(U_2473,U_2472))
      | ~ is_fun_a_bool(U_2474) ),
    inference(definitional_conversion,[status(esa)],[f_862_3]) ).

cnf(f_862_5,plain,
    ( hAPP_fun_a_bool_a(U_2472,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2475),U_2474)) = hAPP_a_a(hAPP_a_fun_a_a(U_2473,U_2475),hAPP_fun_a_bool_a(U_2472,U_2474))
    | U_2474 = bot_bot_fun_a_bool
    | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2475),U_2474))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2474))
    | ~ hBOOL(finite_folding_one_a(U_2473,U_2472))
    | ~ is_fun_a_bool(U_2474) ),
    inference(clausify,[status(thm)],[f_862_4]) ).

fof(f_863_1,plain,
    ! [X_1,A,F,F_1] :
      ( hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,A))
      | A = bot_bot_fun_int_bool
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
      | ~ hBOOL(finite1626084323ne_int(F,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_756_folding__one_Oinsert]) ).

fof(f_863_2,plain,
    ! [U_2479,U_2478,U_2477,U_2476] :
      ( hAPP_f1594865479ol_int(U_2476,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2479),U_2478)) = hAPP_int_int(hAPP_int_fun_int_int(U_2477,U_2479),hAPP_f1594865479ol_int(U_2476,U_2478))
      | U_2478 = bot_bot_fun_int_bool
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2479),U_2478))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2478))
      | ~ hBOOL(finite1626084323ne_int(U_2477,U_2476)) ),
    inference(variable_rename,[status(thm)],[f_863_1]) ).

fof(f_863_3,plain,
    ! [U_2477,U_2478,U_2479,U_2476] :
      ( hAPP_f1594865479ol_int(U_2476,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2479),U_2478)) = hAPP_int_int(hAPP_int_fun_int_int(U_2477,U_2479),hAPP_f1594865479ol_int(U_2476,U_2478))
      | U_2478 = bot_bot_fun_int_bool
      | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2479),U_2478))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2478))
      | ~ hBOOL(finite1626084323ne_int(U_2477,U_2476)) ),
    inference(definitional_conversion,[status(esa)],[f_863_2]) ).

cnf(f_863_4,plain,
    ( hAPP_f1594865479ol_int(U_2476,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2479),U_2478)) = hAPP_int_int(hAPP_int_fun_int_int(U_2477,U_2479),hAPP_f1594865479ol_int(U_2476,U_2478))
    | U_2478 = bot_bot_fun_int_bool
    | hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2479),U_2478))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2478))
    | ~ hBOOL(finite1626084323ne_int(U_2477,U_2476)) ),
    inference(clausify,[status(thm)],[f_863_3]) ).

fof(f_864_1,plain,
    ! [X_1,A,F,F_1] :
      ( hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,A))
      | A = bot_bot_fun_nat_bool
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
      | ~ hBOOL(finite988810631ne_nat(F,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_757_folding__one_Oinsert]) ).

fof(f_864_2,plain,
    ! [U_2483,U_2482,U_2481,U_2480] :
      ( hAPP_f22106695ol_nat(U_2480,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2483),U_2482)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_2481,U_2483),hAPP_f22106695ol_nat(U_2480,U_2482))
      | U_2482 = bot_bot_fun_nat_bool
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2483),U_2482))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2482))
      | ~ hBOOL(finite988810631ne_nat(U_2481,U_2480)) ),
    inference(variable_rename,[status(thm)],[f_864_1]) ).

fof(f_864_3,plain,
    ! [U_2481,U_2483,U_2482,U_2480] :
      ( hAPP_f22106695ol_nat(U_2480,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2483),U_2482)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_2481,U_2483),hAPP_f22106695ol_nat(U_2480,U_2482))
      | U_2482 = bot_bot_fun_nat_bool
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2483),U_2482))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2482))
      | ~ hBOOL(finite988810631ne_nat(U_2481,U_2480)) ),
    inference(definitional_conversion,[status(esa)],[f_864_2]) ).

cnf(f_864_4,plain,
    ( hAPP_f22106695ol_nat(U_2480,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2483),U_2482)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_2481,U_2483),hAPP_f22106695ol_nat(U_2480,U_2482))
    | U_2482 = bot_bot_fun_nat_bool
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2483),U_2482))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2482))
    | ~ hBOOL(finite988810631ne_nat(U_2481,U_2480)) ),
    inference(clausify,[status(thm)],[f_864_3]) ).

fof(f_865_1,plain,
    ! [X_1,A,F,F_1] :
      ( hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(F_1,A))
      | A = bot_bo844097828e_bool
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
      | ~ hBOOL(finite1282449217_pname(F,F_1))
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_758_folding__one_Oinsert]) ).

fof(f_865_2,plain,
    ! [U_2487,U_2486,U_2485,U_2484] :
      ( hAPP_f1297739591_pname(U_2484,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2487),U_2486)) = hAPP_pname_pname(hAPP_p1170154830_pname(U_2485,U_2487),hAPP_f1297739591_pname(U_2484,U_2486))
      | U_2486 = bot_bo844097828e_bool
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2487),U_2486))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2486))
      | ~ hBOOL(finite1282449217_pname(U_2485,U_2484))
      | ~ is_fun_pname_bool(U_2486) ),
    inference(variable_rename,[status(thm)],[f_865_1]) ).

fof(f_865_3,plain,
    ! [U_2487,U_2486] :
      ( ! [U_2485,U_2484] :
          ( hAPP_f1297739591_pname(U_2484,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2487),U_2486)) = hAPP_pname_pname(hAPP_p1170154830_pname(U_2485,U_2487),hAPP_f1297739591_pname(U_2484,U_2486))
          | U_2486 = bot_bo844097828e_bool
          | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2487),U_2486))
          | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2486))
          | ~ hBOOL(finite1282449217_pname(U_2485,U_2484)) )
      | ~ is_fun_pname_bool(U_2486) ),
    inference(miniscope,[status(thm)],[f_865_2]) ).

fof(f_865_4,plain,
    ! [U_2486,U_2487,U_2484,U_2485] :
      ( hAPP_f1297739591_pname(U_2484,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2487),U_2486)) = hAPP_pname_pname(hAPP_p1170154830_pname(U_2485,U_2487),hAPP_f1297739591_pname(U_2484,U_2486))
      | U_2486 = bot_bo844097828e_bool
      | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2487),U_2486))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2486))
      | ~ hBOOL(finite1282449217_pname(U_2485,U_2484))
      | ~ is_fun_pname_bool(U_2486) ),
    inference(definitional_conversion,[status(esa)],[f_865_3]) ).

cnf(f_865_5,plain,
    ( hAPP_f1297739591_pname(U_2484,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2487),U_2486)) = hAPP_pname_pname(hAPP_p1170154830_pname(U_2485,U_2487),hAPP_f1297739591_pname(U_2484,U_2486))
    | U_2486 = bot_bo844097828e_bool
    | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2487),U_2486))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2486))
    | ~ hBOOL(finite1282449217_pname(U_2485,U_2484))
    | ~ is_fun_pname_bool(U_2486) ),
    inference(clausify,[status(thm)],[f_865_4]) ).

fof(f_866_1,plain,
    ! [A,F,F_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_fun_a_bool_a(F_1,A)),A))
      | ? [X_2,Y_2] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_a_a(hAPP_a_fun_a_a(F,X_2),Y_2)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_2),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,Y_2),bot_bot_fun_a_bool))))
          & is_a(Y_2)
          & is_a(X_2) )
      | A = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
      | ~ hBOOL(finite_folding_one_a(F,F_1))
      | ~ is_fun_a_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_759_folding__one_Oclosed]) ).

fof(f_866_2,plain,
    ! [U_2492,U_2491,U_2490] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_fun_a_bool_a(U_2490,U_2492)),U_2492))
      | ? [U_2489,U_2488] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_a_a(hAPP_a_fun_a_a(U_2491,U_2489),U_2488)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2489),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2488),bot_bot_fun_a_bool))))
          & is_a(U_2488)
          & is_a(U_2489) )
      | U_2492 = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2492))
      | ~ hBOOL(finite_folding_one_a(U_2491,U_2490))
      | ~ is_fun_a_bool(U_2492) ),
    inference(variable_rename,[status(thm)],[f_866_1]) ).

fof(f_866_3,plain,
    ! [U_2492] :
      ( ! [U_2491,U_2490] :
          ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_fun_a_bool_a(U_2490,U_2492)),U_2492))
          | ? [U_2489,U_2488] :
              ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_a_a(hAPP_a_fun_a_a(U_2491,U_2489),U_2488)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2489),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2488),bot_bot_fun_a_bool))))
              & is_a(U_2488)
              & is_a(U_2489) )
          | U_2492 = bot_bot_fun_a_bool
          | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2492))
          | ~ hBOOL(finite_folding_one_a(U_2491,U_2490)) )
      | ~ is_fun_a_bool(U_2492) ),
    inference(miniscope,[status(thm)],[f_866_2]) ).

fof(f_866_4,plain,
    ! [U_2492] :
      ( ! [U_2491,U_2490] :
          ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_fun_a_bool_a(U_2490,U_2492)),U_2492))
          | ? [U_2488] :
              ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_a_a(hAPP_a_fun_a_a(U_2491,sK142(U_2492,U_2491,U_2490)),U_2488)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK142(U_2492,U_2491,U_2490)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2488),bot_bot_fun_a_bool))))
              & is_a(U_2488)
              & is_a(sK142(U_2492,U_2491,U_2490)) )
          | U_2492 = bot_bot_fun_a_bool
          | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2492))
          | ~ hBOOL(finite_folding_one_a(U_2491,U_2490)) )
      | ~ is_fun_a_bool(U_2492) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(U_2489,sK142(U_2492,U_2491,U_2490))],[f_866_3]) ).

fof(f_866_5,plain,
    ! [U_2492] :
      ( ! [U_2491,U_2490] :
          ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_fun_a_bool_a(U_2490,U_2492)),U_2492))
          | ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_a_a(hAPP_a_fun_a_a(U_2491,sK142(U_2492,U_2491,U_2490)),sK143(U_2492,U_2491,U_2490))),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK142(U_2492,U_2491,U_2490)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK143(U_2492,U_2491,U_2490)),bot_bot_fun_a_bool))))
            & is_a(sK143(U_2492,U_2491,U_2490))
            & is_a(sK142(U_2492,U_2491,U_2490)) )
          | U_2492 = bot_bot_fun_a_bool
          | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2492))
          | ~ hBOOL(finite_folding_one_a(U_2491,U_2490)) )
      | ~ is_fun_a_bool(U_2492) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(U_2488,sK143(U_2492,U_2491,U_2490))],[f_866_4]) ).

fof(f_866_6,plain,
    ( ! [U_2490,U_2491,U_2492] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_a_a(hAPP_a_fun_a_a(U_2491,sK142(U_2492,U_2491,U_2490)),sK143(U_2492,U_2491,U_2490))),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK142(U_2492,U_2491,U_2490)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK143(U_2492,U_2491,U_2490)),bot_bot_fun_a_bool))))
        | ~ sP236(U_2490,U_2491,U_2492) )
    & ! [U_2490,U_2491,U_2492] :
        ( is_a(sK143(U_2492,U_2491,U_2490))
        | ~ sP236(U_2490,U_2491,U_2492) )
    & ! [U_2490,U_2491,U_2492] :
        ( is_a(sK142(U_2492,U_2491,U_2490))
        | ~ sP236(U_2490,U_2491,U_2492) )
    & ! [U_2490,U_2491,U_2492] :
        ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_fun_a_bool_a(U_2490,U_2492)),U_2492))
        | sP236(U_2490,U_2491,U_2492)
        | U_2492 = bot_bot_fun_a_bool
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2492))
        | ~ hBOOL(finite_folding_one_a(U_2491,U_2490))
        | ~ is_fun_a_bool(U_2492) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP236])],[f_866_5]) ).

cnf(f_866_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_fun_a_bool_a(U_2490,U_2492)),U_2492))
    | sP236(U_2490,U_2491,U_2492)
    | U_2492 = bot_bot_fun_a_bool
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2492))
    | ~ hBOOL(finite_folding_one_a(U_2491,U_2490))
    | ~ is_fun_a_bool(U_2492) ),
    inference(clausify,[status(thm)],[f_866_6]) ).

cnf(f_866_8,plain,
    ( is_a(sK142(U_2492,U_2491,U_2490))
    | ~ sP236(U_2490,U_2491,U_2492) ),
    inference(clausify,[status(thm)],[f_866_6]) ).

cnf(f_866_9,plain,
    ( is_a(sK143(U_2492,U_2491,U_2490))
    | ~ sP236(U_2490,U_2491,U_2492) ),
    inference(clausify,[status(thm)],[f_866_6]) ).

cnf(f_866_10,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_a_a(hAPP_a_fun_a_a(U_2491,sK142(U_2492,U_2491,U_2490)),sK143(U_2492,U_2491,U_2490))),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK142(U_2492,U_2491,U_2490)),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK143(U_2492,U_2491,U_2490)),bot_bot_fun_a_bool))))
    | ~ sP236(U_2490,U_2491,U_2492) ),
    inference(clausify,[status(thm)],[f_866_6]) ).

fof(f_867_1,plain,
    ! [A,F,F_1] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_f1594865479ol_int(F_1,A)),A))
      | ? [X_2,Y_2] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(F,X_2),Y_2)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,Y_2),bot_bot_fun_int_bool))))
      | A = bot_bot_fun_int_bool
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
      | ~ hBOOL(finite1626084323ne_int(F,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_760_folding__one_Oclosed]) ).

fof(f_867_2,plain,
    ! [U_2497,U_2496,U_2495] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_f1594865479ol_int(U_2495,U_2497)),U_2497))
      | ? [U_2494,U_2493] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(U_2496,U_2494),U_2493)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2494),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2493),bot_bot_fun_int_bool))))
      | U_2497 = bot_bot_fun_int_bool
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2497))
      | ~ hBOOL(finite1626084323ne_int(U_2496,U_2495)) ),
    inference(variable_rename,[status(thm)],[f_867_1]) ).

fof(f_867_3,plain,
    ! [U_2497,U_2496,U_2495] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_f1594865479ol_int(U_2495,U_2497)),U_2497))
      | ? [U_2493] : ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(U_2496,sK144(U_2497,U_2496,U_2495)),U_2493)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK144(U_2497,U_2496,U_2495)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2493),bot_bot_fun_int_bool))))
      | U_2497 = bot_bot_fun_int_bool
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2497))
      | ~ hBOOL(finite1626084323ne_int(U_2496,U_2495)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(U_2494,sK144(U_2497,U_2496,U_2495))],[f_867_2]) ).

fof(f_867_4,plain,
    ! [U_2497,U_2496,U_2495] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_f1594865479ol_int(U_2495,U_2497)),U_2497))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(U_2496,sK144(U_2497,U_2496,U_2495)),sK145(U_2497,U_2496,U_2495))),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK144(U_2497,U_2496,U_2495)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK145(U_2497,U_2496,U_2495)),bot_bot_fun_int_bool))))
      | U_2497 = bot_bot_fun_int_bool
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2497))
      | ~ hBOOL(finite1626084323ne_int(U_2496,U_2495)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK145]),skolemize(U_2493,sK145(U_2497,U_2496,U_2495))],[f_867_3]) ).

fof(f_867_5,plain,
    ! [U_2495,U_2496,U_2497] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_f1594865479ol_int(U_2495,U_2497)),U_2497))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(U_2496,sK144(U_2497,U_2496,U_2495)),sK145(U_2497,U_2496,U_2495))),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK144(U_2497,U_2496,U_2495)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK145(U_2497,U_2496,U_2495)),bot_bot_fun_int_bool))))
      | U_2497 = bot_bot_fun_int_bool
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2497))
      | ~ hBOOL(finite1626084323ne_int(U_2496,U_2495)) ),
    inference(definitional_conversion,[status(esa)],[f_867_4]) ).

cnf(f_867_6,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_f1594865479ol_int(U_2495,U_2497)),U_2497))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_int_int(hAPP_int_fun_int_int(U_2496,sK144(U_2497,U_2496,U_2495)),sK145(U_2497,U_2496,U_2495))),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK144(U_2497,U_2496,U_2495)),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK145(U_2497,U_2496,U_2495)),bot_bot_fun_int_bool))))
    | U_2497 = bot_bot_fun_int_bool
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2497))
    | ~ hBOOL(finite1626084323ne_int(U_2496,U_2495)) ),
    inference(clausify,[status(thm)],[f_867_5]) ).

fof(f_868_1,plain,
    ! [A,F,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f22106695ol_nat(F_1,A)),A))
      | ? [X_2,Y_2] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_2),Y_2)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,Y_2),bot_bot_fun_nat_bool))))
      | A = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
      | ~ hBOOL(finite988810631ne_nat(F,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_761_folding__one_Oclosed]) ).

fof(f_868_2,plain,
    ! [U_2502,U_2501,U_2500] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f22106695ol_nat(U_2500,U_2502)),U_2502))
      | ? [U_2499,U_2498] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_2501,U_2499),U_2498)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2499),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2498),bot_bot_fun_nat_bool))))
      | U_2502 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2502))
      | ~ hBOOL(finite988810631ne_nat(U_2501,U_2500)) ),
    inference(variable_rename,[status(thm)],[f_868_1]) ).

fof(f_868_3,plain,
    ! [U_2502,U_2501,U_2500] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f22106695ol_nat(U_2500,U_2502)),U_2502))
      | ? [U_2498] : ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_2501,sK146(U_2502,U_2501,U_2500)),U_2498)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK146(U_2502,U_2501,U_2500)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2498),bot_bot_fun_nat_bool))))
      | U_2502 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2502))
      | ~ hBOOL(finite988810631ne_nat(U_2501,U_2500)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK146]),skolemize(U_2499,sK146(U_2502,U_2501,U_2500))],[f_868_2]) ).

fof(f_868_4,plain,
    ! [U_2502,U_2501,U_2500] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f22106695ol_nat(U_2500,U_2502)),U_2502))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_2501,sK146(U_2502,U_2501,U_2500)),sK147(U_2502,U_2501,U_2500))),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK146(U_2502,U_2501,U_2500)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK147(U_2502,U_2501,U_2500)),bot_bot_fun_nat_bool))))
      | U_2502 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2502))
      | ~ hBOOL(finite988810631ne_nat(U_2501,U_2500)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK147]),skolemize(U_2498,sK147(U_2502,U_2501,U_2500))],[f_868_3]) ).

fof(f_868_5,plain,
    ! [U_2500,U_2501,U_2502] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f22106695ol_nat(U_2500,U_2502)),U_2502))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_2501,sK146(U_2502,U_2501,U_2500)),sK147(U_2502,U_2501,U_2500))),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK146(U_2502,U_2501,U_2500)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK147(U_2502,U_2501,U_2500)),bot_bot_fun_nat_bool))))
      | U_2502 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2502))
      | ~ hBOOL(finite988810631ne_nat(U_2501,U_2500)) ),
    inference(definitional_conversion,[status(esa)],[f_868_4]) ).

cnf(f_868_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_f22106695ol_nat(U_2500,U_2502)),U_2502))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_2501,sK146(U_2502,U_2501,U_2500)),sK147(U_2502,U_2501,U_2500))),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK146(U_2502,U_2501,U_2500)),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK147(U_2502,U_2501,U_2500)),bot_bot_fun_nat_bool))))
    | U_2502 = bot_bot_fun_nat_bool
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2502))
    | ~ hBOOL(finite988810631ne_nat(U_2501,U_2500)) ),
    inference(clausify,[status(thm)],[f_868_5]) ).

fof(f_869_1,plain,
    ! [A,F,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(F_1,A)),A))
      | ? [X_2,Y_2] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(hAPP_p1170154830_pname(F,X_2),Y_2)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,Y_2),bot_bo844097828e_bool))))
          & is_pname(Y_2)
          & is_pname(X_2) )
      | A = bot_bo844097828e_bool
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
      | ~ hBOOL(finite1282449217_pname(F,F_1))
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_762_folding__one_Oclosed]) ).

fof(f_869_2,plain,
    ! [U_2507,U_2506,U_2505] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(U_2505,U_2507)),U_2507))
      | ? [U_2504,U_2503] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(hAPP_p1170154830_pname(U_2506,U_2504),U_2503)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2504),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2503),bot_bo844097828e_bool))))
          & is_pname(U_2503)
          & is_pname(U_2504) )
      | U_2507 = bot_bo844097828e_bool
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2507))
      | ~ hBOOL(finite1282449217_pname(U_2506,U_2505))
      | ~ is_fun_pname_bool(U_2507) ),
    inference(variable_rename,[status(thm)],[f_869_1]) ).

fof(f_869_3,plain,
    ! [U_2507] :
      ( ! [U_2506,U_2505] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(U_2505,U_2507)),U_2507))
          | ? [U_2504,U_2503] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(hAPP_p1170154830_pname(U_2506,U_2504),U_2503)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2504),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2503),bot_bo844097828e_bool))))
              & is_pname(U_2503)
              & is_pname(U_2504) )
          | U_2507 = bot_bo844097828e_bool
          | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2507))
          | ~ hBOOL(finite1282449217_pname(U_2506,U_2505)) )
      | ~ is_fun_pname_bool(U_2507) ),
    inference(miniscope,[status(thm)],[f_869_2]) ).

fof(f_869_4,plain,
    ! [U_2507] :
      ( ! [U_2506,U_2505] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(U_2505,U_2507)),U_2507))
          | ? [U_2503] :
              ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(hAPP_p1170154830_pname(U_2506,sK148(U_2507,U_2506,U_2505)),U_2503)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK148(U_2507,U_2506,U_2505)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2503),bot_bo844097828e_bool))))
              & is_pname(U_2503)
              & is_pname(sK148(U_2507,U_2506,U_2505)) )
          | U_2507 = bot_bo844097828e_bool
          | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2507))
          | ~ hBOOL(finite1282449217_pname(U_2506,U_2505)) )
      | ~ is_fun_pname_bool(U_2507) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(U_2504,sK148(U_2507,U_2506,U_2505))],[f_869_3]) ).

fof(f_869_5,plain,
    ! [U_2507] :
      ( ! [U_2506,U_2505] :
          ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(U_2505,U_2507)),U_2507))
          | ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(hAPP_p1170154830_pname(U_2506,sK148(U_2507,U_2506,U_2505)),sK149(U_2507,U_2506,U_2505))),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK148(U_2507,U_2506,U_2505)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK149(U_2507,U_2506,U_2505)),bot_bo844097828e_bool))))
            & is_pname(sK149(U_2507,U_2506,U_2505))
            & is_pname(sK148(U_2507,U_2506,U_2505)) )
          | U_2507 = bot_bo844097828e_bool
          | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2507))
          | ~ hBOOL(finite1282449217_pname(U_2506,U_2505)) )
      | ~ is_fun_pname_bool(U_2507) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK149]),skolemize(U_2503,sK149(U_2507,U_2506,U_2505))],[f_869_4]) ).

fof(f_869_6,plain,
    ( ! [U_2505,U_2506,U_2507] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(hAPP_p1170154830_pname(U_2506,sK148(U_2507,U_2506,U_2505)),sK149(U_2507,U_2506,U_2505))),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK148(U_2507,U_2506,U_2505)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK149(U_2507,U_2506,U_2505)),bot_bo844097828e_bool))))
        | ~ sP237(U_2505,U_2506,U_2507) )
    & ! [U_2505,U_2506,U_2507] :
        ( is_pname(sK149(U_2507,U_2506,U_2505))
        | ~ sP237(U_2505,U_2506,U_2507) )
    & ! [U_2505,U_2506,U_2507] :
        ( is_pname(sK148(U_2507,U_2506,U_2505))
        | ~ sP237(U_2505,U_2506,U_2507) )
    & ! [U_2505,U_2506,U_2507] :
        ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(U_2505,U_2507)),U_2507))
        | sP237(U_2505,U_2506,U_2507)
        | U_2507 = bot_bo844097828e_bool
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2507))
        | ~ hBOOL(finite1282449217_pname(U_2506,U_2505))
        | ~ is_fun_pname_bool(U_2507) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP237])],[f_869_5]) ).

cnf(f_869_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_f1297739591_pname(U_2505,U_2507)),U_2507))
    | sP237(U_2505,U_2506,U_2507)
    | U_2507 = bot_bo844097828e_bool
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2507))
    | ~ hBOOL(finite1282449217_pname(U_2506,U_2505))
    | ~ is_fun_pname_bool(U_2507) ),
    inference(clausify,[status(thm)],[f_869_6]) ).

cnf(f_869_8,plain,
    ( is_pname(sK148(U_2507,U_2506,U_2505))
    | ~ sP237(U_2505,U_2506,U_2507) ),
    inference(clausify,[status(thm)],[f_869_6]) ).

cnf(f_869_9,plain,
    ( is_pname(sK149(U_2507,U_2506,U_2505))
    | ~ sP237(U_2505,U_2506,U_2507) ),
    inference(clausify,[status(thm)],[f_869_6]) ).

cnf(f_869_10,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,hAPP_pname_pname(hAPP_p1170154830_pname(U_2506,sK148(U_2507,U_2506,U_2505)),sK149(U_2507,U_2506,U_2505))),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK148(U_2507,U_2506,U_2505)),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK149(U_2507,U_2506,U_2505)),bot_bo844097828e_bool))))
    | ~ sP237(U_2505,U_2506,U_2507) ),
    inference(clausify,[status(thm)],[f_869_6]) ).

fof(f_870_1,plain,
    ! [X_1,A] :
      ( hAPP_fun_a_bool_nat(finite_card_a,A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_763_card_Oremove]) ).

fof(f_870_2,plain,
    ! [U_2509,U_2508] :
      ( hAPP_fun_a_bool_nat(finite_card_a,U_2508) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2508),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2509),bot_bot_fun_a_bool))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2509),U_2508))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2508)) ),
    inference(variable_rename,[status(thm)],[f_870_1]) ).

fof(f_870_3,plain,
    ! [U_2509,U_2508] :
      ( hAPP_fun_a_bool_nat(finite_card_a,U_2508) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2508),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2509),bot_bot_fun_a_bool))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2509),U_2508))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2508)) ),
    inference(definitional_conversion,[status(esa)],[f_870_2]) ).

cnf(f_870_4,plain,
    ( hAPP_fun_a_bool_nat(finite_card_a,U_2508) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2508),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2509),bot_bot_fun_a_bool))))
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2509),U_2508))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2508)) ),
    inference(clausify,[status(thm)],[f_870_3]) ).

fof(f_871_1,plain,
    ! [X_1,A] :
      ( hAPP_f957591787ol_nat(finite_card_int,A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_1),A))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_764_card_Oremove]) ).

fof(f_871_2,plain,
    ! [U_2511,U_2510] :
      ( hAPP_f957591787ol_nat(finite_card_int,U_2510) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2510),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2511),bot_bot_fun_int_bool))))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2511),U_2510))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2510)) ),
    inference(variable_rename,[status(thm)],[f_871_1]) ).

fof(f_871_3,plain,
    ! [U_2510,U_2511] :
      ( hAPP_f957591787ol_nat(finite_card_int,U_2510) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2510),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2511),bot_bot_fun_int_bool))))
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2511),U_2510))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2510)) ),
    inference(definitional_conversion,[status(esa)],[f_871_2]) ).

cnf(f_871_4,plain,
    ( hAPP_f957591787ol_nat(finite_card_int,U_2510) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2510),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2511),bot_bot_fun_int_bool))))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2511),U_2510))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2510)) ),
    inference(clausify,[status(thm)],[f_871_3]) ).

fof(f_872_1,plain,
    ! [X_1,A] :
      ( hAPP_f22106695ol_nat(finite_card_nat,A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_765_card_Oremove]) ).

fof(f_872_2,plain,
    ! [U_2513,U_2512] :
      ( hAPP_f22106695ol_nat(finite_card_nat,U_2512) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2512),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2513),bot_bot_fun_nat_bool))))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2513),U_2512))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2512)) ),
    inference(variable_rename,[status(thm)],[f_872_1]) ).

fof(f_872_3,plain,
    ! [U_2512,U_2513] :
      ( hAPP_f22106695ol_nat(finite_card_nat,U_2512) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2512),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2513),bot_bot_fun_nat_bool))))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2513),U_2512))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2512)) ),
    inference(definitional_conversion,[status(esa)],[f_872_2]) ).

cnf(f_872_4,plain,
    ( hAPP_f22106695ol_nat(finite_card_nat,U_2512) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2512),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2513),bot_bot_fun_nat_bool))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2513),U_2512))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2512)) ),
    inference(clausify,[status(thm)],[f_872_3]) ).

fof(f_873_1,plain,
    ! [X_1,A] :
      ( hAPP_f921600141ol_nat(finite_card_pname,A) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_766_card_Oremove]) ).

fof(f_873_2,plain,
    ! [U_2515,U_2514] :
      ( hAPP_f921600141ol_nat(finite_card_pname,U_2514) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2514),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2515),bot_bo844097828e_bool))))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2515),U_2514))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2514)) ),
    inference(variable_rename,[status(thm)],[f_873_1]) ).

fof(f_873_3,plain,
    ! [U_2514,U_2515] :
      ( hAPP_f921600141ol_nat(finite_card_pname,U_2514) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2514),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2515),bot_bo844097828e_bool))))
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2515),U_2514))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2514)) ),
    inference(definitional_conversion,[status(esa)],[f_873_2]) ).

cnf(f_873_4,plain,
    ( hAPP_f921600141ol_nat(finite_card_pname,U_2514) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2514),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2515),bot_bo844097828e_bool))))
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2515),U_2514))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2514)) ),
    inference(clausify,[status(thm)],[f_873_3]) ).

fof(f_874_1,plain,
    ! [X_1,A] :
      ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,A),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),bot_bot_fun_a_bool))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ),
    inference(fof_nnf,[status(thm)],[fact_767_card_Oinsert__remove]) ).

fof(f_874_2,plain,
    ! [U_2517,U_2516] :
      ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2517),U_2516)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2516),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2517),bot_bot_fun_a_bool))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2516)) ),
    inference(variable_rename,[status(thm)],[f_874_1]) ).

fof(f_874_3,plain,
    ! [U_2516,U_2517] :
      ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2517),U_2516)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2516),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2517),bot_bot_fun_a_bool))))
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2516)) ),
    inference(definitional_conversion,[status(esa)],[f_874_2]) ).

cnf(f_874_4,plain,
    ( hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2517),U_2516)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_fun_a_bool_nat(finite_card_a,hAPP_f2050579477a_bool(hAPP_f1791771145a_bool(minus_1762468890a_bool,U_2516),hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2517),bot_bot_fun_a_bool))))
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2516)) ),
    inference(clausify,[status(thm)],[f_874_3]) ).

fof(f_875_1,plain,
    ! [X_1,A] :
      ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,A),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),bot_bot_fun_int_bool))))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A)) ),
    inference(fof_nnf,[status(thm)],[fact_768_card_Oinsert__remove]) ).

fof(f_875_2,plain,
    ! [U_2519,U_2518] :
      ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2519),U_2518)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2518),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2519),bot_bot_fun_int_bool))))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2518)) ),
    inference(variable_rename,[status(thm)],[f_875_1]) ).

fof(f_875_3,plain,
    ! [U_2518,U_2519] :
      ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2519),U_2518)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2518),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2519),bot_bot_fun_int_bool))))
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2518)) ),
    inference(definitional_conversion,[status(esa)],[f_875_2]) ).

cnf(f_875_4,plain,
    ( hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2519),U_2518)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f957591787ol_nat(finite_card_int,hAPP_f1805168059t_bool(hAPP_f1223193598t_bool(minus_1449998731t_bool,U_2518),hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2519),bot_bot_fun_int_bool))))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2518)) ),
    inference(clausify,[status(thm)],[f_875_3]) ).

fof(f_876_1,plain,
    ! [X_1,A] :
      ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,A),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),bot_bot_fun_nat_bool))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ),
    inference(fof_nnf,[status(thm)],[fact_769_card_Oinsert__remove]) ).

fof(f_876_2,plain,
    ! [U_2521,U_2520] :
      ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2521),U_2520)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2520),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2521),bot_bot_fun_nat_bool))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2520)) ),
    inference(variable_rename,[status(thm)],[f_876_1]) ).

fof(f_876_3,plain,
    ! [U_2520,U_2521] :
      ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2521),U_2520)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2520),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2521),bot_bot_fun_nat_bool))))
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2520)) ),
    inference(definitional_conversion,[status(esa)],[f_876_2]) ).

cnf(f_876_4,plain,
    ( hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2521),U_2520)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f22106695ol_nat(finite_card_nat,hAPP_f800510211t_bool(hAPP_f1730770594t_bool(minus_2067140911t_bool,U_2520),hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2521),bot_bot_fun_nat_bool))))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2520)) ),
    inference(clausify,[status(thm)],[f_876_3]) ).

fof(f_877_1,plain,
    ! [X_1,A] :
      ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,A),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),bot_bo844097828e_bool))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ),
    inference(fof_nnf,[status(thm)],[fact_770_card_Oinsert__remove]) ).

fof(f_877_2,plain,
    ! [U_2523,U_2522] :
      ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2523),U_2522)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2522),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2523),bot_bo844097828e_bool))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2522)) ),
    inference(variable_rename,[status(thm)],[f_877_1]) ).

fof(f_877_3,plain,
    ! [U_2522,U_2523] :
      ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2523),U_2522)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2522),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2523),bot_bo844097828e_bool))))
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2522)) ),
    inference(definitional_conversion,[status(esa)],[f_877_2]) ).

cnf(f_877_4,plain,
    ( hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2523),U_2522)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),hAPP_f921600141ol_nat(finite_card_pname,hAPP_f759274231e_bool(hAPP_f1388330588e_bool(minus_1015773161e_bool,U_2522),hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2523),bot_bo844097828e_bool))))
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2522)) ),
    inference(clausify,[status(thm)],[f_877_3]) ).

fof(f_878_1,plain,
    ! [B,A,F,F_1] :
      ( hAPP_int_int(hAPP_int_fun_int_int(F,hAPP_f1594865479ol_int(F_1,B)),hAPP_f1594865479ol_int(F_1,A)) = hAPP_f1594865479ol_int(F_1,A)
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,B),A))
      | B = bot_bot_fun_int_bool
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
      | ~ hBOOL(finite1432773856em_int(F,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_771_folding__one__idem_Osubset__idem]) ).

fof(f_878_2,plain,
    ! [U_2527,U_2526,U_2525,U_2524] :
      ( hAPP_int_int(hAPP_int_fun_int_int(U_2525,hAPP_f1594865479ol_int(U_2524,U_2527)),hAPP_f1594865479ol_int(U_2524,U_2526)) = hAPP_f1594865479ol_int(U_2524,U_2526)
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2527),U_2526))
      | U_2527 = bot_bot_fun_int_bool
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2526))
      | ~ hBOOL(finite1432773856em_int(U_2525,U_2524)) ),
    inference(variable_rename,[status(thm)],[f_878_1]) ).

fof(f_878_3,plain,
    ! [U_2524,U_2525,U_2526,U_2527] :
      ( hAPP_int_int(hAPP_int_fun_int_int(U_2525,hAPP_f1594865479ol_int(U_2524,U_2527)),hAPP_f1594865479ol_int(U_2524,U_2526)) = hAPP_f1594865479ol_int(U_2524,U_2526)
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2527),U_2526))
      | U_2527 = bot_bot_fun_int_bool
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2526))
      | ~ hBOOL(finite1432773856em_int(U_2525,U_2524)) ),
    inference(definitional_conversion,[status(esa)],[f_878_2]) ).

cnf(f_878_4,plain,
    ( hAPP_int_int(hAPP_int_fun_int_int(U_2525,hAPP_f1594865479ol_int(U_2524,U_2527)),hAPP_f1594865479ol_int(U_2524,U_2526)) = hAPP_f1594865479ol_int(U_2524,U_2526)
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,U_2527),U_2526))
    | U_2527 = bot_bot_fun_int_bool
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2526))
    | ~ hBOOL(finite1432773856em_int(U_2525,U_2524)) ),
    inference(clausify,[status(thm)],[f_878_3]) ).

fof(f_879_1,plain,
    ! [B,A,F,F_1] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,hAPP_f22106695ol_nat(F_1,B)),hAPP_f22106695ol_nat(F_1,A)) = hAPP_f22106695ol_nat(F_1,A)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))
      | B = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
      | ~ hBOOL(finite795500164em_nat(F,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_772_folding__one__idem_Osubset__idem]) ).

fof(f_879_2,plain,
    ! [U_2531,U_2530,U_2529,U_2528] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_2529,hAPP_f22106695ol_nat(U_2528,U_2531)),hAPP_f22106695ol_nat(U_2528,U_2530)) = hAPP_f22106695ol_nat(U_2528,U_2530)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2531),U_2530))
      | U_2531 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2530))
      | ~ hBOOL(finite795500164em_nat(U_2529,U_2528)) ),
    inference(variable_rename,[status(thm)],[f_879_1]) ).

fof(f_879_3,plain,
    ! [U_2529,U_2531,U_2530,U_2528] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_2529,hAPP_f22106695ol_nat(U_2528,U_2531)),hAPP_f22106695ol_nat(U_2528,U_2530)) = hAPP_f22106695ol_nat(U_2528,U_2530)
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2531),U_2530))
      | U_2531 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2530))
      | ~ hBOOL(finite795500164em_nat(U_2529,U_2528)) ),
    inference(definitional_conversion,[status(esa)],[f_879_2]) ).

cnf(f_879_4,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_2529,hAPP_f22106695ol_nat(U_2528,U_2531)),hAPP_f22106695ol_nat(U_2528,U_2530)) = hAPP_f22106695ol_nat(U_2528,U_2530)
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_2531),U_2530))
    | U_2531 = bot_bot_fun_nat_bool
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2530))
    | ~ hBOOL(finite795500164em_nat(U_2529,U_2528)) ),
    inference(clausify,[status(thm)],[f_879_3]) ).

fof(f_880_1,plain,
    ! [B,A,F,F_1] :
      ( hAPP_pname_pname(hAPP_p1170154830_pname(F,hAPP_f1297739591_pname(F_1,B)),hAPP_f1297739591_pname(F_1,A)) = hAPP_f1297739591_pname(F_1,A)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
      | B = bot_bo844097828e_bool
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
      | ~ hBOOL(finite89670078_pname(F,F_1))
      | ~ is_fun_pname_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_773_folding__one__idem_Osubset__idem]) ).

fof(f_880_2,plain,
    ! [U_2535,U_2534,U_2533,U_2532] :
      ( hAPP_pname_pname(hAPP_p1170154830_pname(U_2533,hAPP_f1297739591_pname(U_2532,U_2535)),hAPP_f1297739591_pname(U_2532,U_2534)) = hAPP_f1297739591_pname(U_2532,U_2534)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_2535),U_2534))
      | U_2535 = bot_bo844097828e_bool
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2534))
      | ~ hBOOL(finite89670078_pname(U_2533,U_2532))
      | ~ is_fun_pname_bool(U_2535) ),
    inference(variable_rename,[status(thm)],[f_880_1]) ).

fof(f_880_3,plain,
    ! [U_2535] :
      ( ! [U_2534,U_2533,U_2532] :
          ( hAPP_pname_pname(hAPP_p1170154830_pname(U_2533,hAPP_f1297739591_pname(U_2532,U_2535)),hAPP_f1297739591_pname(U_2532,U_2534)) = hAPP_f1297739591_pname(U_2532,U_2534)
          | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_2535),U_2534))
          | U_2535 = bot_bo844097828e_bool
          | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2534))
          | ~ hBOOL(finite89670078_pname(U_2533,U_2532)) )
      | ~ is_fun_pname_bool(U_2535) ),
    inference(miniscope,[status(thm)],[f_880_2]) ).

fof(f_880_4,plain,
    ! [U_2534,U_2535,U_2532,U_2533] :
      ( hAPP_pname_pname(hAPP_p1170154830_pname(U_2533,hAPP_f1297739591_pname(U_2532,U_2535)),hAPP_f1297739591_pname(U_2532,U_2534)) = hAPP_f1297739591_pname(U_2532,U_2534)
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_2535),U_2534))
      | U_2535 = bot_bo844097828e_bool
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2534))
      | ~ hBOOL(finite89670078_pname(U_2533,U_2532))
      | ~ is_fun_pname_bool(U_2535) ),
    inference(definitional_conversion,[status(esa)],[f_880_3]) ).

cnf(f_880_5,plain,
    ( hAPP_pname_pname(hAPP_p1170154830_pname(U_2533,hAPP_f1297739591_pname(U_2532,U_2535)),hAPP_f1297739591_pname(U_2532,U_2534)) = hAPP_f1297739591_pname(U_2532,U_2534)
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,U_2535),U_2534))
    | U_2535 = bot_bo844097828e_bool
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2534))
    | ~ hBOOL(finite89670078_pname(U_2533,U_2532))
    | ~ is_fun_pname_bool(U_2535) ),
    inference(clausify,[status(thm)],[f_880_4]) ).

fof(f_881_1,plain,
    ! [B,A,F,F_1] :
      ( hAPP_a_a(hAPP_a_fun_a_a(F,hAPP_fun_a_bool_a(F_1,B)),hAPP_fun_a_bool_a(F_1,A)) = hAPP_fun_a_bool_a(F_1,A)
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A))
      | B = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
      | ~ hBOOL(finite1819937229idem_a(F,F_1))
      | ~ is_fun_a_bool(B) ),
    inference(fof_nnf,[status(thm)],[fact_774_folding__one__idem_Osubset__idem]) ).

fof(f_881_2,plain,
    ! [U_2539,U_2538,U_2537,U_2536] :
      ( hAPP_a_a(hAPP_a_fun_a_a(U_2537,hAPP_fun_a_bool_a(U_2536,U_2539)),hAPP_fun_a_bool_a(U_2536,U_2538)) = hAPP_fun_a_bool_a(U_2536,U_2538)
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2539),U_2538))
      | U_2539 = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2538))
      | ~ hBOOL(finite1819937229idem_a(U_2537,U_2536))
      | ~ is_fun_a_bool(U_2539) ),
    inference(variable_rename,[status(thm)],[f_881_1]) ).

fof(f_881_3,plain,
    ! [U_2539] :
      ( ! [U_2538,U_2537,U_2536] :
          ( hAPP_a_a(hAPP_a_fun_a_a(U_2537,hAPP_fun_a_bool_a(U_2536,U_2539)),hAPP_fun_a_bool_a(U_2536,U_2538)) = hAPP_fun_a_bool_a(U_2536,U_2538)
          | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2539),U_2538))
          | U_2539 = bot_bot_fun_a_bool
          | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2538))
          | ~ hBOOL(finite1819937229idem_a(U_2537,U_2536)) )
      | ~ is_fun_a_bool(U_2539) ),
    inference(miniscope,[status(thm)],[f_881_2]) ).

fof(f_881_4,plain,
    ! [U_2539,U_2538,U_2537,U_2536] :
      ( hAPP_a_a(hAPP_a_fun_a_a(U_2537,hAPP_fun_a_bool_a(U_2536,U_2539)),hAPP_fun_a_bool_a(U_2536,U_2538)) = hAPP_fun_a_bool_a(U_2536,U_2538)
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2539),U_2538))
      | U_2539 = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2538))
      | ~ hBOOL(finite1819937229idem_a(U_2537,U_2536))
      | ~ is_fun_a_bool(U_2539) ),
    inference(definitional_conversion,[status(esa)],[f_881_3]) ).

cnf(f_881_5,plain,
    ( hAPP_a_a(hAPP_a_fun_a_a(U_2537,hAPP_fun_a_bool_a(U_2536,U_2539)),hAPP_fun_a_bool_a(U_2536,U_2538)) = hAPP_fun_a_bool_a(U_2536,U_2538)
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,U_2539),U_2538))
    | U_2539 = bot_bot_fun_a_bool
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2538))
    | ~ hBOOL(finite1819937229idem_a(U_2537,U_2536))
    | ~ is_fun_a_bool(U_2539) ),
    inference(clausify,[status(thm)],[f_881_4]) ).

fof(f_882_1,plain,
    ! [X_1,A,F,F_1] :
      ( hAPP_fun_a_bool_a(F_1,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_1),A)) = hAPP_a_a(hAPP_a_fun_a_a(F,X_1),hAPP_fun_a_bool_a(F_1,A))
      | A = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
      | ~ hBOOL(finite1819937229idem_a(F,F_1))
      | ~ is_fun_a_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_775_folding__one__idem_Oinsert__idem]) ).

fof(f_882_2,plain,
    ! [U_2543,U_2542,U_2541,U_2540] :
      ( hAPP_fun_a_bool_a(U_2540,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2543),U_2542)) = hAPP_a_a(hAPP_a_fun_a_a(U_2541,U_2543),hAPP_fun_a_bool_a(U_2540,U_2542))
      | U_2542 = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2542))
      | ~ hBOOL(finite1819937229idem_a(U_2541,U_2540))
      | ~ is_fun_a_bool(U_2542) ),
    inference(variable_rename,[status(thm)],[f_882_1]) ).

fof(f_882_3,plain,
    ! [U_2543,U_2542] :
      ( ! [U_2541,U_2540] :
          ( hAPP_fun_a_bool_a(U_2540,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2543),U_2542)) = hAPP_a_a(hAPP_a_fun_a_a(U_2541,U_2543),hAPP_fun_a_bool_a(U_2540,U_2542))
          | U_2542 = bot_bot_fun_a_bool
          | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2542))
          | ~ hBOOL(finite1819937229idem_a(U_2541,U_2540)) )
      | ~ is_fun_a_bool(U_2542) ),
    inference(miniscope,[status(thm)],[f_882_2]) ).

fof(f_882_4,plain,
    ! [U_2542,U_2543,U_2540,U_2541] :
      ( hAPP_fun_a_bool_a(U_2540,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2543),U_2542)) = hAPP_a_a(hAPP_a_fun_a_a(U_2541,U_2543),hAPP_fun_a_bool_a(U_2540,U_2542))
      | U_2542 = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2542))
      | ~ hBOOL(finite1819937229idem_a(U_2541,U_2540))
      | ~ is_fun_a_bool(U_2542) ),
    inference(definitional_conversion,[status(esa)],[f_882_3]) ).

cnf(f_882_5,plain,
    ( hAPP_fun_a_bool_a(U_2540,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2543),U_2542)) = hAPP_a_a(hAPP_a_fun_a_a(U_2541,U_2543),hAPP_fun_a_bool_a(U_2540,U_2542))
    | U_2542 = bot_bot_fun_a_bool
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2542))
    | ~ hBOOL(finite1819937229idem_a(U_2541,U_2540))
    | ~ is_fun_a_bool(U_2542) ),
    inference(clausify,[status(thm)],[f_882_4]) ).

fof(f_883_1,plain,
    ! [X_1,A,F,F_1] :
      ( hAPP_f1594865479ol_int(F_1,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_1),A)) = hAPP_int_int(hAPP_int_fun_int_int(F,X_1),hAPP_f1594865479ol_int(F_1,A))
      | A = bot_bot_fun_int_bool
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,A))
      | ~ hBOOL(finite1432773856em_int(F,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_776_folding__one__idem_Oinsert__idem]) ).

fof(f_883_2,plain,
    ! [U_2547,U_2546,U_2545,U_2544] :
      ( hAPP_f1594865479ol_int(U_2544,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2547),U_2546)) = hAPP_int_int(hAPP_int_fun_int_int(U_2545,U_2547),hAPP_f1594865479ol_int(U_2544,U_2546))
      | U_2546 = bot_bot_fun_int_bool
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2546))
      | ~ hBOOL(finite1432773856em_int(U_2545,U_2544)) ),
    inference(variable_rename,[status(thm)],[f_883_1]) ).

fof(f_883_3,plain,
    ! [U_2545,U_2546,U_2544,U_2547] :
      ( hAPP_f1594865479ol_int(U_2544,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2547),U_2546)) = hAPP_int_int(hAPP_int_fun_int_int(U_2545,U_2547),hAPP_f1594865479ol_int(U_2544,U_2546))
      | U_2546 = bot_bot_fun_int_bool
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2546))
      | ~ hBOOL(finite1432773856em_int(U_2545,U_2544)) ),
    inference(definitional_conversion,[status(esa)],[f_883_2]) ).

cnf(f_883_4,plain,
    ( hAPP_f1594865479ol_int(U_2544,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2547),U_2546)) = hAPP_int_int(hAPP_int_fun_int_int(U_2545,U_2547),hAPP_f1594865479ol_int(U_2544,U_2546))
    | U_2546 = bot_bot_fun_int_bool
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2546))
    | ~ hBOOL(finite1432773856em_int(U_2545,U_2544)) ),
    inference(clausify,[status(thm)],[f_883_3]) ).

fof(f_884_1,plain,
    ! [X_1,A,F,F_1] :
      ( hAPP_f22106695ol_nat(F_1,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_1),A)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(F,X_1),hAPP_f22106695ol_nat(F_1,A))
      | A = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
      | ~ hBOOL(finite795500164em_nat(F,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_777_folding__one__idem_Oinsert__idem]) ).

fof(f_884_2,plain,
    ! [U_2551,U_2550,U_2549,U_2548] :
      ( hAPP_f22106695ol_nat(U_2548,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2551),U_2550)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_2549,U_2551),hAPP_f22106695ol_nat(U_2548,U_2550))
      | U_2550 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2550))
      | ~ hBOOL(finite795500164em_nat(U_2549,U_2548)) ),
    inference(variable_rename,[status(thm)],[f_884_1]) ).

fof(f_884_3,plain,
    ! [U_2549,U_2548,U_2550,U_2551] :
      ( hAPP_f22106695ol_nat(U_2548,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2551),U_2550)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_2549,U_2551),hAPP_f22106695ol_nat(U_2548,U_2550))
      | U_2550 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2550))
      | ~ hBOOL(finite795500164em_nat(U_2549,U_2548)) ),
    inference(definitional_conversion,[status(esa)],[f_884_2]) ).

cnf(f_884_4,plain,
    ( hAPP_f22106695ol_nat(U_2548,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2551),U_2550)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(U_2549,U_2551),hAPP_f22106695ol_nat(U_2548,U_2550))
    | U_2550 = bot_bot_fun_nat_bool
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2550))
    | ~ hBOOL(finite795500164em_nat(U_2549,U_2548)) ),
    inference(clausify,[status(thm)],[f_884_3]) ).

fof(f_885_1,plain,
    ! [X_1,A,F,F_1] :
      ( hAPP_f1297739591_pname(F_1,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_1),A)) = hAPP_pname_pname(hAPP_p1170154830_pname(F,X_1),hAPP_f1297739591_pname(F_1,A))
      | A = bot_bo844097828e_bool
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
      | ~ hBOOL(finite89670078_pname(F,F_1))
      | ~ is_fun_pname_bool(A) ),
    inference(fof_nnf,[status(thm)],[fact_778_folding__one__idem_Oinsert__idem]) ).

fof(f_885_2,plain,
    ! [U_2555,U_2554,U_2553,U_2552] :
      ( hAPP_f1297739591_pname(U_2552,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2555),U_2554)) = hAPP_pname_pname(hAPP_p1170154830_pname(U_2553,U_2555),hAPP_f1297739591_pname(U_2552,U_2554))
      | U_2554 = bot_bo844097828e_bool
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2554))
      | ~ hBOOL(finite89670078_pname(U_2553,U_2552))
      | ~ is_fun_pname_bool(U_2554) ),
    inference(variable_rename,[status(thm)],[f_885_1]) ).

fof(f_885_3,plain,
    ! [U_2555,U_2554] :
      ( ! [U_2553,U_2552] :
          ( hAPP_f1297739591_pname(U_2552,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2555),U_2554)) = hAPP_pname_pname(hAPP_p1170154830_pname(U_2553,U_2555),hAPP_f1297739591_pname(U_2552,U_2554))
          | U_2554 = bot_bo844097828e_bool
          | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2554))
          | ~ hBOOL(finite89670078_pname(U_2553,U_2552)) )
      | ~ is_fun_pname_bool(U_2554) ),
    inference(miniscope,[status(thm)],[f_885_2]) ).

fof(f_885_4,plain,
    ! [U_2553,U_2554,U_2552,U_2555] :
      ( hAPP_f1297739591_pname(U_2552,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2555),U_2554)) = hAPP_pname_pname(hAPP_p1170154830_pname(U_2553,U_2555),hAPP_f1297739591_pname(U_2552,U_2554))
      | U_2554 = bot_bo844097828e_bool
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2554))
      | ~ hBOOL(finite89670078_pname(U_2553,U_2552))
      | ~ is_fun_pname_bool(U_2554) ),
    inference(definitional_conversion,[status(esa)],[f_885_3]) ).

cnf(f_885_5,plain,
    ( hAPP_f1297739591_pname(U_2552,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2555),U_2554)) = hAPP_pname_pname(hAPP_p1170154830_pname(U_2553,U_2555),hAPP_f1297739591_pname(U_2552,U_2554))
    | U_2554 = bot_bo844097828e_bool
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2554))
    | ~ hBOOL(finite89670078_pname(U_2553,U_2552))
    | ~ is_fun_pname_bool(U_2554) ),
    inference(clausify,[status(thm)],[f_885_4]) ).

fof(f_886_1,plain,
    ! [Pa,F_1] :
      ( hBOOL(hAPP_fun_a_bool_bool(Pa,F_1))
      | ? [X_2,F_2] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(Pa,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_2),F_2)))
          & hBOOL(hAPP_fun_a_bool_bool(Pa,F_2))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),F_2))
          & F_2 != bot_bot_fun_a_bool
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_2))
          & is_fun_a_bool(F_2)
          & is_a(X_2) )
      | ? [X_2] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(Pa,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,X_2),bot_bot_fun_a_bool)))
          & is_a(X_2) )
      | F_1 = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1))
      | ~ is_fun_a_bool(F_1) ),
    inference(fof_nnf,[status(thm)],[fact_779_finite__ne__induct]) ).

fof(f_886_2,plain,
    ! [U_2560,U_2559] :
      ( hBOOL(hAPP_fun_a_bool_bool(U_2560,U_2559))
      | ? [U_2558,U_2557] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2560,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2558),U_2557)))
          & hBOOL(hAPP_fun_a_bool_bool(U_2560,U_2557))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2558),U_2557))
          & U_2557 != bot_bot_fun_a_bool
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2557))
          & is_fun_a_bool(U_2557)
          & is_a(U_2558) )
      | ? [U_2556] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2560,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2556),bot_bot_fun_a_bool)))
          & is_a(U_2556) )
      | U_2559 = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2559))
      | ~ is_fun_a_bool(U_2559) ),
    inference(variable_rename,[status(thm)],[f_886_1]) ).

fof(f_886_3,plain,
    ! [U_2560,U_2559] :
      ( hBOOL(hAPP_fun_a_bool_bool(U_2560,U_2559))
      | ? [U_2558,U_2557] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2560,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,U_2558),U_2557)))
          & hBOOL(hAPP_fun_a_bool_bool(U_2560,U_2557))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,U_2558),U_2557))
          & U_2557 != bot_bot_fun_a_bool
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2557))
          & is_fun_a_bool(U_2557)
          & is_a(U_2558) )
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2560,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK150(U_2560,U_2559)),bot_bot_fun_a_bool)))
        & is_a(sK150(U_2560,U_2559)) )
      | U_2559 = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2559))
      | ~ is_fun_a_bool(U_2559) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK150]),skolemize(U_2556,sK150(U_2560,U_2559))],[f_886_2]) ).

fof(f_886_4,plain,
    ! [U_2560,U_2559] :
      ( hBOOL(hAPP_fun_a_bool_bool(U_2560,U_2559))
      | ? [U_2557] :
          ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2560,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK151(U_2560,U_2559)),U_2557)))
          & hBOOL(hAPP_fun_a_bool_bool(U_2560,U_2557))
          & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK151(U_2560,U_2559)),U_2557))
          & U_2557 != bot_bot_fun_a_bool
          & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2557))
          & is_fun_a_bool(U_2557)
          & is_a(sK151(U_2560,U_2559)) )
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2560,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK150(U_2560,U_2559)),bot_bot_fun_a_bool)))
        & is_a(sK150(U_2560,U_2559)) )
      | U_2559 = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2559))
      | ~ is_fun_a_bool(U_2559) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK151]),skolemize(U_2558,sK151(U_2560,U_2559))],[f_886_3]) ).

fof(f_886_5,plain,
    ! [U_2560,U_2559] :
      ( hBOOL(hAPP_fun_a_bool_bool(U_2560,U_2559))
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2560,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK151(U_2560,U_2559)),sK152(U_2560,U_2559))))
        & hBOOL(hAPP_fun_a_bool_bool(U_2560,sK152(U_2560,U_2559)))
        & ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK151(U_2560,U_2559)),sK152(U_2560,U_2559)))
        & sK152(U_2560,U_2559) != bot_bot_fun_a_bool
        & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK152(U_2560,U_2559)))
        & is_fun_a_bool(sK152(U_2560,U_2559))
        & is_a(sK151(U_2560,U_2559)) )
      | ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2560,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK150(U_2560,U_2559)),bot_bot_fun_a_bool)))
        & is_a(sK150(U_2560,U_2559)) )
      | U_2559 = bot_bot_fun_a_bool
      | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2559))
      | ~ is_fun_a_bool(U_2559) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK152]),skolemize(U_2557,sK152(U_2560,U_2559))],[f_886_4]) ).

fof(f_886_6,plain,
    ( ! [U_2560,U_2559] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2560,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK151(U_2560,U_2559)),sK152(U_2560,U_2559))))
        | ~ sP239(U_2560,U_2559) )
    & ! [U_2560,U_2559] :
        ( hBOOL(hAPP_fun_a_bool_bool(U_2560,sK152(U_2560,U_2559)))
        | ~ sP239(U_2560,U_2559) )
    & ! [U_2560,U_2559] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK151(U_2560,U_2559)),sK152(U_2560,U_2559)))
        | ~ sP239(U_2560,U_2559) )
    & ! [U_2560,U_2559] :
        ( sK152(U_2560,U_2559) != bot_bot_fun_a_bool
        | ~ sP239(U_2560,U_2559) )
    & ! [U_2560,U_2559] :
        ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK152(U_2560,U_2559)))
        | ~ sP239(U_2560,U_2559) )
    & ! [U_2560,U_2559] :
        ( is_fun_a_bool(sK152(U_2560,U_2559))
        | ~ sP239(U_2560,U_2559) )
    & ! [U_2560,U_2559] :
        ( is_a(sK151(U_2560,U_2559))
        | ~ sP239(U_2560,U_2559) )
    & ! [U_2560,U_2559] :
        ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2560,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK150(U_2560,U_2559)),bot_bot_fun_a_bool)))
        | ~ sP238(U_2560,U_2559) )
    & ! [U_2560,U_2559] :
        ( is_a(sK150(U_2560,U_2559))
        | ~ sP238(U_2560,U_2559) )
    & ! [U_2560,U_2559] :
        ( hBOOL(hAPP_fun_a_bool_bool(U_2560,U_2559))
        | sP239(U_2560,U_2559)
        | sP238(U_2560,U_2559)
        | U_2559 = bot_bot_fun_a_bool
        | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2559))
        | ~ is_fun_a_bool(U_2559) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP238,sP239])],[f_886_5]) ).

cnf(f_886_7,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(U_2560,U_2559))
    | sP239(U_2560,U_2559)
    | sP238(U_2560,U_2559)
    | U_2559 = bot_bot_fun_a_bool
    | ~ hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,U_2559))
    | ~ is_fun_a_bool(U_2559) ),
    inference(clausify,[status(thm)],[f_886_6]) ).

cnf(f_886_8,plain,
    ( is_a(sK150(U_2560,U_2559))
    | ~ sP238(U_2560,U_2559) ),
    inference(clausify,[status(thm)],[f_886_6]) ).

cnf(f_886_9,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2560,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK150(U_2560,U_2559)),bot_bot_fun_a_bool)))
    | ~ sP238(U_2560,U_2559) ),
    inference(clausify,[status(thm)],[f_886_6]) ).

cnf(f_886_10,plain,
    ( is_a(sK151(U_2560,U_2559))
    | ~ sP239(U_2560,U_2559) ),
    inference(clausify,[status(thm)],[f_886_6]) ).

cnf(f_886_11,plain,
    ( is_fun_a_bool(sK152(U_2560,U_2559))
    | ~ sP239(U_2560,U_2559) ),
    inference(clausify,[status(thm)],[f_886_6]) ).

cnf(f_886_12,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,sK152(U_2560,U_2559)))
    | ~ sP239(U_2560,U_2559) ),
    inference(clausify,[status(thm)],[f_886_6]) ).

cnf(f_886_13,plain,
    ( sK152(U_2560,U_2559) != bot_bot_fun_a_bool
    | ~ sP239(U_2560,U_2559) ),
    inference(clausify,[status(thm)],[f_886_6]) ).

cnf(f_886_14,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,sK151(U_2560,U_2559)),sK152(U_2560,U_2559)))
    | ~ sP239(U_2560,U_2559) ),
    inference(clausify,[status(thm)],[f_886_6]) ).

cnf(f_886_15,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(U_2560,sK152(U_2560,U_2559)))
    | ~ sP239(U_2560,U_2559) ),
    inference(clausify,[status(thm)],[f_886_6]) ).

cnf(f_886_16,plain,
    ( ~ hBOOL(hAPP_fun_a_bool_bool(U_2560,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,sK151(U_2560,U_2559)),sK152(U_2560,U_2559))))
    | ~ sP239(U_2560,U_2559) ),
    inference(clausify,[status(thm)],[f_886_6]) ).

fof(f_887_1,plain,
    ! [Pa,F_1] :
      ( hBOOL(hAPP_f448129468l_bool(Pa,F_1))
      | ? [X_2,F_2] :
          ( ~ hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),F_2)))
          & hBOOL(hAPP_f448129468l_bool(Pa,F_2))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,X_2),F_2))
          & F_2 != bot_bot_fun_int_bool
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_2)) )
      | ? [X_2] : ~ hBOOL(hAPP_f448129468l_bool(Pa,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,X_2),bot_bot_fun_int_bool)))
      | F_1 = bot_bot_fun_int_bool
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_780_finite__ne__induct]) ).

fof(f_887_2,plain,
    ! [U_2565,U_2564] :
      ( hBOOL(hAPP_f448129468l_bool(U_2565,U_2564))
      | ? [U_2563,U_2562] :
          ( ~ hBOOL(hAPP_f448129468l_bool(U_2565,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2563),U_2562)))
          & hBOOL(hAPP_f448129468l_bool(U_2565,U_2562))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2563),U_2562))
          & U_2562 != bot_bot_fun_int_bool
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2562)) )
      | ? [U_2561] : ~ hBOOL(hAPP_f448129468l_bool(U_2565,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2561),bot_bot_fun_int_bool)))
      | U_2564 = bot_bot_fun_int_bool
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2564)) ),
    inference(variable_rename,[status(thm)],[f_887_1]) ).

fof(f_887_3,plain,
    ! [U_2565,U_2564] :
      ( hBOOL(hAPP_f448129468l_bool(U_2565,U_2564))
      | ? [U_2563,U_2562] :
          ( ~ hBOOL(hAPP_f448129468l_bool(U_2565,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,U_2563),U_2562)))
          & hBOOL(hAPP_f448129468l_bool(U_2565,U_2562))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,U_2563),U_2562))
          & U_2562 != bot_bot_fun_int_bool
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2562)) )
      | ~ hBOOL(hAPP_f448129468l_bool(U_2565,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK153(U_2565,U_2564)),bot_bot_fun_int_bool)))
      | U_2564 = bot_bot_fun_int_bool
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2564)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK153]),skolemize(U_2561,sK153(U_2565,U_2564))],[f_887_2]) ).

fof(f_887_4,plain,
    ! [U_2565,U_2564] :
      ( hBOOL(hAPP_f448129468l_bool(U_2565,U_2564))
      | ? [U_2562] :
          ( ~ hBOOL(hAPP_f448129468l_bool(U_2565,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK154(U_2565,U_2564)),U_2562)))
          & hBOOL(hAPP_f448129468l_bool(U_2565,U_2562))
          & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK154(U_2565,U_2564)),U_2562))
          & U_2562 != bot_bot_fun_int_bool
          & hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2562)) )
      | ~ hBOOL(hAPP_f448129468l_bool(U_2565,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK153(U_2565,U_2564)),bot_bot_fun_int_bool)))
      | U_2564 = bot_bot_fun_int_bool
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2564)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK154]),skolemize(U_2563,sK154(U_2565,U_2564))],[f_887_3]) ).

fof(f_887_5,plain,
    ! [U_2565,U_2564] :
      ( hBOOL(hAPP_f448129468l_bool(U_2565,U_2564))
      | ( ~ hBOOL(hAPP_f448129468l_bool(U_2565,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK154(U_2565,U_2564)),sK155(U_2565,U_2564))))
        & hBOOL(hAPP_f448129468l_bool(U_2565,sK155(U_2565,U_2564)))
        & ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK154(U_2565,U_2564)),sK155(U_2565,U_2564)))
        & sK155(U_2565,U_2564) != bot_bot_fun_int_bool
        & hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK155(U_2565,U_2564))) )
      | ~ hBOOL(hAPP_f448129468l_bool(U_2565,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK153(U_2565,U_2564)),bot_bot_fun_int_bool)))
      | U_2564 = bot_bot_fun_int_bool
      | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2564)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK155]),skolemize(U_2562,sK155(U_2565,U_2564))],[f_887_4]) ).

fof(f_887_6,plain,
    ( ! [U_2565,U_2564] :
        ( ~ hBOOL(hAPP_f448129468l_bool(U_2565,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK154(U_2565,U_2564)),sK155(U_2565,U_2564))))
        | ~ sP240(U_2565,U_2564) )
    & ! [U_2565,U_2564] :
        ( hBOOL(hAPP_f448129468l_bool(U_2565,sK155(U_2565,U_2564)))
        | ~ sP240(U_2565,U_2564) )
    & ! [U_2565,U_2564] :
        ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK154(U_2565,U_2564)),sK155(U_2565,U_2564)))
        | ~ sP240(U_2565,U_2564) )
    & ! [U_2565,U_2564] :
        ( sK155(U_2565,U_2564) != bot_bot_fun_int_bool
        | ~ sP240(U_2565,U_2564) )
    & ! [U_2565,U_2564] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK155(U_2565,U_2564)))
        | ~ sP240(U_2565,U_2564) )
    & ! [U_2565,U_2564] :
        ( hBOOL(hAPP_f448129468l_bool(U_2565,U_2564))
        | sP240(U_2565,U_2564)
        | ~ hBOOL(hAPP_f448129468l_bool(U_2565,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK153(U_2565,U_2564)),bot_bot_fun_int_bool)))
        | U_2564 = bot_bot_fun_int_bool
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2564)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP240])],[f_887_5]) ).

cnf(f_887_7,plain,
    ( hBOOL(hAPP_f448129468l_bool(U_2565,U_2564))
    | sP240(U_2565,U_2564)
    | ~ hBOOL(hAPP_f448129468l_bool(U_2565,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK153(U_2565,U_2564)),bot_bot_fun_int_bool)))
    | U_2564 = bot_bot_fun_int_bool
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,U_2564)) ),
    inference(clausify,[status(thm)],[f_887_6]) ).

cnf(f_887_8,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,sK155(U_2565,U_2564)))
    | ~ sP240(U_2565,U_2564) ),
    inference(clausify,[status(thm)],[f_887_6]) ).

cnf(f_887_9,plain,
    ( sK155(U_2565,U_2564) != bot_bot_fun_int_bool
    | ~ sP240(U_2565,U_2564) ),
    inference(clausify,[status(thm)],[f_887_6]) ).

cnf(f_887_10,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,sK154(U_2565,U_2564)),sK155(U_2565,U_2564)))
    | ~ sP240(U_2565,U_2564) ),
    inference(clausify,[status(thm)],[f_887_6]) ).

cnf(f_887_11,plain,
    ( hBOOL(hAPP_f448129468l_bool(U_2565,sK155(U_2565,U_2564)))
    | ~ sP240(U_2565,U_2564) ),
    inference(clausify,[status(thm)],[f_887_6]) ).

cnf(f_887_12,plain,
    ( ~ hBOOL(hAPP_f448129468l_bool(U_2565,hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(insert_int,sK154(U_2565,U_2564)),sK155(U_2565,U_2564))))
    | ~ sP240(U_2565,U_2564) ),
    inference(clausify,[status(thm)],[f_887_6]) ).

fof(f_888_1,plain,
    ! [Pa,F_1] :
      ( hBOOL(hAPP_f54304608l_bool(Pa,F_1))
      | ? [X_2,F_2] :
          ( ~ hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),F_2)))
          & hBOOL(hAPP_f54304608l_bool(Pa,F_2))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),F_2))
          & F_2 != bot_bot_fun_nat_bool
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_2)) )
      | ? [X_2] : ~ hBOOL(hAPP_f54304608l_bool(Pa,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,X_2),bot_bot_fun_nat_bool)))
      | F_1 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1)) ),
    inference(fof_nnf,[status(thm)],[fact_781_finite__ne__induct]) ).

fof(f_888_2,plain,
    ! [U_2570,U_2569] :
      ( hBOOL(hAPP_f54304608l_bool(U_2570,U_2569))
      | ? [U_2568,U_2567] :
          ( ~ hBOOL(hAPP_f54304608l_bool(U_2570,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2568),U_2567)))
          & hBOOL(hAPP_f54304608l_bool(U_2570,U_2567))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2568),U_2567))
          & U_2567 != bot_bot_fun_nat_bool
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2567)) )
      | ? [U_2566] : ~ hBOOL(hAPP_f54304608l_bool(U_2570,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2566),bot_bot_fun_nat_bool)))
      | U_2569 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2569)) ),
    inference(variable_rename,[status(thm)],[f_888_1]) ).

fof(f_888_3,plain,
    ! [U_2570,U_2569] :
      ( hBOOL(hAPP_f54304608l_bool(U_2570,U_2569))
      | ? [U_2568,U_2567] :
          ( ~ hBOOL(hAPP_f54304608l_bool(U_2570,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,U_2568),U_2567)))
          & hBOOL(hAPP_f54304608l_bool(U_2570,U_2567))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2568),U_2567))
          & U_2567 != bot_bot_fun_nat_bool
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2567)) )
      | ~ hBOOL(hAPP_f54304608l_bool(U_2570,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK156(U_2570,U_2569)),bot_bot_fun_nat_bool)))
      | U_2569 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2569)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK156]),skolemize(U_2566,sK156(U_2570,U_2569))],[f_888_2]) ).

fof(f_888_4,plain,
    ! [U_2570,U_2569] :
      ( hBOOL(hAPP_f54304608l_bool(U_2570,U_2569))
      | ? [U_2567] :
          ( ~ hBOOL(hAPP_f54304608l_bool(U_2570,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK157(U_2570,U_2569)),U_2567)))
          & hBOOL(hAPP_f54304608l_bool(U_2570,U_2567))
          & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK157(U_2570,U_2569)),U_2567))
          & U_2567 != bot_bot_fun_nat_bool
          & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2567)) )
      | ~ hBOOL(hAPP_f54304608l_bool(U_2570,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK156(U_2570,U_2569)),bot_bot_fun_nat_bool)))
      | U_2569 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2569)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK157]),skolemize(U_2568,sK157(U_2570,U_2569))],[f_888_3]) ).

fof(f_888_5,plain,
    ! [U_2570,U_2569] :
      ( hBOOL(hAPP_f54304608l_bool(U_2570,U_2569))
      | ( ~ hBOOL(hAPP_f54304608l_bool(U_2570,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK157(U_2570,U_2569)),sK158(U_2570,U_2569))))
        & hBOOL(hAPP_f54304608l_bool(U_2570,sK158(U_2570,U_2569)))
        & ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK157(U_2570,U_2569)),sK158(U_2570,U_2569)))
        & sK158(U_2570,U_2569) != bot_bot_fun_nat_bool
        & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK158(U_2570,U_2569))) )
      | ~ hBOOL(hAPP_f54304608l_bool(U_2570,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK156(U_2570,U_2569)),bot_bot_fun_nat_bool)))
      | U_2569 = bot_bot_fun_nat_bool
      | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2569)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK158]),skolemize(U_2567,sK158(U_2570,U_2569))],[f_888_4]) ).

fof(f_888_6,plain,
    ( ! [U_2569,U_2570] :
        ( ~ hBOOL(hAPP_f54304608l_bool(U_2570,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK157(U_2570,U_2569)),sK158(U_2570,U_2569))))
        | ~ sP241(U_2569,U_2570) )
    & ! [U_2569,U_2570] :
        ( hBOOL(hAPP_f54304608l_bool(U_2570,sK158(U_2570,U_2569)))
        | ~ sP241(U_2569,U_2570) )
    & ! [U_2569,U_2570] :
        ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK157(U_2570,U_2569)),sK158(U_2570,U_2569)))
        | ~ sP241(U_2569,U_2570) )
    & ! [U_2569,U_2570] :
        ( sK158(U_2570,U_2569) != bot_bot_fun_nat_bool
        | ~ sP241(U_2569,U_2570) )
    & ! [U_2569,U_2570] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK158(U_2570,U_2569)))
        | ~ sP241(U_2569,U_2570) )
    & ! [U_2569,U_2570] :
        ( hBOOL(hAPP_f54304608l_bool(U_2570,U_2569))
        | sP241(U_2569,U_2570)
        | ~ hBOOL(hAPP_f54304608l_bool(U_2570,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK156(U_2570,U_2569)),bot_bot_fun_nat_bool)))
        | U_2569 = bot_bot_fun_nat_bool
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2569)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP241])],[f_888_5]) ).

cnf(f_888_7,plain,
    ( hBOOL(hAPP_f54304608l_bool(U_2570,U_2569))
    | sP241(U_2569,U_2570)
    | ~ hBOOL(hAPP_f54304608l_bool(U_2570,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK156(U_2570,U_2569)),bot_bot_fun_nat_bool)))
    | U_2569 = bot_bot_fun_nat_bool
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2569)) ),
    inference(clausify,[status(thm)],[f_888_6]) ).

cnf(f_888_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,sK158(U_2570,U_2569)))
    | ~ sP241(U_2569,U_2570) ),
    inference(clausify,[status(thm)],[f_888_6]) ).

cnf(f_888_9,plain,
    ( sK158(U_2570,U_2569) != bot_bot_fun_nat_bool
    | ~ sP241(U_2569,U_2570) ),
    inference(clausify,[status(thm)],[f_888_6]) ).

cnf(f_888_10,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK157(U_2570,U_2569)),sK158(U_2570,U_2569)))
    | ~ sP241(U_2569,U_2570) ),
    inference(clausify,[status(thm)],[f_888_6]) ).

cnf(f_888_11,plain,
    ( hBOOL(hAPP_f54304608l_bool(U_2570,sK158(U_2570,U_2569)))
    | ~ sP241(U_2569,U_2570) ),
    inference(clausify,[status(thm)],[f_888_6]) ).

cnf(f_888_12,plain,
    ( ~ hBOOL(hAPP_f54304608l_bool(U_2570,hAPP_f800510211t_bool(hAPP_n1512601776t_bool(insert_nat,sK157(U_2570,U_2569)),sK158(U_2570,U_2569))))
    | ~ sP241(U_2569,U_2570) ),
    inference(clausify,[status(thm)],[f_888_6]) ).

fof(f_889_1,plain,
    ! [Pa,F_1] :
      ( hBOOL(hAPP_f1664156314l_bool(Pa,F_1))
      | ? [X_2,F_2] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(Pa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),F_2)))
          & hBOOL(hAPP_f1664156314l_bool(Pa,F_2))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),F_2))
          & F_2 != bot_bo844097828e_bool
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_2))
          & is_fun_pname_bool(F_2)
          & is_pname(X_2) )
      | ? [X_2] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(Pa,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,X_2),bot_bo844097828e_bool)))
          & is_pname(X_2) )
      | F_1 = bot_bo844097828e_bool
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
      | ~ is_fun_pname_bool(F_1) ),
    inference(fof_nnf,[status(thm)],[fact_782_finite__ne__induct]) ).

fof(f_889_2,plain,
    ! [U_2575,U_2574] :
      ( hBOOL(hAPP_f1664156314l_bool(U_2575,U_2574))
      | ? [U_2573,U_2572] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(U_2575,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2573),U_2572)))
          & hBOOL(hAPP_f1664156314l_bool(U_2575,U_2572))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2573),U_2572))
          & U_2572 != bot_bo844097828e_bool
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2572))
          & is_fun_pname_bool(U_2572)
          & is_pname(U_2573) )
      | ? [U_2571] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(U_2575,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2571),bot_bo844097828e_bool)))
          & is_pname(U_2571) )
      | U_2574 = bot_bo844097828e_bool
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2574))
      | ~ is_fun_pname_bool(U_2574) ),
    inference(variable_rename,[status(thm)],[f_889_1]) ).

fof(f_889_3,plain,
    ! [U_2575,U_2574] :
      ( hBOOL(hAPP_f1664156314l_bool(U_2575,U_2574))
      | ? [U_2573,U_2572] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(U_2575,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,U_2573),U_2572)))
          & hBOOL(hAPP_f1664156314l_bool(U_2575,U_2572))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,U_2573),U_2572))
          & U_2572 != bot_bo844097828e_bool
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2572))
          & is_fun_pname_bool(U_2572)
          & is_pname(U_2573) )
      | ( ~ hBOOL(hAPP_f1664156314l_bool(U_2575,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK159(U_2575,U_2574)),bot_bo844097828e_bool)))
        & is_pname(sK159(U_2575,U_2574)) )
      | U_2574 = bot_bo844097828e_bool
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2574))
      | ~ is_fun_pname_bool(U_2574) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK159]),skolemize(U_2571,sK159(U_2575,U_2574))],[f_889_2]) ).

fof(f_889_4,plain,
    ! [U_2575,U_2574] :
      ( hBOOL(hAPP_f1664156314l_bool(U_2575,U_2574))
      | ? [U_2572] :
          ( ~ hBOOL(hAPP_f1664156314l_bool(U_2575,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK160(U_2575,U_2574)),U_2572)))
          & hBOOL(hAPP_f1664156314l_bool(U_2575,U_2572))
          & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK160(U_2575,U_2574)),U_2572))
          & U_2572 != bot_bo844097828e_bool
          & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2572))
          & is_fun_pname_bool(U_2572)
          & is_pname(sK160(U_2575,U_2574)) )
      | ( ~ hBOOL(hAPP_f1664156314l_bool(U_2575,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK159(U_2575,U_2574)),bot_bo844097828e_bool)))
        & is_pname(sK159(U_2575,U_2574)) )
      | U_2574 = bot_bo844097828e_bool
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2574))
      | ~ is_fun_pname_bool(U_2574) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK160]),skolemize(U_2573,sK160(U_2575,U_2574))],[f_889_3]) ).

fof(f_889_5,plain,
    ! [U_2575,U_2574] :
      ( hBOOL(hAPP_f1664156314l_bool(U_2575,U_2574))
      | ( ~ hBOOL(hAPP_f1664156314l_bool(U_2575,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK160(U_2575,U_2574)),sK161(U_2575,U_2574))))
        & hBOOL(hAPP_f1664156314l_bool(U_2575,sK161(U_2575,U_2574)))
        & ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK160(U_2575,U_2574)),sK161(U_2575,U_2574)))
        & sK161(U_2575,U_2574) != bot_bo844097828e_bool
        & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK161(U_2575,U_2574)))
        & is_fun_pname_bool(sK161(U_2575,U_2574))
        & is_pname(sK160(U_2575,U_2574)) )
      | ( ~ hBOOL(hAPP_f1664156314l_bool(U_2575,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK159(U_2575,U_2574)),bot_bo844097828e_bool)))
        & is_pname(sK159(U_2575,U_2574)) )
      | U_2574 = bot_bo844097828e_bool
      | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2574))
      | ~ is_fun_pname_bool(U_2574) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK161]),skolemize(U_2572,sK161(U_2575,U_2574))],[f_889_4]) ).

fof(f_889_6,plain,
    ( ! [U_2574,U_2575] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(U_2575,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK160(U_2575,U_2574)),sK161(U_2575,U_2574))))
        | ~ sP243(U_2574,U_2575) )
    & ! [U_2574,U_2575] :
        ( hBOOL(hAPP_f1664156314l_bool(U_2575,sK161(U_2575,U_2574)))
        | ~ sP243(U_2574,U_2575) )
    & ! [U_2574,U_2575] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK160(U_2575,U_2574)),sK161(U_2575,U_2574)))
        | ~ sP243(U_2574,U_2575) )
    & ! [U_2574,U_2575] :
        ( sK161(U_2575,U_2574) != bot_bo844097828e_bool
        | ~ sP243(U_2574,U_2575) )
    & ! [U_2574,U_2575] :
        ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK161(U_2575,U_2574)))
        | ~ sP243(U_2574,U_2575) )
    & ! [U_2574,U_2575] :
        ( is_fun_pname_bool(sK161(U_2575,U_2574))
        | ~ sP243(U_2574,U_2575) )
    & ! [U_2574,U_2575] :
        ( is_pname(sK160(U_2575,U_2574))
        | ~ sP243(U_2574,U_2575) )
    & ! [U_2574,U_2575] :
        ( ~ hBOOL(hAPP_f1664156314l_bool(U_2575,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK159(U_2575,U_2574)),bot_bo844097828e_bool)))
        | ~ sP242(U_2574,U_2575) )
    & ! [U_2574,U_2575] :
        ( is_pname(sK159(U_2575,U_2574))
        | ~ sP242(U_2574,U_2575) )
    & ! [U_2574,U_2575] :
        ( hBOOL(hAPP_f1664156314l_bool(U_2575,U_2574))
        | sP243(U_2574,U_2575)
        | sP242(U_2574,U_2575)
        | U_2574 = bot_bo844097828e_bool
        | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2574))
        | ~ is_fun_pname_bool(U_2574) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP242,sP243])],[f_889_5]) ).

cnf(f_889_7,plain,
    ( hBOOL(hAPP_f1664156314l_bool(U_2575,U_2574))
    | sP243(U_2574,U_2575)
    | sP242(U_2574,U_2575)
    | U_2574 = bot_bo844097828e_bool
    | ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,U_2574))
    | ~ is_fun_pname_bool(U_2574) ),
    inference(clausify,[status(thm)],[f_889_6]) ).

cnf(f_889_8,plain,
    ( is_pname(sK159(U_2575,U_2574))
    | ~ sP242(U_2574,U_2575) ),
    inference(clausify,[status(thm)],[f_889_6]) ).

cnf(f_889_9,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(U_2575,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK159(U_2575,U_2574)),bot_bo844097828e_bool)))
    | ~ sP242(U_2574,U_2575) ),
    inference(clausify,[status(thm)],[f_889_6]) ).

cnf(f_889_10,plain,
    ( is_pname(sK160(U_2575,U_2574))
    | ~ sP243(U_2574,U_2575) ),
    inference(clausify,[status(thm)],[f_889_6]) ).

cnf(f_889_11,plain,
    ( is_fun_pname_bool(sK161(U_2575,U_2574))
    | ~ sP243(U_2574,U_2575) ),
    inference(clausify,[status(thm)],[f_889_6]) ).

cnf(f_889_12,plain,
    ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,sK161(U_2575,U_2574)))
    | ~ sP243(U_2574,U_2575) ),
    inference(clausify,[status(thm)],[f_889_6]) ).

cnf(f_889_13,plain,
    ( sK161(U_2575,U_2574) != bot_bo844097828e_bool
    | ~ sP243(U_2574,U_2575) ),
    inference(clausify,[status(thm)],[f_889_6]) ).

cnf(f_889_14,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,sK160(U_2575,U_2574)),sK161(U_2575,U_2574)))
    | ~ sP243(U_2574,U_2575) ),
    inference(clausify,[status(thm)],[f_889_6]) ).

cnf(f_889_15,plain,
    ( hBOOL(hAPP_f1664156314l_bool(U_2575,sK161(U_2575,U_2574)))
    | ~ sP243(U_2574,U_2575) ),
    inference(clausify,[status(thm)],[f_889_6]) ).

cnf(f_889_16,plain,
    ( ~ hBOOL(hAPP_f1664156314l_bool(U_2575,hAPP_f759274231e_bool(hAPP_p905327722e_bool(insert_pname,sK160(U_2575,U_2574)),sK161(U_2575,U_2574))))
    | ~ sP243(U_2574,U_2575) ),
    inference(clausify,[status(thm)],[f_889_6]) ).

fof(f_890_1,plain,
    ! [X_3] : hAPP_fun_a_bool_a(the_elem_a,X_3) = hAPP_fun_a_bool_a(the_a,cOMBB_1273333599bool_a(hAPP_f1631501043l_bool(fequal_fun_a_bool,X_3),hAPP_f1038053735a_bool(cOMBC_394484100a_bool(insert_a),bot_bot_fun_a_bool))),
    inference(fof_nnf,[status(thm)],[fact_783_the__elem__def]) ).

fof(f_890_2,plain,
    ! [U_2576] : hAPP_fun_a_bool_a(the_elem_a,U_2576) = hAPP_fun_a_bool_a(the_a,cOMBB_1273333599bool_a(hAPP_f1631501043l_bool(fequal_fun_a_bool,U_2576),hAPP_f1038053735a_bool(cOMBC_394484100a_bool(insert_a),bot_bot_fun_a_bool))),
    inference(variable_rename,[status(thm)],[f_890_1]) ).

fof(f_890_3,plain,
    ! [U_2576] : hAPP_fun_a_bool_a(the_elem_a,U_2576) = hAPP_fun_a_bool_a(the_a,cOMBB_1273333599bool_a(hAPP_f1631501043l_bool(fequal_fun_a_bool,U_2576),hAPP_f1038053735a_bool(cOMBC_394484100a_bool(insert_a),bot_bot_fun_a_bool))),
    inference(definitional_conversion,[status(esa)],[f_890_2]) ).

cnf(f_890_4,plain,
    hAPP_fun_a_bool_a(the_elem_a,U_2576) = hAPP_fun_a_bool_a(the_a,cOMBB_1273333599bool_a(hAPP_f1631501043l_bool(fequal_fun_a_bool,U_2576),hAPP_f1038053735a_bool(cOMBC_394484100a_bool(insert_a),bot_bot_fun_a_bool))),
    inference(clausify,[status(thm)],[f_890_3]) ).

fof(f_891_1,plain,
    ! [X_3] : hAPP_f22106695ol_nat(the_elem_nat,X_3) = hAPP_f22106695ol_nat(the_nat,cOMBB_955900739ol_nat(hAPP_f103356543l_bool(fequal_fun_nat_bool,X_3),hAPP_f1570313510t_bool(cOMBC_178881787t_bool(insert_nat),bot_bot_fun_nat_bool))),
    inference(fof_nnf,[status(thm)],[fact_784_the__elem__def]) ).

fof(f_891_2,plain,
    ! [U_2577] : hAPP_f22106695ol_nat(the_elem_nat,U_2577) = hAPP_f22106695ol_nat(the_nat,cOMBB_955900739ol_nat(hAPP_f103356543l_bool(fequal_fun_nat_bool,U_2577),hAPP_f1570313510t_bool(cOMBC_178881787t_bool(insert_nat),bot_bot_fun_nat_bool))),
    inference(variable_rename,[status(thm)],[f_891_1]) ).

fof(f_891_3,plain,
    ! [U_2577] : hAPP_f22106695ol_nat(the_elem_nat,U_2577) = hAPP_f22106695ol_nat(the_nat,cOMBB_955900739ol_nat(hAPP_f103356543l_bool(fequal_fun_nat_bool,U_2577),hAPP_f1570313510t_bool(cOMBC_178881787t_bool(insert_nat),bot_bot_fun_nat_bool))),
    inference(definitional_conversion,[status(esa)],[f_891_2]) ).

cnf(f_891_4,plain,
    hAPP_f22106695ol_nat(the_elem_nat,U_2577) = hAPP_f22106695ol_nat(the_nat,cOMBB_955900739ol_nat(hAPP_f103356543l_bool(fequal_fun_nat_bool,U_2577),hAPP_f1570313510t_bool(cOMBC_178881787t_bool(insert_nat),bot_bot_fun_nat_bool))),
    inference(clausify,[status(thm)],[f_891_3]) ).

fof(f_892_1,plain,
    ! [X_3] : hAPP_f1594865479ol_int(the_elem_int,X_3) = hAPP_f1594865479ol_int(the_int,cOMBB_1418110531ol_int(hAPP_f284875647l_bool(fequal_fun_int_bool,X_3),hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(insert_int),bot_bot_fun_int_bool))),
    inference(fof_nnf,[status(thm)],[fact_785_the__elem__def]) ).

fof(f_892_2,plain,
    ! [U_2578] : hAPP_f1594865479ol_int(the_elem_int,U_2578) = hAPP_f1594865479ol_int(the_int,cOMBB_1418110531ol_int(hAPP_f284875647l_bool(fequal_fun_int_bool,U_2578),hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(insert_int),bot_bot_fun_int_bool))),
    inference(variable_rename,[status(thm)],[f_892_1]) ).

fof(f_892_3,plain,
    ! [U_2578] : hAPP_f1594865479ol_int(the_elem_int,U_2578) = hAPP_f1594865479ol_int(the_int,cOMBB_1418110531ol_int(hAPP_f284875647l_bool(fequal_fun_int_bool,U_2578),hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(insert_int),bot_bot_fun_int_bool))),
    inference(definitional_conversion,[status(esa)],[f_892_2]) ).

cnf(f_892_4,plain,
    hAPP_f1594865479ol_int(the_elem_int,U_2578) = hAPP_f1594865479ol_int(the_int,cOMBB_1418110531ol_int(hAPP_f284875647l_bool(fequal_fun_int_bool,U_2578),hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(insert_int),bot_bot_fun_int_bool))),
    inference(clausify,[status(thm)],[f_892_3]) ).

fof(f_893_1,plain,
    ! [A_13,B_14,C_10] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_13),B_14)),C_10) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_13),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_14),C_10)),
    inference(fof_nnf,[status(thm)],[fact_786_ab__semigroup__add__class_Oadd__ac_I1_J]) ).

fof(f_893_2,plain,
    ! [U_2581,U_2580,U_2579] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2581),U_2580)),U_2579) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2581),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2580),U_2579)),
    inference(variable_rename,[status(thm)],[f_893_1]) ).

fof(f_893_3,plain,
    ! [U_2579,U_2581,U_2580] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2581),U_2580)),U_2579) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2581),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2580),U_2579)),
    inference(definitional_conversion,[status(esa)],[f_893_2]) ).

cnf(f_893_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2581),U_2580)),U_2579) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2581),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2580),U_2579)),
    inference(clausify,[status(thm)],[f_893_3]) ).

fof(f_894_1,plain,
    ! [A_13,B_14,C_10] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),B_14)),C_10) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_13),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_14),C_10)),
    inference(fof_nnf,[status(thm)],[fact_787_ab__semigroup__add__class_Oadd__ac_I1_J]) ).

fof(f_894_2,plain,
    ! [U_2584,U_2583,U_2582] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2584),U_2583)),U_2582) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2584),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2583),U_2582)),
    inference(variable_rename,[status(thm)],[f_894_1]) ).

fof(f_894_3,plain,
    ! [U_2583,U_2582,U_2584] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2584),U_2583)),U_2582) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2584),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2583),U_2582)),
    inference(definitional_conversion,[status(esa)],[f_894_2]) ).

cnf(f_894_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2584),U_2583)),U_2582) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2584),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2583),U_2582)),
    inference(clausify,[status(thm)],[f_894_3]) ).

fof(f_895_1,plain,
    ! [A_2,B_3,C_6] :
      ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),B_3) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),C_6)
        | B_3 != C_6 )
      & ( B_3 = C_6
        | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),B_3) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),C_6) ) ),
    inference(fof_nnf,[status(thm)],[fact_788_add__left__cancel]) ).

fof(f_895_2,plain,
    ! [U_2587,U_2586,U_2585] :
      ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2587),U_2586) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2587),U_2585)
        | U_2586 != U_2585 )
      & ( U_2586 = U_2585
        | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2587),U_2586) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2587),U_2585) ) ),
    inference(variable_rename,[status(thm)],[f_895_1]) ).

fof(f_895_3,plain,
    ( ! [U_2593,U_2591,U_2589] :
        ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2593),U_2591) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2593),U_2589)
        | U_2591 != U_2589 )
    & ! [U_2592,U_2590,U_2588] :
        ( U_2590 = U_2588
        | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2592),U_2590) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2592),U_2588) ) ),
    inference(miniscope,[status(thm)],[f_895_2]) ).

fof(f_895_4,plain,
    ( ! [U_2589,U_2593,U_2591] :
        ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2593),U_2591) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2593),U_2589)
        | U_2591 != U_2589 )
    & ! [U_2588,U_2590,U_2592] :
        ( U_2590 = U_2588
        | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2592),U_2590) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2592),U_2588) ) ),
    inference(definitional_conversion,[status(esa)],[f_895_3]) ).

cnf(f_895_5,plain,
    ( U_2590 = U_2588
    | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2592),U_2590) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2592),U_2588) ),
    inference(clausify,[status(thm)],[f_895_4]) ).

cnf(f_895_6,plain,
    ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2593),U_2591) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2593),U_2589)
    | U_2591 != U_2589 ),
    inference(clausify,[status(thm)],[f_895_4]) ).

fof(f_896_1,plain,
    ! [A_2,B_3,C_6] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_2),B_3) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_2),C_6)
        | B_3 != C_6 )
      & ( B_3 = C_6
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_2),B_3) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_2),C_6) ) ),
    inference(fof_nnf,[status(thm)],[fact_789_add__left__cancel]) ).

fof(f_896_2,plain,
    ! [U_2596,U_2595,U_2594] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2596),U_2595) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2596),U_2594)
        | U_2595 != U_2594 )
      & ( U_2595 = U_2594
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2596),U_2595) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2596),U_2594) ) ),
    inference(variable_rename,[status(thm)],[f_896_1]) ).

fof(f_896_3,plain,
    ( ! [U_2602,U_2600,U_2598] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2602),U_2600) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2602),U_2598)
        | U_2600 != U_2598 )
    & ! [U_2601,U_2599,U_2597] :
        ( U_2599 = U_2597
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2601),U_2599) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2601),U_2597) ) ),
    inference(miniscope,[status(thm)],[f_896_2]) ).

fof(f_896_4,plain,
    ( ! [U_2600,U_2598,U_2602] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2602),U_2600) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2602),U_2598)
        | U_2600 != U_2598 )
    & ! [U_2599,U_2601,U_2597] :
        ( U_2599 = U_2597
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2601),U_2599) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2601),U_2597) ) ),
    inference(definitional_conversion,[status(esa)],[f_896_3]) ).

cnf(f_896_5,plain,
    ( U_2599 = U_2597
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2601),U_2599) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2601),U_2597) ),
    inference(clausify,[status(thm)],[f_896_4]) ).

cnf(f_896_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2602),U_2600) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2602),U_2598)
    | U_2600 != U_2598 ),
    inference(clausify,[status(thm)],[f_896_4]) ).

fof(f_897_1,plain,
    ! [B_3,A_2,C_6] :
      ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_3),A_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_6),A_2)
        | B_3 != C_6 )
      & ( B_3 = C_6
        | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_3),A_2) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_6),A_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_790_add__right__cancel]) ).

fof(f_897_2,plain,
    ! [U_2605,U_2604,U_2603] :
      ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2605),U_2604) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2603),U_2604)
        | U_2605 != U_2603 )
      & ( U_2605 = U_2603
        | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2605),U_2604) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2603),U_2604) ) ),
    inference(variable_rename,[status(thm)],[f_897_1]) ).

fof(f_897_3,plain,
    ( ! [U_2611,U_2609,U_2607] :
        ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2611),U_2609) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2607),U_2609)
        | U_2611 != U_2607 )
    & ! [U_2610,U_2608,U_2606] :
        ( U_2610 = U_2606
        | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2610),U_2608) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2606),U_2608) ) ),
    inference(miniscope,[status(thm)],[f_897_2]) ).

fof(f_897_4,plain,
    ( ! [U_2607,U_2609,U_2611] :
        ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2611),U_2609) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2607),U_2609)
        | U_2611 != U_2607 )
    & ! [U_2608,U_2610,U_2606] :
        ( U_2610 = U_2606
        | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2610),U_2608) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2606),U_2608) ) ),
    inference(definitional_conversion,[status(esa)],[f_897_3]) ).

cnf(f_897_5,plain,
    ( U_2610 = U_2606
    | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2610),U_2608) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2606),U_2608) ),
    inference(clausify,[status(thm)],[f_897_4]) ).

cnf(f_897_6,plain,
    ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2611),U_2609) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2607),U_2609)
    | U_2611 != U_2607 ),
    inference(clausify,[status(thm)],[f_897_4]) ).

fof(f_898_1,plain,
    ! [B_3,A_2,C_6] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),A_2) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_6),A_2)
        | B_3 != C_6 )
      & ( B_3 = C_6
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),A_2) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_6),A_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_791_add__right__cancel]) ).

fof(f_898_2,plain,
    ! [U_2614,U_2613,U_2612] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2614),U_2613) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2612),U_2613)
        | U_2614 != U_2612 )
      & ( U_2614 = U_2612
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2614),U_2613) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2612),U_2613) ) ),
    inference(variable_rename,[status(thm)],[f_898_1]) ).

fof(f_898_3,plain,
    ( ! [U_2620,U_2618,U_2616] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2620),U_2618) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2616),U_2618)
        | U_2620 != U_2616 )
    & ! [U_2619,U_2617,U_2615] :
        ( U_2619 = U_2615
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2619),U_2617) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2615),U_2617) ) ),
    inference(miniscope,[status(thm)],[f_898_2]) ).

fof(f_898_4,plain,
    ( ! [U_2616,U_2618,U_2620] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2620),U_2618) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2616),U_2618)
        | U_2620 != U_2616 )
    & ! [U_2617,U_2619,U_2615] :
        ( U_2619 = U_2615
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2619),U_2617) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2615),U_2617) ) ),
    inference(definitional_conversion,[status(esa)],[f_898_3]) ).

cnf(f_898_5,plain,
    ( U_2619 = U_2615
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2619),U_2617) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2615),U_2617) ),
    inference(clausify,[status(thm)],[f_898_4]) ).

cnf(f_898_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2620),U_2618) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2616),U_2618)
    | U_2620 != U_2616 ),
    inference(clausify,[status(thm)],[f_898_4]) ).

fof(f_899_1,plain,
    ! [A_12,B_13,C_9] :
      ( B_13 = C_9
      | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_12),B_13) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_12),C_9) ),
    inference(fof_nnf,[status(thm)],[fact_792_add__left__imp__eq]) ).

fof(f_899_2,plain,
    ! [U_2623,U_2622,U_2621] :
      ( U_2622 = U_2621
      | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2623),U_2622) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2623),U_2621) ),
    inference(variable_rename,[status(thm)],[f_899_1]) ).

fof(f_899_3,plain,
    ! [U_2621,U_2622,U_2623] :
      ( U_2622 = U_2621
      | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2623),U_2622) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2623),U_2621) ),
    inference(definitional_conversion,[status(esa)],[f_899_2]) ).

cnf(f_899_4,plain,
    ( U_2622 = U_2621
    | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2623),U_2622) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2623),U_2621) ),
    inference(clausify,[status(thm)],[f_899_3]) ).

fof(f_900_1,plain,
    ! [A_12,B_13,C_9] :
      ( B_13 = C_9
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),B_13) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_12),C_9) ),
    inference(fof_nnf,[status(thm)],[fact_793_add__left__imp__eq]) ).

fof(f_900_2,plain,
    ! [U_2626,U_2625,U_2624] :
      ( U_2625 = U_2624
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2626),U_2625) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2626),U_2624) ),
    inference(variable_rename,[status(thm)],[f_900_1]) ).

fof(f_900_3,plain,
    ! [U_2625,U_2624,U_2626] :
      ( U_2625 = U_2624
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2626),U_2625) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2626),U_2624) ),
    inference(definitional_conversion,[status(esa)],[f_900_2]) ).

cnf(f_900_4,plain,
    ( U_2625 = U_2624
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2626),U_2625) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2626),U_2624) ),
    inference(clausify,[status(thm)],[f_900_3]) ).

fof(f_901_1,plain,
    ! [A_11,B_12,C_8] :
      ( B_12 = C_8
      | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_11),B_12) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_11),C_8) ),
    inference(fof_nnf,[status(thm)],[fact_794_add__imp__eq]) ).

fof(f_901_2,plain,
    ! [U_2629,U_2628,U_2627] :
      ( U_2628 = U_2627
      | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2629),U_2628) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2629),U_2627) ),
    inference(variable_rename,[status(thm)],[f_901_1]) ).

fof(f_901_3,plain,
    ! [U_2627,U_2628,U_2629] :
      ( U_2628 = U_2627
      | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2629),U_2628) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2629),U_2627) ),
    inference(definitional_conversion,[status(esa)],[f_901_2]) ).

cnf(f_901_4,plain,
    ( U_2628 = U_2627
    | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2629),U_2628) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2629),U_2627) ),
    inference(clausify,[status(thm)],[f_901_3]) ).

fof(f_902_1,plain,
    ! [A_11,B_12,C_8] :
      ( B_12 = C_8
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_11),B_12) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_11),C_8) ),
    inference(fof_nnf,[status(thm)],[fact_795_add__imp__eq]) ).

fof(f_902_2,plain,
    ! [U_2632,U_2631,U_2630] :
      ( U_2631 = U_2630
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2632),U_2631) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2632),U_2630) ),
    inference(variable_rename,[status(thm)],[f_902_1]) ).

fof(f_902_3,plain,
    ! [U_2630,U_2631,U_2632] :
      ( U_2631 = U_2630
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2632),U_2631) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2632),U_2630) ),
    inference(definitional_conversion,[status(esa)],[f_902_2]) ).

cnf(f_902_4,plain,
    ( U_2631 = U_2630
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2632),U_2631) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2632),U_2630) ),
    inference(clausify,[status(thm)],[f_902_3]) ).

fof(f_903_1,plain,
    ! [B_11,A_10,C_7] :
      ( B_11 = C_7
      | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_11),A_10) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_7),A_10) ),
    inference(fof_nnf,[status(thm)],[fact_796_add__right__imp__eq]) ).

fof(f_903_2,plain,
    ! [U_2635,U_2634,U_2633] :
      ( U_2635 = U_2633
      | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2635),U_2634) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2633),U_2634) ),
    inference(variable_rename,[status(thm)],[f_903_1]) ).

fof(f_903_3,plain,
    ! [U_2633,U_2634,U_2635] :
      ( U_2635 = U_2633
      | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2635),U_2634) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2633),U_2634) ),
    inference(definitional_conversion,[status(esa)],[f_903_2]) ).

cnf(f_903_4,plain,
    ( U_2635 = U_2633
    | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2635),U_2634) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2633),U_2634) ),
    inference(clausify,[status(thm)],[f_903_3]) ).

fof(f_904_1,plain,
    ! [B_11,A_10,C_7] :
      ( B_11 = C_7
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_11),A_10) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_7),A_10) ),
    inference(fof_nnf,[status(thm)],[fact_797_add__right__imp__eq]) ).

fof(f_904_2,plain,
    ! [U_2638,U_2637,U_2636] :
      ( U_2638 = U_2636
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2638),U_2637) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2636),U_2637) ),
    inference(variable_rename,[status(thm)],[f_904_1]) ).

fof(f_904_3,plain,
    ! [U_2636,U_2637,U_2638] :
      ( U_2638 = U_2636
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2638),U_2637) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2636),U_2637) ),
    inference(definitional_conversion,[status(esa)],[f_904_2]) ).

cnf(f_904_4,plain,
    ( U_2638 = U_2636
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2638),U_2637) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2636),U_2637) ),
    inference(clausify,[status(thm)],[f_904_3]) ).

fof(f_905_1,plain,
    ! [M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M_1),
    inference(fof_nnf,[status(thm)],[fact_798_nat__add__commute]) ).

fof(f_905_2,plain,
    ! [U_2640,U_2639] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2640),U_2639) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2639),U_2640),
    inference(variable_rename,[status(thm)],[f_905_1]) ).

fof(f_905_3,plain,
    ! [U_2639,U_2640] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2640),U_2639) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2639),U_2640),
    inference(definitional_conversion,[status(esa)],[f_905_2]) ).

cnf(f_905_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2640),U_2639) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2639),U_2640),
    inference(clausify,[status(thm)],[f_905_3]) ).

fof(f_906_1,plain,
    ! [X,Y,Z] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),Z)),
    inference(fof_nnf,[status(thm)],[fact_799_nat__add__left__commute]) ).

fof(f_906_2,plain,
    ! [U_2643,U_2642,U_2641] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2643),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2642),U_2641)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2642),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2643),U_2641)),
    inference(variable_rename,[status(thm)],[f_906_1]) ).

fof(f_906_3,plain,
    ! [U_2641,U_2642,U_2643] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2643),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2642),U_2641)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2642),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2643),U_2641)),
    inference(definitional_conversion,[status(esa)],[f_906_2]) ).

cnf(f_906_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2643),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2642),U_2641)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2642),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2643),U_2641)),
    inference(clausify,[status(thm)],[f_906_3]) ).

fof(f_907_1,plain,
    ! [M_1,N,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),K_1)),
    inference(fof_nnf,[status(thm)],[fact_800_nat__add__assoc]) ).

fof(f_907_2,plain,
    ! [U_2646,U_2645,U_2644] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2646),U_2645)),U_2644) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2646),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2645),U_2644)),
    inference(variable_rename,[status(thm)],[f_907_1]) ).

fof(f_907_3,plain,
    ! [U_2646,U_2645,U_2644] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2646),U_2645)),U_2644) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2646),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2645),U_2644)),
    inference(definitional_conversion,[status(esa)],[f_907_2]) ).

cnf(f_907_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2646),U_2645)),U_2644) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2646),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2645),U_2644)),
    inference(clausify,[status(thm)],[f_907_3]) ).

fof(f_908_1,plain,
    ! [K,M,Na] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)
        | M != Na )
      & ( M = Na
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_801_nat__add__left__cancel]) ).

fof(f_908_2,plain,
    ! [U_2649,U_2648,U_2647] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2649),U_2648) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2649),U_2647)
        | U_2648 != U_2647 )
      & ( U_2648 = U_2647
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2649),U_2648) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2649),U_2647) ) ),
    inference(variable_rename,[status(thm)],[f_908_1]) ).

fof(f_908_3,plain,
    ( ! [U_2655,U_2653,U_2651] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2655),U_2653) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2655),U_2651)
        | U_2653 != U_2651 )
    & ! [U_2654,U_2652,U_2650] :
        ( U_2652 = U_2650
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2654),U_2652) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2654),U_2650) ) ),
    inference(miniscope,[status(thm)],[f_908_2]) ).

fof(f_908_4,plain,
    ( ! [U_2651,U_2653,U_2655] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2655),U_2653) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2655),U_2651)
        | U_2653 != U_2651 )
    & ! [U_2652,U_2650,U_2654] :
        ( U_2652 = U_2650
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2654),U_2652) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2654),U_2650) ) ),
    inference(definitional_conversion,[status(esa)],[f_908_3]) ).

cnf(f_908_5,plain,
    ( U_2652 = U_2650
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2654),U_2652) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2654),U_2650) ),
    inference(clausify,[status(thm)],[f_908_4]) ).

cnf(f_908_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2655),U_2653) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2655),U_2651)
    | U_2653 != U_2651 ),
    inference(clausify,[status(thm)],[f_908_4]) ).

fof(f_909_1,plain,
    ! [M,K,Na] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Na),K)
        | M != Na )
      & ( M = Na
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Na),K) ) ),
    inference(fof_nnf,[status(thm)],[fact_802_nat__add__right__cancel]) ).

fof(f_909_2,plain,
    ! [U_2658,U_2657,U_2656] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2658),U_2657) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2656),U_2657)
        | U_2658 != U_2656 )
      & ( U_2658 = U_2656
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2658),U_2657) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2656),U_2657) ) ),
    inference(variable_rename,[status(thm)],[f_909_1]) ).

fof(f_909_3,plain,
    ( ! [U_2664,U_2662,U_2660] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2664),U_2662) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2660),U_2662)
        | U_2664 != U_2660 )
    & ! [U_2663,U_2661,U_2659] :
        ( U_2663 = U_2659
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2663),U_2661) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2659),U_2661) ) ),
    inference(miniscope,[status(thm)],[f_909_2]) ).

fof(f_909_4,plain,
    ( ! [U_2660,U_2662,U_2664] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2664),U_2662) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2660),U_2662)
        | U_2664 != U_2660 )
    & ! [U_2661,U_2663,U_2659] :
        ( U_2663 = U_2659
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2663),U_2661) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2659),U_2661) ) ),
    inference(definitional_conversion,[status(esa)],[f_909_3]) ).

cnf(f_909_5,plain,
    ( U_2663 = U_2659
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2663),U_2661) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2659),U_2661) ),
    inference(clausify,[status(thm)],[f_909_4]) ).

cnf(f_909_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2664),U_2662) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2660),U_2662)
    | U_2664 != U_2660 ),
    inference(clausify,[status(thm)],[f_909_4]) ).

fof(f_910_1,plain,
    ! [A_2,C_6,B_3] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),C_6)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_3),C_6)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),B_3)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),B_3))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_2),C_6)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_3),C_6))) ) ),
    inference(fof_nnf,[status(thm)],[fact_803_add__le__cancel__right]) ).

fof(f_910_2,plain,
    ! [U_2667,U_2666,U_2665] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2667),U_2666)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2665),U_2666)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2667),U_2665)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2667),U_2665))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2667),U_2666)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2665),U_2666))) ) ),
    inference(variable_rename,[status(thm)],[f_910_1]) ).

fof(f_910_3,plain,
    ( ! [U_2673,U_2671,U_2669] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2673),U_2671)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2669),U_2671)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2673),U_2669)) )
    & ! [U_2672,U_2670,U_2668] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2672),U_2668))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2672),U_2670)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2668),U_2670))) ) ),
    inference(miniscope,[status(thm)],[f_910_2]) ).

fof(f_910_4,plain,
    ( ! [U_2671,U_2669,U_2673] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2673),U_2671)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2669),U_2671)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2673),U_2669)) )
    & ! [U_2670,U_2668,U_2672] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2672),U_2668))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2672),U_2670)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2668),U_2670))) ) ),
    inference(definitional_conversion,[status(esa)],[f_910_3]) ).

cnf(f_910_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2672),U_2668))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2672),U_2670)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2668),U_2670))) ),
    inference(clausify,[status(thm)],[f_910_4]) ).

cnf(f_910_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2673),U_2671)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2669),U_2671)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2673),U_2669)) ),
    inference(clausify,[status(thm)],[f_910_4]) ).

fof(f_911_1,plain,
    ! [A_2,C_6,B_3] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_2),C_6)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),C_6)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_2),B_3)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_2),B_3))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_2),C_6)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),C_6))) ) ),
    inference(fof_nnf,[status(thm)],[fact_804_add__le__cancel__right]) ).

fof(f_911_2,plain,
    ! [U_2676,U_2675,U_2674] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2676),U_2675)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2674),U_2675)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2676),U_2674)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2676),U_2674))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2676),U_2675)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2674),U_2675))) ) ),
    inference(variable_rename,[status(thm)],[f_911_1]) ).

fof(f_911_3,plain,
    ( ! [U_2682,U_2680,U_2678] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2682),U_2680)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2678),U_2680)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2682),U_2678)) )
    & ! [U_2681,U_2679,U_2677] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2681),U_2677))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2681),U_2679)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2677),U_2679))) ) ),
    inference(miniscope,[status(thm)],[f_911_2]) ).

fof(f_911_4,plain,
    ( ! [U_2680,U_2678,U_2682] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2682),U_2680)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2678),U_2680)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2682),U_2678)) )
    & ! [U_2679,U_2677,U_2681] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2681),U_2677))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2681),U_2679)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2677),U_2679))) ) ),
    inference(definitional_conversion,[status(esa)],[f_911_3]) ).

cnf(f_911_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2681),U_2677))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2681),U_2679)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2677),U_2679))) ),
    inference(clausify,[status(thm)],[f_911_4]) ).

cnf(f_911_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2682),U_2680)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2678),U_2680)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2682),U_2678)) ),
    inference(clausify,[status(thm)],[f_911_4]) ).

fof(f_912_1,plain,
    ! [C_6,A_2,B_3] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_6),A_2)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_6),B_3)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),B_3)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_2),B_3))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_6),A_2)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_6),B_3))) ) ),
    inference(fof_nnf,[status(thm)],[fact_805_add__le__cancel__left]) ).

fof(f_912_2,plain,
    ! [U_2685,U_2684,U_2683] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2685),U_2684)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2685),U_2683)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2684),U_2683)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2684),U_2683))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2685),U_2684)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2685),U_2683))) ) ),
    inference(variable_rename,[status(thm)],[f_912_1]) ).

fof(f_912_3,plain,
    ( ! [U_2691,U_2689,U_2687] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2691),U_2689)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2691),U_2687)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2689),U_2687)) )
    & ! [U_2690,U_2688,U_2686] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2688),U_2686))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2690),U_2688)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2690),U_2686))) ) ),
    inference(miniscope,[status(thm)],[f_912_2]) ).

fof(f_912_4,plain,
    ( ! [U_2687,U_2689,U_2691] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2691),U_2689)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2691),U_2687)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2689),U_2687)) )
    & ! [U_2688,U_2686,U_2690] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2688),U_2686))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2690),U_2688)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2690),U_2686))) ) ),
    inference(definitional_conversion,[status(esa)],[f_912_3]) ).

cnf(f_912_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2688),U_2686))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2690),U_2688)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2690),U_2686))) ),
    inference(clausify,[status(thm)],[f_912_4]) ).

cnf(f_912_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2691),U_2689)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2691),U_2687)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2689),U_2687)) ),
    inference(clausify,[status(thm)],[f_912_4]) ).

fof(f_913_1,plain,
    ! [C_6,A_2,B_3] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_6),A_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_6),B_3)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_2),B_3)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_2),B_3))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_6),A_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_6),B_3))) ) ),
    inference(fof_nnf,[status(thm)],[fact_806_add__le__cancel__left]) ).

fof(f_913_2,plain,
    ! [U_2694,U_2693,U_2692] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2694),U_2693)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2694),U_2692)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2693),U_2692)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2693),U_2692))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2694),U_2693)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2694),U_2692))) ) ),
    inference(variable_rename,[status(thm)],[f_913_1]) ).

fof(f_913_3,plain,
    ( ! [U_2700,U_2698,U_2696] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2700),U_2698)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2700),U_2696)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2698),U_2696)) )
    & ! [U_2699,U_2697,U_2695] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2697),U_2695))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2699),U_2697)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2699),U_2695))) ) ),
    inference(miniscope,[status(thm)],[f_913_2]) ).

fof(f_913_4,plain,
    ( ! [U_2696,U_2698,U_2700] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2700),U_2698)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2700),U_2696)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2698),U_2696)) )
    & ! [U_2697,U_2695,U_2699] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2697),U_2695))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2699),U_2697)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2699),U_2695))) ) ),
    inference(definitional_conversion,[status(esa)],[f_913_3]) ).

cnf(f_913_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2697),U_2695))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2699),U_2697)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2699),U_2695))) ),
    inference(clausify,[status(thm)],[f_913_4]) ).

cnf(f_913_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2700),U_2698)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2700),U_2696)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2698),U_2696)) ),
    inference(clausify,[status(thm)],[f_913_4]) ).

fof(f_914_1,plain,
    ! [C_5,A_9,B_10] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_9),C_5)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_10),C_5)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_9),B_10)) ),
    inference(fof_nnf,[status(thm)],[fact_807_add__right__mono]) ).

fof(f_914_2,plain,
    ! [U_2703,U_2702,U_2701] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2702),U_2703)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2701),U_2703)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2702),U_2701)) ),
    inference(variable_rename,[status(thm)],[f_914_1]) ).

fof(f_914_3,plain,
    ! [U_2701,U_2702,U_2703] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2702),U_2703)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2701),U_2703)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2702),U_2701)) ),
    inference(definitional_conversion,[status(esa)],[f_914_2]) ).

cnf(f_914_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2702),U_2703)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2701),U_2703)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2702),U_2701)) ),
    inference(clausify,[status(thm)],[f_914_3]) ).

fof(f_915_1,plain,
    ! [C_5,A_9,B_10] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_9),C_5)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_10),C_5)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_9),B_10)) ),
    inference(fof_nnf,[status(thm)],[fact_808_add__right__mono]) ).

fof(f_915_2,plain,
    ! [U_2706,U_2705,U_2704] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2705),U_2706)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2704),U_2706)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2705),U_2704)) ),
    inference(variable_rename,[status(thm)],[f_915_1]) ).

fof(f_915_3,plain,
    ! [U_2704,U_2705,U_2706] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2705),U_2706)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2704),U_2706)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2705),U_2704)) ),
    inference(definitional_conversion,[status(esa)],[f_915_2]) ).

cnf(f_915_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2705),U_2706)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2704),U_2706)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2705),U_2704)) ),
    inference(clausify,[status(thm)],[f_915_3]) ).

fof(f_916_1,plain,
    ! [C_4,A_8,B_9] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_4),A_8)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_4),B_9)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_8),B_9)) ),
    inference(fof_nnf,[status(thm)],[fact_809_add__left__mono]) ).

fof(f_916_2,plain,
    ! [U_2709,U_2708,U_2707] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2709),U_2708)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2709),U_2707)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2708),U_2707)) ),
    inference(variable_rename,[status(thm)],[f_916_1]) ).

fof(f_916_3,plain,
    ! [U_2707,U_2708,U_2709] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2709),U_2708)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2709),U_2707)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2708),U_2707)) ),
    inference(definitional_conversion,[status(esa)],[f_916_2]) ).

cnf(f_916_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2709),U_2708)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2709),U_2707)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2708),U_2707)) ),
    inference(clausify,[status(thm)],[f_916_3]) ).

fof(f_917_1,plain,
    ! [C_4,A_8,B_9] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_4),A_8)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_4),B_9)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_8),B_9)) ),
    inference(fof_nnf,[status(thm)],[fact_810_add__left__mono]) ).

fof(f_917_2,plain,
    ! [U_2712,U_2711,U_2710] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2712),U_2711)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2712),U_2710)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2711),U_2710)) ),
    inference(variable_rename,[status(thm)],[f_917_1]) ).

fof(f_917_3,plain,
    ! [U_2710,U_2711,U_2712] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2712),U_2711)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2712),U_2710)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2711),U_2710)) ),
    inference(definitional_conversion,[status(esa)],[f_917_2]) ).

cnf(f_917_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2712),U_2711)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2712),U_2710)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2711),U_2710)) ),
    inference(clausify,[status(thm)],[f_917_3]) ).

fof(f_918_1,plain,
    ! [C_3,D_3,A_7,B_8] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_7),C_3)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_8),D_3)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,C_3),D_3))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_7),B_8)) ),
    inference(fof_nnf,[status(thm)],[fact_811_add__mono]) ).

fof(f_918_2,plain,
    ! [U_2716,U_2715,U_2714,U_2713] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2714),U_2716)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2713),U_2715)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2716),U_2715))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2714),U_2713)) ),
    inference(variable_rename,[status(thm)],[f_918_1]) ).

fof(f_918_3,plain,
    ! [U_2713,U_2714,U_2715,U_2716] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2714),U_2716)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2713),U_2715)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2716),U_2715))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2714),U_2713)) ),
    inference(definitional_conversion,[status(esa)],[f_918_2]) ).

cnf(f_918_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2714),U_2716)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2713),U_2715)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2716),U_2715))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2714),U_2713)) ),
    inference(clausify,[status(thm)],[f_918_3]) ).

fof(f_919_1,plain,
    ! [C_3,D_3,A_7,B_8] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_7),C_3)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_8),D_3)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C_3),D_3))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_7),B_8)) ),
    inference(fof_nnf,[status(thm)],[fact_812_add__mono]) ).

fof(f_919_2,plain,
    ! [U_2720,U_2719,U_2718,U_2717] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2718),U_2720)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2717),U_2719)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2720),U_2719))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2718),U_2717)) ),
    inference(variable_rename,[status(thm)],[f_919_1]) ).

fof(f_919_3,plain,
    ! [U_2717,U_2718,U_2719,U_2720] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2718),U_2720)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2717),U_2719)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2720),U_2719))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2718),U_2717)) ),
    inference(definitional_conversion,[status(esa)],[f_919_2]) ).

cnf(f_919_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2718),U_2720)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2717),U_2719)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2720),U_2719))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2718),U_2717)) ),
    inference(clausify,[status(thm)],[f_919_3]) ).

fof(f_920_1,plain,
    ! [A_6,C_2,B_7] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_6),B_7))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_6),C_2)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,B_7),C_2))) ),
    inference(fof_nnf,[status(thm)],[fact_813_add__le__imp__le__right]) ).

fof(f_920_2,plain,
    ! [U_2723,U_2722,U_2721] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2723),U_2721))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2723),U_2722)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2721),U_2722))) ),
    inference(variable_rename,[status(thm)],[f_920_1]) ).

fof(f_920_3,plain,
    ! [U_2721,U_2722,U_2723] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2723),U_2721))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2723),U_2722)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2721),U_2722))) ),
    inference(definitional_conversion,[status(esa)],[f_920_2]) ).

cnf(f_920_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2723),U_2721))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2723),U_2722)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2721),U_2722))) ),
    inference(clausify,[status(thm)],[f_920_3]) ).

fof(f_921_1,plain,
    ! [A_6,C_2,B_7] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_6),B_7))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,A_6),C_2)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_7),C_2))) ),
    inference(fof_nnf,[status(thm)],[fact_814_add__le__imp__le__right]) ).

fof(f_921_2,plain,
    ! [U_2726,U_2725,U_2724] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2726),U_2724))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2726),U_2725)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2724),U_2725))) ),
    inference(variable_rename,[status(thm)],[f_921_1]) ).

fof(f_921_3,plain,
    ! [U_2724,U_2725,U_2726] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2726),U_2724))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2726),U_2725)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2724),U_2725))) ),
    inference(definitional_conversion,[status(esa)],[f_921_2]) ).

cnf(f_921_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2726),U_2724))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2726),U_2725)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2724),U_2725))) ),
    inference(clausify,[status(thm)],[f_921_3]) ).

fof(f_922_1,plain,
    ! [C_1,A_5,B_6] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,A_5),B_6))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_1),A_5)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,C_1),B_6))) ),
    inference(fof_nnf,[status(thm)],[fact_815_add__le__imp__le__left]) ).

fof(f_922_2,plain,
    ! [U_2729,U_2728,U_2727] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2728),U_2727))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2729),U_2728)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2729),U_2727))) ),
    inference(variable_rename,[status(thm)],[f_922_1]) ).

fof(f_922_3,plain,
    ! [U_2727,U_2728,U_2729] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2728),U_2727))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2729),U_2728)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2729),U_2727))) ),
    inference(definitional_conversion,[status(esa)],[f_922_2]) ).

cnf(f_922_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_2728),U_2727))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2729),U_2728)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2729),U_2727))) ),
    inference(clausify,[status(thm)],[f_922_3]) ).

fof(f_923_1,plain,
    ! [C_1,A_5,B_6] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,A_5),B_6))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_1),A_5)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,C_1),B_6))) ),
    inference(fof_nnf,[status(thm)],[fact_816_add__le__imp__le__left]) ).

fof(f_923_2,plain,
    ! [U_2732,U_2731,U_2730] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2731),U_2730))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2732),U_2731)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2732),U_2730))) ),
    inference(variable_rename,[status(thm)],[f_923_1]) ).

fof(f_923_3,plain,
    ! [U_2731,U_2730,U_2732] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2731),U_2730))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2732),U_2731)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2732),U_2730))) ),
    inference(definitional_conversion,[status(esa)],[f_923_2]) ).

cnf(f_923_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2731),U_2730))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2732),U_2731)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2732),U_2730))) ),
    inference(clausify,[status(thm)],[f_923_3]) ).

fof(f_924_1,plain,
    ! [A_4,B_5] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,A_4),B_5)),B_5) = A_4,
    inference(fof_nnf,[status(thm)],[fact_817_diff__add__cancel]) ).

fof(f_924_2,plain,
    ! [U_2734,U_2733] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_2734),U_2733)),U_2733) = U_2734,
    inference(variable_rename,[status(thm)],[f_924_1]) ).

fof(f_924_3,plain,
    ! [U_2733,U_2734] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_2734),U_2733)),U_2733) = U_2734,
    inference(definitional_conversion,[status(esa)],[f_924_2]) ).

cnf(f_924_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_2734),U_2733)),U_2733) = U_2734,
    inference(clausify,[status(thm)],[f_924_3]) ).

fof(f_925_1,plain,
    ! [A_3,B_4] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_3),B_4)),B_4) = A_3,
    inference(fof_nnf,[status(thm)],[fact_818_add__diff__cancel]) ).

fof(f_925_2,plain,
    ! [U_2736,U_2735] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2736),U_2735)),U_2735) = U_2736,
    inference(variable_rename,[status(thm)],[f_925_1]) ).

fof(f_925_3,plain,
    ! [U_2735,U_2736] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2736),U_2735)),U_2735) = U_2736,
    inference(definitional_conversion,[status(esa)],[f_925_2]) ).

cnf(f_925_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_2736),U_2735)),U_2735) = U_2736,
    inference(clausify,[status(thm)],[f_925_3]) ).

fof(f_926_1,plain,
    ! [M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N)),
    inference(fof_nnf,[status(thm)],[fact_819_add__Suc__right]) ).

fof(f_926_2,plain,
    ! [U_2738,U_2737] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2738),hAPP_nat_nat(suc,U_2737)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2738),U_2737)),
    inference(variable_rename,[status(thm)],[f_926_1]) ).

fof(f_926_3,plain,
    ! [U_2737,U_2738] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2738),hAPP_nat_nat(suc,U_2737)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2738),U_2737)),
    inference(definitional_conversion,[status(esa)],[f_926_2]) ).

cnf(f_926_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2738),hAPP_nat_nat(suc,U_2737)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2738),U_2737)),
    inference(clausify,[status(thm)],[f_926_3]) ).

fof(f_927_1,plain,
    ! [M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_1)),N) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N)),
    inference(fof_nnf,[status(thm)],[fact_820_add__Suc]) ).

fof(f_927_2,plain,
    ! [U_2740,U_2739] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,U_2740)),U_2739) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2740),U_2739)),
    inference(variable_rename,[status(thm)],[f_927_1]) ).

fof(f_927_3,plain,
    ! [U_2739,U_2740] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,U_2740)),U_2739) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2740),U_2739)),
    inference(definitional_conversion,[status(esa)],[f_927_2]) ).

cnf(f_927_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,U_2740)),U_2739) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2740),U_2739)),
    inference(clausify,[status(thm)],[f_927_3]) ).

fof(f_928_1,plain,
    ! [M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,M_1)),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(suc,N)),
    inference(fof_nnf,[status(thm)],[fact_821_add__Suc__shift]) ).

fof(f_928_2,plain,
    ! [U_2742,U_2741] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,U_2742)),U_2741) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2742),hAPP_nat_nat(suc,U_2741)),
    inference(variable_rename,[status(thm)],[f_928_1]) ).

fof(f_928_3,plain,
    ! [U_2741,U_2742] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,U_2742)),U_2741) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2742),hAPP_nat_nat(suc,U_2741)),
    inference(definitional_conversion,[status(esa)],[f_928_2]) ).

cnf(f_928_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(suc,U_2742)),U_2741) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2742),hAPP_nat_nat(suc,U_2741)),
    inference(clausify,[status(thm)],[f_928_3]) ).

fof(f_929_1,plain,
    ! [N,M_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N))),
    inference(fof_nnf,[status(thm)],[fact_822_le__add2]) ).

fof(f_929_2,plain,
    ! [U_2744,U_2743] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2744),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2743),U_2744))),
    inference(variable_rename,[status(thm)],[f_929_1]) ).

fof(f_929_3,plain,
    ! [U_2743,U_2744] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2744),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2743),U_2744))),
    inference(definitional_conversion,[status(esa)],[f_929_2]) ).

cnf(f_929_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2744),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2743),U_2744))),
    inference(clausify,[status(thm)],[f_929_3]) ).

fof(f_930_1,plain,
    ! [N,M_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M_1))),
    inference(fof_nnf,[status(thm)],[fact_823_le__add1]) ).

fof(f_930_2,plain,
    ! [U_2746,U_2745] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2746),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2746),U_2745))),
    inference(variable_rename,[status(thm)],[f_930_1]) ).

fof(f_930_3,plain,
    ! [U_2745,U_2746] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2746),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2746),U_2745))),
    inference(definitional_conversion,[status(esa)],[f_930_2]) ).

cnf(f_930_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2746),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2746),U_2745))),
    inference(clausify,[status(thm)],[f_930_3]) ).

fof(f_931_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
        | ! [K_2] : Na != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K_2) )
      & ( ? [K_2] : Na = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K_2)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_824_le__iff__add]) ).

fof(f_931_2,plain,
    ! [U_2750,U_2749] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2750),U_2749))
        | ! [U_2748] : U_2749 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2750),U_2748) )
      & ( ? [U_2747] : U_2749 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2750),U_2747)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2750),U_2749)) ) ),
    inference(variable_rename,[status(thm)],[f_931_1]) ).

fof(f_931_3,plain,
    ( ! [U_2754,U_2752] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2754),U_2752))
        | ! [U_2748] : U_2752 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2754),U_2748) )
    & ! [U_2753,U_2751] :
        ( ? [U_2747] : U_2751 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2753),U_2747)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2753),U_2751)) ) ),
    inference(miniscope,[status(thm)],[f_931_2]) ).

fof(f_931_4,plain,
    ( ! [U_2754,U_2752] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2754),U_2752))
        | ! [U_2748] : U_2752 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2754),U_2748) )
    & ! [U_2753,U_2751] :
        ( U_2751 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2753),sK162(U_2753,U_2751))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2753),U_2751)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK162]),skolemize(U_2747,sK162(U_2753,U_2751))],[f_931_3]) ).

fof(f_931_5,plain,
    ( ! [U_2748,U_2752,U_2754] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2754),U_2752))
        | U_2752 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2754),U_2748) )
    & ! [U_2753,U_2751] :
        ( U_2751 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2753),sK162(U_2753,U_2751))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2753),U_2751)) ) ),
    inference(definitional_conversion,[status(esa)],[f_931_4]) ).

cnf(f_931_6,plain,
    ( U_2751 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2753),sK162(U_2753,U_2751))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2753),U_2751)) ),
    inference(clausify,[status(thm)],[f_931_5]) ).

cnf(f_931_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2754),U_2752))
    | U_2752 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2754),U_2748) ),
    inference(clausify,[status(thm)],[f_931_5]) ).

fof(f_932_1,plain,
    ! [K,M,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_825_nat__add__left__cancel__le]) ).

fof(f_932_2,plain,
    ! [U_2757,U_2756,U_2755] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2757),U_2756)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2757),U_2755)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2756),U_2755)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2756),U_2755))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2757),U_2756)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2757),U_2755))) ) ),
    inference(variable_rename,[status(thm)],[f_932_1]) ).

fof(f_932_3,plain,
    ( ! [U_2763,U_2761,U_2759] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2763),U_2761)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2763),U_2759)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2761),U_2759)) )
    & ! [U_2762,U_2760,U_2758] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2760),U_2758))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2762),U_2760)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2762),U_2758))) ) ),
    inference(miniscope,[status(thm)],[f_932_2]) ).

fof(f_932_4,plain,
    ( ! [U_2759,U_2761,U_2763] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2763),U_2761)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2763),U_2759)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2761),U_2759)) )
    & ! [U_2758,U_2760,U_2762] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2760),U_2758))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2762),U_2760)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2762),U_2758))) ) ),
    inference(definitional_conversion,[status(esa)],[f_932_3]) ).

cnf(f_932_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2760),U_2758))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2762),U_2760)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2762),U_2758))) ),
    inference(clausify,[status(thm)],[f_932_4]) ).

cnf(f_932_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2763),U_2761)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2763),U_2759)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2761),U_2759)) ),
    inference(clausify,[status(thm)],[f_932_4]) ).

fof(f_933_1,plain,
    ! [M_1,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),M_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_826_trans__le__add1]) ).

fof(f_933_2,plain,
    ! [U_2766,U_2765,U_2764] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2765),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2764),U_2766)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2765),U_2764)) ),
    inference(variable_rename,[status(thm)],[f_933_1]) ).

fof(f_933_3,plain,
    ! [U_2765,U_2764,U_2766] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2765),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2764),U_2766)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2765),U_2764)) ),
    inference(definitional_conversion,[status(esa)],[f_933_2]) ).

cnf(f_933_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2765),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2764),U_2766)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2765),U_2764)) ),
    inference(clausify,[status(thm)],[f_933_3]) ).

fof(f_934_1,plain,
    ! [M_1,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),J)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_827_trans__le__add2]) ).

fof(f_934_2,plain,
    ! [U_2769,U_2768,U_2767] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2768),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2769),U_2767)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2768),U_2767)) ),
    inference(variable_rename,[status(thm)],[f_934_1]) ).

fof(f_934_3,plain,
    ! [U_2767,U_2768,U_2769] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2768),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2769),U_2767)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2768),U_2767)) ),
    inference(definitional_conversion,[status(esa)],[f_934_2]) ).

cnf(f_934_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2768),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2769),U_2767)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2768),U_2767)) ),
    inference(clausify,[status(thm)],[f_934_3]) ).

fof(f_935_1,plain,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_828_add__le__mono1]) ).

fof(f_935_2,plain,
    ! [U_2772,U_2771,U_2770] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2771),U_2772)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2770),U_2772)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2771),U_2770)) ),
    inference(variable_rename,[status(thm)],[f_935_1]) ).

fof(f_935_3,plain,
    ! [U_2770,U_2771,U_2772] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2771),U_2772)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2770),U_2772)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2771),U_2770)) ),
    inference(definitional_conversion,[status(esa)],[f_935_2]) ).

cnf(f_935_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2771),U_2772)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2770),U_2772)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2771),U_2770)) ),
    inference(clausify,[status(thm)],[f_935_3]) ).

fof(f_936_1,plain,
    ! [K_1,L_1,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),L_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),L_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_829_add__le__mono]) ).

fof(f_936_2,plain,
    ! [U_2776,U_2775,U_2774,U_2773] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2774),U_2776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2773),U_2775)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2776),U_2775))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2774),U_2773)) ),
    inference(variable_rename,[status(thm)],[f_936_1]) ).

fof(f_936_3,plain,
    ! [U_2773,U_2774,U_2775,U_2776] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2774),U_2776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2773),U_2775)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2776),U_2775))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2774),U_2773)) ),
    inference(definitional_conversion,[status(esa)],[f_936_2]) ).

cnf(f_936_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2774),U_2776)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2773),U_2775)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2776),U_2775))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2774),U_2773)) ),
    inference(clausify,[status(thm)],[f_936_3]) ).

fof(f_937_1,plain,
    ! [M_1,K_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_830_add__leD2]) ).

fof(f_937_2,plain,
    ! [U_2779,U_2778,U_2777] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2778),U_2777))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2779),U_2778)),U_2777)) ),
    inference(variable_rename,[status(thm)],[f_937_1]) ).

fof(f_937_3,plain,
    ! [U_2777,U_2778,U_2779] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2778),U_2777))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2779),U_2778)),U_2777)) ),
    inference(definitional_conversion,[status(esa)],[f_937_2]) ).

cnf(f_937_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2778),U_2777))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2779),U_2778)),U_2777)) ),
    inference(clausify,[status(thm)],[f_937_3]) ).

fof(f_938_1,plain,
    ! [M_1,K_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_831_add__leD1]) ).

fof(f_938_2,plain,
    ! [U_2782,U_2781,U_2780] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2782),U_2780))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2782),U_2781)),U_2780)) ),
    inference(variable_rename,[status(thm)],[f_938_1]) ).

fof(f_938_3,plain,
    ! [U_2780,U_2781,U_2782] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2782),U_2780))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2782),U_2781)),U_2780)) ),
    inference(definitional_conversion,[status(esa)],[f_938_2]) ).

cnf(f_938_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2782),U_2780))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2782),U_2781)),U_2780)) ),
    inference(clausify,[status(thm)],[f_938_3]) ).

fof(f_939_1,plain,
    ! [M_1,K_1,N] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_832_add__leE]) ).

fof(f_939_2,plain,
    ! [U_2785,U_2784,U_2783] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2784),U_2783))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2785),U_2783)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2785),U_2784)),U_2783)) ),
    inference(variable_rename,[status(thm)],[f_939_1]) ).

fof(f_939_3,plain,
    ( ! [U_2783,U_2784,U_2785] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2784),U_2783))
        | ~ sP244(U_2783,U_2784,U_2785) )
    & ! [U_2783,U_2784,U_2785] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2785),U_2783))
        | ~ sP244(U_2783,U_2784,U_2785) )
    & ! [U_2783,U_2784,U_2785] :
        ( sP244(U_2783,U_2784,U_2785)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2785),U_2784)),U_2783)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP244])],[f_939_2]) ).

cnf(f_939_4,plain,
    ( sP244(U_2783,U_2784,U_2785)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2785),U_2784)),U_2783)) ),
    inference(clausify,[status(thm)],[f_939_3]) ).

cnf(f_939_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2785),U_2783))
    | ~ sP244(U_2783,U_2784,U_2785) ),
    inference(clausify,[status(thm)],[f_939_3]) ).

cnf(f_939_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2784),U_2783))
    | ~ sP244(U_2783,U_2784,U_2785) ),
    inference(clausify,[status(thm)],[f_939_3]) ).

fof(f_940_1,plain,
    ! [M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N)),N) = M_1,
    inference(fof_nnf,[status(thm)],[fact_833_diff__add__inverse2]) ).

fof(f_940_2,plain,
    ! [U_2787,U_2786] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2787),U_2786)),U_2786) = U_2787,
    inference(variable_rename,[status(thm)],[f_940_1]) ).

fof(f_940_3,plain,
    ! [U_2786,U_2787] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2787),U_2786)),U_2786) = U_2787,
    inference(definitional_conversion,[status(esa)],[f_940_2]) ).

cnf(f_940_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2787),U_2786)),U_2786) = U_2787,
    inference(clausify,[status(thm)],[f_940_3]) ).

fof(f_941_1,plain,
    ! [N,M_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M_1)),N) = M_1,
    inference(fof_nnf,[status(thm)],[fact_834_diff__add__inverse]) ).

fof(f_941_2,plain,
    ! [U_2789,U_2788] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2789),U_2788)),U_2789) = U_2788,
    inference(variable_rename,[status(thm)],[f_941_1]) ).

fof(f_941_3,plain,
    ! [U_2788,U_2789] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2789),U_2788)),U_2789) = U_2788,
    inference(definitional_conversion,[status(esa)],[f_941_2]) ).

cnf(f_941_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2789),U_2788)),U_2789) = U_2788,
    inference(clausify,[status(thm)],[f_941_3]) ).

fof(f_942_1,plain,
    ! [I_1,J,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),J)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K_1)),
    inference(fof_nnf,[status(thm)],[fact_835_diff__diff__left]) ).

fof(f_942_2,plain,
    ! [U_2792,U_2791,U_2790] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2792),U_2791)),U_2790) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2792),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2791),U_2790)),
    inference(variable_rename,[status(thm)],[f_942_1]) ).

fof(f_942_3,plain,
    ! [U_2790,U_2791,U_2792] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2792),U_2791)),U_2790) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2792),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2791),U_2790)),
    inference(definitional_conversion,[status(esa)],[f_942_2]) ).

cnf(f_942_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2792),U_2791)),U_2790) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2792),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2791),U_2790)),
    inference(clausify,[status(thm)],[f_942_3]) ).

fof(f_943_1,plain,
    ! [K_1,M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N),
    inference(fof_nnf,[status(thm)],[fact_836_diff__cancel]) ).

fof(f_943_2,plain,
    ! [U_2795,U_2794,U_2793] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2795),U_2794)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2795),U_2793)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2794),U_2793),
    inference(variable_rename,[status(thm)],[f_943_1]) ).

fof(f_943_3,plain,
    ! [U_2793,U_2794,U_2795] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2795),U_2794)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2795),U_2793)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2794),U_2793),
    inference(definitional_conversion,[status(esa)],[f_943_2]) ).

cnf(f_943_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2795),U_2794)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2795),U_2793)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2794),U_2793),
    inference(clausify,[status(thm)],[f_943_3]) ).

fof(f_944_1,plain,
    ! [M_1,K_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N),
    inference(fof_nnf,[status(thm)],[fact_837_diff__cancel2]) ).

fof(f_944_2,plain,
    ! [U_2798,U_2797,U_2796] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2798),U_2797)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2796),U_2797)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2798),U_2796),
    inference(variable_rename,[status(thm)],[f_944_1]) ).

fof(f_944_3,plain,
    ! [U_2796,U_2797,U_2798] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2798),U_2797)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2796),U_2797)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2798),U_2796),
    inference(definitional_conversion,[status(esa)],[f_944_2]) ).

cnf(f_944_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2798),U_2797)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2796),U_2797)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2798),U_2796),
    inference(clausify,[status(thm)],[f_944_3]) ).

fof(f_945_1,plain,
    ! [I_1,K_1,J] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),J)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_838_diff__diff__right]) ).

fof(f_945_2,plain,
    ! [U_2801,U_2800,U_2799] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2801),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2799),U_2800)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2801),U_2800)),U_2799)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2800),U_2799)) ),
    inference(variable_rename,[status(thm)],[f_945_1]) ).

fof(f_945_3,plain,
    ! [U_2799,U_2800,U_2801] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2801),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2799),U_2800)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2801),U_2800)),U_2799)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2800),U_2799)) ),
    inference(definitional_conversion,[status(esa)],[f_945_2]) ).

cnf(f_945_4,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2801),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2799),U_2800)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2801),U_2800)),U_2799)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2800),U_2799)) ),
    inference(clausify,[status(thm)],[f_945_3]) ).

fof(f_946_1,plain,
    ! [J_1,K,I_2] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K)),I_2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K)),I_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_839_le__diff__conv]) ).

fof(f_946_2,plain,
    ! [U_2804,U_2803,U_2802] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2804),U_2803)),U_2802))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2804),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2802),U_2803))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2804),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2802),U_2803)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2804),U_2803)),U_2802)) ) ),
    inference(variable_rename,[status(thm)],[f_946_1]) ).

fof(f_946_3,plain,
    ( ! [U_2810,U_2808,U_2806] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2810),U_2808)),U_2806))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2810),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2806),U_2808))) )
    & ! [U_2809,U_2807,U_2805] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2809),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2805),U_2807)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2809),U_2807)),U_2805)) ) ),
    inference(miniscope,[status(thm)],[f_946_2]) ).

fof(f_946_4,plain,
    ( ! [U_2806,U_2808,U_2810] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2810),U_2808)),U_2806))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2810),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2806),U_2808))) )
    & ! [U_2807,U_2805,U_2809] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2809),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2805),U_2807)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2809),U_2807)),U_2805)) ) ),
    inference(definitional_conversion,[status(esa)],[f_946_3]) ).

cnf(f_946_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2809),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2805),U_2807)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2809),U_2807)),U_2805)) ),
    inference(clausify,[status(thm)],[f_946_4]) ).

cnf(f_946_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2810),U_2808)),U_2806))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2810),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2806),U_2808))) ),
    inference(clausify,[status(thm)],[f_946_4]) ).

fof(f_947_1,plain,
    ! [M_1,K_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M_1)),K_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_840_le__add__diff]) ).

fof(f_947_2,plain,
    ! [U_2813,U_2812,U_2811] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2813),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2811),U_2813)),U_2812)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2812),U_2811)) ),
    inference(variable_rename,[status(thm)],[f_947_1]) ).

fof(f_947_3,plain,
    ! [U_2811,U_2813,U_2812] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2813),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2811),U_2813)),U_2812)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2812),U_2811)) ),
    inference(definitional_conversion,[status(esa)],[f_947_2]) ).

cnf(f_947_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2813),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2811),U_2813)),U_2812)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2812),U_2811)) ),
    inference(clausify,[status(thm)],[f_947_3]) ).

fof(f_948_1,plain,
    ! [N,M_1] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)) = M_1
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_841_le__add__diff__inverse]) ).

fof(f_948_2,plain,
    ! [U_2815,U_2814] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2815),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2814),U_2815)) = U_2814
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2815),U_2814)) ),
    inference(variable_rename,[status(thm)],[f_948_1]) ).

fof(f_948_3,plain,
    ! [U_2814,U_2815] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2815),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2814),U_2815)) = U_2814
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2815),U_2814)) ),
    inference(definitional_conversion,[status(esa)],[f_948_2]) ).

cnf(f_948_4,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2815),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2814),U_2815)) = U_2814
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2815),U_2814)) ),
    inference(clausify,[status(thm)],[f_948_3]) ).

fof(f_949_1,plain,
    ! [I_1,K_1,J] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),K_1)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_842_add__diff__assoc]) ).

fof(f_949_2,plain,
    ! [U_2818,U_2817,U_2816] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2818),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2816),U_2817)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2818),U_2816)),U_2817)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2817),U_2816)) ),
    inference(variable_rename,[status(thm)],[f_949_1]) ).

fof(f_949_3,plain,
    ! [U_2816,U_2817,U_2818] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2818),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2816),U_2817)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2818),U_2816)),U_2817)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2817),U_2816)) ),
    inference(definitional_conversion,[status(esa)],[f_949_2]) ).

cnf(f_949_4,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2818),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2816),U_2817)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2818),U_2816)),U_2817)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2817),U_2816)) ),
    inference(clausify,[status(thm)],[f_949_3]) ).

fof(f_950_1,plain,
    ! [I_2,K,J_1] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K)),J_1)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K)),J_1))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_843_le__diff__conv2]) ).

fof(f_950_2,plain,
    ! [U_2821,U_2820,U_2819] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2821),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2819),U_2820)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2821),U_2820)),U_2819)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2821),U_2820)),U_2819))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2821),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2819),U_2820))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2820),U_2819)) ),
    inference(variable_rename,[status(thm)],[f_950_1]) ).

fof(f_950_3,plain,
    ( ! [U_2819,U_2820,U_2821] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2821),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2819),U_2820)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2821),U_2820)),U_2819))
        | ~ sP245(U_2819,U_2820,U_2821) )
    & ! [U_2819,U_2820,U_2821] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2821),U_2820)),U_2819))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2821),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2819),U_2820)))
        | ~ sP245(U_2819,U_2820,U_2821) )
    & ! [U_2819,U_2820,U_2821] :
        ( sP245(U_2819,U_2820,U_2821)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2820),U_2819)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP245])],[f_950_2]) ).

cnf(f_950_4,plain,
    ( sP245(U_2819,U_2820,U_2821)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2820),U_2819)) ),
    inference(clausify,[status(thm)],[f_950_3]) ).

cnf(f_950_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2821),U_2820)),U_2819))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2821),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2819),U_2820)))
    | ~ sP245(U_2819,U_2820,U_2821) ),
    inference(clausify,[status(thm)],[f_950_3]) ).

cnf(f_950_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2821),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2819),U_2820)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2821),U_2820)),U_2819))
    | ~ sP245(U_2819,U_2820,U_2821) ),
    inference(clausify,[status(thm)],[f_950_3]) ).

fof(f_951_1,plain,
    ! [N,M_1] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)),N) = M_1
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_844_le__add__diff__inverse2]) ).

fof(f_951_2,plain,
    ! [U_2823,U_2822] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2822),U_2823)),U_2823) = U_2822
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2823),U_2822)) ),
    inference(variable_rename,[status(thm)],[f_951_1]) ).

fof(f_951_3,plain,
    ! [U_2823,U_2822] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2822),U_2823)),U_2823) = U_2822
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2823),U_2822)) ),
    inference(definitional_conversion,[status(esa)],[f_951_2]) ).

cnf(f_951_4,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2822),U_2823)),U_2823) = U_2822
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2823),U_2822)) ),
    inference(clausify,[status(thm)],[f_951_3]) ).

fof(f_952_1,plain,
    ! [K,I_2,J_1] :
      ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),I_2) = K
          | J_1 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),I_2) )
        & ( J_1 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),I_2)
          | hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),I_2) != K ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_845_le__imp__diff__is__add]) ).

fof(f_952_2,plain,
    ! [U_2826,U_2825,U_2824] :
      ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2824),U_2825) = U_2826
          | U_2824 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2826),U_2825) )
        & ( U_2824 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2826),U_2825)
          | hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2824),U_2825) != U_2826 ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2825),U_2824)) ),
    inference(variable_rename,[status(thm)],[f_952_1]) ).

fof(f_952_3,plain,
    ( ! [U_2824,U_2825,U_2826] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2824),U_2825) = U_2826
        | U_2824 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2826),U_2825)
        | ~ sP246(U_2824,U_2825,U_2826) )
    & ! [U_2824,U_2825,U_2826] :
        ( U_2824 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2826),U_2825)
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2824),U_2825) != U_2826
        | ~ sP246(U_2824,U_2825,U_2826) )
    & ! [U_2824,U_2825,U_2826] :
        ( sP246(U_2824,U_2825,U_2826)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2825),U_2824)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP246])],[f_952_2]) ).

cnf(f_952_4,plain,
    ( sP246(U_2824,U_2825,U_2826)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2825),U_2824)) ),
    inference(clausify,[status(thm)],[f_952_3]) ).

cnf(f_952_5,plain,
    ( U_2824 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2826),U_2825)
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2824),U_2825) != U_2826
    | ~ sP246(U_2824,U_2825,U_2826) ),
    inference(clausify,[status(thm)],[f_952_3]) ).

cnf(f_952_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2824),U_2825) = U_2826
    | U_2824 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2826),U_2825)
    | ~ sP246(U_2824,U_2825,U_2826) ),
    inference(clausify,[status(thm)],[f_952_3]) ).

fof(f_953_1,plain,
    ! [I_1,K_1,J] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_846_diff__add__assoc]) ).

fof(f_953_2,plain,
    ! [U_2829,U_2828,U_2827] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2829),U_2827)),U_2828) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2829),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2827),U_2828))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2828),U_2827)) ),
    inference(variable_rename,[status(thm)],[f_953_1]) ).

fof(f_953_3,plain,
    ! [U_2828,U_2829,U_2827] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2829),U_2827)),U_2828) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2829),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2827),U_2828))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2828),U_2827)) ),
    inference(definitional_conversion,[status(esa)],[f_953_2]) ).

cnf(f_953_4,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2829),U_2827)),U_2828) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2829),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2827),U_2828))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2828),U_2827)) ),
    inference(clausify,[status(thm)],[f_953_3]) ).

fof(f_954_1,plain,
    ! [I_1,K_1,J] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)),I_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),I_1)),K_1)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_847_add__diff__assoc2]) ).

fof(f_954_2,plain,
    ! [U_2832,U_2831,U_2830] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2830),U_2831)),U_2832) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2830),U_2832)),U_2831)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2831),U_2830)) ),
    inference(variable_rename,[status(thm)],[f_954_1]) ).

fof(f_954_3,plain,
    ! [U_2830,U_2831,U_2832] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2830),U_2831)),U_2832) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2830),U_2832)),U_2831)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2831),U_2830)) ),
    inference(definitional_conversion,[status(esa)],[f_954_2]) ).

cnf(f_954_4,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2830),U_2831)),U_2832) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2830),U_2832)),U_2831)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2831),U_2830)) ),
    inference(clausify,[status(thm)],[f_954_3]) ).

fof(f_955_1,plain,
    ! [I_1,K_1,J] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),I_1)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1)),I_1)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_848_diff__add__assoc2]) ).

fof(f_955_2,plain,
    ! [U_2835,U_2834,U_2833] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2833),U_2835)),U_2834) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2833),U_2834)),U_2835)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2834),U_2833)) ),
    inference(variable_rename,[status(thm)],[f_955_1]) ).

fof(f_955_3,plain,
    ! [U_2833,U_2834,U_2835] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2833),U_2835)),U_2834) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2833),U_2834)),U_2835)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2834),U_2833)) ),
    inference(definitional_conversion,[status(esa)],[f_955_2]) ).

cnf(f_955_4,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2833),U_2835)),U_2834) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2833),U_2834)),U_2835)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2834),U_2833)) ),
    inference(clausify,[status(thm)],[f_955_3]) ).

fof(f_956_1,plain,
    ! [N] : hAPP_nat_nat(suc,N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N),
    inference(fof_nnf,[status(thm)],[fact_849_Suc__eq__plus1__left]) ).

fof(f_956_2,plain,
    ! [U_2836] : hAPP_nat_nat(suc,U_2836) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),U_2836),
    inference(variable_rename,[status(thm)],[f_956_1]) ).

fof(f_956_3,plain,
    ! [U_2836] : hAPP_nat_nat(suc,U_2836) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),U_2836),
    inference(definitional_conversion,[status(esa)],[f_956_2]) ).

cnf(f_956_4,plain,
    hAPP_nat_nat(suc,U_2836) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),U_2836),
    inference(clausify,[status(thm)],[f_956_3]) ).

fof(f_957_1,plain,
    ! [N] : hAPP_nat_nat(suc,N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),one_one_nat),
    inference(fof_nnf,[status(thm)],[fact_850_Suc__eq__plus1]) ).

fof(f_957_2,plain,
    ! [U_2837] : hAPP_nat_nat(suc,U_2837) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2837),one_one_nat),
    inference(variable_rename,[status(thm)],[f_957_1]) ).

fof(f_957_3,plain,
    ! [U_2837] : hAPP_nat_nat(suc,U_2837) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2837),one_one_nat),
    inference(definitional_conversion,[status(esa)],[f_957_2]) ).

cnf(f_957_4,plain,
    hAPP_nat_nat(suc,U_2837) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2837),one_one_nat),
    inference(clausify,[status(thm)],[f_957_3]) ).

fof(f_958_1,plain,
    ! [M_1,K_1,J] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_1)),hAPP_nat_nat(suc,J))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_851_diff__Suc__diff__eq1]) ).

fof(f_958_2,plain,
    ! [U_2840,U_2839,U_2838] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2840),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2838),U_2839))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2840),U_2839)),hAPP_nat_nat(suc,U_2838))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2839),U_2838)) ),
    inference(variable_rename,[status(thm)],[f_958_1]) ).

fof(f_958_3,plain,
    ! [U_2838,U_2839,U_2840] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2840),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2838),U_2839))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2840),U_2839)),hAPP_nat_nat(suc,U_2838))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2839),U_2838)) ),
    inference(definitional_conversion,[status(esa)],[f_958_2]) ).

cnf(f_958_4,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2840),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2838),U_2839))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2840),U_2839)),hAPP_nat_nat(suc,U_2838))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2839),U_2838)) ),
    inference(clausify,[status(thm)],[f_958_3]) ).

fof(f_959_1,plain,
    ! [M_1,K_1,J] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),K_1))),M_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,J)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),M_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_852_diff__Suc__diff__eq2]) ).

fof(f_959_2,plain,
    ! [U_2843,U_2842,U_2841] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2841),U_2842))),U_2843) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,U_2841)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2842),U_2843))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2842),U_2841)) ),
    inference(variable_rename,[status(thm)],[f_959_1]) ).

fof(f_959_3,plain,
    ! [U_2841,U_2842,U_2843] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2841),U_2842))),U_2843) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,U_2841)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2842),U_2843))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2842),U_2841)) ),
    inference(definitional_conversion,[status(esa)],[f_959_2]) ).

cnf(f_959_4,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2841),U_2842))),U_2843) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(suc,U_2841)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2842),U_2843))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2842),U_2841)) ),
    inference(clausify,[status(thm)],[f_959_3]) ).

fof(f_960_1,plain,
    ! [Y,X,Z] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Z)) ),
    inference(fof_nnf,[status(thm)],[fact_853_termination__basic__simps_I4_J]) ).

fof(f_960_2,plain,
    ! [U_2846,U_2845,U_2844] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2845),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2846),U_2844)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2845),U_2844)) ),
    inference(variable_rename,[status(thm)],[f_960_1]) ).

fof(f_960_3,plain,
    ! [U_2844,U_2845,U_2846] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2845),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2846),U_2844)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2845),U_2844)) ),
    inference(definitional_conversion,[status(esa)],[f_960_2]) ).

cnf(f_960_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2845),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2846),U_2844)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2845),U_2844)) ),
    inference(clausify,[status(thm)],[f_960_3]) ).

fof(f_961_1,plain,
    ! [Z,X,Y] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y)) ),
    inference(fof_nnf,[status(thm)],[fact_854_termination__basic__simps_I3_J]) ).

fof(f_961_2,plain,
    ! [U_2849,U_2848,U_2847] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2848),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2847),U_2849)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2848),U_2847)) ),
    inference(variable_rename,[status(thm)],[f_961_1]) ).

fof(f_961_3,plain,
    ! [U_2847,U_2848,U_2849] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2848),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2847),U_2849)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2848),U_2847)) ),
    inference(definitional_conversion,[status(esa)],[f_961_2]) ).

cnf(f_961_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2848),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2847),U_2849)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2848),U_2847)) ),
    inference(clausify,[status(thm)],[f_961_3]) ).

fof(f_962_1,plain,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,N))),
    inference(fof_nnf,[status(thm)],[fact_855_lessI]) ).

fof(f_962_2,plain,
    ! [U_2850] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2850),hAPP_nat_nat(suc,U_2850))),
    inference(variable_rename,[status(thm)],[f_962_1]) ).

fof(f_962_3,plain,
    ! [U_2850] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2850),hAPP_nat_nat(suc,U_2850))),
    inference(definitional_conversion,[status(esa)],[f_962_2]) ).

cnf(f_962_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2850),hAPP_nat_nat(suc,U_2850))),
    inference(clausify,[status(thm)],[f_962_3]) ).

fof(f_963_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_856_Suc__mono]) ).

fof(f_963_2,plain,
    ! [U_2852,U_2851] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2852)),hAPP_nat_nat(suc,U_2851)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2852),U_2851)) ),
    inference(variable_rename,[status(thm)],[f_963_1]) ).

fof(f_963_3,plain,
    ! [U_2851,U_2852] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2852)),hAPP_nat_nat(suc,U_2851)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2852),U_2851)) ),
    inference(definitional_conversion,[status(esa)],[f_963_2]) ).

cnf(f_963_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2852)),hAPP_nat_nat(suc,U_2851)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2852),U_2851)) ),
    inference(clausify,[status(thm)],[f_963_3]) ).

fof(f_964_1,plain,
    ! [K] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),K)))),
    inference(fof_nnf,[status(thm)],[fact_857_finite__Collect__less__nat]) ).

fof(f_964_2,plain,
    ! [U_2853] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_2853)))),
    inference(variable_rename,[status(thm)],[f_964_1]) ).

fof(f_964_3,plain,
    ! [U_2853] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_2853)))),
    inference(definitional_conversion,[status(esa)],[f_964_2]) ).

cnf(f_964_4,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_2853)))),
    inference(clausify,[status(thm)],[f_964_3]) ).

fof(f_965_1,plain,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N)),
    inference(fof_nnf,[status(thm)],[fact_858_less__not__refl]) ).

fof(f_965_2,plain,
    ! [U_2854] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2854),U_2854)),
    inference(variable_rename,[status(thm)],[f_965_1]) ).

fof(f_965_3,plain,
    ! [U_2854] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2854),U_2854)),
    inference(definitional_conversion,[status(esa)],[f_965_2]) ).

cnf(f_965_4,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2854),U_2854)),
    inference(clausify,[status(thm)],[f_965_3]) ).

fof(f_966_1,plain,
    ! [M,Na] :
      ( ( M != Na
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
        | M = Na ) ),
    inference(fof_nnf,[status(thm)],[fact_859_nat__neq__iff]) ).

fof(f_966_2,plain,
    ! [U_2856,U_2855] :
      ( ( U_2856 != U_2855
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2855),U_2856))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2856),U_2855)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2855),U_2856))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2856),U_2855))
        | U_2856 = U_2855 ) ),
    inference(variable_rename,[status(thm)],[f_966_1]) ).

fof(f_966_3,plain,
    ( ! [U_2860,U_2858] :
        ( U_2860 != U_2858
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2858),U_2860))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2860),U_2858)) ) )
    & ! [U_2859,U_2857] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2857),U_2859))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2859),U_2857))
        | U_2859 = U_2857 ) ),
    inference(miniscope,[status(thm)],[f_966_2]) ).

fof(f_966_4,plain,
    ( ! [U_2860,U_2858] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2858),U_2860))
        | ~ sP247(U_2860,U_2858) )
    & ! [U_2860,U_2858] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2860),U_2858))
        | ~ sP247(U_2860,U_2858) )
    & ! [U_2860,U_2858] :
        ( U_2860 != U_2858
        | sP247(U_2860,U_2858) )
    & ! [U_2859,U_2857] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2857),U_2859))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2859),U_2857))
        | U_2859 = U_2857 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP247])],[f_966_3]) ).

cnf(f_966_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2857),U_2859))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2859),U_2857))
    | U_2859 = U_2857 ),
    inference(clausify,[status(thm)],[f_966_4]) ).

cnf(f_966_6,plain,
    ( U_2860 != U_2858
    | sP247(U_2860,U_2858) ),
    inference(clausify,[status(thm)],[f_966_4]) ).

cnf(f_966_7,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2860),U_2858))
    | ~ sP247(U_2860,U_2858) ),
    inference(clausify,[status(thm)],[f_966_4]) ).

cnf(f_966_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2858),U_2860))
    | ~ sP247(U_2860,U_2858) ),
    inference(clausify,[status(thm)],[f_966_4]) ).

fof(f_967_1,plain,
    ! [X,Y] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Y),X))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y))
      | X = Y ),
    inference(fof_nnf,[status(thm)],[fact_860_linorder__neqE__nat]) ).

fof(f_967_2,plain,
    ! [U_2862,U_2861] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2861),U_2862))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2862),U_2861))
      | U_2862 = U_2861 ),
    inference(variable_rename,[status(thm)],[f_967_1]) ).

fof(f_967_3,plain,
    ! [U_2861,U_2862] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2861),U_2862))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2862),U_2861))
      | U_2862 = U_2861 ),
    inference(definitional_conversion,[status(esa)],[f_967_2]) ).

cnf(f_967_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2861),U_2862))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2862),U_2861))
    | U_2862 = U_2861 ),
    inference(clausify,[status(thm)],[f_967_3]) ).

fof(f_968_1,plain,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),N)),
    inference(fof_nnf,[status(thm)],[fact_861_less__irrefl__nat]) ).

fof(f_968_2,plain,
    ! [U_2863] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2863),U_2863)),
    inference(variable_rename,[status(thm)],[f_968_1]) ).

fof(f_968_3,plain,
    ! [U_2863] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2863),U_2863)),
    inference(definitional_conversion,[status(esa)],[f_968_2]) ).

cnf(f_968_4,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2863),U_2863)),
    inference(clausify,[status(thm)],[f_968_3]) ).

fof(f_969_1,plain,
    ! [N,M_1] :
      ( M_1 != N
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_862_less__not__refl2]) ).

fof(f_969_2,plain,
    ! [U_2865,U_2864] :
      ( U_2864 != U_2865
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2865),U_2864)) ),
    inference(variable_rename,[status(thm)],[f_969_1]) ).

fof(f_969_3,plain,
    ! [U_2865,U_2864] :
      ( U_2864 != U_2865
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2865),U_2864)) ),
    inference(definitional_conversion,[status(esa)],[f_969_2]) ).

cnf(f_969_4,plain,
    ( U_2864 != U_2865
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2865),U_2864)) ),
    inference(clausify,[status(thm)],[f_969_3]) ).

fof(f_970_1,plain,
    ! [S,T] :
      ( S != T
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,S),T)) ),
    inference(fof_nnf,[status(thm)],[fact_863_less__not__refl3]) ).

fof(f_970_2,plain,
    ! [U_2867,U_2866] :
      ( U_2867 != U_2866
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2867),U_2866)) ),
    inference(variable_rename,[status(thm)],[f_970_1]) ).

fof(f_970_3,plain,
    ! [U_2867,U_2866] :
      ( U_2867 != U_2866
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2867),U_2866)) ),
    inference(definitional_conversion,[status(esa)],[f_970_2]) ).

cnf(f_970_4,plain,
    ( U_2867 != U_2866
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2867),U_2866)) ),
    inference(clausify,[status(thm)],[f_970_3]) ).

fof(f_971_1,plain,
    ! [Pa,M,Na] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M)) )
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M))
        & M = Na )
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(Pa,Na),M))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_864_nat__less__cases]) ).

fof(f_971_2,plain,
    ! [U_2870,U_2869,U_2868] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2870,U_2868),U_2869))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2870,U_2868),U_2869))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2868),U_2869)) )
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2870,U_2868),U_2869))
        & U_2869 = U_2868 )
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2870,U_2868),U_2869))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2869),U_2868)) ) ),
    inference(variable_rename,[status(thm)],[f_971_1]) ).

fof(f_971_3,plain,
    ( ! [U_2868,U_2869,U_2870] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2870,U_2868),U_2869))
        | ~ sP250(U_2868,U_2869,U_2870) )
    & ! [U_2868,U_2869,U_2870] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2868),U_2869))
        | ~ sP250(U_2868,U_2869,U_2870) )
    & ! [U_2868,U_2869,U_2870] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2870,U_2868),U_2869))
        | ~ sP249(U_2868,U_2869,U_2870) )
    & ! [U_2868,U_2869,U_2870] :
        ( U_2869 = U_2868
        | ~ sP249(U_2868,U_2869,U_2870) )
    & ! [U_2868,U_2869,U_2870] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2870,U_2868),U_2869))
        | ~ sP248(U_2868,U_2869,U_2870) )
    & ! [U_2868,U_2869,U_2870] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2869),U_2868))
        | ~ sP248(U_2868,U_2869,U_2870) )
    & ! [U_2868,U_2869,U_2870] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2870,U_2868),U_2869))
        | sP250(U_2868,U_2869,U_2870)
        | sP249(U_2868,U_2869,U_2870)
        | sP248(U_2868,U_2869,U_2870) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP248,sP249,sP250])],[f_971_2]) ).

cnf(f_971_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2870,U_2868),U_2869))
    | sP250(U_2868,U_2869,U_2870)
    | sP249(U_2868,U_2869,U_2870)
    | sP248(U_2868,U_2869,U_2870) ),
    inference(clausify,[status(thm)],[f_971_3]) ).

cnf(f_971_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2869),U_2868))
    | ~ sP248(U_2868,U_2869,U_2870) ),
    inference(clausify,[status(thm)],[f_971_3]) ).

cnf(f_971_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2870,U_2868),U_2869))
    | ~ sP248(U_2868,U_2869,U_2870) ),
    inference(clausify,[status(thm)],[f_971_3]) ).

cnf(f_971_7,plain,
    ( U_2869 = U_2868
    | ~ sP249(U_2868,U_2869,U_2870) ),
    inference(clausify,[status(thm)],[f_971_3]) ).

cnf(f_971_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2870,U_2868),U_2869))
    | ~ sP249(U_2868,U_2869,U_2870) ),
    inference(clausify,[status(thm)],[f_971_3]) ).

cnf(f_971_9,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2868),U_2869))
    | ~ sP250(U_2868,U_2869,U_2870) ),
    inference(clausify,[status(thm)],[f_971_3]) ).

cnf(f_971_10,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(U_2870,U_2868),U_2869))
    | ~ sP250(U_2868,U_2869,U_2870) ),
    inference(clausify,[status(thm)],[f_971_3]) ).

fof(f_972_1,plain,
    ! [M,Na] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_865_not__less__eq]) ).

fof(f_972_2,plain,
    ! [U_2872,U_2871] :
      ( ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2872),U_2871))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2871),hAPP_nat_nat(suc,U_2872))) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2871),hAPP_nat_nat(suc,U_2872)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2872),U_2871)) ) ),
    inference(variable_rename,[status(thm)],[f_972_1]) ).

fof(f_972_3,plain,
    ( ! [U_2876,U_2874] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2876),U_2874))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2874),hAPP_nat_nat(suc,U_2876))) )
    & ! [U_2875,U_2873] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2873),hAPP_nat_nat(suc,U_2875)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2875),U_2873)) ) ),
    inference(miniscope,[status(thm)],[f_972_2]) ).

fof(f_972_4,plain,
    ( ! [U_2874,U_2876] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2876),U_2874))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2874),hAPP_nat_nat(suc,U_2876))) )
    & ! [U_2873,U_2875] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2873),hAPP_nat_nat(suc,U_2875)))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2875),U_2873)) ) ),
    inference(definitional_conversion,[status(esa)],[f_972_3]) ).

cnf(f_972_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2873),hAPP_nat_nat(suc,U_2875)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2875),U_2873)) ),
    inference(clausify,[status(thm)],[f_972_4]) ).

cnf(f_972_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2876),U_2874))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2874),hAPP_nat_nat(suc,U_2876))) ),
    inference(clausify,[status(thm)],[f_972_4]) ).

fof(f_973_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,Na)))
        | ( M != Na
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) ) )
      & ( M = Na
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_866_less__Suc__eq]) ).

fof(f_973_2,plain,
    ! [U_2878,U_2877] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2878),hAPP_nat_nat(suc,U_2877)))
        | ( U_2878 != U_2877
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2878),U_2877)) ) )
      & ( U_2878 = U_2877
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2878),U_2877))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2878),hAPP_nat_nat(suc,U_2877))) ) ),
    inference(variable_rename,[status(thm)],[f_973_1]) ).

fof(f_973_3,plain,
    ( ! [U_2882,U_2880] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2882),hAPP_nat_nat(suc,U_2880)))
        | ( U_2882 != U_2880
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2882),U_2880)) ) )
    & ! [U_2881,U_2879] :
        ( U_2881 = U_2879
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2881),U_2879))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2881),hAPP_nat_nat(suc,U_2879))) ) ),
    inference(miniscope,[status(thm)],[f_973_2]) ).

fof(f_973_4,plain,
    ( ! [U_2882,U_2880] :
        ( U_2882 != U_2880
        | ~ sP251(U_2882,U_2880) )
    & ! [U_2882,U_2880] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2882),U_2880))
        | ~ sP251(U_2882,U_2880) )
    & ! [U_2882,U_2880] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2882),hAPP_nat_nat(suc,U_2880)))
        | sP251(U_2882,U_2880) )
    & ! [U_2881,U_2879] :
        ( U_2881 = U_2879
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2881),U_2879))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2881),hAPP_nat_nat(suc,U_2879))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP251])],[f_973_3]) ).

cnf(f_973_5,plain,
    ( U_2881 = U_2879
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2881),U_2879))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2881),hAPP_nat_nat(suc,U_2879))) ),
    inference(clausify,[status(thm)],[f_973_4]) ).

cnf(f_973_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2882),hAPP_nat_nat(suc,U_2880)))
    | sP251(U_2882,U_2880) ),
    inference(clausify,[status(thm)],[f_973_4]) ).

cnf(f_973_7,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2882),U_2880))
    | ~ sP251(U_2882,U_2880) ),
    inference(clausify,[status(thm)],[f_973_4]) ).

cnf(f_973_8,plain,
    ( U_2882 != U_2880
    | ~ sP251(U_2882,U_2880) ),
    inference(clausify,[status(thm)],[f_973_4]) ).

fof(f_974_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M)),hAPP_nat_nat(suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_867_Suc__less__eq]) ).

fof(f_974_2,plain,
    ! [U_2884,U_2883] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2884)),hAPP_nat_nat(suc,U_2883)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2884),U_2883)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2884),U_2883))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2884)),hAPP_nat_nat(suc,U_2883))) ) ),
    inference(variable_rename,[status(thm)],[f_974_1]) ).

fof(f_974_3,plain,
    ( ! [U_2888,U_2886] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2888)),hAPP_nat_nat(suc,U_2886)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2888),U_2886)) )
    & ! [U_2887,U_2885] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2887),U_2885))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2887)),hAPP_nat_nat(suc,U_2885))) ) ),
    inference(miniscope,[status(thm)],[f_974_2]) ).

fof(f_974_4,plain,
    ( ! [U_2888,U_2886] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2888)),hAPP_nat_nat(suc,U_2886)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2888),U_2886)) )
    & ! [U_2887,U_2885] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2887),U_2885))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2887)),hAPP_nat_nat(suc,U_2885))) ) ),
    inference(definitional_conversion,[status(esa)],[f_974_3]) ).

cnf(f_974_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2887),U_2885))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2887)),hAPP_nat_nat(suc,U_2885))) ),
    inference(clausify,[status(thm)],[f_974_4]) ).

cnf(f_974_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2888)),hAPP_nat_nat(suc,U_2886)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2888),U_2886)) ),
    inference(clausify,[status(thm)],[f_974_4]) ).

fof(f_975_1,plain,
    ! [Na,M] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M)))
          | Na != M )
        & ( Na = M
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M))) ) )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M)) ),
    inference(fof_nnf,[status(thm)],[fact_868_not__less__less__Suc__eq]) ).

fof(f_975_2,plain,
    ! [U_2890,U_2889] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2890),hAPP_nat_nat(suc,U_2889)))
          | U_2890 != U_2889 )
        & ( U_2890 = U_2889
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2890),hAPP_nat_nat(suc,U_2889))) ) )
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2890),U_2889)) ),
    inference(variable_rename,[status(thm)],[f_975_1]) ).

fof(f_975_3,plain,
    ( ! [U_2890,U_2889] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2890),hAPP_nat_nat(suc,U_2889)))
        | U_2890 != U_2889
        | ~ sP252(U_2890,U_2889) )
    & ! [U_2890,U_2889] :
        ( U_2890 = U_2889
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2890),hAPP_nat_nat(suc,U_2889)))
        | ~ sP252(U_2890,U_2889) )
    & ! [U_2890,U_2889] :
        ( sP252(U_2890,U_2889)
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2890),U_2889)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP252])],[f_975_2]) ).

cnf(f_975_4,plain,
    ( sP252(U_2890,U_2889)
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2890),U_2889)) ),
    inference(clausify,[status(thm)],[f_975_3]) ).

cnf(f_975_5,plain,
    ( U_2890 = U_2889
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2890),hAPP_nat_nat(suc,U_2889)))
    | ~ sP252(U_2890,U_2889) ),
    inference(clausify,[status(thm)],[f_975_3]) ).

cnf(f_975_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2890),hAPP_nat_nat(suc,U_2889)))
    | U_2890 != U_2889
    | ~ sP252(U_2890,U_2889) ),
    inference(clausify,[status(thm)],[f_975_3]) ).

fof(f_976_1,plain,
    ! [N,M_1] :
      ( M_1 = N
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(suc,M_1)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_869_less__antisym]) ).

fof(f_976_2,plain,
    ! [U_2892,U_2891] :
      ( U_2891 = U_2892
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2892),hAPP_nat_nat(suc,U_2891)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2892),U_2891)) ),
    inference(variable_rename,[status(thm)],[f_976_1]) ).

fof(f_976_3,plain,
    ! [U_2892,U_2891] :
      ( U_2891 = U_2892
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2892),hAPP_nat_nat(suc,U_2891)))
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2892),U_2891)) ),
    inference(definitional_conversion,[status(esa)],[f_976_2]) ).

cnf(f_976_4,plain,
    ( U_2891 = U_2892
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2892),hAPP_nat_nat(suc,U_2891)))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2892),U_2891)) ),
    inference(clausify,[status(thm)],[f_976_3]) ).

fof(f_977_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_870_less__SucI]) ).

fof(f_977_2,plain,
    ! [U_2894,U_2893] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2894),hAPP_nat_nat(suc,U_2893)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2894),U_2893)) ),
    inference(variable_rename,[status(thm)],[f_977_1]) ).

fof(f_977_3,plain,
    ! [U_2894,U_2893] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2894),hAPP_nat_nat(suc,U_2893)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2894),U_2893)) ),
    inference(definitional_conversion,[status(esa)],[f_977_2]) ).

cnf(f_977_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2894),hAPP_nat_nat(suc,U_2893)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2894),U_2893)) ),
    inference(clausify,[status(thm)],[f_977_3]) ).

fof(f_978_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),N))
      | hAPP_nat_nat(suc,M_1) = N
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_871_Suc__lessI]) ).

fof(f_978_2,plain,
    ! [U_2896,U_2895] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2896)),U_2895))
      | hAPP_nat_nat(suc,U_2896) = U_2895
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2896),U_2895)) ),
    inference(variable_rename,[status(thm)],[f_978_1]) ).

fof(f_978_3,plain,
    ! [U_2895,U_2896] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2896)),U_2895))
      | hAPP_nat_nat(suc,U_2896) = U_2895
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2896),U_2895)) ),
    inference(definitional_conversion,[status(esa)],[f_978_2]) ).

cnf(f_978_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2896)),U_2895))
    | hAPP_nat_nat(suc,U_2896) = U_2895
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2896),U_2895)) ),
    inference(clausify,[status(thm)],[f_978_3]) ).

fof(f_979_1,plain,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_1)),K_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_872_less__trans__Suc]) ).

fof(f_979_2,plain,
    ! [U_2899,U_2898,U_2897] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2898)),U_2899))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2897),U_2899))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2898),U_2897)) ),
    inference(variable_rename,[status(thm)],[f_979_1]) ).

fof(f_979_3,plain,
    ! [U_2897,U_2898,U_2899] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2898)),U_2899))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2897),U_2899))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2898),U_2897)) ),
    inference(definitional_conversion,[status(esa)],[f_979_2]) ).

cnf(f_979_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2898)),U_2899))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2897),U_2899))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2898),U_2897)) ),
    inference(clausify,[status(thm)],[f_979_3]) ).

fof(f_980_1,plain,
    ! [M_1,N] :
      ( M_1 = N
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N))) ),
    inference(fof_nnf,[status(thm)],[fact_873_less__SucE]) ).

fof(f_980_2,plain,
    ! [U_2901,U_2900] :
      ( U_2901 = U_2900
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2901),U_2900))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2901),hAPP_nat_nat(suc,U_2900))) ),
    inference(variable_rename,[status(thm)],[f_980_1]) ).

fof(f_980_3,plain,
    ! [U_2901,U_2900] :
      ( U_2901 = U_2900
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2901),U_2900))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2901),hAPP_nat_nat(suc,U_2900))) ),
    inference(definitional_conversion,[status(esa)],[f_980_2]) ).

cnf(f_980_4,plain,
    ( U_2901 = U_2900
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2901),U_2900))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2901),hAPP_nat_nat(suc,U_2900))) ),
    inference(clausify,[status(thm)],[f_980_3]) ).

fof(f_981_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_874_Suc__lessD]) ).

fof(f_981_2,plain,
    ! [U_2903,U_2902] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2903),U_2902))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2903)),U_2902)) ),
    inference(variable_rename,[status(thm)],[f_981_1]) ).

fof(f_981_3,plain,
    ! [U_2903,U_2902] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2903),U_2902))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2903)),U_2902)) ),
    inference(definitional_conversion,[status(esa)],[f_981_2]) ).

cnf(f_981_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2903),U_2902))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2903)),U_2902)) ),
    inference(clausify,[status(thm)],[f_981_3]) ).

fof(f_982_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,M_1)),hAPP_nat_nat(suc,N))) ),
    inference(fof_nnf,[status(thm)],[fact_875_Suc__less__SucD]) ).

fof(f_982_2,plain,
    ! [U_2905,U_2904] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2905),U_2904))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2905)),hAPP_nat_nat(suc,U_2904))) ),
    inference(variable_rename,[status(thm)],[f_982_1]) ).

fof(f_982_3,plain,
    ! [U_2904,U_2905] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2905),U_2904))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2905)),hAPP_nat_nat(suc,U_2904))) ),
    inference(definitional_conversion,[status(esa)],[f_982_2]) ).

cnf(f_982_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2905),U_2904))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_2905)),hAPP_nat_nat(suc,U_2904))) ),
    inference(clausify,[status(thm)],[f_982_3]) ).

fof(f_983_1,plain,
    ! [I_1,J] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),I_1)),
    inference(fof_nnf,[status(thm)],[fact_876_not__add__less1]) ).

fof(f_983_2,plain,
    ! [U_2907,U_2906] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2907),U_2906)),U_2907)),
    inference(variable_rename,[status(thm)],[f_983_1]) ).

fof(f_983_3,plain,
    ! [U_2906,U_2907] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2907),U_2906)),U_2907)),
    inference(definitional_conversion,[status(esa)],[f_983_2]) ).

cnf(f_983_4,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2907),U_2906)),U_2907)),
    inference(clausify,[status(thm)],[f_983_3]) ).

fof(f_984_1,plain,
    ! [J,I_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),I_1)),I_1)),
    inference(fof_nnf,[status(thm)],[fact_877_not__add__less2]) ).

fof(f_984_2,plain,
    ! [U_2909,U_2908] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2909),U_2908)),U_2908)),
    inference(variable_rename,[status(thm)],[f_984_1]) ).

fof(f_984_3,plain,
    ! [U_2908,U_2909] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2909),U_2908)),U_2908)),
    inference(definitional_conversion,[status(esa)],[f_984_2]) ).

cnf(f_984_4,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2909),U_2908)),U_2908)),
    inference(clausify,[status(thm)],[f_984_3]) ).

fof(f_985_1,plain,
    ! [K,M,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_878_nat__add__left__cancel__less]) ).

fof(f_985_2,plain,
    ! [U_2912,U_2911,U_2910] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2912),U_2911)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2912),U_2910)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2911),U_2910)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2911),U_2910))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2912),U_2911)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2912),U_2910))) ) ),
    inference(variable_rename,[status(thm)],[f_985_1]) ).

fof(f_985_3,plain,
    ( ! [U_2918,U_2916,U_2914] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2918),U_2916)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2918),U_2914)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2916),U_2914)) )
    & ! [U_2917,U_2915,U_2913] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2915),U_2913))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2917),U_2915)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2917),U_2913))) ) ),
    inference(miniscope,[status(thm)],[f_985_2]) ).

fof(f_985_4,plain,
    ( ! [U_2914,U_2916,U_2918] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2918),U_2916)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2918),U_2914)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2916),U_2914)) )
    & ! [U_2917,U_2915,U_2913] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2915),U_2913))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2917),U_2915)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2917),U_2913))) ) ),
    inference(definitional_conversion,[status(esa)],[f_985_3]) ).

cnf(f_985_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2915),U_2913))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2917),U_2915)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2917),U_2913))) ),
    inference(clausify,[status(thm)],[f_985_4]) ).

cnf(f_985_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2918),U_2916)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2918),U_2914)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2916),U_2914)) ),
    inference(clausify,[status(thm)],[f_985_4]) ).

fof(f_986_1,plain,
    ! [M_1,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),M_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_879_trans__less__add1]) ).

fof(f_986_2,plain,
    ! [U_2921,U_2920,U_2919] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2920),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2919),U_2921)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2920),U_2919)) ),
    inference(variable_rename,[status(thm)],[f_986_1]) ).

fof(f_986_3,plain,
    ! [U_2920,U_2919,U_2921] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2920),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2919),U_2921)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2920),U_2919)) ),
    inference(definitional_conversion,[status(esa)],[f_986_2]) ).

cnf(f_986_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2920),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2919),U_2921)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2920),U_2919)) ),
    inference(clausify,[status(thm)],[f_986_3]) ).

fof(f_987_1,plain,
    ! [M_1,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),J)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_880_trans__less__add2]) ).

fof(f_987_2,plain,
    ! [U_2924,U_2923,U_2922] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2923),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2924),U_2922)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2923),U_2922)) ),
    inference(variable_rename,[status(thm)],[f_987_1]) ).

fof(f_987_3,plain,
    ! [U_2922,U_2923,U_2924] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2923),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2924),U_2922)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2923),U_2922)) ),
    inference(definitional_conversion,[status(esa)],[f_987_2]) ).

cnf(f_987_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2923),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2924),U_2922)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2923),U_2922)) ),
    inference(clausify,[status(thm)],[f_987_3]) ).

fof(f_988_1,plain,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),K_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_881_add__less__mono1]) ).

fof(f_988_2,plain,
    ! [U_2927,U_2926,U_2925] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2926),U_2927)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2925),U_2927)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2926),U_2925)) ),
    inference(variable_rename,[status(thm)],[f_988_1]) ).

fof(f_988_3,plain,
    ! [U_2925,U_2926,U_2927] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2926),U_2927)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2925),U_2927)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2926),U_2925)) ),
    inference(definitional_conversion,[status(esa)],[f_988_2]) ).

cnf(f_988_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2926),U_2927)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2925),U_2927)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2926),U_2925)) ),
    inference(clausify,[status(thm)],[f_988_3]) ).

fof(f_989_1,plain,
    ! [K_1,L_1,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,J),L_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_882_add__less__mono]) ).

fof(f_989_2,plain,
    ! [U_2931,U_2930,U_2929,U_2928] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2929),U_2931)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2928),U_2930)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2931),U_2930))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2929),U_2928)) ),
    inference(variable_rename,[status(thm)],[f_989_1]) ).

fof(f_989_3,plain,
    ! [U_2928,U_2929,U_2930,U_2931] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2929),U_2931)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2928),U_2930)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2931),U_2930))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2929),U_2928)) ),
    inference(definitional_conversion,[status(esa)],[f_989_2]) ).

cnf(f_989_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2929),U_2931)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2928),U_2930)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2931),U_2930))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2929),U_2928)) ),
    inference(clausify,[status(thm)],[f_989_3]) ).

fof(f_990_1,plain,
    ! [M_1,N,K_1,L_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N))
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),L_1) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_1),N)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_1),L_1)) ),
    inference(fof_nnf,[status(thm)],[fact_883_less__add__eq__less]) ).

fof(f_990_2,plain,
    ! [U_2935,U_2934,U_2933,U_2932] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2935),U_2934))
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2935),U_2932) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2933),U_2934)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2933),U_2932)) ),
    inference(variable_rename,[status(thm)],[f_990_1]) ).

fof(f_990_3,plain,
    ! [U_2932,U_2933,U_2934,U_2935] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2935),U_2934))
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2935),U_2932) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2933),U_2934)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2933),U_2932)) ),
    inference(definitional_conversion,[status(esa)],[f_990_2]) ).

cnf(f_990_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2935),U_2934))
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2935),U_2932) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2933),U_2934)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2933),U_2932)) ),
    inference(clausify,[status(thm)],[f_990_3]) ).

fof(f_991_1,plain,
    ! [I_1,J,K_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),K_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),K_1)) ),
    inference(fof_nnf,[status(thm)],[fact_884_add__lessD1]) ).

fof(f_991_2,plain,
    ! [U_2938,U_2937,U_2936] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2938),U_2936))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2938),U_2937)),U_2936)) ),
    inference(variable_rename,[status(thm)],[f_991_1]) ).

fof(f_991_3,plain,
    ! [U_2937,U_2936,U_2938] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2938),U_2936))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2938),U_2937)),U_2936)) ),
    inference(definitional_conversion,[status(esa)],[f_991_2]) ).

cnf(f_991_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2938),U_2936))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2938),U_2937)),U_2936)) ),
    inference(clausify,[status(thm)],[f_991_3]) ).

fof(f_992_1,plain,
    ! [Z,X,Y] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y)) ),
    inference(fof_nnf,[status(thm)],[fact_885_termination__basic__simps_I1_J]) ).

fof(f_992_2,plain,
    ! [U_2941,U_2940,U_2939] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2940),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2939),U_2941)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2940),U_2939)) ),
    inference(variable_rename,[status(thm)],[f_992_1]) ).

fof(f_992_3,plain,
    ! [U_2939,U_2940,U_2941] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2940),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2939),U_2941)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2940),U_2939)) ),
    inference(definitional_conversion,[status(esa)],[f_992_2]) ).

cnf(f_992_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2940),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2939),U_2941)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2940),U_2939)) ),
    inference(clausify,[status(thm)],[f_992_3]) ).

fof(f_993_1,plain,
    ! [Y,X,Z] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,Y),Z)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Z)) ),
    inference(fof_nnf,[status(thm)],[fact_886_termination__basic__simps_I2_J]) ).

fof(f_993_2,plain,
    ! [U_2944,U_2943,U_2942] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2943),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2944),U_2942)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2943),U_2942)) ),
    inference(variable_rename,[status(thm)],[f_993_1]) ).

fof(f_993_3,plain,
    ! [U_2942,U_2943,U_2944] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2943),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2944),U_2942)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2943),U_2942)) ),
    inference(definitional_conversion,[status(esa)],[f_993_2]) ).

cnf(f_993_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2943),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2944),U_2942)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2943),U_2942)) ),
    inference(clausify,[status(thm)],[f_993_3]) ).

fof(f_994_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
        | M = Na
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) )
      & ( ( M != Na
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_887_nat__less__le]) ).

fof(f_994_2,plain,
    ! [U_2946,U_2945] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2946),U_2945))
        | U_2946 = U_2945
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2946),U_2945)) )
      & ( ( U_2946 != U_2945
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2946),U_2945)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2946),U_2945)) ) ),
    inference(variable_rename,[status(thm)],[f_994_1]) ).

fof(f_994_3,plain,
    ( ! [U_2950,U_2948] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2950),U_2948))
        | U_2950 = U_2948
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2950),U_2948)) )
    & ! [U_2949,U_2947] :
        ( ( U_2949 != U_2947
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2949),U_2947)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2949),U_2947)) ) ),
    inference(miniscope,[status(thm)],[f_994_2]) ).

fof(f_994_4,plain,
    ( ! [U_2949,U_2947] :
        ( U_2949 != U_2947
        | ~ sP253(U_2949,U_2947) )
    & ! [U_2949,U_2947] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2949),U_2947))
        | ~ sP253(U_2949,U_2947) )
    & ! [U_2950,U_2948] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2950),U_2948))
        | U_2950 = U_2948
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2950),U_2948)) )
    & ! [U_2949,U_2947] :
        ( sP253(U_2949,U_2947)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2949),U_2947)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP253])],[f_994_3]) ).

cnf(f_994_5,plain,
    ( sP253(U_2949,U_2947)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2949),U_2947)) ),
    inference(clausify,[status(thm)],[f_994_4]) ).

cnf(f_994_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2950),U_2948))
    | U_2950 = U_2948
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2950),U_2948)) ),
    inference(clausify,[status(thm)],[f_994_4]) ).

cnf(f_994_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2949),U_2947))
    | ~ sP253(U_2949,U_2947) ),
    inference(clausify,[status(thm)],[f_994_4]) ).

cnf(f_994_8,plain,
    ( U_2949 != U_2947
    | ~ sP253(U_2949,U_2947) ),
    inference(clausify,[status(thm)],[f_994_4]) ).

fof(f_995_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
        | ( M != Na
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) ) )
      & ( M = Na
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_888_le__eq__less__or__eq]) ).

fof(f_995_2,plain,
    ! [U_2952,U_2951] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2952),U_2951))
        | ( U_2952 != U_2951
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2952),U_2951)) ) )
      & ( U_2952 = U_2951
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2952),U_2951))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2952),U_2951)) ) ),
    inference(variable_rename,[status(thm)],[f_995_1]) ).

fof(f_995_3,plain,
    ( ! [U_2956,U_2954] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2956),U_2954))
        | ( U_2956 != U_2954
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2956),U_2954)) ) )
    & ! [U_2955,U_2953] :
        ( U_2955 = U_2953
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2955),U_2953))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2955),U_2953)) ) ),
    inference(miniscope,[status(thm)],[f_995_2]) ).

fof(f_995_4,plain,
    ( ! [U_2956,U_2954] :
        ( U_2956 != U_2954
        | ~ sP254(U_2956,U_2954) )
    & ! [U_2956,U_2954] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2956),U_2954))
        | ~ sP254(U_2956,U_2954) )
    & ! [U_2956,U_2954] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2956),U_2954))
        | sP254(U_2956,U_2954) )
    & ! [U_2953,U_2955] :
        ( U_2955 = U_2953
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2955),U_2953))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2955),U_2953)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP254])],[f_995_3]) ).

cnf(f_995_5,plain,
    ( U_2955 = U_2953
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2955),U_2953))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2955),U_2953)) ),
    inference(clausify,[status(thm)],[f_995_4]) ).

cnf(f_995_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2956),U_2954))
    | sP254(U_2956,U_2954) ),
    inference(clausify,[status(thm)],[f_995_4]) ).

cnf(f_995_7,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2956),U_2954))
    | ~ sP254(U_2956,U_2954) ),
    inference(clausify,[status(thm)],[f_995_4]) ).

cnf(f_995_8,plain,
    ( U_2956 != U_2954
    | ~ sP254(U_2956,U_2954) ),
    inference(clausify,[status(thm)],[f_995_4]) ).

fof(f_996_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_889_less__imp__le__nat]) ).

fof(f_996_2,plain,
    ! [U_2958,U_2957] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2958),U_2957))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2958),U_2957)) ),
    inference(variable_rename,[status(thm)],[f_996_1]) ).

fof(f_996_3,plain,
    ! [U_2957,U_2958] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2958),U_2957))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2958),U_2957)) ),
    inference(definitional_conversion,[status(esa)],[f_996_2]) ).

cnf(f_996_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2958),U_2957))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2958),U_2957)) ),
    inference(clausify,[status(thm)],[f_996_3]) ).

fof(f_997_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N))
      | M_1 = N
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_890_le__neq__implies__less]) ).

fof(f_997_2,plain,
    ! [U_2960,U_2959] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2960),U_2959))
      | U_2960 = U_2959
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2960),U_2959)) ),
    inference(variable_rename,[status(thm)],[f_997_1]) ).

fof(f_997_3,plain,
    ! [U_2959,U_2960] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2960),U_2959))
      | U_2960 = U_2959
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2960),U_2959)) ),
    inference(definitional_conversion,[status(esa)],[f_997_2]) ).

cnf(f_997_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2960),U_2959))
    | U_2960 = U_2959
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2960),U_2959)) ),
    inference(clausify,[status(thm)],[f_997_3]) ).

fof(f_998_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N))
      | ( M_1 != N
        & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) ) ),
    inference(fof_nnf,[status(thm)],[fact_891_less__or__eq__imp__le]) ).

fof(f_998_2,plain,
    ! [U_2962,U_2961] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2962),U_2961))
      | ( U_2962 != U_2961
        & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2962),U_2961)) ) ),
    inference(variable_rename,[status(thm)],[f_998_1]) ).

fof(f_998_3,plain,
    ( ! [U_2961,U_2962] :
        ( U_2962 != U_2961
        | ~ sP255(U_2961,U_2962) )
    & ! [U_2961,U_2962] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2962),U_2961))
        | ~ sP255(U_2961,U_2962) )
    & ! [U_2961,U_2962] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2962),U_2961))
        | sP255(U_2961,U_2962) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP255])],[f_998_2]) ).

cnf(f_998_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2962),U_2961))
    | sP255(U_2961,U_2962) ),
    inference(clausify,[status(thm)],[f_998_3]) ).

cnf(f_998_5,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2962),U_2961))
    | ~ sP255(U_2961,U_2962) ),
    inference(clausify,[status(thm)],[f_998_3]) ).

cnf(f_998_6,plain,
    ( U_2962 != U_2961
    | ~ sP255(U_2961,U_2962) ),
    inference(clausify,[status(thm)],[f_998_3]) ).

fof(f_999_1,plain,
    ! [X,Y] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X),Y))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X),Y)) ),
    inference(fof_nnf,[status(thm)],[fact_892_termination__basic__simps_I5_J]) ).

fof(f_999_2,plain,
    ! [U_2964,U_2963] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2964),U_2963))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2964),U_2963)) ),
    inference(variable_rename,[status(thm)],[f_999_1]) ).

fof(f_999_3,plain,
    ! [U_2964,U_2963] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2964),U_2963))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2964),U_2963)) ),
    inference(definitional_conversion,[status(esa)],[f_999_2]) ).

cnf(f_999_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_2964),U_2963))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2964),U_2963)) ),
    inference(clausify,[status(thm)],[f_999_3]) ).

fof(f_1000_1,plain,
    ! [N,J,K_1] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),N)),K_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J),K_1)) ),
    inference(fof_nnf,[status(thm)],[fact_893_less__imp__diff__less]) ).

fof(f_1000_2,plain,
    ! [U_2967,U_2966,U_2965] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2966),U_2967)),U_2965))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2966),U_2965)) ),
    inference(variable_rename,[status(thm)],[f_1000_1]) ).

fof(f_1000_3,plain,
    ! [U_2965,U_2966,U_2967] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2966),U_2967)),U_2965))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2966),U_2965)) ),
    inference(definitional_conversion,[status(esa)],[f_1000_2]) ).

cnf(f_1000_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2966),U_2967)),U_2965))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2966),U_2965)) ),
    inference(clausify,[status(thm)],[f_1000_3]) ).

fof(f_1001_1,plain,
    ! [L_1,M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_1),N)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,L_1),M_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),L_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_894_diff__less__mono2]) ).

fof(f_1001_2,plain,
    ! [U_2970,U_2969,U_2968] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2970),U_2968)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2970),U_2969)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2969),U_2970))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2969),U_2968)) ),
    inference(variable_rename,[status(thm)],[f_1001_1]) ).

fof(f_1001_3,plain,
    ! [U_2968,U_2969,U_2970] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2970),U_2968)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2970),U_2969)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2969),U_2970))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2969),U_2968)) ),
    inference(definitional_conversion,[status(esa)],[f_1001_2]) ).

cnf(f_1001_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2970),U_2968)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_2970),U_2969)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2969),U_2970))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2969),U_2968)) ),
    inference(clausify,[status(thm)],[f_1001_3]) ).

fof(f_1002_1,plain,
    ! [N_2] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2))
        | ! [M_2] :
          ? [X_2] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),M_2))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),N_2)) ) )
      & ( ? [M_2] :
          ! [X_2] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),M_2))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),N_2)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_895_finite__nat__set__iff__bounded]) ).

fof(f_1002_2,plain,
    ! [U_2975] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2975))
        | ! [U_2974] :
          ? [U_2973] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2973),U_2974))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2973),U_2975)) ) )
      & ( ? [U_2972] :
          ! [U_2971] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2971),U_2972))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2971),U_2975)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2975)) ) ),
    inference(variable_rename,[status(thm)],[f_1002_1]) ).

fof(f_1002_3,plain,
    ( ! [U_2977] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2977))
        | ! [U_2974] :
          ? [U_2973] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2973),U_2974))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2973),U_2977)) ) )
    & ! [U_2976] :
        ( ? [U_2972] :
          ! [U_2971] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2971),U_2972))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2971),U_2976)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2976)) ) ),
    inference(miniscope,[status(thm)],[f_1002_2]) ).

fof(f_1002_4,plain,
    ( ! [U_2977] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2977))
        | ! [U_2974] :
          ? [U_2973] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2973),U_2974))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2973),U_2977)) ) )
    & ! [U_2976] :
        ( ! [U_2971] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2971),sK163(U_2976)))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2971),U_2976)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2976)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK163]),skolemize(U_2972,sK163(U_2976))],[f_1002_3]) ).

fof(f_1002_5,plain,
    ( ! [U_2977] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2977))
        | ! [U_2974] :
            ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK164(U_2977,U_2974)),U_2974))
            & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK164(U_2977,U_2974)),U_2977)) ) )
    & ! [U_2976] :
        ( ! [U_2971] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2971),sK163(U_2976)))
            | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2971),U_2976)) )
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2976)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK164]),skolemize(U_2973,sK164(U_2977,U_2974))],[f_1002_4]) ).

fof(f_1002_6,plain,
    ( ! [U_2974,U_2977] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK164(U_2977,U_2974)),U_2974))
        | ~ sP256(U_2974,U_2977) )
    & ! [U_2974,U_2977] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK164(U_2977,U_2974)),U_2977))
        | ~ sP256(U_2974,U_2977) )
    & ! [U_2974,U_2977] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2977))
        | sP256(U_2974,U_2977) )
    & ! [U_2971,U_2976] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2971),sK163(U_2976)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2971),U_2976))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2976)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP256])],[f_1002_5]) ).

cnf(f_1002_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2971),sK163(U_2976)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_2971),U_2976))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2976)) ),
    inference(clausify,[status(thm)],[f_1002_6]) ).

cnf(f_1002_8,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_2977))
    | sP256(U_2974,U_2977) ),
    inference(clausify,[status(thm)],[f_1002_6]) ).

cnf(f_1002_9,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK164(U_2977,U_2974)),U_2977))
    | ~ sP256(U_2974,U_2977) ),
    inference(clausify,[status(thm)],[f_1002_6]) ).

cnf(f_1002_10,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK164(U_2977,U_2974)),U_2974))
    | ~ sP256(U_2974,U_2977) ),
    inference(clausify,[status(thm)],[f_1002_6]) ).

fof(f_1003_1,plain,
    ! [Na] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),Na))) = Na,
    inference(fof_nnf,[status(thm)],[fact_896_card__Collect__less__nat]) ).

fof(f_1003_2,plain,
    ! [U_2978] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_2978))) = U_2978,
    inference(variable_rename,[status(thm)],[f_1003_1]) ).

fof(f_1003_3,plain,
    ! [U_2978] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_2978))) = U_2978,
    inference(definitional_conversion,[status(esa)],[f_1003_2]) ).

cnf(f_1003_4,plain,
    hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_2978))) = U_2978,
    inference(clausify,[status(thm)],[f_1003_3]) ).

fof(f_1004_1,plain,
    ! [Pa,I_2] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,Pa),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),I_2))))),
    inference(fof_nnf,[status(thm)],[fact_897_finite__M__bounded__by__nat]) ).

fof(f_1004_2,plain,
    ! [U_2980,U_2979] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,U_2980),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_2979))))),
    inference(variable_rename,[status(thm)],[f_1004_1]) ).

fof(f_1004_3,plain,
    ! [U_2979,U_2980] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,U_2980),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_2979))))),
    inference(definitional_conversion,[status(esa)],[f_1004_2]) ).

cnf(f_1004_4,plain,
    hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,U_2980),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_2979))))),
    inference(clausify,[status(thm)],[f_1004_3]) ).

fof(f_1005_1,plain,
    ! [I_1,M_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),M_1)))),
    inference(fof_nnf,[status(thm)],[fact_898_less__add__Suc1]) ).

fof(f_1005_2,plain,
    ! [U_2982,U_2981] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2982),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2982),U_2981)))),
    inference(variable_rename,[status(thm)],[f_1005_1]) ).

fof(f_1005_3,plain,
    ! [U_2981,U_2982] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2982),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2982),U_2981)))),
    inference(definitional_conversion,[status(esa)],[f_1005_2]) ).

cnf(f_1005_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2982),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2982),U_2981)))),
    inference(clausify,[status(thm)],[f_1005_3]) ).

fof(f_1006_1,plain,
    ! [I_1,M_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),I_1)))),
    inference(fof_nnf,[status(thm)],[fact_899_less__add__Suc2]) ).

fof(f_1006_2,plain,
    ! [U_2984,U_2983] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2984),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2983),U_2984)))),
    inference(variable_rename,[status(thm)],[f_1006_1]) ).

fof(f_1006_3,plain,
    ! [U_2983,U_2984] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2984),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2983),U_2984)))),
    inference(definitional_conversion,[status(esa)],[f_1006_2]) ).

cnf(f_1006_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2984),hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2983),U_2984)))),
    inference(clausify,[status(thm)],[f_1006_3]) ).

fof(f_1007_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
        | ! [K_2] : Na != hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K_2)) )
      & ( ? [K_2] : Na = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K_2))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_900_less__iff__Suc__add]) ).

fof(f_1007_2,plain,
    ! [U_2988,U_2987] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2988),U_2987))
        | ! [U_2986] : U_2987 != hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2988),U_2986)) )
      & ( ? [U_2985] : U_2987 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2988),U_2985))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2988),U_2987)) ) ),
    inference(variable_rename,[status(thm)],[f_1007_1]) ).

fof(f_1007_3,plain,
    ( ! [U_2992,U_2990] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2992),U_2990))
        | ! [U_2986] : U_2990 != hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2992),U_2986)) )
    & ! [U_2991,U_2989] :
        ( ? [U_2985] : U_2989 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2991),U_2985))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2991),U_2989)) ) ),
    inference(miniscope,[status(thm)],[f_1007_2]) ).

fof(f_1007_4,plain,
    ( ! [U_2992,U_2990] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2992),U_2990))
        | ! [U_2986] : U_2990 != hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2992),U_2986)) )
    & ! [U_2991,U_2989] :
        ( U_2989 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2991),sK165(U_2991,U_2989)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2991),U_2989)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK165]),skolemize(U_2985,sK165(U_2991,U_2989))],[f_1007_3]) ).

fof(f_1007_5,plain,
    ( ! [U_2986,U_2990,U_2992] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2992),U_2990))
        | U_2990 != hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2992),U_2986)) )
    & ! [U_2991,U_2989] :
        ( U_2989 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2991),sK165(U_2991,U_2989)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2991),U_2989)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1007_4]) ).

cnf(f_1007_6,plain,
    ( U_2989 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2991),sK165(U_2991,U_2989)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2991),U_2989)) ),
    inference(clausify,[status(thm)],[f_1007_5]) ).

cnf(f_1007_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2992),U_2990))
    | U_2990 != hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_2992),U_2986)) ),
    inference(clausify,[status(thm)],[f_1007_5]) ).

fof(f_1008_1,plain,
    ! [Na,M] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),M)) ) ),
    inference(fof_nnf,[status(thm)],[fact_901_less__eq__Suc__le]) ).

fof(f_1008_2,plain,
    ! [U_2994,U_2993] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2994),U_2993))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2994)),U_2993)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2994)),U_2993))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2994),U_2993)) ) ),
    inference(variable_rename,[status(thm)],[f_1008_1]) ).

fof(f_1008_3,plain,
    ( ! [U_2998,U_2996] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2998),U_2996))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2998)),U_2996)) )
    & ! [U_2997,U_2995] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2997)),U_2995))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2997),U_2995)) ) ),
    inference(miniscope,[status(thm)],[f_1008_2]) ).

fof(f_1008_4,plain,
    ( ! [U_2996,U_2998] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2998),U_2996))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2998)),U_2996)) )
    & ! [U_2997,U_2995] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2997)),U_2995))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2997),U_2995)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1008_3]) ).

cnf(f_1008_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2997)),U_2995))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2997),U_2995)) ),
    inference(clausify,[status(thm)],[f_1008_4]) ).

cnf(f_1008_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_2998),U_2996))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_2998)),U_2996)) ),
    inference(clausify,[status(thm)],[f_1008_4]) ).

fof(f_1009_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_902_less__Suc__eq__le]) ).

fof(f_1009_2,plain,
    ! [U_3000,U_2999] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3000),hAPP_nat_nat(suc,U_2999)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3000),U_2999)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3000),U_2999))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3000),hAPP_nat_nat(suc,U_2999))) ) ),
    inference(variable_rename,[status(thm)],[f_1009_1]) ).

fof(f_1009_3,plain,
    ( ! [U_3004,U_3002] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3004),hAPP_nat_nat(suc,U_3002)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3004),U_3002)) )
    & ! [U_3003,U_3001] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3003),U_3001))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3003),hAPP_nat_nat(suc,U_3001))) ) ),
    inference(miniscope,[status(thm)],[f_1009_2]) ).

fof(f_1009_4,plain,
    ( ! [U_3002,U_3004] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3004),hAPP_nat_nat(suc,U_3002)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3004),U_3002)) )
    & ! [U_3003,U_3001] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3003),U_3001))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3003),hAPP_nat_nat(suc,U_3001))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1009_3]) ).

cnf(f_1009_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3003),U_3001))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3003),hAPP_nat_nat(suc,U_3001))) ),
    inference(clausify,[status(thm)],[f_1009_4]) ).

cnf(f_1009_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3004),hAPP_nat_nat(suc,U_3002)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3004),U_3002)) ),
    inference(clausify,[status(thm)],[f_1009_4]) ).

fof(f_1010_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M)),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_903_Suc__le__eq]) ).

fof(f_1010_2,plain,
    ! [U_3006,U_3005] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3006)),U_3005))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3006),U_3005)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3006),U_3005))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3006)),U_3005)) ) ),
    inference(variable_rename,[status(thm)],[f_1010_1]) ).

fof(f_1010_3,plain,
    ( ! [U_3010,U_3008] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3010)),U_3008))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3010),U_3008)) )
    & ! [U_3009,U_3007] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3009),U_3007))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3009)),U_3007)) ) ),
    inference(miniscope,[status(thm)],[f_1010_2]) ).

fof(f_1010_4,plain,
    ( ! [U_3008,U_3010] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3010)),U_3008))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3010),U_3008)) )
    & ! [U_3009,U_3007] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3009),U_3007))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3009)),U_3007)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1010_3]) ).

cnf(f_1010_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3009),U_3007))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3009)),U_3007)) ),
    inference(clausify,[status(thm)],[f_1010_4]) ).

cnf(f_1010_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3010)),U_3008))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3010),U_3008)) ),
    inference(clausify,[status(thm)],[f_1010_4]) ).

fof(f_1011_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),hAPP_nat_nat(suc,N)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_904_le__imp__less__Suc]) ).

fof(f_1011_2,plain,
    ! [U_3012,U_3011] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3012),hAPP_nat_nat(suc,U_3011)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3012),U_3011)) ),
    inference(variable_rename,[status(thm)],[f_1011_1]) ).

fof(f_1011_3,plain,
    ! [U_3012,U_3011] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3012),hAPP_nat_nat(suc,U_3011)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3012),U_3011)) ),
    inference(definitional_conversion,[status(esa)],[f_1011_2]) ).

cnf(f_1011_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3012),hAPP_nat_nat(suc,U_3011)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3012),U_3011)) ),
    inference(clausify,[status(thm)],[f_1011_3]) ).

fof(f_1012_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_905_Suc__leI]) ).

fof(f_1012_2,plain,
    ! [U_3014,U_3013] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3014)),U_3013))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3014),U_3013)) ),
    inference(variable_rename,[status(thm)],[f_1012_1]) ).

fof(f_1012_3,plain,
    ! [U_3013,U_3014] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3014)),U_3013))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3014),U_3013)) ),
    inference(definitional_conversion,[status(esa)],[f_1012_2]) ).

cnf(f_1012_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3014)),U_3013))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3014),U_3013)) ),
    inference(clausify,[status(thm)],[f_1012_3]) ).

fof(f_1013_1,plain,
    ! [M,Na] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M)))
          | Na != M )
        & ( Na = M
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,M))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) ),
    inference(fof_nnf,[status(thm)],[fact_906_le__less__Suc__eq]) ).

fof(f_1013_2,plain,
    ! [U_3016,U_3015] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3015),hAPP_nat_nat(suc,U_3016)))
          | U_3015 != U_3016 )
        & ( U_3015 = U_3016
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3015),hAPP_nat_nat(suc,U_3016))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3016),U_3015)) ),
    inference(variable_rename,[status(thm)],[f_1013_1]) ).

fof(f_1013_3,plain,
    ( ! [U_3015,U_3016] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3015),hAPP_nat_nat(suc,U_3016)))
        | U_3015 != U_3016
        | ~ sP257(U_3015,U_3016) )
    & ! [U_3015,U_3016] :
        ( U_3015 = U_3016
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3015),hAPP_nat_nat(suc,U_3016)))
        | ~ sP257(U_3015,U_3016) )
    & ! [U_3015,U_3016] :
        ( sP257(U_3015,U_3016)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3016),U_3015)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP257])],[f_1013_2]) ).

cnf(f_1013_4,plain,
    ( sP257(U_3015,U_3016)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3016),U_3015)) ),
    inference(clausify,[status(thm)],[f_1013_3]) ).

cnf(f_1013_5,plain,
    ( U_3015 = U_3016
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3015),hAPP_nat_nat(suc,U_3016)))
    | ~ sP257(U_3015,U_3016) ),
    inference(clausify,[status(thm)],[f_1013_3]) ).

cnf(f_1013_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3015),hAPP_nat_nat(suc,U_3016)))
    | U_3015 != U_3016
    | ~ sP257(U_3015,U_3016) ),
    inference(clausify,[status(thm)],[f_1013_3]) ).

fof(f_1014_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_1)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_907_Suc__le__lessD]) ).

fof(f_1014_2,plain,
    ! [U_3018,U_3017] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3018),U_3017))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3018)),U_3017)) ),
    inference(variable_rename,[status(thm)],[f_1014_1]) ).

fof(f_1014_3,plain,
    ! [U_3018,U_3017] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3018),U_3017))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3018)),U_3017)) ),
    inference(definitional_conversion,[status(esa)],[f_1014_2]) ).

cnf(f_1014_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3018),U_3017))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3018)),U_3017)) ),
    inference(clausify,[status(thm)],[f_1014_3]) ).

fof(f_1015_1,plain,
    ! [M_1,N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)),hAPP_nat_nat(suc,M_1))),
    inference(fof_nnf,[status(thm)],[fact_908_diff__less__Suc]) ).

fof(f_1015_2,plain,
    ! [U_3020,U_3019] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3020),U_3019)),hAPP_nat_nat(suc,U_3020))),
    inference(variable_rename,[status(thm)],[f_1015_1]) ).

fof(f_1015_3,plain,
    ! [U_3019,U_3020] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3020),U_3019)),hAPP_nat_nat(suc,U_3020))),
    inference(definitional_conversion,[status(esa)],[f_1015_2]) ).

cnf(f_1015_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3020),U_3019)),hAPP_nat_nat(suc,U_3020))),
    inference(clausify,[status(thm)],[f_1015_3]) ).

fof(f_1016_1,plain,
    ! [I_2,J_1,K] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K)),J_1)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_2),K)),J_1))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_2),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),K))) ) ),
    inference(fof_nnf,[status(thm)],[fact_909_less__diff__conv]) ).

fof(f_1016_2,plain,
    ! [U_3023,U_3022,U_3021] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3023),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3022),U_3021)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3023),U_3021)),U_3022)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3023),U_3021)),U_3022))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3023),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3022),U_3021))) ) ),
    inference(variable_rename,[status(thm)],[f_1016_1]) ).

fof(f_1016_3,plain,
    ( ! [U_3029,U_3027,U_3025] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3029),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3027),U_3025)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3029),U_3025)),U_3027)) )
    & ! [U_3028,U_3026,U_3024] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3028),U_3024)),U_3026))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3028),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3026),U_3024))) ) ),
    inference(miniscope,[status(thm)],[f_1016_2]) ).

fof(f_1016_4,plain,
    ( ! [U_3025,U_3027,U_3029] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3029),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3027),U_3025)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3029),U_3025)),U_3027)) )
    & ! [U_3026,U_3024,U_3028] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3028),U_3024)),U_3026))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3028),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3026),U_3024))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1016_3]) ).

cnf(f_1016_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3028),U_3024)),U_3026))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3028),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3026),U_3024))) ),
    inference(clausify,[status(thm)],[f_1016_4]) ).

cnf(f_1016_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3029),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3027),U_3025)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3029),U_3025)),U_3027)) ),
    inference(clausify,[status(thm)],[f_1016_4]) ).

fof(f_1017_1,plain,
    ! [M_1,N] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)) = M_1
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_910_add__diff__inverse]) ).

fof(f_1017_2,plain,
    ! [U_3031,U_3030] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3030),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3031),U_3030)) = U_3031
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3031),U_3030)) ),
    inference(variable_rename,[status(thm)],[f_1017_1]) ).

fof(f_1017_3,plain,
    ! [U_3030,U_3031] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3030),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3031),U_3030)) = U_3031
      | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3031),U_3030)) ),
    inference(definitional_conversion,[status(esa)],[f_1017_2]) ).

cnf(f_1017_4,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3030),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3031),U_3030)) = U_3031
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3031),U_3030)) ),
    inference(clausify,[status(thm)],[f_1017_3]) ).

fof(f_1018_1,plain,
    ! [C,A_1,B_2] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,A_1),C)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,B_2),C)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,C),A_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_1),B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_911_diff__less__mono]) ).

fof(f_1018_2,plain,
    ! [U_3034,U_3033,U_3032] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3033),U_3034)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3032),U_3034)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3034),U_3033))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3033),U_3032)) ),
    inference(variable_rename,[status(thm)],[f_1018_1]) ).

fof(f_1018_3,plain,
    ! [U_3032,U_3033,U_3034] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3033),U_3034)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3032),U_3034)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3034),U_3033))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3033),U_3032)) ),
    inference(definitional_conversion,[status(esa)],[f_1018_2]) ).

cnf(f_1018_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3033),U_3034)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3032),U_3034)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3034),U_3033))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3033),U_3032)) ),
    inference(clausify,[status(thm)],[f_1018_3]) ).

fof(f_1019_1,plain,
    ! [Na,K,M] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,Na),K)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_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)) ),
    inference(fof_nnf,[status(thm)],[fact_912_less__diff__iff]) ).

fof(f_1019_2,plain,
    ! [U_3037,U_3036,U_3035] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3035),U_3036)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3037),U_3036)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3035),U_3037)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3035),U_3037))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3035),U_3036)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3037),U_3036))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3036),U_3037))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3036),U_3035)) ),
    inference(variable_rename,[status(thm)],[f_1019_1]) ).

fof(f_1019_3,plain,
    ( ! [U_3035,U_3036,U_3037] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3035),U_3036)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3037),U_3036)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3035),U_3037))
        | ~ sP258(U_3035,U_3036,U_3037) )
    & ! [U_3035,U_3036,U_3037] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3035),U_3037))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3035),U_3036)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3037),U_3036)))
        | ~ sP258(U_3035,U_3036,U_3037) )
    & ! [U_3035,U_3036,U_3037] :
        ( sP258(U_3035,U_3036,U_3037)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3036),U_3037))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3036),U_3035)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP258])],[f_1019_2]) ).

cnf(f_1019_4,plain,
    ( sP258(U_3035,U_3036,U_3037)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3036),U_3037))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3036),U_3035)) ),
    inference(clausify,[status(thm)],[f_1019_3]) ).

cnf(f_1019_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3035),U_3037))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3035),U_3036)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3037),U_3036)))
    | ~ sP258(U_3035,U_3036,U_3037) ),
    inference(clausify,[status(thm)],[f_1019_3]) ).

cnf(f_1019_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3035),U_3036)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3037),U_3036)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3035),U_3037))
    | ~ sP258(U_3035,U_3036,U_3037) ),
    inference(clausify,[status(thm)],[f_1019_3]) ).

fof(f_1020_1,plain,
    ! [X_2] : hAPP_n1699378549t_bool(ord_less_nat,X_2) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,X_2)),
    inference(fof_nnf,[status(thm)],[fact_913_less__eq__Suc__le__raw]) ).

fof(f_1020_2,plain,
    ! [U_3038] : hAPP_n1699378549t_bool(ord_less_nat,U_3038) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3038)),
    inference(variable_rename,[status(thm)],[f_1020_1]) ).

fof(f_1020_3,plain,
    ! [U_3038] : hAPP_n1699378549t_bool(ord_less_nat,U_3038) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3038)),
    inference(definitional_conversion,[status(esa)],[f_1020_2]) ).

cnf(f_1020_4,plain,
    hAPP_n1699378549t_bool(ord_less_nat,U_3038) = hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,U_3038)),
    inference(clausify,[status(thm)],[f_1020_3]) ).

fof(f_1021_1,plain,
    ! [M,K,F] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(F,M)),K)),hAPP_nat_nat(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),K))))
      | ? [M_2,N_1] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,M_2)),hAPP_nat_nat(F,N_1)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_2),N_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_914_mono__nat__linear__lb]) ).

fof(f_1021_2,plain,
    ! [U_3043,U_3042,U_3041] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(U_3041,U_3043)),U_3042)),hAPP_nat_nat(U_3041,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3043),U_3042))))
      | ? [U_3040,U_3039] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_3041,U_3040)),hAPP_nat_nat(U_3041,U_3039)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3040),U_3039)) ) ),
    inference(variable_rename,[status(thm)],[f_1021_1]) ).

fof(f_1021_3,plain,
    ! [U_3043,U_3042,U_3041] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(U_3041,U_3043)),U_3042)),hAPP_nat_nat(U_3041,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3043),U_3042))))
      | ? [U_3039] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_3041,sK166(U_3043,U_3042,U_3041))),hAPP_nat_nat(U_3041,U_3039)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK166(U_3043,U_3042,U_3041)),U_3039)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK166]),skolemize(U_3040,sK166(U_3043,U_3042,U_3041))],[f_1021_2]) ).

fof(f_1021_4,plain,
    ! [U_3043,U_3042,U_3041] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(U_3041,U_3043)),U_3042)),hAPP_nat_nat(U_3041,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3043),U_3042))))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_3041,sK166(U_3043,U_3042,U_3041))),hAPP_nat_nat(U_3041,sK167(U_3043,U_3042,U_3041))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK166(U_3043,U_3042,U_3041)),sK167(U_3043,U_3042,U_3041))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK167]),skolemize(U_3039,sK167(U_3043,U_3042,U_3041))],[f_1021_3]) ).

fof(f_1021_5,plain,
    ( ! [U_3041,U_3042,U_3043] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_3041,sK166(U_3043,U_3042,U_3041))),hAPP_nat_nat(U_3041,sK167(U_3043,U_3042,U_3041))))
        | ~ sP259(U_3041,U_3042,U_3043) )
    & ! [U_3041,U_3042,U_3043] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK166(U_3043,U_3042,U_3041)),sK167(U_3043,U_3042,U_3041)))
        | ~ sP259(U_3041,U_3042,U_3043) )
    & ! [U_3041,U_3042,U_3043] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(U_3041,U_3043)),U_3042)),hAPP_nat_nat(U_3041,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3043),U_3042))))
        | sP259(U_3041,U_3042,U_3043) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP259])],[f_1021_4]) ).

cnf(f_1021_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(U_3041,U_3043)),U_3042)),hAPP_nat_nat(U_3041,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3043),U_3042))))
    | sP259(U_3041,U_3042,U_3043) ),
    inference(clausify,[status(thm)],[f_1021_5]) ).

cnf(f_1021_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK166(U_3043,U_3042,U_3041)),sK167(U_3043,U_3042,U_3041)))
    | ~ sP259(U_3041,U_3042,U_3043) ),
    inference(clausify,[status(thm)],[f_1021_5]) ).

cnf(f_1021_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_3041,sK166(U_3043,U_3042,U_3041))),hAPP_nat_nat(U_3041,sK167(U_3043,U_3042,U_3041))))
    | ~ sP259(U_3041,U_3042,U_3043) ),
    inference(clausify,[status(thm)],[f_1021_5]) ).

fof(f_1022_1,plain,
    ! [Pa,I_2,J_1] :
      ( hBOOL(hAPP_nat_bool(Pa,I_2))
      | ? [I] :
          ( ~ hBOOL(hAPP_nat_bool(Pa,I))
          & hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,I)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_1)) )
      | ~ hBOOL(hAPP_nat_bool(Pa,J_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_915_inc__induct]) ).

fof(f_1022_2,plain,
    ! [U_3047,U_3046,U_3045] :
      ( hBOOL(hAPP_nat_bool(U_3047,U_3046))
      | ? [U_3044] :
          ( ~ hBOOL(hAPP_nat_bool(U_3047,U_3044))
          & hBOOL(hAPP_nat_bool(U_3047,hAPP_nat_nat(suc,U_3044)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3044),U_3045)) )
      | ~ hBOOL(hAPP_nat_bool(U_3047,U_3045))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3046),U_3045)) ),
    inference(variable_rename,[status(thm)],[f_1022_1]) ).

fof(f_1022_3,plain,
    ! [U_3047,U_3046,U_3045] :
      ( hBOOL(hAPP_nat_bool(U_3047,U_3046))
      | ( ~ hBOOL(hAPP_nat_bool(U_3047,sK168(U_3047,U_3046,U_3045)))
        & hBOOL(hAPP_nat_bool(U_3047,hAPP_nat_nat(suc,sK168(U_3047,U_3046,U_3045))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK168(U_3047,U_3046,U_3045)),U_3045)) )
      | ~ hBOOL(hAPP_nat_bool(U_3047,U_3045))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3046),U_3045)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK168]),skolemize(U_3044,sK168(U_3047,U_3046,U_3045))],[f_1022_2]) ).

fof(f_1022_4,plain,
    ( ! [U_3045,U_3046,U_3047] :
        ( ~ hBOOL(hAPP_nat_bool(U_3047,sK168(U_3047,U_3046,U_3045)))
        | ~ sP260(U_3045,U_3046,U_3047) )
    & ! [U_3045,U_3046,U_3047] :
        ( hBOOL(hAPP_nat_bool(U_3047,hAPP_nat_nat(suc,sK168(U_3047,U_3046,U_3045))))
        | ~ sP260(U_3045,U_3046,U_3047) )
    & ! [U_3045,U_3046,U_3047] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK168(U_3047,U_3046,U_3045)),U_3045))
        | ~ sP260(U_3045,U_3046,U_3047) )
    & ! [U_3045,U_3046,U_3047] :
        ( hBOOL(hAPP_nat_bool(U_3047,U_3046))
        | sP260(U_3045,U_3046,U_3047)
        | ~ hBOOL(hAPP_nat_bool(U_3047,U_3045))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3046),U_3045)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP260])],[f_1022_3]) ).

cnf(f_1022_5,plain,
    ( hBOOL(hAPP_nat_bool(U_3047,U_3046))
    | sP260(U_3045,U_3046,U_3047)
    | ~ hBOOL(hAPP_nat_bool(U_3047,U_3045))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3046),U_3045)) ),
    inference(clausify,[status(thm)],[f_1022_4]) ).

cnf(f_1022_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK168(U_3047,U_3046,U_3045)),U_3045))
    | ~ sP260(U_3045,U_3046,U_3047) ),
    inference(clausify,[status(thm)],[f_1022_4]) ).

cnf(f_1022_7,plain,
    ( hBOOL(hAPP_nat_bool(U_3047,hAPP_nat_nat(suc,sK168(U_3047,U_3046,U_3045))))
    | ~ sP260(U_3045,U_3046,U_3047) ),
    inference(clausify,[status(thm)],[f_1022_4]) ).

cnf(f_1022_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_3047,sK168(U_3047,U_3046,U_3045)))
    | ~ sP260(U_3045,U_3046,U_3047) ),
    inference(clausify,[status(thm)],[f_1022_4]) ).

fof(f_1023_1,plain,
    ! [M_1,N] :
      ( ? [K_2] : N = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),K_2))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_916_less__imp__Suc__add]) ).

fof(f_1023_2,plain,
    ! [U_3050,U_3049] :
      ( ? [U_3048] : U_3049 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3050),U_3048))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3050),U_3049)) ),
    inference(variable_rename,[status(thm)],[f_1023_1]) ).

fof(f_1023_3,plain,
    ! [U_3050,U_3049] :
      ( U_3049 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3050),sK169(U_3050,U_3049)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3050),U_3049)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK169]),skolemize(U_3048,sK169(U_3050,U_3049))],[f_1023_2]) ).

fof(f_1023_4,plain,
    ! [U_3049,U_3050] :
      ( U_3049 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3050),sK169(U_3050,U_3049)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3050),U_3049)) ),
    inference(definitional_conversion,[status(esa)],[f_1023_3]) ).

cnf(f_1023_5,plain,
    ( U_3049 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3050),sK169(U_3050,U_3049)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3050),U_3049)) ),
    inference(clausify,[status(thm)],[f_1023_4]) ).

fof(f_1024_1,plain,
    ! [Na,N_2] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N_2))
      | ? [X_2] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_2),Na))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),N_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_917_bounded__nat__set__is__finite]) ).

fof(f_1024_2,plain,
    ! [U_3053,U_3052] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3052))
      | ? [U_3051] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3051),U_3053))
          & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3051),U_3052)) ) ),
    inference(variable_rename,[status(thm)],[f_1024_1]) ).

fof(f_1024_3,plain,
    ! [U_3053,U_3052] :
      ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3052))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK170(U_3053,U_3052)),U_3053))
        & hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK170(U_3053,U_3052)),U_3052)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK170]),skolemize(U_3051,sK170(U_3053,U_3052))],[f_1024_2]) ).

fof(f_1024_4,plain,
    ( ! [U_3053,U_3052] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK170(U_3053,U_3052)),U_3053))
        | ~ sP261(U_3053,U_3052) )
    & ! [U_3053,U_3052] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK170(U_3053,U_3052)),U_3052))
        | ~ sP261(U_3053,U_3052) )
    & ! [U_3053,U_3052] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3052))
        | sP261(U_3053,U_3052) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP261])],[f_1024_3]) ).

cnf(f_1024_5,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3052))
    | sP261(U_3053,U_3052) ),
    inference(clausify,[status(thm)],[f_1024_4]) ).

cnf(f_1024_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,sK170(U_3053,U_3052)),U_3052))
    | ~ sP261(U_3053,U_3052) ),
    inference(clausify,[status(thm)],[f_1024_4]) ).

cnf(f_1024_7,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK170(U_3053,U_3052)),U_3053))
    | ~ sP261(U_3053,U_3052) ),
    inference(clausify,[status(thm)],[f_1024_4]) ).

fof(f_1025_1,plain,
    ! [I_2,J_1,F] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,I_2)),hAPP_nat_nat(F,J_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1))
      | ? [I,J_2] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(F,I)),hAPP_nat_nat(F,J_2)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),J_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_918_less__mono__imp__le__mono]) ).

fof(f_1025_2,plain,
    ! [U_3058,U_3057,U_3056] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_3056,U_3058)),hAPP_nat_nat(U_3056,U_3057)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3058),U_3057))
      | ? [U_3055,U_3054] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_3056,U_3055)),hAPP_nat_nat(U_3056,U_3054)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3055),U_3054)) ) ),
    inference(variable_rename,[status(thm)],[f_1025_1]) ).

fof(f_1025_3,plain,
    ! [U_3058,U_3057,U_3056] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_3056,U_3058)),hAPP_nat_nat(U_3056,U_3057)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3058),U_3057))
      | ? [U_3054] :
          ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_3056,sK171(U_3058,U_3057,U_3056))),hAPP_nat_nat(U_3056,U_3054)))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK171(U_3058,U_3057,U_3056)),U_3054)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK171]),skolemize(U_3055,sK171(U_3058,U_3057,U_3056))],[f_1025_2]) ).

fof(f_1025_4,plain,
    ! [U_3058,U_3057,U_3056] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_3056,U_3058)),hAPP_nat_nat(U_3056,U_3057)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3058),U_3057))
      | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_3056,sK171(U_3058,U_3057,U_3056))),hAPP_nat_nat(U_3056,sK172(U_3058,U_3057,U_3056))))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK171(U_3058,U_3057,U_3056)),sK172(U_3058,U_3057,U_3056))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK172]),skolemize(U_3054,sK172(U_3058,U_3057,U_3056))],[f_1025_3]) ).

fof(f_1025_5,plain,
    ( ! [U_3056,U_3057,U_3058] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_3056,sK171(U_3058,U_3057,U_3056))),hAPP_nat_nat(U_3056,sK172(U_3058,U_3057,U_3056))))
        | ~ sP262(U_3056,U_3057,U_3058) )
    & ! [U_3056,U_3057,U_3058] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK171(U_3058,U_3057,U_3056)),sK172(U_3058,U_3057,U_3056)))
        | ~ sP262(U_3056,U_3057,U_3058) )
    & ! [U_3056,U_3057,U_3058] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_3056,U_3058)),hAPP_nat_nat(U_3056,U_3057)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3058),U_3057))
        | sP262(U_3056,U_3057,U_3058) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP262])],[f_1025_4]) ).

cnf(f_1025_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(U_3056,U_3058)),hAPP_nat_nat(U_3056,U_3057)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3058),U_3057))
    | sP262(U_3056,U_3057,U_3058) ),
    inference(clausify,[status(thm)],[f_1025_5]) ).

cnf(f_1025_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK171(U_3058,U_3057,U_3056)),sK172(U_3058,U_3057,U_3056)))
    | ~ sP262(U_3056,U_3057,U_3058) ),
    inference(clausify,[status(thm)],[f_1025_5]) ).

cnf(f_1025_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(U_3056,sK171(U_3058,U_3057,U_3056))),hAPP_nat_nat(U_3056,sK172(U_3058,U_3057,U_3056))))
    | ~ sP262(U_3056,U_3057,U_3058) ),
    inference(clausify,[status(thm)],[f_1025_5]) ).

fof(f_1026_1,plain,
    ! [I_1,K_1] :
      ( ? [J_2] :
          ( K_1 = hAPP_nat_nat(suc,J_2)
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_2)) )
      | K_1 = hAPP_nat_nat(suc,I_1)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),K_1)) ),
    inference(fof_nnf,[status(thm)],[fact_919_lessE]) ).

fof(f_1026_2,plain,
    ! [U_3061,U_3060] :
      ( ? [U_3059] :
          ( U_3060 = hAPP_nat_nat(suc,U_3059)
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3061),U_3059)) )
      | U_3060 = hAPP_nat_nat(suc,U_3061)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3061),U_3060)) ),
    inference(variable_rename,[status(thm)],[f_1026_1]) ).

fof(f_1026_3,plain,
    ! [U_3061,U_3060] :
      ( ( U_3060 = hAPP_nat_nat(suc,sK173(U_3061,U_3060))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3061),sK173(U_3061,U_3060))) )
      | U_3060 = hAPP_nat_nat(suc,U_3061)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3061),U_3060)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK173]),skolemize(U_3059,sK173(U_3061,U_3060))],[f_1026_2]) ).

fof(f_1026_4,plain,
    ( ! [U_3060,U_3061] :
        ( U_3060 = hAPP_nat_nat(suc,sK173(U_3061,U_3060))
        | ~ sP263(U_3060,U_3061) )
    & ! [U_3060,U_3061] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3061),sK173(U_3061,U_3060)))
        | ~ sP263(U_3060,U_3061) )
    & ! [U_3060,U_3061] :
        ( sP263(U_3060,U_3061)
        | U_3060 = hAPP_nat_nat(suc,U_3061)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3061),U_3060)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP263])],[f_1026_3]) ).

cnf(f_1026_5,plain,
    ( sP263(U_3060,U_3061)
    | U_3060 = hAPP_nat_nat(suc,U_3061)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3061),U_3060)) ),
    inference(clausify,[status(thm)],[f_1026_4]) ).

cnf(f_1026_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3061),sK173(U_3061,U_3060)))
    | ~ sP263(U_3060,U_3061) ),
    inference(clausify,[status(thm)],[f_1026_4]) ).

cnf(f_1026_7,plain,
    ( U_3060 = hAPP_nat_nat(suc,sK173(U_3061,U_3060))
    | ~ sP263(U_3060,U_3061) ),
    inference(clausify,[status(thm)],[f_1026_4]) ).

fof(f_1027_1,plain,
    ! [I_1,K_1] :
      ( ? [J_2] :
          ( K_1 = hAPP_nat_nat(suc,J_2)
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J_2)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,I_1)),K_1)) ),
    inference(fof_nnf,[status(thm)],[fact_920_Suc__lessE]) ).

fof(f_1027_2,plain,
    ! [U_3064,U_3063] :
      ( ? [U_3062] :
          ( U_3063 = hAPP_nat_nat(suc,U_3062)
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3064),U_3062)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_3064)),U_3063)) ),
    inference(variable_rename,[status(thm)],[f_1027_1]) ).

fof(f_1027_3,plain,
    ! [U_3064,U_3063] :
      ( ( U_3063 = hAPP_nat_nat(suc,sK174(U_3064,U_3063))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3064),sK174(U_3064,U_3063))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_3064)),U_3063)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK174]),skolemize(U_3062,sK174(U_3064,U_3063))],[f_1027_2]) ).

fof(f_1027_4,plain,
    ( ! [U_3063,U_3064] :
        ( U_3063 = hAPP_nat_nat(suc,sK174(U_3064,U_3063))
        | ~ sP264(U_3063,U_3064) )
    & ! [U_3063,U_3064] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3064),sK174(U_3064,U_3063)))
        | ~ sP264(U_3063,U_3064) )
    & ! [U_3063,U_3064] :
        ( sP264(U_3063,U_3064)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_3064)),U_3063)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP264])],[f_1027_3]) ).

cnf(f_1027_5,plain,
    ( sP264(U_3063,U_3064)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,U_3064)),U_3063)) ),
    inference(clausify,[status(thm)],[f_1027_4]) ).

cnf(f_1027_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3064),sK174(U_3064,U_3063)))
    | ~ sP264(U_3063,U_3064) ),
    inference(clausify,[status(thm)],[f_1027_4]) ).

cnf(f_1027_7,plain,
    ( U_3063 = hAPP_nat_nat(suc,sK174(U_3064,U_3063))
    | ~ sP264(U_3063,U_3064) ),
    inference(clausify,[status(thm)],[f_1027_4]) ).

fof(f_1028_1,plain,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)),
    inference(fof_nnf,[status(thm)],[fact_921_less__zeroE]) ).

fof(f_1028_2,plain,
    ! [U_3065] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3065),zero_zero_nat)),
    inference(variable_rename,[status(thm)],[f_1028_1]) ).

fof(f_1028_3,plain,
    ! [U_3065] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3065),zero_zero_nat)),
    inference(definitional_conversion,[status(esa)],[f_1028_2]) ).

cnf(f_1028_4,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3065),zero_zero_nat)),
    inference(clausify,[status(thm)],[f_1028_3]) ).

fof(f_1029_1,plain,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N)),
    inference(fof_nnf,[status(thm)],[fact_922_le0]) ).

fof(f_1029_2,plain,
    ! [U_3066] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_3066)),
    inference(variable_rename,[status(thm)],[f_1029_1]) ).

fof(f_1029_3,plain,
    ! [U_3066] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_3066)),
    inference(definitional_conversion,[status(esa)],[f_1029_2]) ).

cnf(f_1029_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_3066)),
    inference(clausify,[status(thm)],[f_1029_3]) ).

fof(f_1030_1,plain,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,N))),
    inference(fof_nnf,[status(thm)],[fact_923_zero__less__Suc]) ).

fof(f_1030_2,plain,
    ! [U_3067] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,U_3067))),
    inference(variable_rename,[status(thm)],[f_1030_1]) ).

fof(f_1030_3,plain,
    ! [U_3067] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,U_3067))),
    inference(definitional_conversion,[status(esa)],[f_1030_2]) ).

cnf(f_1030_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(suc,U_3067))),
    inference(clausify,[status(thm)],[f_1030_3]) ).

fof(f_1031_1,plain,
    ! [Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),zero_zero_nat))
        | Na != zero_zero_nat )
      & ( Na = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),zero_zero_nat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_924_le__0__eq]) ).

fof(f_1031_2,plain,
    ! [U_3068] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3068),zero_zero_nat))
        | U_3068 != zero_zero_nat )
      & ( U_3068 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3068),zero_zero_nat)) ) ),
    inference(variable_rename,[status(thm)],[f_1031_1]) ).

fof(f_1031_3,plain,
    ( ! [U_3070] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3070),zero_zero_nat))
        | U_3070 != zero_zero_nat )
    & ! [U_3069] :
        ( U_3069 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3069),zero_zero_nat)) ) ),
    inference(miniscope,[status(thm)],[f_1031_2]) ).

fof(f_1031_4,plain,
    ( ! [U_3070] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3070),zero_zero_nat))
        | U_3070 != zero_zero_nat )
    & ! [U_3069] :
        ( U_3069 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3069),zero_zero_nat)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1031_3]) ).

cnf(f_1031_5,plain,
    ( U_3069 = zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3069),zero_zero_nat)) ),
    inference(clausify,[status(thm)],[f_1031_4]) ).

cnf(f_1031_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3070),zero_zero_nat))
    | U_3070 != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1031_4]) ).

fof(f_1032_1,plain,
    ! [N] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),N)),
    inference(fof_nnf,[status(thm)],[fact_925_less__eq__nat_Osimps_I1_J]) ).

fof(f_1032_2,plain,
    ! [U_3071] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_3071)),
    inference(variable_rename,[status(thm)],[f_1032_1]) ).

fof(f_1032_3,plain,
    ! [U_3071] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_3071)),
    inference(definitional_conversion,[status(esa)],[f_1032_2]) ).

cnf(f_1032_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,zero_zero_nat),U_3071)),
    inference(clausify,[status(thm)],[f_1032_3]) ).

fof(f_1033_1,plain,
    ! [M_1,N] :
      ( M_1 = N
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),M_1) != zero_zero_nat
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N) != zero_zero_nat ),
    inference(fof_nnf,[status(thm)],[fact_926_diffs0__imp__equal]) ).

fof(f_1033_2,plain,
    ! [U_3073,U_3072] :
      ( U_3073 = U_3072
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3072),U_3073) != zero_zero_nat
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3073),U_3072) != zero_zero_nat ),
    inference(variable_rename,[status(thm)],[f_1033_1]) ).

fof(f_1033_3,plain,
    ! [U_3072,U_3073] :
      ( U_3073 = U_3072
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3072),U_3073) != zero_zero_nat
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3073),U_3072) != zero_zero_nat ),
    inference(definitional_conversion,[status(esa)],[f_1033_2]) ).

cnf(f_1033_4,plain,
    ( U_3073 = U_3072
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3072),U_3073) != zero_zero_nat
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3073),U_3072) != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1033_3]) ).

fof(f_1034_1,plain,
    ! [M_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),M_1) = zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_927_diff__self__eq__0]) ).

fof(f_1034_2,plain,
    ! [U_3074] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3074),U_3074) = zero_zero_nat,
    inference(variable_rename,[status(thm)],[f_1034_1]) ).

fof(f_1034_3,plain,
    ! [U_3074] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3074),U_3074) = zero_zero_nat,
    inference(definitional_conversion,[status(esa)],[f_1034_2]) ).

cnf(f_1034_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3074),U_3074) = zero_zero_nat,
    inference(clausify,[status(thm)],[f_1034_3]) ).

fof(f_1035_1,plain,
    ! [M_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),zero_zero_nat) = M_1,
    inference(fof_nnf,[status(thm)],[fact_928_minus__nat_Odiff__0]) ).

fof(f_1035_2,plain,
    ! [U_3075] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3075),zero_zero_nat) = U_3075,
    inference(variable_rename,[status(thm)],[f_1035_1]) ).

fof(f_1035_3,plain,
    ! [U_3075] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3075),zero_zero_nat) = U_3075,
    inference(definitional_conversion,[status(esa)],[f_1035_2]) ).

cnf(f_1035_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3075),zero_zero_nat) = U_3075,
    inference(clausify,[status(thm)],[f_1035_3]) ).

fof(f_1036_1,plain,
    ! [N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),N) = zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_929_diff__0__eq__0]) ).

fof(f_1036_2,plain,
    ! [U_3076] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),U_3076) = zero_zero_nat,
    inference(variable_rename,[status(thm)],[f_1036_1]) ).

fof(f_1036_3,plain,
    ! [U_3076] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),U_3076) = zero_zero_nat,
    inference(definitional_conversion,[status(esa)],[f_1036_2]) ).

cnf(f_1036_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,zero_zero_nat),U_3076) = zero_zero_nat,
    inference(clausify,[status(thm)],[f_1036_3]) ).

fof(f_1037_1,plain,
    bot_bot_nat = zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_930_bot__nat__def]) ).

fof(f_1037_2,plain,
    bot_bot_nat = zero_zero_nat,
    inference(definitional_conversion,[status(esa)],[f_1037_1]) ).

cnf(f_1037_3,plain,
    bot_bot_nat = zero_zero_nat,
    inference(clausify,[status(thm)],[f_1037_2]) ).

fof(f_1038_1,plain,
    ! [M_1,N] :
      ( N = zero_zero_nat
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N) != M_1 ),
    inference(fof_nnf,[status(thm)],[fact_931_add__eq__self__zero]) ).

fof(f_1038_2,plain,
    ! [U_3078,U_3077] :
      ( U_3077 = zero_zero_nat
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3078),U_3077) != U_3078 ),
    inference(variable_rename,[status(thm)],[f_1038_1]) ).

fof(f_1038_3,plain,
    ! [U_3077,U_3078] :
      ( U_3077 = zero_zero_nat
      | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3078),U_3077) != U_3078 ),
    inference(definitional_conversion,[status(esa)],[f_1038_2]) ).

cnf(f_1038_4,plain,
    ( U_3077 = zero_zero_nat
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3078),U_3077) != U_3078 ),
    inference(clausify,[status(thm)],[f_1038_3]) ).

fof(f_1039_1,plain,
    ! [M,Na] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),Na) = zero_zero_nat
        | Na != zero_zero_nat
        | M != zero_zero_nat )
      & ( ( Na = zero_zero_nat
          & M = zero_zero_nat )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),Na) != zero_zero_nat ) ),
    inference(fof_nnf,[status(thm)],[fact_932_add__is__0]) ).

fof(f_1039_2,plain,
    ! [U_3080,U_3079] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3080),U_3079) = zero_zero_nat
        | U_3079 != zero_zero_nat
        | U_3080 != zero_zero_nat )
      & ( ( U_3079 = zero_zero_nat
          & U_3080 = zero_zero_nat )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3080),U_3079) != zero_zero_nat ) ),
    inference(variable_rename,[status(thm)],[f_1039_1]) ).

fof(f_1039_3,plain,
    ( ! [U_3084,U_3082] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3084),U_3082) = zero_zero_nat
        | U_3082 != zero_zero_nat
        | U_3084 != zero_zero_nat )
    & ! [U_3083,U_3081] :
        ( ( U_3081 = zero_zero_nat
          & U_3083 = zero_zero_nat )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3083),U_3081) != zero_zero_nat ) ),
    inference(miniscope,[status(thm)],[f_1039_2]) ).

fof(f_1039_4,plain,
    ( ! [U_3083,U_3081] :
        ( U_3081 = zero_zero_nat
        | ~ sP265(U_3083,U_3081) )
    & ! [U_3083,U_3081] :
        ( U_3083 = zero_zero_nat
        | ~ sP265(U_3083,U_3081) )
    & ! [U_3082,U_3084] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3084),U_3082) = zero_zero_nat
        | U_3082 != zero_zero_nat
        | U_3084 != zero_zero_nat )
    & ! [U_3083,U_3081] :
        ( sP265(U_3083,U_3081)
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3083),U_3081) != zero_zero_nat ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP265])],[f_1039_3]) ).

cnf(f_1039_5,plain,
    ( sP265(U_3083,U_3081)
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3083),U_3081) != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1039_4]) ).

cnf(f_1039_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3084),U_3082) = zero_zero_nat
    | U_3082 != zero_zero_nat
    | U_3084 != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1039_4]) ).

cnf(f_1039_7,plain,
    ( U_3083 = zero_zero_nat
    | ~ sP265(U_3083,U_3081) ),
    inference(clausify,[status(thm)],[f_1039_4]) ).

cnf(f_1039_8,plain,
    ( U_3081 = zero_zero_nat
    | ~ sP265(U_3083,U_3081) ),
    inference(clausify,[status(thm)],[f_1039_4]) ).

fof(f_1040_1,plain,
    ! [M_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),zero_zero_nat) = M_1,
    inference(fof_nnf,[status(thm)],[fact_933_Nat_Oadd__0__right]) ).

fof(f_1040_2,plain,
    ! [U_3085] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3085),zero_zero_nat) = U_3085,
    inference(variable_rename,[status(thm)],[f_1040_1]) ).

fof(f_1040_3,plain,
    ! [U_3085] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3085),zero_zero_nat) = U_3085,
    inference(definitional_conversion,[status(esa)],[f_1040_2]) ).

cnf(f_1040_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3085),zero_zero_nat) = U_3085,
    inference(clausify,[status(thm)],[f_1040_3]) ).

fof(f_1041_1,plain,
    ! [N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),N) = N,
    inference(fof_nnf,[status(thm)],[fact_934_plus__nat_Oadd__0]) ).

fof(f_1041_2,plain,
    ! [U_3086] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),U_3086) = U_3086,
    inference(variable_rename,[status(thm)],[f_1041_1]) ).

fof(f_1041_3,plain,
    ! [U_3086] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),U_3086) = U_3086,
    inference(definitional_conversion,[status(esa)],[f_1041_2]) ).

cnf(f_1041_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,zero_zero_nat),U_3086) = U_3086,
    inference(clausify,[status(thm)],[f_1041_3]) ).

fof(f_1042_1,plain,
    ! [N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N))
      | N = zero_zero_nat ),
    inference(fof_nnf,[status(thm)],[fact_935_gr0I]) ).

fof(f_1042_2,plain,
    ! [U_3087] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3087))
      | U_3087 = zero_zero_nat ),
    inference(variable_rename,[status(thm)],[f_1042_1]) ).

fof(f_1042_3,plain,
    ! [U_3087] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3087))
      | U_3087 = zero_zero_nat ),
    inference(definitional_conversion,[status(esa)],[f_1042_2]) ).

cnf(f_1042_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3087))
    | U_3087 = zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1042_3]) ).

fof(f_1043_1,plain,
    ! [M_1,N] :
      ( N != zero_zero_nat
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_936_gr__implies__not0]) ).

fof(f_1043_2,plain,
    ! [U_3089,U_3088] :
      ( U_3088 != zero_zero_nat
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3089),U_3088)) ),
    inference(variable_rename,[status(thm)],[f_1043_1]) ).

fof(f_1043_3,plain,
    ! [U_3088,U_3089] :
      ( U_3088 != zero_zero_nat
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3089),U_3088)) ),
    inference(definitional_conversion,[status(esa)],[f_1043_2]) ).

cnf(f_1043_4,plain,
    ( U_3088 != zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3089),U_3088)) ),
    inference(clausify,[status(thm)],[f_1043_3]) ).

fof(f_1044_1,plain,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)),
    inference(fof_nnf,[status(thm)],[fact_937_less__nat__zero__code]) ).

fof(f_1044_2,plain,
    ! [U_3090] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3090),zero_zero_nat)),
    inference(variable_rename,[status(thm)],[f_1044_1]) ).

fof(f_1044_3,plain,
    ! [U_3090] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3090),zero_zero_nat)),
    inference(definitional_conversion,[status(esa)],[f_1044_2]) ).

cnf(f_1044_4,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3090),zero_zero_nat)),
    inference(clausify,[status(thm)],[f_1044_3]) ).

fof(f_1045_1,plain,
    ! [Na] :
      ( ( Na != zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na))
        | Na = zero_zero_nat ) ),
    inference(fof_nnf,[status(thm)],[fact_938_neq0__conv]) ).

fof(f_1045_2,plain,
    ! [U_3091] :
      ( ( U_3091 != zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3091)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3091))
        | U_3091 = zero_zero_nat ) ),
    inference(variable_rename,[status(thm)],[f_1045_1]) ).

fof(f_1045_3,plain,
    ( ! [U_3093] :
        ( U_3093 != zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3093)) )
    & ! [U_3092] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3092))
        | U_3092 = zero_zero_nat ) ),
    inference(miniscope,[status(thm)],[f_1045_2]) ).

fof(f_1045_4,plain,
    ( ! [U_3093] :
        ( U_3093 != zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3093)) )
    & ! [U_3092] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3092))
        | U_3092 = zero_zero_nat ) ),
    inference(definitional_conversion,[status(esa)],[f_1045_3]) ).

cnf(f_1045_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3092))
    | U_3092 = zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1045_4]) ).

cnf(f_1045_6,plain,
    ( U_3093 != zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3093)) ),
    inference(clausify,[status(thm)],[f_1045_4]) ).

fof(f_1046_1,plain,
    ! [N] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),zero_zero_nat)),
    inference(fof_nnf,[status(thm)],[fact_939_not__less0]) ).

fof(f_1046_2,plain,
    ! [U_3094] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3094),zero_zero_nat)),
    inference(variable_rename,[status(thm)],[f_1046_1]) ).

fof(f_1046_3,plain,
    ! [U_3094] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3094),zero_zero_nat)),
    inference(definitional_conversion,[status(esa)],[f_1046_2]) ).

cnf(f_1046_4,plain,
    ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3094),zero_zero_nat)),
    inference(clausify,[status(thm)],[f_1046_3]) ).

fof(f_1047_1,plain,
    ! [M_1] : hAPP_nat_nat(suc,M_1) != zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_940_Suc__neq__Zero]) ).

fof(f_1047_2,plain,
    ! [U_3095] : hAPP_nat_nat(suc,U_3095) != zero_zero_nat,
    inference(variable_rename,[status(thm)],[f_1047_1]) ).

fof(f_1047_3,plain,
    ! [U_3095] : hAPP_nat_nat(suc,U_3095) != zero_zero_nat,
    inference(definitional_conversion,[status(esa)],[f_1047_2]) ).

cnf(f_1047_4,plain,
    hAPP_nat_nat(suc,U_3095) != zero_zero_nat,
    inference(clausify,[status(thm)],[f_1047_3]) ).

fof(f_1048_1,plain,
    ! [M_1] : zero_zero_nat != hAPP_nat_nat(suc,M_1),
    inference(fof_nnf,[status(thm)],[fact_941_Zero__neq__Suc]) ).

fof(f_1048_2,plain,
    ! [U_3096] : zero_zero_nat != hAPP_nat_nat(suc,U_3096),
    inference(variable_rename,[status(thm)],[f_1048_1]) ).

fof(f_1048_3,plain,
    ! [U_3096] : zero_zero_nat != hAPP_nat_nat(suc,U_3096),
    inference(definitional_conversion,[status(esa)],[f_1048_2]) ).

cnf(f_1048_4,plain,
    zero_zero_nat != hAPP_nat_nat(suc,U_3096),
    inference(clausify,[status(thm)],[f_1048_3]) ).

fof(f_1049_1,plain,
    ! [Nat_2] : hAPP_nat_nat(suc,Nat_2) != zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_942_nat_Osimps_I3_J]) ).

fof(f_1049_2,plain,
    ! [U_3097] : hAPP_nat_nat(suc,U_3097) != zero_zero_nat,
    inference(variable_rename,[status(thm)],[f_1049_1]) ).

fof(f_1049_3,plain,
    ! [U_3097] : hAPP_nat_nat(suc,U_3097) != zero_zero_nat,
    inference(definitional_conversion,[status(esa)],[f_1049_2]) ).

cnf(f_1049_4,plain,
    hAPP_nat_nat(suc,U_3097) != zero_zero_nat,
    inference(clausify,[status(thm)],[f_1049_3]) ).

fof(f_1050_1,plain,
    ! [M_1] : hAPP_nat_nat(suc,M_1) != zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_943_Suc__not__Zero]) ).

fof(f_1050_2,plain,
    ! [U_3098] : hAPP_nat_nat(suc,U_3098) != zero_zero_nat,
    inference(variable_rename,[status(thm)],[f_1050_1]) ).

fof(f_1050_3,plain,
    ! [U_3098] : hAPP_nat_nat(suc,U_3098) != zero_zero_nat,
    inference(definitional_conversion,[status(esa)],[f_1050_2]) ).

cnf(f_1050_4,plain,
    hAPP_nat_nat(suc,U_3098) != zero_zero_nat,
    inference(clausify,[status(thm)],[f_1050_3]) ).

fof(f_1051_1,plain,
    ! [Nat_1] : zero_zero_nat != hAPP_nat_nat(suc,Nat_1),
    inference(fof_nnf,[status(thm)],[fact_944_nat_Osimps_I2_J]) ).

fof(f_1051_2,plain,
    ! [U_3099] : zero_zero_nat != hAPP_nat_nat(suc,U_3099),
    inference(variable_rename,[status(thm)],[f_1051_1]) ).

fof(f_1051_3,plain,
    ! [U_3099] : zero_zero_nat != hAPP_nat_nat(suc,U_3099),
    inference(definitional_conversion,[status(esa)],[f_1051_2]) ).

cnf(f_1051_4,plain,
    zero_zero_nat != hAPP_nat_nat(suc,U_3099),
    inference(clausify,[status(thm)],[f_1051_3]) ).

fof(f_1052_1,plain,
    ! [M_1] : zero_zero_nat != hAPP_nat_nat(suc,M_1),
    inference(fof_nnf,[status(thm)],[fact_945_Zero__not__Suc]) ).

fof(f_1052_2,plain,
    ! [U_3100] : zero_zero_nat != hAPP_nat_nat(suc,U_3100),
    inference(variable_rename,[status(thm)],[f_1052_1]) ).

fof(f_1052_3,plain,
    ! [U_3100] : zero_zero_nat != hAPP_nat_nat(suc,U_3100),
    inference(definitional_conversion,[status(esa)],[f_1052_2]) ).

cnf(f_1052_4,plain,
    zero_zero_nat != hAPP_nat_nat(suc,U_3100),
    inference(clausify,[status(thm)],[f_1052_3]) ).

fof(f_1053_1,plain,
    ! [Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na))
        | ! [M_2] : Na != hAPP_nat_nat(suc,M_2) )
      & ( ? [M_2] : Na = hAPP_nat_nat(suc,M_2)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_946_gr0__conv__Suc]) ).

fof(f_1053_2,plain,
    ! [U_3103] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3103))
        | ! [U_3102] : U_3103 != hAPP_nat_nat(suc,U_3102) )
      & ( ? [U_3101] : U_3103 = hAPP_nat_nat(suc,U_3101)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3103)) ) ),
    inference(variable_rename,[status(thm)],[f_1053_1]) ).

fof(f_1053_3,plain,
    ( ! [U_3105] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3105))
        | ! [U_3102] : U_3105 != hAPP_nat_nat(suc,U_3102) )
    & ! [U_3104] :
        ( ? [U_3101] : U_3104 = hAPP_nat_nat(suc,U_3101)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3104)) ) ),
    inference(miniscope,[status(thm)],[f_1053_2]) ).

fof(f_1053_4,plain,
    ( ! [U_3105] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3105))
        | ! [U_3102] : U_3105 != hAPP_nat_nat(suc,U_3102) )
    & ! [U_3104] :
        ( U_3104 = hAPP_nat_nat(suc,sK175(U_3104))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3104)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK175]),skolemize(U_3101,sK175(U_3104))],[f_1053_3]) ).

fof(f_1053_5,plain,
    ( ! [U_3102,U_3105] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3105))
        | U_3105 != hAPP_nat_nat(suc,U_3102) )
    & ! [U_3104] :
        ( U_3104 = hAPP_nat_nat(suc,sK175(U_3104))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3104)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1053_4]) ).

cnf(f_1053_6,plain,
    ( U_3104 = hAPP_nat_nat(suc,sK175(U_3104))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3104)) ),
    inference(clausify,[status(thm)],[f_1053_5]) ).

cnf(f_1053_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3105))
    | U_3105 != hAPP_nat_nat(suc,U_3102) ),
    inference(clausify,[status(thm)],[f_1053_5]) ).

fof(f_1054_1,plain,
    ! [Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,zero_zero_nat)))
        | Na != zero_zero_nat )
      & ( Na = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,Na),hAPP_nat_nat(suc,zero_zero_nat))) ) ),
    inference(fof_nnf,[status(thm)],[fact_947_less__Suc0]) ).

fof(f_1054_2,plain,
    ! [U_3106] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3106),hAPP_nat_nat(suc,zero_zero_nat)))
        | U_3106 != zero_zero_nat )
      & ( U_3106 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3106),hAPP_nat_nat(suc,zero_zero_nat))) ) ),
    inference(variable_rename,[status(thm)],[f_1054_1]) ).

fof(f_1054_3,plain,
    ( ! [U_3108] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3108),hAPP_nat_nat(suc,zero_zero_nat)))
        | U_3108 != zero_zero_nat )
    & ! [U_3107] :
        ( U_3107 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3107),hAPP_nat_nat(suc,zero_zero_nat))) ) ),
    inference(miniscope,[status(thm)],[f_1054_2]) ).

fof(f_1054_4,plain,
    ( ! [U_3108] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3108),hAPP_nat_nat(suc,zero_zero_nat)))
        | U_3108 != zero_zero_nat )
    & ! [U_3107] :
        ( U_3107 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3107),hAPP_nat_nat(suc,zero_zero_nat))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1054_3]) ).

cnf(f_1054_5,plain,
    ( U_3107 = zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3107),hAPP_nat_nat(suc,zero_zero_nat))) ),
    inference(clausify,[status(thm)],[f_1054_4]) ).

cnf(f_1054_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3108),hAPP_nat_nat(suc,zero_zero_nat)))
    | U_3108 != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1054_4]) ).

fof(f_1055_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,Na)))
        | ( ! [J_2] :
              ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),Na))
              | M != hAPP_nat_nat(suc,J_2) )
          & M != zero_zero_nat ) )
      & ( ? [J_2] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,J_2),Na))
            & M = hAPP_nat_nat(suc,J_2) )
        | M = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(suc,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_948_less__Suc__eq__0__disj]) ).

fof(f_1055_2,plain,
    ! [U_3112,U_3111] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3112),hAPP_nat_nat(suc,U_3111)))
        | ( ! [U_3110] :
              ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3110),U_3111))
              | U_3112 != hAPP_nat_nat(suc,U_3110) )
          & U_3112 != zero_zero_nat ) )
      & ( ? [U_3109] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3109),U_3111))
            & U_3112 = hAPP_nat_nat(suc,U_3109) )
        | U_3112 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3112),hAPP_nat_nat(suc,U_3111))) ) ),
    inference(variable_rename,[status(thm)],[f_1055_1]) ).

fof(f_1055_3,plain,
    ( ! [U_3116,U_3114] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3116),hAPP_nat_nat(suc,U_3114)))
        | ( ! [U_3110] :
              ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3110),U_3114))
              | U_3116 != hAPP_nat_nat(suc,U_3110) )
          & U_3116 != zero_zero_nat ) )
    & ! [U_3115,U_3113] :
        ( ? [U_3109] :
            ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3109),U_3113))
            & U_3115 = hAPP_nat_nat(suc,U_3109) )
        | U_3115 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3115),hAPP_nat_nat(suc,U_3113))) ) ),
    inference(miniscope,[status(thm)],[f_1055_2]) ).

fof(f_1055_4,plain,
    ( ! [U_3116,U_3114] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3116),hAPP_nat_nat(suc,U_3114)))
        | ( ! [U_3110] :
              ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3110),U_3114))
              | U_3116 != hAPP_nat_nat(suc,U_3110) )
          & U_3116 != zero_zero_nat ) )
    & ! [U_3115,U_3113] :
        ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK176(U_3115,U_3113)),U_3113))
          & U_3115 = hAPP_nat_nat(suc,sK176(U_3115,U_3113)) )
        | U_3115 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3115),hAPP_nat_nat(suc,U_3113))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK176]),skolemize(U_3109,sK176(U_3115,U_3113))],[f_1055_3]) ).

fof(f_1055_5,plain,
    ( ! [U_3116,U_3110,U_3114] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3110),U_3114))
        | U_3116 != hAPP_nat_nat(suc,U_3110)
        | ~ sP267(U_3116,U_3110,U_3114) )
    & ! [U_3116,U_3110,U_3114] :
        ( U_3116 != zero_zero_nat
        | ~ sP267(U_3116,U_3110,U_3114) )
    & ! [U_3115,U_3113] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK176(U_3115,U_3113)),U_3113))
        | ~ sP266(U_3115,U_3113) )
    & ! [U_3115,U_3113] :
        ( U_3115 = hAPP_nat_nat(suc,sK176(U_3115,U_3113))
        | ~ sP266(U_3115,U_3113) )
    & ! [U_3116,U_3110,U_3114] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3116),hAPP_nat_nat(suc,U_3114)))
        | sP267(U_3116,U_3110,U_3114) )
    & ! [U_3115,U_3113] :
        ( sP266(U_3115,U_3113)
        | U_3115 = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3115),hAPP_nat_nat(suc,U_3113))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP266,sP267])],[f_1055_4]) ).

cnf(f_1055_6,plain,
    ( sP266(U_3115,U_3113)
    | U_3115 = zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3115),hAPP_nat_nat(suc,U_3113))) ),
    inference(clausify,[status(thm)],[f_1055_5]) ).

cnf(f_1055_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3116),hAPP_nat_nat(suc,U_3114)))
    | sP267(U_3116,U_3110,U_3114) ),
    inference(clausify,[status(thm)],[f_1055_5]) ).

cnf(f_1055_8,plain,
    ( U_3115 = hAPP_nat_nat(suc,sK176(U_3115,U_3113))
    | ~ sP266(U_3115,U_3113) ),
    inference(clausify,[status(thm)],[f_1055_5]) ).

cnf(f_1055_9,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK176(U_3115,U_3113)),U_3113))
    | ~ sP266(U_3115,U_3113) ),
    inference(clausify,[status(thm)],[f_1055_5]) ).

cnf(f_1055_10,plain,
    ( U_3116 != zero_zero_nat
    | ~ sP267(U_3116,U_3110,U_3114) ),
    inference(clausify,[status(thm)],[f_1055_5]) ).

cnf(f_1055_11,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3110),U_3114))
    | U_3116 != hAPP_nat_nat(suc,U_3110)
    | ~ sP267(U_3116,U_3110,U_3114) ),
    inference(clausify,[status(thm)],[f_1055_5]) ).

fof(f_1056_1,plain,
    ! [M,Na] :
      ( ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),Na)
        | ( ( Na != hAPP_nat_nat(suc,zero_zero_nat)
            | M != zero_zero_nat )
          & ( Na != zero_zero_nat
            | M != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
      & ( ( Na = hAPP_nat_nat(suc,zero_zero_nat)
          & M = zero_zero_nat )
        | ( Na = zero_zero_nat
          & M = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_949_one__is__add]) ).

fof(f_1056_2,plain,
    ! [U_3118,U_3117] :
      ( ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3118),U_3117)
        | ( ( U_3117 != hAPP_nat_nat(suc,zero_zero_nat)
            | U_3118 != zero_zero_nat )
          & ( U_3117 != zero_zero_nat
            | U_3118 != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
      & ( ( U_3117 = hAPP_nat_nat(suc,zero_zero_nat)
          & U_3118 = zero_zero_nat )
        | ( U_3117 = zero_zero_nat
          & U_3118 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3118),U_3117) ) ),
    inference(variable_rename,[status(thm)],[f_1056_1]) ).

fof(f_1056_3,plain,
    ( ! [U_3122,U_3120] :
        ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3122),U_3120)
        | ( ( U_3120 != hAPP_nat_nat(suc,zero_zero_nat)
            | U_3122 != zero_zero_nat )
          & ( U_3120 != zero_zero_nat
            | U_3122 != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
    & ! [U_3121,U_3119] :
        ( ( U_3119 = hAPP_nat_nat(suc,zero_zero_nat)
          & U_3121 = zero_zero_nat )
        | ( U_3119 = zero_zero_nat
          & U_3121 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3121),U_3119) ) ),
    inference(miniscope,[status(thm)],[f_1056_2]) ).

fof(f_1056_4,plain,
    ( ! [U_3120,U_3122] :
        ( U_3120 != hAPP_nat_nat(suc,zero_zero_nat)
        | U_3122 != zero_zero_nat
        | ~ sP270(U_3120,U_3122) )
    & ! [U_3120,U_3122] :
        ( U_3120 != zero_zero_nat
        | U_3122 != hAPP_nat_nat(suc,zero_zero_nat)
        | ~ sP270(U_3120,U_3122) )
    & ! [U_3119,U_3121] :
        ( U_3119 = hAPP_nat_nat(suc,zero_zero_nat)
        | ~ sP269(U_3119,U_3121) )
    & ! [U_3119,U_3121] :
        ( U_3121 = zero_zero_nat
        | ~ sP269(U_3119,U_3121) )
    & ! [U_3119,U_3121] :
        ( U_3119 = zero_zero_nat
        | ~ sP268(U_3119,U_3121) )
    & ! [U_3119,U_3121] :
        ( U_3121 = hAPP_nat_nat(suc,zero_zero_nat)
        | ~ sP268(U_3119,U_3121) )
    & ! [U_3120,U_3122] :
        ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3122),U_3120)
        | sP270(U_3120,U_3122) )
    & ! [U_3119,U_3121] :
        ( sP269(U_3119,U_3121)
        | sP268(U_3119,U_3121)
        | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3121),U_3119) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP268,sP269,sP270])],[f_1056_3]) ).

cnf(f_1056_5,plain,
    ( sP269(U_3119,U_3121)
    | sP268(U_3119,U_3121)
    | hAPP_nat_nat(suc,zero_zero_nat) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3121),U_3119) ),
    inference(clausify,[status(thm)],[f_1056_4]) ).

cnf(f_1056_6,plain,
    ( hAPP_nat_nat(suc,zero_zero_nat) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3122),U_3120)
    | sP270(U_3120,U_3122) ),
    inference(clausify,[status(thm)],[f_1056_4]) ).

cnf(f_1056_7,plain,
    ( U_3121 = hAPP_nat_nat(suc,zero_zero_nat)
    | ~ sP268(U_3119,U_3121) ),
    inference(clausify,[status(thm)],[f_1056_4]) ).

cnf(f_1056_8,plain,
    ( U_3119 = zero_zero_nat
    | ~ sP268(U_3119,U_3121) ),
    inference(clausify,[status(thm)],[f_1056_4]) ).

cnf(f_1056_9,plain,
    ( U_3121 = zero_zero_nat
    | ~ sP269(U_3119,U_3121) ),
    inference(clausify,[status(thm)],[f_1056_4]) ).

cnf(f_1056_10,plain,
    ( U_3119 = hAPP_nat_nat(suc,zero_zero_nat)
    | ~ sP269(U_3119,U_3121) ),
    inference(clausify,[status(thm)],[f_1056_4]) ).

cnf(f_1056_11,plain,
    ( U_3120 != zero_zero_nat
    | U_3122 != hAPP_nat_nat(suc,zero_zero_nat)
    | ~ sP270(U_3120,U_3122) ),
    inference(clausify,[status(thm)],[f_1056_4]) ).

cnf(f_1056_12,plain,
    ( U_3120 != hAPP_nat_nat(suc,zero_zero_nat)
    | U_3122 != zero_zero_nat
    | ~ sP270(U_3120,U_3122) ),
    inference(clausify,[status(thm)],[f_1056_4]) ).

fof(f_1057_1,plain,
    ! [M,Na] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),Na) = hAPP_nat_nat(suc,zero_zero_nat)
        | ( ( Na != hAPP_nat_nat(suc,zero_zero_nat)
            | M != zero_zero_nat )
          & ( Na != zero_zero_nat
            | M != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
      & ( ( Na = hAPP_nat_nat(suc,zero_zero_nat)
          & M = zero_zero_nat )
        | ( Na = zero_zero_nat
          & M = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),Na) != hAPP_nat_nat(suc,zero_zero_nat) ) ),
    inference(fof_nnf,[status(thm)],[fact_950_add__is__1]) ).

fof(f_1057_2,plain,
    ! [U_3124,U_3123] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3124),U_3123) = hAPP_nat_nat(suc,zero_zero_nat)
        | ( ( U_3123 != hAPP_nat_nat(suc,zero_zero_nat)
            | U_3124 != zero_zero_nat )
          & ( U_3123 != zero_zero_nat
            | U_3124 != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
      & ( ( U_3123 = hAPP_nat_nat(suc,zero_zero_nat)
          & U_3124 = zero_zero_nat )
        | ( U_3123 = zero_zero_nat
          & U_3124 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3124),U_3123) != hAPP_nat_nat(suc,zero_zero_nat) ) ),
    inference(variable_rename,[status(thm)],[f_1057_1]) ).

fof(f_1057_3,plain,
    ( ! [U_3128,U_3126] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3128),U_3126) = hAPP_nat_nat(suc,zero_zero_nat)
        | ( ( U_3126 != hAPP_nat_nat(suc,zero_zero_nat)
            | U_3128 != zero_zero_nat )
          & ( U_3126 != zero_zero_nat
            | U_3128 != hAPP_nat_nat(suc,zero_zero_nat) ) ) )
    & ! [U_3127,U_3125] :
        ( ( U_3125 = hAPP_nat_nat(suc,zero_zero_nat)
          & U_3127 = zero_zero_nat )
        | ( U_3125 = zero_zero_nat
          & U_3127 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3127),U_3125) != hAPP_nat_nat(suc,zero_zero_nat) ) ),
    inference(miniscope,[status(thm)],[f_1057_2]) ).

fof(f_1057_4,plain,
    ( ! [U_3126,U_3128] :
        ( U_3126 != hAPP_nat_nat(suc,zero_zero_nat)
        | U_3128 != zero_zero_nat
        | ~ sP273(U_3126,U_3128) )
    & ! [U_3126,U_3128] :
        ( U_3126 != zero_zero_nat
        | U_3128 != hAPP_nat_nat(suc,zero_zero_nat)
        | ~ sP273(U_3126,U_3128) )
    & ! [U_3127,U_3125] :
        ( U_3125 = hAPP_nat_nat(suc,zero_zero_nat)
        | ~ sP272(U_3127,U_3125) )
    & ! [U_3127,U_3125] :
        ( U_3127 = zero_zero_nat
        | ~ sP272(U_3127,U_3125) )
    & ! [U_3127,U_3125] :
        ( U_3125 = zero_zero_nat
        | ~ sP271(U_3127,U_3125) )
    & ! [U_3127,U_3125] :
        ( U_3127 = hAPP_nat_nat(suc,zero_zero_nat)
        | ~ sP271(U_3127,U_3125) )
    & ! [U_3126,U_3128] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3128),U_3126) = hAPP_nat_nat(suc,zero_zero_nat)
        | sP273(U_3126,U_3128) )
    & ! [U_3127,U_3125] :
        ( sP272(U_3127,U_3125)
        | sP271(U_3127,U_3125)
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3127),U_3125) != hAPP_nat_nat(suc,zero_zero_nat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP271,sP272,sP273])],[f_1057_3]) ).

cnf(f_1057_5,plain,
    ( sP272(U_3127,U_3125)
    | sP271(U_3127,U_3125)
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3127),U_3125) != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(clausify,[status(thm)],[f_1057_4]) ).

cnf(f_1057_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3128),U_3126) = hAPP_nat_nat(suc,zero_zero_nat)
    | sP273(U_3126,U_3128) ),
    inference(clausify,[status(thm)],[f_1057_4]) ).

cnf(f_1057_7,plain,
    ( U_3127 = hAPP_nat_nat(suc,zero_zero_nat)
    | ~ sP271(U_3127,U_3125) ),
    inference(clausify,[status(thm)],[f_1057_4]) ).

cnf(f_1057_8,plain,
    ( U_3125 = zero_zero_nat
    | ~ sP271(U_3127,U_3125) ),
    inference(clausify,[status(thm)],[f_1057_4]) ).

cnf(f_1057_9,plain,
    ( U_3127 = zero_zero_nat
    | ~ sP272(U_3127,U_3125) ),
    inference(clausify,[status(thm)],[f_1057_4]) ).

cnf(f_1057_10,plain,
    ( U_3125 = hAPP_nat_nat(suc,zero_zero_nat)
    | ~ sP272(U_3127,U_3125) ),
    inference(clausify,[status(thm)],[f_1057_4]) ).

cnf(f_1057_11,plain,
    ( U_3126 != zero_zero_nat
    | U_3128 != hAPP_nat_nat(suc,zero_zero_nat)
    | ~ sP273(U_3126,U_3128) ),
    inference(clausify,[status(thm)],[f_1057_4]) ).

cnf(f_1057_12,plain,
    ( U_3126 != hAPP_nat_nat(suc,zero_zero_nat)
    | U_3128 != zero_zero_nat
    | ~ sP273(U_3126,U_3128) ),
    inference(clausify,[status(thm)],[f_1057_4]) ).

fof(f_1058_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),Na)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_951_add__gr__0]) ).

fof(f_1058_2,plain,
    ! [U_3130,U_3129] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3130),U_3129)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3129))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3130)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3129))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3130))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3130),U_3129))) ) ),
    inference(variable_rename,[status(thm)],[f_1058_1]) ).

fof(f_1058_3,plain,
    ( ! [U_3134,U_3132] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3134),U_3132)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3132))
          & ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3134)) ) )
    & ! [U_3133,U_3131] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3131))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3133))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3133),U_3131))) ) ),
    inference(miniscope,[status(thm)],[f_1058_2]) ).

fof(f_1058_4,plain,
    ( ! [U_3132,U_3134] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3132))
        | ~ sP274(U_3132,U_3134) )
    & ! [U_3132,U_3134] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3134))
        | ~ sP274(U_3132,U_3134) )
    & ! [U_3132,U_3134] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3134),U_3132)))
        | sP274(U_3132,U_3134) )
    & ! [U_3131,U_3133] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3131))
        | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3133))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3133),U_3131))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP274])],[f_1058_3]) ).

cnf(f_1058_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3131))
    | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3133))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3133),U_3131))) ),
    inference(clausify,[status(thm)],[f_1058_4]) ).

cnf(f_1058_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3134),U_3132)))
    | sP274(U_3132,U_3134) ),
    inference(clausify,[status(thm)],[f_1058_4]) ).

cnf(f_1058_7,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3134))
    | ~ sP274(U_3132,U_3134) ),
    inference(clausify,[status(thm)],[f_1058_4]) ).

cnf(f_1058_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3132))
    | ~ sP274(U_3132,U_3134) ),
    inference(clausify,[status(thm)],[f_1058_4]) ).

fof(f_1059_1,plain,
    ! [Na,M] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,Na),M)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,Na),M))) ) ),
    inference(fof_nnf,[status(thm)],[fact_952_zero__less__diff]) ).

fof(f_1059_2,plain,
    ! [U_3136,U_3135] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3136),U_3135)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3135),U_3136)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3135),U_3136))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3136),U_3135))) ) ),
    inference(variable_rename,[status(thm)],[f_1059_1]) ).

fof(f_1059_3,plain,
    ( ! [U_3140,U_3138] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3140),U_3138)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3138),U_3140)) )
    & ! [U_3139,U_3137] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3137),U_3139))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3139),U_3137))) ) ),
    inference(miniscope,[status(thm)],[f_1059_2]) ).

fof(f_1059_4,plain,
    ( ! [U_3138,U_3140] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3140),U_3138)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3138),U_3140)) )
    & ! [U_3139,U_3137] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3137),U_3139))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3139),U_3137))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1059_3]) ).

cnf(f_1059_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3137),U_3139))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3139),U_3137))) ),
    inference(clausify,[status(thm)],[f_1059_4]) ).

cnf(f_1059_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3140),U_3138)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3138),U_3140)) ),
    inference(clausify,[status(thm)],[f_1059_4]) ).

fof(f_1060_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)),M_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) ),
    inference(fof_nnf,[status(thm)],[fact_953_diff__less]) ).

fof(f_1060_2,plain,
    ! [U_3142,U_3141] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3142),U_3141)),U_3142))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3142))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3141)) ),
    inference(variable_rename,[status(thm)],[f_1060_1]) ).

fof(f_1060_3,plain,
    ! [U_3141,U_3142] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3142),U_3141)),U_3142))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3142))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3141)) ),
    inference(definitional_conversion,[status(esa)],[f_1060_2]) ).

cnf(f_1060_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3142),U_3141)),U_3142))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3142))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3141)) ),
    inference(clausify,[status(thm)],[f_1060_3]) ).

fof(f_1061_1,plain,
    ! [N,M_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),M_1)) = zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_954_diff__add__0]) ).

fof(f_1061_2,plain,
    ! [U_3144,U_3143] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3144),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3144),U_3143)) = zero_zero_nat,
    inference(variable_rename,[status(thm)],[f_1061_1]) ).

fof(f_1061_3,plain,
    ! [U_3144,U_3143] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3144),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3144),U_3143)) = zero_zero_nat,
    inference(definitional_conversion,[status(esa)],[f_1061_2]) ).

cnf(f_1061_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3144),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3144),U_3143)) = zero_zero_nat,
    inference(clausify,[status(thm)],[f_1061_3]) ).

fof(f_1062_1,plain,
    ! [M,Na] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),Na) = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),Na) != zero_zero_nat ) ),
    inference(fof_nnf,[status(thm)],[fact_955_diff__is__0__eq]) ).

fof(f_1062_2,plain,
    ! [U_3146,U_3145] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3146),U_3145) = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3146),U_3145)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3146),U_3145))
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3146),U_3145) != zero_zero_nat ) ),
    inference(variable_rename,[status(thm)],[f_1062_1]) ).

fof(f_1062_3,plain,
    ( ! [U_3150,U_3148] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3150),U_3148) = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3150),U_3148)) )
    & ! [U_3149,U_3147] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3149),U_3147))
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3149),U_3147) != zero_zero_nat ) ),
    inference(miniscope,[status(thm)],[f_1062_2]) ).

fof(f_1062_4,plain,
    ( ! [U_3148,U_3150] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3150),U_3148) = zero_zero_nat
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3150),U_3148)) )
    & ! [U_3149,U_3147] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3149),U_3147))
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3149),U_3147) != zero_zero_nat ) ),
    inference(definitional_conversion,[status(esa)],[f_1062_3]) ).

cnf(f_1062_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3149),U_3147))
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3149),U_3147) != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1062_4]) ).

cnf(f_1062_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3150),U_3148) = zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3150),U_3148)) ),
    inference(clausify,[status(thm)],[f_1062_4]) ).

fof(f_1063_1,plain,
    ! [M_1,N] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N) = zero_zero_nat
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),N)) ),
    inference(fof_nnf,[status(thm)],[fact_956_diff__is__0__eq_H]) ).

fof(f_1063_2,plain,
    ! [U_3152,U_3151] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3152),U_3151) = zero_zero_nat
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3152),U_3151)) ),
    inference(variable_rename,[status(thm)],[f_1063_1]) ).

fof(f_1063_3,plain,
    ! [U_3151,U_3152] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3152),U_3151) = zero_zero_nat
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3152),U_3151)) ),
    inference(definitional_conversion,[status(esa)],[f_1063_2]) ).

cnf(f_1063_4,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3152),U_3151) = zero_zero_nat
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3152),U_3151)) ),
    inference(clausify,[status(thm)],[f_1063_3]) ).

fof(f_1064_1,plain,
    one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
    inference(fof_nnf,[status(thm)],[fact_957_One__nat__def]) ).

fof(f_1064_2,plain,
    one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
    inference(definitional_conversion,[status(esa)],[f_1064_1]) ).

cnf(f_1064_3,plain,
    one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
    inference(clausify,[status(thm)],[f_1064_2]) ).

fof(f_1065_1,plain,
    ! [M,Na] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),hAPP_nat_nat(suc,Na)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M),Na)),
    inference(fof_nnf,[status(thm)],[fact_958_diff__Suc]) ).

fof(f_1065_2,plain,
    ! [U_3154,U_3153] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3154),hAPP_nat_nat(suc,U_3153)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3154),U_3153)),
    inference(variable_rename,[status(thm)],[f_1065_1]) ).

fof(f_1065_3,plain,
    ! [U_3153,U_3154] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3154),hAPP_nat_nat(suc,U_3153)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3154),U_3153)),
    inference(definitional_conversion,[status(esa)],[f_1065_2]) ).

cnf(f_1065_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3154),hAPP_nat_nat(suc,U_3153)) = hAPP_nat_nat(nat_case_nat(zero_zero_nat,cOMBI_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3154),U_3153)),
    inference(clausify,[status(thm)],[f_1065_3]) ).

fof(f_1066_1,plain,
    ! [N] :
      ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(suc,zero_zero_nat))) = N
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) ),
    inference(fof_nnf,[status(thm)],[fact_959_Suc__pred]) ).

fof(f_1066_2,plain,
    ! [U_3155] :
      ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3155),hAPP_nat_nat(suc,zero_zero_nat))) = U_3155
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3155)) ),
    inference(variable_rename,[status(thm)],[f_1066_1]) ).

fof(f_1066_3,plain,
    ! [U_3155] :
      ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3155),hAPP_nat_nat(suc,zero_zero_nat))) = U_3155
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3155)) ),
    inference(definitional_conversion,[status(esa)],[f_1066_2]) ).

cnf(f_1066_4,plain,
    ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3155),hAPP_nat_nat(suc,zero_zero_nat))) = U_3155
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3155)) ),
    inference(clausify,[status(thm)],[f_1066_3]) ).

fof(f_1067_1,plain,
    ! [I_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),hAPP_nat_nat(suc,I_1))),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) ),
    inference(fof_nnf,[status(thm)],[fact_960_diff__Suc__less]) ).

fof(f_1067_2,plain,
    ! [U_3157,U_3156] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3156),hAPP_nat_nat(suc,U_3157))),U_3156))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3156)) ),
    inference(variable_rename,[status(thm)],[f_1067_1]) ).

fof(f_1067_3,plain,
    ! [U_3156,U_3157] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3156),hAPP_nat_nat(suc,U_3157))),U_3156))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3156)) ),
    inference(definitional_conversion,[status(esa)],[f_1067_2]) ).

cnf(f_1067_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3156),hAPP_nat_nat(suc,U_3157))),U_3156))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3156)) ),
    inference(clausify,[status(thm)],[f_1067_3]) ).

fof(f_1068_1,plain,
    ! [Pa,A_2,B_3] :
      ( ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,A_2),B_3)))
        | ? [D_2] :
            ( ~ hBOOL(hAPP_nat_bool(Pa,D_2))
            & A_2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),D_2) )
        | ( ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_3)) ) )
      & ( ( ! [D_2] :
              ( hBOOL(hAPP_nat_bool(Pa,D_2))
              | A_2 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),D_2) )
          & ( hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_3)) ) )
        | ~ hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,A_2),B_3))) ) ),
    inference(fof_nnf,[status(thm)],[fact_961_nat__diff__split]) ).

fof(f_1068_2,plain,
    ! [U_3162,U_3161,U_3160] :
      ( ( hBOOL(hAPP_nat_bool(U_3162,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3161),U_3160)))
        | ? [U_3159] :
            ( ~ hBOOL(hAPP_nat_bool(U_3162,U_3159))
            & U_3161 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3160),U_3159) )
        | ( ~ hBOOL(hAPP_nat_bool(U_3162,zero_zero_nat))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3161),U_3160)) ) )
      & ( ( ! [U_3158] :
              ( hBOOL(hAPP_nat_bool(U_3162,U_3158))
              | U_3161 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3160),U_3158) )
          & ( hBOOL(hAPP_nat_bool(U_3162,zero_zero_nat))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3161),U_3160)) ) )
        | ~ hBOOL(hAPP_nat_bool(U_3162,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3161),U_3160))) ) ),
    inference(variable_rename,[status(thm)],[f_1068_1]) ).

fof(f_1068_3,plain,
    ( ! [U_3168,U_3166,U_3164] :
        ( hBOOL(hAPP_nat_bool(U_3168,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3166),U_3164)))
        | ? [U_3159] :
            ( ~ hBOOL(hAPP_nat_bool(U_3168,U_3159))
            & U_3166 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3164),U_3159) )
        | ( ~ hBOOL(hAPP_nat_bool(U_3168,zero_zero_nat))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3166),U_3164)) ) )
    & ! [U_3167,U_3165,U_3163] :
        ( ( ! [U_3158] :
              ( hBOOL(hAPP_nat_bool(U_3167,U_3158))
              | U_3165 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3163),U_3158) )
          & ( hBOOL(hAPP_nat_bool(U_3167,zero_zero_nat))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3165),U_3163)) ) )
        | ~ hBOOL(hAPP_nat_bool(U_3167,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3165),U_3163))) ) ),
    inference(miniscope,[status(thm)],[f_1068_2]) ).

fof(f_1068_4,plain,
    ( ! [U_3168,U_3166,U_3164] :
        ( hBOOL(hAPP_nat_bool(U_3168,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3166),U_3164)))
        | ( ~ hBOOL(hAPP_nat_bool(U_3168,sK177(U_3168,U_3166,U_3164)))
          & U_3166 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3164),sK177(U_3168,U_3166,U_3164)) )
        | ( ~ hBOOL(hAPP_nat_bool(U_3168,zero_zero_nat))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3166),U_3164)) ) )
    & ! [U_3167,U_3165,U_3163] :
        ( ( ! [U_3158] :
              ( hBOOL(hAPP_nat_bool(U_3167,U_3158))
              | U_3165 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3163),U_3158) )
          & ( hBOOL(hAPP_nat_bool(U_3167,zero_zero_nat))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3165),U_3163)) ) )
        | ~ hBOOL(hAPP_nat_bool(U_3167,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3165),U_3163))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK177]),skolemize(U_3159,sK177(U_3168,U_3166,U_3164))],[f_1068_3]) ).

fof(f_1068_5,plain,
    ( ! [U_3164,U_3166,U_3168] :
        ( ~ hBOOL(hAPP_nat_bool(U_3168,sK177(U_3168,U_3166,U_3164)))
        | ~ sP277(U_3164,U_3166,U_3168) )
    & ! [U_3164,U_3166,U_3168] :
        ( U_3166 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3164),sK177(U_3168,U_3166,U_3164))
        | ~ sP277(U_3164,U_3166,U_3168) )
    & ! [U_3164,U_3166,U_3168] :
        ( ~ hBOOL(hAPP_nat_bool(U_3168,zero_zero_nat))
        | ~ sP276(U_3164,U_3166,U_3168) )
    & ! [U_3164,U_3166,U_3168] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3166),U_3164))
        | ~ sP276(U_3164,U_3166,U_3168) )
    & ! [U_3167,U_3158,U_3163,U_3165] :
        ( hBOOL(hAPP_nat_bool(U_3167,U_3158))
        | U_3165 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3163),U_3158)
        | ~ sP275(U_3167,U_3158,U_3163,U_3165) )
    & ! [U_3167,U_3158,U_3163,U_3165] :
        ( hBOOL(hAPP_nat_bool(U_3167,zero_zero_nat))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3165),U_3163))
        | ~ sP275(U_3167,U_3158,U_3163,U_3165) )
    & ! [U_3164,U_3166,U_3168] :
        ( hBOOL(hAPP_nat_bool(U_3168,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3166),U_3164)))
        | sP277(U_3164,U_3166,U_3168)
        | sP276(U_3164,U_3166,U_3168) )
    & ! [U_3167,U_3158,U_3163,U_3165] :
        ( sP275(U_3167,U_3158,U_3163,U_3165)
        | ~ hBOOL(hAPP_nat_bool(U_3167,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3165),U_3163))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP275,sP276,sP277])],[f_1068_4]) ).

cnf(f_1068_6,plain,
    ( sP275(U_3167,U_3158,U_3163,U_3165)
    | ~ hBOOL(hAPP_nat_bool(U_3167,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3165),U_3163))) ),
    inference(clausify,[status(thm)],[f_1068_5]) ).

cnf(f_1068_7,plain,
    ( hBOOL(hAPP_nat_bool(U_3168,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3166),U_3164)))
    | sP277(U_3164,U_3166,U_3168)
    | sP276(U_3164,U_3166,U_3168) ),
    inference(clausify,[status(thm)],[f_1068_5]) ).

cnf(f_1068_8,plain,
    ( hBOOL(hAPP_nat_bool(U_3167,zero_zero_nat))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3165),U_3163))
    | ~ sP275(U_3167,U_3158,U_3163,U_3165) ),
    inference(clausify,[status(thm)],[f_1068_5]) ).

cnf(f_1068_9,plain,
    ( hBOOL(hAPP_nat_bool(U_3167,U_3158))
    | U_3165 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3163),U_3158)
    | ~ sP275(U_3167,U_3158,U_3163,U_3165) ),
    inference(clausify,[status(thm)],[f_1068_5]) ).

cnf(f_1068_10,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3166),U_3164))
    | ~ sP276(U_3164,U_3166,U_3168) ),
    inference(clausify,[status(thm)],[f_1068_5]) ).

cnf(f_1068_11,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_3168,zero_zero_nat))
    | ~ sP276(U_3164,U_3166,U_3168) ),
    inference(clausify,[status(thm)],[f_1068_5]) ).

cnf(f_1068_12,plain,
    ( U_3166 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3164),sK177(U_3168,U_3166,U_3164))
    | ~ sP277(U_3164,U_3166,U_3168) ),
    inference(clausify,[status(thm)],[f_1068_5]) ).

cnf(f_1068_13,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_3168,sK177(U_3168,U_3166,U_3164)))
    | ~ sP277(U_3164,U_3166,U_3168) ),
    inference(clausify,[status(thm)],[f_1068_5]) ).

fof(f_1069_1,plain,
    ! [Pa,A_2,B_3] :
      ( ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,A_2),B_3)))
        | ? [D_2] :
            ( ~ hBOOL(hAPP_nat_bool(Pa,D_2))
            & A_2 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),D_2) )
        | ( ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_3)) ) )
      & ( ( ! [D_2] :
              ( hBOOL(hAPP_nat_bool(Pa,D_2))
              | A_2 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,B_3),D_2) )
          & ( hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,A_2),B_3)) ) )
        | ~ hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,A_2),B_3))) ) ),
    inference(fof_nnf,[status(thm)],[fact_962_nat__diff__split__asm]) ).

fof(f_1069_2,plain,
    ! [U_3173,U_3172,U_3171] :
      ( ( hBOOL(hAPP_nat_bool(U_3173,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3172),U_3171)))
        | ? [U_3170] :
            ( ~ hBOOL(hAPP_nat_bool(U_3173,U_3170))
            & U_3172 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3171),U_3170) )
        | ( ~ hBOOL(hAPP_nat_bool(U_3173,zero_zero_nat))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3172),U_3171)) ) )
      & ( ( ! [U_3169] :
              ( hBOOL(hAPP_nat_bool(U_3173,U_3169))
              | U_3172 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3171),U_3169) )
          & ( hBOOL(hAPP_nat_bool(U_3173,zero_zero_nat))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3172),U_3171)) ) )
        | ~ hBOOL(hAPP_nat_bool(U_3173,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3172),U_3171))) ) ),
    inference(variable_rename,[status(thm)],[f_1069_1]) ).

fof(f_1069_3,plain,
    ( ! [U_3179,U_3177,U_3175] :
        ( hBOOL(hAPP_nat_bool(U_3179,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3177),U_3175)))
        | ? [U_3170] :
            ( ~ hBOOL(hAPP_nat_bool(U_3179,U_3170))
            & U_3177 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3175),U_3170) )
        | ( ~ hBOOL(hAPP_nat_bool(U_3179,zero_zero_nat))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3177),U_3175)) ) )
    & ! [U_3178,U_3176,U_3174] :
        ( ( ! [U_3169] :
              ( hBOOL(hAPP_nat_bool(U_3178,U_3169))
              | U_3176 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3174),U_3169) )
          & ( hBOOL(hAPP_nat_bool(U_3178,zero_zero_nat))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3176),U_3174)) ) )
        | ~ hBOOL(hAPP_nat_bool(U_3178,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3176),U_3174))) ) ),
    inference(miniscope,[status(thm)],[f_1069_2]) ).

fof(f_1069_4,plain,
    ( ! [U_3179,U_3177,U_3175] :
        ( hBOOL(hAPP_nat_bool(U_3179,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3177),U_3175)))
        | ( ~ hBOOL(hAPP_nat_bool(U_3179,sK178(U_3179,U_3177,U_3175)))
          & U_3177 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3175),sK178(U_3179,U_3177,U_3175)) )
        | ( ~ hBOOL(hAPP_nat_bool(U_3179,zero_zero_nat))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3177),U_3175)) ) )
    & ! [U_3178,U_3176,U_3174] :
        ( ( ! [U_3169] :
              ( hBOOL(hAPP_nat_bool(U_3178,U_3169))
              | U_3176 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3174),U_3169) )
          & ( hBOOL(hAPP_nat_bool(U_3178,zero_zero_nat))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3176),U_3174)) ) )
        | ~ hBOOL(hAPP_nat_bool(U_3178,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3176),U_3174))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK178]),skolemize(U_3170,sK178(U_3179,U_3177,U_3175))],[f_1069_3]) ).

fof(f_1069_5,plain,
    ( ! [U_3179,U_3177,U_3175] :
        ( ~ hBOOL(hAPP_nat_bool(U_3179,sK178(U_3179,U_3177,U_3175)))
        | ~ sP280(U_3179,U_3177,U_3175) )
    & ! [U_3179,U_3177,U_3175] :
        ( U_3177 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3175),sK178(U_3179,U_3177,U_3175))
        | ~ sP280(U_3179,U_3177,U_3175) )
    & ! [U_3179,U_3177,U_3175] :
        ( ~ hBOOL(hAPP_nat_bool(U_3179,zero_zero_nat))
        | ~ sP279(U_3179,U_3177,U_3175) )
    & ! [U_3179,U_3177,U_3175] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3177),U_3175))
        | ~ sP279(U_3179,U_3177,U_3175) )
    & ! [U_3169,U_3174,U_3176,U_3178] :
        ( hBOOL(hAPP_nat_bool(U_3178,U_3169))
        | U_3176 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3174),U_3169)
        | ~ sP278(U_3169,U_3174,U_3176,U_3178) )
    & ! [U_3169,U_3174,U_3176,U_3178] :
        ( hBOOL(hAPP_nat_bool(U_3178,zero_zero_nat))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3176),U_3174))
        | ~ sP278(U_3169,U_3174,U_3176,U_3178) )
    & ! [U_3179,U_3177,U_3175] :
        ( hBOOL(hAPP_nat_bool(U_3179,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3177),U_3175)))
        | sP280(U_3179,U_3177,U_3175)
        | sP279(U_3179,U_3177,U_3175) )
    & ! [U_3169,U_3174,U_3176,U_3178] :
        ( sP278(U_3169,U_3174,U_3176,U_3178)
        | ~ hBOOL(hAPP_nat_bool(U_3178,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3176),U_3174))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP278,sP279,sP280])],[f_1069_4]) ).

cnf(f_1069_6,plain,
    ( sP278(U_3169,U_3174,U_3176,U_3178)
    | ~ hBOOL(hAPP_nat_bool(U_3178,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3176),U_3174))) ),
    inference(clausify,[status(thm)],[f_1069_5]) ).

cnf(f_1069_7,plain,
    ( hBOOL(hAPP_nat_bool(U_3179,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3177),U_3175)))
    | sP280(U_3179,U_3177,U_3175)
    | sP279(U_3179,U_3177,U_3175) ),
    inference(clausify,[status(thm)],[f_1069_5]) ).

cnf(f_1069_8,plain,
    ( hBOOL(hAPP_nat_bool(U_3178,zero_zero_nat))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3176),U_3174))
    | ~ sP278(U_3169,U_3174,U_3176,U_3178) ),
    inference(clausify,[status(thm)],[f_1069_5]) ).

cnf(f_1069_9,plain,
    ( hBOOL(hAPP_nat_bool(U_3178,U_3169))
    | U_3176 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3174),U_3169)
    | ~ sP278(U_3169,U_3174,U_3176,U_3178) ),
    inference(clausify,[status(thm)],[f_1069_5]) ).

cnf(f_1069_10,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3177),U_3175))
    | ~ sP279(U_3179,U_3177,U_3175) ),
    inference(clausify,[status(thm)],[f_1069_5]) ).

cnf(f_1069_11,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_3179,zero_zero_nat))
    | ~ sP279(U_3179,U_3177,U_3175) ),
    inference(clausify,[status(thm)],[f_1069_5]) ).

cnf(f_1069_12,plain,
    ( U_3177 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3175),sK178(U_3179,U_3177,U_3175))
    | ~ sP280(U_3179,U_3177,U_3175) ),
    inference(clausify,[status(thm)],[f_1069_5]) ).

cnf(f_1069_13,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_3179,sK178(U_3179,U_3177,U_3175)))
    | ~ sP280(U_3179,U_3177,U_3175) ),
    inference(clausify,[status(thm)],[f_1069_5]) ).

fof(f_1070_1,plain,
    ! [I_2,M_3] :
      ( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),M_3)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),I_2))))) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),M_3)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,I_2)))))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3)) ),
    inference(fof_nnf,[status(thm)],[fact_963_card__less__Suc]) ).

fof(f_1070_2,plain,
    ! [U_3181,U_3180] :
      ( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),U_3180)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_3181))))) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_3180)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,U_3181)))))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),U_3180)) ),
    inference(variable_rename,[status(thm)],[f_1070_1]) ).

fof(f_1070_3,plain,
    ! [U_3181,U_3180] :
      ( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),U_3180)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_3181))))) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_3180)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,U_3181)))))
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),U_3180)) ),
    inference(definitional_conversion,[status(esa)],[f_1070_2]) ).

cnf(f_1070_4,plain,
    ( hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),U_3180)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_3181))))) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_3180)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,U_3181)))))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),U_3180)) ),
    inference(clausify,[status(thm)],[f_1070_3]) ).

fof(f_1071_1,plain,
    ! [I_2,M_3] :
      ( hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),M_3)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,I_2))))) != zero_zero_nat
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3)) ),
    inference(fof_nnf,[status(thm)],[fact_964_card__less]) ).

fof(f_1071_2,plain,
    ! [U_3183,U_3182] :
      ( hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_3182)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,U_3183))))) != zero_zero_nat
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),U_3182)) ),
    inference(variable_rename,[status(thm)],[f_1071_1]) ).

fof(f_1071_3,plain,
    ! [U_3182,U_3183] :
      ( hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_3182)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,U_3183))))) != zero_zero_nat
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),U_3182)) ),
    inference(definitional_conversion,[status(esa)],[f_1071_2]) ).

cnf(f_1071_4,plain,
    ( hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_3182)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,U_3183))))) != zero_zero_nat
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),U_3182)) ),
    inference(clausify,[status(thm)],[f_1071_3]) ).

fof(f_1072_1,plain,
    ! [I_2,M_3] :
      ( hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),M_3)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),I_2)))) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),M_3)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,I_2)))))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),M_3)) ),
    inference(fof_nnf,[status(thm)],[fact_965_card__less__Suc2]) ).

fof(f_1072_2,plain,
    ! [U_3185,U_3184] :
      ( hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),U_3184)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_3185)))) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_3184)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,U_3185)))))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),U_3184)) ),
    inference(variable_rename,[status(thm)],[f_1072_1]) ).

fof(f_1072_3,plain,
    ! [U_3185,U_3184] :
      ( hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),U_3184)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_3185)))) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_3184)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,U_3185)))))
      | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),U_3184)) ),
    inference(definitional_conversion,[status(esa)],[f_1072_2]) ).

cnf(f_1072_4,plain,
    ( hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(cOMBB_1146692694ol_nat(member_nat,suc)),U_3184)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),U_3185)))) = hAPP_f22106695ol_nat(finite_card_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),U_3184)),hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_nat),hAPP_nat_nat(suc,U_3185)))))
    | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,zero_zero_nat),U_3184)) ),
    inference(clausify,[status(thm)],[f_1072_3]) ).

fof(f_1073_1,plain,
    ! [N] :
      ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),one_one_nat)) = N
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) ),
    inference(fof_nnf,[status(thm)],[fact_966_Suc__diff__1]) ).

fof(f_1073_2,plain,
    ! [U_3186] :
      ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3186),one_one_nat)) = U_3186
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3186)) ),
    inference(variable_rename,[status(thm)],[f_1073_1]) ).

fof(f_1073_3,plain,
    ! [U_3186] :
      ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3186),one_one_nat)) = U_3186
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3186)) ),
    inference(definitional_conversion,[status(esa)],[f_1073_2]) ).

cnf(f_1073_4,plain,
    ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3186),one_one_nat)) = U_3186
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3186)) ),
    inference(clausify,[status(thm)],[f_1073_3]) ).

fof(f_1074_1,plain,
    ! [N] :
      ( N = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,N),one_one_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) ),
    inference(fof_nnf,[status(thm)],[fact_967_Suc__pred_H]) ).

fof(f_1074_2,plain,
    ! [U_3187] :
      ( U_3187 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3187),one_one_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3187)) ),
    inference(variable_rename,[status(thm)],[f_1074_1]) ).

fof(f_1074_3,plain,
    ! [U_3187] :
      ( U_3187 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3187),one_one_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3187)) ),
    inference(definitional_conversion,[status(esa)],[f_1074_2]) ).

cnf(f_1074_4,plain,
    ( U_3187 = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3187),one_one_nat))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3187)) ),
    inference(clausify,[status(thm)],[f_1074_3]) ).

fof(f_1075_1,plain,
    ! [N,M_1] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),one_one_nat)),N))
        | M_1 = zero_zero_nat )
      & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N) = N
        | M_1 != zero_zero_nat ) ),
    inference(fof_nnf,[status(thm)],[fact_968_add__eq__if]) ).

fof(f_1075_2,plain,
    ! [U_3189,U_3188] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3188),U_3189) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3188),one_one_nat)),U_3189))
        | U_3188 = zero_zero_nat )
      & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3188),U_3189) = U_3189
        | U_3188 != zero_zero_nat ) ),
    inference(variable_rename,[status(thm)],[f_1075_1]) ).

fof(f_1075_3,plain,
    ( ! [U_3193,U_3191] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3191),U_3193) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3191),one_one_nat)),U_3193))
        | U_3191 = zero_zero_nat )
    & ! [U_3192,U_3190] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3190),U_3192) = U_3192
        | U_3190 != zero_zero_nat ) ),
    inference(miniscope,[status(thm)],[f_1075_2]) ).

fof(f_1075_4,plain,
    ( ! [U_3193,U_3191] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3191),U_3193) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3191),one_one_nat)),U_3193))
        | U_3191 = zero_zero_nat )
    & ! [U_3192,U_3190] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3190),U_3192) = U_3192
        | U_3190 != zero_zero_nat ) ),
    inference(definitional_conversion,[status(esa)],[f_1075_3]) ).

cnf(f_1075_5,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3190),U_3192) = U_3192
    | U_3190 != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1075_4]) ).

cnf(f_1075_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3191),U_3193) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3191),one_one_nat)),U_3193))
    | U_3191 = zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1075_4]) ).

fof(f_1076_1,plain,
    ! [Na,Pa] :
      ( ? [K_2] :
          ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,K_2),one_one_nat)))
          & ! [I] :
              ( ~ hBOOL(hAPP_nat_bool(Pa,I))
              | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),K_2)) )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,K_2),Na)) )
      | ~ hBOOL(hAPP_nat_bool(Pa,Na))
      | hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) ),
    inference(fof_nnf,[status(thm)],[fact_969_ex__least__nat__less]) ).

fof(f_1076_2,plain,
    ! [U_3197,U_3196] :
      ( ? [U_3195] :
          ( hBOOL(hAPP_nat_bool(U_3196,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3195),one_one_nat)))
          & ! [U_3194] :
              ( ~ hBOOL(hAPP_nat_bool(U_3196,U_3194))
              | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3194),U_3195)) )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3195),U_3197)) )
      | ~ hBOOL(hAPP_nat_bool(U_3196,U_3197))
      | hBOOL(hAPP_nat_bool(U_3196,zero_zero_nat)) ),
    inference(variable_rename,[status(thm)],[f_1076_1]) ).

fof(f_1076_3,plain,
    ! [U_3197,U_3196] :
      ( ( hBOOL(hAPP_nat_bool(U_3196,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK179(U_3197,U_3196)),one_one_nat)))
        & ! [U_3194] :
            ( ~ hBOOL(hAPP_nat_bool(U_3196,U_3194))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3194),sK179(U_3197,U_3196))) )
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK179(U_3197,U_3196)),U_3197)) )
      | ~ hBOOL(hAPP_nat_bool(U_3196,U_3197))
      | hBOOL(hAPP_nat_bool(U_3196,zero_zero_nat)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK179]),skolemize(U_3195,sK179(U_3197,U_3196))],[f_1076_2]) ).

fof(f_1076_4,plain,
    ( ! [U_3194,U_3196,U_3197] :
        ( hBOOL(hAPP_nat_bool(U_3196,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK179(U_3197,U_3196)),one_one_nat)))
        | ~ sP281(U_3194,U_3196,U_3197) )
    & ! [U_3194,U_3196,U_3197] :
        ( ~ hBOOL(hAPP_nat_bool(U_3196,U_3194))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3194),sK179(U_3197,U_3196)))
        | ~ sP281(U_3194,U_3196,U_3197) )
    & ! [U_3194,U_3196,U_3197] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK179(U_3197,U_3196)),U_3197))
        | ~ sP281(U_3194,U_3196,U_3197) )
    & ! [U_3194,U_3196,U_3197] :
        ( sP281(U_3194,U_3196,U_3197)
        | ~ hBOOL(hAPP_nat_bool(U_3196,U_3197))
        | hBOOL(hAPP_nat_bool(U_3196,zero_zero_nat)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP281])],[f_1076_3]) ).

cnf(f_1076_5,plain,
    ( sP281(U_3194,U_3196,U_3197)
    | ~ hBOOL(hAPP_nat_bool(U_3196,U_3197))
    | hBOOL(hAPP_nat_bool(U_3196,zero_zero_nat)) ),
    inference(clausify,[status(thm)],[f_1076_4]) ).

cnf(f_1076_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK179(U_3197,U_3196)),U_3197))
    | ~ sP281(U_3194,U_3196,U_3197) ),
    inference(clausify,[status(thm)],[f_1076_4]) ).

cnf(f_1076_7,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_3196,U_3194))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3194),sK179(U_3197,U_3196)))
    | ~ sP281(U_3194,U_3196,U_3197) ),
    inference(clausify,[status(thm)],[f_1076_4]) ).

cnf(f_1076_8,plain,
    ( hBOOL(hAPP_nat_bool(U_3196,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK179(U_3197,U_3196)),one_one_nat)))
    | ~ sP281(U_3194,U_3196,U_3197) ),
    inference(clausify,[status(thm)],[f_1076_4]) ).

fof(f_1077_1,plain,
    ! [Na,Pa] :
      ( ? [K_2] :
          ( hBOOL(hAPP_nat_bool(Pa,K_2))
          & ! [I] :
              ( ~ hBOOL(hAPP_nat_bool(Pa,I))
              | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),K_2)) )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_2),Na)) )
      | ~ hBOOL(hAPP_nat_bool(Pa,Na))
      | hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) ),
    inference(fof_nnf,[status(thm)],[fact_970_ex__least__nat__le]) ).

fof(f_1077_2,plain,
    ! [U_3201,U_3200] :
      ( ? [U_3199] :
          ( hBOOL(hAPP_nat_bool(U_3200,U_3199))
          & ! [U_3198] :
              ( ~ hBOOL(hAPP_nat_bool(U_3200,U_3198))
              | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3198),U_3199)) )
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3199),U_3201)) )
      | ~ hBOOL(hAPP_nat_bool(U_3200,U_3201))
      | hBOOL(hAPP_nat_bool(U_3200,zero_zero_nat)) ),
    inference(variable_rename,[status(thm)],[f_1077_1]) ).

fof(f_1077_3,plain,
    ! [U_3201,U_3200] :
      ( ( hBOOL(hAPP_nat_bool(U_3200,sK180(U_3201,U_3200)))
        & ! [U_3198] :
            ( ~ hBOOL(hAPP_nat_bool(U_3200,U_3198))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3198),sK180(U_3201,U_3200))) )
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK180(U_3201,U_3200)),U_3201)) )
      | ~ hBOOL(hAPP_nat_bool(U_3200,U_3201))
      | hBOOL(hAPP_nat_bool(U_3200,zero_zero_nat)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK180]),skolemize(U_3199,sK180(U_3201,U_3200))],[f_1077_2]) ).

fof(f_1077_4,plain,
    ( ! [U_3200,U_3201,U_3198] :
        ( hBOOL(hAPP_nat_bool(U_3200,sK180(U_3201,U_3200)))
        | ~ sP282(U_3200,U_3201,U_3198) )
    & ! [U_3200,U_3201,U_3198] :
        ( ~ hBOOL(hAPP_nat_bool(U_3200,U_3198))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3198),sK180(U_3201,U_3200)))
        | ~ sP282(U_3200,U_3201,U_3198) )
    & ! [U_3200,U_3201,U_3198] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK180(U_3201,U_3200)),U_3201))
        | ~ sP282(U_3200,U_3201,U_3198) )
    & ! [U_3200,U_3201,U_3198] :
        ( sP282(U_3200,U_3201,U_3198)
        | ~ hBOOL(hAPP_nat_bool(U_3200,U_3201))
        | hBOOL(hAPP_nat_bool(U_3200,zero_zero_nat)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP282])],[f_1077_3]) ).

cnf(f_1077_5,plain,
    ( sP282(U_3200,U_3201,U_3198)
    | ~ hBOOL(hAPP_nat_bool(U_3200,U_3201))
    | hBOOL(hAPP_nat_bool(U_3200,zero_zero_nat)) ),
    inference(clausify,[status(thm)],[f_1077_4]) ).

cnf(f_1077_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK180(U_3201,U_3200)),U_3201))
    | ~ sP282(U_3200,U_3201,U_3198) ),
    inference(clausify,[status(thm)],[f_1077_4]) ).

cnf(f_1077_7,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_3200,U_3198))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3198),sK180(U_3201,U_3200)))
    | ~ sP282(U_3200,U_3201,U_3198) ),
    inference(clausify,[status(thm)],[f_1077_4]) ).

cnf(f_1077_8,plain,
    ( hBOOL(hAPP_nat_bool(U_3200,sK180(U_3201,U_3200)))
    | ~ sP282(U_3200,U_3201,U_3198) ),
    inference(clausify,[status(thm)],[f_1077_4]) ).

fof(f_1078_1,plain,
    ! [I_1,J] :
      ( ? [K_2] :
          ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),K_2) = J
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_2)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_971_less__imp__add__positive]) ).

fof(f_1078_2,plain,
    ! [U_3204,U_3203] :
      ( ? [U_3202] :
          ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3204),U_3202) = U_3203
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3202)) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3204),U_3203)) ),
    inference(variable_rename,[status(thm)],[f_1078_1]) ).

fof(f_1078_3,plain,
    ! [U_3204,U_3203] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3204),sK181(U_3204,U_3203)) = U_3203
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK181(U_3204,U_3203))) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3204),U_3203)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK181]),skolemize(U_3202,sK181(U_3204,U_3203))],[f_1078_2]) ).

fof(f_1078_4,plain,
    ( ! [U_3203,U_3204] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3204),sK181(U_3204,U_3203)) = U_3203
        | ~ sP283(U_3203,U_3204) )
    & ! [U_3203,U_3204] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK181(U_3204,U_3203)))
        | ~ sP283(U_3203,U_3204) )
    & ! [U_3203,U_3204] :
        ( sP283(U_3203,U_3204)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3204),U_3203)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP283])],[f_1078_3]) ).

cnf(f_1078_5,plain,
    ( sP283(U_3203,U_3204)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3204),U_3203)) ),
    inference(clausify,[status(thm)],[f_1078_4]) ).

cnf(f_1078_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK181(U_3204,U_3203)))
    | ~ sP283(U_3203,U_3204) ),
    inference(clausify,[status(thm)],[f_1078_4]) ).

cnf(f_1078_7,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3204),sK181(U_3204,U_3203)) = U_3203
    | ~ sP283(U_3203,U_3204) ),
    inference(clausify,[status(thm)],[f_1078_4]) ).

fof(f_1079_1,plain,
    ! [N] :
      ( ? [M_2] : N = hAPP_nat_nat(suc,M_2)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N)) ),
    inference(fof_nnf,[status(thm)],[fact_972_gr0__implies__Suc]) ).

fof(f_1079_2,plain,
    ! [U_3206] :
      ( ? [U_3205] : U_3206 = hAPP_nat_nat(suc,U_3205)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3206)) ),
    inference(variable_rename,[status(thm)],[f_1079_1]) ).

fof(f_1079_3,plain,
    ! [U_3206] :
      ( U_3206 = hAPP_nat_nat(suc,sK182(U_3206))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3206)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK182]),skolemize(U_3205,sK182(U_3206))],[f_1079_2]) ).

fof(f_1079_4,plain,
    ! [U_3206] :
      ( U_3206 = hAPP_nat_nat(suc,sK182(U_3206))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3206)) ),
    inference(definitional_conversion,[status(esa)],[f_1079_3]) ).

cnf(f_1079_5,plain,
    ( U_3206 = hAPP_nat_nat(suc,sK182(U_3206))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3206)) ),
    inference(clausify,[status(thm)],[f_1079_4]) ).

fof(f_1080_1,plain,
    ! [Y] :
      ( ? [Nat] : Y = hAPP_nat_nat(suc,Nat)
      | Y = zero_zero_nat ),
    inference(fof_nnf,[status(thm)],[fact_973_nat_Oexhaust]) ).

fof(f_1080_2,plain,
    ! [U_3208] :
      ( ? [U_3207] : U_3208 = hAPP_nat_nat(suc,U_3207)
      | U_3208 = zero_zero_nat ),
    inference(variable_rename,[status(thm)],[f_1080_1]) ).

fof(f_1080_3,plain,
    ! [U_3208] :
      ( U_3208 = hAPP_nat_nat(suc,sK183(U_3208))
      | U_3208 = zero_zero_nat ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK183]),skolemize(U_3207,sK183(U_3208))],[f_1080_2]) ).

fof(f_1080_4,plain,
    ! [U_3208] :
      ( U_3208 = hAPP_nat_nat(suc,sK183(U_3208))
      | U_3208 = zero_zero_nat ),
    inference(definitional_conversion,[status(esa)],[f_1080_3]) ).

cnf(f_1080_5,plain,
    ( U_3208 = hAPP_nat_nat(suc,sK183(U_3208))
    | U_3208 = zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1080_4]) ).

fof(f_1081_1,plain,
    ! [Pa,K] :
      ( hBOOL(hAPP_nat_bool(Pa,zero_zero_nat))
      | ? [N_1] :
          ( ~ hBOOL(hAPP_nat_bool(Pa,N_1))
          & hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_1))) )
      | ~ hBOOL(hAPP_nat_bool(Pa,K)) ),
    inference(fof_nnf,[status(thm)],[fact_974_zero__induct]) ).

fof(f_1081_2,plain,
    ! [U_3211,U_3210] :
      ( hBOOL(hAPP_nat_bool(U_3211,zero_zero_nat))
      | ? [U_3209] :
          ( ~ hBOOL(hAPP_nat_bool(U_3211,U_3209))
          & hBOOL(hAPP_nat_bool(U_3211,hAPP_nat_nat(suc,U_3209))) )
      | ~ hBOOL(hAPP_nat_bool(U_3211,U_3210)) ),
    inference(variable_rename,[status(thm)],[f_1081_1]) ).

fof(f_1081_3,plain,
    ! [U_3211] :
      ( ! [U_3210] : ~ hBOOL(hAPP_nat_bool(U_3211,U_3210))
      | hBOOL(hAPP_nat_bool(U_3211,zero_zero_nat))
      | ? [U_3209] :
          ( ~ hBOOL(hAPP_nat_bool(U_3211,U_3209))
          & hBOOL(hAPP_nat_bool(U_3211,hAPP_nat_nat(suc,U_3209))) ) ),
    inference(miniscope,[status(thm)],[f_1081_2]) ).

fof(f_1081_4,plain,
    ! [U_3211] :
      ( ! [U_3210] : ~ hBOOL(hAPP_nat_bool(U_3211,U_3210))
      | hBOOL(hAPP_nat_bool(U_3211,zero_zero_nat))
      | ( ~ hBOOL(hAPP_nat_bool(U_3211,sK184(U_3211)))
        & hBOOL(hAPP_nat_bool(U_3211,hAPP_nat_nat(suc,sK184(U_3211)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK184]),skolemize(U_3209,sK184(U_3211))],[f_1081_3]) ).

fof(f_1081_5,plain,
    ( ! [U_3211] :
        ( ~ hBOOL(hAPP_nat_bool(U_3211,sK184(U_3211)))
        | ~ sP284(U_3211) )
    & ! [U_3211] :
        ( hBOOL(hAPP_nat_bool(U_3211,hAPP_nat_nat(suc,sK184(U_3211))))
        | ~ sP284(U_3211) )
    & ! [U_3210,U_3211] :
        ( ~ hBOOL(hAPP_nat_bool(U_3211,U_3210))
        | hBOOL(hAPP_nat_bool(U_3211,zero_zero_nat))
        | sP284(U_3211) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP284])],[f_1081_4]) ).

cnf(f_1081_6,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_3211,U_3210))
    | hBOOL(hAPP_nat_bool(U_3211,zero_zero_nat))
    | sP284(U_3211) ),
    inference(clausify,[status(thm)],[f_1081_5]) ).

cnf(f_1081_7,plain,
    ( hBOOL(hAPP_nat_bool(U_3211,hAPP_nat_nat(suc,sK184(U_3211))))
    | ~ sP284(U_3211) ),
    inference(clausify,[status(thm)],[f_1081_5]) ).

cnf(f_1081_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_3211,sK184(U_3211)))
    | ~ sP284(U_3211) ),
    inference(clausify,[status(thm)],[f_1081_5]) ).

fof(f_1082_1,plain,
    ! [N] :
      ( ? [M_2] : N = hAPP_nat_nat(suc,M_2)
      | N = zero_zero_nat ),
    inference(fof_nnf,[status(thm)],[fact_975_not0__implies__Suc]) ).

fof(f_1082_2,plain,
    ! [U_3213] :
      ( ? [U_3212] : U_3213 = hAPP_nat_nat(suc,U_3212)
      | U_3213 = zero_zero_nat ),
    inference(variable_rename,[status(thm)],[f_1082_1]) ).

fof(f_1082_3,plain,
    ! [U_3213] :
      ( U_3213 = hAPP_nat_nat(suc,sK185(U_3213))
      | U_3213 = zero_zero_nat ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK185]),skolemize(U_3212,sK185(U_3213))],[f_1082_2]) ).

fof(f_1082_4,plain,
    ! [U_3213] :
      ( U_3213 = hAPP_nat_nat(suc,sK185(U_3213))
      | U_3213 = zero_zero_nat ),
    inference(definitional_conversion,[status(esa)],[f_1082_3]) ).

cnf(f_1082_5,plain,
    ( U_3213 = hAPP_nat_nat(suc,sK185(U_3213))
    | U_3213 = zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1082_4]) ).

fof(f_1083_1,plain,
    ! [Na,Pa] :
      ( hBOOL(hAPP_nat_bool(Pa,Na))
      | ? [N_1] :
          ( ~ hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_1)))
          & hBOOL(hAPP_nat_bool(Pa,N_1)) )
      | ~ hBOOL(hAPP_nat_bool(Pa,zero_zero_nat)) ),
    inference(fof_nnf,[status(thm)],[fact_976_nat__induct]) ).

fof(f_1083_2,plain,
    ! [U_3216,U_3215] :
      ( hBOOL(hAPP_nat_bool(U_3215,U_3216))
      | ? [U_3214] :
          ( ~ hBOOL(hAPP_nat_bool(U_3215,hAPP_nat_nat(suc,U_3214)))
          & hBOOL(hAPP_nat_bool(U_3215,U_3214)) )
      | ~ hBOOL(hAPP_nat_bool(U_3215,zero_zero_nat)) ),
    inference(variable_rename,[status(thm)],[f_1083_1]) ).

fof(f_1083_3,plain,
    ! [U_3216,U_3215] :
      ( hBOOL(hAPP_nat_bool(U_3215,U_3216))
      | ( ~ hBOOL(hAPP_nat_bool(U_3215,hAPP_nat_nat(suc,sK186(U_3216,U_3215))))
        & hBOOL(hAPP_nat_bool(U_3215,sK186(U_3216,U_3215))) )
      | ~ hBOOL(hAPP_nat_bool(U_3215,zero_zero_nat)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK186]),skolemize(U_3214,sK186(U_3216,U_3215))],[f_1083_2]) ).

fof(f_1083_4,plain,
    ( ! [U_3215,U_3216] :
        ( ~ hBOOL(hAPP_nat_bool(U_3215,hAPP_nat_nat(suc,sK186(U_3216,U_3215))))
        | ~ sP285(U_3215,U_3216) )
    & ! [U_3215,U_3216] :
        ( hBOOL(hAPP_nat_bool(U_3215,sK186(U_3216,U_3215)))
        | ~ sP285(U_3215,U_3216) )
    & ! [U_3215,U_3216] :
        ( hBOOL(hAPP_nat_bool(U_3215,U_3216))
        | sP285(U_3215,U_3216)
        | ~ hBOOL(hAPP_nat_bool(U_3215,zero_zero_nat)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP285])],[f_1083_3]) ).

cnf(f_1083_5,plain,
    ( hBOOL(hAPP_nat_bool(U_3215,U_3216))
    | sP285(U_3215,U_3216)
    | ~ hBOOL(hAPP_nat_bool(U_3215,zero_zero_nat)) ),
    inference(clausify,[status(thm)],[f_1083_4]) ).

cnf(f_1083_6,plain,
    ( hBOOL(hAPP_nat_bool(U_3215,sK186(U_3216,U_3215)))
    | ~ sP285(U_3215,U_3216) ),
    inference(clausify,[status(thm)],[f_1083_4]) ).

cnf(f_1083_7,plain,
    ( ~ hBOOL(hAPP_nat_bool(U_3215,hAPP_nat_nat(suc,sK186(U_3216,U_3215))))
    | ~ sP285(U_3215,U_3216) ),
    inference(clausify,[status(thm)],[f_1083_4]) ).

fof(f_1084_1,plain,
    ! [V] :
      ( number_number_of_nat(V) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,number_number_of_nat(V)),one_one_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(V))) ),
    inference(fof_nnf,[status(thm)],[fact_977_expand__Suc]) ).

fof(f_1084_2,plain,
    ! [U_3217] :
      ( number_number_of_nat(U_3217) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,number_number_of_nat(U_3217)),one_one_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(U_3217))) ),
    inference(variable_rename,[status(thm)],[f_1084_1]) ).

fof(f_1084_3,plain,
    ! [U_3217] :
      ( number_number_of_nat(U_3217) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,number_number_of_nat(U_3217)),one_one_nat))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(U_3217))) ),
    inference(definitional_conversion,[status(esa)],[f_1084_2]) ).

cnf(f_1084_4,plain,
    ( number_number_of_nat(U_3217) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,number_number_of_nat(U_3217)),one_one_nat))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),number_number_of_nat(U_3217))) ),
    inference(clausify,[status(thm)],[f_1084_3]) ).

fof(f_1085_1,plain,
    ! [N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),N) = zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_978_mult__0]) ).

fof(f_1085_2,plain,
    ! [U_3218] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),U_3218) = zero_zero_nat,
    inference(variable_rename,[status(thm)],[f_1085_1]) ).

fof(f_1085_3,plain,
    ! [U_3218] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),U_3218) = zero_zero_nat,
    inference(definitional_conversion,[status(esa)],[f_1085_2]) ).

cnf(f_1085_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,zero_zero_nat),U_3218) = zero_zero_nat,
    inference(clausify,[status(thm)],[f_1085_3]) ).

fof(f_1086_1,plain,
    ! [M_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),zero_zero_nat) = zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_979_mult__0__right]) ).

fof(f_1086_2,plain,
    ! [U_3219] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3219),zero_zero_nat) = zero_zero_nat,
    inference(variable_rename,[status(thm)],[f_1086_1]) ).

fof(f_1086_3,plain,
    ! [U_3219] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3219),zero_zero_nat) = zero_zero_nat,
    inference(definitional_conversion,[status(esa)],[f_1086_2]) ).

cnf(f_1086_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3219),zero_zero_nat) = zero_zero_nat,
    inference(clausify,[status(thm)],[f_1086_3]) ).

fof(f_1087_1,plain,
    ! [M,Na] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na) = zero_zero_nat
        | ( Na != zero_zero_nat
          & M != zero_zero_nat ) )
      & ( Na = zero_zero_nat
        | M = zero_zero_nat
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na) != zero_zero_nat ) ),
    inference(fof_nnf,[status(thm)],[fact_980_mult__is__0]) ).

fof(f_1087_2,plain,
    ! [U_3221,U_3220] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3221),U_3220) = zero_zero_nat
        | ( U_3220 != zero_zero_nat
          & U_3221 != zero_zero_nat ) )
      & ( U_3220 = zero_zero_nat
        | U_3221 = zero_zero_nat
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3221),U_3220) != zero_zero_nat ) ),
    inference(variable_rename,[status(thm)],[f_1087_1]) ).

fof(f_1087_3,plain,
    ( ! [U_3225,U_3223] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3225),U_3223) = zero_zero_nat
        | ( U_3223 != zero_zero_nat
          & U_3225 != zero_zero_nat ) )
    & ! [U_3224,U_3222] :
        ( U_3222 = zero_zero_nat
        | U_3224 = zero_zero_nat
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3224),U_3222) != zero_zero_nat ) ),
    inference(miniscope,[status(thm)],[f_1087_2]) ).

fof(f_1087_4,plain,
    ( ! [U_3223,U_3225] :
        ( U_3223 != zero_zero_nat
        | ~ sP286(U_3223,U_3225) )
    & ! [U_3223,U_3225] :
        ( U_3225 != zero_zero_nat
        | ~ sP286(U_3223,U_3225) )
    & ! [U_3223,U_3225] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3225),U_3223) = zero_zero_nat
        | sP286(U_3223,U_3225) )
    & ! [U_3224,U_3222] :
        ( U_3222 = zero_zero_nat
        | U_3224 = zero_zero_nat
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3224),U_3222) != zero_zero_nat ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP286])],[f_1087_3]) ).

cnf(f_1087_5,plain,
    ( U_3222 = zero_zero_nat
    | U_3224 = zero_zero_nat
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3224),U_3222) != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1087_4]) ).

cnf(f_1087_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3225),U_3223) = zero_zero_nat
    | sP286(U_3223,U_3225) ),
    inference(clausify,[status(thm)],[f_1087_4]) ).

cnf(f_1087_7,plain,
    ( U_3225 != zero_zero_nat
    | ~ sP286(U_3223,U_3225) ),
    inference(clausify,[status(thm)],[f_1087_4]) ).

cnf(f_1087_8,plain,
    ( U_3223 != zero_zero_nat
    | ~ sP286(U_3223,U_3225) ),
    inference(clausify,[status(thm)],[f_1087_4]) ).

fof(f_1088_1,plain,
    ! [K,M,Na] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na)
        | ( K != zero_zero_nat
          & M != Na ) )
      & ( K = zero_zero_nat
        | M = Na
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_981_mult__cancel1]) ).

fof(f_1088_2,plain,
    ! [U_3228,U_3227,U_3226] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3228),U_3227) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3228),U_3226)
        | ( U_3228 != zero_zero_nat
          & U_3227 != U_3226 ) )
      & ( U_3228 = zero_zero_nat
        | U_3227 = U_3226
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3228),U_3227) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3228),U_3226) ) ),
    inference(variable_rename,[status(thm)],[f_1088_1]) ).

fof(f_1088_3,plain,
    ( ! [U_3234,U_3232,U_3230] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3234),U_3232) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3234),U_3230)
        | ( U_3234 != zero_zero_nat
          & U_3232 != U_3230 ) )
    & ! [U_3233,U_3231,U_3229] :
        ( U_3233 = zero_zero_nat
        | U_3231 = U_3229
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3233),U_3231) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3233),U_3229) ) ),
    inference(miniscope,[status(thm)],[f_1088_2]) ).

fof(f_1088_4,plain,
    ( ! [U_3232,U_3230,U_3234] :
        ( U_3234 != zero_zero_nat
        | ~ sP287(U_3232,U_3230,U_3234) )
    & ! [U_3232,U_3230,U_3234] :
        ( U_3232 != U_3230
        | ~ sP287(U_3232,U_3230,U_3234) )
    & ! [U_3232,U_3230,U_3234] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3234),U_3232) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3234),U_3230)
        | sP287(U_3232,U_3230,U_3234) )
    & ! [U_3231,U_3229,U_3233] :
        ( U_3233 = zero_zero_nat
        | U_3231 = U_3229
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3233),U_3231) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3233),U_3229) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP287])],[f_1088_3]) ).

cnf(f_1088_5,plain,
    ( U_3233 = zero_zero_nat
    | U_3231 = U_3229
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3233),U_3231) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3233),U_3229) ),
    inference(clausify,[status(thm)],[f_1088_4]) ).

cnf(f_1088_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3234),U_3232) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3234),U_3230)
    | sP287(U_3232,U_3230,U_3234) ),
    inference(clausify,[status(thm)],[f_1088_4]) ).

cnf(f_1088_7,plain,
    ( U_3232 != U_3230
    | ~ sP287(U_3232,U_3230,U_3234) ),
    inference(clausify,[status(thm)],[f_1088_4]) ).

cnf(f_1088_8,plain,
    ( U_3234 != zero_zero_nat
    | ~ sP287(U_3232,U_3230,U_3234) ),
    inference(clausify,[status(thm)],[f_1088_4]) ).

fof(f_1089_1,plain,
    ! [M,K,Na] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Na),K)
        | ( K != zero_zero_nat
          & M != Na ) )
      & ( K = zero_zero_nat
        | M = Na
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Na),K) ) ),
    inference(fof_nnf,[status(thm)],[fact_982_mult__cancel2]) ).

fof(f_1089_2,plain,
    ! [U_3237,U_3236,U_3235] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3237),U_3236) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3235),U_3236)
        | ( U_3236 != zero_zero_nat
          & U_3237 != U_3235 ) )
      & ( U_3236 = zero_zero_nat
        | U_3237 = U_3235
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3237),U_3236) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3235),U_3236) ) ),
    inference(variable_rename,[status(thm)],[f_1089_1]) ).

fof(f_1089_3,plain,
    ( ! [U_3243,U_3241,U_3239] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3243),U_3241) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3239),U_3241)
        | ( U_3241 != zero_zero_nat
          & U_3243 != U_3239 ) )
    & ! [U_3242,U_3240,U_3238] :
        ( U_3240 = zero_zero_nat
        | U_3242 = U_3238
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3242),U_3240) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3238),U_3240) ) ),
    inference(miniscope,[status(thm)],[f_1089_2]) ).

fof(f_1089_4,plain,
    ( ! [U_3239,U_3241,U_3243] :
        ( U_3241 != zero_zero_nat
        | ~ sP288(U_3239,U_3241,U_3243) )
    & ! [U_3239,U_3241,U_3243] :
        ( U_3243 != U_3239
        | ~ sP288(U_3239,U_3241,U_3243) )
    & ! [U_3239,U_3241,U_3243] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3243),U_3241) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3239),U_3241)
        | sP288(U_3239,U_3241,U_3243) )
    & ! [U_3240,U_3238,U_3242] :
        ( U_3240 = zero_zero_nat
        | U_3242 = U_3238
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3242),U_3240) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3238),U_3240) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP288])],[f_1089_3]) ).

cnf(f_1089_5,plain,
    ( U_3240 = zero_zero_nat
    | U_3242 = U_3238
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3242),U_3240) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3238),U_3240) ),
    inference(clausify,[status(thm)],[f_1089_4]) ).

cnf(f_1089_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3243),U_3241) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3239),U_3241)
    | sP288(U_3239,U_3241,U_3243) ),
    inference(clausify,[status(thm)],[f_1089_4]) ).

cnf(f_1089_7,plain,
    ( U_3243 != U_3239
    | ~ sP288(U_3239,U_3241,U_3243) ),
    inference(clausify,[status(thm)],[f_1089_4]) ).

cnf(f_1089_8,plain,
    ( U_3241 != zero_zero_nat
    | ~ sP288(U_3239,U_3241,U_3243) ),
    inference(clausify,[status(thm)],[f_1089_4]) ).

fof(f_1090_1,plain,
    ! [K,M,Na] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),Na)
        | M != Na )
      & ( M = Na
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),M) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_983_Suc__mult__cancel1]) ).

fof(f_1090_2,plain,
    ! [U_3246,U_3245,U_3244] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3246)),U_3245) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3246)),U_3244)
        | U_3245 != U_3244 )
      & ( U_3245 = U_3244
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3246)),U_3245) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3246)),U_3244) ) ),
    inference(variable_rename,[status(thm)],[f_1090_1]) ).

fof(f_1090_3,plain,
    ( ! [U_3252,U_3250,U_3248] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3252)),U_3250) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3252)),U_3248)
        | U_3250 != U_3248 )
    & ! [U_3251,U_3249,U_3247] :
        ( U_3249 = U_3247
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3251)),U_3249) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3251)),U_3247) ) ),
    inference(miniscope,[status(thm)],[f_1090_2]) ).

fof(f_1090_4,plain,
    ( ! [U_3250,U_3248,U_3252] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3252)),U_3250) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3252)),U_3248)
        | U_3250 != U_3248 )
    & ! [U_3251,U_3249,U_3247] :
        ( U_3249 = U_3247
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3251)),U_3249) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3251)),U_3247) ) ),
    inference(definitional_conversion,[status(esa)],[f_1090_3]) ).

cnf(f_1090_5,plain,
    ( U_3249 = U_3247
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3251)),U_3249) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3251)),U_3247) ),
    inference(clausify,[status(thm)],[f_1090_4]) ).

cnf(f_1090_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3252)),U_3250) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3252)),U_3248)
    | U_3250 != U_3248 ),
    inference(clausify,[status(thm)],[f_1090_4]) ).

fof(f_1091_1,plain,
    ! [M_1,N,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),K_1)),
    inference(fof_nnf,[status(thm)],[fact_984_add__mult__distrib]) ).

fof(f_1091_2,plain,
    ! [U_3255,U_3254,U_3253] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3255),U_3254)),U_3253) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3255),U_3253)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3254),U_3253)),
    inference(variable_rename,[status(thm)],[f_1091_1]) ).

fof(f_1091_3,plain,
    ! [U_3253,U_3254,U_3255] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3255),U_3254)),U_3253) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3255),U_3253)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3254),U_3253)),
    inference(definitional_conversion,[status(esa)],[f_1091_2]) ).

cnf(f_1091_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3255),U_3254)),U_3253) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3255),U_3253)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3254),U_3253)),
    inference(clausify,[status(thm)],[f_1091_3]) ).

fof(f_1092_1,plain,
    ! [K_1,M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N)),
    inference(fof_nnf,[status(thm)],[fact_985_add__mult__distrib2]) ).

fof(f_1092_2,plain,
    ! [U_3258,U_3257,U_3256] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3258),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3257),U_3256)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3258),U_3257)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3258),U_3256)),
    inference(variable_rename,[status(thm)],[f_1092_1]) ).

fof(f_1092_3,plain,
    ! [U_3256,U_3257,U_3258] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3258),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3257),U_3256)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3258),U_3257)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3258),U_3256)),
    inference(definitional_conversion,[status(esa)],[f_1092_2]) ).

cnf(f_1092_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3258),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3257),U_3256)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3258),U_3257)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3258),U_3256)),
    inference(clausify,[status(thm)],[f_1092_3]) ).

fof(f_1093_1,plain,
    ! [K_1,L_1,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),L_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),L_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_986_mult__le__mono]) ).

fof(f_1093_2,plain,
    ! [U_3262,U_3261,U_3260,U_3259] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3260),U_3262)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3259),U_3261)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3262),U_3261))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3260),U_3259)) ),
    inference(variable_rename,[status(thm)],[f_1093_1]) ).

fof(f_1093_3,plain,
    ! [U_3259,U_3260,U_3261,U_3262] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3260),U_3262)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3259),U_3261)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3262),U_3261))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3260),U_3259)) ),
    inference(definitional_conversion,[status(esa)],[f_1093_2]) ).

cnf(f_1093_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3260),U_3262)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3259),U_3261)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3262),U_3261))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3260),U_3259)) ),
    inference(clausify,[status(thm)],[f_1093_3]) ).

fof(f_1094_1,plain,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),I_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),J)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_987_mult__le__mono2]) ).

fof(f_1094_2,plain,
    ! [U_3265,U_3264,U_3263] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3265),U_3264)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3265),U_3263)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3264),U_3263)) ),
    inference(variable_rename,[status(thm)],[f_1094_1]) ).

fof(f_1094_3,plain,
    ! [U_3264,U_3263,U_3265] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3265),U_3264)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3265),U_3263)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3264),U_3263)) ),
    inference(definitional_conversion,[status(esa)],[f_1094_2]) ).

cnf(f_1094_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3265),U_3264)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3265),U_3263)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3264),U_3263)) ),
    inference(clausify,[status(thm)],[f_1094_3]) ).

fof(f_1095_1,plain,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),K_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_988_mult__le__mono1]) ).

fof(f_1095_2,plain,
    ! [U_3268,U_3267,U_3266] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3267),U_3268)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3266),U_3268)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3267),U_3266)) ),
    inference(variable_rename,[status(thm)],[f_1095_1]) ).

fof(f_1095_3,plain,
    ! [U_3266,U_3267,U_3268] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3267),U_3268)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3266),U_3268)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3267),U_3266)) ),
    inference(definitional_conversion,[status(esa)],[f_1095_2]) ).

cnf(f_1095_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3267),U_3268)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3266),U_3268)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3267),U_3266)) ),
    inference(clausify,[status(thm)],[f_1095_3]) ).

fof(f_1096_1,plain,
    ! [M_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),M_1)))),
    inference(fof_nnf,[status(thm)],[fact_989_le__cube]) ).

fof(f_1096_2,plain,
    ! [U_3269] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3269),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3269),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3269),U_3269)))),
    inference(variable_rename,[status(thm)],[f_1096_1]) ).

fof(f_1096_3,plain,
    ! [U_3269] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3269),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3269),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3269),U_3269)))),
    inference(definitional_conversion,[status(esa)],[f_1096_2]) ).

cnf(f_1096_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3269),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3269),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3269),U_3269)))),
    inference(clausify,[status(thm)],[f_1096_3]) ).

fof(f_1097_1,plain,
    ! [M_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),M_1))),
    inference(fof_nnf,[status(thm)],[fact_990_le__square]) ).

fof(f_1097_2,plain,
    ! [U_3270] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3270),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3270),U_3270))),
    inference(variable_rename,[status(thm)],[f_1097_1]) ).

fof(f_1097_3,plain,
    ! [U_3270] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3270),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3270),U_3270))),
    inference(definitional_conversion,[status(esa)],[f_1097_2]) ).

cnf(f_1097_4,plain,
    hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3270),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3270),U_3270))),
    inference(clausify,[status(thm)],[f_1097_3]) ).

fof(f_1098_1,plain,
    ! [M_1,N,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),K_1)),
    inference(fof_nnf,[status(thm)],[fact_991_diff__mult__distrib]) ).

fof(f_1098_2,plain,
    ! [U_3273,U_3272,U_3271] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3273),U_3272)),U_3271) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3273),U_3271)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3272),U_3271)),
    inference(variable_rename,[status(thm)],[f_1098_1]) ).

fof(f_1098_3,plain,
    ! [U_3271,U_3272,U_3273] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3273),U_3272)),U_3271) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3273),U_3271)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3272),U_3271)),
    inference(definitional_conversion,[status(esa)],[f_1098_2]) ).

cnf(f_1098_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3273),U_3272)),U_3271) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3273),U_3271)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3272),U_3271)),
    inference(clausify,[status(thm)],[f_1098_3]) ).

fof(f_1099_1,plain,
    ! [K_1,M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),N)),
    inference(fof_nnf,[status(thm)],[fact_992_diff__mult__distrib2]) ).

fof(f_1099_2,plain,
    ! [U_3276,U_3275,U_3274] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3276),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3275),U_3274)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3276),U_3275)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3276),U_3274)),
    inference(variable_rename,[status(thm)],[f_1099_1]) ).

fof(f_1099_3,plain,
    ! [U_3274,U_3275,U_3276] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3276),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3275),U_3274)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3276),U_3275)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3276),U_3274)),
    inference(definitional_conversion,[status(esa)],[f_1099_2]) ).

cnf(f_1099_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3276),hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3275),U_3274)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3276),U_3275)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3276),U_3274)),
    inference(clausify,[status(thm)],[f_1099_3]) ).

fof(f_1100_1,plain,
    ! [M,Na] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na) = one_one_nat
        | Na != one_one_nat
        | M != one_one_nat )
      & ( ( Na = one_one_nat
          & M = one_one_nat )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na) != one_one_nat ) ),
    inference(fof_nnf,[status(thm)],[fact_993_nat__mult__eq__1__iff]) ).

fof(f_1100_2,plain,
    ! [U_3278,U_3277] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3278),U_3277) = one_one_nat
        | U_3277 != one_one_nat
        | U_3278 != one_one_nat )
      & ( ( U_3277 = one_one_nat
          & U_3278 = one_one_nat )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3278),U_3277) != one_one_nat ) ),
    inference(variable_rename,[status(thm)],[f_1100_1]) ).

fof(f_1100_3,plain,
    ( ! [U_3282,U_3280] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3282),U_3280) = one_one_nat
        | U_3280 != one_one_nat
        | U_3282 != one_one_nat )
    & ! [U_3281,U_3279] :
        ( ( U_3279 = one_one_nat
          & U_3281 = one_one_nat )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3281),U_3279) != one_one_nat ) ),
    inference(miniscope,[status(thm)],[f_1100_2]) ).

fof(f_1100_4,plain,
    ( ! [U_3281,U_3279] :
        ( U_3279 = one_one_nat
        | ~ sP289(U_3281,U_3279) )
    & ! [U_3281,U_3279] :
        ( U_3281 = one_one_nat
        | ~ sP289(U_3281,U_3279) )
    & ! [U_3280,U_3282] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3282),U_3280) = one_one_nat
        | U_3280 != one_one_nat
        | U_3282 != one_one_nat )
    & ! [U_3281,U_3279] :
        ( sP289(U_3281,U_3279)
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3281),U_3279) != one_one_nat ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP289])],[f_1100_3]) ).

cnf(f_1100_5,plain,
    ( sP289(U_3281,U_3279)
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3281),U_3279) != one_one_nat ),
    inference(clausify,[status(thm)],[f_1100_4]) ).

cnf(f_1100_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3282),U_3280) = one_one_nat
    | U_3280 != one_one_nat
    | U_3282 != one_one_nat ),
    inference(clausify,[status(thm)],[f_1100_4]) ).

cnf(f_1100_7,plain,
    ( U_3281 = one_one_nat
    | ~ sP289(U_3281,U_3279) ),
    inference(clausify,[status(thm)],[f_1100_4]) ).

cnf(f_1100_8,plain,
    ( U_3279 = one_one_nat
    | ~ sP289(U_3281,U_3279) ),
    inference(clausify,[status(thm)],[f_1100_4]) ).

fof(f_1101_1,plain,
    ! [N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),one_one_nat) = N,
    inference(fof_nnf,[status(thm)],[fact_994_nat__mult__1__right]) ).

fof(f_1101_2,plain,
    ! [U_3283] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3283),one_one_nat) = U_3283,
    inference(variable_rename,[status(thm)],[f_1101_1]) ).

fof(f_1101_3,plain,
    ! [U_3283] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3283),one_one_nat) = U_3283,
    inference(definitional_conversion,[status(esa)],[f_1101_2]) ).

cnf(f_1101_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3283),one_one_nat) = U_3283,
    inference(clausify,[status(thm)],[f_1101_3]) ).

fof(f_1102_1,plain,
    ! [M,Na] :
      ( ( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na)
        | Na != one_one_nat
        | M != one_one_nat )
      & ( ( Na = one_one_nat
          & M = one_one_nat )
        | one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_995_nat__1__eq__mult__iff]) ).

fof(f_1102_2,plain,
    ! [U_3285,U_3284] :
      ( ( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3285),U_3284)
        | U_3284 != one_one_nat
        | U_3285 != one_one_nat )
      & ( ( U_3284 = one_one_nat
          & U_3285 = one_one_nat )
        | one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3285),U_3284) ) ),
    inference(variable_rename,[status(thm)],[f_1102_1]) ).

fof(f_1102_3,plain,
    ( ! [U_3289,U_3287] :
        ( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3289),U_3287)
        | U_3287 != one_one_nat
        | U_3289 != one_one_nat )
    & ! [U_3288,U_3286] :
        ( ( U_3286 = one_one_nat
          & U_3288 = one_one_nat )
        | one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3288),U_3286) ) ),
    inference(miniscope,[status(thm)],[f_1102_2]) ).

fof(f_1102_4,plain,
    ( ! [U_3288,U_3286] :
        ( U_3286 = one_one_nat
        | ~ sP290(U_3288,U_3286) )
    & ! [U_3288,U_3286] :
        ( U_3288 = one_one_nat
        | ~ sP290(U_3288,U_3286) )
    & ! [U_3289,U_3287] :
        ( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3289),U_3287)
        | U_3287 != one_one_nat
        | U_3289 != one_one_nat )
    & ! [U_3288,U_3286] :
        ( sP290(U_3288,U_3286)
        | one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3288),U_3286) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP290])],[f_1102_3]) ).

cnf(f_1102_5,plain,
    ( sP290(U_3288,U_3286)
    | one_one_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3288),U_3286) ),
    inference(clausify,[status(thm)],[f_1102_4]) ).

cnf(f_1102_6,plain,
    ( one_one_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3289),U_3287)
    | U_3287 != one_one_nat
    | U_3289 != one_one_nat ),
    inference(clausify,[status(thm)],[f_1102_4]) ).

cnf(f_1102_7,plain,
    ( U_3288 = one_one_nat
    | ~ sP290(U_3288,U_3286) ),
    inference(clausify,[status(thm)],[f_1102_4]) ).

cnf(f_1102_8,plain,
    ( U_3286 = one_one_nat
    | ~ sP290(U_3288,U_3286) ),
    inference(clausify,[status(thm)],[f_1102_4]) ).

fof(f_1103_1,plain,
    ! [N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),N) = N,
    inference(fof_nnf,[status(thm)],[fact_996_nat__mult__1]) ).

fof(f_1103_2,plain,
    ! [U_3290] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),U_3290) = U_3290,
    inference(variable_rename,[status(thm)],[f_1103_1]) ).

fof(f_1103_3,plain,
    ! [U_3290] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),U_3290) = U_3290,
    inference(definitional_conversion,[status(esa)],[f_1103_2]) ).

cnf(f_1103_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,one_one_nat),U_3290) = U_3290,
    inference(clausify,[status(thm)],[f_1103_3]) ).

fof(f_1104_1,plain,
    ! [M,Na] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na) = hAPP_nat_nat(suc,zero_zero_nat)
        | Na != hAPP_nat_nat(suc,zero_zero_nat)
        | M != hAPP_nat_nat(suc,zero_zero_nat) )
      & ( ( Na = hAPP_nat_nat(suc,zero_zero_nat)
          & M = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na) != hAPP_nat_nat(suc,zero_zero_nat) ) ),
    inference(fof_nnf,[status(thm)],[fact_997_mult__eq__1__iff]) ).

fof(f_1104_2,plain,
    ! [U_3292,U_3291] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3292),U_3291) = hAPP_nat_nat(suc,zero_zero_nat)
        | U_3291 != hAPP_nat_nat(suc,zero_zero_nat)
        | U_3292 != hAPP_nat_nat(suc,zero_zero_nat) )
      & ( ( U_3291 = hAPP_nat_nat(suc,zero_zero_nat)
          & U_3292 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3292),U_3291) != hAPP_nat_nat(suc,zero_zero_nat) ) ),
    inference(variable_rename,[status(thm)],[f_1104_1]) ).

fof(f_1104_3,plain,
    ( ! [U_3296,U_3294] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3296),U_3294) = hAPP_nat_nat(suc,zero_zero_nat)
        | U_3294 != hAPP_nat_nat(suc,zero_zero_nat)
        | U_3296 != hAPP_nat_nat(suc,zero_zero_nat) )
    & ! [U_3295,U_3293] :
        ( ( U_3293 = hAPP_nat_nat(suc,zero_zero_nat)
          & U_3295 = hAPP_nat_nat(suc,zero_zero_nat) )
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3295),U_3293) != hAPP_nat_nat(suc,zero_zero_nat) ) ),
    inference(miniscope,[status(thm)],[f_1104_2]) ).

fof(f_1104_4,plain,
    ( ! [U_3295,U_3293] :
        ( U_3293 = hAPP_nat_nat(suc,zero_zero_nat)
        | ~ sP291(U_3295,U_3293) )
    & ! [U_3295,U_3293] :
        ( U_3295 = hAPP_nat_nat(suc,zero_zero_nat)
        | ~ sP291(U_3295,U_3293) )
    & ! [U_3294,U_3296] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3296),U_3294) = hAPP_nat_nat(suc,zero_zero_nat)
        | U_3294 != hAPP_nat_nat(suc,zero_zero_nat)
        | U_3296 != hAPP_nat_nat(suc,zero_zero_nat) )
    & ! [U_3295,U_3293] :
        ( sP291(U_3295,U_3293)
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3295),U_3293) != hAPP_nat_nat(suc,zero_zero_nat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP291])],[f_1104_3]) ).

cnf(f_1104_5,plain,
    ( sP291(U_3295,U_3293)
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3295),U_3293) != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(clausify,[status(thm)],[f_1104_4]) ).

cnf(f_1104_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3296),U_3294) = hAPP_nat_nat(suc,zero_zero_nat)
    | U_3294 != hAPP_nat_nat(suc,zero_zero_nat)
    | U_3296 != hAPP_nat_nat(suc,zero_zero_nat) ),
    inference(clausify,[status(thm)],[f_1104_4]) ).

cnf(f_1104_7,plain,
    ( U_3295 = hAPP_nat_nat(suc,zero_zero_nat)
    | ~ sP291(U_3295,U_3293) ),
    inference(clausify,[status(thm)],[f_1104_4]) ).

cnf(f_1104_8,plain,
    ( U_3293 = hAPP_nat_nat(suc,zero_zero_nat)
    | ~ sP291(U_3295,U_3293) ),
    inference(clausify,[status(thm)],[f_1104_4]) ).

fof(f_1105_1,plain,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),I_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K_1),J)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_998_mult__less__mono2]) ).

fof(f_1105_2,plain,
    ! [U_3299,U_3298,U_3297] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3299),U_3298)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3299),U_3297)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3299))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3298),U_3297)) ),
    inference(variable_rename,[status(thm)],[f_1105_1]) ).

fof(f_1105_3,plain,
    ! [U_3299,U_3297,U_3298] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3299),U_3298)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3299),U_3297)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3299))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3298),U_3297)) ),
    inference(definitional_conversion,[status(esa)],[f_1105_2]) ).

cnf(f_1105_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3299),U_3298)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3299),U_3297)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3299))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3298),U_3297)) ),
    inference(clausify,[status(thm)],[f_1105_3]) ).

fof(f_1106_1,plain,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),K_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),K_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_999_mult__less__mono1]) ).

fof(f_1106_2,plain,
    ! [U_3302,U_3301,U_3300] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3301),U_3302)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3300),U_3302)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3302))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3301),U_3300)) ),
    inference(variable_rename,[status(thm)],[f_1106_1]) ).

fof(f_1106_3,plain,
    ! [U_3301,U_3300,U_3302] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3301),U_3302)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3300),U_3302)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3302))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3301),U_3300)) ),
    inference(definitional_conversion,[status(esa)],[f_1106_2]) ).

cnf(f_1106_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3301),U_3302)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3300),U_3302)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3302))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3301),U_3300)) ),
    inference(clausify,[status(thm)],[f_1106_3]) ).

fof(f_1107_1,plain,
    ! [M,K,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Na),K)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Na),K))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1000_mult__less__cancel2]) ).

fof(f_1107_2,plain,
    ! [U_3305,U_3304,U_3303] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3305),U_3304)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3303),U_3304)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3305),U_3303))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3304)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3305),U_3303))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3304)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3305),U_3304)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3303),U_3304))) ) ),
    inference(variable_rename,[status(thm)],[f_1107_1]) ).

fof(f_1107_3,plain,
    ( ! [U_3311,U_3309,U_3307] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3311),U_3309)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3307),U_3309)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3311),U_3307))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3309)) )
    & ! [U_3310,U_3308,U_3306] :
        ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3310),U_3306))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3308)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3310),U_3308)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3306),U_3308))) ) ),
    inference(miniscope,[status(thm)],[f_1107_2]) ).

fof(f_1107_4,plain,
    ( ! [U_3308,U_3306,U_3310] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3310),U_3306))
        | ~ sP292(U_3308,U_3306,U_3310) )
    & ! [U_3308,U_3306,U_3310] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3308))
        | ~ sP292(U_3308,U_3306,U_3310) )
    & ! [U_3309,U_3307,U_3311] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3311),U_3309)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3307),U_3309)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3311),U_3307))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3309)) )
    & ! [U_3308,U_3306,U_3310] :
        ( sP292(U_3308,U_3306,U_3310)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3310),U_3308)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3306),U_3308))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP292])],[f_1107_3]) ).

cnf(f_1107_5,plain,
    ( sP292(U_3308,U_3306,U_3310)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3310),U_3308)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3306),U_3308))) ),
    inference(clausify,[status(thm)],[f_1107_4]) ).

cnf(f_1107_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3311),U_3309)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3307),U_3309)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3311),U_3307))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3309)) ),
    inference(clausify,[status(thm)],[f_1107_4]) ).

cnf(f_1107_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3308))
    | ~ sP292(U_3308,U_3306,U_3310) ),
    inference(clausify,[status(thm)],[f_1107_4]) ).

cnf(f_1107_8,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3310),U_3306))
    | ~ sP292(U_3308,U_3306,U_3310) ),
    inference(clausify,[status(thm)],[f_1107_4]) ).

fof(f_1108_1,plain,
    ! [K,M,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1001_mult__less__cancel1]) ).

fof(f_1108_2,plain,
    ! [U_3314,U_3313,U_3312] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3314),U_3313)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3314),U_3312)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3313),U_3312))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3314)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3313),U_3312))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3314)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3314),U_3313)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3314),U_3312))) ) ),
    inference(variable_rename,[status(thm)],[f_1108_1]) ).

fof(f_1108_3,plain,
    ( ! [U_3320,U_3318,U_3316] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3320),U_3318)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3320),U_3316)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3318),U_3316))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3320)) )
    & ! [U_3319,U_3317,U_3315] :
        ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3317),U_3315))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3319)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3319),U_3317)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3319),U_3315))) ) ),
    inference(miniscope,[status(thm)],[f_1108_2]) ).

fof(f_1108_4,plain,
    ( ! [U_3317,U_3315,U_3319] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3317),U_3315))
        | ~ sP293(U_3317,U_3315,U_3319) )
    & ! [U_3317,U_3315,U_3319] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3319))
        | ~ sP293(U_3317,U_3315,U_3319) )
    & ! [U_3318,U_3316,U_3320] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3320),U_3318)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3320),U_3316)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3318),U_3316))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3320)) )
    & ! [U_3317,U_3315,U_3319] :
        ( sP293(U_3317,U_3315,U_3319)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3319),U_3317)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3319),U_3315))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP293])],[f_1108_3]) ).

cnf(f_1108_5,plain,
    ( sP293(U_3317,U_3315,U_3319)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3319),U_3317)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3319),U_3315))) ),
    inference(clausify,[status(thm)],[f_1108_4]) ).

cnf(f_1108_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3320),U_3318)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3320),U_3316)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3318),U_3316))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3320)) ),
    inference(clausify,[status(thm)],[f_1108_4]) ).

cnf(f_1108_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3319))
    | ~ sP293(U_3317,U_3315,U_3319) ),
    inference(clausify,[status(thm)],[f_1108_4]) ).

cnf(f_1108_8,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3317),U_3315))
    | ~ sP293(U_3317,U_3315,U_3319) ),
    inference(clausify,[status(thm)],[f_1108_4]) ).

fof(f_1109_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),M)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1002_nat__0__less__mult__iff]) ).

fof(f_1109_2,plain,
    ! [U_3322,U_3321] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3322),U_3321)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3321))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3322)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3321))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3322)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3322),U_3321))) ) ),
    inference(variable_rename,[status(thm)],[f_1109_1]) ).

fof(f_1109_3,plain,
    ( ! [U_3326,U_3324] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3326),U_3324)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3324))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3326)) )
    & ! [U_3325,U_3323] :
        ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3323))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3325)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3325),U_3323))) ) ),
    inference(miniscope,[status(thm)],[f_1109_2]) ).

fof(f_1109_4,plain,
    ( ! [U_3325,U_3323] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3323))
        | ~ sP294(U_3325,U_3323) )
    & ! [U_3325,U_3323] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3325))
        | ~ sP294(U_3325,U_3323) )
    & ! [U_3326,U_3324] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3326),U_3324)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3324))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3326)) )
    & ! [U_3325,U_3323] :
        ( sP294(U_3325,U_3323)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3325),U_3323))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP294])],[f_1109_3]) ).

cnf(f_1109_5,plain,
    ( sP294(U_3325,U_3323)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3325),U_3323))) ),
    inference(clausify,[status(thm)],[f_1109_4]) ).

cnf(f_1109_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3326),U_3324)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3324))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3326)) ),
    inference(clausify,[status(thm)],[f_1109_4]) ).

cnf(f_1109_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3325))
    | ~ sP294(U_3325,U_3323) ),
    inference(clausify,[status(thm)],[f_1109_4]) ).

cnf(f_1109_8,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3323))
    | ~ sP294(U_3325,U_3323) ),
    inference(clausify,[status(thm)],[f_1109_4]) ).

fof(f_1110_1,plain,
    ! [K,M,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1003_Suc__mult__less__cancel1]) ).

fof(f_1110_2,plain,
    ! [U_3329,U_3328,U_3327] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3329)),U_3328)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3329)),U_3327)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3328),U_3327)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3328),U_3327))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3329)),U_3328)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3329)),U_3327))) ) ),
    inference(variable_rename,[status(thm)],[f_1110_1]) ).

fof(f_1110_3,plain,
    ( ! [U_3335,U_3333,U_3331] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3335)),U_3333)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3335)),U_3331)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3333),U_3331)) )
    & ! [U_3334,U_3332,U_3330] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3332),U_3330))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3334)),U_3332)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3334)),U_3330))) ) ),
    inference(miniscope,[status(thm)],[f_1110_2]) ).

fof(f_1110_4,plain,
    ( ! [U_3331,U_3333,U_3335] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3335)),U_3333)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3335)),U_3331)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3333),U_3331)) )
    & ! [U_3332,U_3330,U_3334] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3332),U_3330))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3334)),U_3332)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3334)),U_3330))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1110_3]) ).

cnf(f_1110_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3332),U_3330))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3334)),U_3332)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3334)),U_3330))) ),
    inference(clausify,[status(thm)],[f_1110_4]) ).

cnf(f_1110_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3335)),U_3333)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3335)),U_3331)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3333),U_3331)) ),
    inference(clausify,[status(thm)],[f_1110_4]) ).

fof(f_1111_1,plain,
    ! [M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),hAPP_nat_nat(suc,N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N)),
    inference(fof_nnf,[status(thm)],[fact_1004_mult__Suc__right]) ).

fof(f_1111_2,plain,
    ! [U_3337,U_3336] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3337),hAPP_nat_nat(suc,U_3336)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3337),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3337),U_3336)),
    inference(variable_rename,[status(thm)],[f_1111_1]) ).

fof(f_1111_3,plain,
    ! [U_3337,U_3336] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3337),hAPP_nat_nat(suc,U_3336)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3337),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3337),U_3336)),
    inference(definitional_conversion,[status(esa)],[f_1111_2]) ).

cnf(f_1111_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3337),hAPP_nat_nat(suc,U_3336)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3337),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3337),U_3336)),
    inference(clausify,[status(thm)],[f_1111_3]) ).

fof(f_1112_1,plain,
    ! [M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,M_1)),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N)),
    inference(fof_nnf,[status(thm)],[fact_1005_mult__Suc]) ).

fof(f_1112_2,plain,
    ! [U_3339,U_3338] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3339)),U_3338) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3338),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3339),U_3338)),
    inference(variable_rename,[status(thm)],[f_1112_1]) ).

fof(f_1112_3,plain,
    ! [U_3338,U_3339] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3339)),U_3338) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3338),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3339),U_3338)),
    inference(definitional_conversion,[status(esa)],[f_1112_2]) ).

cnf(f_1112_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3339)),U_3338) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3338),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3339),U_3338)),
    inference(clausify,[status(thm)],[f_1112_3]) ).

fof(f_1113_1,plain,
    ! [K,M,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,K)),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1006_Suc__mult__le__cancel1]) ).

fof(f_1113_2,plain,
    ! [U_3342,U_3341,U_3340] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3342)),U_3341)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3342)),U_3340)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3341),U_3340)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3341),U_3340))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3342)),U_3341)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3342)),U_3340))) ) ),
    inference(variable_rename,[status(thm)],[f_1113_1]) ).

fof(f_1113_3,plain,
    ( ! [U_3348,U_3346,U_3344] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3348)),U_3346)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3348)),U_3344)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3346),U_3344)) )
    & ! [U_3347,U_3345,U_3343] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3345),U_3343))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3347)),U_3345)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3347)),U_3343))) ) ),
    inference(miniscope,[status(thm)],[f_1113_2]) ).

fof(f_1113_4,plain,
    ( ! [U_3344,U_3346,U_3348] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3348)),U_3346)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3348)),U_3344)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3346),U_3344)) )
    & ! [U_3345,U_3343,U_3347] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3345),U_3343))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3347)),U_3345)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3347)),U_3343))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1113_3]) ).

cnf(f_1113_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3345),U_3343))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3347)),U_3345)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3347)),U_3343))) ),
    inference(clausify,[status(thm)],[f_1113_4]) ).

cnf(f_1113_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3348)),U_3346)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(suc,U_3348)),U_3344)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3346),U_3344)) ),
    inference(clausify,[status(thm)],[f_1113_4]) ).

fof(f_1114_1,plain,
    ! [M_1,N] :
      ( M_1 = zero_zero_nat
      | N = one_one_nat
      | M_1 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N) ),
    inference(fof_nnf,[status(thm)],[fact_1007_mult__eq__self__implies__10]) ).

fof(f_1114_2,plain,
    ! [U_3350,U_3349] :
      ( U_3350 = zero_zero_nat
      | U_3349 = one_one_nat
      | U_3350 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3350),U_3349) ),
    inference(variable_rename,[status(thm)],[f_1114_1]) ).

fof(f_1114_3,plain,
    ! [U_3349,U_3350] :
      ( U_3350 = zero_zero_nat
      | U_3349 = one_one_nat
      | U_3350 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3350),U_3349) ),
    inference(definitional_conversion,[status(esa)],[f_1114_2]) ).

cnf(f_1114_4,plain,
    ( U_3350 = zero_zero_nat
    | U_3349 = one_one_nat
    | U_3350 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3350),U_3349) ),
    inference(clausify,[status(thm)],[f_1114_3]) ).

fof(f_1115_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_1008_n__less__m__mult__n]) ).

fof(f_1115_2,plain,
    ! [U_3352,U_3351] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3351),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3352),U_3351)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3352))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3351)) ),
    inference(variable_rename,[status(thm)],[f_1115_1]) ).

fof(f_1115_3,plain,
    ! [U_3352,U_3351] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3351),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3352),U_3351)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3352))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3351)) ),
    inference(definitional_conversion,[status(esa)],[f_1115_2]) ).

cnf(f_1115_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3351),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3352),U_3351)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3352))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3351)) ),
    inference(clausify,[status(thm)],[f_1115_3]) ).

fof(f_1116_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),M_1)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_1009_n__less__n__mult__m]) ).

fof(f_1116_2,plain,
    ! [U_3354,U_3353] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3353),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3353),U_3354)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3354))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3353)) ),
    inference(variable_rename,[status(thm)],[f_1116_1]) ).

fof(f_1116_3,plain,
    ! [U_3353,U_3354] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3353),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3353),U_3354)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3354))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3353)) ),
    inference(definitional_conversion,[status(esa)],[f_1116_2]) ).

cnf(f_1116_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3353),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3353),U_3354)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3354))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3353)) ),
    inference(clausify,[status(thm)],[f_1116_3]) ).

fof(f_1117_1,plain,
    ! [M_1,N] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),M_1))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),N)) ),
    inference(fof_nnf,[status(thm)],[fact_1010_one__less__mult]) ).

fof(f_1117_2,plain,
    ! [U_3356,U_3355] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3356),U_3355)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3356))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3355)) ),
    inference(variable_rename,[status(thm)],[f_1117_1]) ).

fof(f_1117_3,plain,
    ! [U_3356,U_3355] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3356),U_3355)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3356))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3355)) ),
    inference(definitional_conversion,[status(esa)],[f_1117_2]) ).

cnf(f_1117_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3356),U_3355)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3356))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3355)) ),
    inference(clausify,[status(thm)],[f_1117_3]) ).

fof(f_1118_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),M)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),Na))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),M)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1011_one__le__mult__iff]) ).

fof(f_1118_2,plain,
    ! [U_3358,U_3357] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3358),U_3357)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3357))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3358)) )
      & ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3357))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3358)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3358),U_3357))) ) ),
    inference(variable_rename,[status(thm)],[f_1118_1]) ).

fof(f_1118_3,plain,
    ( ! [U_3362,U_3360] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3362),U_3360)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3360))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3362)) )
    & ! [U_3361,U_3359] :
        ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3359))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3361)) )
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3361),U_3359))) ) ),
    inference(miniscope,[status(thm)],[f_1118_2]) ).

fof(f_1118_4,plain,
    ( ! [U_3361,U_3359] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3359))
        | ~ sP295(U_3361,U_3359) )
    & ! [U_3361,U_3359] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3361))
        | ~ sP295(U_3361,U_3359) )
    & ! [U_3362,U_3360] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3362),U_3360)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3360))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3362)) )
    & ! [U_3361,U_3359] :
        ( sP295(U_3361,U_3359)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3361),U_3359))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP295])],[f_1118_3]) ).

cnf(f_1118_5,plain,
    ( sP295(U_3361,U_3359)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3361),U_3359))) ),
    inference(clausify,[status(thm)],[f_1118_4]) ).

cnf(f_1118_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3362),U_3360)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3360))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3362)) ),
    inference(clausify,[status(thm)],[f_1118_4]) ).

cnf(f_1118_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3361))
    | ~ sP295(U_3361,U_3359) ),
    inference(clausify,[status(thm)],[f_1118_4]) ).

cnf(f_1118_8,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,zero_zero_nat)),U_3359))
    | ~ sP295(U_3361,U_3359) ),
    inference(clausify,[status(thm)],[f_1118_4]) ).

fof(f_1119_1,plain,
    ! [K,M,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1012_mult__le__cancel1]) ).

fof(f_1119_2,plain,
    ! [U_3365,U_3364,U_3363] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3365),U_3364)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3365),U_3363)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3364),U_3363))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3365)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3364),U_3363))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3365))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3365),U_3364)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3365),U_3363))) ) ),
    inference(variable_rename,[status(thm)],[f_1119_1]) ).

fof(f_1119_3,plain,
    ( ! [U_3371,U_3369,U_3367] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3371),U_3369)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3371),U_3367)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3369),U_3367))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3371)) ) )
    & ! [U_3370,U_3368,U_3366] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3368),U_3366))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3370))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3370),U_3368)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3370),U_3366))) ) ),
    inference(miniscope,[status(thm)],[f_1119_2]) ).

fof(f_1119_4,plain,
    ( ! [U_3369,U_3367,U_3371] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3369),U_3367))
        | ~ sP296(U_3369,U_3367,U_3371) )
    & ! [U_3369,U_3367,U_3371] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3371))
        | ~ sP296(U_3369,U_3367,U_3371) )
    & ! [U_3369,U_3367,U_3371] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3371),U_3369)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3371),U_3367)))
        | sP296(U_3369,U_3367,U_3371) )
    & ! [U_3366,U_3368,U_3370] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3368),U_3366))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3370))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3370),U_3368)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3370),U_3366))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP296])],[f_1119_3]) ).

cnf(f_1119_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3368),U_3366))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3370))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3370),U_3368)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3370),U_3366))) ),
    inference(clausify,[status(thm)],[f_1119_4]) ).

cnf(f_1119_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3371),U_3369)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3371),U_3367)))
    | sP296(U_3369,U_3367,U_3371) ),
    inference(clausify,[status(thm)],[f_1119_4]) ).

cnf(f_1119_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3371))
    | ~ sP296(U_3369,U_3367,U_3371) ),
    inference(clausify,[status(thm)],[f_1119_4]) ).

cnf(f_1119_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3369),U_3367))
    | ~ sP296(U_3369,U_3367,U_3371) ),
    inference(clausify,[status(thm)],[f_1119_4]) ).

fof(f_1120_1,plain,
    ! [M,K,Na] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Na),K)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M),K)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,Na),K))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1013_mult__le__cancel2]) ).

fof(f_1120_2,plain,
    ! [U_3374,U_3373,U_3372] :
      ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3374),U_3373)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3372),U_3373)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3374),U_3372))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3373)) ) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3374),U_3372))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3373))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3374),U_3373)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3372),U_3373))) ) ),
    inference(variable_rename,[status(thm)],[f_1120_1]) ).

fof(f_1120_3,plain,
    ( ! [U_3380,U_3378,U_3376] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3380),U_3378)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3376),U_3378)))
        | ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3380),U_3376))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3378)) ) )
    & ! [U_3379,U_3377,U_3375] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3379),U_3375))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3377))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3379),U_3377)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3375),U_3377))) ) ),
    inference(miniscope,[status(thm)],[f_1120_2]) ).

fof(f_1120_4,plain,
    ( ! [U_3378,U_3376,U_3380] :
        ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3380),U_3376))
        | ~ sP297(U_3378,U_3376,U_3380) )
    & ! [U_3378,U_3376,U_3380] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3378))
        | ~ sP297(U_3378,U_3376,U_3380) )
    & ! [U_3378,U_3376,U_3380] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3380),U_3378)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3376),U_3378)))
        | sP297(U_3378,U_3376,U_3380) )
    & ! [U_3379,U_3375,U_3377] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3379),U_3375))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3377))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3379),U_3377)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3375),U_3377))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP297])],[f_1120_3]) ).

cnf(f_1120_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3379),U_3375))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3377))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3379),U_3377)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3375),U_3377))) ),
    inference(clausify,[status(thm)],[f_1120_4]) ).

cnf(f_1120_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3380),U_3378)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3376),U_3378)))
    | sP297(U_3378,U_3376,U_3380) ),
    inference(clausify,[status(thm)],[f_1120_4]) ).

cnf(f_1120_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3378))
    | ~ sP297(U_3378,U_3376,U_3380) ),
    inference(clausify,[status(thm)],[f_1120_4]) ).

cnf(f_1120_8,plain,
    ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3380),U_3376))
    | ~ sP297(U_3378,U_3376,U_3380) ),
    inference(clausify,[status(thm)],[f_1120_4]) ).

fof(f_1121_1,plain,
    ! [N,M_1] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),one_one_nat)),N))
        | M_1 = zero_zero_nat )
      & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N) = zero_zero_nat
        | M_1 != zero_zero_nat ) ),
    inference(fof_nnf,[status(thm)],[fact_1014_mult__eq__if]) ).

fof(f_1121_2,plain,
    ! [U_3382,U_3381] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3381),U_3382) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3382),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3381),one_one_nat)),U_3382))
        | U_3381 = zero_zero_nat )
      & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3381),U_3382) = zero_zero_nat
        | U_3381 != zero_zero_nat ) ),
    inference(variable_rename,[status(thm)],[f_1121_1]) ).

fof(f_1121_3,plain,
    ( ! [U_3386,U_3384] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3384),U_3386) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3386),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3384),one_one_nat)),U_3386))
        | U_3384 = zero_zero_nat )
    & ! [U_3385,U_3383] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3383),U_3385) = zero_zero_nat
        | U_3383 != zero_zero_nat ) ),
    inference(miniscope,[status(thm)],[f_1121_2]) ).

fof(f_1121_4,plain,
    ( ! [U_3384,U_3386] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3384),U_3386) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3386),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3384),one_one_nat)),U_3386))
        | U_3384 = zero_zero_nat )
    & ! [U_3383,U_3385] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3383),U_3385) = zero_zero_nat
        | U_3383 != zero_zero_nat ) ),
    inference(definitional_conversion,[status(esa)],[f_1121_3]) ).

cnf(f_1121_5,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3383),U_3385) = zero_zero_nat
    | U_3383 != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1121_4]) ).

cnf(f_1121_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3384),U_3386) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3386),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3384),one_one_nat)),U_3386))
    | U_3384 = zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1121_4]) ).

fof(f_1122_1,plain,
    ! [U,M,Na,I_2,J_1] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),I_2)),U)),Na))) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),I_2)),U)),Na)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1015_nat__less__add__iff2]) ).

fof(f_1122_2,plain,
    ! [U_3391,U_3390,U_3389,U_3388,U_3387] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3388),U_3391)),U_3390)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3387),U_3391)),U_3389)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3390),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3387),U_3388)),U_3391)),U_3389))) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3390),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3387),U_3388)),U_3391)),U_3389)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3388),U_3391)),U_3390)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3387),U_3391)),U_3389))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3388),U_3387)) ),
    inference(variable_rename,[status(thm)],[f_1122_1]) ).

fof(f_1122_3,plain,
    ( ! [U_3387,U_3388,U_3389,U_3390,U_3391] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3388),U_3391)),U_3390)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3387),U_3391)),U_3389)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3390),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3387),U_3388)),U_3391)),U_3389)))
        | ~ sP298(U_3387,U_3388,U_3389,U_3390,U_3391) )
    & ! [U_3387,U_3388,U_3389,U_3390,U_3391] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3390),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3387),U_3388)),U_3391)),U_3389)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3388),U_3391)),U_3390)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3387),U_3391)),U_3389)))
        | ~ sP298(U_3387,U_3388,U_3389,U_3390,U_3391) )
    & ! [U_3387,U_3388,U_3389,U_3390,U_3391] :
        ( sP298(U_3387,U_3388,U_3389,U_3390,U_3391)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3388),U_3387)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP298])],[f_1122_2]) ).

cnf(f_1122_4,plain,
    ( sP298(U_3387,U_3388,U_3389,U_3390,U_3391)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3388),U_3387)) ),
    inference(clausify,[status(thm)],[f_1122_3]) ).

cnf(f_1122_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3390),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3387),U_3388)),U_3391)),U_3389)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3388),U_3391)),U_3390)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3387),U_3391)),U_3389)))
    | ~ sP298(U_3387,U_3388,U_3389,U_3390,U_3391) ),
    inference(clausify,[status(thm)],[f_1122_3]) ).

cnf(f_1122_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3388),U_3391)),U_3390)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3387),U_3391)),U_3389)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3390),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3387),U_3388)),U_3391)),U_3389)))
    | ~ sP298(U_3387,U_3388,U_3389,U_3390,U_3391) ),
    inference(clausify,[status(thm)],[f_1122_3]) ).

fof(f_1123_1,plain,
    ! [M_1,N] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),M_1),
    inference(fof_nnf,[status(thm)],[fact_1016_nat__mult__commute]) ).

fof(f_1123_2,plain,
    ! [U_3393,U_3392] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3393),U_3392) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3392),U_3393),
    inference(variable_rename,[status(thm)],[f_1123_1]) ).

fof(f_1123_3,plain,
    ! [U_3393,U_3392] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3393),U_3392) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3392),U_3393),
    inference(definitional_conversion,[status(esa)],[f_1123_2]) ).

cnf(f_1123_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3393),U_3392) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3392),U_3393),
    inference(clausify,[status(thm)],[f_1123_3]) ).

fof(f_1124_1,plain,
    ! [M_1,N,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N)),K_1) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),K_1)),
    inference(fof_nnf,[status(thm)],[fact_1017_nat__mult__assoc]) ).

fof(f_1124_2,plain,
    ! [U_3396,U_3395,U_3394] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3396),U_3395)),U_3394) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3396),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3395),U_3394)),
    inference(variable_rename,[status(thm)],[f_1124_1]) ).

fof(f_1124_3,plain,
    ! [U_3395,U_3396,U_3394] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3396),U_3395)),U_3394) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3396),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3395),U_3394)),
    inference(definitional_conversion,[status(esa)],[f_1124_2]) ).

cnf(f_1124_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3396),U_3395)),U_3394) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3396),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3395),U_3394)),
    inference(clausify,[status(thm)],[f_1124_3]) ).

fof(f_1125_1,plain,
    ! [K,L] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(K)),number_number_of_int(L)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(K)),number_number_of_int(L))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1018_less__number__of__int__code]) ).

fof(f_1125_2,plain,
    ! [U_3398,U_3397] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_3398)),number_number_of_int(U_3397)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3398),U_3397)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3398),U_3397))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_3398)),number_number_of_int(U_3397))) ) ),
    inference(variable_rename,[status(thm)],[f_1125_1]) ).

fof(f_1125_3,plain,
    ( ! [U_3402,U_3400] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_3402)),number_number_of_int(U_3400)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3402),U_3400)) )
    & ! [U_3401,U_3399] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3401),U_3399))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_3401)),number_number_of_int(U_3399))) ) ),
    inference(miniscope,[status(thm)],[f_1125_2]) ).

fof(f_1125_4,plain,
    ( ! [U_3400,U_3402] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_3402)),number_number_of_int(U_3400)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3402),U_3400)) )
    & ! [U_3401,U_3399] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3401),U_3399))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_3401)),number_number_of_int(U_3399))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1125_3]) ).

cnf(f_1125_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3401),U_3399))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_3401)),number_number_of_int(U_3399))) ),
    inference(clausify,[status(thm)],[f_1125_4]) ).

cnf(f_1125_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(U_3402)),number_number_of_int(U_3400)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3402),U_3400)) ),
    inference(clausify,[status(thm)],[f_1125_4]) ).

fof(f_1126_1,plain,
    ! [Z] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),Z) = Z,
    inference(fof_nnf,[status(thm)],[fact_1019_zmult__1]) ).

fof(f_1126_2,plain,
    ! [U_3403] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),U_3403) = U_3403,
    inference(variable_rename,[status(thm)],[f_1126_1]) ).

fof(f_1126_3,plain,
    ! [U_3403] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),U_3403) = U_3403,
    inference(definitional_conversion,[status(esa)],[f_1126_2]) ).

cnf(f_1126_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(times_times_int,one_one_int),U_3403) = U_3403,
    inference(clausify,[status(thm)],[f_1126_3]) ).

fof(f_1127_1,plain,
    ! [Z] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z),one_one_int) = Z,
    inference(fof_nnf,[status(thm)],[fact_1020_zmult__1__right]) ).

fof(f_1127_2,plain,
    ! [U_3404] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3404),one_one_int) = U_3404,
    inference(variable_rename,[status(thm)],[f_1127_1]) ).

fof(f_1127_3,plain,
    ! [U_3404] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3404),one_one_int) = U_3404,
    inference(definitional_conversion,[status(esa)],[f_1127_2]) ).

cnf(f_1127_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3404),one_one_int) = U_3404,
    inference(clausify,[status(thm)],[f_1127_3]) ).

fof(f_1128_1,plain,
    ! [Z,W] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z),W) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Z),
    inference(fof_nnf,[status(thm)],[fact_1021_zmult__commute]) ).

fof(f_1128_2,plain,
    ! [U_3406,U_3405] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3406),U_3405) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3405),U_3406),
    inference(variable_rename,[status(thm)],[f_1128_1]) ).

fof(f_1128_3,plain,
    ! [U_3405,U_3406] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3406),U_3405) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3405),U_3406),
    inference(definitional_conversion,[status(esa)],[f_1128_2]) ).

cnf(f_1128_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3406),U_3405) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3405),U_3406),
    inference(clausify,[status(thm)],[f_1128_3]) ).

fof(f_1129_1,plain,
    ! [V,W] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,number_number_of_int(V)),number_number_of_int(W)) = number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,V),W)),
    inference(fof_nnf,[status(thm)],[fact_1022_times__numeral__code_I5_J]) ).

fof(f_1129_2,plain,
    ! [U_3408,U_3407] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,number_number_of_int(U_3408)),number_number_of_int(U_3407)) = number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3408),U_3407)),
    inference(variable_rename,[status(thm)],[f_1129_1]) ).

fof(f_1129_3,plain,
    ! [U_3407,U_3408] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,number_number_of_int(U_3408)),number_number_of_int(U_3407)) = number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3408),U_3407)),
    inference(definitional_conversion,[status(esa)],[f_1129_2]) ).

cnf(f_1129_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(times_times_int,number_number_of_int(U_3408)),number_number_of_int(U_3407)) = number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3408),U_3407)),
    inference(clausify,[status(thm)],[f_1129_3]) ).

fof(f_1130_1,plain,
    ! [Z1,Z2,Z3] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),Z2)),Z3) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z2),Z3)),
    inference(fof_nnf,[status(thm)],[fact_1023_zmult__assoc]) ).

fof(f_1130_2,plain,
    ! [U_3411,U_3410,U_3409] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3411),U_3410)),U_3409) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3411),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3410),U_3409)),
    inference(variable_rename,[status(thm)],[f_1130_1]) ).

fof(f_1130_3,plain,
    ! [U_3409,U_3410,U_3411] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3411),U_3410)),U_3409) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3411),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3410),U_3409)),
    inference(definitional_conversion,[status(esa)],[f_1130_2]) ).

cnf(f_1130_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3411),U_3410)),U_3409) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3411),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3410),U_3409)),
    inference(clausify,[status(thm)],[f_1130_3]) ).

fof(f_1131_1,plain,
    ! [K,L] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(K)),number_number_of_int(L)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(K)),number_number_of_int(L))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1024_less__eq__number__of__int__code]) ).

fof(f_1131_2,plain,
    ! [U_3413,U_3412] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_3413)),number_number_of_int(U_3412)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3413),U_3412)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3413),U_3412))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_3413)),number_number_of_int(U_3412))) ) ),
    inference(variable_rename,[status(thm)],[f_1131_1]) ).

fof(f_1131_3,plain,
    ( ! [U_3417,U_3415] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_3417)),number_number_of_int(U_3415)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3417),U_3415)) )
    & ! [U_3416,U_3414] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3416),U_3414))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_3416)),number_number_of_int(U_3414))) ) ),
    inference(miniscope,[status(thm)],[f_1131_2]) ).

fof(f_1131_4,plain,
    ( ! [U_3415,U_3417] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_3417)),number_number_of_int(U_3415)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3417),U_3415)) )
    & ! [U_3416,U_3414] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3416),U_3414))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_3416)),number_number_of_int(U_3414))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1131_3]) ).

cnf(f_1131_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3416),U_3414))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_3416)),number_number_of_int(U_3414))) ),
    inference(clausify,[status(thm)],[f_1131_4]) ).

cnf(f_1131_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_3417)),number_number_of_int(U_3415)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3417),U_3415)) ),
    inference(clausify,[status(thm)],[f_1131_4]) ).

fof(f_1132_1,plain,
    ! [Z1,Z2,W] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z1),Z2)),W) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),W)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z2),W)),
    inference(fof_nnf,[status(thm)],[fact_1025_zdiff__zmult__distrib]) ).

fof(f_1132_2,plain,
    ! [U_3420,U_3419,U_3418] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3420),U_3419)),U_3418) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3420),U_3418)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3419),U_3418)),
    inference(variable_rename,[status(thm)],[f_1132_1]) ).

fof(f_1132_3,plain,
    ! [U_3419,U_3418,U_3420] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3420),U_3419)),U_3418) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3420),U_3418)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3419),U_3418)),
    inference(definitional_conversion,[status(esa)],[f_1132_2]) ).

cnf(f_1132_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3420),U_3419)),U_3418) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3420),U_3418)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3419),U_3418)),
    inference(clausify,[status(thm)],[f_1132_3]) ).

fof(f_1133_1,plain,
    ! [W,Z1,Z2] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z1),Z2)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Z1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Z2)),
    inference(fof_nnf,[status(thm)],[fact_1026_zdiff__zmult__distrib2]) ).

fof(f_1133_2,plain,
    ! [U_3423,U_3422,U_3421] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3423),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3422),U_3421)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3423),U_3422)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3423),U_3421)),
    inference(variable_rename,[status(thm)],[f_1133_1]) ).

fof(f_1133_3,plain,
    ! [U_3421,U_3422,U_3423] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3423),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3422),U_3421)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3423),U_3422)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3423),U_3421)),
    inference(definitional_conversion,[status(esa)],[f_1133_2]) ).

cnf(f_1133_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3423),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3422),U_3421)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3423),U_3422)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3423),U_3421)),
    inference(clausify,[status(thm)],[f_1133_3]) ).

fof(f_1134_1,plain,
    ! [W,Z1,Z2] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),Z2)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Z1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,W),Z2)),
    inference(fof_nnf,[status(thm)],[fact_1027_zadd__zmult__distrib2]) ).

fof(f_1134_2,plain,
    ! [U_3426,U_3425,U_3424] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3426),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3425),U_3424)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3426),U_3425)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3426),U_3424)),
    inference(variable_rename,[status(thm)],[f_1134_1]) ).

fof(f_1134_3,plain,
    ! [U_3424,U_3425,U_3426] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3426),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3425),U_3424)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3426),U_3425)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3426),U_3424)),
    inference(definitional_conversion,[status(esa)],[f_1134_2]) ).

cnf(f_1134_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3426),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3425),U_3424)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3426),U_3425)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3426),U_3424)),
    inference(clausify,[status(thm)],[f_1134_3]) ).

fof(f_1135_1,plain,
    ! [V,W] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,number_number_of_int(V)),number_number_of_int(W)) = number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V),W)),
    inference(fof_nnf,[status(thm)],[fact_1028_plus__numeral__code_I9_J]) ).

fof(f_1135_2,plain,
    ! [U_3428,U_3427] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,number_number_of_int(U_3428)),number_number_of_int(U_3427)) = number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3428),U_3427)),
    inference(variable_rename,[status(thm)],[f_1135_1]) ).

fof(f_1135_3,plain,
    ! [U_3427,U_3428] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,number_number_of_int(U_3428)),number_number_of_int(U_3427)) = number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3428),U_3427)),
    inference(definitional_conversion,[status(esa)],[f_1135_2]) ).

cnf(f_1135_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,number_number_of_int(U_3428)),number_number_of_int(U_3427)) = number_number_of_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3428),U_3427)),
    inference(clausify,[status(thm)],[f_1135_3]) ).

fof(f_1136_1,plain,
    ! [Z1,Z2,W] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),Z2)),W) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z1),W)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,Z2),W)),
    inference(fof_nnf,[status(thm)],[fact_1029_zadd__zmult__distrib]) ).

fof(f_1136_2,plain,
    ! [U_3431,U_3430,U_3429] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3431),U_3430)),U_3429) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3431),U_3429)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3430),U_3429)),
    inference(variable_rename,[status(thm)],[f_1136_1]) ).

fof(f_1136_3,plain,
    ! [U_3429,U_3430,U_3431] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3431),U_3430)),U_3429) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3431),U_3429)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3430),U_3429)),
    inference(definitional_conversion,[status(esa)],[f_1136_2]) ).

cnf(f_1136_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3431),U_3430)),U_3429) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3431),U_3429)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3430),U_3429)),
    inference(clausify,[status(thm)],[f_1136_3]) ).

fof(f_1137_1,plain,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_1),I_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_1),J)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),K_1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_1030_zmult__zless__mono2]) ).

fof(f_1137_2,plain,
    ! [U_3434,U_3433,U_3432] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3434),U_3433)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3434),U_3432)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3434))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3433),U_3432)) ),
    inference(variable_rename,[status(thm)],[f_1137_1]) ).

fof(f_1137_3,plain,
    ! [U_3432,U_3433,U_3434] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3434),U_3433)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3434),U_3432)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3434))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3433),U_3432)) ),
    inference(definitional_conversion,[status(esa)],[f_1137_2]) ).

cnf(f_1137_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3434),U_3433)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3434),U_3432)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3434))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3433),U_3432)) ),
    inference(clausify,[status(thm)],[f_1137_3]) ).

fof(f_1138_1,plain,
    ! [Na,M] :
      ( ( ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M),Na) = one_one_int
          | Na != one_one_int
          | M != one_one_int )
        & ( ( Na = one_one_int
            & M = one_one_int )
          | hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M),Na) != one_one_int ) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),M)) ),
    inference(fof_nnf,[status(thm)],[fact_1031_pos__zmult__eq__1__iff]) ).

fof(f_1138_2,plain,
    ! [U_3436,U_3435] :
      ( ( ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3435),U_3436) = one_one_int
          | U_3436 != one_one_int
          | U_3435 != one_one_int )
        & ( ( U_3436 = one_one_int
            & U_3435 = one_one_int )
          | hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3435),U_3436) != one_one_int ) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3435)) ),
    inference(variable_rename,[status(thm)],[f_1138_1]) ).

fof(f_1138_3,plain,
    ( ! [U_3435,U_3436] :
        ( U_3436 = one_one_int
        | ~ sP299(U_3435,U_3436) )
    & ! [U_3435,U_3436] :
        ( U_3435 = one_one_int
        | ~ sP299(U_3435,U_3436) )
    & ! [U_3435,U_3436] :
        ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3435),U_3436) = one_one_int
        | U_3436 != one_one_int
        | U_3435 != one_one_int
        | ~ sP300(U_3435,U_3436) )
    & ! [U_3435,U_3436] :
        ( sP299(U_3435,U_3436)
        | hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3435),U_3436) != one_one_int
        | ~ sP300(U_3435,U_3436) )
    & ! [U_3435,U_3436] :
        ( sP300(U_3435,U_3436)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3435)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP299,sP300])],[f_1138_2]) ).

cnf(f_1138_4,plain,
    ( sP300(U_3435,U_3436)
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3435)) ),
    inference(clausify,[status(thm)],[f_1138_3]) ).

cnf(f_1138_5,plain,
    ( sP299(U_3435,U_3436)
    | hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3435),U_3436) != one_one_int
    | ~ sP300(U_3435,U_3436) ),
    inference(clausify,[status(thm)],[f_1138_3]) ).

cnf(f_1138_6,plain,
    ( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3435),U_3436) = one_one_int
    | U_3436 != one_one_int
    | U_3435 != one_one_int
    | ~ sP300(U_3435,U_3436) ),
    inference(clausify,[status(thm)],[f_1138_3]) ).

cnf(f_1138_7,plain,
    ( U_3435 = one_one_int
    | ~ sP299(U_3435,U_3436) ),
    inference(clausify,[status(thm)],[f_1138_3]) ).

cnf(f_1138_8,plain,
    ( U_3436 = one_one_int
    | ~ sP299(U_3435,U_3436) ),
    inference(clausify,[status(thm)],[f_1138_3]) ).

fof(f_1139_1,plain,
    ! [Z] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),Z)),Z) != zero_zero_int,
    inference(fof_nnf,[status(thm)],[fact_1032_odd__nonzero]) ).

fof(f_1139_2,plain,
    ! [U_3437] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),U_3437)),U_3437) != zero_zero_int,
    inference(variable_rename,[status(thm)],[f_1139_1]) ).

fof(f_1139_3,plain,
    ! [U_3437] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),U_3437)),U_3437) != zero_zero_int,
    inference(definitional_conversion,[status(esa)],[f_1139_2]) ).

cnf(f_1139_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),U_3437)),U_3437) != zero_zero_int,
    inference(clausify,[status(thm)],[f_1139_3]) ).

fof(f_1140_1,plain,
    ! [Z] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z),zero_zero_int) = Z,
    inference(fof_nnf,[status(thm)],[fact_1033_zadd__0__right]) ).

fof(f_1140_2,plain,
    ! [U_3438] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3438),zero_zero_int) = U_3438,
    inference(variable_rename,[status(thm)],[f_1140_1]) ).

fof(f_1140_3,plain,
    ! [U_3438] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3438),zero_zero_int) = U_3438,
    inference(definitional_conversion,[status(esa)],[f_1140_2]) ).

cnf(f_1140_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3438),zero_zero_int) = U_3438,
    inference(clausify,[status(thm)],[f_1140_3]) ).

fof(f_1141_1,plain,
    ! [Z] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),Z) = Z,
    inference(fof_nnf,[status(thm)],[fact_1034_zadd__0]) ).

fof(f_1141_2,plain,
    ! [U_3439] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),U_3439) = U_3439,
    inference(variable_rename,[status(thm)],[f_1141_1]) ).

fof(f_1141_3,plain,
    ! [U_3439] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),U_3439) = U_3439,
    inference(definitional_conversion,[status(esa)],[f_1141_2]) ).

cnf(f_1141_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,zero_zero_int),U_3439) = U_3439,
    inference(clausify,[status(thm)],[f_1141_3]) ).

fof(f_1142_1,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
    inference(fof_nnf,[status(thm)],[fact_1035_int__0__less__1]) ).

fof(f_1142_2,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
    inference(definitional_conversion,[status(esa)],[f_1142_1]) ).

cnf(f_1142_3,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),one_one_int)),
    inference(clausify,[status(thm)],[f_1142_2]) ).

fof(f_1143_1,plain,
    ! [Z_2] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Z_2))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Z_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1036_int__one__le__iff__zero__less]) ).

fof(f_1143_2,plain,
    ! [U_3440] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U_3440))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3440)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3440))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U_3440)) ) ),
    inference(variable_rename,[status(thm)],[f_1143_1]) ).

fof(f_1143_3,plain,
    ( ! [U_3442] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U_3442))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3442)) )
    & ! [U_3441] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3441))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U_3441)) ) ),
    inference(miniscope,[status(thm)],[f_1143_2]) ).

fof(f_1143_4,plain,
    ( ! [U_3442] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U_3442))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3442)) )
    & ! [U_3441] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3441))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U_3441)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1143_3]) ).

cnf(f_1143_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3441))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U_3441)) ),
    inference(clausify,[status(thm)],[f_1143_4]) ).

cnf(f_1143_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U_3442))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3442)) ),
    inference(clausify,[status(thm)],[f_1143_4]) ).

fof(f_1144_1,plain,
    ! [K,L] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K),L)),zero_zero_int)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K),L)),zero_zero_int))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1037_less__bin__lemma]) ).

fof(f_1144_2,plain,
    ! [U_3444,U_3443] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3444),U_3443))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3444),U_3443)),zero_zero_int)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3444),U_3443)),zero_zero_int))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3444),U_3443)) ) ),
    inference(variable_rename,[status(thm)],[f_1144_1]) ).

fof(f_1144_3,plain,
    ( ! [U_3448,U_3446] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3448),U_3446))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3448),U_3446)),zero_zero_int)) )
    & ! [U_3447,U_3445] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3447),U_3445)),zero_zero_int))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3447),U_3445)) ) ),
    inference(miniscope,[status(thm)],[f_1144_2]) ).

fof(f_1144_4,plain,
    ( ! [U_3446,U_3448] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3448),U_3446))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3448),U_3446)),zero_zero_int)) )
    & ! [U_3447,U_3445] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3447),U_3445)),zero_zero_int))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3447),U_3445)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1144_3]) ).

cnf(f_1144_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3447),U_3445)),zero_zero_int))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3447),U_3445)) ),
    inference(clausify,[status(thm)],[f_1144_4]) ).

cnf(f_1144_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3448),U_3446))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3448),U_3446)),zero_zero_int)) ),
    inference(clausify,[status(thm)],[f_1144_4]) ).

fof(f_1145_1,plain,
    ! [Z] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),Z)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z)) ),
    inference(fof_nnf,[status(thm)],[fact_1038_le__imp__0__less]) ).

fof(f_1145_2,plain,
    ! [U_3449] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),U_3449)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3449)) ),
    inference(variable_rename,[status(thm)],[f_1145_1]) ).

fof(f_1145_3,plain,
    ! [U_3449] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),U_3449)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3449)) ),
    inference(definitional_conversion,[status(esa)],[f_1145_2]) ).

cnf(f_1145_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),U_3449)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3449)) ),
    inference(clausify,[status(thm)],[f_1145_3]) ).

fof(f_1146_1,plain,
    ! [Z_2] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),Z_2)),Z_2)),zero_zero_int))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_2),zero_zero_int)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_2),zero_zero_int))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),Z_2)),Z_2)),zero_zero_int)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1039_odd__less__0]) ).

fof(f_1146_2,plain,
    ! [U_3450] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),U_3450)),U_3450)),zero_zero_int))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3450),zero_zero_int)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3450),zero_zero_int))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),U_3450)),U_3450)),zero_zero_int)) ) ),
    inference(variable_rename,[status(thm)],[f_1146_1]) ).

fof(f_1146_3,plain,
    ( ! [U_3452] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),U_3452)),U_3452)),zero_zero_int))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3452),zero_zero_int)) )
    & ! [U_3451] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3451),zero_zero_int))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),U_3451)),U_3451)),zero_zero_int)) ) ),
    inference(miniscope,[status(thm)],[f_1146_2]) ).

fof(f_1146_4,plain,
    ( ! [U_3452] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),U_3452)),U_3452)),zero_zero_int))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3452),zero_zero_int)) )
    & ! [U_3451] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3451),zero_zero_int))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),U_3451)),U_3451)),zero_zero_int)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1146_3]) ).

cnf(f_1146_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3451),zero_zero_int))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),U_3451)),U_3451)),zero_zero_int)) ),
    inference(clausify,[status(thm)],[f_1146_4]) ).

cnf(f_1146_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),U_3452)),U_3452)),zero_zero_int))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3452),zero_zero_int)) ),
    inference(clausify,[status(thm)],[f_1146_4]) ).

fof(f_1147_1,plain,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_1),I_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_1),J)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_1040_zadd__left__mono]) ).

fof(f_1147_2,plain,
    ! [U_3455,U_3454,U_3453] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3455),U_3454)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3455),U_3453)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3454),U_3453)) ),
    inference(variable_rename,[status(thm)],[f_1147_1]) ).

fof(f_1147_3,plain,
    ! [U_3454,U_3453,U_3455] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3455),U_3454)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3455),U_3453)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3454),U_3453)) ),
    inference(definitional_conversion,[status(esa)],[f_1147_2]) ).

cnf(f_1147_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3455),U_3454)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3455),U_3453)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3454),U_3453)) ),
    inference(clausify,[status(thm)],[f_1147_3]) ).

fof(f_1148_1,plain,
    ! [Z1,Z2,Z3] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),Z2)),Z3) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z2),Z3)),
    inference(fof_nnf,[status(thm)],[fact_1041_zadd__assoc]) ).

fof(f_1148_2,plain,
    ! [U_3458,U_3457,U_3456] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3458),U_3457)),U_3456) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3458),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3457),U_3456)),
    inference(variable_rename,[status(thm)],[f_1148_1]) ).

fof(f_1148_3,plain,
    ! [U_3456,U_3457,U_3458] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3458),U_3457)),U_3456) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3458),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3457),U_3456)),
    inference(definitional_conversion,[status(esa)],[f_1148_2]) ).

cnf(f_1148_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3458),U_3457)),U_3456) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3458),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3457),U_3456)),
    inference(clausify,[status(thm)],[f_1148_3]) ).

fof(f_1149_1,plain,
    ! [X,Y,Z] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Y),Z)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Y),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),Z)),
    inference(fof_nnf,[status(thm)],[fact_1042_zadd__left__commute]) ).

fof(f_1149_2,plain,
    ! [U_3461,U_3460,U_3459] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3461),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3460),U_3459)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3460),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3461),U_3459)),
    inference(variable_rename,[status(thm)],[f_1149_1]) ).

fof(f_1149_3,plain,
    ! [U_3459,U_3460,U_3461] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3461),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3460),U_3459)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3460),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3461),U_3459)),
    inference(definitional_conversion,[status(esa)],[f_1149_2]) ).

cnf(f_1149_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3461),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3460),U_3459)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3460),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3461),U_3459)),
    inference(clausify,[status(thm)],[f_1149_3]) ).

fof(f_1150_1,plain,
    ! [Z,W] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z),W) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W),Z),
    inference(fof_nnf,[status(thm)],[fact_1043_zadd__commute]) ).

fof(f_1150_2,plain,
    ! [U_3463,U_3462] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3463),U_3462) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3462),U_3463),
    inference(variable_rename,[status(thm)],[f_1150_1]) ).

fof(f_1150_3,plain,
    ! [U_3462,U_3463] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3463),U_3462) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3462),U_3463),
    inference(definitional_conversion,[status(esa)],[f_1150_2]) ).

cnf(f_1150_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3463),U_3462) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3462),U_3463),
    inference(clausify,[status(thm)],[f_1150_3]) ).

fof(f_1151_1,plain,
    ! [W] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),W)),
    inference(fof_nnf,[status(thm)],[fact_1044_zle__refl]) ).

fof(f_1151_2,plain,
    ! [U_3464] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3464),U_3464)),
    inference(variable_rename,[status(thm)],[f_1151_1]) ).

fof(f_1151_3,plain,
    ! [U_3464] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3464),U_3464)),
    inference(definitional_conversion,[status(esa)],[f_1151_2]) ).

cnf(f_1151_4,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3464),U_3464)),
    inference(clausify,[status(thm)],[f_1151_3]) ).

fof(f_1152_1,plain,
    ! [Z,W] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),Z))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z),W)) ),
    inference(fof_nnf,[status(thm)],[fact_1045_zle__linear]) ).

fof(f_1152_2,plain,
    ! [U_3466,U_3465] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3465),U_3466))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3466),U_3465)) ),
    inference(variable_rename,[status(thm)],[f_1152_1]) ).

fof(f_1152_3,plain,
    ! [U_3465,U_3466] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3465),U_3466))
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3466),U_3465)) ),
    inference(definitional_conversion,[status(esa)],[f_1152_2]) ).

cnf(f_1152_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3465),U_3466))
    | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3466),U_3465)) ),
    inference(clausify,[status(thm)],[f_1152_3]) ).

fof(f_1153_1,plain,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),K_1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,J),K_1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_1046_zle__trans]) ).

fof(f_1153_2,plain,
    ! [U_3469,U_3468,U_3467] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3468),U_3469))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3467),U_3469))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3468),U_3467)) ),
    inference(variable_rename,[status(thm)],[f_1153_1]) ).

fof(f_1153_3,plain,
    ! [U_3467,U_3468,U_3469] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3468),U_3469))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3467),U_3469))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3468),U_3467)) ),
    inference(definitional_conversion,[status(esa)],[f_1153_2]) ).

cnf(f_1153_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3468),U_3469))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3467),U_3469))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3468),U_3467)) ),
    inference(clausify,[status(thm)],[f_1153_3]) ).

fof(f_1154_1,plain,
    ! [Z,W] :
      ( Z = W
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W),Z))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z),W)) ),
    inference(fof_nnf,[status(thm)],[fact_1047_zle__antisym]) ).

fof(f_1154_2,plain,
    ! [U_3471,U_3470] :
      ( U_3471 = U_3470
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3470),U_3471))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3471),U_3470)) ),
    inference(variable_rename,[status(thm)],[f_1154_1]) ).

fof(f_1154_3,plain,
    ! [U_3470,U_3471] :
      ( U_3471 = U_3470
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3470),U_3471))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3471),U_3470)) ),
    inference(definitional_conversion,[status(esa)],[f_1154_2]) ).

cnf(f_1154_4,plain,
    ( U_3471 = U_3470
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3470),U_3471))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3471),U_3470)) ),
    inference(clausify,[status(thm)],[f_1154_3]) ).

fof(f_1155_1,plain,
    ! [W_1,Z_2] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z_2),one_one_int)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,Z_2),one_one_int))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1048_zle__diff1__eq]) ).

fof(f_1155_2,plain,
    ! [U_3473,U_3472] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3473),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3472),one_one_int)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3473),U_3472)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3473),U_3472))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3473),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3472),one_one_int))) ) ),
    inference(variable_rename,[status(thm)],[f_1155_1]) ).

fof(f_1155_3,plain,
    ( ! [U_3477,U_3475] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3477),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3475),one_one_int)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3477),U_3475)) )
    & ! [U_3476,U_3474] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3476),U_3474))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3476),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3474),one_one_int))) ) ),
    inference(miniscope,[status(thm)],[f_1155_2]) ).

fof(f_1155_4,plain,
    ( ! [U_3475,U_3477] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3477),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3475),one_one_int)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3477),U_3475)) )
    & ! [U_3476,U_3474] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3476),U_3474))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3476),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3474),one_one_int))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1155_3]) ).

cnf(f_1155_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3476),U_3474))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3476),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3474),one_one_int))) ),
    inference(clausify,[status(thm)],[f_1155_4]) ).

cnf(f_1155_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3477),hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3475),one_one_int)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3477),U_3475)) ),
    inference(clausify,[status(thm)],[f_1155_4]) ).

fof(f_1156_1,plain,
    ! [X,Y] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Y),X))
      | X = Y
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X),Y)) ),
    inference(fof_nnf,[status(thm)],[fact_1049_zless__linear]) ).

fof(f_1156_2,plain,
    ! [U_3479,U_3478] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3478),U_3479))
      | U_3479 = U_3478
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3479),U_3478)) ),
    inference(variable_rename,[status(thm)],[f_1156_1]) ).

fof(f_1156_3,plain,
    ! [U_3479,U_3478] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3478),U_3479))
      | U_3479 = U_3478
      | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3479),U_3478)) ),
    inference(definitional_conversion,[status(esa)],[f_1156_2]) ).

cnf(f_1156_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3478),U_3479))
    | U_3479 = U_3478
    | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3479),U_3478)) ),
    inference(clausify,[status(thm)],[f_1156_3]) ).

fof(f_1157_1,plain,
    ! [Z_2,W_1] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_2),W_1))
        | Z_2 = W_1
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_2),W_1)) )
      & ( ( Z_2 != W_1
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_2),W_1)) )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_2),W_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1050_zless__le]) ).

fof(f_1157_2,plain,
    ! [U_3481,U_3480] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3481),U_3480))
        | U_3481 = U_3480
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3481),U_3480)) )
      & ( ( U_3481 != U_3480
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3481),U_3480)) )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3481),U_3480)) ) ),
    inference(variable_rename,[status(thm)],[f_1157_1]) ).

fof(f_1157_3,plain,
    ( ! [U_3485,U_3483] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3485),U_3483))
        | U_3485 = U_3483
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3485),U_3483)) )
    & ! [U_3484,U_3482] :
        ( ( U_3484 != U_3482
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3484),U_3482)) )
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3484),U_3482)) ) ),
    inference(miniscope,[status(thm)],[f_1157_2]) ).

fof(f_1157_4,plain,
    ( ! [U_3484,U_3482] :
        ( U_3484 != U_3482
        | ~ sP301(U_3484,U_3482) )
    & ! [U_3484,U_3482] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3484),U_3482))
        | ~ sP301(U_3484,U_3482) )
    & ! [U_3485,U_3483] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3485),U_3483))
        | U_3485 = U_3483
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3485),U_3483)) )
    & ! [U_3484,U_3482] :
        ( sP301(U_3484,U_3482)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3484),U_3482)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP301])],[f_1157_3]) ).

cnf(f_1157_5,plain,
    ( sP301(U_3484,U_3482)
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3484),U_3482)) ),
    inference(clausify,[status(thm)],[f_1157_4]) ).

cnf(f_1157_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3485),U_3483))
    | U_3485 = U_3483
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3485),U_3483)) ),
    inference(clausify,[status(thm)],[f_1157_4]) ).

cnf(f_1157_7,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3484),U_3482))
    | ~ sP301(U_3484,U_3482) ),
    inference(clausify,[status(thm)],[f_1157_4]) ).

cnf(f_1157_8,plain,
    ( U_3484 != U_3482
    | ~ sP301(U_3484,U_3482) ),
    inference(clausify,[status(thm)],[f_1157_4]) ).

fof(f_1158_1,plain,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I_1),K_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,J),K_1)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_1051_zadd__strict__right__mono]) ).

fof(f_1158_2,plain,
    ! [U_3488,U_3487,U_3486] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3487),U_3488)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3486),U_3488)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3487),U_3486)) ),
    inference(variable_rename,[status(thm)],[f_1158_1]) ).

fof(f_1158_3,plain,
    ! [U_3487,U_3486,U_3488] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3487),U_3488)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3486),U_3488)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3487),U_3486)) ),
    inference(definitional_conversion,[status(esa)],[f_1158_2]) ).

cnf(f_1158_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3487),U_3488)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3486),U_3488)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3487),U_3486)) ),
    inference(clausify,[status(thm)],[f_1158_3]) ).

fof(f_1159_1,plain,
    ! [Z_4,Z,W_2,W] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_2),Z_4)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W),Z)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Z_4),Z))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_2),W)) ),
    inference(fof_nnf,[status(thm)],[fact_1052_zadd__zless__mono]) ).

fof(f_1159_2,plain,
    ! [U_3492,U_3491,U_3490,U_3489] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3490),U_3492)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3489),U_3491)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3492),U_3491))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3490),U_3489)) ),
    inference(variable_rename,[status(thm)],[f_1159_1]) ).

fof(f_1159_3,plain,
    ! [U_3489,U_3490,U_3491,U_3492] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3490),U_3492)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3489),U_3491)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3492),U_3491))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3490),U_3489)) ),
    inference(definitional_conversion,[status(esa)],[f_1159_2]) ).

cnf(f_1159_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3490),U_3492)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3489),U_3491)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3492),U_3491))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3490),U_3489)) ),
    inference(clausify,[status(thm)],[f_1159_3]) ).

fof(f_1160_1,plain,
    ! [W_1,Z_2] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_2),one_one_int)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),Z_2)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),Z_2))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_2),one_one_int))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1053_zle__add1__eq__le]) ).

fof(f_1160_2,plain,
    ! [U_3494,U_3493] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3494),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3493),one_one_int)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3494),U_3493)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3494),U_3493))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3494),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3493),one_one_int))) ) ),
    inference(variable_rename,[status(thm)],[f_1160_1]) ).

fof(f_1160_3,plain,
    ( ! [U_3498,U_3496] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3498),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3496),one_one_int)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3498),U_3496)) )
    & ! [U_3497,U_3495] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3497),U_3495))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3497),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3495),one_one_int))) ) ),
    inference(miniscope,[status(thm)],[f_1160_2]) ).

fof(f_1160_4,plain,
    ( ! [U_3496,U_3498] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3498),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3496),one_one_int)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3498),U_3496)) )
    & ! [U_3497,U_3495] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3497),U_3495))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3497),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3495),one_one_int))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1160_3]) ).

cnf(f_1160_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3497),U_3495))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3497),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3495),one_one_int))) ),
    inference(clausify,[status(thm)],[f_1160_4]) ).

cnf(f_1160_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3498),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3496),one_one_int)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3498),U_3496)) ),
    inference(clausify,[status(thm)],[f_1160_4]) ).

fof(f_1161_1,plain,
    ! [W_1,Z_2] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_1),one_one_int)),Z_2))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_1),one_one_int)),Z_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1054_add1__zle__eq]) ).

fof(f_1161_2,plain,
    ! [U_3500,U_3499] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3500),one_one_int)),U_3499))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3500),U_3499)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3500),U_3499))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3500),one_one_int)),U_3499)) ) ),
    inference(variable_rename,[status(thm)],[f_1161_1]) ).

fof(f_1161_3,plain,
    ( ! [U_3504,U_3502] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3504),one_one_int)),U_3502))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3504),U_3502)) )
    & ! [U_3503,U_3501] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3503),U_3501))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3503),one_one_int)),U_3501)) ) ),
    inference(miniscope,[status(thm)],[f_1161_2]) ).

fof(f_1161_4,plain,
    ( ! [U_3502,U_3504] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3504),one_one_int)),U_3502))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3504),U_3502)) )
    & ! [U_3503,U_3501] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3503),U_3501))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3503),one_one_int)),U_3501)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1161_3]) ).

cnf(f_1161_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3503),U_3501))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3503),one_one_int)),U_3501)) ),
    inference(clausify,[status(thm)],[f_1161_4]) ).

cnf(f_1161_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3504),one_one_int)),U_3502))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3504),U_3502)) ),
    inference(clausify,[status(thm)],[f_1161_4]) ).

fof(f_1162_1,plain,
    ! [W,Z] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W),one_one_int)),Z))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W),Z)) ),
    inference(fof_nnf,[status(thm)],[fact_1055_zless__imp__add1__zle]) ).

fof(f_1162_2,plain,
    ! [U_3506,U_3505] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3506),one_one_int)),U_3505))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3506),U_3505)) ),
    inference(variable_rename,[status(thm)],[f_1162_1]) ).

fof(f_1162_3,plain,
    ! [U_3506,U_3505] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3506),one_one_int)),U_3505))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3506),U_3505)) ),
    inference(definitional_conversion,[status(esa)],[f_1162_2]) ).

cnf(f_1162_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3506),one_one_int)),U_3505))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3506),U_3505)) ),
    inference(clausify,[status(thm)],[f_1162_3]) ).

fof(f_1163_1,plain,
    ! [W_1,Z_2] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_2),one_one_int)))
        | ( W_1 != Z_2
          & ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) )
      & ( W_1 = Z_2
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_2),one_one_int))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1056_zless__add1__eq]) ).

fof(f_1163_2,plain,
    ! [U_3508,U_3507] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3508),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3507),one_one_int)))
        | ( U_3508 != U_3507
          & ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3508),U_3507)) ) )
      & ( U_3508 = U_3507
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3508),U_3507))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3508),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3507),one_one_int))) ) ),
    inference(variable_rename,[status(thm)],[f_1163_1]) ).

fof(f_1163_3,plain,
    ( ! [U_3512,U_3510] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3512),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3510),one_one_int)))
        | ( U_3512 != U_3510
          & ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3512),U_3510)) ) )
    & ! [U_3511,U_3509] :
        ( U_3511 = U_3509
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3511),U_3509))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3511),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3509),one_one_int))) ) ),
    inference(miniscope,[status(thm)],[f_1163_2]) ).

fof(f_1163_4,plain,
    ( ! [U_3512,U_3510] :
        ( U_3512 != U_3510
        | ~ sP302(U_3512,U_3510) )
    & ! [U_3512,U_3510] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3512),U_3510))
        | ~ sP302(U_3512,U_3510) )
    & ! [U_3512,U_3510] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3512),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3510),one_one_int)))
        | sP302(U_3512,U_3510) )
    & ! [U_3511,U_3509] :
        ( U_3511 = U_3509
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3511),U_3509))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3511),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3509),one_one_int))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP302])],[f_1163_3]) ).

cnf(f_1163_5,plain,
    ( U_3511 = U_3509
    | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3511),U_3509))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3511),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3509),one_one_int))) ),
    inference(clausify,[status(thm)],[f_1163_4]) ).

cnf(f_1163_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3512),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3510),one_one_int)))
    | sP302(U_3512,U_3510) ),
    inference(clausify,[status(thm)],[f_1163_4]) ).

cnf(f_1163_7,plain,
    ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3512),U_3510))
    | ~ sP302(U_3512,U_3510) ),
    inference(clausify,[status(thm)],[f_1163_4]) ).

cnf(f_1163_8,plain,
    ( U_3512 != U_3510
    | ~ sP302(U_3512,U_3510) ),
    inference(clausify,[status(thm)],[f_1163_4]) ).

fof(f_1164_1,plain,
    ! [K,M,Na] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na)
        | ( M != Na
          & K != zero_zero_nat ) )
      & ( M = Na
        | K = zero_zero_nat
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_1057_nat__mult__eq__cancel__disj]) ).

fof(f_1164_2,plain,
    ! [U_3515,U_3514,U_3513] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3515),U_3514) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3515),U_3513)
        | ( U_3514 != U_3513
          & U_3515 != zero_zero_nat ) )
      & ( U_3514 = U_3513
        | U_3515 = zero_zero_nat
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3515),U_3514) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3515),U_3513) ) ),
    inference(variable_rename,[status(thm)],[f_1164_1]) ).

fof(f_1164_3,plain,
    ( ! [U_3521,U_3519,U_3517] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3521),U_3519) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3521),U_3517)
        | ( U_3519 != U_3517
          & U_3521 != zero_zero_nat ) )
    & ! [U_3520,U_3518,U_3516] :
        ( U_3518 = U_3516
        | U_3520 = zero_zero_nat
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3520),U_3518) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3520),U_3516) ) ),
    inference(miniscope,[status(thm)],[f_1164_2]) ).

fof(f_1164_4,plain,
    ( ! [U_3519,U_3517,U_3521] :
        ( U_3519 != U_3517
        | ~ sP303(U_3519,U_3517,U_3521) )
    & ! [U_3519,U_3517,U_3521] :
        ( U_3521 != zero_zero_nat
        | ~ sP303(U_3519,U_3517,U_3521) )
    & ! [U_3519,U_3517,U_3521] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3521),U_3519) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3521),U_3517)
        | sP303(U_3519,U_3517,U_3521) )
    & ! [U_3518,U_3516,U_3520] :
        ( U_3518 = U_3516
        | U_3520 = zero_zero_nat
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3520),U_3518) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3520),U_3516) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP303])],[f_1164_3]) ).

cnf(f_1164_5,plain,
    ( U_3518 = U_3516
    | U_3520 = zero_zero_nat
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3520),U_3518) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3520),U_3516) ),
    inference(clausify,[status(thm)],[f_1164_4]) ).

cnf(f_1164_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3521),U_3519) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3521),U_3517)
    | sP303(U_3519,U_3517,U_3521) ),
    inference(clausify,[status(thm)],[f_1164_4]) ).

cnf(f_1164_7,plain,
    ( U_3521 != zero_zero_nat
    | ~ sP303(U_3519,U_3517,U_3521) ),
    inference(clausify,[status(thm)],[f_1164_4]) ).

cnf(f_1164_8,plain,
    ( U_3519 != U_3517
    | ~ sP303(U_3519,U_3517,U_3521) ),
    inference(clausify,[status(thm)],[f_1164_4]) ).

fof(f_1165_1,plain,
    ! [I_1,U_1,J,K_1] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),U_1)),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I_1),J)),U_1)),K_1),
    inference(fof_nnf,[status(thm)],[fact_1058_left__add__mult__distrib]) ).

fof(f_1165_2,plain,
    ! [U_3525,U_3524,U_3523,U_3522] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3525),U_3524)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3523),U_3524)),U_3522)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3525),U_3523)),U_3524)),U_3522),
    inference(variable_rename,[status(thm)],[f_1165_1]) ).

fof(f_1165_3,plain,
    ! [U_3522,U_3523,U_3524,U_3525] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3525),U_3524)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3523),U_3524)),U_3522)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3525),U_3523)),U_3524)),U_3522),
    inference(definitional_conversion,[status(esa)],[f_1165_2]) ).

cnf(f_1165_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3525),U_3524)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3523),U_3524)),U_3522)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3525),U_3523)),U_3524)),U_3522),
    inference(clausify,[status(thm)],[f_1165_3]) ).

fof(f_1166_1,plain,
    ! [M,Na,K] :
      ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na)
          | M != Na )
        & ( M = Na
          | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) ),
    inference(fof_nnf,[status(thm)],[fact_1059_nat__mult__eq__cancel1]) ).

fof(f_1166_2,plain,
    ! [U_3528,U_3527,U_3526] :
      ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3526),U_3528) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3526),U_3527)
          | U_3528 != U_3527 )
        & ( U_3528 = U_3527
          | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3526),U_3528) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3526),U_3527) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3526)) ),
    inference(variable_rename,[status(thm)],[f_1166_1]) ).

fof(f_1166_3,plain,
    ( ! [U_3526,U_3527,U_3528] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3526),U_3528) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3526),U_3527)
        | U_3528 != U_3527
        | ~ sP304(U_3526,U_3527,U_3528) )
    & ! [U_3526,U_3527,U_3528] :
        ( U_3528 = U_3527
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3526),U_3528) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3526),U_3527)
        | ~ sP304(U_3526,U_3527,U_3528) )
    & ! [U_3526,U_3527,U_3528] :
        ( sP304(U_3526,U_3527,U_3528)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3526)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP304])],[f_1166_2]) ).

cnf(f_1166_4,plain,
    ( sP304(U_3526,U_3527,U_3528)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3526)) ),
    inference(clausify,[status(thm)],[f_1166_3]) ).

cnf(f_1166_5,plain,
    ( U_3528 = U_3527
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3526),U_3528) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3526),U_3527)
    | ~ sP304(U_3526,U_3527,U_3528) ),
    inference(clausify,[status(thm)],[f_1166_3]) ).

cnf(f_1166_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3526),U_3528) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3526),U_3527)
    | U_3528 != U_3527
    | ~ sP304(U_3526,U_3527,U_3528) ),
    inference(clausify,[status(thm)],[f_1166_3]) ).

fof(f_1167_1,plain,
    ! [M,Na,K] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) ),
    inference(fof_nnf,[status(thm)],[fact_1060_nat__mult__less__cancel1]) ).

fof(f_1167_2,plain,
    ! [U_3531,U_3530,U_3529] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3529),U_3531)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3529),U_3530)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3531),U_3530)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3531),U_3530))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3529),U_3531)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3529),U_3530))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3529)) ),
    inference(variable_rename,[status(thm)],[f_1167_1]) ).

fof(f_1167_3,plain,
    ( ! [U_3530,U_3531,U_3529] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3529),U_3531)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3529),U_3530)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3531),U_3530))
        | ~ sP305(U_3530,U_3531,U_3529) )
    & ! [U_3530,U_3531,U_3529] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3531),U_3530))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3529),U_3531)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3529),U_3530)))
        | ~ sP305(U_3530,U_3531,U_3529) )
    & ! [U_3530,U_3531,U_3529] :
        ( sP305(U_3530,U_3531,U_3529)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3529)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP305])],[f_1167_2]) ).

cnf(f_1167_4,plain,
    ( sP305(U_3530,U_3531,U_3529)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3529)) ),
    inference(clausify,[status(thm)],[f_1167_3]) ).

cnf(f_1167_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3531),U_3530))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3529),U_3531)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3529),U_3530)))
    | ~ sP305(U_3530,U_3531,U_3529) ),
    inference(clausify,[status(thm)],[f_1167_3]) ).

cnf(f_1167_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3529),U_3531)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3529),U_3530)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3531),U_3530))
    | ~ sP305(U_3530,U_3531,U_3529) ),
    inference(clausify,[status(thm)],[f_1167_3]) ).

fof(f_1168_1,plain,
    ! [M,Na,K] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,K),Na))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K)) ),
    inference(fof_nnf,[status(thm)],[fact_1061_nat__mult__le__cancel1]) ).

fof(f_1168_2,plain,
    ! [U_3534,U_3533,U_3532] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3532),U_3534)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3532),U_3533)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3534),U_3533)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3534),U_3533))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3532),U_3534)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3532),U_3533))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3532)) ),
    inference(variable_rename,[status(thm)],[f_1168_1]) ).

fof(f_1168_3,plain,
    ( ! [U_3533,U_3532,U_3534] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3532),U_3534)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3532),U_3533)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3534),U_3533))
        | ~ sP306(U_3533,U_3532,U_3534) )
    & ! [U_3533,U_3532,U_3534] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3534),U_3533))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3532),U_3534)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3532),U_3533)))
        | ~ sP306(U_3533,U_3532,U_3534) )
    & ! [U_3533,U_3532,U_3534] :
        ( sP306(U_3533,U_3532,U_3534)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3532)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP306])],[f_1168_2]) ).

cnf(f_1168_4,plain,
    ( sP306(U_3533,U_3532,U_3534)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3532)) ),
    inference(clausify,[status(thm)],[f_1168_3]) ).

cnf(f_1168_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3534),U_3533))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3532),U_3534)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3532),U_3533)))
    | ~ sP306(U_3533,U_3532,U_3534) ),
    inference(clausify,[status(thm)],[f_1168_3]) ).

cnf(f_1168_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3532),U_3534)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3532),U_3533)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3534),U_3533))
    | ~ sP306(U_3533,U_3532,U_3534) ),
    inference(clausify,[status(thm)],[f_1168_3]) ).

fof(f_1169_1,plain,
    ! [U,M,Na,J_1,I_2] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_2),J_1)),U)),M)),Na)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_2),J_1)),U)),M)),Na))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),I_2)) ),
    inference(fof_nnf,[status(thm)],[fact_1062_nat__le__add__iff1]) ).

fof(f_1169_2,plain,
    ! [U_3539,U_3538,U_3537,U_3536,U_3535] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3535),U_3539)),U_3538)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3536),U_3539)),U_3537)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3535),U_3536)),U_3539)),U_3538)),U_3537)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3535),U_3536)),U_3539)),U_3538)),U_3537))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3535),U_3539)),U_3538)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3536),U_3539)),U_3537))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3536),U_3535)) ),
    inference(variable_rename,[status(thm)],[f_1169_1]) ).

fof(f_1169_3,plain,
    ( ! [U_3535,U_3536,U_3537,U_3538,U_3539] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3535),U_3539)),U_3538)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3536),U_3539)),U_3537)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3535),U_3536)),U_3539)),U_3538)),U_3537))
        | ~ sP307(U_3535,U_3536,U_3537,U_3538,U_3539) )
    & ! [U_3535,U_3536,U_3537,U_3538,U_3539] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3535),U_3536)),U_3539)),U_3538)),U_3537))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3535),U_3539)),U_3538)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3536),U_3539)),U_3537)))
        | ~ sP307(U_3535,U_3536,U_3537,U_3538,U_3539) )
    & ! [U_3535,U_3536,U_3537,U_3538,U_3539] :
        ( sP307(U_3535,U_3536,U_3537,U_3538,U_3539)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3536),U_3535)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP307])],[f_1169_2]) ).

cnf(f_1169_4,plain,
    ( sP307(U_3535,U_3536,U_3537,U_3538,U_3539)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3536),U_3535)) ),
    inference(clausify,[status(thm)],[f_1169_3]) ).

cnf(f_1169_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3535),U_3536)),U_3539)),U_3538)),U_3537))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3535),U_3539)),U_3538)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3536),U_3539)),U_3537)))
    | ~ sP307(U_3535,U_3536,U_3537,U_3538,U_3539) ),
    inference(clausify,[status(thm)],[f_1169_3]) ).

cnf(f_1169_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3535),U_3539)),U_3538)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3536),U_3539)),U_3537)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3535),U_3536)),U_3539)),U_3538)),U_3537))
    | ~ sP307(U_3535,U_3536,U_3537,U_3538,U_3539) ),
    inference(clausify,[status(thm)],[f_1169_3]) ).

fof(f_1170_1,plain,
    ! [U_1,M_1,N,J,I_1] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U_1)),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),U_1)),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_1),J)),U_1)),M_1)),N)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),I_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1063_nat__diff__add__eq1]) ).

fof(f_1170_2,plain,
    ! [U_3544,U_3543,U_3542,U_3541,U_3540] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3540),U_3544)),U_3543)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3541),U_3544)),U_3542)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3540),U_3541)),U_3544)),U_3543)),U_3542)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3541),U_3540)) ),
    inference(variable_rename,[status(thm)],[f_1170_1]) ).

fof(f_1170_3,plain,
    ! [U_3544,U_3541,U_3540,U_3542,U_3543] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3540),U_3544)),U_3543)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3541),U_3544)),U_3542)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3540),U_3541)),U_3544)),U_3543)),U_3542)
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3541),U_3540)) ),
    inference(definitional_conversion,[status(esa)],[f_1170_2]) ).

cnf(f_1170_4,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3540),U_3544)),U_3543)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3541),U_3544)),U_3542)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3540),U_3541)),U_3544)),U_3543)),U_3542)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3541),U_3540)) ),
    inference(clausify,[status(thm)],[f_1170_3]) ).

fof(f_1171_1,plain,
    ! [U,M,Na,J_1,I_2] :
      ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na)
          | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_2),J_1)),U)),M) != Na )
        & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_2),J_1)),U)),M) = Na
          | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),I_2)) ),
    inference(fof_nnf,[status(thm)],[fact_1064_nat__eq__add__iff1]) ).

fof(f_1171_2,plain,
    ! [U_3549,U_3548,U_3547,U_3546,U_3545] :
      ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3545),U_3549)),U_3548) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3546),U_3549)),U_3547)
          | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3545),U_3546)),U_3549)),U_3548) != U_3547 )
        & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3545),U_3546)),U_3549)),U_3548) = U_3547
          | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3545),U_3549)),U_3548) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3546),U_3549)),U_3547) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3546),U_3545)) ),
    inference(variable_rename,[status(thm)],[f_1171_1]) ).

fof(f_1171_3,plain,
    ( ! [U_3545,U_3546,U_3547,U_3548,U_3549] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3545),U_3549)),U_3548) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3546),U_3549)),U_3547)
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3545),U_3546)),U_3549)),U_3548) != U_3547
        | ~ sP308(U_3545,U_3546,U_3547,U_3548,U_3549) )
    & ! [U_3545,U_3546,U_3547,U_3548,U_3549] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3545),U_3546)),U_3549)),U_3548) = U_3547
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3545),U_3549)),U_3548) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3546),U_3549)),U_3547)
        | ~ sP308(U_3545,U_3546,U_3547,U_3548,U_3549) )
    & ! [U_3545,U_3546,U_3547,U_3548,U_3549] :
        ( sP308(U_3545,U_3546,U_3547,U_3548,U_3549)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3546),U_3545)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP308])],[f_1171_2]) ).

cnf(f_1171_4,plain,
    ( sP308(U_3545,U_3546,U_3547,U_3548,U_3549)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3546),U_3545)) ),
    inference(clausify,[status(thm)],[f_1171_3]) ).

cnf(f_1171_5,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3545),U_3546)),U_3549)),U_3548) = U_3547
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3545),U_3549)),U_3548) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3546),U_3549)),U_3547)
    | ~ sP308(U_3545,U_3546,U_3547,U_3548,U_3549) ),
    inference(clausify,[status(thm)],[f_1171_3]) ).

cnf(f_1171_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3545),U_3549)),U_3548) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3546),U_3549)),U_3547)
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3545),U_3546)),U_3549)),U_3548) != U_3547
    | ~ sP308(U_3545,U_3546,U_3547,U_3548,U_3549) ),
    inference(clausify,[status(thm)],[f_1171_3]) ).

fof(f_1172_1,plain,
    ! [U,M,Na,I_2,J_1] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),I_2)),U)),Na))) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),I_2)),U)),Na)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1065_nat__le__add__iff2]) ).

fof(f_1172_2,plain,
    ! [U_3554,U_3553,U_3552,U_3551,U_3550] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3551),U_3554)),U_3553)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3550),U_3554)),U_3552)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3553),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3550),U_3551)),U_3554)),U_3552))) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3553),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3550),U_3551)),U_3554)),U_3552)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3551),U_3554)),U_3553)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3550),U_3554)),U_3552))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3551),U_3550)) ),
    inference(variable_rename,[status(thm)],[f_1172_1]) ).

fof(f_1172_3,plain,
    ( ! [U_3550,U_3553,U_3552,U_3554,U_3551] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3551),U_3554)),U_3553)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3550),U_3554)),U_3552)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3553),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3550),U_3551)),U_3554)),U_3552)))
        | ~ sP309(U_3550,U_3553,U_3552,U_3554,U_3551) )
    & ! [U_3550,U_3553,U_3552,U_3554,U_3551] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3553),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3550),U_3551)),U_3554)),U_3552)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3551),U_3554)),U_3553)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3550),U_3554)),U_3552)))
        | ~ sP309(U_3550,U_3553,U_3552,U_3554,U_3551) )
    & ! [U_3550,U_3553,U_3552,U_3554,U_3551] :
        ( sP309(U_3550,U_3553,U_3552,U_3554,U_3551)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3551),U_3550)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP309])],[f_1172_2]) ).

cnf(f_1172_4,plain,
    ( sP309(U_3550,U_3553,U_3552,U_3554,U_3551)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3551),U_3550)) ),
    inference(clausify,[status(thm)],[f_1172_3]) ).

cnf(f_1172_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3553),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3550),U_3551)),U_3554)),U_3552)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3551),U_3554)),U_3553)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3550),U_3554)),U_3552)))
    | ~ sP309(U_3550,U_3553,U_3552,U_3554,U_3551) ),
    inference(clausify,[status(thm)],[f_1172_3]) ).

cnf(f_1172_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3551),U_3554)),U_3553)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3550),U_3554)),U_3552)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3553),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3550),U_3551)),U_3554)),U_3552)))
    | ~ sP309(U_3550,U_3553,U_3552,U_3554,U_3551) ),
    inference(clausify,[status(thm)],[f_1172_3]) ).

fof(f_1173_1,plain,
    ! [U_1,M_1,N,I_1,J] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_1),U_1)),M_1)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J),U_1)),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J),I_1)),U_1)),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_1066_nat__diff__add__eq2]) ).

fof(f_1173_2,plain,
    ! [U_3559,U_3558,U_3557,U_3556,U_3555] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3556),U_3559)),U_3558)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3555),U_3559)),U_3557)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3558),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3555),U_3556)),U_3559)),U_3557))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3556),U_3555)) ),
    inference(variable_rename,[status(thm)],[f_1173_1]) ).

fof(f_1173_3,plain,
    ! [U_3557,U_3558,U_3555,U_3556,U_3559] :
      ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3556),U_3559)),U_3558)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3555),U_3559)),U_3557)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3558),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3555),U_3556)),U_3559)),U_3557))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3556),U_3555)) ),
    inference(definitional_conversion,[status(esa)],[f_1173_2]) ).

cnf(f_1173_4,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3556),U_3559)),U_3558)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3555),U_3559)),U_3557)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3558),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3555),U_3556)),U_3559)),U_3557))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3556),U_3555)) ),
    inference(clausify,[status(thm)],[f_1173_3]) ).

fof(f_1174_1,plain,
    ! [U,M,Na,I_2,J_1] :
      ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na)
          | M != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),I_2)),U)),Na) )
        & ( M = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,J_1),I_2)),U)),Na)
          | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_2),J_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1067_nat__eq__add__iff2]) ).

fof(f_1174_2,plain,
    ! [U_3564,U_3563,U_3562,U_3561,U_3560] :
      ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3561),U_3564)),U_3563) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3560),U_3564)),U_3562)
          | U_3563 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3560),U_3561)),U_3564)),U_3562) )
        & ( U_3563 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3560),U_3561)),U_3564)),U_3562)
          | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3561),U_3564)),U_3563) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3560),U_3564)),U_3562) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3561),U_3560)) ),
    inference(variable_rename,[status(thm)],[f_1174_1]) ).

fof(f_1174_3,plain,
    ( ! [U_3560,U_3561,U_3562,U_3563,U_3564] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3561),U_3564)),U_3563) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3560),U_3564)),U_3562)
        | U_3563 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3560),U_3561)),U_3564)),U_3562)
        | ~ sP310(U_3560,U_3561,U_3562,U_3563,U_3564) )
    & ! [U_3560,U_3561,U_3562,U_3563,U_3564] :
        ( U_3563 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3560),U_3561)),U_3564)),U_3562)
        | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3561),U_3564)),U_3563) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3560),U_3564)),U_3562)
        | ~ sP310(U_3560,U_3561,U_3562,U_3563,U_3564) )
    & ! [U_3560,U_3561,U_3562,U_3563,U_3564] :
        ( sP310(U_3560,U_3561,U_3562,U_3563,U_3564)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3561),U_3560)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP310])],[f_1174_2]) ).

cnf(f_1174_4,plain,
    ( sP310(U_3560,U_3561,U_3562,U_3563,U_3564)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3561),U_3560)) ),
    inference(clausify,[status(thm)],[f_1174_3]) ).

cnf(f_1174_5,plain,
    ( U_3563 = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3560),U_3561)),U_3564)),U_3562)
    | hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3561),U_3564)),U_3563) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3560),U_3564)),U_3562)
    | ~ sP310(U_3560,U_3561,U_3562,U_3563,U_3564) ),
    inference(clausify,[status(thm)],[f_1174_3]) ).

cnf(f_1174_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3561),U_3564)),U_3563) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3560),U_3564)),U_3562)
    | U_3563 != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3560),U_3561)),U_3564)),U_3562)
    | ~ sP310(U_3560,U_3561,U_3562,U_3563,U_3564) ),
    inference(clausify,[status(thm)],[f_1174_3]) ).

fof(f_1175_1,plain,
    ! [U,M,Na,J_1,I_2] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_2),J_1)),U)),M)),Na)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,I_2),J_1)),U)),M)),Na))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,I_2),U)),M)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,J_1),U)),Na))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J_1),I_2)) ),
    inference(fof_nnf,[status(thm)],[fact_1068_nat__less__add__iff1]) ).

fof(f_1175_2,plain,
    ! [U_3569,U_3568,U_3567,U_3566,U_3565] :
      ( ( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3565),U_3569)),U_3568)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3566),U_3569)),U_3567)))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3565),U_3566)),U_3569)),U_3568)),U_3567)) )
        & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3565),U_3566)),U_3569)),U_3568)),U_3567))
          | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3565),U_3569)),U_3568)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3566),U_3569)),U_3567))) ) )
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3566),U_3565)) ),
    inference(variable_rename,[status(thm)],[f_1175_1]) ).

fof(f_1175_3,plain,
    ( ! [U_3565,U_3566,U_3568,U_3567,U_3569] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3565),U_3569)),U_3568)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3566),U_3569)),U_3567)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3565),U_3566)),U_3569)),U_3568)),U_3567))
        | ~ sP311(U_3565,U_3566,U_3568,U_3567,U_3569) )
    & ! [U_3565,U_3566,U_3568,U_3567,U_3569] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3565),U_3566)),U_3569)),U_3568)),U_3567))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3565),U_3569)),U_3568)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3566),U_3569)),U_3567)))
        | ~ sP311(U_3565,U_3566,U_3568,U_3567,U_3569) )
    & ! [U_3565,U_3566,U_3568,U_3567,U_3569] :
        ( sP311(U_3565,U_3566,U_3568,U_3567,U_3569)
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3566),U_3565)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP311])],[f_1175_2]) ).

cnf(f_1175_4,plain,
    ( sP311(U_3565,U_3566,U_3568,U_3567,U_3569)
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3566),U_3565)) ),
    inference(clausify,[status(thm)],[f_1175_3]) ).

cnf(f_1175_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3565),U_3566)),U_3569)),U_3568)),U_3567))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3565),U_3569)),U_3568)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3566),U_3569)),U_3567)))
    | ~ sP311(U_3565,U_3566,U_3568,U_3567,U_3569) ),
    inference(clausify,[status(thm)],[f_1175_3]) ).

cnf(f_1175_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3565),U_3569)),U_3568)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3566),U_3569)),U_3567)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3565),U_3566)),U_3569)),U_3568)),U_3567))
    | ~ sP311(U_3565,U_3566,U_3568,U_3567,U_3569) ),
    inference(clausify,[status(thm)],[f_1175_3]) ).

fof(f_1176_1,plain,
    ! [B_2,Q_2,R_2,B_1,Q_1,R_1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),Q_2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_1),B_2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_2),B_2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_1)),zero_zero_int))
      | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),Q_2)),R_2) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_1) ),
    inference(fof_nnf,[status(thm)],[fact_1069_zdiv__mono2__neg__lemma]) ).

fof(f_1176_2,plain,
    ! [U_3575,U_3574,U_3573,U_3572,U_3571,U_3570] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3571),U_3574))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3572),U_3575))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3572))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3570))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3573),U_3575))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3572),U_3571)),U_3570)),zero_zero_int))
      | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3575),U_3574)),U_3573) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3572),U_3571)),U_3570) ),
    inference(variable_rename,[status(thm)],[f_1176_1]) ).

fof(f_1176_3,plain,
    ! [U_3572,U_3571,U_3573,U_3570,U_3574,U_3575] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3571),U_3574))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3572),U_3575))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3572))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3570))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3573),U_3575))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3572),U_3571)),U_3570)),zero_zero_int))
      | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3575),U_3574)),U_3573) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3572),U_3571)),U_3570) ),
    inference(definitional_conversion,[status(esa)],[f_1176_2]) ).

cnf(f_1176_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3571),U_3574))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3572),U_3575))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3572))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3570))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3573),U_3575))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3572),U_3571)),U_3570)),zero_zero_int))
    | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3575),U_3574)),U_3573) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3572),U_3571)),U_3570) ),
    inference(clausify,[status(thm)],[f_1176_3]) ).

fof(f_1177_1,plain,
    ! [B_2,Q_1,R_1,Q_2,R_2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_2),Q_1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_2),R_1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,B_2),R_2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,R_2),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),Q_1)),R_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),Q_2)),R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_1070_unique__quotient__lemma__neg]) ).

fof(f_1177_2,plain,
    ! [U_3580,U_3579,U_3578,U_3577,U_3576] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3577),U_3579))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3580),U_3578))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3580),U_3576))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3576),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3580),U_3579)),U_3578)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3580),U_3577)),U_3576))) ),
    inference(variable_rename,[status(thm)],[f_1177_1]) ).

fof(f_1177_3,plain,
    ! [U_3577,U_3579,U_3578,U_3576,U_3580] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3577),U_3579))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3580),U_3578))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3580),U_3576))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3576),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3580),U_3579)),U_3578)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3580),U_3577)),U_3576))) ),
    inference(definitional_conversion,[status(esa)],[f_1177_2]) ).

cnf(f_1177_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3577),U_3579))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3580),U_3578))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3580),U_3576))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3576),zero_zero_int))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3580),U_3579)),U_3578)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3580),U_3577)),U_3576))) ),
    inference(clausify,[status(thm)],[f_1177_3]) ).

fof(f_1178_1,plain,
    ! [K_1] : number_number_of_int(K_1) = K_1,
    inference(fof_nnf,[status(thm)],[fact_1071_number__of__is__id]) ).

fof(f_1178_2,plain,
    ! [U_3581] : number_number_of_int(U_3581) = U_3581,
    inference(variable_rename,[status(thm)],[f_1178_1]) ).

fof(f_1178_3,plain,
    ! [U_3581] : number_number_of_int(U_3581) = U_3581,
    inference(definitional_conversion,[status(esa)],[f_1178_2]) ).

cnf(f_1178_4,plain,
    number_number_of_int(U_3581) = U_3581,
    inference(clausify,[status(thm)],[f_1178_3]) ).

fof(f_1179_1,plain,
    zero_zero_int != one_one_int,
    inference(fof_nnf,[status(thm)],[fact_1072_int__0__neq__1]) ).

fof(f_1179_2,plain,
    zero_zero_int != one_one_int,
    inference(definitional_conversion,[status(esa)],[f_1179_1]) ).

cnf(f_1179_3,plain,
    zero_zero_int != one_one_int,
    inference(clausify,[status(thm)],[f_1179_2]) ).

fof(f_1180_1,plain,
    ! [R_2,Q_2,A_1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Q_2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_2),A_1))
      | A_1 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,R_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_1),Q_2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1073_self__quotient__aux1]) ).

fof(f_1180_2,plain,
    ! [U_3584,U_3583,U_3582] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U_3583))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3584),U_3582))
      | U_3582 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3584),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3582),U_3583))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3582)) ),
    inference(variable_rename,[status(thm)],[f_1180_1]) ).

fof(f_1180_3,plain,
    ! [U_3584,U_3582,U_3583] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U_3583))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3584),U_3582))
      | U_3582 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3584),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3582),U_3583))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3582)) ),
    inference(definitional_conversion,[status(esa)],[f_1180_2]) ).

cnf(f_1180_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),U_3583))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3584),U_3582))
    | U_3582 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3584),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3582),U_3583))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3582)) ),
    inference(clausify,[status(thm)],[f_1180_3]) ).

fof(f_1181_1,plain,
    ! [R_2,Q_2,A_1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_2),one_one_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_2))
      | A_1 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,R_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_1),Q_2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1074_self__quotient__aux2]) ).

fof(f_1181_2,plain,
    ! [U_3587,U_3586,U_3585] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3586),one_one_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3587))
      | U_3585 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3587),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3585),U_3586))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3585)) ),
    inference(variable_rename,[status(thm)],[f_1181_1]) ).

fof(f_1181_3,plain,
    ! [U_3585,U_3586,U_3587] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3586),one_one_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3587))
      | U_3585 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3587),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3585),U_3586))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3585)) ),
    inference(definitional_conversion,[status(esa)],[f_1181_2]) ).

cnf(f_1181_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3586),one_one_int))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3587))
    | U_3585 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3587),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3585),U_3586))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3585)) ),
    inference(clausify,[status(thm)],[f_1181_3]) ).

fof(f_1182_1,plain,
    ! [B_1,Q_1,R_1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Q_1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B_1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_1))) ),
    inference(fof_nnf,[status(thm)],[fact_1075_q__pos__lemma]) ).

fof(f_1182_2,plain,
    ! [U_3590,U_3589,U_3588] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3589))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3590))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3588),U_3590))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3590),U_3589)),U_3588))) ),
    inference(variable_rename,[status(thm)],[f_1182_1]) ).

fof(f_1182_3,plain,
    ! [U_3588,U_3589,U_3590] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3589))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3590))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3588),U_3590))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3590),U_3589)),U_3588))) ),
    inference(definitional_conversion,[status(esa)],[f_1182_2]) ).

cnf(f_1182_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3589))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3590))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3588),U_3590))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3590),U_3589)),U_3588))) ),
    inference(clausify,[status(thm)],[f_1182_3]) ).

fof(f_1183_1,plain,
    ! [B_1,Q_1,R_1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_1)),zero_zero_int)) ),
    inference(fof_nnf,[status(thm)],[fact_1076_q__neg__lemma]) ).

fof(f_1183_2,plain,
    ! [U_3593,U_3592,U_3591] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3592),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3593))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3591))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3593),U_3592)),U_3591)),zero_zero_int)) ),
    inference(variable_rename,[status(thm)],[f_1183_1]) ).

fof(f_1183_3,plain,
    ! [U_3591,U_3592,U_3593] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3592),zero_zero_int))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3593))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3591))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3593),U_3592)),U_3591)),zero_zero_int)) ),
    inference(definitional_conversion,[status(esa)],[f_1183_2]) ).

cnf(f_1183_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3592),zero_zero_int))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3593))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3591))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3593),U_3592)),U_3591)),zero_zero_int)) ),
    inference(clausify,[status(thm)],[f_1183_3]) ).

fof(f_1184_1,plain,
    ! [B_2,Q_1,R_1,Q_2,R_2] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_1),Q_2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_2),B_2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B_2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),Q_1)),R_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),Q_2)),R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_1077_unique__quotient__lemma]) ).

fof(f_1184_2,plain,
    ! [U_3598,U_3597,U_3596,U_3595,U_3594] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3597),U_3595))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3594),U_3598))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3596),U_3598))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3596))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3598),U_3597)),U_3596)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3598),U_3595)),U_3594))) ),
    inference(variable_rename,[status(thm)],[f_1184_1]) ).

fof(f_1184_3,plain,
    ! [U_3594,U_3595,U_3596,U_3597,U_3598] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3597),U_3595))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3594),U_3598))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3596),U_3598))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3596))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3598),U_3597)),U_3596)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3598),U_3595)),U_3594))) ),
    inference(definitional_conversion,[status(esa)],[f_1184_2]) ).

cnf(f_1184_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3597),U_3595))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3594),U_3598))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3596),U_3598))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3596))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3598),U_3597)),U_3596)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3598),U_3595)),U_3594))) ),
    inference(clausify,[status(thm)],[f_1184_3]) ).

fof(f_1185_1,plain,
    ! [B_2,Q_2,R_2,B_1,Q_1,R_1] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Q_2),Q_1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,B_1),B_2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),R_2))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,R_1),B_1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_1)))
      | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_2),Q_2)),R_2) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,B_1),Q_1)),R_1) ),
    inference(fof_nnf,[status(thm)],[fact_1078_zdiv__mono2__lemma]) ).

fof(f_1185_2,plain,
    ! [U_3604,U_3603,U_3602,U_3601,U_3600,U_3599] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3603),U_3600))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3601),U_3604))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3601))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3602))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3599),U_3601))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3601),U_3600)),U_3599)))
      | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3604),U_3603)),U_3602) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3601),U_3600)),U_3599) ),
    inference(variable_rename,[status(thm)],[f_1185_1]) ).

fof(f_1185_3,plain,
    ! [U_3599,U_3600,U_3601,U_3602,U_3603,U_3604] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3603),U_3600))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3601),U_3604))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3601))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3602))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3599),U_3601))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3601),U_3600)),U_3599)))
      | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3604),U_3603)),U_3602) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3601),U_3600)),U_3599) ),
    inference(definitional_conversion,[status(esa)],[f_1185_2]) ).

cnf(f_1185_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3603),U_3600))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3601),U_3604))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3601))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3602))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3599),U_3601))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3601),U_3600)),U_3599)))
    | hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3604),U_3603)),U_3602) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3601),U_3600)),U_3599) ),
    inference(clausify,[status(thm)],[f_1185_3]) ).

fof(f_1186_1,plain,
    ! [Pa,I_2,K] :
      ( hBOOL(hAPP_int_bool(Pa,I_2))
      | ? [I] :
          ( ~ hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,I),one_one_int)))
          & hBOOL(hAPP_int_bool(Pa,I))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I),K)) )
      | ~ hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_2),K)) ),
    inference(fof_nnf,[status(thm)],[fact_1079_int__less__induct]) ).

fof(f_1186_2,plain,
    ! [U_3608,U_3607,U_3606] :
      ( hBOOL(hAPP_int_bool(U_3608,U_3607))
      | ? [U_3605] :
          ( ~ hBOOL(hAPP_int_bool(U_3608,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3605),one_one_int)))
          & hBOOL(hAPP_int_bool(U_3608,U_3605))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3605),U_3606)) )
      | ~ hBOOL(hAPP_int_bool(U_3608,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3606),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3607),U_3606)) ),
    inference(variable_rename,[status(thm)],[f_1186_1]) ).

fof(f_1186_3,plain,
    ! [U_3608,U_3607,U_3606] :
      ( hBOOL(hAPP_int_bool(U_3608,U_3607))
      | ( ~ hBOOL(hAPP_int_bool(U_3608,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK187(U_3608,U_3607,U_3606)),one_one_int)))
        & hBOOL(hAPP_int_bool(U_3608,sK187(U_3608,U_3607,U_3606)))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK187(U_3608,U_3607,U_3606)),U_3606)) )
      | ~ hBOOL(hAPP_int_bool(U_3608,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3606),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3607),U_3606)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK187]),skolemize(U_3605,sK187(U_3608,U_3607,U_3606))],[f_1186_2]) ).

fof(f_1186_4,plain,
    ( ! [U_3606,U_3608,U_3607] :
        ( ~ hBOOL(hAPP_int_bool(U_3608,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK187(U_3608,U_3607,U_3606)),one_one_int)))
        | ~ sP312(U_3606,U_3608,U_3607) )
    & ! [U_3606,U_3608,U_3607] :
        ( hBOOL(hAPP_int_bool(U_3608,sK187(U_3608,U_3607,U_3606)))
        | ~ sP312(U_3606,U_3608,U_3607) )
    & ! [U_3606,U_3608,U_3607] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK187(U_3608,U_3607,U_3606)),U_3606))
        | ~ sP312(U_3606,U_3608,U_3607) )
    & ! [U_3606,U_3608,U_3607] :
        ( hBOOL(hAPP_int_bool(U_3608,U_3607))
        | sP312(U_3606,U_3608,U_3607)
        | ~ hBOOL(hAPP_int_bool(U_3608,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3606),one_one_int)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3607),U_3606)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP312])],[f_1186_3]) ).

cnf(f_1186_5,plain,
    ( hBOOL(hAPP_int_bool(U_3608,U_3607))
    | sP312(U_3606,U_3608,U_3607)
    | ~ hBOOL(hAPP_int_bool(U_3608,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3606),one_one_int)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3607),U_3606)) ),
    inference(clausify,[status(thm)],[f_1186_4]) ).

cnf(f_1186_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK187(U_3608,U_3607,U_3606)),U_3606))
    | ~ sP312(U_3606,U_3608,U_3607) ),
    inference(clausify,[status(thm)],[f_1186_4]) ).

cnf(f_1186_7,plain,
    ( hBOOL(hAPP_int_bool(U_3608,sK187(U_3608,U_3607,U_3606)))
    | ~ sP312(U_3606,U_3608,U_3607) ),
    inference(clausify,[status(thm)],[f_1186_4]) ).

cnf(f_1186_8,plain,
    ( ~ hBOOL(hAPP_int_bool(U_3608,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK187(U_3608,U_3607,U_3606)),one_one_int)))
    | ~ sP312(U_3606,U_3608,U_3607) ),
    inference(clausify,[status(thm)],[f_1186_4]) ).

fof(f_1187_1,plain,
    ! [Pa,I_2,K] :
      ( hBOOL(hAPP_int_bool(Pa,I_2))
      | ? [I] :
          ( ~ hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,I),one_one_int)))
          & hBOOL(hAPP_int_bool(Pa,I))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I),K)) )
      | ~ hBOOL(hAPP_int_bool(Pa,K))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I_2),K)) ),
    inference(fof_nnf,[status(thm)],[fact_1080_int__le__induct]) ).

fof(f_1187_2,plain,
    ! [U_3612,U_3611,U_3610] :
      ( hBOOL(hAPP_int_bool(U_3612,U_3611))
      | ? [U_3609] :
          ( ~ hBOOL(hAPP_int_bool(U_3612,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3609),one_one_int)))
          & hBOOL(hAPP_int_bool(U_3612,U_3609))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3609),U_3610)) )
      | ~ hBOOL(hAPP_int_bool(U_3612,U_3610))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3611),U_3610)) ),
    inference(variable_rename,[status(thm)],[f_1187_1]) ).

fof(f_1187_3,plain,
    ! [U_3612,U_3611,U_3610] :
      ( hBOOL(hAPP_int_bool(U_3612,U_3611))
      | ( ~ hBOOL(hAPP_int_bool(U_3612,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK188(U_3612,U_3611,U_3610)),one_one_int)))
        & hBOOL(hAPP_int_bool(U_3612,sK188(U_3612,U_3611,U_3610)))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK188(U_3612,U_3611,U_3610)),U_3610)) )
      | ~ hBOOL(hAPP_int_bool(U_3612,U_3610))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3611),U_3610)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK188]),skolemize(U_3609,sK188(U_3612,U_3611,U_3610))],[f_1187_2]) ).

fof(f_1187_4,plain,
    ( ! [U_3611,U_3612,U_3610] :
        ( ~ hBOOL(hAPP_int_bool(U_3612,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK188(U_3612,U_3611,U_3610)),one_one_int)))
        | ~ sP313(U_3611,U_3612,U_3610) )
    & ! [U_3611,U_3612,U_3610] :
        ( hBOOL(hAPP_int_bool(U_3612,sK188(U_3612,U_3611,U_3610)))
        | ~ sP313(U_3611,U_3612,U_3610) )
    & ! [U_3611,U_3612,U_3610] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK188(U_3612,U_3611,U_3610)),U_3610))
        | ~ sP313(U_3611,U_3612,U_3610) )
    & ! [U_3611,U_3612,U_3610] :
        ( hBOOL(hAPP_int_bool(U_3612,U_3611))
        | sP313(U_3611,U_3612,U_3610)
        | ~ hBOOL(hAPP_int_bool(U_3612,U_3610))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3611),U_3610)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP313])],[f_1187_3]) ).

cnf(f_1187_5,plain,
    ( hBOOL(hAPP_int_bool(U_3612,U_3611))
    | sP313(U_3611,U_3612,U_3610)
    | ~ hBOOL(hAPP_int_bool(U_3612,U_3610))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3611),U_3610)) ),
    inference(clausify,[status(thm)],[f_1187_4]) ).

cnf(f_1187_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK188(U_3612,U_3611,U_3610)),U_3610))
    | ~ sP313(U_3611,U_3612,U_3610) ),
    inference(clausify,[status(thm)],[f_1187_4]) ).

cnf(f_1187_7,plain,
    ( hBOOL(hAPP_int_bool(U_3612,sK188(U_3612,U_3611,U_3610)))
    | ~ sP313(U_3611,U_3612,U_3610) ),
    inference(clausify,[status(thm)],[f_1187_4]) ).

cnf(f_1187_8,plain,
    ( ~ hBOOL(hAPP_int_bool(U_3612,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK188(U_3612,U_3611,U_3610)),one_one_int)))
    | ~ sP313(U_3611,U_3612,U_3610) ),
    inference(clausify,[status(thm)],[f_1187_4]) ).

fof(f_1188_1,plain,
    ! [Pa,K,I_2] :
      ( hBOOL(hAPP_int_bool(Pa,I_2))
      | ? [I] :
          ( ~ hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I),one_one_int)))
          & hBOOL(hAPP_int_bool(Pa,I))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),I)) )
      | ~ hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),I_2)) ),
    inference(fof_nnf,[status(thm)],[fact_1081_int__gr__induct]) ).

fof(f_1188_2,plain,
    ! [U_3616,U_3615,U_3614] :
      ( hBOOL(hAPP_int_bool(U_3616,U_3614))
      | ? [U_3613] :
          ( ~ hBOOL(hAPP_int_bool(U_3616,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3613),one_one_int)))
          & hBOOL(hAPP_int_bool(U_3616,U_3613))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3615),U_3613)) )
      | ~ hBOOL(hAPP_int_bool(U_3616,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3615),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3615),U_3614)) ),
    inference(variable_rename,[status(thm)],[f_1188_1]) ).

fof(f_1188_3,plain,
    ! [U_3616,U_3615,U_3614] :
      ( hBOOL(hAPP_int_bool(U_3616,U_3614))
      | ( ~ hBOOL(hAPP_int_bool(U_3616,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,sK189(U_3616,U_3615,U_3614)),one_one_int)))
        & hBOOL(hAPP_int_bool(U_3616,sK189(U_3616,U_3615,U_3614)))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3615),sK189(U_3616,U_3615,U_3614))) )
      | ~ hBOOL(hAPP_int_bool(U_3616,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3615),one_one_int)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3615),U_3614)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK189]),skolemize(U_3613,sK189(U_3616,U_3615,U_3614))],[f_1188_2]) ).

fof(f_1188_4,plain,
    ( ! [U_3614,U_3615,U_3616] :
        ( ~ hBOOL(hAPP_int_bool(U_3616,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,sK189(U_3616,U_3615,U_3614)),one_one_int)))
        | ~ sP314(U_3614,U_3615,U_3616) )
    & ! [U_3614,U_3615,U_3616] :
        ( hBOOL(hAPP_int_bool(U_3616,sK189(U_3616,U_3615,U_3614)))
        | ~ sP314(U_3614,U_3615,U_3616) )
    & ! [U_3614,U_3615,U_3616] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3615),sK189(U_3616,U_3615,U_3614)))
        | ~ sP314(U_3614,U_3615,U_3616) )
    & ! [U_3614,U_3615,U_3616] :
        ( hBOOL(hAPP_int_bool(U_3616,U_3614))
        | sP314(U_3614,U_3615,U_3616)
        | ~ hBOOL(hAPP_int_bool(U_3616,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3615),one_one_int)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3615),U_3614)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP314])],[f_1188_3]) ).

cnf(f_1188_5,plain,
    ( hBOOL(hAPP_int_bool(U_3616,U_3614))
    | sP314(U_3614,U_3615,U_3616)
    | ~ hBOOL(hAPP_int_bool(U_3616,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3615),one_one_int)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3615),U_3614)) ),
    inference(clausify,[status(thm)],[f_1188_4]) ).

cnf(f_1188_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3615),sK189(U_3616,U_3615,U_3614)))
    | ~ sP314(U_3614,U_3615,U_3616) ),
    inference(clausify,[status(thm)],[f_1188_4]) ).

cnf(f_1188_7,plain,
    ( hBOOL(hAPP_int_bool(U_3616,sK189(U_3616,U_3615,U_3614)))
    | ~ sP314(U_3614,U_3615,U_3616) ),
    inference(clausify,[status(thm)],[f_1188_4]) ).

cnf(f_1188_8,plain,
    ( ~ hBOOL(hAPP_int_bool(U_3616,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,sK189(U_3616,U_3615,U_3614)),one_one_int)))
    | ~ sP314(U_3614,U_3615,U_3616) ),
    inference(clausify,[status(thm)],[f_1188_4]) ).

fof(f_1189_1,plain,
    ! [Pa,K,I_2] :
      ( hBOOL(hAPP_int_bool(Pa,I_2))
      | ? [I] :
          ( ~ hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I),one_one_int)))
          & hBOOL(hAPP_int_bool(Pa,I))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),I)) )
      | ~ hBOOL(hAPP_int_bool(Pa,K))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),I_2)) ),
    inference(fof_nnf,[status(thm)],[fact_1082_int__ge__induct]) ).

fof(f_1189_2,plain,
    ! [U_3620,U_3619,U_3618] :
      ( hBOOL(hAPP_int_bool(U_3620,U_3618))
      | ? [U_3617] :
          ( ~ hBOOL(hAPP_int_bool(U_3620,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3617),one_one_int)))
          & hBOOL(hAPP_int_bool(U_3620,U_3617))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3619),U_3617)) )
      | ~ hBOOL(hAPP_int_bool(U_3620,U_3619))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3619),U_3618)) ),
    inference(variable_rename,[status(thm)],[f_1189_1]) ).

fof(f_1189_3,plain,
    ! [U_3620,U_3619,U_3618] :
      ( hBOOL(hAPP_int_bool(U_3620,U_3618))
      | ( ~ hBOOL(hAPP_int_bool(U_3620,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,sK190(U_3620,U_3619,U_3618)),one_one_int)))
        & hBOOL(hAPP_int_bool(U_3620,sK190(U_3620,U_3619,U_3618)))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3619),sK190(U_3620,U_3619,U_3618))) )
      | ~ hBOOL(hAPP_int_bool(U_3620,U_3619))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3619),U_3618)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK190]),skolemize(U_3617,sK190(U_3620,U_3619,U_3618))],[f_1189_2]) ).

fof(f_1189_4,plain,
    ( ! [U_3620,U_3618,U_3619] :
        ( ~ hBOOL(hAPP_int_bool(U_3620,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,sK190(U_3620,U_3619,U_3618)),one_one_int)))
        | ~ sP315(U_3620,U_3618,U_3619) )
    & ! [U_3620,U_3618,U_3619] :
        ( hBOOL(hAPP_int_bool(U_3620,sK190(U_3620,U_3619,U_3618)))
        | ~ sP315(U_3620,U_3618,U_3619) )
    & ! [U_3620,U_3618,U_3619] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3619),sK190(U_3620,U_3619,U_3618)))
        | ~ sP315(U_3620,U_3618,U_3619) )
    & ! [U_3620,U_3618,U_3619] :
        ( hBOOL(hAPP_int_bool(U_3620,U_3618))
        | sP315(U_3620,U_3618,U_3619)
        | ~ hBOOL(hAPP_int_bool(U_3620,U_3619))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3619),U_3618)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP315])],[f_1189_3]) ).

cnf(f_1189_5,plain,
    ( hBOOL(hAPP_int_bool(U_3620,U_3618))
    | sP315(U_3620,U_3618,U_3619)
    | ~ hBOOL(hAPP_int_bool(U_3620,U_3619))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3619),U_3618)) ),
    inference(clausify,[status(thm)],[f_1189_4]) ).

cnf(f_1189_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3619),sK190(U_3620,U_3619,U_3618)))
    | ~ sP315(U_3620,U_3618,U_3619) ),
    inference(clausify,[status(thm)],[f_1189_4]) ).

cnf(f_1189_7,plain,
    ( hBOOL(hAPP_int_bool(U_3620,sK190(U_3620,U_3619,U_3618)))
    | ~ sP315(U_3620,U_3618,U_3619) ),
    inference(clausify,[status(thm)],[f_1189_4]) ).

cnf(f_1189_8,plain,
    ( ~ hBOOL(hAPP_int_bool(U_3620,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,sK190(U_3620,U_3619,U_3618)),one_one_int)))
    | ~ sP315(U_3620,U_3618,U_3619) ),
    inference(clausify,[status(thm)],[f_1189_4]) ).

fof(f_1190_1,plain,
    ! [Y,X] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,X),Y)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X)) ),
    inference(fof_nnf,[status(thm)],[fact_1083_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J]) ).

fof(f_1190_2,plain,
    ! [U_3622,U_3621] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3621),U_3622)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3622))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3621)) ),
    inference(variable_rename,[status(thm)],[f_1190_1]) ).

fof(f_1190_3,plain,
    ! [U_3621,U_3622] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3621),U_3622)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3622))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3621)) ),
    inference(definitional_conversion,[status(esa)],[f_1190_2]) ).

cnf(f_1190_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3621),U_3622)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3622))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3621)) ),
    inference(clausify,[status(thm)],[f_1190_3]) ).

fof(f_1191_1,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)),
    inference(fof_nnf,[status(thm)],[fact_1084_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J]) ).

fof(f_1191_2,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)),
    inference(definitional_conversion,[status(esa)],[f_1191_1]) ).

cnf(f_1191_3,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)),
    inference(clausify,[status(thm)],[f_1191_2]) ).

fof(f_1192_1,plain,
    ! [Y,X] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),Y)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X)) ),
    inference(fof_nnf,[status(thm)],[fact_1085_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J]) ).

fof(f_1192_2,plain,
    ! [U_3624,U_3623] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3623),U_3624)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3624))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3623)) ),
    inference(variable_rename,[status(thm)],[f_1192_1]) ).

fof(f_1192_3,plain,
    ! [U_3623,U_3624] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3623),U_3624)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3624))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3623)) ),
    inference(definitional_conversion,[status(esa)],[f_1192_2]) ).

cnf(f_1192_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3623),U_3624)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3624))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3623)) ),
    inference(clausify,[status(thm)],[f_1192_3]) ).

fof(f_1193_1,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
    inference(fof_nnf,[status(thm)],[fact_1086_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]) ).

fof(f_1193_2,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
    inference(definitional_conversion,[status(esa)],[f_1193_1]) ).

cnf(f_1193_3,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
    inference(clausify,[status(thm)],[f_1193_2]) ).

fof(f_1194_1,plain,
    ! [P_1,Pa] :
      ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),Pa)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),P_1))
      | ? [X_2] :
          ( ( ( ~ hBOOL(hAPP_int_bool(Pa,X_2))
              & hBOOL(hAPP_int_bool(P_1,X_2)) )
            | ( ~ hBOOL(hAPP_int_bool(P_1,X_2))
              & hBOOL(hAPP_int_bool(Pa,X_2)) ) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1087_transfer__nat__int__set__cong]) ).

fof(f_1194_2,plain,
    ! [U_3627,U_3626] :
      ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),U_3626)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),U_3627))
      | ? [U_3625] :
          ( ( ( ~ hBOOL(hAPP_int_bool(U_3626,U_3625))
              & hBOOL(hAPP_int_bool(U_3627,U_3625)) )
            | ( ~ hBOOL(hAPP_int_bool(U_3627,U_3625))
              & hBOOL(hAPP_int_bool(U_3626,U_3625)) ) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3625)) ) ),
    inference(variable_rename,[status(thm)],[f_1194_1]) ).

fof(f_1194_3,plain,
    ! [U_3627,U_3626] :
      ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),U_3626)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),U_3627))
      | ( ( ( ~ hBOOL(hAPP_int_bool(U_3626,sK191(U_3627,U_3626)))
            & hBOOL(hAPP_int_bool(U_3627,sK191(U_3627,U_3626))) )
          | ( ~ hBOOL(hAPP_int_bool(U_3627,sK191(U_3627,U_3626)))
            & hBOOL(hAPP_int_bool(U_3626,sK191(U_3627,U_3626))) ) )
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK191(U_3627,U_3626))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK191]),skolemize(U_3625,sK191(U_3627,U_3626))],[f_1194_2]) ).

fof(f_1194_4,plain,
    ( ! [U_3626,U_3627] :
        ( ~ hBOOL(hAPP_int_bool(U_3626,sK191(U_3627,U_3626)))
        | ~ sP317(U_3626,U_3627) )
    & ! [U_3626,U_3627] :
        ( hBOOL(hAPP_int_bool(U_3627,sK191(U_3627,U_3626)))
        | ~ sP317(U_3626,U_3627) )
    & ! [U_3626,U_3627] :
        ( ~ hBOOL(hAPP_int_bool(U_3627,sK191(U_3627,U_3626)))
        | ~ sP316(U_3626,U_3627) )
    & ! [U_3626,U_3627] :
        ( hBOOL(hAPP_int_bool(U_3626,sK191(U_3627,U_3626)))
        | ~ sP316(U_3626,U_3627) )
    & ! [U_3626,U_3627] :
        ( sP317(U_3626,U_3627)
        | sP316(U_3626,U_3627)
        | ~ sP318(U_3626,U_3627) )
    & ! [U_3626,U_3627] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK191(U_3627,U_3626)))
        | ~ sP318(U_3626,U_3627) )
    & ! [U_3626,U_3627] :
        ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),U_3626)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),U_3627))
        | sP318(U_3626,U_3627) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP316,sP317,sP318])],[f_1194_3]) ).

cnf(f_1194_5,plain,
    ( collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),U_3626)) = collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),U_3627))
    | sP318(U_3626,U_3627) ),
    inference(clausify,[status(thm)],[f_1194_4]) ).

cnf(f_1194_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK191(U_3627,U_3626)))
    | ~ sP318(U_3626,U_3627) ),
    inference(clausify,[status(thm)],[f_1194_4]) ).

cnf(f_1194_7,plain,
    ( sP317(U_3626,U_3627)
    | sP316(U_3626,U_3627)
    | ~ sP318(U_3626,U_3627) ),
    inference(clausify,[status(thm)],[f_1194_4]) ).

cnf(f_1194_8,plain,
    ( hBOOL(hAPP_int_bool(U_3626,sK191(U_3627,U_3626)))
    | ~ sP316(U_3626,U_3627) ),
    inference(clausify,[status(thm)],[f_1194_4]) ).

cnf(f_1194_9,plain,
    ( ~ hBOOL(hAPP_int_bool(U_3627,sK191(U_3627,U_3626)))
    | ~ sP316(U_3626,U_3627) ),
    inference(clausify,[status(thm)],[f_1194_4]) ).

cnf(f_1194_10,plain,
    ( hBOOL(hAPP_int_bool(U_3627,sK191(U_3627,U_3626)))
    | ~ sP317(U_3626,U_3627) ),
    inference(clausify,[status(thm)],[f_1194_4]) ).

cnf(f_1194_11,plain,
    ( ~ hBOOL(hAPP_int_bool(U_3626,sK191(U_3627,U_3626)))
    | ~ sP317(U_3626,U_3627) ),
    inference(clausify,[status(thm)],[f_1194_4]) ).

fof(f_1195_1,plain,
    ! [K,Pa,D_1] :
      ( ! [X_2] :
          ( hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K),D_1))))
          | ~ hBOOL(hAPP_int_bool(Pa,X_2)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K))
      | ? [X_2] :
          ( ~ hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),D_1)))
          & hBOOL(hAPP_int_bool(Pa,X_2)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1088_decr__mult__lemma]) ).

fof(f_1195_2,plain,
    ! [U_3632,U_3631,U_3630] :
      ( ! [U_3629] :
          ( hBOOL(hAPP_int_bool(U_3631,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3629),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3632),U_3630))))
          | ~ hBOOL(hAPP_int_bool(U_3631,U_3629)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3632))
      | ? [U_3628] :
          ( ~ hBOOL(hAPP_int_bool(U_3631,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3628),U_3630)))
          & hBOOL(hAPP_int_bool(U_3631,U_3628)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3630)) ),
    inference(variable_rename,[status(thm)],[f_1195_1]) ).

fof(f_1195_3,plain,
    ! [U_3632,U_3631,U_3630] :
      ( ! [U_3629] :
          ( hBOOL(hAPP_int_bool(U_3631,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3629),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3632),U_3630))))
          | ~ hBOOL(hAPP_int_bool(U_3631,U_3629)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3632))
      | ( ~ hBOOL(hAPP_int_bool(U_3631,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK192(U_3632,U_3631,U_3630)),U_3630)))
        & hBOOL(hAPP_int_bool(U_3631,sK192(U_3632,U_3631,U_3630))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3630)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK192]),skolemize(U_3628,sK192(U_3632,U_3631,U_3630))],[f_1195_2]) ).

fof(f_1195_4,plain,
    ( ! [U_3630,U_3632,U_3631] :
        ( ~ hBOOL(hAPP_int_bool(U_3631,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK192(U_3632,U_3631,U_3630)),U_3630)))
        | ~ sP319(U_3630,U_3632,U_3631) )
    & ! [U_3630,U_3632,U_3631] :
        ( hBOOL(hAPP_int_bool(U_3631,sK192(U_3632,U_3631,U_3630)))
        | ~ sP319(U_3630,U_3632,U_3631) )
    & ! [U_3630,U_3632,U_3631,U_3629] :
        ( hBOOL(hAPP_int_bool(U_3631,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3629),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3632),U_3630))))
        | ~ hBOOL(hAPP_int_bool(U_3631,U_3629))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3632))
        | sP319(U_3630,U_3632,U_3631)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3630)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP319])],[f_1195_3]) ).

cnf(f_1195_5,plain,
    ( hBOOL(hAPP_int_bool(U_3631,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3629),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3632),U_3630))))
    | ~ hBOOL(hAPP_int_bool(U_3631,U_3629))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3632))
    | sP319(U_3630,U_3632,U_3631)
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3630)) ),
    inference(clausify,[status(thm)],[f_1195_4]) ).

cnf(f_1195_6,plain,
    ( hBOOL(hAPP_int_bool(U_3631,sK192(U_3632,U_3631,U_3630)))
    | ~ sP319(U_3630,U_3632,U_3631) ),
    inference(clausify,[status(thm)],[f_1195_4]) ).

cnf(f_1195_7,plain,
    ( ~ hBOOL(hAPP_int_bool(U_3631,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK192(U_3632,U_3631,U_3630)),U_3630)))
    | ~ sP319(U_3630,U_3632,U_3631) ),
    inference(clausify,[status(thm)],[f_1195_4]) ).

fof(f_1196_1,plain,
    ! [P_1,Pa,X_1] :
      ( ( ( ( hBOOL(Pa)
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) )
          | ~ hBOOL(P_1)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) )
        & ( ( hBOOL(P_1)
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) )
          | ~ hBOOL(Pa)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) ) )
      | ( ( ( ~ hBOOL(Pa)
            & hBOOL(P_1) )
          | ( ~ hBOOL(P_1)
            & hBOOL(Pa) ) )
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1089_conj__le__cong]) ).

fof(f_1196_2,plain,
    ! [U_3635,U_3634,U_3633] :
      ( ( ( ( hBOOL(U_3634)
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3633)) )
          | ~ hBOOL(U_3635)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3633)) )
        & ( ( hBOOL(U_3635)
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3633)) )
          | ~ hBOOL(U_3634)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3633)) ) )
      | ( ( ( ~ hBOOL(U_3634)
            & hBOOL(U_3635) )
          | ( ~ hBOOL(U_3635)
            & hBOOL(U_3634) ) )
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3633)) ) ),
    inference(variable_rename,[status(thm)],[f_1196_1]) ).

fof(f_1196_3,plain,
    ( ! [U_3633,U_3634] :
        ( hBOOL(U_3634)
        | ~ sP324(U_3633,U_3634) )
    & ! [U_3633,U_3634] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3633))
        | ~ sP324(U_3633,U_3634) )
    & ! [U_3635,U_3633] :
        ( hBOOL(U_3635)
        | ~ sP323(U_3635,U_3633) )
    & ! [U_3635,U_3633] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3633))
        | ~ sP323(U_3635,U_3633) )
    & ! [U_3635,U_3633,U_3634] :
        ( sP324(U_3633,U_3634)
        | ~ hBOOL(U_3635)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3633))
        | ~ sP325(U_3635,U_3633,U_3634) )
    & ! [U_3635,U_3633,U_3634] :
        ( sP323(U_3635,U_3633)
        | ~ hBOOL(U_3634)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3633))
        | ~ sP325(U_3635,U_3633,U_3634) )
    & ! [U_3635,U_3634] :
        ( ~ hBOOL(U_3634)
        | ~ sP321(U_3635,U_3634) )
    & ! [U_3635,U_3634] :
        ( hBOOL(U_3635)
        | ~ sP321(U_3635,U_3634) )
    & ! [U_3635,U_3634] :
        ( ~ hBOOL(U_3635)
        | ~ sP320(U_3635,U_3634) )
    & ! [U_3635,U_3634] :
        ( hBOOL(U_3634)
        | ~ sP320(U_3635,U_3634) )
    & ! [U_3635,U_3633,U_3634] :
        ( sP321(U_3635,U_3634)
        | sP320(U_3635,U_3634)
        | ~ sP322(U_3635,U_3633,U_3634) )
    & ! [U_3635,U_3633,U_3634] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3633))
        | ~ sP322(U_3635,U_3633,U_3634) )
    & ! [U_3635,U_3633,U_3634] :
        ( sP325(U_3635,U_3633,U_3634)
        | sP322(U_3635,U_3633,U_3634) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP320,sP321,sP322,sP323,sP324,sP325])],[f_1196_2]) ).

cnf(f_1196_4,plain,
    ( sP325(U_3635,U_3633,U_3634)
    | sP322(U_3635,U_3633,U_3634) ),
    inference(clausify,[status(thm)],[f_1196_3]) ).

cnf(f_1196_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3633))
    | ~ sP322(U_3635,U_3633,U_3634) ),
    inference(clausify,[status(thm)],[f_1196_3]) ).

cnf(f_1196_6,plain,
    ( sP321(U_3635,U_3634)
    | sP320(U_3635,U_3634)
    | ~ sP322(U_3635,U_3633,U_3634) ),
    inference(clausify,[status(thm)],[f_1196_3]) ).

cnf(f_1196_7,plain,
    ( hBOOL(U_3634)
    | ~ sP320(U_3635,U_3634) ),
    inference(clausify,[status(thm)],[f_1196_3]) ).

cnf(f_1196_8,plain,
    ( ~ hBOOL(U_3635)
    | ~ sP320(U_3635,U_3634) ),
    inference(clausify,[status(thm)],[f_1196_3]) ).

cnf(f_1196_9,plain,
    ( hBOOL(U_3635)
    | ~ sP321(U_3635,U_3634) ),
    inference(clausify,[status(thm)],[f_1196_3]) ).

cnf(f_1196_10,plain,
    ( ~ hBOOL(U_3634)
    | ~ sP321(U_3635,U_3634) ),
    inference(clausify,[status(thm)],[f_1196_3]) ).

cnf(f_1196_11,plain,
    ( sP323(U_3635,U_3633)
    | ~ hBOOL(U_3634)
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3633))
    | ~ sP325(U_3635,U_3633,U_3634) ),
    inference(clausify,[status(thm)],[f_1196_3]) ).

cnf(f_1196_12,plain,
    ( sP324(U_3633,U_3634)
    | ~ hBOOL(U_3635)
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3633))
    | ~ sP325(U_3635,U_3633,U_3634) ),
    inference(clausify,[status(thm)],[f_1196_3]) ).

cnf(f_1196_13,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3633))
    | ~ sP323(U_3635,U_3633) ),
    inference(clausify,[status(thm)],[f_1196_3]) ).

cnf(f_1196_14,plain,
    ( hBOOL(U_3635)
    | ~ sP323(U_3635,U_3633) ),
    inference(clausify,[status(thm)],[f_1196_3]) ).

cnf(f_1196_15,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3633))
    | ~ sP324(U_3633,U_3634) ),
    inference(clausify,[status(thm)],[f_1196_3]) ).

cnf(f_1196_16,plain,
    ( hBOOL(U_3634)
    | ~ sP324(U_3633,U_3634) ),
    inference(clausify,[status(thm)],[f_1196_3]) ).

fof(f_1197_1,plain,
    ! [P_1,Pa,X_1] :
      ( ( ( hBOOL(Pa)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1))
          | ( ~ hBOOL(P_1)
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) ) )
        & ( hBOOL(P_1)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1))
          | ( ~ hBOOL(Pa)
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) ) ) )
      | ( ( ( ~ hBOOL(Pa)
            & hBOOL(P_1) )
          | ( ~ hBOOL(P_1)
            & hBOOL(Pa) ) )
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1090_imp__le__cong]) ).

fof(f_1197_2,plain,
    ! [U_3638,U_3637,U_3636] :
      ( ( ( hBOOL(U_3637)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3636))
          | ( ~ hBOOL(U_3638)
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3636)) ) )
        & ( hBOOL(U_3638)
          | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3636))
          | ( ~ hBOOL(U_3637)
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3636)) ) ) )
      | ( ( ( ~ hBOOL(U_3637)
            & hBOOL(U_3638) )
          | ( ~ hBOOL(U_3638)
            & hBOOL(U_3637) ) )
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3636)) ) ),
    inference(variable_rename,[status(thm)],[f_1197_1]) ).

fof(f_1197_3,plain,
    ( ! [U_3636,U_3638] :
        ( ~ hBOOL(U_3638)
        | ~ sP330(U_3636,U_3638) )
    & ! [U_3636,U_3638] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3636))
        | ~ sP330(U_3636,U_3638) )
    & ! [U_3636,U_3637] :
        ( ~ hBOOL(U_3637)
        | ~ sP329(U_3636,U_3637) )
    & ! [U_3636,U_3637] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3636))
        | ~ sP329(U_3636,U_3637) )
    & ! [U_3636,U_3638,U_3637] :
        ( hBOOL(U_3637)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3636))
        | sP330(U_3636,U_3638)
        | ~ sP331(U_3636,U_3638,U_3637) )
    & ! [U_3636,U_3638,U_3637] :
        ( hBOOL(U_3638)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3636))
        | sP329(U_3636,U_3637)
        | ~ sP331(U_3636,U_3638,U_3637) )
    & ! [U_3638,U_3637] :
        ( ~ hBOOL(U_3637)
        | ~ sP327(U_3638,U_3637) )
    & ! [U_3638,U_3637] :
        ( hBOOL(U_3638)
        | ~ sP327(U_3638,U_3637) )
    & ! [U_3638,U_3637] :
        ( ~ hBOOL(U_3638)
        | ~ sP326(U_3638,U_3637) )
    & ! [U_3638,U_3637] :
        ( hBOOL(U_3637)
        | ~ sP326(U_3638,U_3637) )
    & ! [U_3636,U_3638,U_3637] :
        ( sP327(U_3638,U_3637)
        | sP326(U_3638,U_3637)
        | ~ sP328(U_3636,U_3638,U_3637) )
    & ! [U_3636,U_3638,U_3637] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3636))
        | ~ sP328(U_3636,U_3638,U_3637) )
    & ! [U_3636,U_3638,U_3637] :
        ( sP331(U_3636,U_3638,U_3637)
        | sP328(U_3636,U_3638,U_3637) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP326,sP327,sP328,sP329,sP330,sP331])],[f_1197_2]) ).

cnf(f_1197_4,plain,
    ( sP331(U_3636,U_3638,U_3637)
    | sP328(U_3636,U_3638,U_3637) ),
    inference(clausify,[status(thm)],[f_1197_3]) ).

cnf(f_1197_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3636))
    | ~ sP328(U_3636,U_3638,U_3637) ),
    inference(clausify,[status(thm)],[f_1197_3]) ).

cnf(f_1197_6,plain,
    ( sP327(U_3638,U_3637)
    | sP326(U_3638,U_3637)
    | ~ sP328(U_3636,U_3638,U_3637) ),
    inference(clausify,[status(thm)],[f_1197_3]) ).

cnf(f_1197_7,plain,
    ( hBOOL(U_3637)
    | ~ sP326(U_3638,U_3637) ),
    inference(clausify,[status(thm)],[f_1197_3]) ).

cnf(f_1197_8,plain,
    ( ~ hBOOL(U_3638)
    | ~ sP326(U_3638,U_3637) ),
    inference(clausify,[status(thm)],[f_1197_3]) ).

cnf(f_1197_9,plain,
    ( hBOOL(U_3638)
    | ~ sP327(U_3638,U_3637) ),
    inference(clausify,[status(thm)],[f_1197_3]) ).

cnf(f_1197_10,plain,
    ( ~ hBOOL(U_3637)
    | ~ sP327(U_3638,U_3637) ),
    inference(clausify,[status(thm)],[f_1197_3]) ).

cnf(f_1197_11,plain,
    ( hBOOL(U_3638)
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3636))
    | sP329(U_3636,U_3637)
    | ~ sP331(U_3636,U_3638,U_3637) ),
    inference(clausify,[status(thm)],[f_1197_3]) ).

cnf(f_1197_12,plain,
    ( hBOOL(U_3637)
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3636))
    | sP330(U_3636,U_3638)
    | ~ sP331(U_3636,U_3638,U_3637) ),
    inference(clausify,[status(thm)],[f_1197_3]) ).

cnf(f_1197_13,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3636))
    | ~ sP329(U_3636,U_3637) ),
    inference(clausify,[status(thm)],[f_1197_3]) ).

cnf(f_1197_14,plain,
    ( ~ hBOOL(U_3637)
    | ~ sP329(U_3636,U_3637) ),
    inference(clausify,[status(thm)],[f_1197_3]) ).

cnf(f_1197_15,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3636))
    | ~ sP330(U_3636,U_3638) ),
    inference(clausify,[status(thm)],[f_1197_3]) ).

cnf(f_1197_16,plain,
    ( ~ hBOOL(U_3638)
    | ~ sP330(U_3636,U_3638) ),
    inference(clausify,[status(thm)],[f_1197_3]) ).

fof(f_1198_1,plain,
    ! [K,Pa,D_1] :
      ( ! [X_2] :
          ( hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K),D_1))))
          | ~ hBOOL(hAPP_int_bool(Pa,X_2)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K))
      | ? [X_2] :
          ( ~ hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X_2),D_1)))
          & hBOOL(hAPP_int_bool(Pa,X_2)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1091_incr__mult__lemma]) ).

fof(f_1198_2,plain,
    ! [U_3643,U_3642,U_3641] :
      ( ! [U_3640] :
          ( hBOOL(hAPP_int_bool(U_3642,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3640),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3643),U_3641))))
          | ~ hBOOL(hAPP_int_bool(U_3642,U_3640)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3643))
      | ? [U_3639] :
          ( ~ hBOOL(hAPP_int_bool(U_3642,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3639),U_3641)))
          & hBOOL(hAPP_int_bool(U_3642,U_3639)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3641)) ),
    inference(variable_rename,[status(thm)],[f_1198_1]) ).

fof(f_1198_3,plain,
    ! [U_3643,U_3642,U_3641] :
      ( ! [U_3640] :
          ( hBOOL(hAPP_int_bool(U_3642,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3640),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3643),U_3641))))
          | ~ hBOOL(hAPP_int_bool(U_3642,U_3640)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3643))
      | ( ~ hBOOL(hAPP_int_bool(U_3642,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,sK193(U_3643,U_3642,U_3641)),U_3641)))
        & hBOOL(hAPP_int_bool(U_3642,sK193(U_3643,U_3642,U_3641))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3641)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK193]),skolemize(U_3639,sK193(U_3643,U_3642,U_3641))],[f_1198_2]) ).

fof(f_1198_4,plain,
    ( ! [U_3642,U_3643,U_3641] :
        ( ~ hBOOL(hAPP_int_bool(U_3642,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,sK193(U_3643,U_3642,U_3641)),U_3641)))
        | ~ sP332(U_3642,U_3643,U_3641) )
    & ! [U_3642,U_3643,U_3641] :
        ( hBOOL(hAPP_int_bool(U_3642,sK193(U_3643,U_3642,U_3641)))
        | ~ sP332(U_3642,U_3643,U_3641) )
    & ! [U_3642,U_3643,U_3641,U_3640] :
        ( hBOOL(hAPP_int_bool(U_3642,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3640),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3643),U_3641))))
        | ~ hBOOL(hAPP_int_bool(U_3642,U_3640))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3643))
        | sP332(U_3642,U_3643,U_3641)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3641)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP332])],[f_1198_3]) ).

cnf(f_1198_5,plain,
    ( hBOOL(hAPP_int_bool(U_3642,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3640),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3643),U_3641))))
    | ~ hBOOL(hAPP_int_bool(U_3642,U_3640))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3643))
    | sP332(U_3642,U_3643,U_3641)
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3641)) ),
    inference(clausify,[status(thm)],[f_1198_4]) ).

cnf(f_1198_6,plain,
    ( hBOOL(hAPP_int_bool(U_3642,sK193(U_3643,U_3642,U_3641)))
    | ~ sP332(U_3642,U_3643,U_3641) ),
    inference(clausify,[status(thm)],[f_1198_4]) ).

cnf(f_1198_7,plain,
    ( ~ hBOOL(hAPP_int_bool(U_3642,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,sK193(U_3643,U_3642,U_3641)),U_3641)))
    | ~ sP332(U_3642,U_3643,U_3641) ),
    inference(clausify,[status(thm)],[f_1198_4]) ).

fof(f_1199_1,plain,
    ! [I_2,Pa,K] :
      ( hBOOL(hAPP_int_bool(Pa,I_2))
      | ? [I] :
          ( ~ hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,I),one_one_int)))
          & hBOOL(hAPP_int_bool(Pa,I))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,I),K)) )
      | ? [I] :
          ( ~ hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,I),one_one_int)))
          & hBOOL(hAPP_int_bool(Pa,I))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),I)) )
      | ~ hBOOL(hAPP_int_bool(Pa,K)) ),
    inference(fof_nnf,[status(thm)],[fact_1092_int__induct]) ).

fof(f_1199_2,plain,
    ! [U_3648,U_3647,U_3646] :
      ( hBOOL(hAPP_int_bool(U_3647,U_3648))
      | ? [U_3645] :
          ( ~ hBOOL(hAPP_int_bool(U_3647,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3645),one_one_int)))
          & hBOOL(hAPP_int_bool(U_3647,U_3645))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3645),U_3646)) )
      | ? [U_3644] :
          ( ~ hBOOL(hAPP_int_bool(U_3647,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3644),one_one_int)))
          & hBOOL(hAPP_int_bool(U_3647,U_3644))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3646),U_3644)) )
      | ~ hBOOL(hAPP_int_bool(U_3647,U_3646)) ),
    inference(variable_rename,[status(thm)],[f_1199_1]) ).

fof(f_1199_3,plain,
    ! [U_3648,U_3647,U_3646] :
      ( hBOOL(hAPP_int_bool(U_3647,U_3648))
      | ? [U_3645] :
          ( ~ hBOOL(hAPP_int_bool(U_3647,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3645),one_one_int)))
          & hBOOL(hAPP_int_bool(U_3647,U_3645))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3645),U_3646)) )
      | ( ~ hBOOL(hAPP_int_bool(U_3647,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,sK194(U_3648,U_3647,U_3646)),one_one_int)))
        & hBOOL(hAPP_int_bool(U_3647,sK194(U_3648,U_3647,U_3646)))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3646),sK194(U_3648,U_3647,U_3646))) )
      | ~ hBOOL(hAPP_int_bool(U_3647,U_3646)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK194]),skolemize(U_3644,sK194(U_3648,U_3647,U_3646))],[f_1199_2]) ).

fof(f_1199_4,plain,
    ! [U_3648,U_3647,U_3646] :
      ( hBOOL(hAPP_int_bool(U_3647,U_3648))
      | ( ~ hBOOL(hAPP_int_bool(U_3647,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK195(U_3648,U_3647,U_3646)),one_one_int)))
        & hBOOL(hAPP_int_bool(U_3647,sK195(U_3648,U_3647,U_3646)))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK195(U_3648,U_3647,U_3646)),U_3646)) )
      | ( ~ hBOOL(hAPP_int_bool(U_3647,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,sK194(U_3648,U_3647,U_3646)),one_one_int)))
        & hBOOL(hAPP_int_bool(U_3647,sK194(U_3648,U_3647,U_3646)))
        & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3646),sK194(U_3648,U_3647,U_3646))) )
      | ~ hBOOL(hAPP_int_bool(U_3647,U_3646)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK195]),skolemize(U_3645,sK195(U_3648,U_3647,U_3646))],[f_1199_3]) ).

fof(f_1199_5,plain,
    ( ! [U_3646,U_3647,U_3648] :
        ( ~ hBOOL(hAPP_int_bool(U_3647,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK195(U_3648,U_3647,U_3646)),one_one_int)))
        | ~ sP334(U_3646,U_3647,U_3648) )
    & ! [U_3646,U_3647,U_3648] :
        ( hBOOL(hAPP_int_bool(U_3647,sK195(U_3648,U_3647,U_3646)))
        | ~ sP334(U_3646,U_3647,U_3648) )
    & ! [U_3646,U_3647,U_3648] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK195(U_3648,U_3647,U_3646)),U_3646))
        | ~ sP334(U_3646,U_3647,U_3648) )
    & ! [U_3646,U_3647,U_3648] :
        ( ~ hBOOL(hAPP_int_bool(U_3647,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,sK194(U_3648,U_3647,U_3646)),one_one_int)))
        | ~ sP333(U_3646,U_3647,U_3648) )
    & ! [U_3646,U_3647,U_3648] :
        ( hBOOL(hAPP_int_bool(U_3647,sK194(U_3648,U_3647,U_3646)))
        | ~ sP333(U_3646,U_3647,U_3648) )
    & ! [U_3646,U_3647,U_3648] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3646),sK194(U_3648,U_3647,U_3646)))
        | ~ sP333(U_3646,U_3647,U_3648) )
    & ! [U_3646,U_3647,U_3648] :
        ( hBOOL(hAPP_int_bool(U_3647,U_3648))
        | sP334(U_3646,U_3647,U_3648)
        | sP333(U_3646,U_3647,U_3648)
        | ~ hBOOL(hAPP_int_bool(U_3647,U_3646)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP333,sP334])],[f_1199_4]) ).

cnf(f_1199_6,plain,
    ( hBOOL(hAPP_int_bool(U_3647,U_3648))
    | sP334(U_3646,U_3647,U_3648)
    | sP333(U_3646,U_3647,U_3648)
    | ~ hBOOL(hAPP_int_bool(U_3647,U_3646)) ),
    inference(clausify,[status(thm)],[f_1199_5]) ).

cnf(f_1199_7,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3646),sK194(U_3648,U_3647,U_3646)))
    | ~ sP333(U_3646,U_3647,U_3648) ),
    inference(clausify,[status(thm)],[f_1199_5]) ).

cnf(f_1199_8,plain,
    ( hBOOL(hAPP_int_bool(U_3647,sK194(U_3648,U_3647,U_3646)))
    | ~ sP333(U_3646,U_3647,U_3648) ),
    inference(clausify,[status(thm)],[f_1199_5]) ).

cnf(f_1199_9,plain,
    ( ~ hBOOL(hAPP_int_bool(U_3647,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,sK194(U_3648,U_3647,U_3646)),one_one_int)))
    | ~ sP333(U_3646,U_3647,U_3648) ),
    inference(clausify,[status(thm)],[f_1199_5]) ).

cnf(f_1199_10,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,sK195(U_3648,U_3647,U_3646)),U_3646))
    | ~ sP334(U_3646,U_3647,U_3648) ),
    inference(clausify,[status(thm)],[f_1199_5]) ).

cnf(f_1199_11,plain,
    ( hBOOL(hAPP_int_bool(U_3647,sK195(U_3648,U_3647,U_3646)))
    | ~ sP334(U_3646,U_3647,U_3648) ),
    inference(clausify,[status(thm)],[f_1199_5]) ).

cnf(f_1199_12,plain,
    ( ~ hBOOL(hAPP_int_bool(U_3647,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK195(U_3648,U_3647,U_3646)),one_one_int)))
    | ~ sP334(U_3646,U_3647,U_3648) ),
    inference(clausify,[status(thm)],[f_1199_5]) ).

fof(f_1200_1,plain,
    ! [Pa,P1,D_1] :
      ( ? [X1] : hBOOL(hAPP_int_bool(Pa,X1))
      | ! [X1] : ~ hBOOL(hAPP_int_bool(P1,X1))
      | ! [Z_3] :
        ? [X_2] :
          ( ( ( ~ hBOOL(hAPP_int_bool(Pa,X_2))
              & hBOOL(hAPP_int_bool(P1,X_2)) )
            | ( ~ hBOOL(hAPP_int_bool(P1,X_2))
              & hBOOL(hAPP_int_bool(Pa,X_2)) ) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_2),Z_3)) )
      | ? [X_2,K_2] :
          ( ( ~ hBOOL(hAPP_int_bool(P1,X_2))
            & hBOOL(hAPP_int_bool(P1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),D_1)))) )
          | ( ~ hBOOL(hAPP_int_bool(P1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),D_1))))
            & hBOOL(hAPP_int_bool(P1,X_2)) ) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1093_minusinfinity]) ).

fof(f_1200_2,plain,
    ! [U_3657,U_3656,U_3655] :
      ( ? [U_3654] : hBOOL(hAPP_int_bool(U_3657,U_3654))
      | ! [U_3653] : ~ hBOOL(hAPP_int_bool(U_3656,U_3653))
      | ! [U_3652] :
        ? [U_3651] :
          ( ( ( ~ hBOOL(hAPP_int_bool(U_3657,U_3651))
              & hBOOL(hAPP_int_bool(U_3656,U_3651)) )
            | ( ~ hBOOL(hAPP_int_bool(U_3656,U_3651))
              & hBOOL(hAPP_int_bool(U_3657,U_3651)) ) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3651),U_3652)) )
      | ? [U_3650,U_3649] :
          ( ( ~ hBOOL(hAPP_int_bool(U_3656,U_3650))
            & hBOOL(hAPP_int_bool(U_3656,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3650),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3649),U_3655)))) )
          | ( ~ hBOOL(hAPP_int_bool(U_3656,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3650),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3649),U_3655))))
            & hBOOL(hAPP_int_bool(U_3656,U_3650)) ) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3655)) ),
    inference(variable_rename,[status(thm)],[f_1200_1]) ).

fof(f_1200_3,plain,
    ! [U_3657,U_3656,U_3655] :
      ( ? [U_3654] : hBOOL(hAPP_int_bool(U_3657,U_3654))
      | ! [U_3653] : ~ hBOOL(hAPP_int_bool(U_3656,U_3653))
      | ! [U_3652] :
        ? [U_3651] :
          ( ( ( ~ hBOOL(hAPP_int_bool(U_3657,U_3651))
              & hBOOL(hAPP_int_bool(U_3656,U_3651)) )
            | ( ~ hBOOL(hAPP_int_bool(U_3656,U_3651))
              & hBOOL(hAPP_int_bool(U_3657,U_3651)) ) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3651),U_3652)) )
      | ? [U_3661] :
          ( ? [U_3659] : hBOOL(hAPP_int_bool(U_3656,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3661),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3659),U_3655))))
          & ~ hBOOL(hAPP_int_bool(U_3656,U_3661)) )
      | ? [U_3660] :
          ( ? [U_3658] : ~ hBOOL(hAPP_int_bool(U_3656,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3660),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3658),U_3655))))
          & hBOOL(hAPP_int_bool(U_3656,U_3660)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3655)) ),
    inference(miniscope,[status(thm)],[f_1200_2]) ).

fof(f_1200_4,plain,
    ! [U_3657,U_3656,U_3655] :
      ( ? [U_3654] : hBOOL(hAPP_int_bool(U_3657,U_3654))
      | ! [U_3653] : ~ hBOOL(hAPP_int_bool(U_3656,U_3653))
      | ! [U_3652] :
        ? [U_3651] :
          ( ( ( ~ hBOOL(hAPP_int_bool(U_3657,U_3651))
              & hBOOL(hAPP_int_bool(U_3656,U_3651)) )
            | ( ~ hBOOL(hAPP_int_bool(U_3656,U_3651))
              & hBOOL(hAPP_int_bool(U_3657,U_3651)) ) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3651),U_3652)) )
      | ? [U_3661] :
          ( ? [U_3659] : hBOOL(hAPP_int_bool(U_3656,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3661),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3659),U_3655))))
          & ~ hBOOL(hAPP_int_bool(U_3656,U_3661)) )
      | ( ? [U_3658] : ~ hBOOL(hAPP_int_bool(U_3656,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK196(U_3657,U_3656,U_3655)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3658),U_3655))))
        & hBOOL(hAPP_int_bool(U_3656,sK196(U_3657,U_3656,U_3655))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3655)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK196]),skolemize(U_3660,sK196(U_3657,U_3656,U_3655))],[f_1200_3]) ).

fof(f_1200_5,plain,
    ! [U_3657,U_3656,U_3655] :
      ( ? [U_3654] : hBOOL(hAPP_int_bool(U_3657,U_3654))
      | ! [U_3653] : ~ hBOOL(hAPP_int_bool(U_3656,U_3653))
      | ! [U_3652] :
        ? [U_3651] :
          ( ( ( ~ hBOOL(hAPP_int_bool(U_3657,U_3651))
              & hBOOL(hAPP_int_bool(U_3656,U_3651)) )
            | ( ~ hBOOL(hAPP_int_bool(U_3656,U_3651))
              & hBOOL(hAPP_int_bool(U_3657,U_3651)) ) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3651),U_3652)) )
      | ? [U_3661] :
          ( ? [U_3659] : hBOOL(hAPP_int_bool(U_3656,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3661),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3659),U_3655))))
          & ~ hBOOL(hAPP_int_bool(U_3656,U_3661)) )
      | ( ~ hBOOL(hAPP_int_bool(U_3656,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK196(U_3657,U_3656,U_3655)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK197(U_3657,U_3656,U_3655)),U_3655))))
        & hBOOL(hAPP_int_bool(U_3656,sK196(U_3657,U_3656,U_3655))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3655)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK197]),skolemize(U_3658,sK197(U_3657,U_3656,U_3655))],[f_1200_4]) ).

fof(f_1200_6,plain,
    ! [U_3657,U_3656,U_3655] :
      ( ? [U_3654] : hBOOL(hAPP_int_bool(U_3657,U_3654))
      | ! [U_3653] : ~ hBOOL(hAPP_int_bool(U_3656,U_3653))
      | ! [U_3652] :
        ? [U_3651] :
          ( ( ( ~ hBOOL(hAPP_int_bool(U_3657,U_3651))
              & hBOOL(hAPP_int_bool(U_3656,U_3651)) )
            | ( ~ hBOOL(hAPP_int_bool(U_3656,U_3651))
              & hBOOL(hAPP_int_bool(U_3657,U_3651)) ) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3651),U_3652)) )
      | ( ? [U_3659] : hBOOL(hAPP_int_bool(U_3656,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK198(U_3657,U_3656,U_3655)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3659),U_3655))))
        & ~ hBOOL(hAPP_int_bool(U_3656,sK198(U_3657,U_3656,U_3655))) )
      | ( ~ hBOOL(hAPP_int_bool(U_3656,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK196(U_3657,U_3656,U_3655)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK197(U_3657,U_3656,U_3655)),U_3655))))
        & hBOOL(hAPP_int_bool(U_3656,sK196(U_3657,U_3656,U_3655))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3655)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK198]),skolemize(U_3661,sK198(U_3657,U_3656,U_3655))],[f_1200_5]) ).

fof(f_1200_7,plain,
    ! [U_3657,U_3656,U_3655] :
      ( ? [U_3654] : hBOOL(hAPP_int_bool(U_3657,U_3654))
      | ! [U_3653] : ~ hBOOL(hAPP_int_bool(U_3656,U_3653))
      | ! [U_3652] :
        ? [U_3651] :
          ( ( ( ~ hBOOL(hAPP_int_bool(U_3657,U_3651))
              & hBOOL(hAPP_int_bool(U_3656,U_3651)) )
            | ( ~ hBOOL(hAPP_int_bool(U_3656,U_3651))
              & hBOOL(hAPP_int_bool(U_3657,U_3651)) ) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3651),U_3652)) )
      | ( hBOOL(hAPP_int_bool(U_3656,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK198(U_3657,U_3656,U_3655)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK199(U_3657,U_3656,U_3655)),U_3655))))
        & ~ hBOOL(hAPP_int_bool(U_3656,sK198(U_3657,U_3656,U_3655))) )
      | ( ~ hBOOL(hAPP_int_bool(U_3656,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK196(U_3657,U_3656,U_3655)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK197(U_3657,U_3656,U_3655)),U_3655))))
        & hBOOL(hAPP_int_bool(U_3656,sK196(U_3657,U_3656,U_3655))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3655)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK199]),skolemize(U_3659,sK199(U_3657,U_3656,U_3655))],[f_1200_6]) ).

fof(f_1200_8,plain,
    ! [U_3657,U_3656,U_3655] :
      ( ? [U_3654] : hBOOL(hAPP_int_bool(U_3657,U_3654))
      | ! [U_3653] : ~ hBOOL(hAPP_int_bool(U_3656,U_3653))
      | ! [U_3652] :
          ( ( ( ~ hBOOL(hAPP_int_bool(U_3657,sK200(U_3657,U_3656,U_3655,U_3652)))
              & hBOOL(hAPP_int_bool(U_3656,sK200(U_3657,U_3656,U_3655,U_3652))) )
            | ( ~ hBOOL(hAPP_int_bool(U_3656,sK200(U_3657,U_3656,U_3655,U_3652)))
              & hBOOL(hAPP_int_bool(U_3657,sK200(U_3657,U_3656,U_3655,U_3652))) ) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK200(U_3657,U_3656,U_3655,U_3652)),U_3652)) )
      | ( hBOOL(hAPP_int_bool(U_3656,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK198(U_3657,U_3656,U_3655)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK199(U_3657,U_3656,U_3655)),U_3655))))
        & ~ hBOOL(hAPP_int_bool(U_3656,sK198(U_3657,U_3656,U_3655))) )
      | ( ~ hBOOL(hAPP_int_bool(U_3656,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK196(U_3657,U_3656,U_3655)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK197(U_3657,U_3656,U_3655)),U_3655))))
        & hBOOL(hAPP_int_bool(U_3656,sK196(U_3657,U_3656,U_3655))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3655)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK200]),skolemize(U_3651,sK200(U_3657,U_3656,U_3655,U_3652))],[f_1200_7]) ).

fof(f_1200_9,plain,
    ! [U_3657,U_3656,U_3655] :
      ( hBOOL(hAPP_int_bool(U_3657,sK201(U_3657,U_3656,U_3655)))
      | ! [U_3653] : ~ hBOOL(hAPP_int_bool(U_3656,U_3653))
      | ! [U_3652] :
          ( ( ( ~ hBOOL(hAPP_int_bool(U_3657,sK200(U_3657,U_3656,U_3655,U_3652)))
              & hBOOL(hAPP_int_bool(U_3656,sK200(U_3657,U_3656,U_3655,U_3652))) )
            | ( ~ hBOOL(hAPP_int_bool(U_3656,sK200(U_3657,U_3656,U_3655,U_3652)))
              & hBOOL(hAPP_int_bool(U_3657,sK200(U_3657,U_3656,U_3655,U_3652))) ) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK200(U_3657,U_3656,U_3655,U_3652)),U_3652)) )
      | ( hBOOL(hAPP_int_bool(U_3656,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK198(U_3657,U_3656,U_3655)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK199(U_3657,U_3656,U_3655)),U_3655))))
        & ~ hBOOL(hAPP_int_bool(U_3656,sK198(U_3657,U_3656,U_3655))) )
      | ( ~ hBOOL(hAPP_int_bool(U_3656,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK196(U_3657,U_3656,U_3655)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK197(U_3657,U_3656,U_3655)),U_3655))))
        & hBOOL(hAPP_int_bool(U_3656,sK196(U_3657,U_3656,U_3655))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3655)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK201]),skolemize(U_3654,sK201(U_3657,U_3656,U_3655))],[f_1200_8]) ).

fof(f_1200_10,plain,
    ( ! [U_3656,U_3655,U_3652,U_3657] :
        ( ~ hBOOL(hAPP_int_bool(U_3657,sK200(U_3657,U_3656,U_3655,U_3652)))
        | ~ sP338(U_3656,U_3655,U_3652,U_3657) )
    & ! [U_3656,U_3655,U_3652,U_3657] :
        ( hBOOL(hAPP_int_bool(U_3656,sK200(U_3657,U_3656,U_3655,U_3652)))
        | ~ sP338(U_3656,U_3655,U_3652,U_3657) )
    & ! [U_3656,U_3655,U_3652,U_3657] :
        ( ~ hBOOL(hAPP_int_bool(U_3656,sK200(U_3657,U_3656,U_3655,U_3652)))
        | ~ sP337(U_3656,U_3655,U_3652,U_3657) )
    & ! [U_3656,U_3655,U_3652,U_3657] :
        ( hBOOL(hAPP_int_bool(U_3657,sK200(U_3657,U_3656,U_3655,U_3652)))
        | ~ sP337(U_3656,U_3655,U_3652,U_3657) )
    & ! [U_3656,U_3655,U_3652,U_3657] :
        ( sP338(U_3656,U_3655,U_3652,U_3657)
        | sP337(U_3656,U_3655,U_3652,U_3657)
        | ~ sP339(U_3656,U_3655,U_3652,U_3657) )
    & ! [U_3656,U_3655,U_3652,U_3657] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK200(U_3657,U_3656,U_3655,U_3652)),U_3652))
        | ~ sP339(U_3656,U_3655,U_3652,U_3657) )
    & ! [U_3656,U_3655,U_3657] :
        ( hBOOL(hAPP_int_bool(U_3656,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK198(U_3657,U_3656,U_3655)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK199(U_3657,U_3656,U_3655)),U_3655))))
        | ~ sP336(U_3656,U_3655,U_3657) )
    & ! [U_3656,U_3655,U_3657] :
        ( ~ hBOOL(hAPP_int_bool(U_3656,sK198(U_3657,U_3656,U_3655)))
        | ~ sP336(U_3656,U_3655,U_3657) )
    & ! [U_3656,U_3655,U_3657] :
        ( ~ hBOOL(hAPP_int_bool(U_3656,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK196(U_3657,U_3656,U_3655)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK197(U_3657,U_3656,U_3655)),U_3655))))
        | ~ sP335(U_3656,U_3655,U_3657) )
    & ! [U_3656,U_3655,U_3657] :
        ( hBOOL(hAPP_int_bool(U_3656,sK196(U_3657,U_3656,U_3655)))
        | ~ sP335(U_3656,U_3655,U_3657) )
    & ! [U_3656,U_3653,U_3655,U_3652,U_3657] :
        ( hBOOL(hAPP_int_bool(U_3657,sK201(U_3657,U_3656,U_3655)))
        | ~ hBOOL(hAPP_int_bool(U_3656,U_3653))
        | sP339(U_3656,U_3655,U_3652,U_3657)
        | sP336(U_3656,U_3655,U_3657)
        | sP335(U_3656,U_3655,U_3657)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3655)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP335,sP336,sP337,sP338,sP339])],[f_1200_9]) ).

cnf(f_1200_11,plain,
    ( hBOOL(hAPP_int_bool(U_3657,sK201(U_3657,U_3656,U_3655)))
    | ~ hBOOL(hAPP_int_bool(U_3656,U_3653))
    | sP339(U_3656,U_3655,U_3652,U_3657)
    | sP336(U_3656,U_3655,U_3657)
    | sP335(U_3656,U_3655,U_3657)
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3655)) ),
    inference(clausify,[status(thm)],[f_1200_10]) ).

cnf(f_1200_12,plain,
    ( hBOOL(hAPP_int_bool(U_3656,sK196(U_3657,U_3656,U_3655)))
    | ~ sP335(U_3656,U_3655,U_3657) ),
    inference(clausify,[status(thm)],[f_1200_10]) ).

cnf(f_1200_13,plain,
    ( ~ hBOOL(hAPP_int_bool(U_3656,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK196(U_3657,U_3656,U_3655)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK197(U_3657,U_3656,U_3655)),U_3655))))
    | ~ sP335(U_3656,U_3655,U_3657) ),
    inference(clausify,[status(thm)],[f_1200_10]) ).

cnf(f_1200_14,plain,
    ( ~ hBOOL(hAPP_int_bool(U_3656,sK198(U_3657,U_3656,U_3655)))
    | ~ sP336(U_3656,U_3655,U_3657) ),
    inference(clausify,[status(thm)],[f_1200_10]) ).

cnf(f_1200_15,plain,
    ( hBOOL(hAPP_int_bool(U_3656,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK198(U_3657,U_3656,U_3655)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK199(U_3657,U_3656,U_3655)),U_3655))))
    | ~ sP336(U_3656,U_3655,U_3657) ),
    inference(clausify,[status(thm)],[f_1200_10]) ).

cnf(f_1200_16,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,sK200(U_3657,U_3656,U_3655,U_3652)),U_3652))
    | ~ sP339(U_3656,U_3655,U_3652,U_3657) ),
    inference(clausify,[status(thm)],[f_1200_10]) ).

cnf(f_1200_17,plain,
    ( sP338(U_3656,U_3655,U_3652,U_3657)
    | sP337(U_3656,U_3655,U_3652,U_3657)
    | ~ sP339(U_3656,U_3655,U_3652,U_3657) ),
    inference(clausify,[status(thm)],[f_1200_10]) ).

cnf(f_1200_18,plain,
    ( hBOOL(hAPP_int_bool(U_3657,sK200(U_3657,U_3656,U_3655,U_3652)))
    | ~ sP337(U_3656,U_3655,U_3652,U_3657) ),
    inference(clausify,[status(thm)],[f_1200_10]) ).

cnf(f_1200_19,plain,
    ( ~ hBOOL(hAPP_int_bool(U_3656,sK200(U_3657,U_3656,U_3655,U_3652)))
    | ~ sP337(U_3656,U_3655,U_3652,U_3657) ),
    inference(clausify,[status(thm)],[f_1200_10]) ).

cnf(f_1200_20,plain,
    ( hBOOL(hAPP_int_bool(U_3656,sK200(U_3657,U_3656,U_3655,U_3652)))
    | ~ sP338(U_3656,U_3655,U_3652,U_3657) ),
    inference(clausify,[status(thm)],[f_1200_10]) ).

cnf(f_1200_21,plain,
    ( ~ hBOOL(hAPP_int_bool(U_3657,sK200(U_3657,U_3656,U_3655,U_3652)))
    | ~ sP338(U_3656,U_3655,U_3652,U_3657) ),
    inference(clausify,[status(thm)],[f_1200_10]) ).

fof(f_1201_1,plain,
    ! [Pa,P_1,D_1] :
      ( ? [X1] : hBOOL(hAPP_int_bool(Pa,X1))
      | ! [X1] : ~ hBOOL(hAPP_int_bool(P_1,X1))
      | ! [Z_3] :
        ? [X_2] :
          ( ( ( ~ hBOOL(hAPP_int_bool(Pa,X_2))
              & hBOOL(hAPP_int_bool(P_1,X_2)) )
            | ( ~ hBOOL(hAPP_int_bool(P_1,X_2))
              & hBOOL(hAPP_int_bool(Pa,X_2)) ) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_3),X_2)) )
      | ? [X_2,K_2] :
          ( ( ~ hBOOL(hAPP_int_bool(P_1,X_2))
            & hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),D_1)))) )
          | ( ~ hBOOL(hAPP_int_bool(P_1,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X_2),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,K_2),D_1))))
            & hBOOL(hAPP_int_bool(P_1,X_2)) ) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1094_plusinfinity]) ).

fof(f_1201_2,plain,
    ! [U_3670,U_3669,U_3668] :
      ( ? [U_3667] : hBOOL(hAPP_int_bool(U_3670,U_3667))
      | ! [U_3666] : ~ hBOOL(hAPP_int_bool(U_3669,U_3666))
      | ! [U_3665] :
        ? [U_3664] :
          ( ( ( ~ hBOOL(hAPP_int_bool(U_3670,U_3664))
              & hBOOL(hAPP_int_bool(U_3669,U_3664)) )
            | ( ~ hBOOL(hAPP_int_bool(U_3669,U_3664))
              & hBOOL(hAPP_int_bool(U_3670,U_3664)) ) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3665),U_3664)) )
      | ? [U_3663,U_3662] :
          ( ( ~ hBOOL(hAPP_int_bool(U_3669,U_3663))
            & hBOOL(hAPP_int_bool(U_3669,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3663),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3662),U_3668)))) )
          | ( ~ hBOOL(hAPP_int_bool(U_3669,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3663),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3662),U_3668))))
            & hBOOL(hAPP_int_bool(U_3669,U_3663)) ) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3668)) ),
    inference(variable_rename,[status(thm)],[f_1201_1]) ).

fof(f_1201_3,plain,
    ! [U_3670,U_3669,U_3668] :
      ( ? [U_3667] : hBOOL(hAPP_int_bool(U_3670,U_3667))
      | ! [U_3666] : ~ hBOOL(hAPP_int_bool(U_3669,U_3666))
      | ! [U_3665] :
        ? [U_3664] :
          ( ( ( ~ hBOOL(hAPP_int_bool(U_3670,U_3664))
              & hBOOL(hAPP_int_bool(U_3669,U_3664)) )
            | ( ~ hBOOL(hAPP_int_bool(U_3669,U_3664))
              & hBOOL(hAPP_int_bool(U_3670,U_3664)) ) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3665),U_3664)) )
      | ? [U_3674] :
          ( ? [U_3672] : hBOOL(hAPP_int_bool(U_3669,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3674),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3672),U_3668))))
          & ~ hBOOL(hAPP_int_bool(U_3669,U_3674)) )
      | ? [U_3673] :
          ( ? [U_3671] : ~ hBOOL(hAPP_int_bool(U_3669,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3673),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3671),U_3668))))
          & hBOOL(hAPP_int_bool(U_3669,U_3673)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3668)) ),
    inference(miniscope,[status(thm)],[f_1201_2]) ).

fof(f_1201_4,plain,
    ! [U_3670,U_3669,U_3668] :
      ( ? [U_3667] : hBOOL(hAPP_int_bool(U_3670,U_3667))
      | ! [U_3666] : ~ hBOOL(hAPP_int_bool(U_3669,U_3666))
      | ! [U_3665] :
        ? [U_3664] :
          ( ( ( ~ hBOOL(hAPP_int_bool(U_3670,U_3664))
              & hBOOL(hAPP_int_bool(U_3669,U_3664)) )
            | ( ~ hBOOL(hAPP_int_bool(U_3669,U_3664))
              & hBOOL(hAPP_int_bool(U_3670,U_3664)) ) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3665),U_3664)) )
      | ? [U_3674] :
          ( ? [U_3672] : hBOOL(hAPP_int_bool(U_3669,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3674),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3672),U_3668))))
          & ~ hBOOL(hAPP_int_bool(U_3669,U_3674)) )
      | ( ? [U_3671] : ~ hBOOL(hAPP_int_bool(U_3669,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK202(U_3670,U_3669,U_3668)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3671),U_3668))))
        & hBOOL(hAPP_int_bool(U_3669,sK202(U_3670,U_3669,U_3668))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3668)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK202]),skolemize(U_3673,sK202(U_3670,U_3669,U_3668))],[f_1201_3]) ).

fof(f_1201_5,plain,
    ! [U_3670,U_3669,U_3668] :
      ( ? [U_3667] : hBOOL(hAPP_int_bool(U_3670,U_3667))
      | ! [U_3666] : ~ hBOOL(hAPP_int_bool(U_3669,U_3666))
      | ! [U_3665] :
        ? [U_3664] :
          ( ( ( ~ hBOOL(hAPP_int_bool(U_3670,U_3664))
              & hBOOL(hAPP_int_bool(U_3669,U_3664)) )
            | ( ~ hBOOL(hAPP_int_bool(U_3669,U_3664))
              & hBOOL(hAPP_int_bool(U_3670,U_3664)) ) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3665),U_3664)) )
      | ? [U_3674] :
          ( ? [U_3672] : hBOOL(hAPP_int_bool(U_3669,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3674),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3672),U_3668))))
          & ~ hBOOL(hAPP_int_bool(U_3669,U_3674)) )
      | ( ~ hBOOL(hAPP_int_bool(U_3669,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK202(U_3670,U_3669,U_3668)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK203(U_3670,U_3669,U_3668)),U_3668))))
        & hBOOL(hAPP_int_bool(U_3669,sK202(U_3670,U_3669,U_3668))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3668)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK203]),skolemize(U_3671,sK203(U_3670,U_3669,U_3668))],[f_1201_4]) ).

fof(f_1201_6,plain,
    ! [U_3670,U_3669,U_3668] :
      ( ? [U_3667] : hBOOL(hAPP_int_bool(U_3670,U_3667))
      | ! [U_3666] : ~ hBOOL(hAPP_int_bool(U_3669,U_3666))
      | ! [U_3665] :
        ? [U_3664] :
          ( ( ( ~ hBOOL(hAPP_int_bool(U_3670,U_3664))
              & hBOOL(hAPP_int_bool(U_3669,U_3664)) )
            | ( ~ hBOOL(hAPP_int_bool(U_3669,U_3664))
              & hBOOL(hAPP_int_bool(U_3670,U_3664)) ) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3665),U_3664)) )
      | ( ? [U_3672] : hBOOL(hAPP_int_bool(U_3669,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK204(U_3670,U_3669,U_3668)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3672),U_3668))))
        & ~ hBOOL(hAPP_int_bool(U_3669,sK204(U_3670,U_3669,U_3668))) )
      | ( ~ hBOOL(hAPP_int_bool(U_3669,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK202(U_3670,U_3669,U_3668)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK203(U_3670,U_3669,U_3668)),U_3668))))
        & hBOOL(hAPP_int_bool(U_3669,sK202(U_3670,U_3669,U_3668))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3668)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK204]),skolemize(U_3674,sK204(U_3670,U_3669,U_3668))],[f_1201_5]) ).

fof(f_1201_7,plain,
    ! [U_3670,U_3669,U_3668] :
      ( ? [U_3667] : hBOOL(hAPP_int_bool(U_3670,U_3667))
      | ! [U_3666] : ~ hBOOL(hAPP_int_bool(U_3669,U_3666))
      | ! [U_3665] :
        ? [U_3664] :
          ( ( ( ~ hBOOL(hAPP_int_bool(U_3670,U_3664))
              & hBOOL(hAPP_int_bool(U_3669,U_3664)) )
            | ( ~ hBOOL(hAPP_int_bool(U_3669,U_3664))
              & hBOOL(hAPP_int_bool(U_3670,U_3664)) ) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3665),U_3664)) )
      | ( hBOOL(hAPP_int_bool(U_3669,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK204(U_3670,U_3669,U_3668)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK205(U_3670,U_3669,U_3668)),U_3668))))
        & ~ hBOOL(hAPP_int_bool(U_3669,sK204(U_3670,U_3669,U_3668))) )
      | ( ~ hBOOL(hAPP_int_bool(U_3669,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK202(U_3670,U_3669,U_3668)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK203(U_3670,U_3669,U_3668)),U_3668))))
        & hBOOL(hAPP_int_bool(U_3669,sK202(U_3670,U_3669,U_3668))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3668)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK205]),skolemize(U_3672,sK205(U_3670,U_3669,U_3668))],[f_1201_6]) ).

fof(f_1201_8,plain,
    ! [U_3670,U_3669,U_3668] :
      ( ? [U_3667] : hBOOL(hAPP_int_bool(U_3670,U_3667))
      | ! [U_3666] : ~ hBOOL(hAPP_int_bool(U_3669,U_3666))
      | ! [U_3665] :
          ( ( ( ~ hBOOL(hAPP_int_bool(U_3670,sK206(U_3670,U_3669,U_3668,U_3665)))
              & hBOOL(hAPP_int_bool(U_3669,sK206(U_3670,U_3669,U_3668,U_3665))) )
            | ( ~ hBOOL(hAPP_int_bool(U_3669,sK206(U_3670,U_3669,U_3668,U_3665)))
              & hBOOL(hAPP_int_bool(U_3670,sK206(U_3670,U_3669,U_3668,U_3665))) ) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3665),sK206(U_3670,U_3669,U_3668,U_3665))) )
      | ( hBOOL(hAPP_int_bool(U_3669,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK204(U_3670,U_3669,U_3668)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK205(U_3670,U_3669,U_3668)),U_3668))))
        & ~ hBOOL(hAPP_int_bool(U_3669,sK204(U_3670,U_3669,U_3668))) )
      | ( ~ hBOOL(hAPP_int_bool(U_3669,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK202(U_3670,U_3669,U_3668)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK203(U_3670,U_3669,U_3668)),U_3668))))
        & hBOOL(hAPP_int_bool(U_3669,sK202(U_3670,U_3669,U_3668))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3668)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK206]),skolemize(U_3664,sK206(U_3670,U_3669,U_3668,U_3665))],[f_1201_7]) ).

fof(f_1201_9,plain,
    ! [U_3670,U_3669,U_3668] :
      ( hBOOL(hAPP_int_bool(U_3670,sK207(U_3670,U_3669,U_3668)))
      | ! [U_3666] : ~ hBOOL(hAPP_int_bool(U_3669,U_3666))
      | ! [U_3665] :
          ( ( ( ~ hBOOL(hAPP_int_bool(U_3670,sK206(U_3670,U_3669,U_3668,U_3665)))
              & hBOOL(hAPP_int_bool(U_3669,sK206(U_3670,U_3669,U_3668,U_3665))) )
            | ( ~ hBOOL(hAPP_int_bool(U_3669,sK206(U_3670,U_3669,U_3668,U_3665)))
              & hBOOL(hAPP_int_bool(U_3670,sK206(U_3670,U_3669,U_3668,U_3665))) ) )
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3665),sK206(U_3670,U_3669,U_3668,U_3665))) )
      | ( hBOOL(hAPP_int_bool(U_3669,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK204(U_3670,U_3669,U_3668)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK205(U_3670,U_3669,U_3668)),U_3668))))
        & ~ hBOOL(hAPP_int_bool(U_3669,sK204(U_3670,U_3669,U_3668))) )
      | ( ~ hBOOL(hAPP_int_bool(U_3669,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK202(U_3670,U_3669,U_3668)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK203(U_3670,U_3669,U_3668)),U_3668))))
        & hBOOL(hAPP_int_bool(U_3669,sK202(U_3670,U_3669,U_3668))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3668)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK207]),skolemize(U_3667,sK207(U_3670,U_3669,U_3668))],[f_1201_8]) ).

fof(f_1201_10,plain,
    ( ! [U_3665,U_3669,U_3670,U_3668] :
        ( ~ hBOOL(hAPP_int_bool(U_3670,sK206(U_3670,U_3669,U_3668,U_3665)))
        | ~ sP343(U_3665,U_3669,U_3670,U_3668) )
    & ! [U_3665,U_3669,U_3670,U_3668] :
        ( hBOOL(hAPP_int_bool(U_3669,sK206(U_3670,U_3669,U_3668,U_3665)))
        | ~ sP343(U_3665,U_3669,U_3670,U_3668) )
    & ! [U_3665,U_3669,U_3670,U_3668] :
        ( ~ hBOOL(hAPP_int_bool(U_3669,sK206(U_3670,U_3669,U_3668,U_3665)))
        | ~ sP342(U_3665,U_3669,U_3670,U_3668) )
    & ! [U_3665,U_3669,U_3670,U_3668] :
        ( hBOOL(hAPP_int_bool(U_3670,sK206(U_3670,U_3669,U_3668,U_3665)))
        | ~ sP342(U_3665,U_3669,U_3670,U_3668) )
    & ! [U_3665,U_3669,U_3670,U_3668] :
        ( sP343(U_3665,U_3669,U_3670,U_3668)
        | sP342(U_3665,U_3669,U_3670,U_3668)
        | ~ sP344(U_3665,U_3669,U_3670,U_3668) )
    & ! [U_3665,U_3669,U_3670,U_3668] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3665),sK206(U_3670,U_3669,U_3668,U_3665)))
        | ~ sP344(U_3665,U_3669,U_3670,U_3668) )
    & ! [U_3669,U_3670,U_3668] :
        ( hBOOL(hAPP_int_bool(U_3669,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK204(U_3670,U_3669,U_3668)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK205(U_3670,U_3669,U_3668)),U_3668))))
        | ~ sP341(U_3669,U_3670,U_3668) )
    & ! [U_3669,U_3670,U_3668] :
        ( ~ hBOOL(hAPP_int_bool(U_3669,sK204(U_3670,U_3669,U_3668)))
        | ~ sP341(U_3669,U_3670,U_3668) )
    & ! [U_3669,U_3670,U_3668] :
        ( ~ hBOOL(hAPP_int_bool(U_3669,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK202(U_3670,U_3669,U_3668)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK203(U_3670,U_3669,U_3668)),U_3668))))
        | ~ sP340(U_3669,U_3670,U_3668) )
    & ! [U_3669,U_3670,U_3668] :
        ( hBOOL(hAPP_int_bool(U_3669,sK202(U_3670,U_3669,U_3668)))
        | ~ sP340(U_3669,U_3670,U_3668) )
    & ! [U_3665,U_3666,U_3669,U_3670,U_3668] :
        ( hBOOL(hAPP_int_bool(U_3670,sK207(U_3670,U_3669,U_3668)))
        | ~ hBOOL(hAPP_int_bool(U_3669,U_3666))
        | sP344(U_3665,U_3669,U_3670,U_3668)
        | sP341(U_3669,U_3670,U_3668)
        | sP340(U_3669,U_3670,U_3668)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3668)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP340,sP341,sP342,sP343,sP344])],[f_1201_9]) ).

cnf(f_1201_11,plain,
    ( hBOOL(hAPP_int_bool(U_3670,sK207(U_3670,U_3669,U_3668)))
    | ~ hBOOL(hAPP_int_bool(U_3669,U_3666))
    | sP344(U_3665,U_3669,U_3670,U_3668)
    | sP341(U_3669,U_3670,U_3668)
    | sP340(U_3669,U_3670,U_3668)
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3668)) ),
    inference(clausify,[status(thm)],[f_1201_10]) ).

cnf(f_1201_12,plain,
    ( hBOOL(hAPP_int_bool(U_3669,sK202(U_3670,U_3669,U_3668)))
    | ~ sP340(U_3669,U_3670,U_3668) ),
    inference(clausify,[status(thm)],[f_1201_10]) ).

cnf(f_1201_13,plain,
    ( ~ hBOOL(hAPP_int_bool(U_3669,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK202(U_3670,U_3669,U_3668)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK203(U_3670,U_3669,U_3668)),U_3668))))
    | ~ sP340(U_3669,U_3670,U_3668) ),
    inference(clausify,[status(thm)],[f_1201_10]) ).

cnf(f_1201_14,plain,
    ( ~ hBOOL(hAPP_int_bool(U_3669,sK204(U_3670,U_3669,U_3668)))
    | ~ sP341(U_3669,U_3670,U_3668) ),
    inference(clausify,[status(thm)],[f_1201_10]) ).

cnf(f_1201_15,plain,
    ( hBOOL(hAPP_int_bool(U_3669,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,sK204(U_3670,U_3669,U_3668)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,sK205(U_3670,U_3669,U_3668)),U_3668))))
    | ~ sP341(U_3669,U_3670,U_3668) ),
    inference(clausify,[status(thm)],[f_1201_10]) ).

cnf(f_1201_16,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3665),sK206(U_3670,U_3669,U_3668,U_3665)))
    | ~ sP344(U_3665,U_3669,U_3670,U_3668) ),
    inference(clausify,[status(thm)],[f_1201_10]) ).

cnf(f_1201_17,plain,
    ( sP343(U_3665,U_3669,U_3670,U_3668)
    | sP342(U_3665,U_3669,U_3670,U_3668)
    | ~ sP344(U_3665,U_3669,U_3670,U_3668) ),
    inference(clausify,[status(thm)],[f_1201_10]) ).

cnf(f_1201_18,plain,
    ( hBOOL(hAPP_int_bool(U_3670,sK206(U_3670,U_3669,U_3668,U_3665)))
    | ~ sP342(U_3665,U_3669,U_3670,U_3668) ),
    inference(clausify,[status(thm)],[f_1201_10]) ).

cnf(f_1201_19,plain,
    ( ~ hBOOL(hAPP_int_bool(U_3669,sK206(U_3670,U_3669,U_3668,U_3665)))
    | ~ sP342(U_3665,U_3669,U_3670,U_3668) ),
    inference(clausify,[status(thm)],[f_1201_10]) ).

cnf(f_1201_20,plain,
    ( hBOOL(hAPP_int_bool(U_3669,sK206(U_3670,U_3669,U_3668,U_3665)))
    | ~ sP343(U_3665,U_3669,U_3670,U_3668) ),
    inference(clausify,[status(thm)],[f_1201_10]) ).

cnf(f_1201_21,plain,
    ( ~ hBOOL(hAPP_int_bool(U_3670,sK206(U_3670,U_3669,U_3668,U_3665)))
    | ~ sP343(U_3665,U_3669,U_3670,U_3668) ),
    inference(clausify,[status(thm)],[f_1201_10]) ).

fof(f_1202_1,plain,
    ! [Y,X] :
      ( ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X),Y) = zero_zero_int
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),X)) )
      & ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X),Y) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Y)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),X)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1095_tsub__def]) ).

fof(f_1202_2,plain,
    ! [U_3676,U_3675] :
      ( ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,U_3675),U_3676) = zero_zero_int
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3676),U_3675)) )
      & ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,U_3675),U_3676) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3675),U_3676)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3676),U_3675)) ) ),
    inference(variable_rename,[status(thm)],[f_1202_1]) ).

fof(f_1202_3,plain,
    ( ! [U_3680,U_3678] :
        ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,U_3678),U_3680) = zero_zero_int
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3680),U_3678)) )
    & ! [U_3679,U_3677] :
        ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,U_3677),U_3679) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3677),U_3679)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3679),U_3677)) ) ),
    inference(miniscope,[status(thm)],[f_1202_2]) ).

fof(f_1202_4,plain,
    ( ! [U_3680,U_3678] :
        ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,U_3678),U_3680) = zero_zero_int
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3680),U_3678)) )
    & ! [U_3679,U_3677] :
        ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,U_3677),U_3679) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3677),U_3679)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3679),U_3677)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1202_3]) ).

cnf(f_1202_5,plain,
    ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,U_3677),U_3679) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3677),U_3679)
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3679),U_3677)) ),
    inference(clausify,[status(thm)],[f_1202_4]) ).

cnf(f_1202_6,plain,
    ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,U_3678),U_3680) = zero_zero_int
    | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3680),U_3678)) ),
    inference(clausify,[status(thm)],[f_1202_4]) ).

fof(f_1203_1,plain,
    ! [N] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,N))),
    inference(fof_nnf,[status(thm)],[fact_1096_zero__zle__int]) ).

fof(f_1203_2,plain,
    ! [U_3681] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,U_3681))),
    inference(variable_rename,[status(thm)],[f_1203_1]) ).

fof(f_1203_3,plain,
    ! [U_3681] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,U_3681))),
    inference(definitional_conversion,[status(esa)],[f_1203_2]) ).

cnf(f_1203_4,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,U_3681))),
    inference(clausify,[status(thm)],[f_1203_3]) ).

fof(f_1204_1,plain,
    ! [K_1] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,K_1)),zero_zero_int)),
    inference(fof_nnf,[status(thm)],[fact_1097_int__less__0__conv]) ).

fof(f_1204_2,plain,
    ! [U_3682] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,U_3682)),zero_zero_int)),
    inference(variable_rename,[status(thm)],[f_1204_1]) ).

fof(f_1204_3,plain,
    ! [U_3682] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,U_3682)),zero_zero_int)),
    inference(definitional_conversion,[status(esa)],[f_1204_2]) ).

cnf(f_1204_4,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,U_3682)),zero_zero_int)),
    inference(clausify,[status(thm)],[f_1204_3]) ).

fof(f_1205_1,plain,
    hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int,
    inference(fof_nnf,[status(thm)],[fact_1098_int__1]) ).

fof(f_1205_2,plain,
    hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int,
    inference(definitional_conversion,[status(esa)],[f_1205_1]) ).

cnf(f_1205_3,plain,
    hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int,
    inference(clausify,[status(thm)],[f_1205_2]) ).

fof(f_1206_1,plain,
    hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
    inference(fof_nnf,[status(thm)],[fact_1099_int__0]) ).

fof(f_1206_2,plain,
    hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
    inference(definitional_conversion,[status(esa)],[f_1206_1]) ).

cnf(f_1206_3,plain,
    hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
    inference(clausify,[status(thm)],[f_1206_2]) ).

fof(f_1207_1,plain,
    ! [Na] :
      ( ( hAPP_nat_int(semiri1621563631at_int,Na) = zero_zero_int
        | Na != zero_zero_nat )
      & ( Na = zero_zero_nat
        | hAPP_nat_int(semiri1621563631at_int,Na) != zero_zero_int ) ),
    inference(fof_nnf,[status(thm)],[fact_1100_int__eq__0__conv]) ).

fof(f_1207_2,plain,
    ! [U_3683] :
      ( ( hAPP_nat_int(semiri1621563631at_int,U_3683) = zero_zero_int
        | U_3683 != zero_zero_nat )
      & ( U_3683 = zero_zero_nat
        | hAPP_nat_int(semiri1621563631at_int,U_3683) != zero_zero_int ) ),
    inference(variable_rename,[status(thm)],[f_1207_1]) ).

fof(f_1207_3,plain,
    ( ! [U_3685] :
        ( hAPP_nat_int(semiri1621563631at_int,U_3685) = zero_zero_int
        | U_3685 != zero_zero_nat )
    & ! [U_3684] :
        ( U_3684 = zero_zero_nat
        | hAPP_nat_int(semiri1621563631at_int,U_3684) != zero_zero_int ) ),
    inference(miniscope,[status(thm)],[f_1207_2]) ).

fof(f_1207_4,plain,
    ( ! [U_3685] :
        ( hAPP_nat_int(semiri1621563631at_int,U_3685) = zero_zero_int
        | U_3685 != zero_zero_nat )
    & ! [U_3684] :
        ( U_3684 = zero_zero_nat
        | hAPP_nat_int(semiri1621563631at_int,U_3684) != zero_zero_int ) ),
    inference(definitional_conversion,[status(esa)],[f_1207_3]) ).

cnf(f_1207_5,plain,
    ( U_3684 = zero_zero_nat
    | hAPP_nat_int(semiri1621563631at_int,U_3684) != zero_zero_int ),
    inference(clausify,[status(thm)],[f_1207_4]) ).

cnf(f_1207_6,plain,
    ( hAPP_nat_int(semiri1621563631at_int,U_3685) = zero_zero_int
    | U_3685 != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1207_4]) ).

fof(f_1208_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1101_zless__int]) ).

fof(f_1208_2,plain,
    ! [U_3687,U_3686] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,U_3687)),hAPP_nat_int(semiri1621563631at_int,U_3686)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3687),U_3686)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3687),U_3686))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,U_3687)),hAPP_nat_int(semiri1621563631at_int,U_3686))) ) ),
    inference(variable_rename,[status(thm)],[f_1208_1]) ).

fof(f_1208_3,plain,
    ( ! [U_3691,U_3689] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,U_3691)),hAPP_nat_int(semiri1621563631at_int,U_3689)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3691),U_3689)) )
    & ! [U_3690,U_3688] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3690),U_3688))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,U_3690)),hAPP_nat_int(semiri1621563631at_int,U_3688))) ) ),
    inference(miniscope,[status(thm)],[f_1208_2]) ).

fof(f_1208_4,plain,
    ( ! [U_3689,U_3691] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,U_3691)),hAPP_nat_int(semiri1621563631at_int,U_3689)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3691),U_3689)) )
    & ! [U_3690,U_3688] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3690),U_3688))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,U_3690)),hAPP_nat_int(semiri1621563631at_int,U_3688))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1208_3]) ).

cnf(f_1208_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3690),U_3688))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,U_3690)),hAPP_nat_int(semiri1621563631at_int,U_3688))) ),
    inference(clausify,[status(thm)],[f_1208_4]) ).

cnf(f_1208_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,U_3691)),hAPP_nat_int(semiri1621563631at_int,U_3689)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3691),U_3689)) ),
    inference(clausify,[status(thm)],[f_1208_4]) ).

fof(f_1209_1,plain,
    ! [M,Na] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),Na))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1102_zle__int]) ).

fof(f_1209_2,plain,
    ! [U_3693,U_3692] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3693)),hAPP_nat_int(semiri1621563631at_int,U_3692)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3693),U_3692)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3693),U_3692))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3693)),hAPP_nat_int(semiri1621563631at_int,U_3692))) ) ),
    inference(variable_rename,[status(thm)],[f_1209_1]) ).

fof(f_1209_3,plain,
    ( ! [U_3697,U_3695] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3697)),hAPP_nat_int(semiri1621563631at_int,U_3695)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3697),U_3695)) )
    & ! [U_3696,U_3694] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3696),U_3694))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3696)),hAPP_nat_int(semiri1621563631at_int,U_3694))) ) ),
    inference(miniscope,[status(thm)],[f_1209_2]) ).

fof(f_1209_4,plain,
    ( ! [U_3695,U_3697] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3697)),hAPP_nat_int(semiri1621563631at_int,U_3695)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3697),U_3695)) )
    & ! [U_3694,U_3696] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3696),U_3694))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3696)),hAPP_nat_int(semiri1621563631at_int,U_3694))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1209_3]) ).

cnf(f_1209_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3696),U_3694))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3696)),hAPP_nat_int(semiri1621563631at_int,U_3694))) ),
    inference(clausify,[status(thm)],[f_1209_4]) ).

cnf(f_1209_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3697)),hAPP_nat_int(semiri1621563631at_int,U_3695)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3697),U_3695)) ),
    inference(clausify,[status(thm)],[f_1209_4]) ).

fof(f_1210_1,plain,
    ! [M_1,N] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N)),
    inference(fof_nnf,[status(thm)],[fact_1103_zadd__int]) ).

fof(f_1210_2,plain,
    ! [U_3699,U_3698] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,U_3699)),hAPP_nat_int(semiri1621563631at_int,U_3698)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3699),U_3698)),
    inference(variable_rename,[status(thm)],[f_1210_1]) ).

fof(f_1210_3,plain,
    ! [U_3698,U_3699] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,U_3699)),hAPP_nat_int(semiri1621563631at_int,U_3698)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3699),U_3698)),
    inference(definitional_conversion,[status(esa)],[f_1210_2]) ).

cnf(f_1210_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,U_3699)),hAPP_nat_int(semiri1621563631at_int,U_3698)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3699),U_3698)),
    inference(clausify,[status(thm)],[f_1210_3]) ).

fof(f_1211_1,plain,
    ! [M_1,N,Z] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,N)),Z)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,M_1),N))),Z),
    inference(fof_nnf,[status(thm)],[fact_1104_zadd__int__left]) ).

fof(f_1211_2,plain,
    ! [U_3702,U_3701,U_3700] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,U_3702)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,U_3701)),U_3700)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3702),U_3701))),U_3700),
    inference(variable_rename,[status(thm)],[f_1211_1]) ).

fof(f_1211_3,plain,
    ! [U_3700,U_3701,U_3702] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,U_3702)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,U_3701)),U_3700)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3702),U_3701))),U_3700),
    inference(definitional_conversion,[status(esa)],[f_1211_2]) ).

cnf(f_1211_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,U_3702)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,U_3701)),U_3700)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3702),U_3701))),U_3700),
    inference(clausify,[status(thm)],[f_1211_3]) ).

fof(f_1212_1,plain,
    ! [W_1,Z_2] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),Z_2))
        | ! [N_1] : Z_2 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_1),hAPP_nat_int(semiri1621563631at_int,N_1)) )
      & ( ? [N_1] : Z_2 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_1),hAPP_nat_int(semiri1621563631at_int,N_1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,W_1),Z_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1105_zle__iff__zadd]) ).

fof(f_1212_2,plain,
    ! [U_3706,U_3705] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3706),U_3705))
        | ! [U_3704] : U_3705 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3706),hAPP_nat_int(semiri1621563631at_int,U_3704)) )
      & ( ? [U_3703] : U_3705 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3706),hAPP_nat_int(semiri1621563631at_int,U_3703))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3706),U_3705)) ) ),
    inference(variable_rename,[status(thm)],[f_1212_1]) ).

fof(f_1212_3,plain,
    ( ! [U_3710,U_3708] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3710),U_3708))
        | ! [U_3704] : U_3708 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3710),hAPP_nat_int(semiri1621563631at_int,U_3704)) )
    & ! [U_3709,U_3707] :
        ( ? [U_3703] : U_3707 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3709),hAPP_nat_int(semiri1621563631at_int,U_3703))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3709),U_3707)) ) ),
    inference(miniscope,[status(thm)],[f_1212_2]) ).

fof(f_1212_4,plain,
    ( ! [U_3710,U_3708] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3710),U_3708))
        | ! [U_3704] : U_3708 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3710),hAPP_nat_int(semiri1621563631at_int,U_3704)) )
    & ! [U_3709,U_3707] :
        ( U_3707 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3709),hAPP_nat_int(semiri1621563631at_int,sK208(U_3709,U_3707)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3709),U_3707)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK208]),skolemize(U_3703,sK208(U_3709,U_3707))],[f_1212_3]) ).

fof(f_1212_5,plain,
    ( ! [U_3704,U_3708,U_3710] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3710),U_3708))
        | U_3708 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3710),hAPP_nat_int(semiri1621563631at_int,U_3704)) )
    & ! [U_3709,U_3707] :
        ( U_3707 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3709),hAPP_nat_int(semiri1621563631at_int,sK208(U_3709,U_3707)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3709),U_3707)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1212_4]) ).

cnf(f_1212_6,plain,
    ( U_3707 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3709),hAPP_nat_int(semiri1621563631at_int,sK208(U_3709,U_3707)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3709),U_3707)) ),
    inference(clausify,[status(thm)],[f_1212_5]) ).

cnf(f_1212_7,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3710),U_3708))
    | U_3708 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3710),hAPP_nat_int(semiri1621563631at_int,U_3704)) ),
    inference(clausify,[status(thm)],[f_1212_5]) ).

fof(f_1213_1,plain,
    ! [M_1,N] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N)),
    inference(fof_nnf,[status(thm)],[fact_1106_zmult__int]) ).

fof(f_1213_2,plain,
    ! [U_3712,U_3711] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,U_3712)),hAPP_nat_int(semiri1621563631at_int,U_3711)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3712),U_3711)),
    inference(variable_rename,[status(thm)],[f_1213_1]) ).

fof(f_1213_3,plain,
    ! [U_3711,U_3712] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,U_3712)),hAPP_nat_int(semiri1621563631at_int,U_3711)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3712),U_3711)),
    inference(definitional_conversion,[status(esa)],[f_1213_2]) ).

cnf(f_1213_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,U_3712)),hAPP_nat_int(semiri1621563631at_int,U_3711)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3712),U_3711)),
    inference(clausify,[status(thm)],[f_1213_3]) ).

fof(f_1214_1,plain,
    ! [M_1,N] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_1),N)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N)),
    inference(fof_nnf,[status(thm)],[fact_1107_int__mult]) ).

fof(f_1214_2,plain,
    ! [U_3714,U_3713] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3714),U_3713)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,U_3714)),hAPP_nat_int(semiri1621563631at_int,U_3713)),
    inference(variable_rename,[status(thm)],[f_1214_1]) ).

fof(f_1214_3,plain,
    ! [U_3713,U_3714] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3714),U_3713)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,U_3714)),hAPP_nat_int(semiri1621563631at_int,U_3713)),
    inference(definitional_conversion,[status(esa)],[f_1214_2]) ).

cnf(f_1214_4,plain,
    hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3714),U_3713)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,U_3714)),hAPP_nat_int(semiri1621563631at_int,U_3713)),
    inference(clausify,[status(thm)],[f_1214_3]) ).

fof(f_1215_1,plain,
    ! [X,Y] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,X)),hAPP_nat_int(semiri1621563631at_int,Y)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X),Y)),
    inference(fof_nnf,[status(thm)],[fact_1108_Nat__Transfer_Otransfer__int__nat__functions_I2_J]) ).

fof(f_1215_2,plain,
    ! [U_3716,U_3715] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,U_3716)),hAPP_nat_int(semiri1621563631at_int,U_3715)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3716),U_3715)),
    inference(variable_rename,[status(thm)],[f_1215_1]) ).

fof(f_1215_3,plain,
    ! [U_3716,U_3715] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,U_3716)),hAPP_nat_int(semiri1621563631at_int,U_3715)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3716),U_3715)),
    inference(definitional_conversion,[status(esa)],[f_1215_2]) ).

cnf(f_1215_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,U_3716)),hAPP_nat_int(semiri1621563631at_int,U_3715)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,U_3716),U_3715)),
    inference(clausify,[status(thm)],[f_1215_3]) ).

fof(f_1216_1,plain,
    ! [X_1,Y_1] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1109_transfer__int__nat__relations_I2_J]) ).

fof(f_1216_2,plain,
    ! [U_3718,U_3717] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,U_3718)),hAPP_nat_int(semiri1621563631at_int,U_3717)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3718),U_3717)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3718),U_3717))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,U_3718)),hAPP_nat_int(semiri1621563631at_int,U_3717))) ) ),
    inference(variable_rename,[status(thm)],[f_1216_1]) ).

fof(f_1216_3,plain,
    ( ! [U_3722,U_3720] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,U_3722)),hAPP_nat_int(semiri1621563631at_int,U_3720)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3722),U_3720)) )
    & ! [U_3721,U_3719] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3721),U_3719))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,U_3721)),hAPP_nat_int(semiri1621563631at_int,U_3719))) ) ),
    inference(miniscope,[status(thm)],[f_1216_2]) ).

fof(f_1216_4,plain,
    ( ! [U_3720,U_3722] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,U_3722)),hAPP_nat_int(semiri1621563631at_int,U_3720)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3722),U_3720)) )
    & ! [U_3721,U_3719] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3721),U_3719))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,U_3721)),hAPP_nat_int(semiri1621563631at_int,U_3719))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1216_3]) ).

cnf(f_1216_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3721),U_3719))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,U_3721)),hAPP_nat_int(semiri1621563631at_int,U_3719))) ),
    inference(clausify,[status(thm)],[f_1216_4]) ).

cnf(f_1216_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_nat_int(semiri1621563631at_int,U_3722)),hAPP_nat_int(semiri1621563631at_int,U_3720)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3722),U_3720)) ),
    inference(clausify,[status(thm)],[f_1216_4]) ).

fof(f_1217_1,plain,
    ! [X_1,Y_1] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_1)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),Y_1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_1))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1110_transfer__int__nat__relations_I3_J]) ).

fof(f_1217_2,plain,
    ! [U_3724,U_3723] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3724)),hAPP_nat_int(semiri1621563631at_int,U_3723)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3724),U_3723)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3724),U_3723))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3724)),hAPP_nat_int(semiri1621563631at_int,U_3723))) ) ),
    inference(variable_rename,[status(thm)],[f_1217_1]) ).

fof(f_1217_3,plain,
    ( ! [U_3728,U_3726] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3728)),hAPP_nat_int(semiri1621563631at_int,U_3726)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3728),U_3726)) )
    & ! [U_3727,U_3725] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3727),U_3725))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3727)),hAPP_nat_int(semiri1621563631at_int,U_3725))) ) ),
    inference(miniscope,[status(thm)],[f_1217_2]) ).

fof(f_1217_4,plain,
    ( ! [U_3726,U_3728] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3728)),hAPP_nat_int(semiri1621563631at_int,U_3726)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3728),U_3726)) )
    & ! [U_3727,U_3725] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3727),U_3725))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3727)),hAPP_nat_int(semiri1621563631at_int,U_3725))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1217_3]) ).

cnf(f_1217_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3727),U_3725))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3727)),hAPP_nat_int(semiri1621563631at_int,U_3725))) ),
    inference(clausify,[status(thm)],[f_1217_4]) ).

cnf(f_1217_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3728)),hAPP_nat_int(semiri1621563631at_int,U_3726)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3728),U_3726)) ),
    inference(clausify,[status(thm)],[f_1217_4]) ).

fof(f_1218_1,plain,
    ! [X,Y] : hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,hAPP_nat_int(semiri1621563631at_int,X)),hAPP_nat_int(semiri1621563631at_int,Y)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X),Y)),
    inference(fof_nnf,[status(thm)],[fact_1111_Nat__Transfer_Otransfer__int__nat__functions_I3_J]) ).

fof(f_1218_2,plain,
    ! [U_3730,U_3729] : hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,hAPP_nat_int(semiri1621563631at_int,U_3730)),hAPP_nat_int(semiri1621563631at_int,U_3729)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3730),U_3729)),
    inference(variable_rename,[status(thm)],[f_1218_1]) ).

fof(f_1218_3,plain,
    ! [U_3729,U_3730] : hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,hAPP_nat_int(semiri1621563631at_int,U_3730)),hAPP_nat_int(semiri1621563631at_int,U_3729)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3730),U_3729)),
    inference(definitional_conversion,[status(esa)],[f_1218_2]) ).

cnf(f_1218_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,hAPP_nat_int(semiri1621563631at_int,U_3730)),hAPP_nat_int(semiri1621563631at_int,U_3729)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3730),U_3729)),
    inference(clausify,[status(thm)],[f_1218_3]) ).

fof(f_1219_1,plain,
    ! [X,Y] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,X)),hAPP_nat_int(semiri1621563631at_int,Y)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,X),Y)),
    inference(fof_nnf,[status(thm)],[fact_1112_Nat__Transfer_Otransfer__int__nat__functions_I1_J]) ).

fof(f_1219_2,plain,
    ! [U_3732,U_3731] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,U_3732)),hAPP_nat_int(semiri1621563631at_int,U_3731)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3732),U_3731)),
    inference(variable_rename,[status(thm)],[f_1219_1]) ).

fof(f_1219_3,plain,
    ! [U_3731,U_3732] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,U_3732)),hAPP_nat_int(semiri1621563631at_int,U_3731)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3732),U_3731)),
    inference(definitional_conversion,[status(esa)],[f_1219_2]) ).

cnf(f_1219_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,U_3732)),hAPP_nat_int(semiri1621563631at_int,U_3731)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3732),U_3731)),
    inference(clausify,[status(thm)],[f_1219_3]) ).

fof(f_1220_1,plain,
    ! [A] : hAPP_f22106695ol_nat(finite_card_nat,A) = hAPP_f957591787ol_nat(finite_card_int,image_nat_int(semiri1621563631at_int,A)),
    inference(fof_nnf,[status(thm)],[fact_1113_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J]) ).

fof(f_1220_2,plain,
    ! [U_3733] : hAPP_f22106695ol_nat(finite_card_nat,U_3733) = hAPP_f957591787ol_nat(finite_card_int,image_nat_int(semiri1621563631at_int,U_3733)),
    inference(variable_rename,[status(thm)],[f_1220_1]) ).

fof(f_1220_3,plain,
    ! [U_3733] : hAPP_f22106695ol_nat(finite_card_nat,U_3733) = hAPP_f957591787ol_nat(finite_card_int,image_nat_int(semiri1621563631at_int,U_3733)),
    inference(definitional_conversion,[status(esa)],[f_1220_2]) ).

cnf(f_1220_4,plain,
    hAPP_f22106695ol_nat(finite_card_nat,U_3733) = hAPP_f957591787ol_nat(finite_card_int,image_nat_int(semiri1621563631at_int,U_3733)),
    inference(clausify,[status(thm)],[f_1220_3]) ).

fof(f_1221_1,plain,
    ! [A] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,A))) )
      & ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,A)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1114_transfer__nat__int__set__relations_I1_J]) ).

fof(f_1221_2,plain,
    ! [U_3734] :
      ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3734))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,U_3734))) )
      & ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,U_3734)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3734)) ) ),
    inference(variable_rename,[status(thm)],[f_1221_1]) ).

fof(f_1221_3,plain,
    ( ! [U_3736] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3736))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,U_3736))) )
    & ! [U_3735] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,U_3735)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3735)) ) ),
    inference(miniscope,[status(thm)],[f_1221_2]) ).

fof(f_1221_4,plain,
    ( ! [U_3736] :
        ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3736))
        | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,U_3736))) )
    & ! [U_3735] :
        ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,U_3735)))
        | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3735)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1221_3]) ).

cnf(f_1221_5,plain,
    ( hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,U_3735)))
    | ~ hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3735)) ),
    inference(clausify,[status(thm)],[f_1221_4]) ).

cnf(f_1221_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,U_3736))
    | ~ hBOOL(hAPP_f448129468l_bool(finite_finite_int,image_nat_int(semiri1621563631at_int,U_3736))) ),
    inference(clausify,[status(thm)],[f_1221_4]) ).

fof(f_1222_1,plain,
    one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
    inference(fof_nnf,[status(thm)],[fact_1115_transfer__int__nat__numerals_I2_J]) ).

fof(f_1222_2,plain,
    one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
    inference(definitional_conversion,[status(esa)],[f_1222_1]) ).

cnf(f_1222_3,plain,
    one_one_int = hAPP_nat_int(semiri1621563631at_int,one_one_nat),
    inference(clausify,[status(thm)],[f_1222_2]) ).

fof(f_1223_1,plain,
    zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
    inference(fof_nnf,[status(thm)],[fact_1116_transfer__int__nat__numerals_I1_J]) ).

fof(f_1223_2,plain,
    zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
    inference(definitional_conversion,[status(esa)],[f_1223_1]) ).

cnf(f_1223_3,plain,
    zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
    inference(clausify,[status(thm)],[f_1223_2]) ).

fof(f_1224_1,plain,
    ! [Pa] : collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),Pa)) = image_nat_int(semiri1621563631at_int,collect_nat(cOMBB_int_bool_nat(Pa,semiri1621563631at_int))),
    inference(fof_nnf,[status(thm)],[fact_1117_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J]) ).

fof(f_1224_2,plain,
    ! [U_3737] : collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),U_3737)) = image_nat_int(semiri1621563631at_int,collect_nat(cOMBB_int_bool_nat(U_3737,semiri1621563631at_int))),
    inference(variable_rename,[status(thm)],[f_1224_1]) ).

fof(f_1224_3,plain,
    ! [U_3737] : collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),U_3737)) = image_nat_int(semiri1621563631at_int,collect_nat(cOMBB_int_bool_nat(U_3737,semiri1621563631at_int))),
    inference(definitional_conversion,[status(esa)],[f_1224_2]) ).

cnf(f_1224_4,plain,
    collect_int(cOMBS_int_bool_bool(cOMBB_1652995168ol_int(fconj,hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int)),U_3737)) = image_nat_int(semiri1621563631at_int,collect_nat(cOMBB_int_bool_nat(U_3737,semiri1621563631at_int))),
    inference(clausify,[status(thm)],[f_1224_3]) ).

fof(f_1225_1,plain,
    ! [Z] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z))),
    inference(fof_nnf,[status(thm)],[fact_1118_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J]) ).

fof(f_1225_2,plain,
    ! [U_3738] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,U_3738))),
    inference(variable_rename,[status(thm)],[f_1225_1]) ).

fof(f_1225_3,plain,
    ! [U_3738] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,U_3738))),
    inference(definitional_conversion,[status(esa)],[f_1225_2]) ).

cnf(f_1225_4,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,U_3738))),
    inference(clausify,[status(thm)],[f_1225_3]) ).

fof(f_1226_1,plain,
    ! [Pa] :
      ( ( ? [X_2] :
            ( hBOOL(hAPP_int_bool(Pa,X_2))
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) )
        | ! [X_2] : ~ hBOOL(hAPP_int_bool(Pa,hAPP_nat_int(semiri1621563631at_int,X_2))) )
      & ( ? [X_2] : hBOOL(hAPP_int_bool(Pa,hAPP_nat_int(semiri1621563631at_int,X_2)))
        | ! [X_2] :
            ( ~ hBOOL(hAPP_int_bool(Pa,X_2))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_1119_transfer__int__nat__quantifiers_I2_J]) ).

fof(f_1226_2,plain,
    ! [U_3743] :
      ( ( ? [U_3742] :
            ( hBOOL(hAPP_int_bool(U_3743,U_3742))
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3742)) )
        | ! [U_3741] : ~ hBOOL(hAPP_int_bool(U_3743,hAPP_nat_int(semiri1621563631at_int,U_3741))) )
      & ( ? [U_3740] : hBOOL(hAPP_int_bool(U_3743,hAPP_nat_int(semiri1621563631at_int,U_3740)))
        | ! [U_3739] :
            ( ~ hBOOL(hAPP_int_bool(U_3743,U_3739))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3739)) ) ) ),
    inference(variable_rename,[status(thm)],[f_1226_1]) ).

fof(f_1226_3,plain,
    ( ! [U_3745] :
        ( ? [U_3742] :
            ( hBOOL(hAPP_int_bool(U_3745,U_3742))
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3742)) )
        | ! [U_3741] : ~ hBOOL(hAPP_int_bool(U_3745,hAPP_nat_int(semiri1621563631at_int,U_3741))) )
    & ! [U_3744] :
        ( ? [U_3740] : hBOOL(hAPP_int_bool(U_3744,hAPP_nat_int(semiri1621563631at_int,U_3740)))
        | ! [U_3739] :
            ( ~ hBOOL(hAPP_int_bool(U_3744,U_3739))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3739)) ) ) ),
    inference(miniscope,[status(thm)],[f_1226_2]) ).

fof(f_1226_4,plain,
    ( ! [U_3745] :
        ( ? [U_3742] :
            ( hBOOL(hAPP_int_bool(U_3745,U_3742))
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3742)) )
        | ! [U_3741] : ~ hBOOL(hAPP_int_bool(U_3745,hAPP_nat_int(semiri1621563631at_int,U_3741))) )
    & ! [U_3744] :
        ( hBOOL(hAPP_int_bool(U_3744,hAPP_nat_int(semiri1621563631at_int,sK209(U_3744))))
        | ! [U_3739] :
            ( ~ hBOOL(hAPP_int_bool(U_3744,U_3739))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3739)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK209]),skolemize(U_3740,sK209(U_3744))],[f_1226_3]) ).

fof(f_1226_5,plain,
    ( ! [U_3745] :
        ( ( hBOOL(hAPP_int_bool(U_3745,sK210(U_3745)))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK210(U_3745))) )
        | ! [U_3741] : ~ hBOOL(hAPP_int_bool(U_3745,hAPP_nat_int(semiri1621563631at_int,U_3741))) )
    & ! [U_3744] :
        ( hBOOL(hAPP_int_bool(U_3744,hAPP_nat_int(semiri1621563631at_int,sK209(U_3744))))
        | ! [U_3739] :
            ( ~ hBOOL(hAPP_int_bool(U_3744,U_3739))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3739)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK210]),skolemize(U_3742,sK210(U_3745))],[f_1226_4]) ).

fof(f_1226_6,plain,
    ( ! [U_3745] :
        ( hBOOL(hAPP_int_bool(U_3745,sK210(U_3745)))
        | ~ sP345(U_3745) )
    & ! [U_3745] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK210(U_3745)))
        | ~ sP345(U_3745) )
    & ! [U_3741,U_3745] :
        ( sP345(U_3745)
        | ~ hBOOL(hAPP_int_bool(U_3745,hAPP_nat_int(semiri1621563631at_int,U_3741))) )
    & ! [U_3739,U_3744] :
        ( hBOOL(hAPP_int_bool(U_3744,hAPP_nat_int(semiri1621563631at_int,sK209(U_3744))))
        | ~ hBOOL(hAPP_int_bool(U_3744,U_3739))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3739)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP345])],[f_1226_5]) ).

cnf(f_1226_7,plain,
    ( hBOOL(hAPP_int_bool(U_3744,hAPP_nat_int(semiri1621563631at_int,sK209(U_3744))))
    | ~ hBOOL(hAPP_int_bool(U_3744,U_3739))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3739)) ),
    inference(clausify,[status(thm)],[f_1226_6]) ).

cnf(f_1226_8,plain,
    ( sP345(U_3745)
    | ~ hBOOL(hAPP_int_bool(U_3745,hAPP_nat_int(semiri1621563631at_int,U_3741))) ),
    inference(clausify,[status(thm)],[f_1226_6]) ).

cnf(f_1226_9,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK210(U_3745)))
    | ~ sP345(U_3745) ),
    inference(clausify,[status(thm)],[f_1226_6]) ).

cnf(f_1226_10,plain,
    ( hBOOL(hAPP_int_bool(U_3745,sK210(U_3745)))
    | ~ sP345(U_3745) ),
    inference(clausify,[status(thm)],[f_1226_6]) ).

fof(f_1227_1,plain,
    ! [Pa] :
      ( ( ! [X_2] :
            ( hBOOL(hAPP_int_bool(Pa,X_2))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) )
        | ? [X_2] : ~ hBOOL(hAPP_int_bool(Pa,hAPP_nat_int(semiri1621563631at_int,X_2))) )
      & ( ! [X_2] : hBOOL(hAPP_int_bool(Pa,hAPP_nat_int(semiri1621563631at_int,X_2)))
        | ? [X_2] :
            ( ~ hBOOL(hAPP_int_bool(Pa,X_2))
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_2)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_1120_transfer__int__nat__quantifiers_I1_J]) ).

fof(f_1227_2,plain,
    ! [U_3750] :
      ( ( ! [U_3749] :
            ( hBOOL(hAPP_int_bool(U_3750,U_3749))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3749)) )
        | ? [U_3748] : ~ hBOOL(hAPP_int_bool(U_3750,hAPP_nat_int(semiri1621563631at_int,U_3748))) )
      & ( ! [U_3747] : hBOOL(hAPP_int_bool(U_3750,hAPP_nat_int(semiri1621563631at_int,U_3747)))
        | ? [U_3746] :
            ( ~ hBOOL(hAPP_int_bool(U_3750,U_3746))
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3746)) ) ) ),
    inference(variable_rename,[status(thm)],[f_1227_1]) ).

fof(f_1227_3,plain,
    ( ! [U_3752] :
        ( ! [U_3749] :
            ( hBOOL(hAPP_int_bool(U_3752,U_3749))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3749)) )
        | ? [U_3748] : ~ hBOOL(hAPP_int_bool(U_3752,hAPP_nat_int(semiri1621563631at_int,U_3748))) )
    & ! [U_3751] :
        ( ! [U_3747] : hBOOL(hAPP_int_bool(U_3751,hAPP_nat_int(semiri1621563631at_int,U_3747)))
        | ? [U_3746] :
            ( ~ hBOOL(hAPP_int_bool(U_3751,U_3746))
            & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3746)) ) ) ),
    inference(miniscope,[status(thm)],[f_1227_2]) ).

fof(f_1227_4,plain,
    ( ! [U_3752] :
        ( ! [U_3749] :
            ( hBOOL(hAPP_int_bool(U_3752,U_3749))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3749)) )
        | ? [U_3748] : ~ hBOOL(hAPP_int_bool(U_3752,hAPP_nat_int(semiri1621563631at_int,U_3748))) )
    & ! [U_3751] :
        ( ! [U_3747] : hBOOL(hAPP_int_bool(U_3751,hAPP_nat_int(semiri1621563631at_int,U_3747)))
        | ( ~ hBOOL(hAPP_int_bool(U_3751,sK211(U_3751)))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK211(U_3751))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK211]),skolemize(U_3746,sK211(U_3751))],[f_1227_3]) ).

fof(f_1227_5,plain,
    ( ! [U_3752] :
        ( ! [U_3749] :
            ( hBOOL(hAPP_int_bool(U_3752,U_3749))
            | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3749)) )
        | ~ hBOOL(hAPP_int_bool(U_3752,hAPP_nat_int(semiri1621563631at_int,sK212(U_3752)))) )
    & ! [U_3751] :
        ( ! [U_3747] : hBOOL(hAPP_int_bool(U_3751,hAPP_nat_int(semiri1621563631at_int,U_3747)))
        | ( ~ hBOOL(hAPP_int_bool(U_3751,sK211(U_3751)))
          & hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK211(U_3751))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK212]),skolemize(U_3748,sK212(U_3752))],[f_1227_4]) ).

fof(f_1227_6,plain,
    ( ! [U_3751] :
        ( ~ hBOOL(hAPP_int_bool(U_3751,sK211(U_3751)))
        | ~ sP346(U_3751) )
    & ! [U_3751] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK211(U_3751)))
        | ~ sP346(U_3751) )
    & ! [U_3749,U_3752] :
        ( hBOOL(hAPP_int_bool(U_3752,U_3749))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3749))
        | ~ hBOOL(hAPP_int_bool(U_3752,hAPP_nat_int(semiri1621563631at_int,sK212(U_3752)))) )
    & ! [U_3747,U_3751] :
        ( hBOOL(hAPP_int_bool(U_3751,hAPP_nat_int(semiri1621563631at_int,U_3747)))
        | sP346(U_3751) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP346])],[f_1227_5]) ).

cnf(f_1227_7,plain,
    ( hBOOL(hAPP_int_bool(U_3751,hAPP_nat_int(semiri1621563631at_int,U_3747)))
    | sP346(U_3751) ),
    inference(clausify,[status(thm)],[f_1227_6]) ).

cnf(f_1227_8,plain,
    ( hBOOL(hAPP_int_bool(U_3752,U_3749))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3749))
    | ~ hBOOL(hAPP_int_bool(U_3752,hAPP_nat_int(semiri1621563631at_int,sK212(U_3752)))) ),
    inference(clausify,[status(thm)],[f_1227_6]) ).

cnf(f_1227_9,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),sK211(U_3751)))
    | ~ sP346(U_3751) ),
    inference(clausify,[status(thm)],[f_1227_6]) ).

cnf(f_1227_10,plain,
    ( ~ hBOOL(hAPP_int_bool(U_3751,sK211(U_3751)))
    | ~ sP346(U_3751) ),
    inference(clausify,[status(thm)],[f_1227_6]) ).

fof(f_1228_1,plain,
    ! [Na] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,Na)),zero_zero_int))
        | Na != zero_zero_nat )
      & ( Na = zero_zero_nat
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,Na)),zero_zero_int)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1121_int__le__0__conv]) ).

fof(f_1228_2,plain,
    ! [U_3753] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3753)),zero_zero_int))
        | U_3753 != zero_zero_nat )
      & ( U_3753 = zero_zero_nat
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3753)),zero_zero_int)) ) ),
    inference(variable_rename,[status(thm)],[f_1228_1]) ).

fof(f_1228_3,plain,
    ( ! [U_3755] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3755)),zero_zero_int))
        | U_3755 != zero_zero_nat )
    & ! [U_3754] :
        ( U_3754 = zero_zero_nat
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3754)),zero_zero_int)) ) ),
    inference(miniscope,[status(thm)],[f_1228_2]) ).

fof(f_1228_4,plain,
    ( ! [U_3755] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3755)),zero_zero_int))
        | U_3755 != zero_zero_nat )
    & ! [U_3754] :
        ( U_3754 = zero_zero_nat
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3754)),zero_zero_int)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1228_3]) ).

cnf(f_1228_5,plain,
    ( U_3754 = zero_zero_nat
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3754)),zero_zero_int)) ),
    inference(clausify,[status(thm)],[f_1228_4]) ).

cnf(f_1228_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(semiri1621563631at_int,U_3755)),zero_zero_int))
    | U_3755 != zero_zero_nat ),
    inference(clausify,[status(thm)],[f_1228_4]) ).

fof(f_1229_1,plain,
    hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,zero_zero_nat)) = one_one_int,
    inference(fof_nnf,[status(thm)],[fact_1122_int__Suc0__eq__1]) ).

fof(f_1229_2,plain,
    hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,zero_zero_nat)) = one_one_int,
    inference(definitional_conversion,[status(esa)],[f_1229_1]) ).

cnf(f_1229_3,plain,
    hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,zero_zero_nat)) = one_one_int,
    inference(clausify,[status(thm)],[f_1229_2]) ).

fof(f_1230_1,plain,
    ! [W_1,Z_2] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2))
        | ! [N_1] : Z_2 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_1),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,N_1))) )
      & ( ? [N_1] : Z_2 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W_1),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,N_1)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1123_zless__iff__Suc__zadd]) ).

fof(f_1230_2,plain,
    ! [U_3759,U_3758] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3759),U_3758))
        | ! [U_3757] : U_3758 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3759),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,U_3757))) )
      & ( ? [U_3756] : U_3758 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3759),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,U_3756)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3759),U_3758)) ) ),
    inference(variable_rename,[status(thm)],[f_1230_1]) ).

fof(f_1230_3,plain,
    ( ! [U_3763,U_3761] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3763),U_3761))
        | ! [U_3757] : U_3761 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3763),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,U_3757))) )
    & ! [U_3762,U_3760] :
        ( ? [U_3756] : U_3760 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3762),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,U_3756)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3762),U_3760)) ) ),
    inference(miniscope,[status(thm)],[f_1230_2]) ).

fof(f_1230_4,plain,
    ( ! [U_3763,U_3761] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3763),U_3761))
        | ! [U_3757] : U_3761 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3763),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,U_3757))) )
    & ! [U_3762,U_3760] :
        ( U_3760 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3762),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,sK213(U_3762,U_3760))))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3762),U_3760)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK213]),skolemize(U_3756,sK213(U_3762,U_3760))],[f_1230_3]) ).

fof(f_1230_5,plain,
    ( ! [U_3757,U_3761,U_3763] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3763),U_3761))
        | U_3761 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3763),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,U_3757))) )
    & ! [U_3762,U_3760] :
        ( U_3760 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3762),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,sK213(U_3762,U_3760))))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3762),U_3760)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1230_4]) ).

cnf(f_1230_6,plain,
    ( U_3760 = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3762),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,sK213(U_3762,U_3760))))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3762),U_3760)) ),
    inference(clausify,[status(thm)],[f_1230_5]) ).

cnf(f_1230_7,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3763),U_3761))
    | U_3761 != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3763),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,U_3757))) ),
    inference(clausify,[status(thm)],[f_1230_5]) ).

fof(f_1231_1,plain,
    ! [M_1] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M_1)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,M_1)),
    inference(fof_nnf,[status(thm)],[fact_1124_int__Suc]) ).

fof(f_1231_2,plain,
    ! [U_3764] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,U_3764)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,U_3764)),
    inference(variable_rename,[status(thm)],[f_1231_1]) ).

fof(f_1231_3,plain,
    ! [U_3764] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,U_3764)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,U_3764)),
    inference(definitional_conversion,[status(esa)],[f_1231_2]) ).

cnf(f_1231_4,plain,
    hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,U_3764)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,U_3764)),
    inference(clausify,[status(thm)],[f_1231_3]) ).

fof(f_1232_1,plain,
    ! [N,M_1] :
      ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,M_1),N))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N),M_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1125_zdiff__int]) ).

fof(f_1232_2,plain,
    ! [U_3766,U_3765] :
      ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,U_3765)),hAPP_nat_int(semiri1621563631at_int,U_3766)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3765),U_3766))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3766),U_3765)) ),
    inference(variable_rename,[status(thm)],[f_1232_1]) ).

fof(f_1232_3,plain,
    ! [U_3765,U_3766] :
      ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,U_3765)),hAPP_nat_int(semiri1621563631at_int,U_3766)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3765),U_3766))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3766),U_3765)) ),
    inference(definitional_conversion,[status(esa)],[f_1232_2]) ).

cnf(f_1232_4,plain,
    ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,U_3765)),hAPP_nat_int(semiri1621563631at_int,U_3766)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3765),U_3766))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3766),U_3765)) ),
    inference(clausify,[status(thm)],[f_1232_3]) ).

fof(f_1233_1,plain,
    ! [Na] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Na)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),Na))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Na))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1126_zero__less__int__conv]) ).

fof(f_1233_2,plain,
    ! [U_3767] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,U_3767)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3767)) )
      & ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3767))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,U_3767))) ) ),
    inference(variable_rename,[status(thm)],[f_1233_1]) ).

fof(f_1233_3,plain,
    ( ! [U_3769] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,U_3769)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3769)) )
    & ! [U_3768] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3768))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,U_3768))) ) ),
    inference(miniscope,[status(thm)],[f_1233_2]) ).

fof(f_1233_4,plain,
    ( ! [U_3769] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,U_3769)))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3769)) )
    & ! [U_3768] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3768))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,U_3768))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1233_3]) ).

cnf(f_1233_5,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3768))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,U_3768))) ),
    inference(clausify,[status(thm)],[f_1233_4]) ).

cnf(f_1233_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,U_3769)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3769)) ),
    inference(clausify,[status(thm)],[f_1233_4]) ).

fof(f_1234_1,plain,
    ! [K_1,I_1,J] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,K_1)),I_1)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,K_1)),J)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),K_1))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,I_1),J)) ),
    inference(fof_nnf,[status(thm)],[fact_1127_zmult__zless__mono2__lemma]) ).

fof(f_1234_2,plain,
    ! [U_3772,U_3771,U_3770] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,U_3772)),U_3771)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,U_3772)),U_3770)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3772))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3771),U_3770)) ),
    inference(variable_rename,[status(thm)],[f_1234_1]) ).

fof(f_1234_3,plain,
    ! [U_3770,U_3771,U_3772] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,U_3772)),U_3771)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,U_3772)),U_3770)))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3772))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3771),U_3770)) ),
    inference(definitional_conversion,[status(esa)],[f_1234_2]) ).

cnf(f_1234_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,U_3772)),U_3771)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_nat_int(semiri1621563631at_int,U_3772)),U_3770)))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3772))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3771),U_3770)) ),
    inference(clausify,[status(thm)],[f_1234_3]) ).

fof(f_1235_1,plain,
    ! [Y,X] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X),Y)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X)) ),
    inference(fof_nnf,[status(thm)],[fact_1128_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J]) ).

fof(f_1235_2,plain,
    ! [U_3774,U_3773] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,U_3773),U_3774)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3774))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3773)) ),
    inference(variable_rename,[status(thm)],[f_1235_1]) ).

fof(f_1235_3,plain,
    ! [U_3773,U_3774] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,U_3773),U_3774)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3774))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3773)) ),
    inference(definitional_conversion,[status(esa)],[f_1235_2]) ).

cnf(f_1235_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,U_3773),U_3774)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3774))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3773)) ),
    inference(clausify,[status(thm)],[f_1235_3]) ).

fof(f_1236_1,plain,
    ! [Pa,X_1,Y_1] :
      ( ( hBOOL(hAPP_int_bool(Pa,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X_1),Y_1))))
        | ( ~ hBOOL(hAPP_int_bool(Pa,zero_zero_int))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) )
        | ( ~ hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_1))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) ) )
      & ( ( ( hBOOL(hAPP_int_bool(Pa,zero_zero_int))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,X_1),Y_1)) )
          & ( hBOOL(hAPP_int_bool(Pa,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,X_1)),hAPP_nat_int(semiri1621563631at_int,Y_1))))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Y_1),X_1)) ) )
        | ~ hBOOL(hAPP_int_bool(Pa,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,X_1),Y_1)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1129_zdiff__int__split]) ).

fof(f_1236_2,plain,
    ! [U_3777,U_3776,U_3775] :
      ( ( hBOOL(hAPP_int_bool(U_3777,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3776),U_3775))))
        | ( ~ hBOOL(hAPP_int_bool(U_3777,zero_zero_int))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3776),U_3775)) )
        | ( ~ hBOOL(hAPP_int_bool(U_3777,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,U_3776)),hAPP_nat_int(semiri1621563631at_int,U_3775))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3775),U_3776)) ) )
      & ( ( ( hBOOL(hAPP_int_bool(U_3777,zero_zero_int))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3776),U_3775)) )
          & ( hBOOL(hAPP_int_bool(U_3777,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,U_3776)),hAPP_nat_int(semiri1621563631at_int,U_3775))))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3775),U_3776)) ) )
        | ~ hBOOL(hAPP_int_bool(U_3777,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3776),U_3775)))) ) ),
    inference(variable_rename,[status(thm)],[f_1236_1]) ).

fof(f_1236_3,plain,
    ( ! [U_3783,U_3781,U_3779] :
        ( hBOOL(hAPP_int_bool(U_3783,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3781),U_3779))))
        | ( ~ hBOOL(hAPP_int_bool(U_3783,zero_zero_int))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3781),U_3779)) )
        | ( ~ hBOOL(hAPP_int_bool(U_3783,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,U_3781)),hAPP_nat_int(semiri1621563631at_int,U_3779))))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3779),U_3781)) ) )
    & ! [U_3782,U_3780,U_3778] :
        ( ( ( hBOOL(hAPP_int_bool(U_3782,zero_zero_int))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3780),U_3778)) )
          & ( hBOOL(hAPP_int_bool(U_3782,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,U_3780)),hAPP_nat_int(semiri1621563631at_int,U_3778))))
            | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3778),U_3780)) ) )
        | ~ hBOOL(hAPP_int_bool(U_3782,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3780),U_3778)))) ) ),
    inference(miniscope,[status(thm)],[f_1236_2]) ).

fof(f_1236_4,plain,
    ( ! [U_3779,U_3781,U_3783] :
        ( ~ hBOOL(hAPP_int_bool(U_3783,zero_zero_int))
        | ~ sP349(U_3779,U_3781,U_3783) )
    & ! [U_3779,U_3781,U_3783] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3781),U_3779))
        | ~ sP349(U_3779,U_3781,U_3783) )
    & ! [U_3779,U_3781,U_3783] :
        ( ~ hBOOL(hAPP_int_bool(U_3783,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,U_3781)),hAPP_nat_int(semiri1621563631at_int,U_3779))))
        | ~ sP348(U_3779,U_3781,U_3783) )
    & ! [U_3779,U_3781,U_3783] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3779),U_3781))
        | ~ sP348(U_3779,U_3781,U_3783) )
    & ! [U_3778,U_3780,U_3782] :
        ( hBOOL(hAPP_int_bool(U_3782,zero_zero_int))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3780),U_3778))
        | ~ sP347(U_3778,U_3780,U_3782) )
    & ! [U_3778,U_3780,U_3782] :
        ( hBOOL(hAPP_int_bool(U_3782,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,U_3780)),hAPP_nat_int(semiri1621563631at_int,U_3778))))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3778),U_3780))
        | ~ sP347(U_3778,U_3780,U_3782) )
    & ! [U_3779,U_3781,U_3783] :
        ( hBOOL(hAPP_int_bool(U_3783,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3781),U_3779))))
        | sP349(U_3779,U_3781,U_3783)
        | sP348(U_3779,U_3781,U_3783) )
    & ! [U_3778,U_3780,U_3782] :
        ( sP347(U_3778,U_3780,U_3782)
        | ~ hBOOL(hAPP_int_bool(U_3782,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3780),U_3778)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP347,sP348,sP349])],[f_1236_3]) ).

cnf(f_1236_5,plain,
    ( sP347(U_3778,U_3780,U_3782)
    | ~ hBOOL(hAPP_int_bool(U_3782,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3780),U_3778)))) ),
    inference(clausify,[status(thm)],[f_1236_4]) ).

cnf(f_1236_6,plain,
    ( hBOOL(hAPP_int_bool(U_3783,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(minus_minus_nat,U_3781),U_3779))))
    | sP349(U_3779,U_3781,U_3783)
    | sP348(U_3779,U_3781,U_3783) ),
    inference(clausify,[status(thm)],[f_1236_4]) ).

cnf(f_1236_7,plain,
    ( hBOOL(hAPP_int_bool(U_3782,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,U_3780)),hAPP_nat_int(semiri1621563631at_int,U_3778))))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3778),U_3780))
    | ~ sP347(U_3778,U_3780,U_3782) ),
    inference(clausify,[status(thm)],[f_1236_4]) ).

cnf(f_1236_8,plain,
    ( hBOOL(hAPP_int_bool(U_3782,zero_zero_int))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3780),U_3778))
    | ~ sP347(U_3778,U_3780,U_3782) ),
    inference(clausify,[status(thm)],[f_1236_4]) ).

cnf(f_1236_9,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3779),U_3781))
    | ~ sP348(U_3779,U_3781,U_3783) ),
    inference(clausify,[status(thm)],[f_1236_4]) ).

cnf(f_1236_10,plain,
    ( ~ hBOOL(hAPP_int_bool(U_3783,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,U_3781)),hAPP_nat_int(semiri1621563631at_int,U_3779))))
    | ~ sP348(U_3779,U_3781,U_3783) ),
    inference(clausify,[status(thm)],[f_1236_4]) ).

cnf(f_1236_11,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3781),U_3779))
    | ~ sP349(U_3779,U_3781,U_3783) ),
    inference(clausify,[status(thm)],[f_1236_4]) ).

cnf(f_1236_12,plain,
    ( ~ hBOOL(hAPP_int_bool(U_3783,zero_zero_int))
    | ~ sP349(U_3779,U_3781,U_3783) ),
    inference(clausify,[status(thm)],[f_1236_4]) ).

fof(f_1237_1,plain,
    ! [Y,X] :
      ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,X),Y) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Y)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Y),X)) ),
    inference(fof_nnf,[status(thm)],[fact_1130_tsub__eq]) ).

fof(f_1237_2,plain,
    ! [U_3785,U_3784] :
      ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,U_3784),U_3785) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3784),U_3785)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3785),U_3784)) ),
    inference(variable_rename,[status(thm)],[f_1237_1]) ).

fof(f_1237_3,plain,
    ! [U_3785,U_3784] :
      ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,U_3784),U_3785) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3784),U_3785)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3785),U_3784)) ),
    inference(definitional_conversion,[status(esa)],[f_1237_2]) ).

cnf(f_1237_4,plain,
    ( hAPP_int_int(hAPP_int_fun_int_int(nat_tsub,U_3784),U_3785) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3784),U_3785)
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3785),U_3784)) ),
    inference(clausify,[status(thm)],[f_1237_3]) ).

fof(f_1238_1,plain,
    ! [K_1] :
      ( ? [N_1] :
          ( K_1 = hAPP_nat_int(semiri1621563631at_int,N_1)
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),N_1)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),K_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1131_zero__less__imp__eq__int]) ).

fof(f_1238_2,plain,
    ! [U_3787] :
      ( ? [U_3786] :
          ( U_3787 = hAPP_nat_int(semiri1621563631at_int,U_3786)
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),U_3786)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3787)) ),
    inference(variable_rename,[status(thm)],[f_1238_1]) ).

fof(f_1238_3,plain,
    ! [U_3787] :
      ( ( U_3787 = hAPP_nat_int(semiri1621563631at_int,sK214(U_3787))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK214(U_3787))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3787)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK214]),skolemize(U_3786,sK214(U_3787))],[f_1238_2]) ).

fof(f_1238_4,plain,
    ( ! [U_3787] :
        ( U_3787 = hAPP_nat_int(semiri1621563631at_int,sK214(U_3787))
        | ~ sP350(U_3787) )
    & ! [U_3787] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK214(U_3787)))
        | ~ sP350(U_3787) )
    & ! [U_3787] :
        ( sP350(U_3787)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3787)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP350])],[f_1238_3]) ).

cnf(f_1238_5,plain,
    ( sP350(U_3787)
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3787)) ),
    inference(clausify,[status(thm)],[f_1238_4]) ).

cnf(f_1238_6,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,zero_zero_nat),sK214(U_3787)))
    | ~ sP350(U_3787) ),
    inference(clausify,[status(thm)],[f_1238_4]) ).

cnf(f_1238_7,plain,
    ( U_3787 = hAPP_nat_int(semiri1621563631at_int,sK214(U_3787))
    | ~ sP350(U_3787) ),
    inference(clausify,[status(thm)],[f_1238_4]) ).

fof(f_1239_1,plain,
    ! [M,Na] :
      ( ( hAPP_nat_int(semiri1621563631at_int,M) = hAPP_nat_int(semiri1621563631at_int,Na)
        | M != Na )
      & ( M = Na
        | hAPP_nat_int(semiri1621563631at_int,M) != hAPP_nat_int(semiri1621563631at_int,Na) ) ),
    inference(fof_nnf,[status(thm)],[fact_1132_int__int__eq]) ).

fof(f_1239_2,plain,
    ! [U_3789,U_3788] :
      ( ( hAPP_nat_int(semiri1621563631at_int,U_3789) = hAPP_nat_int(semiri1621563631at_int,U_3788)
        | U_3789 != U_3788 )
      & ( U_3789 = U_3788
        | hAPP_nat_int(semiri1621563631at_int,U_3789) != hAPP_nat_int(semiri1621563631at_int,U_3788) ) ),
    inference(variable_rename,[status(thm)],[f_1239_1]) ).

fof(f_1239_3,plain,
    ( ! [U_3793,U_3791] :
        ( hAPP_nat_int(semiri1621563631at_int,U_3793) = hAPP_nat_int(semiri1621563631at_int,U_3791)
        | U_3793 != U_3791 )
    & ! [U_3792,U_3790] :
        ( U_3792 = U_3790
        | hAPP_nat_int(semiri1621563631at_int,U_3792) != hAPP_nat_int(semiri1621563631at_int,U_3790) ) ),
    inference(miniscope,[status(thm)],[f_1239_2]) ).

fof(f_1239_4,plain,
    ( ! [U_3793,U_3791] :
        ( hAPP_nat_int(semiri1621563631at_int,U_3793) = hAPP_nat_int(semiri1621563631at_int,U_3791)
        | U_3793 != U_3791 )
    & ! [U_3792,U_3790] :
        ( U_3792 = U_3790
        | hAPP_nat_int(semiri1621563631at_int,U_3792) != hAPP_nat_int(semiri1621563631at_int,U_3790) ) ),
    inference(definitional_conversion,[status(esa)],[f_1239_3]) ).

cnf(f_1239_5,plain,
    ( U_3792 = U_3790
    | hAPP_nat_int(semiri1621563631at_int,U_3792) != hAPP_nat_int(semiri1621563631at_int,U_3790) ),
    inference(clausify,[status(thm)],[f_1239_4]) ).

cnf(f_1239_6,plain,
    ( hAPP_nat_int(semiri1621563631at_int,U_3793) = hAPP_nat_int(semiri1621563631at_int,U_3791)
    | U_3793 != U_3791 ),
    inference(clausify,[status(thm)],[f_1239_4]) ).

fof(f_1240_1,plain,
    ! [A,B] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,A)),image_nat_int(semiri1621563631at_int,B))) )
      & ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,A)),image_nat_int(semiri1621563631at_int,B)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,A),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1133_transfer__nat__int__set__relations_I4_J]) ).

fof(f_1240_2,plain,
    ! [U_3795,U_3794] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3795),U_3794))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,U_3795)),image_nat_int(semiri1621563631at_int,U_3794))) )
      & ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,U_3795)),image_nat_int(semiri1621563631at_int,U_3794)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3795),U_3794)) ) ),
    inference(variable_rename,[status(thm)],[f_1240_1]) ).

fof(f_1240_3,plain,
    ( ! [U_3799,U_3797] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3799),U_3797))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,U_3799)),image_nat_int(semiri1621563631at_int,U_3797))) )
    & ! [U_3798,U_3796] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,U_3798)),image_nat_int(semiri1621563631at_int,U_3796)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3798),U_3796)) ) ),
    inference(miniscope,[status(thm)],[f_1240_2]) ).

fof(f_1240_4,plain,
    ( ! [U_3797,U_3799] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3799),U_3797))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,U_3799)),image_nat_int(semiri1621563631at_int,U_3797))) )
    & ! [U_3798,U_3796] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,U_3798)),image_nat_int(semiri1621563631at_int,U_3796)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3798),U_3796)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1240_3]) ).

cnf(f_1240_5,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,U_3798)),image_nat_int(semiri1621563631at_int,U_3796)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3798),U_3796)) ),
    inference(clausify,[status(thm)],[f_1240_4]) ).

cnf(f_1240_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le382113706t_bool,U_3799),U_3797))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le1912455174t_bool,image_nat_int(semiri1621563631at_int,U_3799)),image_nat_int(semiri1621563631at_int,U_3797))) ),
    inference(clausify,[status(thm)],[f_1240_4]) ).

fof(f_1241_1,plain,
    ! [A,B] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,A)),image_nat_int(semiri1621563631at_int,B))) )
      & ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,A)),image_nat_int(semiri1621563631at_int,B)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1134_transfer__nat__int__set__relations_I5_J]) ).

fof(f_1241_2,plain,
    ! [U_3801,U_3800] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3801),U_3800))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,U_3801)),image_nat_int(semiri1621563631at_int,U_3800))) )
      & ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,U_3801)),image_nat_int(semiri1621563631at_int,U_3800)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3801),U_3800)) ) ),
    inference(variable_rename,[status(thm)],[f_1241_1]) ).

fof(f_1241_3,plain,
    ( ! [U_3805,U_3803] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3805),U_3803))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,U_3805)),image_nat_int(semiri1621563631at_int,U_3803))) )
    & ! [U_3804,U_3802] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,U_3804)),image_nat_int(semiri1621563631at_int,U_3802)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3804),U_3802)) ) ),
    inference(miniscope,[status(thm)],[f_1241_2]) ).

fof(f_1241_4,plain,
    ( ! [U_3803,U_3805] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3805),U_3803))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,U_3805)),image_nat_int(semiri1621563631at_int,U_3803))) )
    & ! [U_3802,U_3804] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,U_3804)),image_nat_int(semiri1621563631at_int,U_3802)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3804),U_3802)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1241_3]) ).

cnf(f_1241_5,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,U_3804)),image_nat_int(semiri1621563631at_int,U_3802)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3804),U_3802)) ),
    inference(clausify,[status(thm)],[f_1241_4]) ).

cnf(f_1241_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,U_3805),U_3803))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(ord_le951220754t_bool,image_nat_int(semiri1621563631at_int,U_3805)),image_nat_int(semiri1621563631at_int,U_3803))) ),
    inference(clausify,[status(thm)],[f_1241_4]) ).

fof(f_1242_1,plain,
    bot_bot_fun_int_bool = image_nat_int(semiri1621563631at_int,bot_bot_fun_nat_bool),
    inference(fof_nnf,[status(thm)],[fact_1135_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J]) ).

fof(f_1242_2,plain,
    bot_bot_fun_int_bool = image_nat_int(semiri1621563631at_int,bot_bot_fun_nat_bool),
    inference(definitional_conversion,[status(esa)],[f_1242_1]) ).

cnf(f_1242_3,plain,
    bot_bot_fun_int_bool = image_nat_int(semiri1621563631at_int,bot_bot_fun_nat_bool),
    inference(clausify,[status(thm)],[f_1242_2]) ).

fof(f_1243_1,plain,
    ! [A,B] :
      ( ( A = B
        | image_nat_int(semiri1621563631at_int,A) != image_nat_int(semiri1621563631at_int,B) )
      & ( image_nat_int(semiri1621563631at_int,A) = image_nat_int(semiri1621563631at_int,B)
        | A != B ) ),
    inference(fof_nnf,[status(thm)],[fact_1136_transfer__nat__int__set__relations_I3_J]) ).

fof(f_1243_2,plain,
    ! [U_3807,U_3806] :
      ( ( U_3807 = U_3806
        | image_nat_int(semiri1621563631at_int,U_3807) != image_nat_int(semiri1621563631at_int,U_3806) )
      & ( image_nat_int(semiri1621563631at_int,U_3807) = image_nat_int(semiri1621563631at_int,U_3806)
        | U_3807 != U_3806 ) ),
    inference(variable_rename,[status(thm)],[f_1243_1]) ).

fof(f_1243_3,plain,
    ( ! [U_3811,U_3809] :
        ( U_3811 = U_3809
        | image_nat_int(semiri1621563631at_int,U_3811) != image_nat_int(semiri1621563631at_int,U_3809) )
    & ! [U_3810,U_3808] :
        ( image_nat_int(semiri1621563631at_int,U_3810) = image_nat_int(semiri1621563631at_int,U_3808)
        | U_3810 != U_3808 ) ),
    inference(miniscope,[status(thm)],[f_1243_2]) ).

fof(f_1243_4,plain,
    ( ! [U_3809,U_3811] :
        ( U_3811 = U_3809
        | image_nat_int(semiri1621563631at_int,U_3811) != image_nat_int(semiri1621563631at_int,U_3809) )
    & ! [U_3808,U_3810] :
        ( image_nat_int(semiri1621563631at_int,U_3810) = image_nat_int(semiri1621563631at_int,U_3808)
        | U_3810 != U_3808 ) ),
    inference(definitional_conversion,[status(esa)],[f_1243_3]) ).

cnf(f_1243_5,plain,
    ( image_nat_int(semiri1621563631at_int,U_3810) = image_nat_int(semiri1621563631at_int,U_3808)
    | U_3810 != U_3808 ),
    inference(clausify,[status(thm)],[f_1243_4]) ).

cnf(f_1243_6,plain,
    ( U_3811 = U_3809
    | image_nat_int(semiri1621563631at_int,U_3811) != image_nat_int(semiri1621563631at_int,U_3809) ),
    inference(clausify,[status(thm)],[f_1243_4]) ).

fof(f_1244_1,plain,
    ! [X_1,A] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,X_1)),image_nat_int(semiri1621563631at_int,A))) )
      & ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,X_1)),image_nat_int(semiri1621563631at_int,A)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1137_transfer__nat__int__set__relations_I2_J]) ).

fof(f_1244_2,plain,
    ! [U_3813,U_3812] :
      ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3813),U_3812))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,U_3813)),image_nat_int(semiri1621563631at_int,U_3812))) )
      & ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,U_3813)),image_nat_int(semiri1621563631at_int,U_3812)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3813),U_3812)) ) ),
    inference(variable_rename,[status(thm)],[f_1244_1]) ).

fof(f_1244_3,plain,
    ( ! [U_3817,U_3815] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3817),U_3815))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,U_3817)),image_nat_int(semiri1621563631at_int,U_3815))) )
    & ! [U_3816,U_3814] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,U_3816)),image_nat_int(semiri1621563631at_int,U_3814)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3816),U_3814)) ) ),
    inference(miniscope,[status(thm)],[f_1244_2]) ).

fof(f_1244_4,plain,
    ( ! [U_3815,U_3817] :
        ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3817),U_3815))
        | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,U_3817)),image_nat_int(semiri1621563631at_int,U_3815))) )
    & ! [U_3816,U_3814] :
        ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,U_3816)),image_nat_int(semiri1621563631at_int,U_3814)))
        | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3816),U_3814)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1244_3]) ).

cnf(f_1244_5,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,U_3816)),image_nat_int(semiri1621563631at_int,U_3814)))
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3816),U_3814)) ),
    inference(clausify,[status(thm)],[f_1244_4]) ).

cnf(f_1244_6,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,U_3817),U_3815))
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_i2112223885l_bool(member_int,hAPP_nat_int(semiri1621563631at_int,U_3817)),image_nat_int(semiri1621563631at_int,U_3815))) ),
    inference(clausify,[status(thm)],[f_1244_4]) ).

fof(f_1245_1,plain,
    ! [X_1,Y_1,Pa] :
      ( ( hAPP_nat_int(semiri1621563631at_int,Y_1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(Pa),X_1),Y_1))
        | hBOOL(Pa) )
      & ( hAPP_nat_int(semiri1621563631at_int,X_1) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(Pa),X_1),Y_1))
        | ~ hBOOL(Pa) ) ),
    inference(fof_nnf,[status(thm)],[fact_1138_int__if__cong]) ).

fof(f_1245_2,plain,
    ! [U_3820,U_3819,U_3818] :
      ( ( hAPP_nat_int(semiri1621563631at_int,U_3819) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(U_3818),U_3820),U_3819))
        | hBOOL(U_3818) )
      & ( hAPP_nat_int(semiri1621563631at_int,U_3820) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(U_3818),U_3820),U_3819))
        | ~ hBOOL(U_3818) ) ),
    inference(variable_rename,[status(thm)],[f_1245_1]) ).

fof(f_1245_3,plain,
    ( ! [U_3826,U_3824,U_3822] :
        ( hAPP_nat_int(semiri1621563631at_int,U_3824) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(U_3822),U_3826),U_3824))
        | hBOOL(U_3822) )
    & ! [U_3825,U_3823,U_3821] :
        ( hAPP_nat_int(semiri1621563631at_int,U_3825) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(U_3821),U_3825),U_3823))
        | ~ hBOOL(U_3821) ) ),
    inference(miniscope,[status(thm)],[f_1245_2]) ).

fof(f_1245_4,plain,
    ( ! [U_3822,U_3824,U_3826] :
        ( hAPP_nat_int(semiri1621563631at_int,U_3824) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(U_3822),U_3826),U_3824))
        | hBOOL(U_3822) )
    & ! [U_3825,U_3821,U_3823] :
        ( hAPP_nat_int(semiri1621563631at_int,U_3825) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(U_3821),U_3825),U_3823))
        | ~ hBOOL(U_3821) ) ),
    inference(definitional_conversion,[status(esa)],[f_1245_3]) ).

cnf(f_1245_5,plain,
    ( hAPP_nat_int(semiri1621563631at_int,U_3825) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(U_3821),U_3825),U_3823))
    | ~ hBOOL(U_3821) ),
    inference(clausify,[status(thm)],[f_1245_4]) ).

cnf(f_1245_6,plain,
    ( hAPP_nat_int(semiri1621563631at_int,U_3824) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(U_3822),U_3826),U_3824))
    | hBOOL(U_3822) ),
    inference(clausify,[status(thm)],[f_1245_4]) ).

fof(f_1246_1,plain,
    ! [X_1,Y_1] :
      ( ( hAPP_nat_int(semiri1621563631at_int,X_1) = hAPP_nat_int(semiri1621563631at_int,Y_1)
        | X_1 != Y_1 )
      & ( X_1 = Y_1
        | hAPP_nat_int(semiri1621563631at_int,X_1) != hAPP_nat_int(semiri1621563631at_int,Y_1) ) ),
    inference(fof_nnf,[status(thm)],[fact_1139_transfer__int__nat__relations_I1_J]) ).

fof(f_1246_2,plain,
    ! [U_3828,U_3827] :
      ( ( hAPP_nat_int(semiri1621563631at_int,U_3828) = hAPP_nat_int(semiri1621563631at_int,U_3827)
        | U_3828 != U_3827 )
      & ( U_3828 = U_3827
        | hAPP_nat_int(semiri1621563631at_int,U_3828) != hAPP_nat_int(semiri1621563631at_int,U_3827) ) ),
    inference(variable_rename,[status(thm)],[f_1246_1]) ).

fof(f_1246_3,plain,
    ( ! [U_3832,U_3830] :
        ( hAPP_nat_int(semiri1621563631at_int,U_3832) = hAPP_nat_int(semiri1621563631at_int,U_3830)
        | U_3832 != U_3830 )
    & ! [U_3831,U_3829] :
        ( U_3831 = U_3829
        | hAPP_nat_int(semiri1621563631at_int,U_3831) != hAPP_nat_int(semiri1621563631at_int,U_3829) ) ),
    inference(miniscope,[status(thm)],[f_1246_2]) ).

fof(f_1246_4,plain,
    ( ! [U_3830,U_3832] :
        ( hAPP_nat_int(semiri1621563631at_int,U_3832) = hAPP_nat_int(semiri1621563631at_int,U_3830)
        | U_3832 != U_3830 )
    & ! [U_3831,U_3829] :
        ( U_3831 = U_3829
        | hAPP_nat_int(semiri1621563631at_int,U_3831) != hAPP_nat_int(semiri1621563631at_int,U_3829) ) ),
    inference(definitional_conversion,[status(esa)],[f_1246_3]) ).

cnf(f_1246_5,plain,
    ( U_3831 = U_3829
    | hAPP_nat_int(semiri1621563631at_int,U_3831) != hAPP_nat_int(semiri1621563631at_int,U_3829) ),
    inference(clausify,[status(thm)],[f_1246_4]) ).

cnf(f_1246_6,plain,
    ( hAPP_nat_int(semiri1621563631at_int,U_3832) = hAPP_nat_int(semiri1621563631at_int,U_3830)
    | U_3832 != U_3830 ),
    inference(clausify,[status(thm)],[f_1246_4]) ).

fof(f_1247_1,plain,
    ! [K_1] :
      ( ? [N_1] : K_1 = hAPP_nat_int(semiri1621563631at_int,N_1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1140_nonneg__int__cases]) ).

fof(f_1247_2,plain,
    ! [U_3834] :
      ( ? [U_3833] : U_3834 = hAPP_nat_int(semiri1621563631at_int,U_3833)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3834)) ),
    inference(variable_rename,[status(thm)],[f_1247_1]) ).

fof(f_1247_3,plain,
    ! [U_3834] :
      ( U_3834 = hAPP_nat_int(semiri1621563631at_int,sK215(U_3834))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3834)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK215]),skolemize(U_3833,sK215(U_3834))],[f_1247_2]) ).

fof(f_1247_4,plain,
    ! [U_3834] :
      ( U_3834 = hAPP_nat_int(semiri1621563631at_int,sK215(U_3834))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3834)) ),
    inference(definitional_conversion,[status(esa)],[f_1247_3]) ).

cnf(f_1247_5,plain,
    ( U_3834 = hAPP_nat_int(semiri1621563631at_int,sK215(U_3834))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3834)) ),
    inference(clausify,[status(thm)],[f_1247_4]) ).

fof(f_1248_1,plain,
    ! [Z] :
      ( ? [M_2] : Z = hAPP_nat_int(semiri1621563631at_int,M_2)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Z)) ),
    inference(fof_nnf,[status(thm)],[fact_1141_nonneg__eq__int]) ).

fof(f_1248_2,plain,
    ! [U_3836] :
      ( ? [U_3835] : U_3836 = hAPP_nat_int(semiri1621563631at_int,U_3835)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3836)) ),
    inference(variable_rename,[status(thm)],[f_1248_1]) ).

fof(f_1248_3,plain,
    ! [U_3836] :
      ( U_3836 = hAPP_nat_int(semiri1621563631at_int,sK216(U_3836))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3836)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK216]),skolemize(U_3835,sK216(U_3836))],[f_1248_2]) ).

fof(f_1248_4,plain,
    ! [U_3836] :
      ( U_3836 = hAPP_nat_int(semiri1621563631at_int,sK216(U_3836))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3836)) ),
    inference(definitional_conversion,[status(esa)],[f_1248_3]) ).

cnf(f_1248_5,plain,
    ( U_3836 = hAPP_nat_int(semiri1621563631at_int,sK216(U_3836))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3836)) ),
    inference(clausify,[status(thm)],[f_1248_4]) ).

fof(f_1249_1,plain,
    ! [K_1] :
      ( ? [N_1] : K_1 = hAPP_nat_int(semiri1621563631at_int,N_1)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),K_1)) ),
    inference(fof_nnf,[status(thm)],[fact_1142_zero__le__imp__eq__int]) ).

fof(f_1249_2,plain,
    ! [U_3838] :
      ( ? [U_3837] : U_3838 = hAPP_nat_int(semiri1621563631at_int,U_3837)
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3838)) ),
    inference(variable_rename,[status(thm)],[f_1249_1]) ).

fof(f_1249_3,plain,
    ! [U_3838] :
      ( U_3838 = hAPP_nat_int(semiri1621563631at_int,sK217(U_3838))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3838)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK217]),skolemize(U_3837,sK217(U_3838))],[f_1249_2]) ).

fof(f_1249_4,plain,
    ! [U_3838] :
      ( U_3838 = hAPP_nat_int(semiri1621563631at_int,sK217(U_3838))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3838)) ),
    inference(definitional_conversion,[status(esa)],[f_1249_3]) ).

cnf(f_1249_5,plain,
    ( U_3838 = hAPP_nat_int(semiri1621563631at_int,sK217(U_3838))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3838)) ),
    inference(clausify,[status(thm)],[f_1249_4]) ).

fof(f_1250_1,plain,
    ! [Z] :
    ? [M_2,N_1] : Z = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,M_2)),hAPP_nat_int(semiri1621563631at_int,N_1)),
    inference(fof_nnf,[status(thm)],[fact_1143_int__diff__cases]) ).

fof(f_1250_2,plain,
    ! [U_3841] :
    ? [U_3840,U_3839] : U_3841 = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,U_3840)),hAPP_nat_int(semiri1621563631at_int,U_3839)),
    inference(variable_rename,[status(thm)],[f_1250_1]) ).

fof(f_1250_3,plain,
    ! [U_3841] :
    ? [U_3839] : U_3841 = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,sK218(U_3841))),hAPP_nat_int(semiri1621563631at_int,U_3839)),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK218]),skolemize(U_3840,sK218(U_3841))],[f_1250_2]) ).

fof(f_1250_4,plain,
    ! [U_3841] : U_3841 = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,sK218(U_3841))),hAPP_nat_int(semiri1621563631at_int,sK219(U_3841))),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK219]),skolemize(U_3839,sK219(U_3841))],[f_1250_3]) ).

fof(f_1250_5,plain,
    ! [U_3841] : U_3841 = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,sK218(U_3841))),hAPP_nat_int(semiri1621563631at_int,sK219(U_3841))),
    inference(definitional_conversion,[status(esa)],[f_1250_4]) ).

cnf(f_1250_6,plain,
    U_3841 = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(semiri1621563631at_int,sK218(U_3841))),hAPP_nat_int(semiri1621563631at_int,sK219(U_3841))),
    inference(clausify,[status(thm)],[f_1250_5]) ).

fof(f_1251_1,plain,
    ! [X,Z,D] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Z))),one_one_int)),D))),Z))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D)) ),
    inference(fof_nnf,[status(thm)],[fact_1144_decr__lemma]) ).

fof(f_1251_2,plain,
    ! [U_3844,U_3843,U_3842] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3844),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3844),U_3843))),one_one_int)),U_3842))),U_3843))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3842)) ),
    inference(variable_rename,[status(thm)],[f_1251_1]) ).

fof(f_1251_3,plain,
    ! [U_3842,U_3843,U_3844] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3844),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3844),U_3843))),one_one_int)),U_3842))),U_3843))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3842)) ),
    inference(definitional_conversion,[status(esa)],[f_1251_2]) ).

cnf(f_1251_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3844),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3844),U_3843))),one_one_int)),U_3842))),U_3843))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3842)) ),
    inference(clausify,[status(thm)],[f_1251_3]) ).

fof(f_1252_1,plain,
    ! [Z_2] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(Z_2)),one_one_int))
        | Z_2 != zero_zero_int )
      & ( Z_2 = zero_zero_int
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(Z_2)),one_one_int)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1145_zabs__less__one__iff]) ).

fof(f_1252_2,plain,
    ! [U_3845] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(U_3845)),one_one_int))
        | U_3845 != zero_zero_int )
      & ( U_3845 = zero_zero_int
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(U_3845)),one_one_int)) ) ),
    inference(variable_rename,[status(thm)],[f_1252_1]) ).

fof(f_1252_3,plain,
    ( ! [U_3847] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(U_3847)),one_one_int))
        | U_3847 != zero_zero_int )
    & ! [U_3846] :
        ( U_3846 = zero_zero_int
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(U_3846)),one_one_int)) ) ),
    inference(miniscope,[status(thm)],[f_1252_2]) ).

fof(f_1252_4,plain,
    ( ! [U_3847] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(U_3847)),one_one_int))
        | U_3847 != zero_zero_int )
    & ! [U_3846] :
        ( U_3846 = zero_zero_int
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(U_3846)),one_one_int)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1252_3]) ).

cnf(f_1252_5,plain,
    ( U_3846 = zero_zero_int
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(U_3846)),one_one_int)) ),
    inference(clausify,[status(thm)],[f_1252_4]) ).

cnf(f_1252_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,abs_abs_int(U_3847)),one_one_int))
    | U_3847 != zero_zero_int ),
    inference(clausify,[status(thm)],[f_1252_4]) ).

fof(f_1253_1,plain,
    ! [Z_1] :
      ( ( hBOOL(hAPP_int_bool(nat_neg,Z_1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_1),zero_zero_int)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z_1),zero_zero_int))
        | ~ hBOOL(hAPP_int_bool(nat_neg,Z_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1146_neg__def]) ).

fof(f_1253_2,plain,
    ! [U_3848] :
      ( ( hBOOL(hAPP_int_bool(nat_neg,U_3848))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3848),zero_zero_int)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3848),zero_zero_int))
        | ~ hBOOL(hAPP_int_bool(nat_neg,U_3848)) ) ),
    inference(variable_rename,[status(thm)],[f_1253_1]) ).

fof(f_1253_3,plain,
    ( ! [U_3850] :
        ( hBOOL(hAPP_int_bool(nat_neg,U_3850))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3850),zero_zero_int)) )
    & ! [U_3849] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3849),zero_zero_int))
        | ~ hBOOL(hAPP_int_bool(nat_neg,U_3849)) ) ),
    inference(miniscope,[status(thm)],[f_1253_2]) ).

fof(f_1253_4,plain,
    ( ! [U_3850] :
        ( hBOOL(hAPP_int_bool(nat_neg,U_3850))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3850),zero_zero_int)) )
    & ! [U_3849] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3849),zero_zero_int))
        | ~ hBOOL(hAPP_int_bool(nat_neg,U_3849)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1253_3]) ).

cnf(f_1253_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3849),zero_zero_int))
    | ~ hBOOL(hAPP_int_bool(nat_neg,U_3849)) ),
    inference(clausify,[status(thm)],[f_1253_4]) ).

cnf(f_1253_6,plain,
    ( hBOOL(hAPP_int_bool(nat_neg,U_3850))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3850),zero_zero_int)) ),
    inference(clausify,[status(thm)],[f_1253_4]) ).

fof(f_1254_1,plain,
    ! [X_1] :
      ( ( ~ hBOOL(hAPP_int_bool(nat_neg,X_1))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_1))
        | hBOOL(hAPP_int_bool(nat_neg,X_1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1147_not__neg__eq__ge__0]) ).

fof(f_1254_2,plain,
    ! [U_3851] :
      ( ( ~ hBOOL(hAPP_int_bool(nat_neg,U_3851))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3851)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3851))
        | hBOOL(hAPP_int_bool(nat_neg,U_3851)) ) ),
    inference(variable_rename,[status(thm)],[f_1254_1]) ).

fof(f_1254_3,plain,
    ( ! [U_3853] :
        ( ~ hBOOL(hAPP_int_bool(nat_neg,U_3853))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3853)) )
    & ! [U_3852] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3852))
        | hBOOL(hAPP_int_bool(nat_neg,U_3852)) ) ),
    inference(miniscope,[status(thm)],[f_1254_2]) ).

fof(f_1254_4,plain,
    ( ! [U_3853] :
        ( ~ hBOOL(hAPP_int_bool(nat_neg,U_3853))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3853)) )
    & ! [U_3852] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3852))
        | hBOOL(hAPP_int_bool(nat_neg,U_3852)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1254_3]) ).

cnf(f_1254_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3852))
    | hBOOL(hAPP_int_bool(nat_neg,U_3852)) ),
    inference(clausify,[status(thm)],[f_1254_4]) ).

cnf(f_1254_6,plain,
    ( ~ hBOOL(hAPP_int_bool(nat_neg,U_3853))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),U_3853)) ),
    inference(clausify,[status(thm)],[f_1254_4]) ).

fof(f_1255_1,plain,
    ~ hBOOL(hAPP_int_bool(nat_neg,one_one_int)),
    inference(fof_nnf,[status(thm)],[fact_1148_not__neg__1]) ).

fof(f_1255_2,plain,
    ~ hBOOL(hAPP_int_bool(nat_neg,one_one_int)),
    inference(definitional_conversion,[status(esa)],[f_1255_1]) ).

cnf(f_1255_3,plain,
    ~ hBOOL(hAPP_int_bool(nat_neg,one_one_int)),
    inference(clausify,[status(thm)],[f_1255_2]) ).

fof(f_1256_1,plain,
    ~ hBOOL(hAPP_int_bool(nat_neg,zero_zero_int)),
    inference(fof_nnf,[status(thm)],[fact_1149_not__neg__0]) ).

fof(f_1256_2,plain,
    ~ hBOOL(hAPP_int_bool(nat_neg,zero_zero_int)),
    inference(definitional_conversion,[status(esa)],[f_1256_1]) ).

cnf(f_1256_3,plain,
    ~ hBOOL(hAPP_int_bool(nat_neg,zero_zero_int)),
    inference(clausify,[status(thm)],[f_1256_2]) ).

fof(f_1257_1,plain,
    ! [M_1,N] :
      ( abs_abs_int(M_1) = one_one_int
      | abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,M_1),N)) != one_one_int ),
    inference(fof_nnf,[status(thm)],[fact_1150_abs__zmult__eq__1]) ).

fof(f_1257_2,plain,
    ! [U_3855,U_3854] :
      ( abs_abs_int(U_3855) = one_one_int
      | abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3855),U_3854)) != one_one_int ),
    inference(variable_rename,[status(thm)],[f_1257_1]) ).

fof(f_1257_3,plain,
    ! [U_3855] :
      ( ! [U_3854] : abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3855),U_3854)) != one_one_int
      | abs_abs_int(U_3855) = one_one_int ),
    inference(miniscope,[status(thm)],[f_1257_2]) ).

fof(f_1257_4,plain,
    ! [U_3854,U_3855] :
      ( abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3855),U_3854)) != one_one_int
      | abs_abs_int(U_3855) = one_one_int ),
    inference(definitional_conversion,[status(esa)],[f_1257_3]) ).

cnf(f_1257_5,plain,
    ( abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,U_3855),U_3854)) != one_one_int
    | abs_abs_int(U_3855) = one_one_int ),
    inference(clausify,[status(thm)],[f_1257_4]) ).

fof(f_1258_1,plain,
    ! [N] : ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_nat_int(semiri1621563631at_int,N))),
    inference(fof_nnf,[status(thm)],[fact_1151_not__neg__int]) ).

fof(f_1258_2,plain,
    ! [U_3856] : ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_nat_int(semiri1621563631at_int,U_3856))),
    inference(variable_rename,[status(thm)],[f_1258_1]) ).

fof(f_1258_3,plain,
    ! [U_3856] : ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_nat_int(semiri1621563631at_int,U_3856))),
    inference(definitional_conversion,[status(esa)],[f_1258_2]) ).

cnf(f_1258_4,plain,
    ~ hBOOL(hAPP_int_bool(nat_neg,hAPP_nat_int(semiri1621563631at_int,U_3856))),
    inference(clausify,[status(thm)],[f_1258_3]) ).

fof(f_1259_1,plain,
    ! [M_1] : abs_abs_int(hAPP_nat_int(semiri1621563631at_int,M_1)) = hAPP_nat_int(semiri1621563631at_int,M_1),
    inference(fof_nnf,[status(thm)],[fact_1152_abs__int__eq]) ).

fof(f_1259_2,plain,
    ! [U_3857] : abs_abs_int(hAPP_nat_int(semiri1621563631at_int,U_3857)) = hAPP_nat_int(semiri1621563631at_int,U_3857),
    inference(variable_rename,[status(thm)],[f_1259_1]) ).

fof(f_1259_3,plain,
    ! [U_3857] : abs_abs_int(hAPP_nat_int(semiri1621563631at_int,U_3857)) = hAPP_nat_int(semiri1621563631at_int,U_3857),
    inference(definitional_conversion,[status(esa)],[f_1259_2]) ).

cnf(f_1259_4,plain,
    abs_abs_int(hAPP_nat_int(semiri1621563631at_int,U_3857)) = hAPP_nat_int(semiri1621563631at_int,U_3857),
    inference(clausify,[status(thm)],[f_1259_3]) ).

fof(f_1260_1,plain,
    ! [V] :
      ( number_number_of_nat(V) = zero_zero_nat
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) ),
    inference(fof_nnf,[status(thm)],[fact_1153_neg__imp__number__of__eq__0]) ).

fof(f_1260_2,plain,
    ! [U_3858] :
      ( number_number_of_nat(U_3858) = zero_zero_nat
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3858))) ),
    inference(variable_rename,[status(thm)],[f_1260_1]) ).

fof(f_1260_3,plain,
    ! [U_3858] :
      ( number_number_of_nat(U_3858) = zero_zero_nat
      | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3858))) ),
    inference(definitional_conversion,[status(esa)],[f_1260_2]) ).

cnf(f_1260_4,plain,
    ( number_number_of_nat(U_3858) = zero_zero_nat
    | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3858))) ),
    inference(clausify,[status(thm)],[f_1260_3]) ).

fof(f_1261_1,plain,
    ! [V_3,V_2] :
      ( ( number_number_of_nat(V_3) = number_number_of_nat(V_2)
        | ( ( ( V_3 != V_2
              & ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_2))) )
            | ( number_number_of_int(V_3) != zero_zero_int
              & hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_2))) ) )
          & ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_3))) )
        | ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(V_2)),zero_zero_int))
          & hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_3))) ) )
      & ( ( ( ( ( V_3 = V_2
                | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_2))) )
              & ( number_number_of_int(V_3) = zero_zero_int
                | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_2))) ) )
            | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_3))) )
          & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(V_2)),zero_zero_int))
            | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_3))) ) )
        | number_number_of_nat(V_3) != number_number_of_nat(V_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_1154_eq__nat__number__of]) ).

fof(f_1261_2,plain,
    ! [U_3860,U_3859] :
      ( ( number_number_of_nat(U_3860) = number_number_of_nat(U_3859)
        | ( ( ( U_3860 != U_3859
              & ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3859))) )
            | ( number_number_of_int(U_3860) != zero_zero_int
              & hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3859))) ) )
          & ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3860))) )
        | ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_3859)),zero_zero_int))
          & hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3860))) ) )
      & ( ( ( ( ( U_3860 = U_3859
                | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3859))) )
              & ( number_number_of_int(U_3860) = zero_zero_int
                | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3859))) ) )
            | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3860))) )
          & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_3859)),zero_zero_int))
            | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3860))) ) )
        | number_number_of_nat(U_3860) != number_number_of_nat(U_3859) ) ),
    inference(variable_rename,[status(thm)],[f_1261_1]) ).

fof(f_1261_3,plain,
    ( ! [U_3864,U_3862] :
        ( number_number_of_nat(U_3864) = number_number_of_nat(U_3862)
        | ( ( ( U_3864 != U_3862
              & ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3862))) )
            | ( number_number_of_int(U_3864) != zero_zero_int
              & hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3862))) ) )
          & ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3864))) )
        | ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_3862)),zero_zero_int))
          & hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3864))) ) )
    & ! [U_3863,U_3861] :
        ( ( ( ( ( U_3863 = U_3861
                | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3861))) )
              & ( number_number_of_int(U_3863) = zero_zero_int
                | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3861))) ) )
            | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3863))) )
          & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_3861)),zero_zero_int))
            | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3863))) ) )
        | number_number_of_nat(U_3863) != number_number_of_nat(U_3861) ) ),
    inference(miniscope,[status(thm)],[f_1261_2]) ).

fof(f_1261_4,plain,
    ( ! [U_3862,U_3864] :
        ( U_3864 != U_3862
        | ~ sP355(U_3862,U_3864) )
    & ! [U_3862,U_3864] :
        ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3862)))
        | ~ sP355(U_3862,U_3864) )
    & ! [U_3862,U_3864] :
        ( number_number_of_int(U_3864) != zero_zero_int
        | ~ sP354(U_3862,U_3864) )
    & ! [U_3862,U_3864] :
        ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3862)))
        | ~ sP354(U_3862,U_3864) )
    & ! [U_3862,U_3864] :
        ( sP355(U_3862,U_3864)
        | sP354(U_3862,U_3864)
        | ~ sP356(U_3862,U_3864) )
    & ! [U_3862,U_3864] :
        ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3864)))
        | ~ sP356(U_3862,U_3864) )
    & ! [U_3862,U_3864] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_3862)),zero_zero_int))
        | ~ sP353(U_3862,U_3864) )
    & ! [U_3862,U_3864] :
        ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3864)))
        | ~ sP353(U_3862,U_3864) )
    & ! [U_3861,U_3863] :
        ( U_3863 = U_3861
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3861)))
        | ~ sP351(U_3861,U_3863) )
    & ! [U_3861,U_3863] :
        ( number_number_of_int(U_3863) = zero_zero_int
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3861)))
        | ~ sP351(U_3861,U_3863) )
    & ! [U_3861,U_3863] :
        ( sP351(U_3861,U_3863)
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3863)))
        | ~ sP352(U_3861,U_3863) )
    & ! [U_3861,U_3863] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_3861)),zero_zero_int))
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3863)))
        | ~ sP352(U_3861,U_3863) )
    & ! [U_3862,U_3864] :
        ( number_number_of_nat(U_3864) = number_number_of_nat(U_3862)
        | sP356(U_3862,U_3864)
        | sP353(U_3862,U_3864) )
    & ! [U_3861,U_3863] :
        ( sP352(U_3861,U_3863)
        | number_number_of_nat(U_3863) != number_number_of_nat(U_3861) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP351,sP352,sP353,sP354,sP355,sP356])],[f_1261_3]) ).

cnf(f_1261_5,plain,
    ( sP352(U_3861,U_3863)
    | number_number_of_nat(U_3863) != number_number_of_nat(U_3861) ),
    inference(clausify,[status(thm)],[f_1261_4]) ).

cnf(f_1261_6,plain,
    ( number_number_of_nat(U_3864) = number_number_of_nat(U_3862)
    | sP356(U_3862,U_3864)
    | sP353(U_3862,U_3864) ),
    inference(clausify,[status(thm)],[f_1261_4]) ).

cnf(f_1261_7,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_3861)),zero_zero_int))
    | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3863)))
    | ~ sP352(U_3861,U_3863) ),
    inference(clausify,[status(thm)],[f_1261_4]) ).

cnf(f_1261_8,plain,
    ( sP351(U_3861,U_3863)
    | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3863)))
    | ~ sP352(U_3861,U_3863) ),
    inference(clausify,[status(thm)],[f_1261_4]) ).

cnf(f_1261_9,plain,
    ( number_number_of_int(U_3863) = zero_zero_int
    | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3861)))
    | ~ sP351(U_3861,U_3863) ),
    inference(clausify,[status(thm)],[f_1261_4]) ).

cnf(f_1261_10,plain,
    ( U_3863 = U_3861
    | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3861)))
    | ~ sP351(U_3861,U_3863) ),
    inference(clausify,[status(thm)],[f_1261_4]) ).

cnf(f_1261_11,plain,
    ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3864)))
    | ~ sP353(U_3862,U_3864) ),
    inference(clausify,[status(thm)],[f_1261_4]) ).

cnf(f_1261_12,plain,
    ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,number_number_of_int(U_3862)),zero_zero_int))
    | ~ sP353(U_3862,U_3864) ),
    inference(clausify,[status(thm)],[f_1261_4]) ).

cnf(f_1261_13,plain,
    ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3864)))
    | ~ sP356(U_3862,U_3864) ),
    inference(clausify,[status(thm)],[f_1261_4]) ).

cnf(f_1261_14,plain,
    ( sP355(U_3862,U_3864)
    | sP354(U_3862,U_3864)
    | ~ sP356(U_3862,U_3864) ),
    inference(clausify,[status(thm)],[f_1261_4]) ).

cnf(f_1261_15,plain,
    ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3862)))
    | ~ sP354(U_3862,U_3864) ),
    inference(clausify,[status(thm)],[f_1261_4]) ).

cnf(f_1261_16,plain,
    ( number_number_of_int(U_3864) != zero_zero_int
    | ~ sP354(U_3862,U_3864) ),
    inference(clausify,[status(thm)],[f_1261_4]) ).

cnf(f_1261_17,plain,
    ( ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3862)))
    | ~ sP355(U_3862,U_3864) ),
    inference(clausify,[status(thm)],[f_1261_4]) ).

cnf(f_1261_18,plain,
    ( U_3864 != U_3862
    | ~ sP355(U_3862,U_3864) ),
    inference(clausify,[status(thm)],[f_1261_4]) ).

fof(f_1262_1,plain,
    ! [V_1,K_1,V] :
      ( ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V_1)),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,V),V_1))),K_1)
            | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_1))) )
          & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V_1)),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V)),K_1)
            | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V_1))) ) )
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) )
      & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V_1)),K_1)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V_1)),K_1)
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1155_nat__number__of__add__left]) ).

fof(f_1262_2,plain,
    ! [U_3867,U_3866,U_3865] :
      ( ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3865)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3867)),U_3866)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3865),U_3867))),U_3866)
            | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3867))) )
          & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3865)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3867)),U_3866)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3865)),U_3866)
            | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3867))) ) )
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3865))) )
      & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3865)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3867)),U_3866)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3867)),U_3866)
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3865))) ) ),
    inference(variable_rename,[status(thm)],[f_1262_1]) ).

fof(f_1262_3,plain,
    ( ! [U_3873,U_3871,U_3869] :
        ( ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3869)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3873)),U_3871)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3869),U_3873))),U_3871)
            | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3873))) )
          & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3869)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3873)),U_3871)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3869)),U_3871)
            | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3873))) ) )
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3869))) )
    & ! [U_3872,U_3870,U_3868] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3868)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3872)),U_3870)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3872)),U_3870)
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3868))) ) ),
    inference(miniscope,[status(thm)],[f_1262_2]) ).

fof(f_1262_4,plain,
    ( ! [U_3871,U_3869,U_3873] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3869)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3873)),U_3871)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3869),U_3873))),U_3871)
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3873)))
        | ~ sP357(U_3871,U_3869,U_3873) )
    & ! [U_3871,U_3869,U_3873] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3869)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3873)),U_3871)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3869)),U_3871)
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3873)))
        | ~ sP357(U_3871,U_3869,U_3873) )
    & ! [U_3871,U_3869,U_3873] :
        ( sP357(U_3871,U_3869,U_3873)
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3869))) )
    & ! [U_3870,U_3868,U_3872] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3868)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3872)),U_3870)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3872)),U_3870)
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3868))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP357])],[f_1262_3]) ).

cnf(f_1262_5,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3868)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3872)),U_3870)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3872)),U_3870)
    | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3868))) ),
    inference(clausify,[status(thm)],[f_1262_4]) ).

cnf(f_1262_6,plain,
    ( sP357(U_3871,U_3869,U_3873)
    | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3869))) ),
    inference(clausify,[status(thm)],[f_1262_4]) ).

cnf(f_1262_7,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3869)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3873)),U_3871)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3869)),U_3871)
    | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3873)))
    | ~ sP357(U_3871,U_3869,U_3873) ),
    inference(clausify,[status(thm)],[f_1262_4]) ).

cnf(f_1262_8,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3869)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3873)),U_3871)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3869),U_3873))),U_3871)
    | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3873)))
    | ~ sP357(U_3871,U_3869,U_3873) ),
    inference(clausify,[status(thm)],[f_1262_4]) ).

fof(f_1263_1,plain,
    ! [V] :
      ( ( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(V)) = number_number_of_int(V)
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) )
      & ( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(V)) = zero_zero_int
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1156_int__nat__number__of]) ).

fof(f_1263_2,plain,
    ! [U_3874] :
      ( ( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(U_3874)) = number_number_of_int(U_3874)
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3874))) )
      & ( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(U_3874)) = zero_zero_int
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3874))) ) ),
    inference(variable_rename,[status(thm)],[f_1263_1]) ).

fof(f_1263_3,plain,
    ( ! [U_3876] :
        ( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(U_3876)) = number_number_of_int(U_3876)
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3876))) )
    & ! [U_3875] :
        ( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(U_3875)) = zero_zero_int
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3875))) ) ),
    inference(miniscope,[status(thm)],[f_1263_2]) ).

fof(f_1263_4,plain,
    ( ! [U_3876] :
        ( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(U_3876)) = number_number_of_int(U_3876)
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3876))) )
    & ! [U_3875] :
        ( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(U_3875)) = zero_zero_int
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3875))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1263_3]) ).

cnf(f_1263_5,plain,
    ( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(U_3875)) = zero_zero_int
    | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3875))) ),
    inference(clausify,[status(thm)],[f_1263_4]) ).

cnf(f_1263_6,plain,
    ( hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(U_3876)) = number_number_of_int(U_3876)
    | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3876))) ),
    inference(clausify,[status(thm)],[f_1263_4]) ).

fof(f_1264_1,plain,
    ! [Z,X,D] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,Z),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,X),Z))),one_one_int)),D))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),D)) ),
    inference(fof_nnf,[status(thm)],[fact_1157_incr__lemma]) ).

fof(f_1264_2,plain,
    ! [U_3879,U_3878,U_3877] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3879),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3878),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3878),U_3879))),one_one_int)),U_3877))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3877)) ),
    inference(variable_rename,[status(thm)],[f_1264_1]) ).

fof(f_1264_3,plain,
    ! [U_3877,U_3878,U_3879] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3879),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3878),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3878),U_3879))),one_one_int)),U_3877))))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3877)) ),
    inference(definitional_conversion,[status(esa)],[f_1264_2]) ).

cnf(f_1264_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3879),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3878),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3878),U_3879))),one_one_int)),U_3877))))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),U_3877)) ),
    inference(clausify,[status(thm)],[f_1264_3]) ).

fof(f_1265_1,plain,
    ! [K,F,Na] :
      ( ? [I] :
          ( hAPP_nat_int(F,I) = K
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),Na)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),hAPP_nat_int(F,Na)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(F,zero_zero_nat)),K))
      | ? [I] :
          ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),one_one_nat))),hAPP_nat_int(F,I)))),one_one_int))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1158_int__val__lemma]) ).

fof(f_1265_2,plain,
    ! [U_3884,U_3883,U_3882] :
      ( ? [U_3881] :
          ( hAPP_nat_int(U_3883,U_3881) = U_3884
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3881),U_3882)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3884),hAPP_nat_int(U_3883,U_3882)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(U_3883,zero_zero_nat)),U_3884))
      | ? [U_3880] :
          ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(U_3883,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3880),one_one_nat))),hAPP_nat_int(U_3883,U_3880)))),one_one_int))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3880),U_3882)) ) ),
    inference(variable_rename,[status(thm)],[f_1265_1]) ).

fof(f_1265_3,plain,
    ! [U_3884,U_3883,U_3882] :
      ( ? [U_3881] :
          ( hAPP_nat_int(U_3883,U_3881) = U_3884
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3881),U_3882)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3884),hAPP_nat_int(U_3883,U_3882)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(U_3883,zero_zero_nat)),U_3884))
      | ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(U_3883,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK220(U_3884,U_3883,U_3882)),one_one_nat))),hAPP_nat_int(U_3883,sK220(U_3884,U_3883,U_3882))))),one_one_int))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK220(U_3884,U_3883,U_3882)),U_3882)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK220]),skolemize(U_3880,sK220(U_3884,U_3883,U_3882))],[f_1265_2]) ).

fof(f_1265_4,plain,
    ! [U_3884,U_3883,U_3882] :
      ( ( hAPP_nat_int(U_3883,sK221(U_3884,U_3883,U_3882)) = U_3884
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK221(U_3884,U_3883,U_3882)),U_3882)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3884),hAPP_nat_int(U_3883,U_3882)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(U_3883,zero_zero_nat)),U_3884))
      | ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(U_3883,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK220(U_3884,U_3883,U_3882)),one_one_nat))),hAPP_nat_int(U_3883,sK220(U_3884,U_3883,U_3882))))),one_one_int))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK220(U_3884,U_3883,U_3882)),U_3882)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK221]),skolemize(U_3881,sK221(U_3884,U_3883,U_3882))],[f_1265_3]) ).

fof(f_1265_5,plain,
    ( ! [U_3882,U_3883,U_3884] :
        ( hAPP_nat_int(U_3883,sK221(U_3884,U_3883,U_3882)) = U_3884
        | ~ sP359(U_3882,U_3883,U_3884) )
    & ! [U_3882,U_3883,U_3884] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK221(U_3884,U_3883,U_3882)),U_3882))
        | ~ sP359(U_3882,U_3883,U_3884) )
    & ! [U_3882,U_3883,U_3884] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(U_3883,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK220(U_3884,U_3883,U_3882)),one_one_nat))),hAPP_nat_int(U_3883,sK220(U_3884,U_3883,U_3882))))),one_one_int))
        | ~ sP358(U_3882,U_3883,U_3884) )
    & ! [U_3882,U_3883,U_3884] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK220(U_3884,U_3883,U_3882)),U_3882))
        | ~ sP358(U_3882,U_3883,U_3884) )
    & ! [U_3882,U_3883,U_3884] :
        ( sP359(U_3882,U_3883,U_3884)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3884),hAPP_nat_int(U_3883,U_3882)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(U_3883,zero_zero_nat)),U_3884))
        | sP358(U_3882,U_3883,U_3884) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP358,sP359])],[f_1265_4]) ).

cnf(f_1265_6,plain,
    ( sP359(U_3882,U_3883,U_3884)
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3884),hAPP_nat_int(U_3883,U_3882)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(U_3883,zero_zero_nat)),U_3884))
    | sP358(U_3882,U_3883,U_3884) ),
    inference(clausify,[status(thm)],[f_1265_5]) ).

cnf(f_1265_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK220(U_3884,U_3883,U_3882)),U_3882))
    | ~ sP358(U_3882,U_3883,U_3884) ),
    inference(clausify,[status(thm)],[f_1265_5]) ).

cnf(f_1265_8,plain,
    ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(U_3883,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK220(U_3884,U_3883,U_3882)),one_one_nat))),hAPP_nat_int(U_3883,sK220(U_3884,U_3883,U_3882))))),one_one_int))
    | ~ sP358(U_3882,U_3883,U_3884) ),
    inference(clausify,[status(thm)],[f_1265_5]) ).

cnf(f_1265_9,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK221(U_3884,U_3883,U_3882)),U_3882))
    | ~ sP359(U_3882,U_3883,U_3884) ),
    inference(clausify,[status(thm)],[f_1265_5]) ).

cnf(f_1265_10,plain,
    ( hAPP_nat_int(U_3883,sK221(U_3884,U_3883,U_3882)) = U_3884
    | ~ sP359(U_3882,U_3883,U_3884) ),
    inference(clausify,[status(thm)],[f_1265_5]) ).

fof(f_1266_1,plain,
    ! [K,F,Na] :
      ( ? [I] :
          ( hAPP_nat_int(F,I) = K
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),Na)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),hAPP_nat_int(F,Na)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(F,zero_zero_nat)),K))
      | ? [I] :
          ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),one_one_nat))),hAPP_nat_int(F,I)))),one_one_int))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),Na)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1159_nat0__intermed__int__val]) ).

fof(f_1266_2,plain,
    ! [U_3889,U_3888,U_3887] :
      ( ? [U_3886] :
          ( hAPP_nat_int(U_3888,U_3886) = U_3889
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3886),U_3887)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3889),hAPP_nat_int(U_3888,U_3887)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(U_3888,zero_zero_nat)),U_3889))
      | ? [U_3885] :
          ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(U_3888,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3885),one_one_nat))),hAPP_nat_int(U_3888,U_3885)))),one_one_int))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3885),U_3887)) ) ),
    inference(variable_rename,[status(thm)],[f_1266_1]) ).

fof(f_1266_3,plain,
    ! [U_3889,U_3888,U_3887] :
      ( ? [U_3886] :
          ( hAPP_nat_int(U_3888,U_3886) = U_3889
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3886),U_3887)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3889),hAPP_nat_int(U_3888,U_3887)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(U_3888,zero_zero_nat)),U_3889))
      | ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(U_3888,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK222(U_3889,U_3888,U_3887)),one_one_nat))),hAPP_nat_int(U_3888,sK222(U_3889,U_3888,U_3887))))),one_one_int))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK222(U_3889,U_3888,U_3887)),U_3887)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK222]),skolemize(U_3885,sK222(U_3889,U_3888,U_3887))],[f_1266_2]) ).

fof(f_1266_4,plain,
    ! [U_3889,U_3888,U_3887] :
      ( ( hAPP_nat_int(U_3888,sK223(U_3889,U_3888,U_3887)) = U_3889
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK223(U_3889,U_3888,U_3887)),U_3887)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3889),hAPP_nat_int(U_3888,U_3887)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(U_3888,zero_zero_nat)),U_3889))
      | ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(U_3888,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK222(U_3889,U_3888,U_3887)),one_one_nat))),hAPP_nat_int(U_3888,sK222(U_3889,U_3888,U_3887))))),one_one_int))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK222(U_3889,U_3888,U_3887)),U_3887)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK223]),skolemize(U_3886,sK223(U_3889,U_3888,U_3887))],[f_1266_3]) ).

fof(f_1266_5,plain,
    ( ! [U_3888,U_3889,U_3887] :
        ( hAPP_nat_int(U_3888,sK223(U_3889,U_3888,U_3887)) = U_3889
        | ~ sP361(U_3888,U_3889,U_3887) )
    & ! [U_3888,U_3889,U_3887] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK223(U_3889,U_3888,U_3887)),U_3887))
        | ~ sP361(U_3888,U_3889,U_3887) )
    & ! [U_3888,U_3889,U_3887] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(U_3888,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK222(U_3889,U_3888,U_3887)),one_one_nat))),hAPP_nat_int(U_3888,sK222(U_3889,U_3888,U_3887))))),one_one_int))
        | ~ sP360(U_3888,U_3889,U_3887) )
    & ! [U_3888,U_3889,U_3887] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK222(U_3889,U_3888,U_3887)),U_3887))
        | ~ sP360(U_3888,U_3889,U_3887) )
    & ! [U_3888,U_3889,U_3887] :
        ( sP361(U_3888,U_3889,U_3887)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3889),hAPP_nat_int(U_3888,U_3887)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(U_3888,zero_zero_nat)),U_3889))
        | sP360(U_3888,U_3889,U_3887) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP360,sP361])],[f_1266_4]) ).

cnf(f_1266_6,plain,
    ( sP361(U_3888,U_3889,U_3887)
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3889),hAPP_nat_int(U_3888,U_3887)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(U_3888,zero_zero_nat)),U_3889))
    | sP360(U_3888,U_3889,U_3887) ),
    inference(clausify,[status(thm)],[f_1266_5]) ).

cnf(f_1266_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK222(U_3889,U_3888,U_3887)),U_3887))
    | ~ sP360(U_3888,U_3889,U_3887) ),
    inference(clausify,[status(thm)],[f_1266_5]) ).

cnf(f_1266_8,plain,
    ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(U_3888,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK222(U_3889,U_3888,U_3887)),one_one_nat))),hAPP_nat_int(U_3888,sK222(U_3889,U_3888,U_3887))))),one_one_int))
    | ~ sP360(U_3888,U_3889,U_3887) ),
    inference(clausify,[status(thm)],[f_1266_5]) ).

cnf(f_1266_9,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK223(U_3889,U_3888,U_3887)),U_3887))
    | ~ sP361(U_3888,U_3889,U_3887) ),
    inference(clausify,[status(thm)],[f_1266_5]) ).

cnf(f_1266_10,plain,
    ( hAPP_nat_int(U_3888,sK223(U_3889,U_3888,U_3887)) = U_3889
    | ~ sP361(U_3888,U_3889,U_3887) ),
    inference(clausify,[status(thm)],[f_1266_5]) ).

fof(f_1267_1,plain,
    ! [K,F,Na,M] :
      ( ? [I] :
          ( hAPP_nat_int(F,I) = K
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I),Na))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),I)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),hAPP_nat_int(F,Na)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(F,M)),K))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,M),Na))
      | ? [I] :
          ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(F,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,I),one_one_nat))),hAPP_nat_int(F,I)))),one_one_int))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,I),Na))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M),I)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1160_nat__intermed__int__val]) ).

fof(f_1267_2,plain,
    ! [U_3895,U_3894,U_3893,U_3892] :
      ( ? [U_3891] :
          ( hAPP_nat_int(U_3894,U_3891) = U_3895
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3891),U_3893))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3892),U_3891)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3895),hAPP_nat_int(U_3894,U_3893)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(U_3894,U_3892)),U_3895))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3892),U_3893))
      | ? [U_3890] :
          ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(U_3894,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,U_3890),one_one_nat))),hAPP_nat_int(U_3894,U_3890)))),one_one_int))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3890),U_3893))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3892),U_3890)) ) ),
    inference(variable_rename,[status(thm)],[f_1267_1]) ).

fof(f_1267_3,plain,
    ! [U_3895,U_3894,U_3893,U_3892] :
      ( ? [U_3891] :
          ( hAPP_nat_int(U_3894,U_3891) = U_3895
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3891),U_3893))
          & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3892),U_3891)) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3895),hAPP_nat_int(U_3894,U_3893)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(U_3894,U_3892)),U_3895))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3892),U_3893))
      | ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(U_3894,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK224(U_3895,U_3894,U_3893,U_3892)),one_one_nat))),hAPP_nat_int(U_3894,sK224(U_3895,U_3894,U_3893,U_3892))))),one_one_int))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK224(U_3895,U_3894,U_3893,U_3892)),U_3893))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3892),sK224(U_3895,U_3894,U_3893,U_3892))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK224]),skolemize(U_3890,sK224(U_3895,U_3894,U_3893,U_3892))],[f_1267_2]) ).

fof(f_1267_4,plain,
    ! [U_3895,U_3894,U_3893,U_3892] :
      ( ( hAPP_nat_int(U_3894,sK225(U_3895,U_3894,U_3893,U_3892)) = U_3895
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK225(U_3895,U_3894,U_3893,U_3892)),U_3893))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3892),sK225(U_3895,U_3894,U_3893,U_3892))) )
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3895),hAPP_nat_int(U_3894,U_3893)))
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(U_3894,U_3892)),U_3895))
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3892),U_3893))
      | ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(U_3894,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK224(U_3895,U_3894,U_3893,U_3892)),one_one_nat))),hAPP_nat_int(U_3894,sK224(U_3895,U_3894,U_3893,U_3892))))),one_one_int))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK224(U_3895,U_3894,U_3893,U_3892)),U_3893))
        & hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3892),sK224(U_3895,U_3894,U_3893,U_3892))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK225]),skolemize(U_3891,sK225(U_3895,U_3894,U_3893,U_3892))],[f_1267_3]) ).

fof(f_1267_5,plain,
    ( ! [U_3892,U_3893,U_3894,U_3895] :
        ( hAPP_nat_int(U_3894,sK225(U_3895,U_3894,U_3893,U_3892)) = U_3895
        | ~ sP363(U_3892,U_3893,U_3894,U_3895) )
    & ! [U_3892,U_3893,U_3894,U_3895] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK225(U_3895,U_3894,U_3893,U_3892)),U_3893))
        | ~ sP363(U_3892,U_3893,U_3894,U_3895) )
    & ! [U_3892,U_3893,U_3894,U_3895] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3892),sK225(U_3895,U_3894,U_3893,U_3892)))
        | ~ sP363(U_3892,U_3893,U_3894,U_3895) )
    & ! [U_3892,U_3893,U_3894,U_3895] :
        ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(U_3894,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK224(U_3895,U_3894,U_3893,U_3892)),one_one_nat))),hAPP_nat_int(U_3894,sK224(U_3895,U_3894,U_3893,U_3892))))),one_one_int))
        | ~ sP362(U_3892,U_3893,U_3894,U_3895) )
    & ! [U_3892,U_3893,U_3894,U_3895] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK224(U_3895,U_3894,U_3893,U_3892)),U_3893))
        | ~ sP362(U_3892,U_3893,U_3894,U_3895) )
    & ! [U_3892,U_3893,U_3894,U_3895] :
        ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3892),sK224(U_3895,U_3894,U_3893,U_3892)))
        | ~ sP362(U_3892,U_3893,U_3894,U_3895) )
    & ! [U_3892,U_3893,U_3894,U_3895] :
        ( sP363(U_3892,U_3893,U_3894,U_3895)
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3895),hAPP_nat_int(U_3894,U_3893)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(U_3894,U_3892)),U_3895))
        | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3892),U_3893))
        | sP362(U_3892,U_3893,U_3894,U_3895) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP362,sP363])],[f_1267_4]) ).

cnf(f_1267_6,plain,
    ( sP363(U_3892,U_3893,U_3894,U_3895)
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3895),hAPP_nat_int(U_3894,U_3893)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_nat_int(U_3894,U_3892)),U_3895))
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,U_3892),U_3893))
    | sP362(U_3892,U_3893,U_3894,U_3895) ),
    inference(clausify,[status(thm)],[f_1267_5]) ).

cnf(f_1267_7,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3892),sK224(U_3895,U_3894,U_3893,U_3892)))
    | ~ sP362(U_3892,U_3893,U_3894,U_3895) ),
    inference(clausify,[status(thm)],[f_1267_5]) ).

cnf(f_1267_8,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,sK224(U_3895,U_3894,U_3893,U_3892)),U_3893))
    | ~ sP362(U_3892,U_3893,U_3894,U_3895) ),
    inference(clausify,[status(thm)],[f_1267_5]) ).

cnf(f_1267_9,plain,
    ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,abs_abs_int(hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,hAPP_nat_int(U_3894,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,sK224(U_3895,U_3894,U_3893,U_3892)),one_one_nat))),hAPP_nat_int(U_3894,sK224(U_3895,U_3894,U_3893,U_3892))))),one_one_int))
    | ~ sP362(U_3892,U_3893,U_3894,U_3895) ),
    inference(clausify,[status(thm)],[f_1267_5]) ).

cnf(f_1267_10,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,U_3892),sK225(U_3895,U_3894,U_3893,U_3892)))
    | ~ sP363(U_3892,U_3893,U_3894,U_3895) ),
    inference(clausify,[status(thm)],[f_1267_5]) ).

cnf(f_1267_11,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,sK225(U_3895,U_3894,U_3893,U_3892)),U_3893))
    | ~ sP363(U_3892,U_3893,U_3894,U_3895) ),
    inference(clausify,[status(thm)],[f_1267_5]) ).

cnf(f_1267_12,plain,
    ( hAPP_nat_int(U_3894,sK225(U_3895,U_3894,U_3893,U_3892)) = U_3895
    | ~ sP363(U_3892,U_3893,U_3894,U_3895) ),
    inference(clausify,[status(thm)],[f_1267_5]) ).

fof(f_1268_1,plain,
    ! [N,V] :
      ( ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V)),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(succ(V))),N)
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) )
      & ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(V)),N)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N)
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1161_Suc__nat__number__of__add]) ).

fof(f_1268_2,plain,
    ! [U_3897,U_3896] :
      ( ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3896)),U_3897)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(succ(U_3896))),U_3897)
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3896))) )
      & ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3896)),U_3897)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),U_3897)
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3896))) ) ),
    inference(variable_rename,[status(thm)],[f_1268_1]) ).

fof(f_1268_3,plain,
    ( ! [U_3901,U_3899] :
        ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3899)),U_3901)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(succ(U_3899))),U_3901)
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3899))) )
    & ! [U_3900,U_3898] :
        ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3898)),U_3900)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),U_3900)
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3898))) ) ),
    inference(miniscope,[status(thm)],[f_1268_2]) ).

fof(f_1268_4,plain,
    ( ! [U_3901,U_3899] :
        ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3899)),U_3901)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(succ(U_3899))),U_3901)
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3899))) )
    & ! [U_3898,U_3900] :
        ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3898)),U_3900)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),U_3900)
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3898))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1268_3]) ).

cnf(f_1268_5,plain,
    ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3898)),U_3900)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),U_3900)
    | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3898))) ),
    inference(clausify,[status(thm)],[f_1268_4]) ).

cnf(f_1268_6,plain,
    ( hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3899)),U_3901)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(succ(U_3899))),U_3901)
    | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3899))) ),
    inference(clausify,[status(thm)],[f_1268_4]) ).

fof(f_1269_1,plain,
    ! [K_1] : succ(K_1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_1),one_one_int),
    inference(fof_nnf,[status(thm)],[fact_1162_succ__def]) ).

fof(f_1269_2,plain,
    ! [U_3902] : succ(U_3902) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3902),one_one_int),
    inference(variable_rename,[status(thm)],[f_1269_1]) ).

fof(f_1269_3,plain,
    ! [U_3902] : succ(U_3902) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3902),one_one_int),
    inference(definitional_conversion,[status(esa)],[f_1269_2]) ).

cnf(f_1269_4,plain,
    succ(U_3902) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3902),one_one_int),
    inference(clausify,[status(thm)],[f_1269_3]) ).

fof(f_1270_1,plain,
    ! [V] :
      ( ( hAPP_nat_nat(suc,number_number_of_nat(V)) = number_number_of_nat(succ(V))
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) )
      & ( hAPP_nat_nat(suc,number_number_of_nat(V)) = one_one_nat
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(V))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1163_Suc__nat__number__of]) ).

fof(f_1270_2,plain,
    ! [U_3903] :
      ( ( hAPP_nat_nat(suc,number_number_of_nat(U_3903)) = number_number_of_nat(succ(U_3903))
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3903))) )
      & ( hAPP_nat_nat(suc,number_number_of_nat(U_3903)) = one_one_nat
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3903))) ) ),
    inference(variable_rename,[status(thm)],[f_1270_1]) ).

fof(f_1270_3,plain,
    ( ! [U_3905] :
        ( hAPP_nat_nat(suc,number_number_of_nat(U_3905)) = number_number_of_nat(succ(U_3905))
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3905))) )
    & ! [U_3904] :
        ( hAPP_nat_nat(suc,number_number_of_nat(U_3904)) = one_one_nat
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3904))) ) ),
    inference(miniscope,[status(thm)],[f_1270_2]) ).

fof(f_1270_4,plain,
    ( ! [U_3905] :
        ( hAPP_nat_nat(suc,number_number_of_nat(U_3905)) = number_number_of_nat(succ(U_3905))
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3905))) )
    & ! [U_3904] :
        ( hAPP_nat_nat(suc,number_number_of_nat(U_3904)) = one_one_nat
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3904))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1270_3]) ).

cnf(f_1270_5,plain,
    ( hAPP_nat_nat(suc,number_number_of_nat(U_3904)) = one_one_nat
    | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3904))) ),
    inference(clausify,[status(thm)],[f_1270_4]) ).

cnf(f_1270_6,plain,
    ( hAPP_nat_nat(suc,number_number_of_nat(U_3905)) = number_number_of_nat(succ(U_3905))
    | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3905))) ),
    inference(clausify,[status(thm)],[f_1270_4]) ).

fof(f_1271_1,plain,
    ! [W] :
      ( ( number_number_of_nat(bit1(W)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(W)),number_number_of_nat(W)))
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(W))) )
      & ( number_number_of_nat(bit1(W)) = zero_zero_nat
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(W))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1164_nat__number__of__Bit1]) ).

fof(f_1271_2,plain,
    ! [U_3906] :
      ( ( number_number_of_nat(bit1(U_3906)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3906)),number_number_of_nat(U_3906)))
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3906))) )
      & ( number_number_of_nat(bit1(U_3906)) = zero_zero_nat
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3906))) ) ),
    inference(variable_rename,[status(thm)],[f_1271_1]) ).

fof(f_1271_3,plain,
    ( ! [U_3908] :
        ( number_number_of_nat(bit1(U_3908)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3908)),number_number_of_nat(U_3908)))
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3908))) )
    & ! [U_3907] :
        ( number_number_of_nat(bit1(U_3907)) = zero_zero_nat
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3907))) ) ),
    inference(miniscope,[status(thm)],[f_1271_2]) ).

fof(f_1271_4,plain,
    ( ! [U_3908] :
        ( number_number_of_nat(bit1(U_3908)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3908)),number_number_of_nat(U_3908)))
        | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3908))) )
    & ! [U_3907] :
        ( number_number_of_nat(bit1(U_3907)) = zero_zero_nat
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3907))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1271_3]) ).

cnf(f_1271_5,plain,
    ( number_number_of_nat(bit1(U_3907)) = zero_zero_nat
    | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3907))) ),
    inference(clausify,[status(thm)],[f_1271_4]) ).

cnf(f_1271_6,plain,
    ( number_number_of_nat(bit1(U_3908)) = hAPP_nat_nat(suc,hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(U_3908)),number_number_of_nat(U_3908)))
    | hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3908))) ),
    inference(clausify,[status(thm)],[f_1271_4]) ).

fof(f_1272_1,plain,
    ! [V] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(V)) = number_number_of_nat(succ(V))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls)) )
      & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(V)) = one_one_nat
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,V),pls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1165_nat__1__add__number__of]) ).

fof(f_1272_2,plain,
    ! [U_3909] :
      ( ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(U_3909)) = number_number_of_nat(succ(U_3909))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3909),pls)) )
      & ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(U_3909)) = one_one_nat
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3909),pls)) ) ),
    inference(variable_rename,[status(thm)],[f_1272_1]) ).

fof(f_1272_3,plain,
    ( ! [U_3911] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(U_3911)) = number_number_of_nat(succ(U_3911))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3911),pls)) )
    & ! [U_3910] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(U_3910)) = one_one_nat
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3910),pls)) ) ),
    inference(miniscope,[status(thm)],[f_1272_2]) ).

fof(f_1272_4,plain,
    ( ! [U_3911] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(U_3911)) = number_number_of_nat(succ(U_3911))
        | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3911),pls)) )
    & ! [U_3910] :
        ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(U_3910)) = one_one_nat
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3910),pls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1272_3]) ).

cnf(f_1272_5,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(U_3910)) = one_one_nat
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3910),pls)) ),
    inference(clausify,[status(thm)],[f_1272_4]) ).

cnf(f_1272_6,plain,
    ( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),number_number_of_nat(U_3911)) = number_number_of_nat(succ(U_3911))
    | hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3911),pls)) ),
    inference(clausify,[status(thm)],[f_1272_4]) ).

fof(f_1273_1,plain,
    succ(pls) = bit1(pls),
    inference(fof_nnf,[status(thm)],[fact_1166_succ__Pls]) ).

fof(f_1273_2,plain,
    succ(pls) = bit1(pls),
    inference(definitional_conversion,[status(esa)],[f_1273_1]) ).

cnf(f_1273_3,plain,
    succ(pls) = bit1(pls),
    inference(clausify,[status(thm)],[f_1273_2]) ).

fof(f_1274_1,plain,
    ! [W_1] :
      ( ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(W_1))))
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(W_1))) )
      & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(W_1)))
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(W_1)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1167_neg__number__of__Bit1]) ).

fof(f_1274_2,plain,
    ! [U_3912] :
      ( ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(U_3912))))
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3912))) )
      & ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3912)))
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(U_3912)))) ) ),
    inference(variable_rename,[status(thm)],[f_1274_1]) ).

fof(f_1274_3,plain,
    ( ! [U_3914] :
        ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(U_3914))))
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3914))) )
    & ! [U_3913] :
        ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3913)))
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(U_3913)))) ) ),
    inference(miniscope,[status(thm)],[f_1274_2]) ).

fof(f_1274_4,plain,
    ( ! [U_3914] :
        ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(U_3914))))
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3914))) )
    & ! [U_3913] :
        ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3913)))
        | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(U_3913)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1274_3]) ).

cnf(f_1274_5,plain,
    ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3913)))
    | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(U_3913)))) ),
    inference(clausify,[status(thm)],[f_1274_4]) ).

cnf(f_1274_6,plain,
    ( hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(bit1(U_3914))))
    | ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(U_3914))) ),
    inference(clausify,[status(thm)],[f_1274_4]) ).

fof(f_1275_1,plain,
    ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(pls))),
    inference(fof_nnf,[status(thm)],[fact_1168_not__neg__number__of__Pls]) ).

fof(f_1275_2,plain,
    ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(pls))),
    inference(definitional_conversion,[status(esa)],[f_1275_1]) ).

cnf(f_1275_3,plain,
    ~ hBOOL(hAPP_int_bool(nat_neg,number_number_of_int(pls))),
    inference(clausify,[status(thm)],[f_1275_2]) ).

fof(f_1276_1,plain,
    number_number_of_int(bit1(bit1(pls))) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(bit1(bit1(pls)))),
    inference(fof_nnf,[status(thm)],[fact_1169_transfer__int__nat__numerals_I4_J]) ).

fof(f_1276_2,plain,
    number_number_of_int(bit1(bit1(pls))) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(bit1(bit1(pls)))),
    inference(definitional_conversion,[status(esa)],[f_1276_1]) ).

cnf(f_1276_3,plain,
    number_number_of_int(bit1(bit1(pls))) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(bit1(bit1(pls)))),
    inference(clausify,[status(thm)],[f_1276_2]) ).

fof(f_1277_1,plain,
    number_number_of_nat(bit1(pls)) = hAPP_nat_nat(suc,zero_zero_nat),
    inference(fof_nnf,[status(thm)],[fact_1170_numeral__1__eq__Suc__0]) ).

fof(f_1277_2,plain,
    number_number_of_nat(bit1(pls)) = hAPP_nat_nat(suc,zero_zero_nat),
    inference(definitional_conversion,[status(esa)],[f_1277_1]) ).

cnf(f_1277_3,plain,
    number_number_of_nat(bit1(pls)) = hAPP_nat_nat(suc,zero_zero_nat),
    inference(clausify,[status(thm)],[f_1277_2]) ).

fof(f_1278_1,plain,
    number_number_of_nat(bit1(bit1(pls))) = hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))),
    inference(fof_nnf,[status(thm)],[fact_1171_numeral__3__eq__3]) ).

fof(f_1278_2,plain,
    number_number_of_nat(bit1(bit1(pls))) = hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))),
    inference(definitional_conversion,[status(esa)],[f_1278_1]) ).

cnf(f_1278_3,plain,
    number_number_of_nat(bit1(bit1(pls))) = hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat))),
    inference(clausify,[status(thm)],[f_1278_2]) ).

fof(f_1279_1,plain,
    ! [N] : hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,N))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(bit1(bit1(pls)))),N),
    inference(fof_nnf,[status(thm)],[fact_1172_Suc3__eq__add__3]) ).

fof(f_1279_2,plain,
    ! [U_3915] : hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,U_3915))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(bit1(bit1(pls)))),U_3915),
    inference(variable_rename,[status(thm)],[f_1279_1]) ).

fof(f_1279_3,plain,
    ! [U_3915] : hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,U_3915))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(bit1(bit1(pls)))),U_3915),
    inference(definitional_conversion,[status(esa)],[f_1279_2]) ).

cnf(f_1279_4,plain,
    hAPP_nat_nat(suc,hAPP_nat_nat(suc,hAPP_nat_nat(suc,U_3915))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,number_number_of_nat(bit1(bit1(pls)))),U_3915),
    inference(clausify,[status(thm)],[f_1279_3]) ).

fof(f_1280_1,plain,
    one_one_nat = number_number_of_nat(bit1(pls)),
    inference(fof_nnf,[status(thm)],[fact_1173_Numeral1__eq1__nat]) ).

fof(f_1280_2,plain,
    one_one_nat = number_number_of_nat(bit1(pls)),
    inference(definitional_conversion,[status(esa)],[f_1280_1]) ).

cnf(f_1280_3,plain,
    one_one_nat = number_number_of_nat(bit1(pls)),
    inference(clausify,[status(thm)],[f_1280_2]) ).

fof(f_1281_1,plain,
    number_number_of_nat(bit1(pls)) = one_one_nat,
    inference(fof_nnf,[status(thm)],[fact_1174_nat__numeral__1__eq__1]) ).

fof(f_1281_2,plain,
    number_number_of_nat(bit1(pls)) = one_one_nat,
    inference(definitional_conversion,[status(esa)],[f_1281_1]) ).

cnf(f_1281_3,plain,
    number_number_of_nat(bit1(pls)) = one_one_nat,
    inference(clausify,[status(thm)],[f_1281_2]) ).

fof(f_1282_1,plain,
    one_one_int = number_number_of_int(bit1(pls)),
    inference(fof_nnf,[status(thm)],[fact_1175_one__is__num__one]) ).

fof(f_1282_2,plain,
    one_one_int = number_number_of_int(bit1(pls)),
    inference(definitional_conversion,[status(esa)],[f_1282_1]) ).

cnf(f_1282_3,plain,
    one_one_int = number_number_of_int(bit1(pls)),
    inference(clausify,[status(thm)],[f_1282_2]) ).

fof(f_1283_1,plain,
    zero_zero_int = number_number_of_int(pls),
    inference(fof_nnf,[status(thm)],[fact_1176_zero__is__num__zero]) ).

fof(f_1283_2,plain,
    zero_zero_int = number_number_of_int(pls),
    inference(definitional_conversion,[status(esa)],[f_1283_1]) ).

cnf(f_1283_3,plain,
    zero_zero_int = number_number_of_int(pls),
    inference(clausify,[status(thm)],[f_1283_2]) ).

fof(f_1284_1,plain,
    ! [K_1] : bit1(K_1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_1)),K_1),
    inference(fof_nnf,[status(thm)],[fact_1177_Bit1__def]) ).

fof(f_1284_2,plain,
    ! [U_3916] : bit1(U_3916) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),U_3916)),U_3916),
    inference(variable_rename,[status(thm)],[f_1284_1]) ).

fof(f_1284_3,plain,
    ! [U_3916] : bit1(U_3916) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),U_3916)),U_3916),
    inference(definitional_conversion,[status(esa)],[f_1284_2]) ).

cnf(f_1284_4,plain,
    bit1(U_3916) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),U_3916)),U_3916),
    inference(clausify,[status(thm)],[f_1284_3]) ).

fof(f_1285_1,plain,
    number_number_of_nat(pls) = zero_zero_nat,
    inference(fof_nnf,[status(thm)],[fact_1178_nat__number__of__Pls]) ).

fof(f_1285_2,plain,
    number_number_of_nat(pls) = zero_zero_nat,
    inference(definitional_conversion,[status(esa)],[f_1285_1]) ).

cnf(f_1285_3,plain,
    number_number_of_nat(pls) = zero_zero_nat,
    inference(clausify,[status(thm)],[f_1285_2]) ).

fof(f_1286_1,plain,
    zero_zero_nat = number_number_of_nat(pls),
    inference(fof_nnf,[status(thm)],[fact_1179_semiring__norm_I113_J]) ).

fof(f_1286_2,plain,
    zero_zero_nat = number_number_of_nat(pls),
    inference(definitional_conversion,[status(esa)],[f_1286_1]) ).

cnf(f_1286_3,plain,
    zero_zero_nat = number_number_of_nat(pls),
    inference(clausify,[status(thm)],[f_1286_2]) ).

fof(f_1287_1,plain,
    pls = zero_zero_int,
    inference(fof_nnf,[status(thm)],[fact_1180_Pls__def]) ).

fof(f_1287_2,plain,
    pls = zero_zero_int,
    inference(definitional_conversion,[status(esa)],[f_1287_1]) ).

cnf(f_1287_3,plain,
    pls = zero_zero_int,
    inference(clausify,[status(thm)],[f_1287_2]) ).

fof(f_1288_1,plain,
    ! [K,L] :
      ( ( bit1(K) = bit1(L)
        | K != L )
      & ( K = L
        | bit1(K) != bit1(L) ) ),
    inference(fof_nnf,[status(thm)],[fact_1181_rel__simps_I51_J]) ).

fof(f_1288_2,plain,
    ! [U_3918,U_3917] :
      ( ( bit1(U_3918) = bit1(U_3917)
        | U_3918 != U_3917 )
      & ( U_3918 = U_3917
        | bit1(U_3918) != bit1(U_3917) ) ),
    inference(variable_rename,[status(thm)],[f_1288_1]) ).

fof(f_1288_3,plain,
    ( ! [U_3922,U_3920] :
        ( bit1(U_3922) = bit1(U_3920)
        | U_3922 != U_3920 )
    & ! [U_3921,U_3919] :
        ( U_3921 = U_3919
        | bit1(U_3921) != bit1(U_3919) ) ),
    inference(miniscope,[status(thm)],[f_1288_2]) ).

fof(f_1288_4,plain,
    ( ! [U_3920,U_3922] :
        ( bit1(U_3922) = bit1(U_3920)
        | U_3922 != U_3920 )
    & ! [U_3921,U_3919] :
        ( U_3921 = U_3919
        | bit1(U_3921) != bit1(U_3919) ) ),
    inference(definitional_conversion,[status(esa)],[f_1288_3]) ).

cnf(f_1288_5,plain,
    ( U_3921 = U_3919
    | bit1(U_3921) != bit1(U_3919) ),
    inference(clausify,[status(thm)],[f_1288_4]) ).

cnf(f_1288_6,plain,
    ( bit1(U_3922) = bit1(U_3920)
    | U_3922 != U_3920 ),
    inference(clausify,[status(thm)],[f_1288_4]) ).

fof(f_1289_1,plain,
    ! [K_1] : bit1(K_1) != pls,
    inference(fof_nnf,[status(thm)],[fact_1182_rel__simps_I46_J]) ).

fof(f_1289_2,plain,
    ! [U_3923] : bit1(U_3923) != pls,
    inference(variable_rename,[status(thm)],[f_1289_1]) ).

fof(f_1289_3,plain,
    ! [U_3923] : bit1(U_3923) != pls,
    inference(definitional_conversion,[status(esa)],[f_1289_2]) ).

cnf(f_1289_4,plain,
    bit1(U_3923) != pls,
    inference(clausify,[status(thm)],[f_1289_3]) ).

fof(f_1290_1,plain,
    ! [L_1] : pls != bit1(L_1),
    inference(fof_nnf,[status(thm)],[fact_1183_rel__simps_I39_J]) ).

fof(f_1290_2,plain,
    ! [U_3924] : pls != bit1(U_3924),
    inference(variable_rename,[status(thm)],[f_1290_1]) ).

fof(f_1290_3,plain,
    ! [U_3924] : pls != bit1(U_3924),
    inference(definitional_conversion,[status(esa)],[f_1290_2]) ).

cnf(f_1290_4,plain,
    pls != bit1(U_3924),
    inference(clausify,[status(thm)],[f_1290_3]) ).

fof(f_1291_1,plain,
    ! [K_1] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,K_1),pls) = K_1,
    inference(fof_nnf,[status(thm)],[fact_1184_diff__bin__simps_I1_J]) ).

fof(f_1291_2,plain,
    ! [U_3925] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3925),pls) = U_3925,
    inference(variable_rename,[status(thm)],[f_1291_1]) ).

fof(f_1291_3,plain,
    ! [U_3925] : hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3925),pls) = U_3925,
    inference(definitional_conversion,[status(esa)],[f_1291_2]) ).

cnf(f_1291_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(minus_minus_int,U_3925),pls) = U_3925,
    inference(clausify,[status(thm)],[f_1291_3]) ).

fof(f_1292_1,plain,
    ! [K_1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),K_1) = K_1,
    inference(fof_nnf,[status(thm)],[fact_1185_add__Pls]) ).

fof(f_1292_2,plain,
    ! [U_3926] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),U_3926) = U_3926,
    inference(variable_rename,[status(thm)],[f_1292_1]) ).

fof(f_1292_3,plain,
    ! [U_3926] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),U_3926) = U_3926,
    inference(definitional_conversion,[status(esa)],[f_1292_2]) ).

cnf(f_1292_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,pls),U_3926) = U_3926,
    inference(clausify,[status(thm)],[f_1292_3]) ).

fof(f_1293_1,plain,
    ! [K_1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_1),pls) = K_1,
    inference(fof_nnf,[status(thm)],[fact_1186_add__Pls__right]) ).

fof(f_1293_2,plain,
    ! [U_3927] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3927),pls) = U_3927,
    inference(variable_rename,[status(thm)],[f_1293_1]) ).

fof(f_1293_3,plain,
    ! [U_3927] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3927),pls) = U_3927,
    inference(definitional_conversion,[status(esa)],[f_1293_2]) ).

cnf(f_1293_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,U_3927),pls) = U_3927,
    inference(clausify,[status(thm)],[f_1293_3]) ).

fof(f_1294_1,plain,
    ! [W] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,pls),W) = pls,
    inference(fof_nnf,[status(thm)],[fact_1187_mult__Pls]) ).

fof(f_1294_2,plain,
    ! [U_3928] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,pls),U_3928) = pls,
    inference(variable_rename,[status(thm)],[f_1294_1]) ).

fof(f_1294_3,plain,
    ! [U_3928] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,pls),U_3928) = pls,
    inference(definitional_conversion,[status(esa)],[f_1294_2]) ).

cnf(f_1294_4,plain,
    hAPP_int_int(hAPP_int_fun_int_int(times_times_int,pls),U_3928) = pls,
    inference(clausify,[status(thm)],[f_1294_3]) ).

fof(f_1295_1,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(bit1(pls))))),
    inference(fof_nnf,[status(thm)],[fact_1188_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J]) ).

fof(f_1295_2,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(bit1(pls))))),
    inference(definitional_conversion,[status(esa)],[f_1295_1]) ).

cnf(f_1295_3,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),number_number_of_int(bit1(bit1(pls))))),
    inference(clausify,[status(thm)],[f_1295_2]) ).

fof(f_1296_1,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls)),
    inference(fof_nnf,[status(thm)],[fact_1189_rel__simps_I19_J]) ).

fof(f_1296_2,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls)),
    inference(definitional_conversion,[status(esa)],[f_1296_1]) ).

cnf(f_1296_3,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls)),
    inference(clausify,[status(thm)],[f_1296_2]) ).

fof(f_1297_1,plain,
    ! [K] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(K)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),K)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),K))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(K))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1190_rel__simps_I22_J]) ).

fof(f_1297_2,plain,
    ! [U_3929] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(U_3929)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_3929)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_3929))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(U_3929))) ) ),
    inference(variable_rename,[status(thm)],[f_1297_1]) ).

fof(f_1297_3,plain,
    ( ! [U_3931] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(U_3931)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_3931)) )
    & ! [U_3930] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_3930))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(U_3930))) ) ),
    inference(miniscope,[status(thm)],[f_1297_2]) ).

fof(f_1297_4,plain,
    ( ! [U_3931] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(U_3931)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_3931)) )
    & ! [U_3930] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_3930))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(U_3930))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1297_3]) ).

cnf(f_1297_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_3930))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(U_3930))) ),
    inference(clausify,[status(thm)],[f_1297_4]) ).

cnf(f_1297_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),bit1(U_3931)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_3931)) ),
    inference(clausify,[status(thm)],[f_1297_4]) ).

fof(f_1298_1,plain,
    ! [K,L] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K)),bit1(L)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K),L))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K)),bit1(L))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1191_rel__simps_I34_J]) ).

fof(f_1298_2,plain,
    ! [U_3933,U_3932] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3933)),bit1(U_3932)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3933),U_3932)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3933),U_3932))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3933)),bit1(U_3932))) ) ),
    inference(variable_rename,[status(thm)],[f_1298_1]) ).

fof(f_1298_3,plain,
    ( ! [U_3937,U_3935] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3937)),bit1(U_3935)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3937),U_3935)) )
    & ! [U_3936,U_3934] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3936),U_3934))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3936)),bit1(U_3934))) ) ),
    inference(miniscope,[status(thm)],[f_1298_2]) ).

fof(f_1298_4,plain,
    ( ! [U_3937,U_3935] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3937)),bit1(U_3935)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3937),U_3935)) )
    & ! [U_3934,U_3936] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3936),U_3934))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3936)),bit1(U_3934))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1298_3]) ).

cnf(f_1298_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3936),U_3934))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3936)),bit1(U_3934))) ),
    inference(clausify,[status(thm)],[f_1298_4]) ).

cnf(f_1298_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3937)),bit1(U_3935)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3937),U_3935)) ),
    inference(clausify,[status(thm)],[f_1298_4]) ).

fof(f_1299_1,plain,
    ! [K1,K2] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K1)),bit1(K2)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K1),K2)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,K1),K2))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K1)),bit1(K2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1192_less__eq__int__code_I16_J]) ).

fof(f_1299_2,plain,
    ! [U_3939,U_3938] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3939)),bit1(U_3938)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3939),U_3938)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3939),U_3938))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3939)),bit1(U_3938))) ) ),
    inference(variable_rename,[status(thm)],[f_1299_1]) ).

fof(f_1299_3,plain,
    ( ! [U_3943,U_3941] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3943)),bit1(U_3941)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3943),U_3941)) )
    & ! [U_3942,U_3940] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3942),U_3940))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3942)),bit1(U_3940))) ) ),
    inference(miniscope,[status(thm)],[f_1299_2]) ).

fof(f_1299_4,plain,
    ( ! [U_3941,U_3943] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3943)),bit1(U_3941)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3943),U_3941)) )
    & ! [U_3942,U_3940] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3942),U_3940))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3942)),bit1(U_3940))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1299_3]) ).

cnf(f_1299_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3942),U_3940))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3942)),bit1(U_3940))) ),
    inference(clausify,[status(thm)],[f_1299_4]) ).

cnf(f_1299_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3943)),bit1(U_3941)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,U_3943),U_3941)) ),
    inference(clausify,[status(thm)],[f_1299_4]) ).

fof(f_1300_1,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
    inference(fof_nnf,[status(thm)],[fact_1193_rel__simps_I2_J]) ).

fof(f_1300_2,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
    inference(definitional_conversion,[status(esa)],[f_1300_1]) ).

cnf(f_1300_3,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
    inference(clausify,[status(thm)],[f_1300_2]) ).

fof(f_1301_1,plain,
    ! [K] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K)),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),pls)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K)),pls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1194_rel__simps_I12_J]) ).

fof(f_1301_2,plain,
    ! [U_3944] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3944)),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3944),pls)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3944),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3944)),pls)) ) ),
    inference(variable_rename,[status(thm)],[f_1301_1]) ).

fof(f_1301_3,plain,
    ( ! [U_3946] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3946)),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3946),pls)) )
    & ! [U_3945] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3945),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3945)),pls)) ) ),
    inference(miniscope,[status(thm)],[f_1301_2]) ).

fof(f_1301_4,plain,
    ( ! [U_3946] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3946)),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3946),pls)) )
    & ! [U_3945] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3945),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3945)),pls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1301_3]) ).

cnf(f_1301_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3945),pls))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3945)),pls)) ),
    inference(clausify,[status(thm)],[f_1301_4]) ).

cnf(f_1301_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3946)),pls))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3946),pls)) ),
    inference(clausify,[status(thm)],[f_1301_4]) ).

fof(f_1302_1,plain,
    ! [K,L] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K)),bit1(L)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),L))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K)),bit1(L))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1195_rel__simps_I17_J]) ).

fof(f_1302_2,plain,
    ! [U_3948,U_3947] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3948)),bit1(U_3947)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3948),U_3947)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3948),U_3947))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3948)),bit1(U_3947))) ) ),
    inference(variable_rename,[status(thm)],[f_1302_1]) ).

fof(f_1302_3,plain,
    ( ! [U_3952,U_3950] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3952)),bit1(U_3950)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3952),U_3950)) )
    & ! [U_3951,U_3949] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3951),U_3949))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3951)),bit1(U_3949))) ) ),
    inference(miniscope,[status(thm)],[f_1302_2]) ).

fof(f_1302_4,plain,
    ( ! [U_3950,U_3952] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3952)),bit1(U_3950)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3952),U_3950)) )
    & ! [U_3951,U_3949] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3951),U_3949))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3951)),bit1(U_3949))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1302_3]) ).

cnf(f_1302_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3951),U_3949))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3951)),bit1(U_3949))) ),
    inference(clausify,[status(thm)],[f_1302_4]) ).

cnf(f_1302_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3952)),bit1(U_3950)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3952),U_3950)) ),
    inference(clausify,[status(thm)],[f_1302_4]) ).

fof(f_1303_1,plain,
    ! [K1,K2] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K1)),bit1(K2)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K1),K2)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K1),K2))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(K1)),bit1(K2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1196_less__int__code_I16_J]) ).

fof(f_1303_2,plain,
    ! [U_3954,U_3953] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3954)),bit1(U_3953)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3954),U_3953)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3954),U_3953))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3954)),bit1(U_3953))) ) ),
    inference(variable_rename,[status(thm)],[f_1303_1]) ).

fof(f_1303_3,plain,
    ( ! [U_3958,U_3956] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3958)),bit1(U_3956)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3958),U_3956)) )
    & ! [U_3957,U_3955] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3957),U_3955))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3957)),bit1(U_3955))) ) ),
    inference(miniscope,[status(thm)],[f_1303_2]) ).

fof(f_1303_4,plain,
    ( ! [U_3956,U_3958] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3958)),bit1(U_3956)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3958),U_3956)) )
    & ! [U_3957,U_3955] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3957),U_3955))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3957)),bit1(U_3955))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1303_3]) ).

cnf(f_1303_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3957),U_3955))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3957)),bit1(U_3955))) ),
    inference(clausify,[status(thm)],[f_1303_4]) ).

cnf(f_1303_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,bit1(U_3958)),bit1(U_3956)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3958),U_3956)) ),
    inference(clausify,[status(thm)],[f_1303_4]) ).

fof(f_1304_1,plain,
    ! [K] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K)),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),pls)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,K),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(K)),pls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_1197_rel__simps_I29_J]) ).

fof(f_1304_2,plain,
    ! [U_3959] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3959)),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3959),pls)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3959),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3959)),pls)) ) ),
    inference(variable_rename,[status(thm)],[f_1304_1]) ).

fof(f_1304_3,plain,
    ( ! [U_3961] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3961)),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3961),pls)) )
    & ! [U_3960] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3960),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3960)),pls)) ) ),
    inference(miniscope,[status(thm)],[f_1304_2]) ).

fof(f_1304_4,plain,
    ( ! [U_3961] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3961)),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3961),pls)) )
    & ! [U_3960] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3960),pls))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3960)),pls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1304_3]) ).

cnf(f_1304_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3960),pls))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3960)),pls)) ),
    inference(clausify,[status(thm)],[f_1304_4]) ).

cnf(f_1304_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,bit1(U_3961)),pls))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,U_3961),pls)) ),
    inference(clausify,[status(thm)],[f_1304_4]) ).

fof(f_1305_1,plain,
    ! [K] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(K)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),K)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),K))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(K))) ) ),
    inference(fof_nnf,[status(thm)],[fact_1198_rel__simps_I5_J]) ).

fof(f_1305_2,plain,
    ! [U_3962] :
      ( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(U_3962)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_3962)) )
      & ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_3962))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(U_3962))) ) ),
    inference(variable_rename,[status(thm)],[f_1305_1]) ).

fof(f_1305_3,plain,
    ( ! [U_3964] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(U_3964)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_3964)) )
    & ! [U_3963] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_3963))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(U_3963))) ) ),
    inference(miniscope,[status(thm)],[f_1305_2]) ).

fof(f_1305_4,plain,
    ( ! [U_3964] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(U_3964)))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_3964)) )
    & ! [U_3963] :
        ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_3963))
        | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(U_3963))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1305_3]) ).

cnf(f_1305_5,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_3963))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(U_3963))) ),
    inference(clausify,[status(thm)],[f_1305_4]) ).

cnf(f_1305_6,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),bit1(U_3964)))
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),U_3964)) ),
    inference(clausify,[status(thm)],[f_1305_4]) ).

fof(f_1306_1,plain,
    ! [P] :
      ( ~ hBOOL(P)
      | ~ hBOOL(hAPP_bool_bool(fNot,P)) ),
    inference(fof_nnf,[status(thm)],[help_fNot_1_1_U]) ).

fof(f_1306_2,plain,
    ! [U_3965] :
      ( ~ hBOOL(U_3965)
      | ~ hBOOL(hAPP_bool_bool(fNot,U_3965)) ),
    inference(variable_rename,[status(thm)],[f_1306_1]) ).

fof(f_1306_3,plain,
    ! [U_3965] :
      ( ~ hBOOL(U_3965)
      | ~ hBOOL(hAPP_bool_bool(fNot,U_3965)) ),
    inference(definitional_conversion,[status(esa)],[f_1306_2]) ).

cnf(f_1306_4,plain,
    ( ~ hBOOL(U_3965)
    | ~ hBOOL(hAPP_bool_bool(fNot,U_3965)) ),
    inference(clausify,[status(thm)],[f_1306_3]) ).

fof(f_1307_1,plain,
    ! [P] :
      ( hBOOL(hAPP_bool_bool(fNot,P))
      | hBOOL(P) ),
    inference(fof_nnf,[status(thm)],[help_fNot_2_1_U]) ).

fof(f_1307_2,plain,
    ! [U_3966] :
      ( hBOOL(hAPP_bool_bool(fNot,U_3966))
      | hBOOL(U_3966) ),
    inference(variable_rename,[status(thm)],[f_1307_1]) ).

fof(f_1307_3,plain,
    ! [U_3966] :
      ( hBOOL(hAPP_bool_bool(fNot,U_3966))
      | hBOOL(U_3966) ),
    inference(definitional_conversion,[status(esa)],[f_1307_2]) ).

cnf(f_1307_4,plain,
    ( hBOOL(hAPP_bool_bool(fNot,U_3966))
    | hBOOL(U_3966) ),
    inference(clausify,[status(thm)],[f_1307_3]) ).

fof(f_1308_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_1308_2,plain,
    ! [U_3968,U_3967] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_3967),U_3968))
      | ~ hBOOL(U_3968)
      | ~ hBOOL(U_3967) ),
    inference(variable_rename,[status(thm)],[f_1308_1]) ).

fof(f_1308_3,plain,
    ! [U_3968] :
      ( ! [U_3967] :
          ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_3967),U_3968))
          | ~ hBOOL(U_3967) )
      | ~ hBOOL(U_3968) ),
    inference(miniscope,[status(thm)],[f_1308_2]) ).

fof(f_1308_4,plain,
    ! [U_3967,U_3968] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_3967),U_3968))
      | ~ hBOOL(U_3967)
      | ~ hBOOL(U_3968) ),
    inference(definitional_conversion,[status(esa)],[f_1308_3]) ).

cnf(f_1308_5,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_3967),U_3968))
    | ~ hBOOL(U_3967)
    | ~ hBOOL(U_3968) ),
    inference(clausify,[status(thm)],[f_1308_4]) ).

fof(f_1309_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_1309_2,plain,
    ! [U_3970,U_3969] :
      ( hBOOL(U_3970)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_3970),U_3969)) ),
    inference(variable_rename,[status(thm)],[f_1309_1]) ).

fof(f_1309_3,plain,
    ! [U_3970] :
      ( ! [U_3969] : ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_3970),U_3969))
      | hBOOL(U_3970) ),
    inference(miniscope,[status(thm)],[f_1309_2]) ).

fof(f_1309_4,plain,
    ! [U_3970,U_3969] :
      ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_3970),U_3969))
      | hBOOL(U_3970) ),
    inference(definitional_conversion,[status(esa)],[f_1309_3]) ).

cnf(f_1309_5,plain,
    ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_3970),U_3969))
    | hBOOL(U_3970) ),
    inference(clausify,[status(thm)],[f_1309_4]) ).

fof(f_1310_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_1310_2,plain,
    ! [U_3972,U_3971] :
      ( hBOOL(U_3971)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_3972),U_3971)) ),
    inference(variable_rename,[status(thm)],[f_1310_1]) ).

fof(f_1310_3,plain,
    ! [U_3971,U_3972] :
      ( hBOOL(U_3971)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_3972),U_3971)) ),
    inference(definitional_conversion,[status(esa)],[f_1310_2]) ).

cnf(f_1310_4,plain,
    ( hBOOL(U_3971)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,U_3972),U_3971)) ),
    inference(clausify,[status(thm)],[f_1310_3]) ).

fof(f_1311_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_1311_2,plain,
    ! [U_3974,U_3973] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_3973),U_3974))
      | ~ hBOOL(U_3973) ),
    inference(variable_rename,[status(thm)],[f_1311_1]) ).

fof(f_1311_3,plain,
    ! [U_3973,U_3974] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_3973),U_3974))
      | ~ hBOOL(U_3973) ),
    inference(definitional_conversion,[status(esa)],[f_1311_2]) ).

cnf(f_1311_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_3973),U_3974))
    | ~ hBOOL(U_3973) ),
    inference(clausify,[status(thm)],[f_1311_3]) ).

fof(f_1312_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_1312_2,plain,
    ! [U_3976,U_3975] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_3976),U_3975))
      | ~ hBOOL(U_3975) ),
    inference(variable_rename,[status(thm)],[f_1312_1]) ).

fof(f_1312_3,plain,
    ! [U_3975,U_3976] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_3976),U_3975))
      | ~ hBOOL(U_3975) ),
    inference(definitional_conversion,[status(esa)],[f_1312_2]) ).

cnf(f_1312_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_3976),U_3975))
    | ~ hBOOL(U_3975) ),
    inference(clausify,[status(thm)],[f_1312_3]) ).

fof(f_1313_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_1313_2,plain,
    ! [U_3978,U_3977] :
      ( hBOOL(U_3977)
      | hBOOL(U_3978)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_3978),U_3977)) ),
    inference(variable_rename,[status(thm)],[f_1313_1]) ).

fof(f_1313_3,plain,
    ! [U_3978] :
      ( ! [U_3977] :
          ( hBOOL(U_3977)
          | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_3978),U_3977)) )
      | hBOOL(U_3978) ),
    inference(miniscope,[status(thm)],[f_1313_2]) ).

fof(f_1313_4,plain,
    ! [U_3977,U_3978] :
      ( hBOOL(U_3977)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_3978),U_3977))
      | hBOOL(U_3978) ),
    inference(definitional_conversion,[status(esa)],[f_1313_3]) ).

cnf(f_1313_5,plain,
    ( hBOOL(U_3977)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,U_3978),U_3977))
    | hBOOL(U_3978) ),
    inference(clausify,[status(thm)],[f_1313_4]) ).

fof(f_1314_1,plain,
    ~ hBOOL(fFalse),
    inference(fof_nnf,[status(thm)],[help_fFalse_1_1_U]) ).

fof(f_1314_2,plain,
    ~ hBOOL(fFalse),
    inference(definitional_conversion,[status(esa)],[f_1314_1]) ).

cnf(f_1314_3,plain,
    ~ hBOOL(fFalse),
    inference(clausify,[status(thm)],[f_1314_2]) ).

fof(f_1315_1,plain,
    ! [P] :
      ( P = fFalse
      | P = fTrue
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_fFalse_1_1_T]) ).

fof(f_1315_2,plain,
    ! [U_3979] :
      ( U_3979 = fFalse
      | U_3979 = fTrue
      | ~ is_bool(U_3979) ),
    inference(variable_rename,[status(thm)],[f_1315_1]) ).

fof(f_1315_3,plain,
    ! [U_3979] :
      ( U_3979 = fFalse
      | U_3979 = fTrue
      | ~ is_bool(U_3979) ),
    inference(definitional_conversion,[status(esa)],[f_1315_2]) ).

cnf(f_1315_4,plain,
    ( U_3979 = fFalse
    | U_3979 = fTrue
    | ~ is_bool(U_3979) ),
    inference(clausify,[status(thm)],[f_1315_3]) ).

fof(f_1316_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_1316_2,plain,
    ! [U_3981,U_3980] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_3980),U_3981))
      | hBOOL(U_3980) ),
    inference(variable_rename,[status(thm)],[f_1316_1]) ).

fof(f_1316_3,plain,
    ! [U_3980,U_3981] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_3980),U_3981))
      | hBOOL(U_3980) ),
    inference(definitional_conversion,[status(esa)],[f_1316_2]) ).

cnf(f_1316_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_3980),U_3981))
    | hBOOL(U_3980) ),
    inference(clausify,[status(thm)],[f_1316_3]) ).

fof(f_1317_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_1317_2,plain,
    ! [U_3983,U_3982] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_3983),U_3982))
      | ~ hBOOL(U_3982) ),
    inference(variable_rename,[status(thm)],[f_1317_1]) ).

fof(f_1317_3,plain,
    ! [U_3982,U_3983] :
      ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_3983),U_3982))
      | ~ hBOOL(U_3982) ),
    inference(definitional_conversion,[status(esa)],[f_1317_2]) ).

cnf(f_1317_4,plain,
    ( hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_3983),U_3982))
    | ~ hBOOL(U_3982) ),
    inference(clausify,[status(thm)],[f_1317_3]) ).

fof(f_1318_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_1318_2,plain,
    ! [U_3985,U_3984] :
      ( hBOOL(U_3984)
      | ~ hBOOL(U_3985)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_3985),U_3984)) ),
    inference(variable_rename,[status(thm)],[f_1318_1]) ).

fof(f_1318_3,plain,
    ! [U_3985] :
      ( ! [U_3984] :
          ( hBOOL(U_3984)
          | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_3985),U_3984)) )
      | ~ hBOOL(U_3985) ),
    inference(miniscope,[status(thm)],[f_1318_2]) ).

fof(f_1318_4,plain,
    ! [U_3984,U_3985] :
      ( hBOOL(U_3984)
      | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_3985),U_3984))
      | ~ hBOOL(U_3985) ),
    inference(definitional_conversion,[status(esa)],[f_1318_3]) ).

cnf(f_1318_5,plain,
    ( hBOOL(U_3984)
    | ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,U_3985),U_3984))
    | ~ hBOOL(U_3985) ),
    inference(clausify,[status(thm)],[f_1318_4]) ).

fof(f_1319_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_1319_2,plain,
    ! [U_3987,U_3986] :
      ( U_3987 = U_3986
      | ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,U_3987),U_3986))
      | ~ is_a(U_3986)
      | ~ is_a(U_3987) ),
    inference(variable_rename,[status(thm)],[f_1319_1]) ).

fof(f_1319_3,plain,
    ! [U_3986,U_3987] :
      ( U_3987 = U_3986
      | ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,U_3987),U_3986))
      | ~ is_a(U_3986)
      | ~ is_a(U_3987) ),
    inference(definitional_conversion,[status(esa)],[f_1319_2]) ).

cnf(f_1319_4,plain,
    ( U_3987 = U_3986
    | ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,U_3987),U_3986))
    | ~ is_a(U_3986)
    | ~ is_a(U_3987) ),
    inference(clausify,[status(thm)],[f_1319_3]) ).

fof(f_1320_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_1320_2,plain,
    ! [U_3989,U_3988] :
      ( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,U_3989),U_3988))
      | U_3989 != U_3988 ),
    inference(variable_rename,[status(thm)],[f_1320_1]) ).

fof(f_1320_3,plain,
    ! [U_3989,U_3988] :
      ( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,U_3989),U_3988))
      | U_3989 != U_3988 ),
    inference(definitional_conversion,[status(esa)],[f_1320_2]) ).

cnf(f_1320_4,plain,
    ( hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,U_3989),U_3988))
    | U_3989 != U_3988 ),
    inference(clausify,[status(thm)],[f_1320_3]) ).

fof(f_1321_1,plain,
    ! [X,Y] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fTrue),X),Y) = X,
    inference(fof_nnf,[status(thm)],[help_If_1_1_If_000tc__Nat__Onat_T]) ).

fof(f_1321_2,plain,
    ! [U_3991,U_3990] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fTrue),U_3991),U_3990) = U_3991,
    inference(variable_rename,[status(thm)],[f_1321_1]) ).

fof(f_1321_3,plain,
    ! [U_3991,U_3990] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fTrue),U_3991),U_3990) = U_3991,
    inference(definitional_conversion,[status(esa)],[f_1321_2]) ).

cnf(f_1321_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fTrue),U_3991),U_3990) = U_3991,
    inference(clausify,[status(thm)],[f_1321_3]) ).

fof(f_1322_1,plain,
    ! [X,Y] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fFalse),X),Y) = Y,
    inference(fof_nnf,[status(thm)],[help_If_2_1_If_000tc__Nat__Onat_T]) ).

fof(f_1322_2,plain,
    ! [U_3993,U_3992] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fFalse),U_3993),U_3992) = U_3992,
    inference(variable_rename,[status(thm)],[f_1322_1]) ).

fof(f_1322_3,plain,
    ! [U_3993,U_3992] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fFalse),U_3993),U_3992) = U_3992,
    inference(definitional_conversion,[status(esa)],[f_1322_2]) ).

cnf(f_1322_4,plain,
    hAPP_nat_nat(hAPP_nat_fun_nat_nat(if_nat(fFalse),U_3993),U_3992) = U_3992,
    inference(clausify,[status(thm)],[f_1322_3]) ).

fof(f_1323_1,plain,
    ! [P] :
      ( P = fFalse
      | P = fTrue
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_If_3_1_If_000tc__Nat__Onat_T]) ).

fof(f_1323_2,plain,
    ! [U_3994] :
      ( U_3994 = fFalse
      | U_3994 = fTrue
      | ~ is_bool(U_3994) ),
    inference(variable_rename,[status(thm)],[f_1323_1]) ).

fof(f_1323_3,plain,
    ! [U_3994] :
      ( U_3994 = fFalse
      | U_3994 = fTrue
      | ~ is_bool(U_3994) ),
    inference(definitional_conversion,[status(esa)],[f_1323_2]) ).

cnf(f_1323_4,plain,
    ( U_3994 = fFalse
    | U_3994 = fTrue
    | ~ is_bool(U_3994) ),
    inference(clausify,[status(thm)],[f_1323_3]) ).

fof(f_1324_1,plain,
    ! [P] : hAPP_nat_nat(cOMBI_nat,P) = P,
    inference(fof_nnf,[status(thm)],[help_COMBI_1_1_COMBI_000tc__Nat__Onat_U]) ).

fof(f_1324_2,plain,
    ! [U_3995] : hAPP_nat_nat(cOMBI_nat,U_3995) = U_3995,
    inference(variable_rename,[status(thm)],[f_1324_1]) ).

fof(f_1324_3,plain,
    ! [U_3995] : hAPP_nat_nat(cOMBI_nat,U_3995) = U_3995,
    inference(definitional_conversion,[status(esa)],[f_1324_2]) ).

cnf(f_1324_4,plain,
    hAPP_nat_nat(cOMBI_nat,U_3995) = U_3995,
    inference(clausify,[status(thm)],[f_1324_3]) ).

fof(f_1325_1,plain,
    ! [X,Y] :
      ( X = Y
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X),Y)) ),
    inference(fof_nnf,[status(thm)],[help_fequal_1_1_fequal_000tc__Int__Oint_T]) ).

fof(f_1325_2,plain,
    ! [U_3997,U_3996] :
      ( U_3997 = U_3996
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,U_3997),U_3996)) ),
    inference(variable_rename,[status(thm)],[f_1325_1]) ).

fof(f_1325_3,plain,
    ! [U_3996,U_3997] :
      ( U_3997 = U_3996
      | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,U_3997),U_3996)) ),
    inference(definitional_conversion,[status(esa)],[f_1325_2]) ).

cnf(f_1325_4,plain,
    ( U_3997 = U_3996
    | ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,U_3997),U_3996)) ),
    inference(clausify,[status(thm)],[f_1325_3]) ).

fof(f_1326_1,plain,
    ! [X,Y] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,X),Y))
      | X != Y ),
    inference(fof_nnf,[status(thm)],[help_fequal_2_1_fequal_000tc__Int__Oint_T]) ).

fof(f_1326_2,plain,
    ! [U_3999,U_3998] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,U_3999),U_3998))
      | U_3999 != U_3998 ),
    inference(variable_rename,[status(thm)],[f_1326_1]) ).

fof(f_1326_3,plain,
    ! [U_3998,U_3999] :
      ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,U_3999),U_3998))
      | U_3999 != U_3998 ),
    inference(definitional_conversion,[status(esa)],[f_1326_2]) ).

cnf(f_1326_4,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(fequal_int,U_3999),U_3998))
    | U_3999 != U_3998 ),
    inference(clausify,[status(thm)],[f_1326_3]) ).

fof(f_1327_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_1327_2,plain,
    ! [U_4001,U_4000] :
      ( U_4001 = U_4000
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_4001),U_4000)) ),
    inference(variable_rename,[status(thm)],[f_1327_1]) ).

fof(f_1327_3,plain,
    ! [U_4000,U_4001] :
      ( U_4001 = U_4000
      | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_4001),U_4000)) ),
    inference(definitional_conversion,[status(esa)],[f_1327_2]) ).

cnf(f_1327_4,plain,
    ( U_4001 = U_4000
    | ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_4001),U_4000)) ),
    inference(clausify,[status(thm)],[f_1327_3]) ).

fof(f_1328_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_1328_2,plain,
    ! [U_4003,U_4002] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_4003),U_4002))
      | U_4003 != U_4002 ),
    inference(variable_rename,[status(thm)],[f_1328_1]) ).

fof(f_1328_3,plain,
    ! [U_4002,U_4003] :
      ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_4003),U_4002))
      | U_4003 != U_4002 ),
    inference(definitional_conversion,[status(esa)],[f_1328_2]) ).

cnf(f_1328_4,plain,
    ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,U_4003),U_4002))
    | U_4003 != U_4002 ),
    inference(clausify,[status(thm)],[f_1328_3]) ).

fof(f_1329_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_1329_2,plain,
    ! [U_4005,U_4004] :
      ( U_4005 = U_4004
      | ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,U_4005),U_4004))
      | ~ is_pname(U_4004)
      | ~ is_pname(U_4005) ),
    inference(variable_rename,[status(thm)],[f_1329_1]) ).

fof(f_1329_3,plain,
    ! [U_4004,U_4005] :
      ( U_4005 = U_4004
      | ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,U_4005),U_4004))
      | ~ is_pname(U_4004)
      | ~ is_pname(U_4005) ),
    inference(definitional_conversion,[status(esa)],[f_1329_2]) ).

cnf(f_1329_4,plain,
    ( U_4005 = U_4004
    | ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,U_4005),U_4004))
    | ~ is_pname(U_4004)
    | ~ is_pname(U_4005) ),
    inference(clausify,[status(thm)],[f_1329_3]) ).

fof(f_1330_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_1330_2,plain,
    ! [U_4007,U_4006] :
      ( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,U_4007),U_4006))
      | U_4007 != U_4006 ),
    inference(variable_rename,[status(thm)],[f_1330_1]) ).

fof(f_1330_3,plain,
    ! [U_4007,U_4006] :
      ( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,U_4007),U_4006))
      | U_4007 != U_4006 ),
    inference(definitional_conversion,[status(esa)],[f_1330_2]) ).

cnf(f_1330_4,plain,
    ( hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,U_4007),U_4006))
    | U_4007 != U_4006 ),
    inference(clausify,[status(thm)],[f_1330_3]) ).

fof(f_1331_1,plain,
    ! [P,Q] :
      ( hAPP_a_bool(cOMBK_bool_a(P),Q) = P
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000t__a_U]) ).

fof(f_1331_2,plain,
    ! [U_4009,U_4008] :
      ( hAPP_a_bool(cOMBK_bool_a(U_4009),U_4008) = U_4009
      | ~ is_bool(U_4009) ),
    inference(variable_rename,[status(thm)],[f_1331_1]) ).

fof(f_1331_3,plain,
    ! [U_4009] :
      ( ! [U_4008] : hAPP_a_bool(cOMBK_bool_a(U_4009),U_4008) = U_4009
      | ~ is_bool(U_4009) ),
    inference(miniscope,[status(thm)],[f_1331_2]) ).

fof(f_1331_4,plain,
    ! [U_4008,U_4009] :
      ( hAPP_a_bool(cOMBK_bool_a(U_4009),U_4008) = U_4009
      | ~ is_bool(U_4009) ),
    inference(definitional_conversion,[status(esa)],[f_1331_3]) ).

cnf(f_1331_5,plain,
    ( hAPP_a_bool(cOMBK_bool_a(U_4009),U_4008) = U_4009
    | ~ is_bool(U_4009) ),
    inference(clausify,[status(thm)],[f_1331_4]) ).

fof(f_1332_1,plain,
    ! [P,Q] :
      ( hAPP_pname_a(cOMBK_a_pname(P),Q) = P
      | ~ is_a(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000t__a_000tc__Com__Opname_U]) ).

fof(f_1332_2,plain,
    ! [U_4011,U_4010] :
      ( hAPP_pname_a(cOMBK_a_pname(U_4011),U_4010) = U_4011
      | ~ is_a(U_4011) ),
    inference(variable_rename,[status(thm)],[f_1332_1]) ).

fof(f_1332_3,plain,
    ! [U_4011] :
      ( ! [U_4010] : hAPP_pname_a(cOMBK_a_pname(U_4011),U_4010) = U_4011
      | ~ is_a(U_4011) ),
    inference(miniscope,[status(thm)],[f_1332_2]) ).

fof(f_1332_4,plain,
    ! [U_4010,U_4011] :
      ( hAPP_pname_a(cOMBK_a_pname(U_4011),U_4010) = U_4011
      | ~ is_a(U_4011) ),
    inference(definitional_conversion,[status(esa)],[f_1332_3]) ).

cnf(f_1332_5,plain,
    ( hAPP_pname_a(cOMBK_a_pname(U_4011),U_4010) = U_4011
    | ~ is_a(U_4011) ),
    inference(clausify,[status(thm)],[f_1332_4]) ).

fof(f_1333_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_1333_2,plain,
    ! [U_4014,U_4013,U_4012] : hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(U_4014),U_4013),U_4012) = hAPP_a_bool(hAPP_a_fun_a_bool(U_4014,U_4012),U_4013),
    inference(variable_rename,[status(thm)],[f_1333_1]) ).

fof(f_1333_3,plain,
    ! [U_4012,U_4013,U_4014] : hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(U_4014),U_4013),U_4012) = hAPP_a_bool(hAPP_a_fun_a_bool(U_4014,U_4012),U_4013),
    inference(definitional_conversion,[status(esa)],[f_1333_2]) ).

cnf(f_1333_4,plain,
    hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(U_4014),U_4013),U_4012) = hAPP_a_bool(hAPP_a_fun_a_bool(U_4014,U_4012),U_4013),
    inference(clausify,[status(thm)],[f_1333_3]) ).

fof(f_1334_1,plain,
    ! [P,Q] : hAPP_nat_int(cOMBK_int_nat(P),Q) = P,
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__Int__Oint_000tc__Nat__Onat_U]) ).

fof(f_1334_2,plain,
    ! [U_4016,U_4015] : hAPP_nat_int(cOMBK_int_nat(U_4016),U_4015) = U_4016,
    inference(variable_rename,[status(thm)],[f_1334_1]) ).

fof(f_1334_3,plain,
    ! [U_4015,U_4016] : hAPP_nat_int(cOMBK_int_nat(U_4016),U_4015) = U_4016,
    inference(definitional_conversion,[status(esa)],[f_1334_2]) ).

cnf(f_1334_4,plain,
    hAPP_nat_int(cOMBK_int_nat(U_4016),U_4015) = U_4016,
    inference(clausify,[status(thm)],[f_1334_3]) ).

fof(f_1335_1,plain,
    ! [P,Q] :
      ( hAPP_int_bool(cOMBK_bool_int(P),Q) = P
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Int__Oint_U]) ).

fof(f_1335_2,plain,
    ! [U_4018,U_4017] :
      ( hAPP_int_bool(cOMBK_bool_int(U_4018),U_4017) = U_4018
      | ~ is_bool(U_4018) ),
    inference(variable_rename,[status(thm)],[f_1335_1]) ).

fof(f_1335_3,plain,
    ! [U_4018] :
      ( ! [U_4017] : hAPP_int_bool(cOMBK_bool_int(U_4018),U_4017) = U_4018
      | ~ is_bool(U_4018) ),
    inference(miniscope,[status(thm)],[f_1335_2]) ).

fof(f_1335_4,plain,
    ! [U_4017,U_4018] :
      ( hAPP_int_bool(cOMBK_bool_int(U_4018),U_4017) = U_4018
      | ~ is_bool(U_4018) ),
    inference(definitional_conversion,[status(esa)],[f_1335_3]) ).

cnf(f_1335_5,plain,
    ( hAPP_int_bool(cOMBK_bool_int(U_4018),U_4017) = U_4018
    | ~ is_bool(U_4018) ),
    inference(clausify,[status(thm)],[f_1335_4]) ).

fof(f_1336_1,plain,
    ! [P,Q] :
      ( hAPP_nat_bool(cOMBK_bool_nat(P),Q) = P
      | ~ is_bool(P) ),
    inference(fof_nnf,[status(thm)],[help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U]) ).

fof(f_1336_2,plain,
    ! [U_4020,U_4019] :
      ( hAPP_nat_bool(cOMBK_bool_nat(U_4020),U_4019) = U_4020
      | ~ is_bool(U_4020) ),
    inference(variable_rename,[status(thm)],[f_1336_1]) ).

fof(f_1336_3,plain,
    ! [U_4020] :
      ( ! [U_4019] : hAPP_nat_bool(cOMBK_bool_nat(U_4020),U_4019) = U_4020
      | ~ is_bool(U_4020) ),
    inference(miniscope,[status(thm)],[f_1336_2]) ).

fof(f_1336_4,plain,
    ! [U_4019,U_4020] :
      ( hAPP_nat_bool(cOMBK_bool_nat(U_4020),U_4019) = U_4020
      | ~ is_bool(U_4020) ),
    inference(definitional_conversion,[status(esa)],[f_1336_3]) ).

cnf(f_1336_5,plain,
    ( hAPP_nat_bool(cOMBK_bool_nat(U_4020),U_4019) = U_4020
    | ~ is_bool(U_4020) ),
    inference(clausify,[status(thm)],[f_1336_4]) ).

fof(f_1337_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_1337_2,plain,
    ! [U_4022,U_4021] :
      ( U_4022 = U_4021
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,U_4022),U_4021))
      | ~ is_fun_a_bool(U_4021)
      | ~ is_fun_a_bool(U_4022) ),
    inference(variable_rename,[status(thm)],[f_1337_1]) ).

fof(f_1337_3,plain,
    ! [U_4021,U_4022] :
      ( U_4022 = U_4021
      | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,U_4022),U_4021))
      | ~ is_fun_a_bool(U_4021)
      | ~ is_fun_a_bool(U_4022) ),
    inference(definitional_conversion,[status(esa)],[f_1337_2]) ).

cnf(f_1337_4,plain,
    ( U_4022 = U_4021
    | ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,U_4022),U_4021))
    | ~ is_fun_a_bool(U_4021)
    | ~ is_fun_a_bool(U_4022) ),
    inference(clausify,[status(thm)],[f_1337_3]) ).

fof(f_1338_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_1338_2,plain,
    ! [U_4024,U_4023] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,U_4024),U_4023))
      | U_4024 != U_4023 ),
    inference(variable_rename,[status(thm)],[f_1338_1]) ).

fof(f_1338_3,plain,
    ! [U_4023,U_4024] :
      ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,U_4024),U_4023))
      | U_4024 != U_4023 ),
    inference(definitional_conversion,[status(esa)],[f_1338_2]) ).

cnf(f_1338_4,plain,
    ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,U_4024),U_4023))
    | U_4024 != U_4023 ),
    inference(clausify,[status(thm)],[f_1338_3]) ).

fof(f_1339_1,plain,
    ! [P,Q,R] : hAPP_int_bool(hAPP_a_fun_int_bool(cOMBC_int_a_bool(P),Q),R) = hAPP_a_bool(hAPP_int_fun_a_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Int__Oint_000t__a_000tc__HOL__Obool_U]) ).

fof(f_1339_2,plain,
    ! [U_4027,U_4026,U_4025] : hAPP_int_bool(hAPP_a_fun_int_bool(cOMBC_int_a_bool(U_4027),U_4026),U_4025) = hAPP_a_bool(hAPP_int_fun_a_bool(U_4027,U_4025),U_4026),
    inference(variable_rename,[status(thm)],[f_1339_1]) ).

fof(f_1339_3,plain,
    ! [U_4025,U_4026,U_4027] : hAPP_int_bool(hAPP_a_fun_int_bool(cOMBC_int_a_bool(U_4027),U_4026),U_4025) = hAPP_a_bool(hAPP_int_fun_a_bool(U_4027,U_4025),U_4026),
    inference(definitional_conversion,[status(esa)],[f_1339_2]) ).

cnf(f_1339_4,plain,
    hAPP_int_bool(hAPP_a_fun_int_bool(cOMBC_int_a_bool(U_4027),U_4026),U_4025) = hAPP_a_bool(hAPP_int_fun_a_bool(U_4027,U_4025),U_4026),
    inference(clausify,[status(thm)],[f_1339_3]) ).

fof(f_1340_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_1340_2,plain,
    ! [U_4030,U_4029,U_4028] : hAPP_a_bool(cOMBB_bool_bool_a(U_4030,U_4029),U_4028) = hAPP_bool_bool(U_4030,hAPP_a_bool(U_4029,U_4028)),
    inference(variable_rename,[status(thm)],[f_1340_1]) ).

fof(f_1340_3,plain,
    ! [U_4028,U_4029,U_4030] : hAPP_a_bool(cOMBB_bool_bool_a(U_4030,U_4029),U_4028) = hAPP_bool_bool(U_4030,hAPP_a_bool(U_4029,U_4028)),
    inference(definitional_conversion,[status(esa)],[f_1340_2]) ).

cnf(f_1340_4,plain,
    hAPP_a_bool(cOMBB_bool_bool_a(U_4030,U_4029),U_4028) = hAPP_bool_bool(U_4030,hAPP_a_bool(U_4029,U_4028)),
    inference(clausify,[status(thm)],[f_1340_3]) ).

fof(f_1341_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_1341_2,plain,
    ! [U_4033,U_4032,U_4031] : hAPP_a_bool(cOMBS_a_bool_bool(U_4033,U_4032),U_4031) = hAPP_bool_bool(hAPP_a_fun_bool_bool(U_4033,U_4031),hAPP_a_bool(U_4032,U_4031)),
    inference(variable_rename,[status(thm)],[f_1341_1]) ).

fof(f_1341_3,plain,
    ! [U_4031,U_4032,U_4033] : hAPP_a_bool(cOMBS_a_bool_bool(U_4033,U_4032),U_4031) = hAPP_bool_bool(hAPP_a_fun_bool_bool(U_4033,U_4031),hAPP_a_bool(U_4032,U_4031)),
    inference(definitional_conversion,[status(esa)],[f_1341_2]) ).

cnf(f_1341_4,plain,
    hAPP_a_bool(cOMBS_a_bool_bool(U_4033,U_4032),U_4031) = hAPP_bool_bool(hAPP_a_fun_bool_bool(U_4033,U_4031),hAPP_a_bool(U_4032,U_4031)),
    inference(clausify,[status(thm)],[f_1341_3]) ).

fof(f_1342_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_1342_2,plain,
    ! [U_4036,U_4035,U_4034] : hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(U_4036),U_4035),U_4034) = hAPP_a_bool(hAPP_p1534023578a_bool(U_4036,U_4034),U_4035),
    inference(variable_rename,[status(thm)],[f_1342_1]) ).

fof(f_1342_3,plain,
    ! [U_4034,U_4035,U_4036] : hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(U_4036),U_4035),U_4034) = hAPP_a_bool(hAPP_p1534023578a_bool(U_4036,U_4034),U_4035),
    inference(definitional_conversion,[status(esa)],[f_1342_2]) ).

cnf(f_1342_4,plain,
    hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(U_4036),U_4035),U_4034) = hAPP_a_bool(hAPP_p1534023578a_bool(U_4036,U_4034),U_4035),
    inference(clausify,[status(thm)],[f_1342_3]) ).

fof(f_1343_1,plain,
    ! [X,Y] :
      ( X = Y
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X),Y)) ),
    inference(fof_nnf,[status(thm)],[help_fequal_1_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T]) ).

fof(f_1343_2,plain,
    ! [U_4038,U_4037] :
      ( U_4038 = U_4037
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,U_4038),U_4037)) ),
    inference(variable_rename,[status(thm)],[f_1343_1]) ).

fof(f_1343_3,plain,
    ! [U_4037,U_4038] :
      ( U_4038 = U_4037
      | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,U_4038),U_4037)) ),
    inference(definitional_conversion,[status(esa)],[f_1343_2]) ).

cnf(f_1343_4,plain,
    ( U_4038 = U_4037
    | ~ hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,U_4038),U_4037)) ),
    inference(clausify,[status(thm)],[f_1343_3]) ).

fof(f_1344_1,plain,
    ! [X,Y] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,X),Y))
      | X != Y ),
    inference(fof_nnf,[status(thm)],[help_fequal_2_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T]) ).

fof(f_1344_2,plain,
    ! [U_4040,U_4039] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,U_4040),U_4039))
      | U_4040 != U_4039 ),
    inference(variable_rename,[status(thm)],[f_1344_1]) ).

fof(f_1344_3,plain,
    ! [U_4039,U_4040] :
      ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,U_4040),U_4039))
      | U_4040 != U_4039 ),
    inference(definitional_conversion,[status(esa)],[f_1344_2]) ).

cnf(f_1344_4,plain,
    ( hBOOL(hAPP_f448129468l_bool(hAPP_f284875647l_bool(fequal_fun_int_bool,U_4040),U_4039))
    | U_4040 != U_4039 ),
    inference(clausify,[status(thm)],[f_1344_3]) ).

fof(f_1345_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_1345_2,plain,
    ! [U_4042,U_4041] :
      ( U_4042 = U_4041
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,U_4042),U_4041)) ),
    inference(variable_rename,[status(thm)],[f_1345_1]) ).

fof(f_1345_3,plain,
    ! [U_4041,U_4042] :
      ( U_4042 = U_4041
      | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,U_4042),U_4041)) ),
    inference(definitional_conversion,[status(esa)],[f_1345_2]) ).

cnf(f_1345_4,plain,
    ( U_4042 = U_4041
    | ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,U_4042),U_4041)) ),
    inference(clausify,[status(thm)],[f_1345_3]) ).

fof(f_1346_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_1346_2,plain,
    ! [U_4044,U_4043] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,U_4044),U_4043))
      | U_4044 != U_4043 ),
    inference(variable_rename,[status(thm)],[f_1346_1]) ).

fof(f_1346_3,plain,
    ! [U_4043,U_4044] :
      ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,U_4044),U_4043))
      | U_4044 != U_4043 ),
    inference(definitional_conversion,[status(esa)],[f_1346_2]) ).

cnf(f_1346_4,plain,
    ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,U_4044),U_4043))
    | U_4044 != U_4043 ),
    inference(clausify,[status(thm)],[f_1346_3]) ).

fof(f_1347_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_1347_2,plain,
    ! [U_4046,U_4045] :
      ( U_4046 = U_4045
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_4046),U_4045))
      | ~ is_fun_pname_bool(U_4045)
      | ~ is_fun_pname_bool(U_4046) ),
    inference(variable_rename,[status(thm)],[f_1347_1]) ).

fof(f_1347_3,plain,
    ! [U_4045,U_4046] :
      ( U_4046 = U_4045
      | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_4046),U_4045))
      | ~ is_fun_pname_bool(U_4045)
      | ~ is_fun_pname_bool(U_4046) ),
    inference(definitional_conversion,[status(esa)],[f_1347_2]) ).

cnf(f_1347_4,plain,
    ( U_4046 = U_4045
    | ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_4046),U_4045))
    | ~ is_fun_pname_bool(U_4045)
    | ~ is_fun_pname_bool(U_4046) ),
    inference(clausify,[status(thm)],[f_1347_3]) ).

fof(f_1348_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_1348_2,plain,
    ! [U_4048,U_4047] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_4048),U_4047))
      | U_4048 != U_4047 ),
    inference(variable_rename,[status(thm)],[f_1348_1]) ).

fof(f_1348_3,plain,
    ! [U_4047,U_4048] :
      ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_4048),U_4047))
      | U_4048 != U_4047 ),
    inference(definitional_conversion,[status(esa)],[f_1348_2]) ).

cnf(f_1348_4,plain,
    ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,U_4048),U_4047))
    | U_4048 != U_4047 ),
    inference(clausify,[status(thm)],[f_1348_3]) ).

fof(f_1349_1,plain,
    ! [P,Q,R] : hAPP_nat_bool(cOMBB_int_bool_nat(P,Q),R) = hAPP_int_bool(P,hAPP_nat_int(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__HOL__Obool_000tc__Nat__Onat_U]) ).

fof(f_1349_2,plain,
    ! [U_4051,U_4050,U_4049] : hAPP_nat_bool(cOMBB_int_bool_nat(U_4051,U_4050),U_4049) = hAPP_int_bool(U_4051,hAPP_nat_int(U_4050,U_4049)),
    inference(variable_rename,[status(thm)],[f_1349_1]) ).

fof(f_1349_3,plain,
    ! [U_4049,U_4050,U_4051] : hAPP_nat_bool(cOMBB_int_bool_nat(U_4051,U_4050),U_4049) = hAPP_int_bool(U_4051,hAPP_nat_int(U_4050,U_4049)),
    inference(definitional_conversion,[status(esa)],[f_1349_2]) ).

cnf(f_1349_4,plain,
    hAPP_nat_bool(cOMBB_int_bool_nat(U_4051,U_4050),U_4049) = hAPP_int_bool(U_4051,hAPP_nat_int(U_4050,U_4049)),
    inference(clausify,[status(thm)],[f_1349_3]) ).

fof(f_1350_1,plain,
    ! [P,Q,R] : hAPP_int_bool(hAPP_i1948725293t_bool(cOMBC_int_int_bool(P),Q),R) = hAPP_int_bool(hAPP_i1948725293t_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__HOL__Obool_U]) ).

fof(f_1350_2,plain,
    ! [U_4054,U_4053,U_4052] : hAPP_int_bool(hAPP_i1948725293t_bool(cOMBC_int_int_bool(U_4054),U_4053),U_4052) = hAPP_int_bool(hAPP_i1948725293t_bool(U_4054,U_4052),U_4053),
    inference(variable_rename,[status(thm)],[f_1350_1]) ).

fof(f_1350_3,plain,
    ! [U_4052,U_4053,U_4054] : hAPP_int_bool(hAPP_i1948725293t_bool(cOMBC_int_int_bool(U_4054),U_4053),U_4052) = hAPP_int_bool(hAPP_i1948725293t_bool(U_4054,U_4052),U_4053),
    inference(definitional_conversion,[status(esa)],[f_1350_2]) ).

cnf(f_1350_4,plain,
    hAPP_int_bool(hAPP_i1948725293t_bool(cOMBC_int_int_bool(U_4054),U_4053),U_4052) = hAPP_int_bool(hAPP_i1948725293t_bool(U_4054,U_4052),U_4053),
    inference(clausify,[status(thm)],[f_1350_3]) ).

fof(f_1351_1,plain,
    ! [P,Q,R] : hAPP_nat_bool(hAPP_i418383825t_bool(cOMBC_nat_int_bool(P),Q),R) = hAPP_int_bool(hAPP_n1082236369t_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Int__Oint_000tc__HOL__Obool_U]) ).

fof(f_1351_2,plain,
    ! [U_4057,U_4056,U_4055] : hAPP_nat_bool(hAPP_i418383825t_bool(cOMBC_nat_int_bool(U_4057),U_4056),U_4055) = hAPP_int_bool(hAPP_n1082236369t_bool(U_4057,U_4055),U_4056),
    inference(variable_rename,[status(thm)],[f_1351_1]) ).

fof(f_1351_3,plain,
    ! [U_4055,U_4056,U_4057] : hAPP_nat_bool(hAPP_i418383825t_bool(cOMBC_nat_int_bool(U_4057),U_4056),U_4055) = hAPP_int_bool(hAPP_n1082236369t_bool(U_4057,U_4055),U_4056),
    inference(definitional_conversion,[status(esa)],[f_1351_2]) ).

cnf(f_1351_4,plain,
    hAPP_nat_bool(hAPP_i418383825t_bool(cOMBC_nat_int_bool(U_4057),U_4056),U_4055) = hAPP_int_bool(hAPP_n1082236369t_bool(U_4057,U_4055),U_4056),
    inference(clausify,[status(thm)],[f_1351_3]) ).

fof(f_1352_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_1352_2,plain,
    ! [U_4060,U_4059,U_4058] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(U_4060),U_4059),U_4058) = hAPP_nat_bool(hAPP_n1699378549t_bool(U_4060,U_4058),U_4059),
    inference(variable_rename,[status(thm)],[f_1352_1]) ).

fof(f_1352_3,plain,
    ! [U_4058,U_4059,U_4060] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(U_4060),U_4059),U_4058) = hAPP_nat_bool(hAPP_n1699378549t_bool(U_4060,U_4058),U_4059),
    inference(definitional_conversion,[status(esa)],[f_1352_2]) ).

cnf(f_1352_4,plain,
    hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(U_4060),U_4059),U_4058) = hAPP_nat_bool(hAPP_n1699378549t_bool(U_4060,U_4058),U_4059),
    inference(clausify,[status(thm)],[f_1352_3]) ).

fof(f_1353_1,plain,
    ! [P,Q,R] : hAPP_int_bool(cOMBB_bool_bool_int(P,Q),R) = hAPP_bool_bool(P,hAPP_int_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Int__Oint_U]) ).

fof(f_1353_2,plain,
    ! [U_4063,U_4062,U_4061] : hAPP_int_bool(cOMBB_bool_bool_int(U_4063,U_4062),U_4061) = hAPP_bool_bool(U_4063,hAPP_int_bool(U_4062,U_4061)),
    inference(variable_rename,[status(thm)],[f_1353_1]) ).

fof(f_1353_3,plain,
    ! [U_4061,U_4062,U_4063] : hAPP_int_bool(cOMBB_bool_bool_int(U_4063,U_4062),U_4061) = hAPP_bool_bool(U_4063,hAPP_int_bool(U_4062,U_4061)),
    inference(definitional_conversion,[status(esa)],[f_1353_2]) ).

cnf(f_1353_4,plain,
    hAPP_int_bool(cOMBB_bool_bool_int(U_4063,U_4062),U_4061) = hAPP_bool_bool(U_4063,hAPP_int_bool(U_4062,U_4061)),
    inference(clausify,[status(thm)],[f_1353_3]) ).

fof(f_1354_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_1354_2,plain,
    ! [U_4066,U_4065,U_4064] : hAPP_nat_bool(cOMBB_bool_bool_nat(U_4066,U_4065),U_4064) = hAPP_bool_bool(U_4066,hAPP_nat_bool(U_4065,U_4064)),
    inference(variable_rename,[status(thm)],[f_1354_1]) ).

fof(f_1354_3,plain,
    ! [U_4064,U_4065,U_4066] : hAPP_nat_bool(cOMBB_bool_bool_nat(U_4066,U_4065),U_4064) = hAPP_bool_bool(U_4066,hAPP_nat_bool(U_4065,U_4064)),
    inference(definitional_conversion,[status(esa)],[f_1354_2]) ).

cnf(f_1354_4,plain,
    hAPP_nat_bool(cOMBB_bool_bool_nat(U_4066,U_4065),U_4064) = hAPP_bool_bool(U_4066,hAPP_nat_bool(U_4065,U_4064)),
    inference(clausify,[status(thm)],[f_1354_3]) ).

fof(f_1355_1,plain,
    ! [P,Q,R] : hAPP_int_bool(cOMBS_int_bool_bool(P,Q),R) = hAPP_bool_bool(hAPP_i68813070l_bool(P,R),hAPP_int_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBS_1_1_COMBS_000tc__Int__Oint_000tc__HOL__Obool_000tc__HOL__Obool_U]) ).

fof(f_1355_2,plain,
    ! [U_4069,U_4068,U_4067] : hAPP_int_bool(cOMBS_int_bool_bool(U_4069,U_4068),U_4067) = hAPP_bool_bool(hAPP_i68813070l_bool(U_4069,U_4067),hAPP_int_bool(U_4068,U_4067)),
    inference(variable_rename,[status(thm)],[f_1355_1]) ).

fof(f_1355_3,plain,
    ! [U_4067,U_4068,U_4069] : hAPP_int_bool(cOMBS_int_bool_bool(U_4069,U_4068),U_4067) = hAPP_bool_bool(hAPP_i68813070l_bool(U_4069,U_4067),hAPP_int_bool(U_4068,U_4067)),
    inference(definitional_conversion,[status(esa)],[f_1355_2]) ).

cnf(f_1355_4,plain,
    hAPP_int_bool(cOMBS_int_bool_bool(U_4069,U_4068),U_4067) = hAPP_bool_bool(hAPP_i68813070l_bool(U_4069,U_4067),hAPP_int_bool(U_4068,U_4067)),
    inference(clausify,[status(thm)],[f_1355_3]) ).

fof(f_1356_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_1356_2,plain,
    ! [U_4072,U_4071,U_4070] : hAPP_nat_bool(cOMBS_nat_bool_bool(U_4072,U_4071),U_4070) = hAPP_bool_bool(hAPP_n1006566506l_bool(U_4072,U_4070),hAPP_nat_bool(U_4071,U_4070)),
    inference(variable_rename,[status(thm)],[f_1356_1]) ).

fof(f_1356_3,plain,
    ! [U_4070,U_4071,U_4072] : hAPP_nat_bool(cOMBS_nat_bool_bool(U_4072,U_4071),U_4070) = hAPP_bool_bool(hAPP_n1006566506l_bool(U_4072,U_4070),hAPP_nat_bool(U_4071,U_4070)),
    inference(definitional_conversion,[status(esa)],[f_1356_2]) ).

cnf(f_1356_4,plain,
    hAPP_nat_bool(cOMBS_nat_bool_bool(U_4072,U_4071),U_4070) = hAPP_bool_bool(hAPP_n1006566506l_bool(U_4072,U_4070),hAPP_nat_bool(U_4071,U_4070)),
    inference(clausify,[status(thm)],[f_1356_3]) ).

fof(f_1357_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_1357_2,plain,
    ! [U_4075,U_4074,U_4073] : hAPP_pname_bool(cOMBB_647938656_pname(U_4075,U_4074),U_4073) = hAPP_bool_bool(U_4075,hAPP_pname_bool(U_4074,U_4073)),
    inference(variable_rename,[status(thm)],[f_1357_1]) ).

fof(f_1357_3,plain,
    ! [U_4073,U_4074,U_4075] : hAPP_pname_bool(cOMBB_647938656_pname(U_4075,U_4074),U_4073) = hAPP_bool_bool(U_4075,hAPP_pname_bool(U_4074,U_4073)),
    inference(definitional_conversion,[status(esa)],[f_1357_2]) ).

cnf(f_1357_4,plain,
    hAPP_pname_bool(cOMBB_647938656_pname(U_4075,U_4074),U_4073) = hAPP_bool_bool(U_4075,hAPP_pname_bool(U_4074,U_4073)),
    inference(clausify,[status(thm)],[f_1357_3]) ).

fof(f_1358_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_1358_2,plain,
    ! [U_4078,U_4077,U_4076] : hAPP_pname_bool(cOMBS_568398431l_bool(U_4078,U_4077),U_4076) = hAPP_bool_bool(hAPP_p393069232l_bool(U_4078,U_4076),hAPP_pname_bool(U_4077,U_4076)),
    inference(variable_rename,[status(thm)],[f_1358_1]) ).

fof(f_1358_3,plain,
    ! [U_4076,U_4077,U_4078] : hAPP_pname_bool(cOMBS_568398431l_bool(U_4078,U_4077),U_4076) = hAPP_bool_bool(hAPP_p393069232l_bool(U_4078,U_4076),hAPP_pname_bool(U_4077,U_4076)),
    inference(definitional_conversion,[status(esa)],[f_1358_2]) ).

cnf(f_1358_4,plain,
    hAPP_pname_bool(cOMBS_568398431l_bool(U_4078,U_4077),U_4076) = hAPP_bool_bool(hAPP_p393069232l_bool(U_4078,U_4076),hAPP_pname_bool(U_4077,U_4076)),
    inference(clausify,[status(thm)],[f_1358_3]) ).

fof(f_1359_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_1359_2,plain,
    ! [U_4081,U_4080,U_4079] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(U_4081),U_4080),U_4079) = hAPP_pname_bool(hAPP_p61793385e_bool(U_4081,U_4079),U_4080),
    inference(variable_rename,[status(thm)],[f_1359_1]) ).

fof(f_1359_3,plain,
    ! [U_4079,U_4080,U_4081] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(U_4081),U_4080),U_4079) = hAPP_pname_bool(hAPP_p61793385e_bool(U_4081,U_4079),U_4080),
    inference(definitional_conversion,[status(esa)],[f_1359_2]) ).

cnf(f_1359_4,plain,
    hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(U_4081),U_4080),U_4079) = hAPP_pname_bool(hAPP_p61793385e_bool(U_4081,U_4079),U_4080),
    inference(clausify,[status(thm)],[f_1359_3]) ).

fof(f_1360_1,plain,
    ! [P,Q,R] : hAPP_int_fun_a_bool(cOMBB_375279840ol_int(P,Q),R) = hAPP_a_fun_a_bool(P,hAPP_int_a(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Int__Oint]) ).

fof(f_1360_2,plain,
    ! [U_4084,U_4083,U_4082] : hAPP_int_fun_a_bool(cOMBB_375279840ol_int(U_4084,U_4083),U_4082) = hAPP_a_fun_a_bool(U_4084,hAPP_int_a(U_4083,U_4082)),
    inference(variable_rename,[status(thm)],[f_1360_1]) ).

fof(f_1360_3,plain,
    ! [U_4082,U_4083,U_4084] : hAPP_int_fun_a_bool(cOMBB_375279840ol_int(U_4084,U_4083),U_4082) = hAPP_a_fun_a_bool(U_4084,hAPP_int_a(U_4083,U_4082)),
    inference(definitional_conversion,[status(esa)],[f_1360_2]) ).

cnf(f_1360_4,plain,
    hAPP_int_fun_a_bool(cOMBB_375279840ol_int(U_4084,U_4083),U_4082) = hAPP_a_fun_a_bool(U_4084,hAPP_int_a(U_4083,U_4082)),
    inference(clausify,[status(thm)],[f_1360_3]) ).

fof(f_1361_1,plain,
    ! [P,Q,R] : hAPP_a_bool(cOMBB_1273333599bool_a(P,Q),R) = hAPP_fun_a_bool_bool(P,hAPP_a_fun_a_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t__]) ).

fof(f_1361_2,plain,
    ! [U_4087,U_4086,U_4085] : hAPP_a_bool(cOMBB_1273333599bool_a(U_4087,U_4086),U_4085) = hAPP_fun_a_bool_bool(U_4087,hAPP_a_fun_a_bool(U_4086,U_4085)),
    inference(variable_rename,[status(thm)],[f_1361_1]) ).

fof(f_1361_3,plain,
    ! [U_4085,U_4086,U_4087] : hAPP_a_bool(cOMBB_1273333599bool_a(U_4087,U_4086),U_4085) = hAPP_fun_a_bool_bool(U_4087,hAPP_a_fun_a_bool(U_4086,U_4085)),
    inference(definitional_conversion,[status(esa)],[f_1361_2]) ).

cnf(f_1361_4,plain,
    hAPP_a_bool(cOMBB_1273333599bool_a(U_4087,U_4086),U_4085) = hAPP_fun_a_bool_bool(U_4087,hAPP_a_fun_a_bool(U_4086,U_4085)),
    inference(clausify,[status(thm)],[f_1361_3]) ).

fof(f_1362_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_1362_2,plain,
    ! [U_4090,U_4089,U_4088] : hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(U_4090),U_4089),U_4088) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(U_4090,U_4088),U_4089),
    inference(variable_rename,[status(thm)],[f_1362_1]) ).

fof(f_1362_3,plain,
    ! [U_4088,U_4089,U_4090] : hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(U_4090),U_4089),U_4088) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(U_4090,U_4088),U_4089),
    inference(definitional_conversion,[status(esa)],[f_1362_2]) ).

cnf(f_1362_4,plain,
    hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(U_4090),U_4089),U_4088) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(U_4090,U_4088),U_4089),
    inference(clausify,[status(thm)],[f_1362_3]) ).

fof(f_1363_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_1363_2,plain,
    ! [U_4093,U_4092,U_4091] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(U_4093,U_4092),U_4091) = hAPP_a_fun_a_bool(U_4093,hAPP_pname_a(U_4092,U_4091)),
    inference(variable_rename,[status(thm)],[f_1363_1]) ).

fof(f_1363_3,plain,
    ! [U_4091,U_4092,U_4093] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(U_4093,U_4092),U_4091) = hAPP_a_fun_a_bool(U_4093,hAPP_pname_a(U_4092,U_4091)),
    inference(definitional_conversion,[status(esa)],[f_1363_2]) ).

cnf(f_1363_4,plain,
    hAPP_p1534023578a_bool(cOMBB_1897541054_pname(U_4093,U_4092),U_4091) = hAPP_a_fun_a_bool(U_4093,hAPP_pname_a(U_4092,U_4091)),
    inference(clausify,[status(thm)],[f_1363_3]) ).

fof(f_1364_1,plain,
    ! [P,Q,R] : hAPP_int_bool(hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(P),Q),R) = hAPP_fun_a_bool_bool(hAPP_i888906320l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__]) ).

fof(f_1364_2,plain,
    ! [U_4096,U_4095,U_4094] : hAPP_int_bool(hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(U_4096),U_4095),U_4094) = hAPP_fun_a_bool_bool(hAPP_i888906320l_bool(U_4096,U_4094),U_4095),
    inference(variable_rename,[status(thm)],[f_1364_1]) ).

fof(f_1364_3,plain,
    ! [U_4094,U_4095,U_4096] : hAPP_int_bool(hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(U_4096),U_4095),U_4094) = hAPP_fun_a_bool_bool(hAPP_i888906320l_bool(U_4096,U_4094),U_4095),
    inference(definitional_conversion,[status(esa)],[f_1364_2]) ).

cnf(f_1364_4,plain,
    hAPP_int_bool(hAPP_f1812805200t_bool(cOMBC_1753430397l_bool(U_4096),U_4095),U_4094) = hAPP_fun_a_bool_bool(hAPP_i888906320l_bool(U_4096,U_4094),U_4095),
    inference(clausify,[status(thm)],[f_1364_3]) ).

fof(f_1365_1,plain,
    ! [P,Q,R] : hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(P),Q),R) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__]) ).

fof(f_1365_2,plain,
    ! [U_4099,U_4098,U_4097] : hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(U_4099),U_4098),U_4097) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(U_4099,U_4097),U_4098),
    inference(variable_rename,[status(thm)],[f_1365_1]) ).

fof(f_1365_3,plain,
    ! [U_4097,U_4098,U_4099] : hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(U_4099),U_4098),U_4097) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(U_4099,U_4097),U_4098),
    inference(definitional_conversion,[status(esa)],[f_1365_2]) ).

cnf(f_1365_4,plain,
    hAPP_nat_bool(hAPP_f282463732t_bool(cOMBC_1928494297l_bool(U_4099),U_4098),U_4097) = hAPP_fun_a_bool_bool(hAPP_n1414589940l_bool(U_4099,U_4097),U_4098),
    inference(clausify,[status(thm)],[f_1365_3]) ).

fof(f_1366_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_1366_2,plain,
    ! [U_4102,U_4101,U_4100] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(U_4102,U_4101),U_4100) = hAPP_b589554111l_bool(U_4102,hAPP_a_bool(U_4101,U_4100)),
    inference(variable_rename,[status(thm)],[f_1366_1]) ).

fof(f_1366_3,plain,
    ! [U_4100,U_4101,U_4102] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(U_4102,U_4101),U_4100) = hAPP_b589554111l_bool(U_4102,hAPP_a_bool(U_4101,U_4100)),
    inference(definitional_conversion,[status(esa)],[f_1366_2]) ).

cnf(f_1366_4,plain,
    hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(U_4102,U_4101),U_4100) = hAPP_b589554111l_bool(U_4102,hAPP_a_bool(U_4101,U_4100)),
    inference(clausify,[status(thm)],[f_1366_3]) ).

fof(f_1367_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_1367_2,plain,
    ! [U_4105,U_4104,U_4103] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(U_4105,U_4104),U_4103) = hAPP_bool_bool(hAPP_f198738859l_bool(U_4105,U_4103),hAPP_fun_a_bool_bool(U_4104,U_4103)),
    inference(variable_rename,[status(thm)],[f_1367_1]) ).

fof(f_1367_3,plain,
    ! [U_4103,U_4104,U_4105] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(U_4105,U_4104),U_4103) = hAPP_bool_bool(hAPP_f198738859l_bool(U_4105,U_4103),hAPP_fun_a_bool_bool(U_4104,U_4103)),
    inference(definitional_conversion,[status(esa)],[f_1367_2]) ).

cnf(f_1367_4,plain,
    hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(U_4105,U_4104),U_4103) = hAPP_bool_bool(hAPP_f198738859l_bool(U_4105,U_4103),hAPP_fun_a_bool_bool(U_4104,U_4103)),
    inference(clausify,[status(thm)],[f_1367_3]) ).

fof(f_1368_1,plain,
    ! [P,Q,R] : hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(P,Q),R) = hAPP_i1948725293t_bool(P,hAPP_nat_int(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_]) ).

fof(f_1368_2,plain,
    ! [U_4108,U_4107,U_4106] : hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(U_4108,U_4107),U_4106) = hAPP_i1948725293t_bool(U_4108,hAPP_nat_int(U_4107,U_4106)),
    inference(variable_rename,[status(thm)],[f_1368_1]) ).

fof(f_1368_3,plain,
    ! [U_4106,U_4107,U_4108] : hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(U_4108,U_4107),U_4106) = hAPP_i1948725293t_bool(U_4108,hAPP_nat_int(U_4107,U_4106)),
    inference(definitional_conversion,[status(esa)],[f_1368_2]) ).

cnf(f_1368_4,plain,
    hAPP_n1082236369t_bool(cOMBB_1628441366ol_nat(U_4108,U_4107),U_4106) = hAPP_i1948725293t_bool(U_4108,hAPP_nat_int(U_4107,U_4106)),
    inference(clausify,[status(thm)],[f_1368_3]) ).

fof(f_1369_1,plain,
    ! [P,Q,R] : hAPP_n1699378549t_bool(cOMBB_800536526ol_nat(P,Q),R) = hAPP_n1699378549t_bool(P,hAPP_nat_nat(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_]) ).

fof(f_1369_2,plain,
    ! [U_4111,U_4110,U_4109] : hAPP_n1699378549t_bool(cOMBB_800536526ol_nat(U_4111,U_4110),U_4109) = hAPP_n1699378549t_bool(U_4111,hAPP_nat_nat(U_4110,U_4109)),
    inference(variable_rename,[status(thm)],[f_1369_1]) ).

fof(f_1369_3,plain,
    ! [U_4109,U_4110,U_4111] : hAPP_n1699378549t_bool(cOMBB_800536526ol_nat(U_4111,U_4110),U_4109) = hAPP_n1699378549t_bool(U_4111,hAPP_nat_nat(U_4110,U_4109)),
    inference(definitional_conversion,[status(esa)],[f_1369_2]) ).

cnf(f_1369_4,plain,
    hAPP_n1699378549t_bool(cOMBB_800536526ol_nat(U_4111,U_4110),U_4109) = hAPP_n1699378549t_bool(U_4111,hAPP_nat_nat(U_4110,U_4109)),
    inference(clausify,[status(thm)],[f_1369_3]) ).

fof(f_1370_1,plain,
    ! [P,Q,R] : hAPP_a_fun_a_bool(hAPP_f1038053735a_bool(cOMBC_394484100a_bool(P),Q),R) = hAPP_f2050579477a_bool(hAPP_a1206381875a_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__fun_It__a]) ).

fof(f_1370_2,plain,
    ! [U_4114,U_4113,U_4112] : hAPP_a_fun_a_bool(hAPP_f1038053735a_bool(cOMBC_394484100a_bool(U_4114),U_4113),U_4112) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(U_4114,U_4112),U_4113),
    inference(variable_rename,[status(thm)],[f_1370_1]) ).

fof(f_1370_3,plain,
    ! [U_4112,U_4113,U_4114] : hAPP_a_fun_a_bool(hAPP_f1038053735a_bool(cOMBC_394484100a_bool(U_4114),U_4113),U_4112) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(U_4114,U_4112),U_4113),
    inference(definitional_conversion,[status(esa)],[f_1370_2]) ).

cnf(f_1370_4,plain,
    hAPP_a_fun_a_bool(hAPP_f1038053735a_bool(cOMBC_394484100a_bool(U_4114),U_4113),U_4112) = hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(U_4114,U_4112),U_4113),
    inference(clausify,[status(thm)],[f_1370_3]) ).

fof(f_1371_1,plain,
    ! [P,Q,R] : hAPP_int_bool(cOMBB_1418110531ol_int(P,Q),R) = hAPP_f448129468l_bool(P,hAPP_i1948725293t_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obo]) ).

fof(f_1371_2,plain,
    ! [U_4117,U_4116,U_4115] : hAPP_int_bool(cOMBB_1418110531ol_int(U_4117,U_4116),U_4115) = hAPP_f448129468l_bool(U_4117,hAPP_i1948725293t_bool(U_4116,U_4115)),
    inference(variable_rename,[status(thm)],[f_1371_1]) ).

fof(f_1371_3,plain,
    ! [U_4115,U_4116,U_4117] : hAPP_int_bool(cOMBB_1418110531ol_int(U_4117,U_4116),U_4115) = hAPP_f448129468l_bool(U_4117,hAPP_i1948725293t_bool(U_4116,U_4115)),
    inference(definitional_conversion,[status(esa)],[f_1371_2]) ).

cnf(f_1371_4,plain,
    hAPP_int_bool(cOMBB_1418110531ol_int(U_4117,U_4116),U_4115) = hAPP_f448129468l_bool(U_4117,hAPP_i1948725293t_bool(U_4116,U_4115)),
    inference(clausify,[status(thm)],[f_1371_3]) ).

fof(f_1372_1,plain,
    ! [P,Q,R] : hAPP_nat_bool(cOMBB_955900739ol_nat(P,Q),R) = hAPP_f54304608l_bool(P,hAPP_n1699378549t_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo]) ).

fof(f_1372_2,plain,
    ! [U_4120,U_4119,U_4118] : hAPP_nat_bool(cOMBB_955900739ol_nat(U_4120,U_4119),U_4118) = hAPP_f54304608l_bool(U_4120,hAPP_n1699378549t_bool(U_4119,U_4118)),
    inference(variable_rename,[status(thm)],[f_1372_1]) ).

fof(f_1372_3,plain,
    ! [U_4118,U_4119,U_4120] : hAPP_nat_bool(cOMBB_955900739ol_nat(U_4120,U_4119),U_4118) = hAPP_f54304608l_bool(U_4120,hAPP_n1699378549t_bool(U_4119,U_4118)),
    inference(definitional_conversion,[status(esa)],[f_1372_2]) ).

cnf(f_1372_4,plain,
    hAPP_nat_bool(cOMBB_955900739ol_nat(U_4120,U_4119),U_4118) = hAPP_f54304608l_bool(U_4120,hAPP_n1699378549t_bool(U_4119,U_4118)),
    inference(clausify,[status(thm)],[f_1372_3]) ).

fof(f_1373_1,plain,
    ! [P,Q,R] : hAPP_int_bool(hAPP_f1805168059t_bool(cOMBC_94739984l_bool(P),Q),R) = hAPP_f448129468l_bool(hAPP_i2112223885l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_]) ).

fof(f_1373_2,plain,
    ! [U_4123,U_4122,U_4121] : hAPP_int_bool(hAPP_f1805168059t_bool(cOMBC_94739984l_bool(U_4123),U_4122),U_4121) = hAPP_f448129468l_bool(hAPP_i2112223885l_bool(U_4123,U_4121),U_4122),
    inference(variable_rename,[status(thm)],[f_1373_1]) ).

fof(f_1373_3,plain,
    ! [U_4121,U_4122,U_4123] : hAPP_int_bool(hAPP_f1805168059t_bool(cOMBC_94739984l_bool(U_4123),U_4122),U_4121) = hAPP_f448129468l_bool(hAPP_i2112223885l_bool(U_4123,U_4121),U_4122),
    inference(definitional_conversion,[status(esa)],[f_1373_2]) ).

cnf(f_1373_4,plain,
    hAPP_int_bool(hAPP_f1805168059t_bool(cOMBC_94739984l_bool(U_4123),U_4122),U_4121) = hAPP_f448129468l_bool(hAPP_i2112223885l_bool(U_4123,U_4121),U_4122),
    inference(clausify,[status(thm)],[f_1373_3]) ).

fof(f_1374_1,plain,
    ! [P,Q,R] : hAPP_int_bool(hAPP_f183368031t_bool(cOMBC_1848398772l_bool(P),Q),R) = hAPP_f54304608l_bool(hAPP_i1718399025l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_]) ).

fof(f_1374_2,plain,
    ! [U_4126,U_4125,U_4124] : hAPP_int_bool(hAPP_f183368031t_bool(cOMBC_1848398772l_bool(U_4126),U_4125),U_4124) = hAPP_f54304608l_bool(hAPP_i1718399025l_bool(U_4126,U_4124),U_4125),
    inference(variable_rename,[status(thm)],[f_1374_1]) ).

fof(f_1374_3,plain,
    ! [U_4124,U_4125,U_4126] : hAPP_int_bool(hAPP_f183368031t_bool(cOMBC_1848398772l_bool(U_4126),U_4125),U_4124) = hAPP_f54304608l_bool(hAPP_i1718399025l_bool(U_4126,U_4124),U_4125),
    inference(definitional_conversion,[status(esa)],[f_1374_2]) ).

cnf(f_1374_4,plain,
    hAPP_int_bool(hAPP_f183368031t_bool(cOMBC_1848398772l_bool(U_4126),U_4125),U_4124) = hAPP_f54304608l_bool(hAPP_i1718399025l_bool(U_4126,U_4124),U_4125),
    inference(clausify,[status(thm)],[f_1374_3]) ).

fof(f_1375_1,plain,
    ! [P,Q,R] : hAPP_nat_bool(hAPP_f274826591t_bool(cOMBC_620423604l_bool(P),Q),R) = hAPP_f448129468l_bool(hAPP_n609083369l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_]) ).

fof(f_1375_2,plain,
    ! [U_4129,U_4128,U_4127] : hAPP_nat_bool(hAPP_f274826591t_bool(cOMBC_620423604l_bool(U_4129),U_4128),U_4127) = hAPP_f448129468l_bool(hAPP_n609083369l_bool(U_4129,U_4127),U_4128),
    inference(variable_rename,[status(thm)],[f_1375_1]) ).

fof(f_1375_3,plain,
    ! [U_4127,U_4128,U_4129] : hAPP_nat_bool(hAPP_f274826591t_bool(cOMBC_620423604l_bool(U_4129),U_4128),U_4127) = hAPP_f448129468l_bool(hAPP_n609083369l_bool(U_4129,U_4127),U_4128),
    inference(definitional_conversion,[status(esa)],[f_1375_2]) ).

cnf(f_1375_4,plain,
    hAPP_nat_bool(hAPP_f274826591t_bool(cOMBC_620423604l_bool(U_4129),U_4128),U_4127) = hAPP_f448129468l_bool(hAPP_n609083369l_bool(U_4129,U_4127),U_4128),
    inference(clausify,[status(thm)],[f_1375_3]) ).

fof(f_1376_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_1376_2,plain,
    ! [U_4132,U_4131,U_4130] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(U_4132),U_4131),U_4130) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(U_4132,U_4130),U_4131),
    inference(variable_rename,[status(thm)],[f_1376_1]) ).

fof(f_1376_3,plain,
    ! [U_4130,U_4131,U_4132] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(U_4132),U_4131),U_4130) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(U_4132,U_4130),U_4131),
    inference(definitional_conversion,[status(esa)],[f_1376_2]) ).

cnf(f_1376_4,plain,
    hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(U_4132),U_4131),U_4130) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(U_4132,U_4130),U_4131),
    inference(clausify,[status(thm)],[f_1376_3]) ).

fof(f_1377_1,plain,
    ! [P,Q,R] : hAPP_i68813070l_bool(cOMBB_1652995168ol_int(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_int_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_003]) ).

fof(f_1377_2,plain,
    ! [U_4135,U_4134,U_4133] : hAPP_i68813070l_bool(cOMBB_1652995168ol_int(U_4135,U_4134),U_4133) = hAPP_b589554111l_bool(U_4135,hAPP_int_bool(U_4134,U_4133)),
    inference(variable_rename,[status(thm)],[f_1377_1]) ).

fof(f_1377_3,plain,
    ! [U_4133,U_4134,U_4135] : hAPP_i68813070l_bool(cOMBB_1652995168ol_int(U_4135,U_4134),U_4133) = hAPP_b589554111l_bool(U_4135,hAPP_int_bool(U_4134,U_4133)),
    inference(definitional_conversion,[status(esa)],[f_1377_2]) ).

cnf(f_1377_4,plain,
    hAPP_i68813070l_bool(cOMBB_1652995168ol_int(U_4135,U_4134),U_4133) = hAPP_b589554111l_bool(U_4135,hAPP_int_bool(U_4134,U_4133)),
    inference(clausify,[status(thm)],[f_1377_3]) ).

fof(f_1378_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_004]) ).

fof(f_1378_2,plain,
    ! [U_4138,U_4137,U_4136] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(U_4138,U_4137),U_4136) = hAPP_b589554111l_bool(U_4138,hAPP_nat_bool(U_4137,U_4136)),
    inference(variable_rename,[status(thm)],[f_1378_1]) ).

fof(f_1378_3,plain,
    ! [U_4136,U_4137,U_4138] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(U_4138,U_4137),U_4136) = hAPP_b589554111l_bool(U_4138,hAPP_nat_bool(U_4137,U_4136)),
    inference(definitional_conversion,[status(esa)],[f_1378_2]) ).

cnf(f_1378_4,plain,
    hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(U_4138,U_4137),U_4136) = hAPP_b589554111l_bool(U_4138,hAPP_nat_bool(U_4137,U_4136)),
    inference(clausify,[status(thm)],[f_1378_3]) ).

fof(f_1379_1,plain,
    ! [P,Q,R] : hAPP_f448129468l_bool(cOMBS_1912792529l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f1721100032l_bool(P,R),hAPP_f448129468l_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBS_1_1_COMBS_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__HOL__Obo]) ).

fof(f_1379_2,plain,
    ! [U_4141,U_4140,U_4139] : hAPP_f448129468l_bool(cOMBS_1912792529l_bool(U_4141,U_4140),U_4139) = hAPP_bool_bool(hAPP_f1721100032l_bool(U_4141,U_4139),hAPP_f448129468l_bool(U_4140,U_4139)),
    inference(variable_rename,[status(thm)],[f_1379_1]) ).

fof(f_1379_3,plain,
    ! [U_4139,U_4140,U_4141] : hAPP_f448129468l_bool(cOMBS_1912792529l_bool(U_4141,U_4140),U_4139) = hAPP_bool_bool(hAPP_f1721100032l_bool(U_4141,U_4139),hAPP_f448129468l_bool(U_4140,U_4139)),
    inference(definitional_conversion,[status(esa)],[f_1379_2]) ).

cnf(f_1379_4,plain,
    hAPP_f448129468l_bool(cOMBS_1912792529l_bool(U_4141,U_4140),U_4139) = hAPP_bool_bool(hAPP_f1721100032l_bool(U_4141,U_4139),hAPP_f448129468l_bool(U_4140,U_4139)),
    inference(clausify,[status(thm)],[f_1379_3]) ).

fof(f_1380_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_1380_2,plain,
    ! [U_4144,U_4143,U_4142] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(U_4144,U_4143),U_4142) = hAPP_bool_bool(hAPP_f1748468828l_bool(U_4144,U_4142),hAPP_f54304608l_bool(U_4143,U_4142)),
    inference(variable_rename,[status(thm)],[f_1380_1]) ).

fof(f_1380_3,plain,
    ! [U_4142,U_4143,U_4144] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(U_4144,U_4143),U_4142) = hAPP_bool_bool(hAPP_f1748468828l_bool(U_4144,U_4142),hAPP_f54304608l_bool(U_4143,U_4142)),
    inference(definitional_conversion,[status(esa)],[f_1380_2]) ).

cnf(f_1380_4,plain,
    hAPP_f54304608l_bool(cOMBS_1187019125l_bool(U_4144,U_4143),U_4142) = hAPP_bool_bool(hAPP_f1748468828l_bool(U_4144,U_4142),hAPP_f54304608l_bool(U_4143,U_4142)),
    inference(clausify,[status(thm)],[f_1380_3]) ).

fof(f_1381_1,plain,
    ! [P,Q,R] : hAPP_int_bool(hAPP_f449020825t_bool(cOMBC_316919022l_bool(P),Q),R) = hAPP_f1664156314l_bool(hAPP_i1587699435l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo]) ).

fof(f_1381_2,plain,
    ! [U_4147,U_4146,U_4145] : hAPP_int_bool(hAPP_f449020825t_bool(cOMBC_316919022l_bool(U_4147),U_4146),U_4145) = hAPP_f1664156314l_bool(hAPP_i1587699435l_bool(U_4147,U_4145),U_4146),
    inference(variable_rename,[status(thm)],[f_1381_1]) ).

fof(f_1381_3,plain,
    ! [U_4145,U_4146,U_4147] : hAPP_int_bool(hAPP_f449020825t_bool(cOMBC_316919022l_bool(U_4147),U_4146),U_4145) = hAPP_f1664156314l_bool(hAPP_i1587699435l_bool(U_4147,U_4145),U_4146),
    inference(definitional_conversion,[status(esa)],[f_1381_2]) ).

cnf(f_1381_4,plain,
    hAPP_int_bool(hAPP_f449020825t_bool(cOMBC_316919022l_bool(U_4147),U_4146),U_4145) = hAPP_f1664156314l_bool(hAPP_i1587699435l_bool(U_4147,U_4145),U_4146),
    inference(clausify,[status(thm)],[f_1381_3]) ).

fof(f_1382_1,plain,
    ! [P,Q,R] : hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(P),Q),R) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo]) ).

fof(f_1382_2,plain,
    ! [U_4150,U_4149,U_4148] : hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(U_4150),U_4149),U_4148) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(U_4150,U_4148),U_4149),
    inference(variable_rename,[status(thm)],[f_1382_1]) ).

fof(f_1382_3,plain,
    ! [U_4148,U_4149,U_4150] : hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(U_4150),U_4149),U_4148) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(U_4150,U_4148),U_4149),
    inference(definitional_conversion,[status(esa)],[f_1382_2]) ).

cnf(f_1382_4,plain,
    hAPP_nat_bool(hAPP_f1066163005t_bool(cOMBC_386238098l_bool(U_4150),U_4149),U_4148) = hAPP_f1664156314l_bool(hAPP_n850744903l_bool(U_4150,U_4148),U_4149),
    inference(clausify,[status(thm)],[f_1382_3]) ).

fof(f_1383_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_005]) ).

fof(f_1383_2,plain,
    ! [U_4153,U_4152,U_4151] : hAPP_p393069232l_bool(cOMBB_675860798_pname(U_4153,U_4152),U_4151) = hAPP_b589554111l_bool(U_4153,hAPP_pname_bool(U_4152,U_4151)),
    inference(variable_rename,[status(thm)],[f_1383_1]) ).

fof(f_1383_3,plain,
    ! [U_4151,U_4152,U_4153] : hAPP_p393069232l_bool(cOMBB_675860798_pname(U_4153,U_4152),U_4151) = hAPP_b589554111l_bool(U_4153,hAPP_pname_bool(U_4152,U_4151)),
    inference(definitional_conversion,[status(esa)],[f_1383_2]) ).

cnf(f_1383_4,plain,
    hAPP_p393069232l_bool(cOMBB_675860798_pname(U_4153,U_4152),U_4151) = hAPP_b589554111l_bool(U_4153,hAPP_pname_bool(U_4152,U_4151)),
    inference(clausify,[status(thm)],[f_1383_3]) ).

fof(f_1384_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_1384_2,plain,
    ! [U_4156,U_4155,U_4154] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(U_4156,U_4155),U_4154) = hAPP_bool_bool(hAPP_f1476298914l_bool(U_4156,U_4154),hAPP_f1664156314l_bool(U_4155,U_4154)),
    inference(variable_rename,[status(thm)],[f_1384_1]) ).

fof(f_1384_3,plain,
    ! [U_4154,U_4155,U_4156] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(U_4156,U_4155),U_4154) = hAPP_bool_bool(hAPP_f1476298914l_bool(U_4156,U_4154),hAPP_f1664156314l_bool(U_4155,U_4154)),
    inference(definitional_conversion,[status(esa)],[f_1384_2]) ).

cnf(f_1384_4,plain,
    hAPP_f1664156314l_bool(cOMBS_350070575l_bool(U_4156,U_4155),U_4154) = hAPP_bool_bool(hAPP_f1476298914l_bool(U_4156,U_4154),hAPP_f1664156314l_bool(U_4155,U_4154)),
    inference(clausify,[status(thm)],[f_1384_3]) ).

fof(f_1385_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_1385_2,plain,
    ! [U_4159,U_4158,U_4157] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(U_4159),U_4158),U_4157) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(U_4159,U_4157),U_4158),
    inference(variable_rename,[status(thm)],[f_1385_1]) ).

fof(f_1385_3,plain,
    ! [U_4157,U_4158,U_4159] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(U_4159),U_4158),U_4157) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(U_4159,U_4157),U_4158),
    inference(definitional_conversion,[status(esa)],[f_1385_2]) ).

cnf(f_1385_4,plain,
    hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(U_4159),U_4158),U_4157) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(U_4159,U_4157),U_4158),
    inference(clausify,[status(thm)],[f_1385_3]) ).

fof(f_1386_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_1386_2,plain,
    ! [U_4162,U_4161,U_4160] : hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(U_4162),U_4161),U_4160) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(U_4162,U_4160),U_4161),
    inference(variable_rename,[status(thm)],[f_1386_1]) ).

fof(f_1386_3,plain,
    ! [U_4160,U_4161,U_4162] : hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(U_4162),U_4161),U_4160) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(U_4162,U_4160),U_4161),
    inference(definitional_conversion,[status(esa)],[f_1386_2]) ).

cnf(f_1386_4,plain,
    hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(U_4162),U_4161),U_4160) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(U_4162,U_4160),U_4161),
    inference(clausify,[status(thm)],[f_1386_3]) ).

fof(f_1387_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_006]) ).

fof(f_1387_2,plain,
    ! [U_4165,U_4164,U_4163] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(U_4165,U_4164),U_4163) = hAPP_b589554111l_bool(U_4165,hAPP_fun_a_bool_bool(U_4164,U_4163)),
    inference(variable_rename,[status(thm)],[f_1387_1]) ).

fof(f_1387_3,plain,
    ! [U_4163,U_4164,U_4165] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(U_4165,U_4164),U_4163) = hAPP_b589554111l_bool(U_4165,hAPP_fun_a_bool_bool(U_4164,U_4163)),
    inference(definitional_conversion,[status(esa)],[f_1387_2]) ).

cnf(f_1387_4,plain,
    hAPP_f198738859l_bool(cOMBB_338059395a_bool(U_4165,U_4164),U_4163) = hAPP_b589554111l_bool(U_4165,hAPP_fun_a_bool_bool(U_4164,U_4163)),
    inference(clausify,[status(thm)],[f_1387_3]) ).

fof(f_1388_1,plain,
    ! [P,Q,R] : hAPP_n215258509l_bool(cOMBB_1146692694ol_nat(P,Q),R) = hAPP_n215258509l_bool(P,hAPP_nat_nat(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO]) ).

fof(f_1388_2,plain,
    ! [U_4168,U_4167,U_4166] : hAPP_n215258509l_bool(cOMBB_1146692694ol_nat(U_4168,U_4167),U_4166) = hAPP_n215258509l_bool(U_4168,hAPP_nat_nat(U_4167,U_4166)),
    inference(variable_rename,[status(thm)],[f_1388_1]) ).

fof(f_1388_3,plain,
    ! [U_4166,U_4167,U_4168] : hAPP_n215258509l_bool(cOMBB_1146692694ol_nat(U_4168,U_4167),U_4166) = hAPP_n215258509l_bool(U_4168,hAPP_nat_nat(U_4167,U_4166)),
    inference(definitional_conversion,[status(esa)],[f_1388_2]) ).

cnf(f_1388_4,plain,
    hAPP_n215258509l_bool(cOMBB_1146692694ol_nat(U_4168,U_4167),U_4166) = hAPP_n215258509l_bool(U_4168,hAPP_nat_nat(U_4167,U_4166)),
    inference(clausify,[status(thm)],[f_1388_3]) ).

fof(f_1389_1,plain,
    ! [P,Q,R] : hAPP_i1948725293t_bool(hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(P),Q),R) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool__007]) ).

fof(f_1389_2,plain,
    ! [U_4171,U_4170,U_4169] : hAPP_i1948725293t_bool(hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(U_4171),U_4170),U_4169) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(U_4171,U_4169),U_4170),
    inference(variable_rename,[status(thm)],[f_1389_1]) ).

fof(f_1389_3,plain,
    ! [U_4169,U_4170,U_4171] : hAPP_i1948725293t_bool(hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(U_4171),U_4170),U_4169) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(U_4171,U_4169),U_4170),
    inference(definitional_conversion,[status(esa)],[f_1389_2]) ).

cnf(f_1389_4,plain,
    hAPP_i1948725293t_bool(hAPP_f1048215610t_bool(cOMBC_1683390479t_bool(U_4171),U_4170),U_4169) = hAPP_f1805168059t_bool(hAPP_i1529485324t_bool(U_4171,U_4169),U_4170),
    inference(clausify,[status(thm)],[f_1389_3]) ).

fof(f_1390_1,plain,
    ! [P,Q,R] : hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBC_178881787t_bool(P),Q),R) = hAPP_f800510211t_bool(hAPP_n1512601776t_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__008]) ).

fof(f_1390_2,plain,
    ! [U_4174,U_4173,U_4172] : hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBC_178881787t_bool(U_4174),U_4173),U_4172) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(U_4174,U_4172),U_4173),
    inference(variable_rename,[status(thm)],[f_1390_1]) ).

fof(f_1390_3,plain,
    ! [U_4172,U_4173,U_4174] : hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBC_178881787t_bool(U_4174),U_4173),U_4172) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(U_4174,U_4172),U_4173),
    inference(definitional_conversion,[status(esa)],[f_1390_2]) ).

cnf(f_1390_4,plain,
    hAPP_n1699378549t_bool(hAPP_f1570313510t_bool(cOMBC_178881787t_bool(U_4174),U_4173),U_4172) = hAPP_f800510211t_bool(hAPP_n1512601776t_bool(U_4174,U_4172),U_4173),
    inference(clausify,[status(thm)],[f_1390_3]) ).

fof(f_1391_1,plain,
    ! [P,Q,R] : hAPP_f448129468l_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(P),Q),R) = hAPP_f448129468l_bool(hAPP_f284875647l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc_]) ).

fof(f_1391_2,plain,
    ! [U_4177,U_4176,U_4175] : hAPP_f448129468l_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(U_4177),U_4176),U_4175) = hAPP_f448129468l_bool(hAPP_f284875647l_bool(U_4177,U_4175),U_4176),
    inference(variable_rename,[status(thm)],[f_1391_1]) ).

fof(f_1391_3,plain,
    ! [U_4175,U_4176,U_4177] : hAPP_f448129468l_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(U_4177),U_4176),U_4175) = hAPP_f448129468l_bool(hAPP_f284875647l_bool(U_4177,U_4175),U_4176),
    inference(definitional_conversion,[status(esa)],[f_1391_2]) ).

cnf(f_1391_4,plain,
    hAPP_f448129468l_bool(hAPP_f284875647l_bool(cOMBC_605892544l_bool(U_4177),U_4176),U_4175) = hAPP_f448129468l_bool(hAPP_f284875647l_bool(U_4177,U_4175),U_4176),
    inference(clausify,[status(thm)],[f_1391_3]) ).

fof(f_1392_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_1392_2,plain,
    ! [U_4180,U_4179,U_4178] : hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(U_4180),U_4179),U_4178) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(U_4180,U_4178),U_4179),
    inference(variable_rename,[status(thm)],[f_1392_1]) ).

fof(f_1392_3,plain,
    ! [U_4178,U_4179,U_4180] : hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(U_4180),U_4179),U_4178) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(U_4180,U_4178),U_4179),
    inference(definitional_conversion,[status(esa)],[f_1392_2]) ).

cnf(f_1392_4,plain,
    hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(U_4180),U_4179),U_4178) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(U_4180,U_4178),U_4179),
    inference(clausify,[status(thm)],[f_1392_3]) ).

fof(f_1393_1,plain,
    ! [P,Q,R] : hAPP_f1721100032l_bool(cOMBB_1974511970t_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f448129468l_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_1393_2,plain,
    ! [U_4183,U_4182,U_4181] : hAPP_f1721100032l_bool(cOMBB_1974511970t_bool(U_4183,U_4182),U_4181) = hAPP_b589554111l_bool(U_4183,hAPP_f448129468l_bool(U_4182,U_4181)),
    inference(variable_rename,[status(thm)],[f_1393_1]) ).

fof(f_1393_3,plain,
    ! [U_4181,U_4182,U_4183] : hAPP_f1721100032l_bool(cOMBB_1974511970t_bool(U_4183,U_4182),U_4181) = hAPP_b589554111l_bool(U_4183,hAPP_f448129468l_bool(U_4182,U_4181)),
    inference(definitional_conversion,[status(esa)],[f_1393_2]) ).

cnf(f_1393_4,plain,
    hAPP_f1721100032l_bool(cOMBB_1974511970t_bool(U_4183,U_4182),U_4181) = hAPP_b589554111l_bool(U_4183,hAPP_f448129468l_bool(U_4182,U_4181)),
    inference(clausify,[status(thm)],[f_1393_3]) ).

fof(f_1394_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_010]) ).

fof(f_1394_2,plain,
    ! [U_4186,U_4185,U_4184] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(U_4186,U_4185),U_4184) = hAPP_b589554111l_bool(U_4186,hAPP_f54304608l_bool(U_4185,U_4184)),
    inference(variable_rename,[status(thm)],[f_1394_1]) ).

fof(f_1394_3,plain,
    ! [U_4184,U_4185,U_4186] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(U_4186,U_4185),U_4184) = hAPP_b589554111l_bool(U_4186,hAPP_f54304608l_bool(U_4185,U_4184)),
    inference(definitional_conversion,[status(esa)],[f_1394_2]) ).

cnf(f_1394_4,plain,
    hAPP_f1748468828l_bool(cOMBB_444170502t_bool(U_4186,U_4185),U_4184) = hAPP_b589554111l_bool(U_4186,hAPP_f54304608l_bool(U_4185,U_4184)),
    inference(clausify,[status(thm)],[f_1394_3]) ).

fof(f_1395_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_011]) ).

fof(f_1395_2,plain,
    ! [U_4189,U_4188,U_4187] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(U_4189,U_4188),U_4187) = hAPP_b589554111l_bool(U_4189,hAPP_f1664156314l_bool(U_4188,U_4187)),
    inference(variable_rename,[status(thm)],[f_1395_1]) ).

fof(f_1395_3,plain,
    ! [U_4187,U_4188,U_4189] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(U_4189,U_4188),U_4187) = hAPP_b589554111l_bool(U_4189,hAPP_f1664156314l_bool(U_4188,U_4187)),
    inference(definitional_conversion,[status(esa)],[f_1395_2]) ).

cnf(f_1395_4,plain,
    hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(U_4189,U_4188),U_4187) = hAPP_b589554111l_bool(U_4189,hAPP_f1664156314l_bool(U_4188,U_4187)),
    inference(clausify,[status(thm)],[f_1395_3]) ).

fof(f_1396_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_1396_2,plain,
    ! [U_4192,U_4191,U_4190] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(U_4192),U_4191),U_4190) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(U_4192,U_4190),U_4191),
    inference(variable_rename,[status(thm)],[f_1396_1]) ).

fof(f_1396_3,plain,
    ! [U_4190,U_4191,U_4192] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(U_4192),U_4191),U_4190) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(U_4192,U_4190),U_4191),
    inference(definitional_conversion,[status(esa)],[f_1396_2]) ).

cnf(f_1396_4,plain,
    hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(U_4192),U_4191),U_4190) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(U_4192,U_4190),U_4191),
    inference(clausify,[status(thm)],[f_1396_3]) ).

fof(f_1397_1,plain,
    ! [P,Q,R] : hAPP_i888906320l_bool(cOMBB_313729068ol_int(P,Q),R) = hAPP_f1631501043l_bool(P,hAPP_int_fun_a_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__]) ).

fof(f_1397_2,plain,
    ! [U_4195,U_4194,U_4193] : hAPP_i888906320l_bool(cOMBB_313729068ol_int(U_4195,U_4194),U_4193) = hAPP_f1631501043l_bool(U_4195,hAPP_int_fun_a_bool(U_4194,U_4193)),
    inference(variable_rename,[status(thm)],[f_1397_1]) ).

fof(f_1397_3,plain,
    ! [U_4193,U_4194,U_4195] : hAPP_i888906320l_bool(cOMBB_313729068ol_int(U_4195,U_4194),U_4193) = hAPP_f1631501043l_bool(U_4195,hAPP_int_fun_a_bool(U_4194,U_4193)),
    inference(definitional_conversion,[status(esa)],[f_1397_2]) ).

cnf(f_1397_4,plain,
    hAPP_i888906320l_bool(cOMBB_313729068ol_int(U_4195,U_4194),U_4193) = hAPP_f1631501043l_bool(U_4195,hAPP_int_fun_a_bool(U_4194,U_4193)),
    inference(clausify,[status(thm)],[f_1397_3]) ).

fof(f_1398_1,plain,
    ! [P,Q,R] : hAPP_n1414589940l_bool(cOMBB_1823939024ol_nat(P,Q),R) = hAPP_f1631501043l_bool(P,hAPP_nat_fun_a_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___012]) ).

fof(f_1398_2,plain,
    ! [U_4198,U_4197,U_4196] : hAPP_n1414589940l_bool(cOMBB_1823939024ol_nat(U_4198,U_4197),U_4196) = hAPP_f1631501043l_bool(U_4198,hAPP_nat_fun_a_bool(U_4197,U_4196)),
    inference(variable_rename,[status(thm)],[f_1398_1]) ).

fof(f_1398_3,plain,
    ! [U_4196,U_4197,U_4198] : hAPP_n1414589940l_bool(cOMBB_1823939024ol_nat(U_4198,U_4197),U_4196) = hAPP_f1631501043l_bool(U_4198,hAPP_nat_fun_a_bool(U_4197,U_4196)),
    inference(definitional_conversion,[status(esa)],[f_1398_2]) ).

cnf(f_1398_4,plain,
    hAPP_n1414589940l_bool(cOMBB_1823939024ol_nat(U_4198,U_4197),U_4196) = hAPP_f1631501043l_bool(U_4198,hAPP_nat_fun_a_bool(U_4197,U_4196)),
    inference(clausify,[status(thm)],[f_1398_3]) ).

fof(f_1399_1,plain,
    ! [P,Q,R] : hAPP_i2112223885l_bool(cOMBB_1761098400ol_int(P,Q),R) = hAPP_f284875647l_bool(P,hAPP_i1948725293t_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc_]) ).

fof(f_1399_2,plain,
    ! [U_4201,U_4200,U_4199] : hAPP_i2112223885l_bool(cOMBB_1761098400ol_int(U_4201,U_4200),U_4199) = hAPP_f284875647l_bool(U_4201,hAPP_i1948725293t_bool(U_4200,U_4199)),
    inference(variable_rename,[status(thm)],[f_1399_1]) ).

fof(f_1399_3,plain,
    ! [U_4199,U_4200,U_4201] : hAPP_i2112223885l_bool(cOMBB_1761098400ol_int(U_4201,U_4200),U_4199) = hAPP_f284875647l_bool(U_4201,hAPP_i1948725293t_bool(U_4200,U_4199)),
    inference(definitional_conversion,[status(esa)],[f_1399_2]) ).

cnf(f_1399_4,plain,
    hAPP_i2112223885l_bool(cOMBB_1761098400ol_int(U_4201,U_4200),U_4199) = hAPP_f284875647l_bool(U_4201,hAPP_i1948725293t_bool(U_4200,U_4199)),
    inference(clausify,[status(thm)],[f_1399_3]) ).

fof(f_1400_1,plain,
    ! [P,Q,R] : hAPP_n609083369l_bool(cOMBB_1123824708ol_nat(P,Q),R) = hAPP_f284875647l_bool(P,hAPP_n1082236369t_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc__013]) ).

fof(f_1400_2,plain,
    ! [U_4204,U_4203,U_4202] : hAPP_n609083369l_bool(cOMBB_1123824708ol_nat(U_4204,U_4203),U_4202) = hAPP_f284875647l_bool(U_4204,hAPP_n1082236369t_bool(U_4203,U_4202)),
    inference(variable_rename,[status(thm)],[f_1400_1]) ).

fof(f_1400_3,plain,
    ! [U_4202,U_4203,U_4204] : hAPP_n609083369l_bool(cOMBB_1123824708ol_nat(U_4204,U_4203),U_4202) = hAPP_f284875647l_bool(U_4204,hAPP_n1082236369t_bool(U_4203,U_4202)),
    inference(definitional_conversion,[status(esa)],[f_1400_2]) ).

cnf(f_1400_4,plain,
    hAPP_n609083369l_bool(cOMBB_1123824708ol_nat(U_4204,U_4203),U_4202) = hAPP_f284875647l_bool(U_4204,hAPP_n1082236369t_bool(U_4203,U_4202)),
    inference(clausify,[status(thm)],[f_1400_3]) ).

fof(f_1401_1,plain,
    ! [P,Q,R] : hAPP_i1718399025l_bool(cOMBB_516767136ol_int(P,Q),R) = hAPP_f103356543l_bool(P,hAPP_i418383825t_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_]) ).

fof(f_1401_2,plain,
    ! [U_4207,U_4206,U_4205] : hAPP_i1718399025l_bool(cOMBB_516767136ol_int(U_4207,U_4206),U_4205) = hAPP_f103356543l_bool(U_4207,hAPP_i418383825t_bool(U_4206,U_4205)),
    inference(variable_rename,[status(thm)],[f_1401_1]) ).

fof(f_1401_3,plain,
    ! [U_4205,U_4206,U_4207] : hAPP_i1718399025l_bool(cOMBB_516767136ol_int(U_4207,U_4206),U_4205) = hAPP_f103356543l_bool(U_4207,hAPP_i418383825t_bool(U_4206,U_4205)),
    inference(definitional_conversion,[status(esa)],[f_1401_2]) ).

cnf(f_1401_4,plain,
    hAPP_i1718399025l_bool(cOMBB_516767136ol_int(U_4207,U_4206),U_4205) = hAPP_f103356543l_bool(U_4207,hAPP_i418383825t_bool(U_4206,U_4205)),
    inference(clausify,[status(thm)],[f_1401_3]) ).

fof(f_1402_1,plain,
    ! [P,Q,R] : hAPP_n215258509l_bool(cOMBB_2026977092ol_nat(P,Q),R) = hAPP_f103356543l_bool(P,hAPP_n1699378549t_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__014]) ).

fof(f_1402_2,plain,
    ! [U_4210,U_4209,U_4208] : hAPP_n215258509l_bool(cOMBB_2026977092ol_nat(U_4210,U_4209),U_4208) = hAPP_f103356543l_bool(U_4210,hAPP_n1699378549t_bool(U_4209,U_4208)),
    inference(variable_rename,[status(thm)],[f_1402_1]) ).

fof(f_1402_3,plain,
    ! [U_4208,U_4209,U_4210] : hAPP_n215258509l_bool(cOMBB_2026977092ol_nat(U_4210,U_4209),U_4208) = hAPP_f103356543l_bool(U_4210,hAPP_n1699378549t_bool(U_4209,U_4208)),
    inference(definitional_conversion,[status(esa)],[f_1402_2]) ).

cnf(f_1402_4,plain,
    hAPP_n215258509l_bool(cOMBB_2026977092ol_nat(U_4210,U_4209),U_4208) = hAPP_f103356543l_bool(U_4210,hAPP_n1699378549t_bool(U_4209,U_4208)),
    inference(clausify,[status(thm)],[f_1402_3]) ).

fof(f_1403_1,plain,
    ! [P,Q,R] : hAPP_i1587699435l_bool(cOMBB_607112096ol_int(P,Q),R) = hAPP_f434788991l_bool(P,hAPP_i7355787e_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It]) ).

fof(f_1403_2,plain,
    ! [U_4213,U_4212,U_4211] : hAPP_i1587699435l_bool(cOMBB_607112096ol_int(U_4213,U_4212),U_4211) = hAPP_f434788991l_bool(U_4213,hAPP_i7355787e_bool(U_4212,U_4211)),
    inference(variable_rename,[status(thm)],[f_1403_1]) ).

fof(f_1403_3,plain,
    ! [U_4211,U_4212,U_4213] : hAPP_i1587699435l_bool(cOMBB_607112096ol_int(U_4213,U_4212),U_4211) = hAPP_f434788991l_bool(U_4213,hAPP_i7355787e_bool(U_4212,U_4211)),
    inference(definitional_conversion,[status(esa)],[f_1403_2]) ).

cnf(f_1403_4,plain,
    hAPP_i1587699435l_bool(cOMBB_607112096ol_int(U_4213,U_4212),U_4211) = hAPP_f434788991l_bool(U_4213,hAPP_i7355787e_bool(U_4212,U_4211)),
    inference(clausify,[status(thm)],[f_1403_3]) ).

fof(f_1404_1,plain,
    ! [P,Q,R] : hAPP_n850744903l_bool(cOMBB_2117322052ol_nat(P,Q),R) = hAPP_f434788991l_bool(P,hAPP_n1025906991e_bool(Q,R)),
    inference(fof_nnf,[status(thm)],[help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_015]) ).

fof(f_1404_2,plain,
    ! [U_4216,U_4215,U_4214] : hAPP_n850744903l_bool(cOMBB_2117322052ol_nat(U_4216,U_4215),U_4214) = hAPP_f434788991l_bool(U_4216,hAPP_n1025906991e_bool(U_4215,U_4214)),
    inference(variable_rename,[status(thm)],[f_1404_1]) ).

fof(f_1404_3,plain,
    ! [U_4214,U_4215,U_4216] : hAPP_n850744903l_bool(cOMBB_2117322052ol_nat(U_4216,U_4215),U_4214) = hAPP_f434788991l_bool(U_4216,hAPP_n1025906991e_bool(U_4215,U_4214)),
    inference(definitional_conversion,[status(esa)],[f_1404_2]) ).

cnf(f_1404_4,plain,
    hAPP_n850744903l_bool(cOMBB_2117322052ol_nat(U_4216,U_4215),U_4214) = hAPP_f434788991l_bool(U_4216,hAPP_n1025906991e_bool(U_4215,U_4214)),
    inference(clausify,[status(thm)],[f_1404_3]) ).

fof(f_1405_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_1405_2,plain,
    ! [U_4219,U_4218,U_4217] : hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(U_4219),U_4218),U_4217) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(U_4219,U_4217),U_4218),
    inference(variable_rename,[status(thm)],[f_1405_1]) ).

fof(f_1405_3,plain,
    ! [U_4217,U_4218,U_4219] : hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(U_4219),U_4218),U_4217) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(U_4219,U_4217),U_4218),
    inference(definitional_conversion,[status(esa)],[f_1405_2]) ).

cnf(f_1405_4,plain,
    hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(U_4219),U_4218),U_4217) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(U_4219,U_4217),U_4218),
    inference(clausify,[status(thm)],[f_1405_3]) ).

fof(f_1406_1,plain,
    ! [P,Q,R] : hAPP_f215623910l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(P),Q),R) = hAPP_f215623910l_bool(hAPP_f317860125l_bool(P,R),Q),
    inference(fof_nnf,[status(thm)],[help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__H]) ).

fof(f_1406_2,plain,
    ! [U_4222,U_4221,U_4220] : hAPP_f215623910l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(U_4222),U_4221),U_4220) = hAPP_f215623910l_bool(hAPP_f317860125l_bool(U_4222,U_4220),U_4221),
    inference(variable_rename,[status(thm)],[f_1406_1]) ).

fof(f_1406_3,plain,
    ! [U_4220,U_4221,U_4222] : hAPP_f215623910l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(U_4222),U_4221),U_4220) = hAPP_f215623910l_bool(hAPP_f317860125l_bool(U_4222,U_4220),U_4221),
    inference(definitional_conversion,[status(esa)],[f_1406_2]) ).

cnf(f_1406_4,plain,
    hAPP_f215623910l_bool(hAPP_f317860125l_bool(cOMBC_348868698l_bool(U_4222),U_4221),U_4220) = hAPP_f215623910l_bool(hAPP_f317860125l_bool(U_4222,U_4220),U_4221),
    inference(clausify,[status(thm)],[f_1406_3]) ).

fof(f_1407_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_1407_2,plain,
    ! [U_4225,U_4224,U_4223] : hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(U_4225),U_4224),U_4223) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(U_4225,U_4223),U_4224),
    inference(variable_rename,[status(thm)],[f_1407_1]) ).

fof(f_1407_3,plain,
    ! [U_4223,U_4224,U_4225] : hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(U_4225),U_4224),U_4223) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(U_4225,U_4223),U_4224),
    inference(definitional_conversion,[status(esa)],[f_1407_2]) ).

cnf(f_1407_4,plain,
    hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(U_4225),U_4224),U_4223) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(U_4225,U_4223),U_4224),
    inference(clausify,[status(thm)],[f_1407_3]) ).

fof(f_1408_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_1408_2,plain,
    ! [U_4228,U_4227,U_4226] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(U_4228),U_4227),U_4226) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(U_4228,U_4226),U_4227),
    inference(variable_rename,[status(thm)],[f_1408_1]) ).

fof(f_1408_3,plain,
    ! [U_4226,U_4227,U_4228] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(U_4228),U_4227),U_4226) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(U_4228,U_4226),U_4227),
    inference(definitional_conversion,[status(esa)],[f_1408_2]) ).

cnf(f_1408_4,plain,
    hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(U_4228),U_4227),U_4226) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(U_4228,U_4226),U_4227),
    inference(clausify,[status(thm)],[f_1408_3]) ).

fof(f_1409_1,plain,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
    inference(fof_nnf,[status(thm)],[conj_0]) ).

fof(f_1409_2,plain,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
    inference(definitional_conversion,[status(esa)],[f_1409_1]) ).

cnf(f_1409_3,plain,
    hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)),
    inference(clausify,[status(thm)],[f_1409_2]) ).

fof(f_1410_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]) ).

fof(f_1410_2,plain,
    hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))),
    inference(definitional_conversion,[status(esa)],[f_1410_1]) ).

cnf(f_1410_3,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_1410_2]) ).

fof(f_1411_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]) ).

fof(f_1411_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(definitional_conversion,[status(esa)],[f_1411_1]) ).

cnf(f_1411_3,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_1411_2]) ).

fof(f_1412_1,plain,
    hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(hAPP_nat_fun_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]) ).

fof(f_1412_2,plain,
    hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(hAPP_nat_fun_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(definitional_conversion,[status(esa)],[f_1412_1]) ).

cnf(f_1412_3,plain,
    hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(hAPP_nat_fun_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_1412_2]) ).

fof(f_1413_1,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
    inference(fof_nnf,[status(thm)],[conj_4]) ).

fof(f_1413_2,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
    inference(definitional_conversion,[status(esa)],[f_1413_1]) ).

cnf(f_1413_3,plain,
    hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)),
    inference(clausify,[status(thm)],[f_1413_2]) ).

fof(f_1414_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]) ).

fof(f_1414_2,plain,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)),
    inference(definitional_conversion,[status(esa)],[f_1414_1]) ).

cnf(f_1414_3,plain,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)),
    inference(clausify,[status(thm)],[f_1414_2]) ).

fof(f_1415_1,negated_conjecture,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
    inference(negate,[status(cth)],[conj_6]) ).

fof(f_1415_2,negated_conjecture,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
    inference(definitional_conversion,[status(esa)],[f_1415_1]) ).

cnf(f_1415_3,negated_conjecture,
    ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_f2050579477a_bool(hAPP_a1206381875a_bool(insert_a,hAPP_pname_a(mgt_call,pn)),g)),image_pname_a(mgt_call,u))),
    inference(clausify,[status(thm)],[f_1415_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_1273333599bool_a(Eq_x_0,Eq_x_1) = cOMBB_1273333599bool_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_7,axiom,
    ( cOMBK_bool_a(Eq_x_0) = cOMBK_bool_a(Eq_y_0)
    | 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,
    ( finite_folding_one_a(Eq_x_0,Eq_x_1) = finite_folding_one_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_13,axiom,
    ( finite1282449217_pname(Eq_x_0,Eq_x_1) = finite1282449217_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_14,axiom,
    ( finite1626084323ne_int(Eq_x_0,Eq_x_1) = finite1626084323ne_int(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,
    ( finite988810631ne_nat(Eq_x_0,Eq_x_1) = finite988810631ne_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_16,axiom,
    ( finite1819937229idem_a(Eq_x_0,Eq_x_1) = finite1819937229idem_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_17,axiom,
    ( finite89670078_pname(Eq_x_0,Eq_x_1) = finite89670078_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_18,axiom,
    ( finite1432773856em_int(Eq_x_0,Eq_x_1) = finite1432773856em_int(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_19,axiom,
    ( finite795500164em_nat(Eq_x_0,Eq_x_1) = finite795500164em_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_20,axiom,
    ( undefined_a(Eq_x_0) = undefined_a(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_21,axiom,
    ( undefined_pname(Eq_x_0) = undefined_pname(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_22,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_23,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_24,axiom,
    ( undefi17486888e_bool(Eq_x_0) = undefi17486888e_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_25,axiom,
    ( undefi1699038445l_bool(Eq_x_0) = undefi1699038445l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_26,axiom,
    ( undefi64961550l_bool(Eq_x_0) = undefi64961550l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_27,axiom,
    ( collect_a(Eq_x_0) = collect_a(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_28,axiom,
    ( collect_pname(Eq_x_0) = collect_pname(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_29,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_30,axiom,
    ( collec1974731493e_bool(Eq_x_0) = collec1974731493e_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_31,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_32,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_33,axiom,
    ( image_a_fun_a_bool(Eq_x_0,Eq_x_1) = image_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_34,axiom,
    ( image_819518260e_bool(Eq_x_0,Eq_x_1) = image_819518260e_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_35,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_36,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_37,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_38,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_39,axiom,
    ( image_int_a(Eq_x_0,Eq_x_1) = image_int_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_int_pname(Eq_x_0,Eq_x_1) = image_int_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_int_fun_a_bool(Eq_x_0,Eq_x_1) = image_int_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_42,axiom,
    ( image_637364955e_bool(Eq_x_0,Eq_x_1) = image_637364955e_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_43,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_44,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_45,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_46,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_47,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_48,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_49,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_50,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_51,axiom,
    ( image_fun_int_bool_a(Eq_x_0,Eq_x_1) = image_fun_int_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_52,axiom,
    ( image_62782965_pname(Eq_x_0,Eq_x_1) = image_62782965_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_53,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_54,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_55,axiom,
    ( hAPP_a_a(Eq_x_0,Eq_x_1) = hAPP_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_56,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_57,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_58,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_59,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_60,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_61,axiom,
    ( hAPP_pname_pname(Eq_x_0,Eq_x_1) = hAPP_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_62,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_63,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_64,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_65,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_66,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_67,axiom,
    ( hAPP_int_a(Eq_x_0,Eq_x_1) = hAPP_int_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_68,axiom,
    ( hAPP_int_bool(Eq_x_0,Eq_x_1) = hAPP_int_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_int_fun_a_bool(Eq_x_0,Eq_x_1) = hAPP_int_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_70,axiom,
    ( hAPP_i7355787e_bool(Eq_x_0,Eq_x_1) = hAPP_i7355787e_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_i888906320l_bool(Eq_x_0,Eq_x_1) = hAPP_i888906320l_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_i1587699435l_bool(Eq_x_0,Eq_x_1) = hAPP_i1587699435l_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_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_74,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_75,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_76,axiom,
    ( hAPP_n1414589940l_bool(Eq_x_0,Eq_x_1) = hAPP_n1414589940l_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_n850744903l_bool(Eq_x_0,Eq_x_1) = hAPP_n850744903l_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_fun_a_bool_a(Eq_x_0,Eq_x_1) = hAPP_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_79,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_80,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_81,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_82,axiom,
    ( hAPP_f1297739591_pname(Eq_x_0,Eq_x_1) = hAPP_f1297739591_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_83,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_84,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_85,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_86,axiom,
    ( hAPP_f448129468l_bool(Eq_x_0,Eq_x_1) = hAPP_f448129468l_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_87,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_88,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_89,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_90,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_91,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_92,axiom,
    ( hAPP_f215623910l_bool(Eq_x_0,Eq_x_1) = hAPP_f215623910l_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_93,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_94,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_95,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_96,axiom,
    ( hAPP_f1593524852l_bool(Eq_x_0,Eq_x_1) = hAPP_f1593524852l_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,
    ( 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_98,axiom,
    ( p(Eq_x_0) = p(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_99,axiom,
    ( mgt(Eq_x_0) = mgt(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_100,axiom,
    ( wt(Eq_x_0) = wt(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_101,axiom,
    ( cOMBC_348868698l_bool(Eq_x_0) = cOMBC_348868698l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_102,axiom,
    ( hAPP_f317860125l_bool(Eq_x_0,Eq_x_1) = hAPP_f317860125l_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,
    ( collec1409689523l_bool(Eq_x_0) = collec1409689523l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_104,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_105,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_106,axiom,
    ( collec1015864663l_bool(Eq_x_0) = collec1015864663l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_107,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_108,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_109,axiom,
    ( collec1613912337l_bool(Eq_x_0) = collec1613912337l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_110,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_111,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_112,axiom,
    ( collec707592106l_bool(Eq_x_0) = collec707592106l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_113,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_114,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_115,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_116,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_117,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_118,axiom,
    ( cOMBC_605892544l_bool(Eq_x_0) = cOMBC_605892544l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_119,axiom,
    ( hAPP_f284875647l_bool(Eq_x_0,Eq_x_1) = hAPP_f284875647l_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_120,axiom,
    ( collect_fun_int_bool(Eq_x_0) = collect_fun_int_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_121,axiom,
    ( image_1512837979t_bool(Eq_x_0,Eq_x_1) = image_1512837979t_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,
    ( 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_123,axiom,
    ( image_1556378401t_bool(Eq_x_0,Eq_x_1) = image_1556378401t_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,
    ( 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_125,axiom,
    ( image_275383677t_bool(Eq_x_0,Eq_x_1) = image_275383677t_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_126,axiom,
    ( image_892525857t_bool(Eq_x_0,Eq_x_1) = image_892525857t_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,
    ( 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_128,axiom,
    ( image_1431733819ol_nat(Eq_x_0,Eq_x_1) = image_1431733819ol_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,
    ( 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_130,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_131,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_132,axiom,
    ( image_a_int(Eq_x_0,Eq_x_1) = image_a_int(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,
    ( image_2069007511ol_int(Eq_x_0,Eq_x_1) = image_2069007511ol_int(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,
    ( image_1133522419ol_int(Eq_x_0,Eq_x_1) = image_1133522419ol_int(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,
    ( image_41399353ol_int(Eq_x_0,Eq_x_1) = image_41399353ol_int(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,
    ( image_fun_a_bool_int(Eq_x_0,Eq_x_1) = image_fun_a_bool_int(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,
    ( image_nat_int(Eq_x_0,Eq_x_1) = image_nat_int(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_f587666462l_bool(Eq_x_0,Eq_x_1) = hAPP_f587666462l_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_f1948010709l_bool(Eq_x_0,Eq_x_1) = hAPP_f1948010709l_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,
    ( hAPP_f633452666l_bool(Eq_x_0,Eq_x_1) = hAPP_f633452666l_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,
    ( 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_142,axiom,
    ( hAPP_f1320879424l_bool(Eq_x_0,Eq_x_1) = hAPP_f1320879424l_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,
    ( hAPP_f1531278575l_bool(Eq_x_0,Eq_x_1) = hAPP_f1531278575l_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,
    ( hAPP_p905327722e_bool(Eq_x_0,Eq_x_1) = hAPP_p905327722e_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_145,axiom,
    ( hAPP_n1512601776t_bool(Eq_x_0,Eq_x_1) = hAPP_n1512601776t_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_146,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_147,axiom,
    ( hAPP_i1529485324t_bool(Eq_x_0,Eq_x_1) = hAPP_i1529485324t_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_148,axiom,
    ( hAPP_f1805168059t_bool(Eq_x_0,Eq_x_1) = hAPP_f1805168059t_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,
    ( hAPP_a1206381875a_bool(Eq_x_0,Eq_x_1) = hAPP_a1206381875a_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_150,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_151,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_152,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_153,axiom,
    ( hAPP_f521865025ol_nat(Eq_x_0,Eq_x_1) = hAPP_f521865025ol_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_154,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_155,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_156,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_157,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_158,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_159,axiom,
    ( image_pname_int(Eq_x_0,Eq_x_1) = image_pname_int(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_160,axiom,
    ( hAPP_f957591787ol_nat(Eq_x_0,Eq_x_1) = hAPP_f957591787ol_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_161,axiom,
    ( hAPP_f628503027l_bool(Eq_x_0,Eq_x_1) = hAPP_f628503027l_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_162,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_163,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_164,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_165,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_166,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_167,axiom,
    ( hAPP_i2112223885l_bool(Eq_x_0,Eq_x_1) = hAPP_i2112223885l_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,
    ( 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_169,axiom,
    ( cOMBB_1974511970t_bool(Eq_x_0,Eq_x_1) = cOMBB_1974511970t_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,
    ( cOMBS_1912792529l_bool(Eq_x_0,Eq_x_1) = cOMBS_1912792529l_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,
    ( 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_172,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_173,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_174,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_175,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_176,axiom,
    ( collect_nat(Eq_x_0) = collect_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_177,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_178,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_179,axiom,
    ( collect_int(Eq_x_0) = collect_int(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_180,axiom,
    ( cOMBB_1652995168ol_int(Eq_x_0,Eq_x_1) = cOMBB_1652995168ol_int(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_181,axiom,
    ( cOMBS_int_bool_bool(Eq_x_0,Eq_x_1) = cOMBS_int_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_182,axiom,
    ( hAPP_nat_fun_nat_nat(Eq_x_0,Eq_x_1) = hAPP_nat_fun_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_183,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_184,axiom,
    ( image_a_fun_int_bool(Eq_x_0,Eq_x_1) = image_a_fun_int_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_185,axiom,
    ( image_a_fun_nat_bool(Eq_x_0,Eq_x_1) = image_a_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_186,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_187,axiom,
    ( hAPP_nat_int(Eq_x_0,Eq_x_1) = hAPP_nat_int(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_188,axiom,
    ( hAPP_i1948725293t_bool(Eq_x_0,Eq_x_1) = hAPP_i1948725293t_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_189,axiom,
    ( hAPP_n1082236369t_bool(Eq_x_0,Eq_x_1) = hAPP_n1082236369t_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_190,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_191,axiom,
    ( cOMBB_1123824708ol_nat(Eq_x_0,Eq_x_1) = cOMBB_1123824708ol_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_192,axiom,
    ( cOMBC_620423604l_bool(Eq_x_0) = cOMBC_620423604l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_193,axiom,
    ( hAPP_f274826591t_bool(Eq_x_0,Eq_x_1) = hAPP_f274826591t_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_194,axiom,
    ( cOMBB_2026977092ol_nat(Eq_x_0,Eq_x_1) = cOMBB_2026977092ol_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_195,axiom,
    ( cOMBB_2117322052ol_nat(Eq_x_0,Eq_x_1) = cOMBB_2117322052ol_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_196,axiom,
    ( cOMBC_386238098l_bool(Eq_x_0) = cOMBC_386238098l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_197,axiom,
    ( hAPP_f1066163005t_bool(Eq_x_0,Eq_x_1) = hAPP_f1066163005t_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_198,axiom,
    ( cOMBB_1823939024ol_nat(Eq_x_0,Eq_x_1) = cOMBB_1823939024ol_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_199,axiom,
    ( cOMBC_1928494297l_bool(Eq_x_0) = cOMBC_1928494297l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_200,axiom,
    ( hAPP_f282463732t_bool(Eq_x_0,Eq_x_1) = hAPP_f282463732t_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_201,axiom,
    ( cOMBC_94739984l_bool(Eq_x_0) = cOMBC_94739984l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_202,axiom,
    ( cOMBB_375279840ol_int(Eq_x_0,Eq_x_1) = cOMBB_375279840ol_int(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_203,axiom,
    ( cOMBC_int_a_bool(Eq_x_0) = cOMBC_int_a_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_204,axiom,
    ( hAPP_a_fun_int_bool(Eq_x_0,Eq_x_1) = hAPP_a_fun_int_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_205,axiom,
    ( cOMBB_1761098400ol_int(Eq_x_0,Eq_x_1) = cOMBB_1761098400ol_int(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_206,axiom,
    ( cOMBB_516767136ol_int(Eq_x_0,Eq_x_1) = cOMBB_516767136ol_int(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_207,axiom,
    ( cOMBC_1848398772l_bool(Eq_x_0) = cOMBC_1848398772l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_208,axiom,
    ( hAPP_i418383825t_bool(Eq_x_0,Eq_x_1) = hAPP_i418383825t_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_209,axiom,
    ( hAPP_f183368031t_bool(Eq_x_0,Eq_x_1) = hAPP_f183368031t_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_210,axiom,
    ( cOMBB_607112096ol_int(Eq_x_0,Eq_x_1) = cOMBB_607112096ol_int(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_211,axiom,
    ( cOMBC_316919022l_bool(Eq_x_0) = cOMBC_316919022l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_212,axiom,
    ( hAPP_f449020825t_bool(Eq_x_0,Eq_x_1) = hAPP_f449020825t_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_213,axiom,
    ( cOMBB_313729068ol_int(Eq_x_0,Eq_x_1) = cOMBB_313729068ol_int(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_214,axiom,
    ( cOMBC_1753430397l_bool(Eq_x_0) = cOMBC_1753430397l_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_215,axiom,
    ( hAPP_f1812805200t_bool(Eq_x_0,Eq_x_1) = hAPP_f1812805200t_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_216,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_217,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_218,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_219,axiom,
    ( cOMBB_1628441366ol_nat(Eq_x_0,Eq_x_1) = cOMBB_1628441366ol_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_220,axiom,
    ( cOMBC_nat_int_bool(Eq_x_0) = cOMBC_nat_int_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_221,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_222,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_223,axiom,
    ( cOMBC_int_int_bool(Eq_x_0) = cOMBC_int_int_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_224,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_225,axiom,
    ( cOMBB_bool_bool_int(Eq_x_0,Eq_x_1) = cOMBB_bool_bool_int(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_226,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_227,axiom,
    ( hAPP_int_fun_int_int(Eq_x_0,Eq_x_1) = hAPP_int_fun_int_int(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_228,axiom,
    ( hAPP_int_int(Eq_x_0,Eq_x_1) = hAPP_int_int(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_229,axiom,
    ( nat_case_bool(Eq_x_0,Eq_x_1) = nat_case_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_230,axiom,
    ( hAPP_f1223193598t_bool(Eq_x_0,Eq_x_1) = hAPP_f1223193598t_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_231,axiom,
    ( hAPP_f1730770594t_bool(Eq_x_0,Eq_x_1) = hAPP_f1730770594t_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_232,axiom,
    ( hAPP_f1388330588e_bool(Eq_x_0,Eq_x_1) = hAPP_f1388330588e_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_233,axiom,
    ( hAPP_f1791771145a_bool(Eq_x_0,Eq_x_1) = hAPP_f1791771145a_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_234,axiom,
    ( cOMBK_bool_int(Eq_x_0) = cOMBK_bool_int(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_235,axiom,
    ( cOMBK_bool_nat(Eq_x_0) = cOMBK_bool_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_236,axiom,
    ( nat_case_nat(Eq_x_0,Eq_x_1) = nat_case_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_237,axiom,
    ( cOMBK_int_nat(Eq_x_0) = cOMBK_int_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_238,axiom,
    ( cOMBK_a_pname(Eq_x_0) = cOMBK_a_pname(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_239,axiom,
    ( body(Eq_x_0) = body(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_240,axiom,
    ( the_com(Eq_x_0) = the_com(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_241,axiom,
    ( cOMBB_800536526ol_nat(Eq_x_0,Eq_x_1) = cOMBB_800536526ol_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_242,axiom,
    ( hAPP_f1594865479ol_int(Eq_x_0,Eq_x_1) = hAPP_f1594865479ol_int(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_243,axiom,
    ( hAPP_a_fun_a_a(Eq_x_0,Eq_x_1) = hAPP_a_fun_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_244,axiom,
    ( hAPP_p1170154830_pname(Eq_x_0,Eq_x_1) = hAPP_p1170154830_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_245,axiom,
    ( cOMBC_394484100a_bool(Eq_x_0) = cOMBC_394484100a_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_246,axiom,
    ( hAPP_f1038053735a_bool(Eq_x_0,Eq_x_1) = hAPP_f1038053735a_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_247,axiom,
    ( cOMBC_178881787t_bool(Eq_x_0) = cOMBC_178881787t_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_248,axiom,
    ( hAPP_f1570313510t_bool(Eq_x_0,Eq_x_1) = hAPP_f1570313510t_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_249,axiom,
    ( cOMBB_955900739ol_nat(Eq_x_0,Eq_x_1) = cOMBB_955900739ol_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_250,axiom,
    ( cOMBC_1683390479t_bool(Eq_x_0) = cOMBC_1683390479t_bool(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_251,axiom,
    ( hAPP_f1048215610t_bool(Eq_x_0,Eq_x_1) = hAPP_f1048215610t_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_252,axiom,
    ( cOMBB_1418110531ol_int(Eq_x_0,Eq_x_1) = cOMBB_1418110531ol_int(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_253,axiom,
    ( cOMBB_1146692694ol_nat(Eq_x_0,Eq_x_1) = cOMBB_1146692694ol_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_254,axiom,
    ( number_number_of_nat(Eq_x_0) = number_number_of_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_255,axiom,
    ( number_number_of_int(Eq_x_0) = number_number_of_int(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_256,axiom,
    ( cOMBB_int_bool_nat(Eq_x_0,Eq_x_1) = cOMBB_int_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_257,axiom,
    ( if_nat(Eq_x_0) = if_nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_258,axiom,
    ( abs_abs_int(Eq_x_0) = abs_abs_int(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_259,axiom,
    ( succ(Eq_x_0) = succ(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_260,axiom,
    ( bit1(Eq_x_0) = bit1(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_261,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_262,axiom,
    ( hAPP_i68813070l_bool(Eq_x_0,Eq_x_1) = hAPP_i68813070l_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_263,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_264,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_265,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_266,axiom,
    ( hAPP_i1718399025l_bool(Eq_x_0,Eq_x_1) = hAPP_i1718399025l_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_267,axiom,
    ( hAPP_n609083369l_bool(Eq_x_0,Eq_x_1) = hAPP_n609083369l_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_268,axiom,
    ( hAPP_f1721100032l_bool(Eq_x_0,Eq_x_1) = hAPP_f1721100032l_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_269,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_270,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_271,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_272,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_273,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_274,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_275,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_276,axiom,
    ( sK6(Eq_x_0,Eq_x_1,Eq_x_2) = sK6(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_277,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_278,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_279,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_280,axiom,
    ( sK10(Eq_x_0,Eq_x_1,Eq_x_2) = sK10(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_281,axiom,
    ( sK11(Eq_x_0,Eq_x_1,Eq_x_2) = sK11(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_282,axiom,
    ( sK12(Eq_x_0,Eq_x_1,Eq_x_2) = sK12(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_283,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_284,axiom,
    ( sK14(Eq_x_0,Eq_x_1,Eq_x_2) = sK14(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_285,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_286,axiom,
    ( sK16(Eq_x_0,Eq_x_1,Eq_x_2) = sK16(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_287,axiom,
    ( sK17(Eq_x_0,Eq_x_1,Eq_x_2) = sK17(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_288,axiom,
    ( sK18(Eq_x_0,Eq_x_1,Eq_x_2) = sK18(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_289,axiom,
    ( sK19(Eq_x_0,Eq_x_1,Eq_x_2) = sK19(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_290,axiom,
    ( sK20(Eq_x_0,Eq_x_1,Eq_x_2) = sK20(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_291,axiom,
    ( sK21(Eq_x_0,Eq_x_1,Eq_x_2) = sK21(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_292,axiom,
    ( sK22(Eq_x_0,Eq_x_1,Eq_x_2) = sK22(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_293,axiom,
    ( sK23(Eq_x_0,Eq_x_1,Eq_x_2) = sK23(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_294,axiom,
    ( sK24(Eq_x_0,Eq_x_1,Eq_x_2) = sK24(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_295,axiom,
    ( sK25(Eq_x_0,Eq_x_1,Eq_x_2) = sK25(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_296,axiom,
    ( sK26(Eq_x_0,Eq_x_1,Eq_x_2) = sK26(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_297,axiom,
    ( sK27(Eq_x_0,Eq_x_1,Eq_x_2) = sK27(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_298,axiom,
    ( sK28(Eq_x_0,Eq_x_1,Eq_x_2) = sK28(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_299,axiom,
    ( sK29(Eq_x_0,Eq_x_1,Eq_x_2) = sK29(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_300,axiom,
    ( sK30(Eq_x_0,Eq_x_1,Eq_x_2) = sK30(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_301,axiom,
    ( sK31(Eq_x_0,Eq_x_1,Eq_x_2) = sK31(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_302,axiom,
    ( sK32(Eq_x_0,Eq_x_1,Eq_x_2) = sK32(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_303,axiom,
    ( sK33(Eq_x_0,Eq_x_1,Eq_x_2) = sK33(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_304,axiom,
    ( sK34(Eq_x_0,Eq_x_1,Eq_x_2) = sK34(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_305,axiom,
    ( sK35(Eq_x_0,Eq_x_1,Eq_x_2) = sK35(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_306,axiom,
    ( sK36(Eq_x_0,Eq_x_1,Eq_x_2) = sK36(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_307,axiom,
    ( sK37(Eq_x_0,Eq_x_1,Eq_x_2) = sK37(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_308,axiom,
    ( sK38(Eq_x_0,Eq_x_1,Eq_x_2) = sK38(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_309,axiom,
    ( sK39(Eq_x_0,Eq_x_1,Eq_x_2) = sK39(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_310,axiom,
    ( sK40(Eq_x_0,Eq_x_1,Eq_x_2) = sK40(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_311,axiom,
    ( sK41(Eq_x_0,Eq_x_1,Eq_x_2) = sK41(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_312,axiom,
    ( sK42(Eq_x_0,Eq_x_1,Eq_x_2) = sK42(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_313,axiom,
    ( sK43(Eq_x_0,Eq_x_1,Eq_x_2) = sK43(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_314,axiom,
    ( sK44(Eq_x_0,Eq_x_1,Eq_x_2) = sK44(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_315,axiom,
    ( sK45(Eq_x_0,Eq_x_1,Eq_x_2) = sK45(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_316,axiom,
    ( sK46(Eq_x_0,Eq_x_1,Eq_x_2) = sK46(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_317,axiom,
    ( sK47(Eq_x_0,Eq_x_1,Eq_x_2) = sK47(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_318,axiom,
    ( sK48(Eq_x_0,Eq_x_1,Eq_x_2) = sK48(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_319,axiom,
    ( sK49(Eq_x_0,Eq_x_1,Eq_x_2) = sK49(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_320,axiom,
    ( sK50(Eq_x_0,Eq_x_1,Eq_x_2) = sK50(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_321,axiom,
    ( sK51(Eq_x_0,Eq_x_1,Eq_x_2) = sK51(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_322,axiom,
    ( sK52(Eq_x_0,Eq_x_1,Eq_x_2) = sK52(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_323,axiom,
    ( sK53(Eq_x_0,Eq_x_1) = sK53(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_324,axiom,
    ( sK54(Eq_x_0,Eq_x_1) = sK54(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_325,axiom,
    ( sK55(Eq_x_0,Eq_x_1) = sK55(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_326,axiom,
    ( sK56(Eq_x_0,Eq_x_1) = sK56(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_327,axiom,
    ( sK57(Eq_x_0,Eq_x_1) = sK57(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_328,axiom,
    ( sK58(Eq_x_0,Eq_x_1) = sK58(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_329,axiom,
    ( sK59(Eq_x_0,Eq_x_1) = sK59(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_330,axiom,
    ( sK60(Eq_x_0,Eq_x_1) = sK60(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_331,axiom,
    ( sK61(Eq_x_0,Eq_x_1) = sK61(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_332,axiom,
    ( sK62(Eq_x_0,Eq_x_1) = sK62(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_333,axiom,
    ( sK63(Eq_x_0,Eq_x_1) = sK63(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_334,axiom,
    ( sK64(Eq_x_0,Eq_x_1,Eq_x_2) = sK64(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_335,axiom,
    ( sK65(Eq_x_0,Eq_x_1) = sK65(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_336,axiom,
    ( sK66(Eq_x_0,Eq_x_1,Eq_x_2) = sK66(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_337,axiom,
    ( sK67(Eq_x_0,Eq_x_1,Eq_x_2) = sK67(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_338,axiom,
    ( sK68(Eq_x_0,Eq_x_1) = sK68(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_339,axiom,
    ( sK69(Eq_x_0,Eq_x_1) = sK69(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_340,axiom,
    ( sK70(Eq_x_0,Eq_x_1) = sK70(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_341,axiom,
    ( sK71(Eq_x_0,Eq_x_1,Eq_x_2) = sK71(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_342,axiom,
    ( sK72(Eq_x_0,Eq_x_1,Eq_x_2) = sK72(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_343,axiom,
    ( sK73(Eq_x_0,Eq_x_1,Eq_x_2) = sK73(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_344,axiom,
    ( sK74(Eq_x_0,Eq_x_1,Eq_x_2) = sK74(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_345,axiom,
    ( sK75(Eq_x_0,Eq_x_1) = sK75(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_346,axiom,
    ( sK76(Eq_x_0,Eq_x_1) = sK76(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_347,axiom,
    ( sK77(Eq_x_0,Eq_x_1) = sK77(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_348,axiom,
    ( sK78(Eq_x_0,Eq_x_1) = sK78(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_349,axiom,
    ( sK79(Eq_x_0,Eq_x_1,Eq_x_2) = sK79(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_350,axiom,
    ( sK80(Eq_x_0,Eq_x_1,Eq_x_2) = sK80(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_351,axiom,
    ( sK81(Eq_x_0,Eq_x_1) = sK81(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_352,axiom,
    ( sK82(Eq_x_0,Eq_x_1) = sK82(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_353,axiom,
    ( sK83(Eq_x_0,Eq_x_1) = sK83(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_354,axiom,
    ( sK84(Eq_x_0) = sK84(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_355,axiom,
    ( sK85(Eq_x_0,Eq_x_1) = sK85(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_356,axiom,
    ( sK86(Eq_x_0,Eq_x_1) = sK86(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_357,axiom,
    ( sK87(Eq_x_0) = sK87(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_358,axiom,
    ( sK88(Eq_x_0) = sK88(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_359,axiom,
    ( sK89(Eq_x_0) = sK89(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_360,axiom,
    ( sK90(Eq_x_0) = sK90(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_361,axiom,
    ( sK91(Eq_x_0) = sK91(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_362,axiom,
    ( sK92(Eq_x_0) = sK92(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_363,axiom,
    ( sK93(Eq_x_0) = sK93(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_364,axiom,
    ( sK94(Eq_x_0) = sK94(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_365,axiom,
    ( sK95(Eq_x_0) = sK95(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_366,axiom,
    ( sK96(Eq_x_0) = sK96(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_367,axiom,
    ( sK97(Eq_x_0) = sK97(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_368,axiom,
    ( sK98(Eq_x_0) = sK98(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_369,axiom,
    ( sK99(Eq_x_0) = sK99(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_370,axiom,
    ( sK100(Eq_x_0) = sK100(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_371,axiom,
    ( sK101(Eq_x_0,Eq_x_1,Eq_x_2) = sK101(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_372,axiom,
    ( sK102(Eq_x_0,Eq_x_1,Eq_x_2) = sK102(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_373,axiom,
    ( sK103(Eq_x_0,Eq_x_1,Eq_x_2) = sK103(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_374,axiom,
    ( sK104(Eq_x_0,Eq_x_1,Eq_x_2) = sK104(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_375,axiom,
    ( sK105(Eq_x_0,Eq_x_1,Eq_x_2) = sK105(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_376,axiom,
    ( sK106(Eq_x_0,Eq_x_1,Eq_x_2) = sK106(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_377,axiom,
    ( sK107(Eq_x_0,Eq_x_1,Eq_x_2) = sK107(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_378,axiom,
    ( sK108(Eq_x_0,Eq_x_1,Eq_x_2) = sK108(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_379,axiom,
    ( sK109(Eq_x_0,Eq_x_1) = sK109(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_380,axiom,
    ( sK110(Eq_x_0,Eq_x_1) = sK110(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_381,axiom,
    ( sK111(Eq_x_0,Eq_x_1) = sK111(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_382,axiom,
    ( sK112(Eq_x_0,Eq_x_1) = sK112(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_383,axiom,
    ( sK113(Eq_x_0,Eq_x_1) = sK113(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_384,axiom,
    ( sK114(Eq_x_0,Eq_x_1) = sK114(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_385,axiom,
    ( sK115(Eq_x_0,Eq_x_1) = sK115(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_386,axiom,
    ( sK116(Eq_x_0,Eq_x_1) = sK116(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_387,axiom,
    ( sK117(Eq_x_0,Eq_x_1) = sK117(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_388,axiom,
    ( sK118(Eq_x_0,Eq_x_1) = sK118(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_389,axiom,
    ( sK119(Eq_x_0,Eq_x_1) = sK119(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_390,axiom,
    ( sK120(Eq_x_0,Eq_x_1) = sK120(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_391,axiom,
    ( sK121(Eq_x_0,Eq_x_1) = sK121(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_392,axiom,
    ( sK122(Eq_x_0,Eq_x_1) = sK122(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_393,axiom,
    ( sK123(Eq_x_0,Eq_x_1) = sK123(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_394,axiom,
    ( sK124(Eq_x_0,Eq_x_1) = sK124(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_395,axiom,
    ( sK125(Eq_x_0) = sK125(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_396,axiom,
    ( sK126(Eq_x_0) = sK126(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_397,axiom,
    ( sK127(Eq_x_0) = sK127(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_398,axiom,
    ( sK128(Eq_x_0) = sK128(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_399,axiom,
    ( sK129(Eq_x_0) = sK129(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_400,axiom,
    ( sK130(Eq_x_0) = sK130(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_401,axiom,
    ( sK131(Eq_x_0) = sK131(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_402,axiom,
    ( sK132(Eq_x_0) = sK132(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_403,axiom,
    ( sK133(Eq_x_0,Eq_x_1) = sK133(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_404,axiom,
    ( sK134(Eq_x_0) = sK134(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_405,axiom,
    ( sK135(Eq_x_0) = sK135(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_406,axiom,
    ( sK136(Eq_x_0) = sK136(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_407,axiom,
    ( sK137(Eq_x_0) = sK137(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_408,axiom,
    ( sK138(Eq_x_0) = sK138(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_409,axiom,
    ( sK139(Eq_x_0) = sK139(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_410,axiom,
    ( sK140(Eq_x_0) = sK140(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_411,axiom,
    ( sK141(Eq_x_0) = sK141(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_412,axiom,
    ( sK142(Eq_x_0,Eq_x_1,Eq_x_2) = sK142(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_413,axiom,
    ( sK143(Eq_x_0,Eq_x_1,Eq_x_2) = sK143(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_414,axiom,
    ( sK144(Eq_x_0,Eq_x_1,Eq_x_2) = sK144(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_415,axiom,
    ( sK145(Eq_x_0,Eq_x_1,Eq_x_2) = sK145(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_416,axiom,
    ( sK146(Eq_x_0,Eq_x_1,Eq_x_2) = sK146(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_417,axiom,
    ( sK147(Eq_x_0,Eq_x_1,Eq_x_2) = sK147(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_418,axiom,
    ( sK148(Eq_x_0,Eq_x_1,Eq_x_2) = sK148(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_419,axiom,
    ( sK149(Eq_x_0,Eq_x_1,Eq_x_2) = sK149(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_420,axiom,
    ( sK150(Eq_x_0,Eq_x_1) = sK150(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_421,axiom,
    ( sK151(Eq_x_0,Eq_x_1) = sK151(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_422,axiom,
    ( sK152(Eq_x_0,Eq_x_1) = sK152(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_423,axiom,
    ( sK153(Eq_x_0,Eq_x_1) = sK153(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_424,axiom,
    ( sK154(Eq_x_0,Eq_x_1) = sK154(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_425,axiom,
    ( sK155(Eq_x_0,Eq_x_1) = sK155(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_426,axiom,
    ( sK156(Eq_x_0,Eq_x_1) = sK156(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_427,axiom,
    ( sK157(Eq_x_0,Eq_x_1) = sK157(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_428,axiom,
    ( sK158(Eq_x_0,Eq_x_1) = sK158(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_429,axiom,
    ( sK159(Eq_x_0,Eq_x_1) = sK159(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_430,axiom,
    ( sK160(Eq_x_0,Eq_x_1) = sK160(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_431,axiom,
    ( sK161(Eq_x_0,Eq_x_1) = sK161(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_432,axiom,
    ( sK162(Eq_x_0,Eq_x_1) = sK162(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_433,axiom,
    ( sK163(Eq_x_0) = sK163(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_434,axiom,
    ( sK164(Eq_x_0,Eq_x_1) = sK164(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_435,axiom,
    ( sK165(Eq_x_0,Eq_x_1) = sK165(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_436,axiom,
    ( sK166(Eq_x_0,Eq_x_1,Eq_x_2) = sK166(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_437,axiom,
    ( sK167(Eq_x_0,Eq_x_1,Eq_x_2) = sK167(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_438,axiom,
    ( sK168(Eq_x_0,Eq_x_1,Eq_x_2) = sK168(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_439,axiom,
    ( sK169(Eq_x_0,Eq_x_1) = sK169(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_440,axiom,
    ( sK170(Eq_x_0,Eq_x_1) = sK170(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_441,axiom,
    ( sK171(Eq_x_0,Eq_x_1,Eq_x_2) = sK171(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_442,axiom,
    ( sK172(Eq_x_0,Eq_x_1,Eq_x_2) = sK172(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_443,axiom,
    ( sK173(Eq_x_0,Eq_x_1) = sK173(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_444,axiom,
    ( sK174(Eq_x_0,Eq_x_1) = sK174(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_445,axiom,
    ( sK175(Eq_x_0) = sK175(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_446,axiom,
    ( sK176(Eq_x_0,Eq_x_1) = sK176(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_447,axiom,
    ( sK177(Eq_x_0,Eq_x_1,Eq_x_2) = sK177(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_448,axiom,
    ( sK178(Eq_x_0,Eq_x_1,Eq_x_2) = sK178(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_449,axiom,
    ( sK179(Eq_x_0,Eq_x_1) = sK179(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_450,axiom,
    ( sK180(Eq_x_0,Eq_x_1) = sK180(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_451,axiom,
    ( sK181(Eq_x_0,Eq_x_1) = sK181(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_452,axiom,
    ( sK182(Eq_x_0) = sK182(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_453,axiom,
    ( sK183(Eq_x_0) = sK183(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_454,axiom,
    ( sK184(Eq_x_0) = sK184(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_455,axiom,
    ( sK185(Eq_x_0) = sK185(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_456,axiom,
    ( sK186(Eq_x_0,Eq_x_1) = sK186(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_457,axiom,
    ( sK187(Eq_x_0,Eq_x_1,Eq_x_2) = sK187(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_458,axiom,
    ( sK188(Eq_x_0,Eq_x_1,Eq_x_2) = sK188(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_459,axiom,
    ( sK189(Eq_x_0,Eq_x_1,Eq_x_2) = sK189(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_460,axiom,
    ( sK190(Eq_x_0,Eq_x_1,Eq_x_2) = sK190(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_461,axiom,
    ( sK191(Eq_x_0,Eq_x_1) = sK191(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_462,axiom,
    ( sK192(Eq_x_0,Eq_x_1,Eq_x_2) = sK192(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_463,axiom,
    ( sK193(Eq_x_0,Eq_x_1,Eq_x_2) = sK193(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_464,axiom,
    ( sK194(Eq_x_0,Eq_x_1,Eq_x_2) = sK194(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_465,axiom,
    ( sK195(Eq_x_0,Eq_x_1,Eq_x_2) = sK195(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_466,axiom,
    ( sK196(Eq_x_0,Eq_x_1,Eq_x_2) = sK196(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_467,axiom,
    ( sK197(Eq_x_0,Eq_x_1,Eq_x_2) = sK197(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_468,axiom,
    ( sK198(Eq_x_0,Eq_x_1,Eq_x_2) = sK198(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_469,axiom,
    ( sK199(Eq_x_0,Eq_x_1,Eq_x_2) = sK199(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_470,axiom,
    ( sK200(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK200(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_471,axiom,
    ( sK201(Eq_x_0,Eq_x_1,Eq_x_2) = sK201(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_472,axiom,
    ( sK202(Eq_x_0,Eq_x_1,Eq_x_2) = sK202(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_473,axiom,
    ( sK203(Eq_x_0,Eq_x_1,Eq_x_2) = sK203(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_474,axiom,
    ( sK204(Eq_x_0,Eq_x_1,Eq_x_2) = sK204(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_475,axiom,
    ( sK205(Eq_x_0,Eq_x_1,Eq_x_2) = sK205(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_476,axiom,
    ( sK206(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK206(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_477,axiom,
    ( sK207(Eq_x_0,Eq_x_1,Eq_x_2) = sK207(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_478,axiom,
    ( sK208(Eq_x_0,Eq_x_1) = sK208(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_479,axiom,
    ( sK209(Eq_x_0) = sK209(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_480,axiom,
    ( sK210(Eq_x_0) = sK210(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_481,axiom,
    ( sK211(Eq_x_0) = sK211(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_482,axiom,
    ( sK212(Eq_x_0) = sK212(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_483,axiom,
    ( sK213(Eq_x_0,Eq_x_1) = sK213(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_484,axiom,
    ( sK214(Eq_x_0) = sK214(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_485,axiom,
    ( sK215(Eq_x_0) = sK215(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_486,axiom,
    ( sK216(Eq_x_0) = sK216(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_487,axiom,
    ( sK217(Eq_x_0) = sK217(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_488,axiom,
    ( sK218(Eq_x_0) = sK218(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_489,axiom,
    ( sK219(Eq_x_0) = sK219(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_490,axiom,
    ( sK220(Eq_x_0,Eq_x_1,Eq_x_2) = sK220(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_491,axiom,
    ( sK221(Eq_x_0,Eq_x_1,Eq_x_2) = sK221(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_492,axiom,
    ( sK222(Eq_x_0,Eq_x_1,Eq_x_2) = sK222(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_493,axiom,
    ( sK223(Eq_x_0,Eq_x_1,Eq_x_2) = sK223(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_494,axiom,
    ( sK224(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK224(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_495,axiom,
    ( sK225(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK225(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_496,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_497,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_498,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_499,axiom,
    ( is_bool(Eq_y_0)
    | ~ is_bool(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_500,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_501,axiom,
    ( is_a(Eq_y_0)
    | ~ is_a(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_502,axiom,
    ( is_pname(Eq_y_0)
    | ~ is_pname(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_503,axiom,
    ( hBOOL(Eq_y_0)
    | ~ hBOOL(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_504,axiom,
    ( sP0(Eq_y_0,Eq_y_1)
    | ~ sP0(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_505,axiom,
    ( sP1(Eq_y_0,Eq_y_1)
    | ~ sP1(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_506,axiom,
    ( sP2(Eq_y_0,Eq_y_1)
    | ~ sP2(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_507,axiom,
    ( sP3(Eq_y_0,Eq_y_1)
    | ~ sP3(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_508,axiom,
    ( sP4(Eq_y_0,Eq_y_1)
    | ~ sP4(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_509,axiom,
    ( sP5(Eq_y_0,Eq_y_1)
    | ~ sP5(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_510,axiom,
    ( sP6(Eq_y_0,Eq_y_1)
    | ~ sP6(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_511,axiom,
    ( sP7(Eq_y_0,Eq_y_1)
    | ~ sP7(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_512,axiom,
    ( sP8(Eq_y_0,Eq_y_1)
    | ~ sP8(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_513,axiom,
    ( sP9(Eq_y_0,Eq_y_1)
    | ~ sP9(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_514,axiom,
    ( sP10(Eq_y_0,Eq_y_1)
    | ~ sP10(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_515,axiom,
    ( sP11(Eq_y_0,Eq_y_1)
    | ~ sP11(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_516,axiom,
    ( sP12(Eq_y_0,Eq_y_1)
    | ~ sP12(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_517,axiom,
    ( sP13(Eq_y_0,Eq_y_1)
    | ~ sP13(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_518,axiom,
    ( sP14(Eq_y_0,Eq_y_1)
    | ~ sP14(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_519,axiom,
    ( sP15(Eq_y_0,Eq_y_1)
    | ~ sP15(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_520,axiom,
    ( sP16(Eq_y_0,Eq_y_1)
    | ~ sP16(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_521,axiom,
    ( sP17(Eq_y_0,Eq_y_1)
    | ~ sP17(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_522,axiom,
    ( sP18(Eq_y_0,Eq_y_1)
    | ~ sP18(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_523,axiom,
    ( sP19(Eq_y_0,Eq_y_1)
    | ~ sP19(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_524,axiom,
    ( sP20(Eq_y_0,Eq_y_1)
    | ~ sP20(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_525,axiom,
    ( sP21(Eq_y_0,Eq_y_1)
    | ~ sP21(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_526,axiom,
    ( sP22(Eq_y_0,Eq_y_1)
    | ~ sP22(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_527,axiom,
    ( sP23(Eq_y_0,Eq_y_1)
    | ~ sP23(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_528,axiom,
    ( sP24(Eq_y_0,Eq_y_1)
    | ~ sP24(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_529,axiom,
    ( sP25(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP25(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_530,axiom,
    ( sP26(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP26(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_531,axiom,
    ( sP27(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP27(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_532,axiom,
    ( sP28(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP28(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_533,axiom,
    ( sP29(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP29(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_534,axiom,
    ( sP30(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP30(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_535,axiom,
    ( sP31(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP31(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_536,axiom,
    ( sP32(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP32(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_537,axiom,
    ( sP33(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP33(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_538,axiom,
    ( sP34(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP34(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_539,axiom,
    ( sP35(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP35(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_540,axiom,
    ( sP36(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP36(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_541,axiom,
    ( sP37(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP37(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_542,axiom,
    ( sP38(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP38(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_543,axiom,
    ( sP39(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP39(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_544,axiom,
    ( sP40(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP40(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_545,axiom,
    ( sP41(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP41(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_546,axiom,
    ( sP42(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP42(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_547,axiom,
    ( sP43(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP43(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_548,axiom,
    ( sP44(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP44(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_549,axiom,
    ( sP45(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP45(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_550,axiom,
    ( sP46(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP46(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_551,axiom,
    ( sP47(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP47(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_552,axiom,
    ( sP48(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP48(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_553,axiom,
    ( sP49(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP49(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_554,axiom,
    ( sP50(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP50(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_555,axiom,
    ( sP51(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP51(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_556,axiom,
    ( sP52(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP52(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_557,axiom,
    ( sP53(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP53(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_558,axiom,
    ( sP54(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP54(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_559,axiom,
    ( sP55(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP55(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_560,axiom,
    ( sP56(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP56(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_561,axiom,
    ( sP57(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP57(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_562,axiom,
    ( sP58(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP58(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_563,axiom,
    ( sP59(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP59(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_564,axiom,
    ( sP60(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP60(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_565,axiom,
    ( sP61(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP61(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_566,axiom,
    ( sP62(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP62(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_567,axiom,
    ( sP63(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP63(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_568,axiom,
    ( sP64(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP64(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_569,axiom,
    ( sP65(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP65(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_570,axiom,
    ( sP66(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP66(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_571,axiom,
    ( sP67(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP67(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_572,axiom,
    ( sP68(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP68(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_573,axiom,
    ( sP69(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP69(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_574,axiom,
    ( sP70(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP70(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_575,axiom,
    ( sP71(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP71(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_576,axiom,
    ( sP72(Eq_y_0,Eq_y_1)
    | ~ sP72(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_577,axiom,
    ( sP73(Eq_y_0,Eq_y_1)
    | ~ sP73(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_578,axiom,
    ( sP74(Eq_y_0,Eq_y_1)
    | ~ sP74(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_579,axiom,
    ( sP75(Eq_y_0,Eq_y_1)
    | ~ sP75(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_580,axiom,
    ( sP76(Eq_y_0,Eq_y_1)
    | ~ sP76(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_581,axiom,
    ( sP77(Eq_y_0,Eq_y_1)
    | ~ sP77(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_582,axiom,
    ( sP78(Eq_y_0,Eq_y_1)
    | ~ sP78(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_583,axiom,
    ( sP79(Eq_y_0,Eq_y_1)
    | ~ sP79(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_584,axiom,
    ( sP80(Eq_y_0,Eq_y_1)
    | ~ sP80(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_585,axiom,
    ( sP81(Eq_y_0,Eq_y_1)
    | ~ sP81(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_586,axiom,
    ( sP82(Eq_y_0,Eq_y_1)
    | ~ sP82(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_587,axiom,
    ( sP83(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP83(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_588,axiom,
    ( sP84(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP84(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_589,axiom,
    ( sP85(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP85(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_590,axiom,
    ( sP86(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP86(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_591,axiom,
    ( sP87(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP87(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_592,axiom,
    ( sP88(Eq_y_0,Eq_y_1)
    | ~ sP88(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_593,axiom,
    ( sP89(Eq_y_0,Eq_y_1)
    | ~ sP89(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_594,axiom,
    ( sP90(Eq_y_0,Eq_y_1)
    | ~ sP90(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_595,axiom,
    ( sP91(Eq_y_0,Eq_y_1)
    | ~ sP91(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_596,axiom,
    ( sP92(Eq_y_0,Eq_y_1)
    | ~ sP92(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_597,axiom,
    ( sP93(Eq_y_0,Eq_y_1)
    | ~ sP93(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_598,axiom,
    ( sP94(Eq_y_0,Eq_y_1)
    | ~ sP94(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_599,axiom,
    ( sP95(Eq_y_0,Eq_y_1)
    | ~ sP95(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_600,axiom,
    ( sP96(Eq_y_0,Eq_y_1)
    | ~ sP96(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_601,axiom,
    ( sP97(Eq_y_0,Eq_y_1)
    | ~ sP97(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_602,axiom,
    ( sP98(Eq_y_0,Eq_y_1)
    | ~ sP98(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_603,axiom,
    ( sP99(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP99(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_604,axiom,
    ( sP100(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP100(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_605,axiom,
    ( sP101(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP101(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_606,axiom,
    ( sP102(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP102(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_607,axiom,
    ( sP103(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP103(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_608,axiom,
    ( sP104(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP104(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_609,axiom,
    ( sP105(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP105(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_610,axiom,
    ( sP106(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP106(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_611,axiom,
    ( sP107(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP107(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_612,axiom,
    ( sP108(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP108(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_613,axiom,
    ( sP109(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP109(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_614,axiom,
    ( sP110(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP110(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_615,axiom,
    ( sP111(Eq_y_0,Eq_y_1)
    | ~ sP111(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_616,axiom,
    ( sP112(Eq_y_0,Eq_y_1)
    | ~ sP112(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_617,axiom,
    ( sP113(Eq_y_0,Eq_y_1)
    | ~ sP113(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_618,axiom,
    ( sP114(Eq_y_0,Eq_y_1)
    | ~ sP114(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_619,axiom,
    ( sP115(Eq_y_0,Eq_y_1)
    | ~ sP115(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_620,axiom,
    ( sP116(Eq_y_0,Eq_y_1)
    | ~ sP116(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_621,axiom,
    ( sP117(Eq_y_0,Eq_y_1)
    | ~ sP117(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_622,axiom,
    ( sP118(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP118(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_623,axiom,
    ( sP119(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP119(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_624,axiom,
    ( sP120(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP120(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_625,axiom,
    ( sP121(Eq_y_0,Eq_y_1)
    | ~ sP121(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_626,axiom,
    ( sP122(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP122(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_627,axiom,
    ( sP123(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP123(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_628,axiom,
    ( sP124(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP124(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_629,axiom,
    ( sP125(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP125(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_630,axiom,
    ( sP126(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP126(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_631,axiom,
    ( sP127(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP127(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_632,axiom,
    ( sP128(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP128(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_633,axiom,
    ( sP129(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP129(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_634,axiom,
    ( sP130(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP130(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_635,axiom,
    ( sP131(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP131(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_636,axiom,
    ( sP132(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP132(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_637,axiom,
    ( sP133(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP133(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_638,axiom,
    ( sP134(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP134(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_639,axiom,
    ( sP135(Eq_y_0,Eq_y_1)
    | ~ sP135(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_640,axiom,
    ( sP136(Eq_y_0,Eq_y_1)
    | ~ sP136(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_641,axiom,
    ( sP137(Eq_y_0,Eq_y_1)
    | ~ sP137(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_642,axiom,
    ( sP138(Eq_y_0,Eq_y_1)
    | ~ sP138(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_643,axiom,
    ( sP139(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP139(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_644,axiom,
    ( sP140(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP140(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_645,axiom,
    ( sP141(Eq_y_0,Eq_y_1)
    | ~ sP141(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_646,axiom,
    ( sP142(Eq_y_0,Eq_y_1)
    | ~ sP142(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_647,axiom,
    ( sP143(Eq_y_0,Eq_y_1)
    | ~ sP143(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_648,axiom,
    ( sP144(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP144(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_649,axiom,
    ( sP145(Eq_y_0)
    | ~ sP145(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_650,axiom,
    ( sP146(Eq_y_0)
    | ~ sP146(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_651,axiom,
    ( sP147(Eq_y_0)
    | ~ sP147(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_652,axiom,
    ( sP148(Eq_y_0,Eq_y_1)
    | ~ sP148(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_653,axiom,
    ( sP149(Eq_y_0)
    | ~ sP149(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_654,axiom,
    ( sP150(Eq_y_0,Eq_y_1)
    | ~ sP150(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_655,axiom,
    ( sP151(Eq_y_0)
    | ~ sP151(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_656,axiom,
    ( sP152(Eq_y_0,Eq_y_1)
    | ~ sP152(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_657,axiom,
    ( sP153(Eq_y_0)
    | ~ sP153(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_658,axiom,
    ( sP154(Eq_y_0,Eq_y_1)
    | ~ sP154(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_659,axiom,
    ( sP155(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP155(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_660,axiom,
    ( sP156(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP156(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_661,axiom,
    ( sP157(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP157(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_662,axiom,
    ( sP158(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP158(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_663,axiom,
    ( sP159(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP159(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_664,axiom,
    ( sP160(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP160(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_665,axiom,
    ( sP161(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP161(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_666,axiom,
    ( sP162(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP162(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_667,axiom,
    ( sP163(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP163(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_668,axiom,
    ( sP164(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP164(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_669,axiom,
    ( sP165(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP165(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_670,axiom,
    ( sP166(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP166(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_671,axiom,
    ( sP167(Eq_y_0,Eq_y_1)
    | ~ sP167(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_672,axiom,
    ( sP168(Eq_y_0,Eq_y_1)
    | ~ sP168(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_673,axiom,
    ( sP169(Eq_y_0,Eq_y_1)
    | ~ sP169(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_674,axiom,
    ( sP170(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP170(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_675,axiom,
    ( sP171(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP171(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_676,axiom,
    ( sP172(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP172(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_677,axiom,
    ( sP173(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP173(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_678,axiom,
    ( sP174(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP174(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_679,axiom,
    ( sP175(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP175(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_680,axiom,
    ( sP176(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP176(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_681,axiom,
    ( sP177(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP177(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_682,axiom,
    ( sP178(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP178(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_683,axiom,
    ( sP179(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP179(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_684,axiom,
    ( sP180(Eq_y_0,Eq_y_1)
    | ~ sP180(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_685,axiom,
    ( sP181(Eq_y_0,Eq_y_1)
    | ~ sP181(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_686,axiom,
    ( sP182(Eq_y_0)
    | ~ sP182(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_687,axiom,
    ( sP183(Eq_y_0,Eq_y_1)
    | ~ sP183(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_688,axiom,
    ( sP184(Eq_y_0,Eq_y_1)
    | ~ sP184(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_689,axiom,
    ( sP185(Eq_y_0)
    | ~ sP185(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_690,axiom,
    ( sP186(Eq_y_0,Eq_y_1)
    | ~ sP186(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_691,axiom,
    ( sP187(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP187(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_692,axiom,
    ( sP188(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP188(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_693,axiom,
    ( sP189(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP189(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_694,axiom,
    ( sP190(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP190(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_695,axiom,
    ( sP191(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP191(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_696,axiom,
    ( sP192(Eq_y_0,Eq_y_1)
    | ~ sP192(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_697,axiom,
    ( sP193(Eq_y_0,Eq_y_1)
    | ~ sP193(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_698,axiom,
    ( sP194(Eq_y_0,Eq_y_1)
    | ~ sP194(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_699,axiom,
    ( sP195(Eq_y_0,Eq_y_1)
    | ~ sP195(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_700,axiom,
    ( sP196(Eq_y_0,Eq_y_1)
    | ~ sP196(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_701,axiom,
    ( sP197(Eq_y_0,Eq_y_1)
    | ~ sP197(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_702,axiom,
    ( sP198(Eq_y_0,Eq_y_1)
    | ~ sP198(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_703,axiom,
    ( sP199(Eq_y_0,Eq_y_1)
    | ~ sP199(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_704,axiom,
    ( sP200(Eq_y_0)
    | ~ sP200(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_705,axiom,
    ( sP201(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP201(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_706,axiom,
    ( sP202(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP202(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_707,axiom,
    ( sP203(Eq_y_0)
    | ~ sP203(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_708,axiom,
    ( sP204(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP204(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_709,axiom,
    ( sP205(Eq_y_0)
    | ~ sP205(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_710,axiom,
    ( sP206(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP206(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_711,axiom,
    ( sP207(Eq_y_0)
    | ~ sP207(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_712,axiom,
    ( sP208(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP208(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_713,axiom,
    ( sP209(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP209(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_714,axiom,
    ( sP210(Eq_y_0)
    | ~ sP210(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_715,axiom,
    ( sP211(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP211(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_716,axiom,
    ( sP212(Eq_y_0)
    | ~ sP212(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_717,axiom,
    ( sP213(Eq_y_0)
    | ~ sP213(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_718,axiom,
    ( sP214(Eq_y_0)
    | ~ sP214(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_719,axiom,
    ( sP215(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP215(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_720,axiom,
    ( sP216(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP216(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_721,axiom,
    ( sP217(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP217(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_722,axiom,
    ( sP218(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP218(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_723,axiom,
    ( sP219(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP219(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_724,axiom,
    ( sP220(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP220(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_725,axiom,
    ( sP221(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP221(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_726,axiom,
    ( sP222(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP222(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_727,axiom,
    ( sP223(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP223(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_728,axiom,
    ( sP224(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP224(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_729,axiom,
    ( sP225(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP225(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_730,axiom,
    ( sP226(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP226(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_731,axiom,
    ( sP227(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP227(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_732,axiom,
    ( sP228(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP228(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_733,axiom,
    ( sP229(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP229(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_734,axiom,
    ( sP230(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP230(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_735,axiom,
    ( sP231(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP231(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_736,axiom,
    ( sP232(Eq_y_0,Eq_y_1)
    | ~ sP232(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_737,axiom,
    ( sP233(Eq_y_0,Eq_y_1)
    | ~ sP233(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_738,axiom,
    ( sP234(Eq_y_0,Eq_y_1)
    | ~ sP234(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_739,axiom,
    ( sP235(Eq_y_0,Eq_y_1)
    | ~ sP235(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_740,axiom,
    ( sP236(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP236(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_741,axiom,
    ( sP237(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP237(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_742,axiom,
    ( sP238(Eq_y_0,Eq_y_1)
    | ~ sP238(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_743,axiom,
    ( sP239(Eq_y_0,Eq_y_1)
    | ~ sP239(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_744,axiom,
    ( sP240(Eq_y_0,Eq_y_1)
    | ~ sP240(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_745,axiom,
    ( sP241(Eq_y_0,Eq_y_1)
    | ~ sP241(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_746,axiom,
    ( sP242(Eq_y_0,Eq_y_1)
    | ~ sP242(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_747,axiom,
    ( sP243(Eq_y_0,Eq_y_1)
    | ~ sP243(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_748,axiom,
    ( sP244(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP244(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_749,axiom,
    ( sP245(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP245(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_750,axiom,
    ( sP246(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP246(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_751,axiom,
    ( sP247(Eq_y_0,Eq_y_1)
    | ~ sP247(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_752,axiom,
    ( sP248(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP248(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_753,axiom,
    ( sP249(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP249(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_754,axiom,
    ( sP250(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP250(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_755,axiom,
    ( sP251(Eq_y_0,Eq_y_1)
    | ~ sP251(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_756,axiom,
    ( sP252(Eq_y_0,Eq_y_1)
    | ~ sP252(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_757,axiom,
    ( sP253(Eq_y_0,Eq_y_1)
    | ~ sP253(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_758,axiom,
    ( sP254(Eq_y_0,Eq_y_1)
    | ~ sP254(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_759,axiom,
    ( sP255(Eq_y_0,Eq_y_1)
    | ~ sP255(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_760,axiom,
    ( sP256(Eq_y_0,Eq_y_1)
    | ~ sP256(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_761,axiom,
    ( sP257(Eq_y_0,Eq_y_1)
    | ~ sP257(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_762,axiom,
    ( sP258(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP258(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_763,axiom,
    ( sP259(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP259(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_764,axiom,
    ( sP260(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP260(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_765,axiom,
    ( sP261(Eq_y_0,Eq_y_1)
    | ~ sP261(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_766,axiom,
    ( sP262(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP262(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_767,axiom,
    ( sP263(Eq_y_0,Eq_y_1)
    | ~ sP263(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_768,axiom,
    ( sP264(Eq_y_0,Eq_y_1)
    | ~ sP264(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_769,axiom,
    ( sP265(Eq_y_0,Eq_y_1)
    | ~ sP265(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_770,axiom,
    ( sP266(Eq_y_0,Eq_y_1)
    | ~ sP266(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_771,axiom,
    ( sP267(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP267(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_772,axiom,
    ( sP268(Eq_y_0,Eq_y_1)
    | ~ sP268(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_773,axiom,
    ( sP269(Eq_y_0,Eq_y_1)
    | ~ sP269(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_774,axiom,
    ( sP270(Eq_y_0,Eq_y_1)
    | ~ sP270(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_775,axiom,
    ( sP271(Eq_y_0,Eq_y_1)
    | ~ sP271(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_776,axiom,
    ( sP272(Eq_y_0,Eq_y_1)
    | ~ sP272(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_777,axiom,
    ( sP273(Eq_y_0,Eq_y_1)
    | ~ sP273(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_778,axiom,
    ( sP274(Eq_y_0,Eq_y_1)
    | ~ sP274(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_779,axiom,
    ( sP275(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP275(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_780,axiom,
    ( sP276(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP276(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_781,axiom,
    ( sP277(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP277(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_782,axiom,
    ( sP278(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP278(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_783,axiom,
    ( sP279(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP279(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_784,axiom,
    ( sP280(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP280(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_785,axiom,
    ( sP281(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP281(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_786,axiom,
    ( sP282(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP282(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_787,axiom,
    ( sP283(Eq_y_0,Eq_y_1)
    | ~ sP283(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_788,axiom,
    ( sP284(Eq_y_0)
    | ~ sP284(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_789,axiom,
    ( sP285(Eq_y_0,Eq_y_1)
    | ~ sP285(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_790,axiom,
    ( sP286(Eq_y_0,Eq_y_1)
    | ~ sP286(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_791,axiom,
    ( sP287(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP287(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_792,axiom,
    ( sP288(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP288(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_793,axiom,
    ( sP289(Eq_y_0,Eq_y_1)
    | ~ sP289(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_794,axiom,
    ( sP290(Eq_y_0,Eq_y_1)
    | ~ sP290(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_795,axiom,
    ( sP291(Eq_y_0,Eq_y_1)
    | ~ sP291(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_796,axiom,
    ( sP292(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP292(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_797,axiom,
    ( sP293(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP293(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_798,axiom,
    ( sP294(Eq_y_0,Eq_y_1)
    | ~ sP294(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_799,axiom,
    ( sP295(Eq_y_0,Eq_y_1)
    | ~ sP295(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_800,axiom,
    ( sP296(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP296(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_801,axiom,
    ( sP297(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP297(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_802,axiom,
    ( sP298(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP298(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_803,axiom,
    ( sP299(Eq_y_0,Eq_y_1)
    | ~ sP299(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_804,axiom,
    ( sP300(Eq_y_0,Eq_y_1)
    | ~ sP300(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_805,axiom,
    ( sP301(Eq_y_0,Eq_y_1)
    | ~ sP301(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_806,axiom,
    ( sP302(Eq_y_0,Eq_y_1)
    | ~ sP302(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_807,axiom,
    ( sP303(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP303(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_808,axiom,
    ( sP304(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP304(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_809,axiom,
    ( sP305(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP305(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_810,axiom,
    ( sP306(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP306(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_811,axiom,
    ( sP307(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP307(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_812,axiom,
    ( sP308(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP308(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_813,axiom,
    ( sP309(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP309(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_814,axiom,
    ( sP310(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP310(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_815,axiom,
    ( sP311(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP311(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_816,axiom,
    ( sP312(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP312(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_817,axiom,
    ( sP313(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP313(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_818,axiom,
    ( sP314(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP314(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_819,axiom,
    ( sP315(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP315(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_820,axiom,
    ( sP316(Eq_y_0,Eq_y_1)
    | ~ sP316(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_821,axiom,
    ( sP317(Eq_y_0,Eq_y_1)
    | ~ sP317(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_822,axiom,
    ( sP318(Eq_y_0,Eq_y_1)
    | ~ sP318(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_823,axiom,
    ( sP319(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP319(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_824,axiom,
    ( sP320(Eq_y_0,Eq_y_1)
    | ~ sP320(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_825,axiom,
    ( sP321(Eq_y_0,Eq_y_1)
    | ~ sP321(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_826,axiom,
    ( sP322(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP322(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_827,axiom,
    ( sP323(Eq_y_0,Eq_y_1)
    | ~ sP323(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_828,axiom,
    ( sP324(Eq_y_0,Eq_y_1)
    | ~ sP324(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_829,axiom,
    ( sP325(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP325(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_830,axiom,
    ( sP326(Eq_y_0,Eq_y_1)
    | ~ sP326(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_831,axiom,
    ( sP327(Eq_y_0,Eq_y_1)
    | ~ sP327(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_832,axiom,
    ( sP328(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP328(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_833,axiom,
    ( sP329(Eq_y_0,Eq_y_1)
    | ~ sP329(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_834,axiom,
    ( sP330(Eq_y_0,Eq_y_1)
    | ~ sP330(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_835,axiom,
    ( sP331(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP331(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_836,axiom,
    ( sP332(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP332(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_837,axiom,
    ( sP333(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP333(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_838,axiom,
    ( sP334(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP334(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_839,axiom,
    ( sP335(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP335(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_840,axiom,
    ( sP336(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP336(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_841,axiom,
    ( sP337(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP337(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_842,axiom,
    ( sP338(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP338(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_843,axiom,
    ( sP339(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP339(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_844,axiom,
    ( sP340(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP340(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_845,axiom,
    ( sP341(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP341(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_846,axiom,
    ( sP342(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP342(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_847,axiom,
    ( sP343(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP343(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_848,axiom,
    ( sP344(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP344(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_849,axiom,
    ( sP345(Eq_y_0)
    | ~ sP345(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_850,axiom,
    ( sP346(Eq_y_0)
    | ~ sP346(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_851,axiom,
    ( sP347(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP347(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_852,axiom,
    ( sP348(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP348(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_853,axiom,
    ( sP349(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP349(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_854,axiom,
    ( sP350(Eq_y_0)
    | ~ sP350(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_855,axiom,
    ( sP351(Eq_y_0,Eq_y_1)
    | ~ sP351(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_856,axiom,
    ( sP352(Eq_y_0,Eq_y_1)
    | ~ sP352(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_857,axiom,
    ( sP353(Eq_y_0,Eq_y_1)
    | ~ sP353(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_858,axiom,
    ( sP354(Eq_y_0,Eq_y_1)
    | ~ sP354(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_859,axiom,
    ( sP355(Eq_y_0,Eq_y_1)
    | ~ sP355(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_860,axiom,
    ( sP356(Eq_y_0,Eq_y_1)
    | ~ sP356(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_861,axiom,
    ( sP357(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP357(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_862,axiom,
    ( sP358(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP358(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_863,axiom,
    ( sP359(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP359(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_864,axiom,
    ( sP360(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP360(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_865,axiom,
    ( sP361(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP361(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_866,axiom,
    ( sP362(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP362(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_867,axiom,
    ( sP363(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP363(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | 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+3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04  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
% 0.11/3.99  % Computer : n013.cluster.edu
% 0.11/3.99  % Model    : x86_64 x86_64
% 0.11/3.99  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/3.99  % Memory   : 8046.5625MB
% 0.11/3.99  % OS       : Linux 6.8.0-71-generic
% 0.11/3.99  % CPULimit : 300
% 0.11/3.99  % WCLimit  : 300
% 0.11/3.99  % DateTime : Sun Sep 20 05:41:36 UTC 2026
% 0.11/4.00  % CPUTime  : 
% 46.74/50.67  % SZS status Theorem for theBenchmark
% 46.74/50.67  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------